title: Washington appeals court upholds juveniles arson convictions

text:
Washington law provides special protections to children in criminal investigations. Pursuant to RCW 13.40.740, which became effective January 1, 2022, a juvenile being questioned in a custodial interrogation, detained based on probable cause of involvement in criminal activity, or asked to consent to an evidentiary search can only knowingly, intelligently, and voluntarily waive their Miranda rights after consulting with an attorney. This consultation cannot be waived. A Washington juvenile defendant recently challenged his convictions, arguing in part the consultation requirement should apply even though he was interviewed before the statute’s effective date.
According to the unpublished appeals court opinion, the thirteen-year-old juvenile told his father there was a fire at the dumpster of their apartment complex when he returned from taking out the trash on May 7.
He was home alone on the morning of May 16 and two more fires occurred. He was home alone again that afternoon and three more fires were set. No one saw how the fires started or who started them.
The juvenile called and sent audio and video messages to his family. In one message, he referenced “the fire I was trying to start” and said “that’s four fires I tried to start or whoever tried to start” in another message. He told his mother he told another resident “about all of the fires I was trying to get started.”
The fires were started similarly, with paper, cardboard, and cloth. Remnants from one afternoon fire were similar to cloth found that morning. The fire marshal opined the fires were started with an open flame device like a lighter. He also noticed a burn mark by the juvenile’s apartment that appeared to have been caused by such a device.
The juvenile’s mother agreed to allow him to speak to a detective. His mother and brother were present, and his father listened on speakerphone. The detective asked to see and recorded a copy of the video and audio messages the juvenile sent his mother. The juvenile said the statements in the messages were not what he meant to say. He signed a statement his statements were made “freely, voluntarily, and without threats or promises of any kind.”
Another detective interviewed him at the police station. He told the detective he had previously been fascinated by the noise of a fire, but was not any longer. He denied being involved with the fires. He suggested young people may have started the fires by messing with a parent’s lighter. He gestured a motion like flicking a lighter, but later said he did not know how to use a lighter. He said the words in his messages “accidentally slipped out” due to adrenaline. The interview ultimately ended when he asked to go home.
The juvenile was charged with two criminal counts for the May 7 fire and five counts for the May 16 fires. He moved to sever the May 7 charges from the May 16 charges. He subsequently proposed also severing the morning fires from the afternoon fires. The trial court denied the motion.
The trial court concluded the juvenile was not in custody during either interview and his statements were admissible.
At trial, the juvenile denied starting the fires. He testified he was scared and panicked when he sent his mother the messages and that he had a lot of adrenaline. He said these factors sometimes cause him to stutter and mess up his words. His father also testified he gets “really jittery” when nervous and “stumbles over his words.”
The trial court found him not guilty of second degree arson and reckless burning for the May 7 fire. The court found him guilty of first degree attempted arson for three counts and arson in the first degree for two other counts for the May 16 fires.
Motion to Sever
The juvenile appealed, arguing the trial court denied him a fair trial by denying his motion to sever. He argued the trial court “cumulated evidence and inferred [he] had a propensity for arson.”
The trial court has discretion to grant severance “to promote a fair determination of the guilt or innocence of a defendant.” CrR 4.4. On appeal, a defendant must show the prejudicial effect of trying the counts together outweighed the benefits. The appeals court must consider certain factors to determine if the trial court mitigated the prejudice.
There was eyewitness evidence for the first fire but only circumstantial evidence for the other fires. Because the strength of the evidence varied, that factor favored severance.
The juvenile’s defense for all counts at trial was general denial. He argued on appeal he presented evidence of different suspects for each day of fires. He did not provide argument for how his defenses were frustrated, however, and he had not raised the issue below. The appeals court therefore declined to consider the new argument and concluded his general denial was the same for all offenses. The clarity of defenses factor therefore weighed against severance.
The court must also consider the admissibility of evidence of the other charges if not joined. The trial court found this factor weighed against severance because the evidence would have been admissible as a link needed to depict the complete picture of events.
The juvenile argued the evidence for the May 16 morning counts was weaker than that for the afternoon. The appeals court pointed out the fires were started with the same type of device and similar materials. The juvenile had a personal connection to two of the fires, one morning fire set in the stairwell by his apartment and an afternoon fire set in front of the apartment where he previously lived. In a message to his mother, he referenced “four fires I tried to start…”
The appeals court found “no link in the chain of an unbroken sequence of events between the May 7 fire and the May 16 fires,” however. The factor therefore weighed in favor of severing the May 7 counts from the May 16 counts, but against severing the morning fires from the afternoon fires. The appeals court noted, however, that this was a bench trial and the trial court was aware of separating the counts.
The appeals court judicial economy outweighed any possible prejudice. There was an overlap of eight witnesses, one a child and two of whom had material witness warrants issued.
Admissibility of Statements
The juvenile argued the court should hold children cannot waive their Miranda rights without consulting an attorney, although his interviews occurred before the effective date of RCW 13.40.140(1). The appeals court noted statutes are presumed to apply only prospectively unless there is legislative intent otherwise. The appeals court concluded RCW 13.40.740(1) would not apply regardless of the retroactivity issue because the juvenile was not in custody during the interviews.
The juvenile argued he was in custody during the initial interview, challenging the court’s finding he was aware he was free to leave. The appeals court noted his family was present. He was on the side of the room with the door. The fire marshal testified he was told he could leave at any time. The appeals court concluded there was substantial evidence supporting the trial court’s finding. The juvenile also challenged the court’s finding the first interview was voluntary. He testified he did not remember if he was told it was voluntary and felt he could not leave at certain points. The detective and fire marshal testified the detective told him it was voluntary. His parents testified it was voluntary, and the juvenile signed a statement indicating the same. The appeals court concluded there was substantial evidence supporting the trial court’s findings and the findings supported its conclusions the juvenile was not in custody during the first interview.
The juvenile also challenged a number of findings regarding the second interview. The juvenile sat nearest the door. His father testified the juvenile volunteered to be interviewed. The juvenile testified he “had the option” to do the interview or not. He testified he knew he was going to the station for an interview. The detective talked to the juvenile and his father for about 40 minutes and advised him of his rights. Both the juvenile and his father signed a form setting forth his constitutional rights. The juvenile testified he understood everything read to him from the form, that he was free to leave, and that the interview was recorded and could be used against him. The interview ended when he said he wanted to go home.
The appeals court concluded there was substantial evidence supporting the findings and the findings supported the conclusions the juvenile was not in custody and his statements were admissible.
Seek Skilled Legal Counsel
Children can be especially vulnerable to interrogation techniques. If you believe your child is being investigated for a crime, you should contact an experienced Washington juvenile defense attorney right away so your child’s rights are protected. Schedule a consultation with Blair & Kim, PLLC, at (206) 622-6562 for a consultation.


tier: polar

shelf: science-engineering

title: Israeli food tech company announces worlds first burger made chickpea protein

text:
Meat. The End (MTE), an Israeli food tech company, that produces nuggets and burgers that are sold at Burger King Israel, said it has developed the first-ever burger made from texturized chickpea protein.
Founded in 2020, MTE has combined protein science, data science and food engineering to create their product.
The company uses 100% chickpea protein concentrate in powder or granular form, which is undergoing an advanced extrusion process to transform the texture of plants into the texture of meat.
The Tel Aviv-based company said it focused on improving the texture, firmness and juiciness of their chickpea protein.
The company said it believes that industrial meat farming is harmful since, "the meat and dairy industry create 19% of our greenhouse gases, and 32% of methane emissions that drive climate change."
"Climate change and its impact on agriculture and crops, the ongoing rise in beef prices, and most recently other crises such as the war in Ukraine put enormous pressure on the global food supply chain and the need to rethink and seek diverse protein sources," MTE founder and CEO Dr. Yishai Mishor told The Times of Israel. "As result of our unique scientific and technological work, we present a texturized chickpea protein burger which once in your mouth mimics the texture, firmness and juiciness of a ‘real’ meat burger, without any competition as far as we know."
In September 2022, MTE rose to the challenge when Burger King in Israel was looking for a meat-alternative for their burgers and chicken nuggets. Burger King Israel chose MTE out of 20 other companies that the large fast food chain had sampled from.
Across Israel, consumers can buy MTE's Burger King options which include the popular whopper and soy-based veggie nuggets.


shelf: software-docs

text:
Isolation-based security technologies are gaining prominence
Cyberinc shared its insights into the key trends that will shape the cybersecurity industry in the coming year. With evolving tactics that increase the risk and impact of ransomware and phishing, combined with the new normal of remote workforces, Cyberinc CEO Samir Shah believes that remote browser isolation (RBI) will prove its value as a critical must-have enterprise technology in 2021.
“As mass-scale ransomware and other malware attacks continue to make headlines, companies and IT leaders are concerned about being the next victim,” said Shah.
“Security teams continue to face the hard truth that no matter how much training or what protective measures are in place, a percentage of employees will always inadvertently click on harmful links. This reality creates significant challenges for companies in knowing how best to protect employees, devices, and corporate assets.
“Isolation-based security technologies are gaining prominence as more companies realize the value they deliver in bolstering cyber defenses with minimal investment,” he continued.
“Additionally, with industry analysts increasingly recommending remote browser isolation as part of any corporate cybersecurity program, we expect to see more widespread adoption of these solutions in the coming months and beyond.”
Attackers will double down on double extortion
“Hack-and-leak” ransomware attacks, also referred to as double extortion attacks, will become the go-to method of ransomware in 2021. Double extortion refers to attackers now having two aims: stealing a company’s data and locking organizations out of their own systems or network.
While ransomware protection guidelines include data backups and a well thought out recovery process, that approach is no longer enough when data can fall into the hands of malicious actors. In the coming year, Cyberinc expects to see companies focusing on use of technologies for ransomware prevention in 2021.
Organizations will exit the ransomware arms race by preventing the initial stages of ransomware attacks (e.g., web and email phishing) using emerging technologies like remote browser isolation, which can stop a ransomware attack before it causes damage.
Companies will focus on securing the browser as a critical endpoint
Patching and updating software to reduce the attack surface will take precedence over connecting remote workers in 2021. While 2020 was about enabling and securing remote workers, in 2021 the focus will be on keeping employees and organizations safe in the work-anywhere environment.
As attackers continue to take advantage of new vulnerabilities and opportunities for social engineering, routine tasks such as remediation, patching, and incident response will continue to be more challenging for security teams.
Additionally, with a greater reliance on cloud applications as employees work from any location, the browser will become a more critical endpoint through which ransomware and other malware attacks are carried out. This means that security teams will need to make securing the browser a top priority in the coming year.
This also presents a new set of challenges. For example, companies may standardize all corporate devices on a particular browser for supported cloud apps, yet security teams find themselves needing to support additional browsers for compatibility with legacy apps and websites outside of their control.
Additionally, end users often install and use multiple browsers on their managed and unmanaged devices (referred to as shadow IT), presenting additional complexity and a wider attack surface.
Innovative organizations will move from trying to keep every browser on every device updated and secure to a single remote browser, which will isolate online activities to block or prevent attacks and transform all internet content into harmless visual streams delivered to the endpoint. This process also means that routine maintenance and emergency patching are provided by the remote browser isolation vendor in the process.
End users will continue to be the weakest link
Striking the right balance between security and usability is tricky. Users must click on links to do their work yet clicking on links puts organizations at risk. Even after one year of security awareness training, 3-5% of users will still inadvertently click on a phishing link, according to the KnowBe4 Phishing by Industry 2020 benchmark report.
The rise of technologies like RBI in 2021 will enable organizations to prevent bad things from happening when users click on dangerous links, without compromising user productivity for security.
The increasing cost of mitigating ransomware and phishing attacks will sharpen the focus on isolation-based technologies to protect the weakest link, because prevention beats remediation every time.


tier: cub

shelf: health

text:
The Benefits of Using Biocidal Products in Healthcare Settings
In healthcare settings, maintaining a high level of cleanliness and hygiene is crucial to prevent the spread of infections and ensure the well-being of patients, staff, and visitors. One way to achieve this is by using biocidal products, which are formulated to kill or inhibit the growth of harmful microorganisms such as bacteria, viruses, fungi, and other pathogens.
One of the key benefits of using biocidal products in healthcare settings is the prevention of healthcare-associated infections (HAIs). HAIs are infections that patients acquire while receiving medical treatment in a healthcare facility, and they can have serious consequences, including prolonged hospital stays, increased healthcare costs, and even death. By using biocidal products to disinfect surfaces, equipment, and other high-touch areas, healthcare facilities can effectively reduce the risk of HAIs and improve patient outcomes.
Additionally, biocidal products are also effective in controlling the spread of infectious diseases, such as influenza, norovirus, and COVID-19. These products can help to disinfect surfaces and objects that may be contaminated with infectious agents, thereby reducing the risk of transmission to patients, staff, and visitors. This is especially important in healthcare settings, where the close proximity of individuals and the constant flow of patients make it easy for infections to spread.
Furthermore, using biocidal products can also help to protect individuals with underlying health conditions, such as asthma. Asthma is a chronic respiratory condition that can be triggered or exacerbated by exposure to allergens, pollutants, and infectious agents. By using biocidal products to maintain a clean and hygienic environment, healthcare facilities can help to reduce the risk of asthma attacks and other respiratory symptoms in patients with asthma.
In addition to the health benefits, using biocidal products in healthcare settings can also lead to cost savings and increased efficiency. By preventing infections and reducing the need for costly treatments, such as antibiotics and hospitalizations, healthcare facilities can save money and resources. Moreover, by improving cleanliness and hygiene, biocidal products can help to create a more pleasant and comfortable environment for patients, staff, and visitors.
Overall, the benefits of using biocidal products in healthcare settings are clear. From preventing HAIs and controlling the spread of infectious diseases to protecting individuals with asthma and improving cost savings and efficiency, biocidal products play a crucial role in maintaining a safe and healthy environment in healthcare facilities. By incorporating these products into their cleaning and disinfection protocols, healthcare facilities can ensure the well-being of their patients and staff while promoting better overall health outcomes.


shelf: finance

text:
Understanding Token Sale Structures for Bitcoin (BTC)
The world of cryptocurrencies has come a long way since the introduction of Bitcoin in 2009. One of the key factors driving the success of these digital currencies is their ability to facilitate efficient and secure transactions, without the need for intermediaries like banks. However, one crucial aspect that sets Bitcoin apart from other cryptocurrencies is its token sale structure.
In this article, we will delve into the world of token sales and explain the various structures used in different cryptocurrency projects, specifically focusing on Bitcoin’s (BTC) token sale mechanisms.
What are Token Sales?
A token sale, also known as an initial coin offering (ICO), is a process where a company issues a certain number of its own digital tokens to investors in exchange for a predetermined amount of fiat currency or other assets. This allows the company to raise capital and issue new tokens to the public.
Token Sale Structures for Bitcoin
There are several token sale structures used by different cryptocurrency projects, including:
- Bribe Model: This structure involves paying a fixed price per token in exchange for an investor’s commitment to support the project. The majority of the funding is raised through this model.
- Discounted Price Model: In this structure, investors receive a lower price per token than the market value, often due to discounts offered by the project. This allows projects to raise more money and invest in research and development.
- Token Swap Model: This structure involves exchanging fiat currency or other assets for tokens at a predetermined exchange rate. The investor is essentially swapping their existing assets for new ones.
- Bootstrapped Model: In this structure, the project uses its own funds to raise capital, rather than relying on an external investor.
Bitcoin (BTC) Token Sale Structure
In 2017, Bitcoin’s creator, Satoshi Nakamoto, introduced a token sale mechanism that allowed the project to raise funds from early adopters. This model involved offering 1 million Bitcoins at a fixed price of $2,500 each.
The token sale structure used in this case can be broken down into two phases:
In this phase, investors bid for Bitcoins using a decentralized exchange (DEX). The prices are determined by the bids and offers from other investors. The highest bidder wins the entire supply of 1 million Bitcoins.
After the bidding phase, the project verifies the winners and distributes the 1 million Bitcoins to them. This ensures that each winner receives exactly $2,500 worth of Bitcoin.
Understanding token sale structures is crucial for investors looking to participate in the cryptocurrency market. By analyzing different models and their characteristics, individuals can make informed decisions about which projects are worth investing in.
In the case of Bitcoin (BTC), its token sale structure played a significant role in raising funds from early adopters and fueling its growth. The success of this model demonstrates the potential for token sales to facilitate efficient and secure transactions in the cryptocurrency market.
Tips for Investors
- Research: Before investing, research the project thoroughly and understand its token sale structure.
- Verify Information: Verify information about the project’s team, roadmap, and community involvement.
: Spread your investments across different projects to minimize risk.
- Be Cautious: Be wary of overly promotional campaigns or high-pressure sales tactics.
By understanding the token sale structures used by different cryptocurrency projects, including Bitcoin (BTC), investors can make more informed decisions about which projects to support and which ones to avoid.


shelf: education

title: Making an impact the role of teaching in prisoner rehabilitation

text:
Ask any passionate and talented teacher why they chose a career in education, and they are likely to highlight the pride in inspiring, challenging and improving the life chances of their students. There are perhaps none in need of this energy more than those studying within the prison sector, but despite this, many teachers just have not considered a role in this environment. Are they missing out on a huge opportunity to fulfil their ambition to make an impact and leave a positive impression on people’s lives?
Through my decade long career as an education manager in one of Britain’s largest prisons, every day I see prisoners take on new skills and grow. Before entering the sector, I was teaching in a mainstream FE college, and on my first day, I vividly remember not being sure what to expect. I quickly found an exceptionally rewarding and wide-ranging career, giving prisoners the second chance at life that they may not otherwise have had.
Teaching in a prison environment requires the same qualifications as a role in an FE college – and our teachers have the same passion and commitment as a teacher in any other setting. What is essential, however, is creative thinking. We sometimes need to take unconventional approaches to allow us to overcome barriers that aren’t present in other teaching environments, so being able to think outside the box is a hugely important skill.
This creativity can come to the fore when delivering some of the more traditional subjects. It is common for our learners to have previously had a negative experience with education – or in some cases, never received any. This means we may need to take a fresh approach and teach subjects such as English and Maths through more appealing ways, using football or baking as a framing device. This is often an easier way for prisoners to access these subjects than through a textbook and notepad.
As part of this, the arts have become invaluable in helping prisoners to engage with the wider education process. Forming part of a personal social development programme, subjects like music can help increase motivation and self-confidence. The impact of this can mean prisoners completely change their outlook within a short space of time, and welcome other subjects that they had previously refused to engage with.
We have to remember that we are working in a prison and, as you would expect, this brings its own challenges. When teaching, you quickly find that a form of education that works for one prisoner just does not fit for another. But being able to tailor a learning programme to a prisoner’s needs allows them to make progress in their own way. The flexibility in our role means, depending on a learner’s needs, you could be supporting a student with anything from basic reading and writing skills, up to a university degree. As teachers, we are there to support them every step of the way.
What quickly becomes clear is that we are not delivering education for education’s sake. The ultimate goal is to make prisoners more employable on release – and we recognise our role in making this happen. Finding work is one of the most difficult things for an ex-offender to do, and they still suffer from an undeserved stigma. We work closely with local employers to make sure our learning programmes correlate with the skills they need, and this is where we see the power education has to break the vicious circle of reoffending.
One of the most rewarding parts of our job is when former students write to thank us for our support. This is where we can see exactly how our teaching is having an impact. Some of our former students have gone on to get stable jobs, reconcile with their families, and even start their own businesses. To help the reintegration process, we have dedicated employment brokers to help put offenders in touch with employers, find housing, and gain further external support.
While delivering teaching in the prison sector has its own distinct challenges, it is exceptionally rewarding vocation. It is unfortunate that many teachers are unaware that they can deliver teaching in this environment, but there are many opportunities for motivated, ambitious educators. For experienced FE teachers looking at a new challenge, or for newly qualified teachers looking for their first job, a career in prison education presents an opportunity to influence and improve the life chances of prisoners, giving our learners a genuine second chance.
Amina Bodhania, Education Manager, Novus


shelf: home-craft

title: 10 approaches to protect yourself from bad fats

text:
Melt the soap in a double boiler maybe a micro-wave. Using a microwave will be faster,but the double boiler provides more control of the heat level. If you are doing larger quantities the double boiler may well be more convenient. The soap contains a melting point of 60 C, overheating rrt’s going to result a soap losing its clarity and whether it gets hot enough will smell adverse.
Hemp Body Butter for Men is along with intense 100 % natural ingredients life shea butter, what is Vita Labs CBD Gummies oil, babassu oil, cocoa butter, and vitamins. These ingredients are easily absorbed by a gentleman’s skin that it can look healthy and feel soft and smooth. All of these natural ingredients will also help repair and protect a man’s skin from air pollutants, cold air, dry air, the sun, and other harsh environmental factors while they are at work which is really a plus several of everyone.
The sun keeps shining and the waves keep rolling on in.Once television . is in, buried unseen in the sand have. basically just need to buy functional blades greased. cbd oil benefits would probably work. Have tubes get higher to a sm. maintenance shack and dump a bucket in ever sometimes. The buried lines start on to compromised electric switch.The cost of these endeavors goes down, and continues to so, considering that the grids on evolve!
What are their stuff? Hemp products include nutritional supplements, skin care, fashion and accessories and much more now. As they say.if it’s usually made from hemp this will be part of the Hemp Network series.
The Hoki fish from New Zealand is among the many abundant and pure regarding Omega 3s. They are highly recommended by doctors and health officials’ planet wide.
Social Problems: Cannabidiol, book censorship: should some books be against the law? Parental kidnapping. Alcohol and tobacco should be banned. Does poverty cause crime? The us is contributing to Mexican drug lords. Ethics of animal experimentation. Counterfeit prescription medications. No-fault divorce should be abolished.
Like all living organisms, carp possess a requirement for several trace elements and minerals in their diet plan. Minamino is one of the most commonly used supplements. Is actually very readily available and can provide for a carp’s complete mineral wishe. Carp know this and can’t help but be enthusiastic about it.
All of your Dr. Bronner’s Magic Soaps are Fair Trade and contain no synthetics or petrochemicals, along with the bottles are prepared with 100% post consumer recycled plastic.


shelf: history-culture

text:
Now is best time for Ukraine peace talks: Hungarian FM
Russian President Vladimir Putin has expressed that Russia is all for a diplomatic solution, but Kiev and its supporters, particularly the US and NATO, are unwilling to engage in dialogue.
The crisis between Moscow and Kiev cannot be settled on the battlefield, Hungarian Foreign Minister Peter Szijjarto said.
The situation for peace talks to settle the Ukrainian war will deteriorate further, Szijjarto stated in Budapest on Friday. The Foreign Minister feels that the two parties are in a better position for discussions at the moment.
Last month, Hungarian Prime Minister Viktor Orban told German tabloid Bild that a Ukrainian triumph on the battlefield would be "impossible" for Kiev and its supporters.
Russian President Vladimir Putin has expressed that Russia is all for a diplomatic solution, but Kiev and its supporters are unwilling to engage in dialogue.
After meeting with Turkish Foreign Minister Hakan Fidan, Szijjarto told journalists Friday that “there will be no better conditions for peace negotiations than the present," adding that “yesterday’s conditions were better than today’s, and tomorrow’s conditions will be worse than today’s."
Hungary prevented the European Union from offering the eighth €500 million package from the so-called European Peace Fund to the Kiev authorities in May. Hence, Orban has insisted that the ongoing hostilities stem from a "failure of diplomacy."
Instead of continuing a strategy of further escalation, the senior Hungarian leader asked the West to stop escalation immediately. Viktor Orban has also been particularly scathing in his criticism of the European Union's anti-Russian actions.
Orban has also stated recently that Ukraine had "run out of strength," only persevering due to Western financial assistance.
Ukraine abandoned the agreements established when Russian soldiers withdrew from the Kiev area, and Moscow does not understand why Western countries are pulling Ukraine into NATO, posing a security concern, according to Russian President Vladimir Putin.
Putin added that Moscow has repeatedly publicly voiced its readiness for talks with Kiev, stressing that "after the withdrawal of our troops from near Kiev - and we were asked to do this in order to create conditions for the conclusion of a final agreement - the Kiev authorities abandoned all previous agreements" and adding that now "the ball is completely on their side."
He also emphasized that, despite the West's inability to comply with the UN Charter, Russia is prepared to seek a peaceful resolution to the war in Ukraine.
Doubling down, Putin stated that Russia has never violated the UN Charter and always acts in accordance with its ideals, adding that its principles should be recognized by everybody. "There should not be any double standards, unilateral sanctions, and attempts to ensure their own security at the expense of others," he said.


shelf: civic-law

title: Newly created nlrb rules drastically change the process for unions seeking recognition of most private sector employees in the u s and substantially limits employee voting in secret ballot election

text:
At the end of last week, the National Labor Relations Board (the “Board”) issued two huge blows to employers that give significant advantages to unions and ease their ability to achieve status as a certified bargaining representative.
As we previously reported and discussed here, the General Counsel of the Board (the “General Counsel”) sought reinstatement of union recognition without requiring the Board to hold a representation election. On August 25, 2023, the Board, through its decision in Cemex Const. Materials Pac. LLC, 372 NLRB No. 310 (Aug 25, 2023), created a new standard that essentially revived the dormant Joy Silk Mills doctrine with some modifications, thus allowing unions to achieve recognition as the certified bargaining representative of employees without requiring a formal NLRB secret-ballot election.
Additionally, on August 24, 2023, the Board issued a direct final rule which will reinstate many of the 2014 “quickie election” rules for representation cases that greatly accelerates the timeline for elections and makes it much easier for unions to organize.
In practice, if this new standard is not reversed by the federal courts, we expect most unions will organize by demanding immediate employer recognition or by virtue of NLRB determinations that the employer committed at least one unfair labor practice before an election was held, thereby nullifying the election results and declaring the union certified based on a pre-election claim of majority support.
These changes radically shift the legal landscape for companies addressing demands for recognition and organizing campaigns, and require significant proactive approaches to address the new reality for how unions will organize and win certifications going forward.
The Cemex Decision
In Cemex, the General Counsel asked that the Board overturn Linden Lumber Division, Summer & Co., 190 NLRB 718 (1971), revd. sub. nom. Truck Drivers Union Local No. 413 v. NLRB, 487 F.2d 1099 (D.C. Cir. 1973), revd. 419 U.S. 301 (1974) which allowed employers to lawfully reject a demand for recognition and require filing of a petition with the Board, and reinstate the standard from Joy Silk Mills Inc., 85 NLRB 1263 (1949), enfd. in relevant part, 185 F.2d 732 (D.C. Cir. 1950), cert denied 341 U.S. 914 (1951). Under the Joy Silk standard, an employer would be in violation of Section 8(a)(5) and 8(a)(1) by refusing to agree to bargain with a union who demanded recognition and contended that they had majority support absent good-faith doubt as to the union’s majority status.
The Board, agreeing with the General Counsel that the current scheme for remedying an employer’s unlawful refusal to recognize and bargain with the employees’ designated bargaining representative is inadequate to safeguard the right to organize, overruled Linden Lumber. Instead of adopting the standard from Joy Silk as is, the Board announced a new framework that modifies Joy Silk for determining when an employer has unlawfully refused to recognize and bargain with a designated majority representative of its employees.
The New Cemex Standard and Obligations for Employers Presented With a Demand for Recognition
Under this new standard, when presented with a claim of majority support, an employer has two options:
- Immediately grant recognition without any NLRB election; or
- File its own NLRB petition seeking an election within 2 weeks of a union’s demand for recognition in order to test the union’s majority status or the appropriateness of the unit (assuming the union has not already filed a petition pursuant to Section 9(c)(1)(A)).
If the employer fails to take either step, the NLRB will order mandatory union recognition (with no NLRB election) unless the employer – in a later unfair labor practice (ULP) proceeding – proves that the union did not have majority support or that the claimed bargaining unit was inappropriate.
According to the Board, the filing of an employer’s own NLRB petition pursuant to Section 9(c)(1)(B) will provide employers with the opportunity to challenge the union’s majority status through a representation election if the Board, upon investigation and hearing, finds that a question of representation exists. Should an employer refuse to recognize the union and fail to promptly file a NLRB petition, a union still may file a 8(a)(5) refusal to bargain unfair labor practice charge against the employer and, if majority support in an appropriate unit is proven, the Board will find a 8(a)(5) violation for refusal to recognize and bargain and will issue a remedial bargaining order. The risk of a union filing an unfair labor practice charge for failure to act essentially creates an obligation that employers either (i) file a NLRB petition, or (ii) recognize and bargain with the union.
Most importantly, employers should be aware that the standard outlined in the Board’s majority opinion will allow the Board to issue remedial bargaining orders more widely to deter employers from engaging in misconduct and unfair labor practices before an election as a dilatory tactic. Stated differently, where there is a pending petition, regardless of the filing party, and the employer commits even a single unfair labor practice under 8(a)(1) or 8(a)(3) that would require setting aside the election, the petition will be dismissed and the Board will issue a remedial bargaining order requiring union recognition. The Board emphasized that the new standard and availability of remedial bargaining orders will more properly focus the impact of unfair labor practices on the pending petition and election (if one is held), instead of focusing the potential impact of unfair labor practices on the success of future rerun elections.
Thus, while the Cemex rules permit the employer to petition the NLRB for an election in response to a union recognition demand, virtually any unlawful conduct during the period preceding an election will prompt the Board to issue a mandatory “bargaining order” requiring union recognition. In light of this, Cemex has radically changed the threshold that will prompt the NLRB to issue mandatory “bargaining orders” based on any unlawful conduct that sets aside an election, and dramatically changes the much higher threshold embraced in two U.S. Supreme Court cases that validated the NLRB’s issuance of “bargaining orders” only when unlawful conduct made it “improbable” that a ”fair election” can be held.
The Board also held that the Cemex decision applies retroactively in order to avoid inconsistency in pending cases, restore judicially approved standards, and ensure the decision serves its intended goal of adequately protecting employees exercising their Section 7 rights.
Member Kaplan dissented in part from the majority opinion with respect to the standard that would allow the Board to issue the remedial bargaining orders more easily when an employer has engaged in conduct that could be classified as a ULP under 8(a)(3) or (1), and classified that portion of the majority opinion as dicta given that the employer in Cemex engaged in over 20 unfair labor practices, not one or a few. Further, in his dissent Member Kaplan emphasized that the majority opinion effectively takes away an employee’s right under the National Labor Relations Act (the “Act”) to participate in a secret ballot election and warns that the decision will likely create much litigation.
We anticipate that legal challenges to the Cemex decision will materialize in the coming months, with the overriding challenge to the decision premised on material deviation of NLRB elections as the standard method to determine union majority status and the reliance on card check despite well-established U.S. Supreme Court precedent and repeated legislative failures to adopt this method for union certification.
Final Rule on Representation Procedures
On August 24, 2023, the day before the Board handed down the Cemex decision, the Board issued a direct final rule which will reinstate many of the 2014 “quickie election” procedures for representation cases with the intent of enhancing the “fair, efficient, and expeditious resolution of representation cases.” The Final Rule will take effect on December 26, 2023.
The Amendments of the Final Rule are as follows:
Shortening the Timing of Opening of Pre-Election Hearing to 8 Calendar Days from Service of the Notice of Hearing.
Under the Final Rule, the pre-election hearing will generally be scheduled to open 8 calendar days from service of the notice of hearing. This is a shortening of the timeline from the 2019 Rule which allowed for a pre-election hearing to open 14 business days from service of the Notice of Hearing. Not only is the Board shortening the overall number of days between the Notice of Hearing and the opening of a pre-election hearing, it has shifted the timeline from use of business days to calendar days.
Limits on Regional Director Discretion to Postpone Pre-Election Hearings.
Regional Directors will only have discretion to postpone a pre-election hearing for up to 2 business days upon request of a party showing “special circumstances” and for more than 2 business days upon request of a party showing “extraordinary circumstances”. This is a dramatic change from the 2019 Rule that gave Regional Directors discretion to postpone a pre-election hearing for an unlimited amount of time upon request of a party showing good cause. In addition to shortening the time for postponement of a pre-election hearing, the Board raised the standard a party must demonstrate in order to receive a postponement from “good cause” to “special circumstances” for 2 business days and “extraordinary circumstances” for more than 2 business days.
Time for Nonpetitioning Party to File a Statement of Position.
A nonpetitioning party’s Statement of Position will be due to be filed by noon the business day before the opening of the pre-election hearing,thus the Statement of Position is due 7 calendar days after service of the Notice of Hearing. Under the 2019 Rule, a nonpetitioning party’s Statement of Position was due 8 business days after service of the Notice of Hearing.
Limits on Regional Director Discretion to Postpone Statement of Position Filing Deadline.
Regional Directors have discretion to postpone the due date for filing a Statement of Position for up to 2 business days upon request of a party showing “special circumstances” and for more than 2 business days upon request of a party showing “extraordinary circumstances.” Under the 2019 Rule, Regional Directors could postpone the filing deadline for an unlimited amount of time for a showing of good cause. Again, the Board heightened the standard a party must demonstrate in order to receive a postponement from “good cause” to “special circumstances” for 2 business days and “extraordinary circumstances” for more than 2 business days.
Removing the Requirement That a Petitioner File a Responsive Statement of Position.
Under the Final Rule, a petitioner will verbally respond to the nonpetitioning party’s Statement of Position at the start of a pre-election hearing. Under the 2019 Rule, the petitioner was required to file and serve a responsive Statement of Position 3 business days prior to the pre-election hearing. In addition to removing the burden of a filing from the petitioner, this amendment puts nonpetitioning parties at a disadvantage of not knowing what issues the petitioner will highlight at the hearing.
Shortening of Timeline for Employer to Post Notice of Petition for Election.
An employer will be required to post the Notice of Petition for Election in conspicuous places in the workplace and distribute electronically within 2 business days after service of the Notice of Hearing. This is in contrast to the 2019 Rule which provided an employer with 5 business days for posting and electronic distribution.
Limits on Litigable Issues During Pre-Election Hearing.
Disputes concerning an individual’s eligibility to vote or inclusion in an appropriate unit will not be litigated or resolved prior to an election. The pre-election hearing is reserved for resolution of questions of representation. Regional Directors have authority to exclude evidence that is not relevant to determining whether there is a question of representation. The 2019 Rule provided that questions regarding individual eligibility and inclusion were normally litigated at the pre-election hearing and resolved by the Regional Director prior to the election. By limiting pre-election hearings to questions concerning representation, the Board states that the parties will have the opportunity to resolve issues regarding unit placement during bargaining should the employees vote in favor of representation or through the use of the Board’s unit clarification procedure, thus severely limiting an employer’s ability to ever challenge employee eligibility. Not knowing whether certain employees will be eligible to vote ahead of an election can cause risk for employers when they seek to utilize managers and supervisors in any campaign activities.
Limit on Ability to File Post-Hearing Briefs.
Following a pre-election hearing, parties may only file post-hearing briefs with the Regional Director’s special permission and may only address subjects permitted by the Regional Director within the timeframe permitted by the Regional Director.
Following a post-election hearing, parties may only file post-hearing briefs with the hearing officer’s special permission and may only address subjects permitted by the hearing officer within the timeframe permitted by the hearing officer. The 2019 Rule allowed parties to file post-hearing briefs up to 5 business days following the close of a hearing and extensions of an additional 10 business days could be sought upon showing of good cause.
Simultaneous Transmission of Decision and Direction of Election, and Notice of Election That Contain Specific Election Details.
Regional Directors are to specify election details such as the type of election, date of election, time of election, location of election, and the eligibility period in the decision and direction of election, and are required to simultaneously transmit the Notice of Election with the decision and direction of election. Previously, under the 2019 Rule, Regional Directors had discretion to provide election details in a Notice of Election which could issue after a decision and direction of election.
Elections Will be Scheduled for “The Earliest Date Practicable” After Issuance of Decision and Direction of Election.
Regional Directors shall schedule elections for “the earliest date practicable” after issuance of a decision and direction of election. This eliminates the 20-business day waiting period between the decision and direction of election and the election that was contained in the 2019 Rule.
With the issuance of the Cemex decision and the Final Rule, we expect an increase in demands by unions for voluntary recognition by employers and the number of unfair labor practice charges filed.
Given that the Board’s decision in Cemex takes effect before the Final Rule, and the expectation of an increase in the number of demands for voluntary recognition, it is unclear how many elections will actually be held pursuant to the new procedures outlined in the Final Rule once they take effect in December. Since Cemex, in effect, creates an obligation for an employer to voluntarily recognize or otherwise risk the Board issuing a remedial bargaining order for virtually any allegations of an unfair labor practice, it is possible that the number of elections that are actually held pursuant to the Board’s Final Rule may actually decrease.
Since the Board’s recent actions substantially change representation procedures and create a large risk for employers to be subject to a remedial bargaining order, it is important that employers take the following steps to understand the recent changes and how best to continue to manage their workforces under a threat of organizing.
Understand the Updated Timelines and Obligations.
Both the Cemex decision and the Board’s final rule accelerate the timelines associated with representation procedures. It is important that employers are aware of these deadlines should they be presented with a demand for recognition or an organizing petition. Employers will want to ensure they preserve their right to file a NLRB petition under Cemex and understand that once approached with a demand for bargaining, an employer must decide whether to recognize and bargain with the union or file a petition. Employers that receive a demand for recognition from a union that alleges majority status should consider requesting that the union voluntarily share its evidence of majority support before the employer decides to reject the demand or file a NLRB petition. In addition, employers should assess the appropriateness of the unit and potential challenges to claims of majority and recognition demands (e.g., misrepresentations by union organizers about the purpose of a union authorization card that could invalidate cards, revocation of cards, contesting authenticity of cards, whether the union actually possessed valid authorization cards for a majority of employees given turnover or changes in the unit size and scope claimed by the union, etc.).
Properly Educate Management on Employee Rights Under the Act, and the Importance of Early Education on Authorization Cards and Union Advances.
Employers should take a proactive approach in educating supervisors and managers of employee rights under the Act, even if there is currently no reason to suspect organizing. This includes education regarding conduct that is unlawful during an organizing campaign. Given the shortened time frame with which an employer must file a NLRB petition to challenge a union’s majority status coupled with the future accelerated timelines under the Final Rule, there is a very small window for employers to prepare for an organizing campaign, pre-election hearing, and election, particularly if an employer is caught by surprise with a demand for recognition and/or a petition.
In addition, unions have often secured signed authorization cards from employees under the theme of “sign up to hear more”—without making clear that authorization cards could become an automatic basis for union recognition with no campaign and no election. It seems suspect that unions will change their tactics with authorization cards going forward, even though the cards will have a much greater chance of serving as the evidence of majority support and a union certification. Thus, employers have a much greater incentive now to proactively educate employees about authorization cards and the consequences of signing them.
Further, with the risk of a remedial bargaining order, an employer must prepare its managers and supervisors adequately so that they do not engage in conduct that could be deemed an unfair labor practice under 8(a)(1) or 8(a)(3), thus opening the door for such an order that would cause dismissal of any pending petition and require the employer to recognize and bargain with the union. For companies that follow the NLRB election petition route, avoiding an unfair labor practice will be critical to evading an automatic bargaining order after the election even if the union loses. While the types of violations found in Cemex would have always led to the invalidation of an election (e.g., threats of plant closure, discipline and discharge of union supporters, surveillance and interrogation), recent NLRB pronouncements greatly increase employers’ risk of unfair labor practices. For example, the General Counsel announced new limits on employers’ free speech rights, such as captive-audience speeches and other employer communications occurring during typical union elections. These activities—which until recently would not have resulted in an unfair labor practice charge—may now be a violation that could threaten the validity of an election and result in a subsequent bargaining order.
Review Employment Documents, Including Employee Policies and Handbooks.
In his partial dissent in Cemex, Member Kaplan voiced the concern that the majority standard that allows the Board to more easily issue remedial bargaining orders, coupled with the Board’s recent decision in Stericycle, Inc., 372 NLRB No. 113 (2023), which we discussed in detail here, makes it impossible for an employer not to commit an unfair labor practice that requires setting aside the election. Given the presumption established in Stericycle that a work rule is unlawful if a reasonable employee could interpret any isolated word or phrase in a work rule to restrict the exercise of Section 7 rights, it is important that employers review their employment policies and procedures for any language that could be deemed unlawful. The majority’s citation to Stericycle and statement that the standard in Cemex does not require a bargaining order as “the first and only option,” read in tandem with Board precedent that has deemed handbook policies as restrictive enough to warrant setting aside an election, indicate that even a single policy or incident of conduct could result in a remedial bargaining order under the Cemex standard.
Thus, if an employer decides to file a NLRB petition and wishes for the election results to be determinative of the union’s certification rights, careful review of all employment documents (policies and handbooks) is recommended and any campaign activity beyond sharing voluntary, written communications reviewed by labor relations counsel could provide a basis to challenge and void the election results—thereby certifying the union via the original majority status claim.
We will continue to monitor any new developments with respect to the Cemex standard and the Final Rule.
Prior to its decision in Cemex, remedial bargaining orders or “Gissel bargaining orders” were only issued in cases where an employer had engaged in such severe and pervasive unfair labor practices that the fairness of a future rerun election was unlikely. NLRB v. Gissel Packing Co., 395 US 575 (1969).
The Board contends that it may rescind the 2019 Rule by direct final rule in order to return to procedures similar to those that were in effect following the implementation of the 2014 Rule because the provisions concern agency procedure and therefore are not required to go through notice and comment. Additionally, the Board points out that the provisions of the 2014 Rule it is reinstating previously went through notice and comment, where as the 2019 Rule was a result of direct rulemaking.
The Final Rule amends 29 CFR §§ 102.63; 102.64(a); 102.66(a), (c), and (h); 102.67(b); and 102.69(c)(1)(iii).


tier: kodiak

title: 186

text:
In this paper, we continue the study of the Euler equation describing gas flows on space curves in a constant gravity field. Symmetry algebras and differential invariant fields, as well as their dependence on thermodynamic state equations and the form of a space curve, were considered in [
1]. Here, we find a quotient PDE for the Euler equation and show its role in solving the original equation.
Recall that the system of PDEs describing such flows is the following:
is the flow velocity,
are the pressure, density, specific entropy, and temperature of the fluid, respectively,
k is the constant thermal conductivity,
is the gravitational acceleration, and
z-component of a naturally parametrized space curve.
1) is incomplete, i.e., it has two more unknown functions than equations. In the present paper, we put aside the question of classification of possible thermodynamic relations, since it was described in detail in [
1]. We assume that these relations are given either in the forms
, or in terms of the Planck potential [
2]. In particular, we consider the ideal gas equation.
This paper is organized as follows. In
Section 2, the notion of PDE quotients is discussed. In
Section 3, we recall the symmetry algebra and differential invariants for the Euler system. In
Section 4, we find the quotient for the Euler equation and discuss possible symmetries and solutions.
All calculations for this paper were performed with the DifferentialGeometry package in Maple. The corresponding Maple files can be found on the webpage
2. PDE Quotients
2.1. Algebraic Structures in PDE Geometry
Let be a smooth bundle over a manifold M and let , be the k-jet bundles of sections of the bundle . To simplify the notations, we use instead of .
, the jet geometry [
3] is defined by the following pseudogroups.
If , it is defined by the pseudogroup of the local contact transformations of the manifold .
For , the jet geometry is defined by the pseudogroup of the local point transformations, i.e., local diffeomorphisms of the manifold .
It is also known that the prolongations of these pseudogroups to the jet bundles exhaust all Lie transformations, i.e., local diffeomorphisms of jet spaces that preserve the Cartan distributions (see, for example, [
Moreover, bundles ( when , and when ) have affine structures, which are invariant with respect to the Lie transformations, and prolongations of the pseudogroups or are given by rational functions of in the standard jet coordinates .
The last statement means that, in the case of , the fibers of the projections at a point are algebraic manifolds, and the stationary subgroup gives us birational isomorphisms of the manifold.
In the case of , the fibers of the projections at a point are algebraic manifolds too, and the stationary subgroup gives us birational isomorphisms of the manifold.
Following this picture, we say that a differential equation is algebraic if fibers of the projections are algebraic manifolds when , or when .
All differential equations here are assumed to be formally integrable; then, the prolongations of an algebraic equation are algebraic, too.
By a symmetry algebra of an algebraic differential equation, we mean the Lie algebra of point vector fields if or contact vector fields if that act transitively on in the case of or in the case of . Moreover, the stationary sub-algebra where or produces actions of algebraic Lie algebras on algebraic manifolds for all .
2.2. The Rosenlicht Theorem
Let B be an algebraic manifold, i.e., an irreducible variety without singularities over a field of characteristic zero, let G be an algebraic group, and let be an algebraic action.
Denote by the field of rational functions on the manifold B, and, by , denote the field of rational G-invariants on B.
We say that an orbit is regular (as well as a point b itself) if there are G-invariants such that their differentials are linearly independent at the points of the orbit.
Let be the set of all regular points and let be the set of all regular orbits.
The Rosenlicht theorem [
4] states that
is open and dense in
Moreover, if the above invariants are considered as local coordinates on the quotient at the point , then on the intersections of the coordinate charts, the coordinates are connected by rational functions. In other words, is an algebraic manifold of the dimension , and the rational map of algebraic manifolds gives us the field isomorphism .
To apply this theorem to algebraic differential equations, we should reformulate it for the case of Lie algebras.
Let B be an algebraic manifold and let be a Lie sub-algebra of the Lie algebra of the vector fields on B.
We say that is an algebraic Lie algebra if there is an algebraic action of an algebraic group G on B such that coincides with the image of Lie algebra under this action.
By an algebraic closure of a Lie algebra , we mean the intersection of all algebraic Lie algebras that contain .
Example 1. Let ; then, Lie algebrais algebraic because it corresponds to the projective action of the algebraic group . Example 2. Let be a torus and , where ϕ and ψ are the angles, . Then, is algebraic if and only if . Otherwise, . A similar situation occurs in the case of andwhere if , and otherwise. The Rosenlicht theorem is also true for algebraic Lie algebras or for their algebraic closure in the case of general Lie algebras.
Let us be given a Lie algebra of vector fields on an algebraic manifold B and let be its algebraic closure. Then, the field of rational -invariants has a transcendence degree equal to the codimension of regular -orbits, and it is also equal to the dimension of the quotient algebraic manifold .
2.3. Quotients of Algebraic Differential Equations
be an algebraic symmetry Lie algebra of an algebraic formally integrable differential equation
, and let
-th prolongations of
. Then, all equations
are algebraic, and we have the tower of algebraic bundles:
Let be the set of strongly regular points and let be the set of all strongly regular -orbits, where, by a strongly regular point (and orbit), we mean such points of that are regular with respect to -action and whose projections on are regular, too.
Then, as we have seen, are algebraic manifolds, and the projections are rational maps such that the fields (the field of rational functions on ), and (the field of rational functions on ), which are -invariants (rational differential invariants), coincide: .
The -action preserves the Cartan distributions on the equations, and therefore, projections define distributions on the quotients .
Finally, we get the tower of algebraic bundles of the quotients
such that the projection of the distribution
2.4. Tresse Derivatives
be a differential 1-form on a
k-jet manifold. Then, the class
is called a horizontal part of
In the standard jet coordinates
, the horizontal part has the following representation:
As a particular case of this construction, we get the total differential
, or, in the standard jet coordinates,
are the total derivations.
It is important to observe that the operation of taking a horizontal part, as well as the total differential, is invariant with respect to the point and contact transformations.
We say that functions
are in general position on a domain
on this domain.
f be a smooth function on this domain; then, we get decomposition in
are smooth functions on the domain
We call them Tresse derivatives [
5] and denote them by
As we have seen, the operation of taking a horizontal part, as well as the total differential, is invariant with respect to the point and contact transformations.
Therefore, we have the following.
Proposition 1. Let be -invariants of order that are in general position. Then, for any -invariant f of order , the Tresse derivatives are -invariants of order .
2.5. The Lie–Tresse Theorem
Theorem 1.  Let be a formally integrable algebraic differential equation and let be an algebraic symmetry Lie algebra. Then, there are rational differential -invariants of order such that the field of all rational differential -invariants is generated by rational functions of these invariants and their Tresse derivatives . We call invariants Lie–Tresse coordinates.
It is noteworthy that, in contrast to algebraic invariants, for which we have the algebraic operations only, in the case of differential invariants, we have additional operations, i.e., Tresse derivatives, that allow us to get really new invariants.
Syzygies, in the case of differential invariants, provide us with new differential equations that we call quotient equations.
From the geometrical point of view, the above theorem states that there is a level
l and a domain
where the invariants
can be considered as local coordinates, and the preimage of
D in the tower
is just an infinitely prolonged differential equation given by the syzygy.
For this reason, we call the quotient tower (
2) an algebraic diffiety.
2.6. Relations between Differential Equations and Their Quotients
Let be a solution of differential equation and let and be values of the invariants and on the section f. Then, locally, , and therefore, is the solution of the quotient equation.
The above construction is local. In general, the correspondence between solutions is valid on the level of generalized solutions, i.e., on the level of integral manifolds of the Cartan distributions. In addition, the correspondence will lead us to integral manifolds with singularities.
Now let be a solution of the quotient equation. Then, considering equations as a differential constraint for the equation , we get a finite-type equation with a solution that is a -orbit of a solution of .
Symmetries of the quotient equation are Bäcklund-type transformations of the original equation .
Example 3. The Lie algebra of the projective transformations of the line , has the following generators in rational differential invariants for the -action on functions: Letbe a fourth-order -invariant equation. Then, the quotient equation has the first order: Example 4. The Lie algebra of translations of the plane has the following Lie–Tresse coordinates for the -action on functions: Then,where is a Hessian determinant, and the syzygy is Thus, the quotient of an equation is the last equation for , where letter C stands for c.
3. Euler Equations on a Curve
In this section, we briefly recall the necessary results obtained in [
Consideration of flows of an inviscid medium on a space curve
in a field of constant gravitational force leads to the system
s are expressed in terms of Planck potential [
R is the universal gas constant.
To describe this Lie algebra, we consider a Lie algebra
of point symmetries of the PDE system (
be the following Lie algebra’s homomorphism
is a Lie algebra generated by vector fields that act on the thermodynamic values
It was demonstrated [
1] that if
, the Lie algebra
of point symmetries of the system (
1) is generated by the vector fields
The pure thermodynamic part
of the symmetry algebra is generated by the vector fields
Thus, the Euler system has a Lie algebra of point symmetries .
It has been shown in [
1] that, for
, the basis differential invariants are
and the basis invariant derivatives are
4. Quotient Equation
as Lie–Tresse coordinates
as unknown functions, respectively, we get the quotient equation for (
Direct computations show that the system (
4) has no symmetries if the function
is arbitrary. Nevertheless, it is possible to find symmetries for some classes of
. Some of these cases are listed below.
Proposition 2. If the system (4) admits a symmetry of the formthen the function Φ
is of the formwhere are constants. Proposition 3. If the system (4) admits a symmetry of the formthen the function Φ
is the followingwhere are constants. Particular solutions of (
4) for some special classes of the function
can be found. For example, consider the Planck potential for the ideal gas model:
n is the number of freedom degrees of a gas particle.
Then, for simplicity, let , then these are some of the solutions for L and M:
Here, are constants and is an arbitrary function.
Let us illustrate how we can solve the original Euler PDE system using its quotient. To this end, we consider the system (
3) for ideal gas together with the solution (for example,
), which is equivalent to a finite-type system:
Solving the latter, we get
are arbitrary constants.
Another approach we can take is to exploit the fact that it is often possible to consider the Planck potential
in the form of virial expansion:
Then, we can find solutions of the system (
4) in the form of power series of
are the integer constants that should be chosen such that (
4) can be expanded as a power series of
x. It can be shown that
. Hence, the zeroth-order term of this expansion is a system of ordinary differential equations:
The first-order term of the expansion is a system of linear ordinary differential equations:
The solutions of (
6) must be substituted into (
7); thus, we obtain more simple differential equations for the functions
. Repeating this process, we can obtain any number of terms in the expansions of the functions


text:
Cover image by https://www.flickr.com/photos/francesc_2000/
In the Catalan region of Spain, people have long recognized the power of books. On April 23rd, in commemoration of Cervantes’ death, people are presented a single rose and a book. More recently, UNESCO named April 23rd, which is also Shakespeare’s birthday, as the International Day of the Book. From a regional tradition in Spain to schoolchildren receiving book tokens in Great Britain and Ireland on World Book Day, the idea for World Book Night was born at London’s Book Industry Conference. This event has spread the love of reading to tens of thousands of readers and non-readers alike who are “gifted” a book through the generosity of a national network of book givers, bookstores, libraries, authors, publishers and donors. In 2011, World Book Night UK launched this “quixotic” venture to expand UNESCO’s program to adult readers. One year later, the program expanded to the United States and has been growing ever since.
25,000 passionate book givers spread the love of reading by volunteering to personally go out into their communities and hand out 20 books to potential new readers on April 23rd. That’s how WBN shares half a million books in just one day. Selected books are specially produced, not-for-resale paperbacks. Book givers receive twenty copies of one book, a title they choose from a list of 39 selections. (See 2014 Selections) In their applications, givers pick their first three best choices, and WBN does its best to fulfill those requests. The week prior to April 23rd, givers go to designated pick-up locations but have to wait until the 23rd to hand out their books.
Libraries Lend A Hand
Public libraries are the mainstay for WBN’s national advocacy and distribution network. Libraries make two commitments as participants, to be a pick-up location for book giver volunteers to retrieve their shipment of books, and to be active advocates in local communities for World Book Night by doing what comes naturally, spreading the love of reading, “person to person.” The program makes it easy for libraries to participate. They offer some wonderful marketing tools including logos, stickers, a town proclamation, thank you letters, and other easy and useful ideas—like donating books that haven’t been picked up to a local prison, hospital, or juvenile detention center.
World Book Night US 2014 Events
Small bookstores and public libraries are celebrating World Book Night 2014 in many different ways. Comedian Amy Poehler is this year’s honorary chairperson, adding interest and entertainment. To celebrate, The New York Public Library will host Victoria Bond, Malcolm Gladwell, Garrison Keillor, Walter Dean Myers, Esmeralda Santiago, T.R. Simon, and Tobias Wolff at 6:30 pm on April 22nd while Althea Kontis will appear at the Gum Springs Library in Stone Ridge, Virginia at 7:00 PM. Readers in Chicago can hear Scott Turow at the Chicago Public Library’s main branch while none other than Walter the Giant Storyteller will be at the Alameda Free Library in Alameda, California. World Book Night US 2014 celebrates reading everywhere.
The Gift of A Book
World Book Night has a two-fold mission: “spreading the love of reading, person to person”. A book can be given; the love of reading must be emulated. That is the promise of World Book Night. From its inception, Anne Cucci, school librarian at W.T. Clarke High School in Westbury, New York, took part. The first year, she gifted the boys at the School Program for Incarcerated Youth at the Nassau County Correctional Center in East Meadow, NY. That April, a population that rarely received gifts was given a carton full of The Glass Castle,.
As the transitional counselor in the school program there, I wrote Anne:
“Our rolling library is quite popular here and our students’ appetite for reading is enormous. Being able to lend them a book is one thing, being able to give them a book was a ‘feast’.
The inscription over the library at Thebes: Medicine for the soul. We all understand a book as a place of escape. But also healing for the soul. What better appeal than for those in jail. And what better place for your service to World Book Night. Thank you.”
Since then, Anne has become a “reading ambassador”. The boys and I look forward to the carton she will deliver this year.
Through her efforts as a book giver and the cooperation of the public library system where she picks up the books, she and thousands of other volunteers are spreading the love of reading one book at a time.


title: Publications poster abstracts presentations

text: CAUTION: Federal (USA) law restricts this device to sale by or on the order of a physician. For healthcare professionals only. Prior to use, refer to the instruction for use supplied with this device for indications, contraindications, side effects, suggested procedure, warnings and precautions. WARNINGS: Use of the Tryton Side Branch Stent in appropriately sized main vessels and side branches is required for safe and effective performance of the device. Do not use the Tryton Stent in small side branches [<2.50 mm in diameter by visual assessment or <2.25 mm in diameter by quantitative coronary angiography (QCA)], as its use may lead to an increased risk of adverse cardiac events such as myocardial infarction and the need for repeat revascularization. To confirm appropriately-sized side branch diameters, the diameter of the pre-dilation balloon inflated to nominal pressure may be used as a reference. Alternatively, the use of quantitative imaging methods such as on-line quantitative coronary angiography, intravascular ultrasound or optimal coherence tomography should be considered. Use of the Tryton Side Branch Stent, as with percutaneous coronary stent implantation procedures in general, is known to be associated with the following risks: Vessel thrombosis. Increased length of hospital stay relative to those of coronary balloon angioplasty alone. Judicious selection of patients to receive this device rather than balloon angioplasty alone is strongly advised. infection secondary to contamination of the stent may lead to thrombosis, pseudoaneurysm or rupture. The stent may cause spasm, distal embolization, thrombus, or could migrate from the site of implantation. Excessive dilatation of the artery may cause vessel rupture and life-threatening bleeding. Stents may not be fully expanded during deployment, particularly in resistant lesions. Stent dislodgment from the balloon surface during deployment and/or dislodgment from the target site post-deployment can occur. Major bleeding.


title: Image source: Getty Images

text:
Image source: Getty Images
The FTSE 100 might have hit fresh all-time highs earlier in February, but that doesn’t mean all its constituents are flying high. For a variety of reasons, there are some that could be perceived to be cheap shares right now. Yet just because a share price might look attractive, more research needs to be done to try and spot red flags. Here’s one that I feel investors should consider and also one I’m steering clear of.
Changes are coming
Let’s start with the one that I believe is cheap. I’m talking about BP (LSE:BP). I wrote about the stock earlier this month following a share price rise after news of a large activist hedge fund taking a stake in the business. The 7% jump with Elliott Investment Management getting involved shows investors are happy about a possible restructuring and strategy changes that will be pushed for in the coming year.
Such changes are needed, with the recent 2024 annual results showing a sharp profits drop. The share price might only be down 5% in the past year. But at 447p it’s well off the 52-week highs of 540p and even further off all-time highs! So, from that angle, some would consider it to be cheap.
Another reason it could be an attractive value purchase is because Elliott clearly see long-term value here. BP CEO Murray Auchincloss announced plans to “fundamentally reset” BP’s strategy, which should help to unlock more profitability going forward. Coming changes include abandoning previous goals of reducing oil and gas output. It’s also looking to fund more profitable oil projects in places like the Middle East.
One risk is that the strategy shift doesn’t go to plan. In that case, the company might still be undervalued, but it could need another shift in direction before finding the right lane to move into.
Numbers not adding up
On the other hand, I’m not convinced that Vodafone (LSE:VOD) is the bargain that some people think it is. The stock is flat over the past year, but is down a whopping 57% over the past five years.
I struggle to see the share price rallying any time soon for a few reasons. To begin with, it’s laden with debt. The latest half-year report showed net debt at €31.8bn. Although this was a fall from the previous year’s €33.2bn, it’s still very high. For perspective, it made a half-year profit of €1.2bn!
Another factor is that the business isn’t really growing. Full-year 2024 revenue fell 2.4% versus 2023. We’ll have to wait and see in May for the next round of reporting, but I struggle to see revenue materially growing. As a result, the share price is unlikely to rally until revenue (and profit) start to tick higher.
Despite my concerns, it’s true that the dividend yield looks very attractive. Even with the recent dividend cut, a 5.63% yield is generous. Some might be happy to own the stock to pick up income and wait for a long-term recovery in the stock. But I’m keeping away and won’t be investing here for the foreseeable future.


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Meet Christina Koch: Head of Central IT Processes at Lufthansa Group, Lecturer and MBA alumni
Today, we are having a chat with Christina Koch, Head of Central IT Processes at Lufthansa Group, Lecturer and MBA alumni.
Back in 2011, Christina was one of the first students that enrolled in our MBA Aviation Management. More than 10 years later, Christina looks back at an exemplary career with a special peak in 2021, when she got awarded as one of Germany’s 25 female Future Thinkers by the magazine Business Insider Germany.
Christina, you graduated in 2008 with a Bachelor of Business Administration in International Business Administration at FH Ingolstadt. What made you decide to take on our MBA program?
My ultimate passion for aviation was my motivation to take on the program – with the specification on aviation know-how. Aspiring to climb the career ladder step by step, I expected the MBA to be a helpful boost – and a proper educational foundation rather than just the Bachelors. I aimed to expand my network by looking beyond the airlines, curious to gain insights into the world of the relevant business partners (e.g. airport, air traffic control) and to get to know their perspectives. The program enabled this while having renowned lecturers with manifold expertise on board as well as best-in-class partners such as the DFS, Fraport and MUC Airport. The international side of the program is of course very attractive: studies in English, a diverse set of students and lectures all around the world. I am a fan of the program’s holistic approach, not only focusing on the theoretical coursework but also on personal development. Plus, being the heart of the German airline industry, there is no better location than Frankfurt to pass this MBA. Summa summarum - the perfect match for a travel-enthusiast with a fascination for aviation and leadership ambitions.
Looking back, how did the MBA prepare you for your career?
In large corporations, an MBA is a prerequisite for a certain level of executive positions. In addition to this mandatory qualification, the program has equipped me with a broad knowledge of the aviation industry and helped me to improve my management skills such as negotiations, leadership, business behavior and rhetoric. The 2,5 years was an exceptional time with constant deadlines for papers, holidays spent in the classroom, upcoming exams – along with a demanding full-time job. Thus, I got to know my own limits and found methods of compensation which contribute to an effective work-life balance. Even today, I profit from these learnings so that I improved in assessing how much workload I can handle – and when it’s time to say “no”. Through the MBA I had the pleasure of broadening my network among fellow students. More than 10 years have passed, however we rely on each other as mutual sparring partners in case of any tricky professional situation – and became friends for life. This program trained and prepared me well for my leadership role. Thus, the tough period of combining studies and work paid off.
Do you have any career advice for our future students?
Expert knowledge can easily be trained. The drive, self-motivation and curiosity to step out of your individual comfort zone, is key to grow beyond your imagination. For me, a day is a successful day whenever I have learned something new – this is my way to shape my skills.
The word “career” is so subjective and has so different meanings to all of us. Whatever “career” means to you, I experienced that one can’t really plan a career upfront. Consequently, my advice is: keep your eyes open for opportunities and communicate clearly how much responsibility you are willing to take. Go through business life attentively and observe others – what can you adopt from role models in order to fine-tune your own repertoire of behaviors?
In September 2020 you started as a lecturer in Innovation Management here at Frankfurt University of Applied Sciences. What does innovation and actively shaping the future mean to you?
There are two aspects which make me love this topic. First, innovation is the elixir of enterprises. Only by constant improvement and wow-moments, can companies fascinate and retain customers.
Secondly, innovation derives in added value for society and changes the world. Just think of the incredible potential of sustainable, CO2-neutral flying. I can't wait for the upcoming generation of smart experts to revolutionize the mobility sector with creative ideas so that we all can travel with a good conscience, whether by car, train, ship or plane.
And on a personal note – isn’t it super cool and fulfilling to invent something new, or to inspire others to do so and thus, leave one’s own footprint in the long-run?!
Thanks for your time.


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Landscape Design: Where Nature Fuses with Fun
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title: Viking helmets and the haunting legends of draugr

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The Vikings are famous for their helmets, but many ideas about them come from myths, not facts. Popular culture shows Viking helmets with big, curved horns. However, history tells us that most helmets were just simple, conical metal caps with a nose guard. When talking about Viking helmets, we must mention the scary legends of the Draugr. These undead warriors wore burial armor and struck fear into everyone they encountered.
The Truth About Viking Helmets
Archaeological findings show that craftsmen primarily used iron to make Viking helmets. Designers created them for practicality, not intimidation. Archaeologists found the Gjermundbu helmet in Norway. It is the only complete Viking helmet discovered so far. Unlike modern images, it does not have dramatic horns. Instead, it features a rounded cap, a protective eye guard, and a nasal bar. Viking warriors used chainmail, shields, and clever tactics to win battles. They didn’t rely on fancy helmets.
Helmets were rare and valuable in the Viking Age. They were often for wealthier warriors and chieftains. Many lower-ranking fighters would rely on padded leather caps or simple metal-reinforced headgear. Horned helmets came about later. Their inspiration originated from 19th-century art and costumes associated with Wagnerian operas. These depictions, despite their historical inaccuracies, became part of our shared beliefs. They shaped how we see Viking warriors today.
The Legend of the Draugr Warriors
Draugr are spooky beings from Norse mythology. They are undead warriors that won’t stay in their graves. Legend says these ghostly beings wear their burial armor, which consists of helmets. They rise from their tombs to haunt the living. Some tales depict them as spectral spirits. Others show them as strong beings. They can shape-shift and control the weather. These scary beings protect their treasure. They create chaos for anyone who disturbs their graves.
The idea of the Draugr comes from strong fears of death and bad burial practices. In Viking culture, honoring the dead was very important. If someone did the task poorly, people thought angry spirits would haunt the living. These beliefs caused people to take extra care when burying their dead. They placed heavy stones on graves and buried bodies with protective charms.
Viking Helmets and the Supernatural
Helmets played a crucial role in Viking burial traditions. Sometimes, they buried warriors with their weapons and helmets. This showed their status in the afterlife. This might have added to the tale of Draugr warriors. They return from the dead, still wearing their battle gear. Viking communities had a strong belief in the Draugr. To stop the undead from rising, they often took extreme steps. They would place heavy stones on graves or even behead corpses.
Some sagas mention special helmets with magical powers. These helmets give wearers supernatural strength or protection from harm. Legendary Viking heroes often wore these enchanted helms. People said that they emit a strange glow when danger is near. Historians and archaeologists still argue about these stories. Are they myths, or do they come from real rituals?
Influence on Modern Culture
Viking helmets and Draugr warriors are popular in today’s media. You can see them in fantasy books and video games. The eerie image of undead Viking warriors inspires tales of the supernatural. It mixes history with folklore. Video games like The Elder Scrolls V: Skyrim and God of War feature Draugr as tough foes. They highlight their spooky presence and strange powers. Television series like Vikings and movies like The 13th Warrior use Norse mythology. They create exciting stories rich in history and legend.
Beyond entertainment, the influence of Viking helmets extends into reenactments, art, and fashion. Many enthusiasts join historical reenactments to portray Viking warriors. They wear replica helmets based on real archaeological finds, not Hollywood fakes. The Draugr image brings up discussions about ancient burial customs and beliefs. It highlights the fine line between the living and the dead.
The Enduring Legacy
Viking helmets and Draugr warriors appear in both history and fantasy. They remind us of the intriguing and eerie Norse mythology. Viking helmets might not be as fancy as we once believed. Their ties to the supernatural and rich history make them a strong symbol of Viking culture. Scholars keep finding new discoveries and rethinking old legends. So, the interest in Viking warriors, alive or undead, remains strong.