The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928, which provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. It was the first theory to account fully for relativity in the context of quantum mechanics. The standard form of the Dirac equation is written as:
iħ ∂ψ/∂t = [cα·p + βmc²] ψ
- i is the imaginary unit.
- ħ is the reduced Planck’s constant (h/2π), a fundamental constant in quantum mechanics.
- c is the speed of light.
- t represents time.
- ∂/∂t denotes the partial derivative with respect to time.
- α and β are 4x4 matrices (with complex elements), known as the Dirac matrices. They were introduced by Dirac as a way to make the equation compatible with the special theory of relativity.
- p is the momentum operator, conventionally given by -iħ∇ (where ∇ is the gradient operator, usually expressed in three dimensions, and represents spatial derivatives).
- m is the mass of the particle.
- ψ is the wave function of the particle which encapsulates all the information about the system, and in this case, it’s a four-component object known as a ‘spinor’. The four components of the spinor represent two degrees of freedom for the electron (spin up or spin down), and two for the corresponding antiparticle, the positron. The Dirac equation correctly describes particles with spin -1/2, and its solutions have negative energy states. This was a problem until Dirac proposed the concept of the sea of electrons, where all these negative energy states are filled up by electrons in what we call the ‘Dirac sea’, except for a few missing electrons which we observe as positrons (antielectrons) with positive energy. Thus, the Dirac equation led to the prediction of the existence of antimatter, revolutionizing the field of quantum physics. It should be noted that the Dirac equation isn’t entirely perfect. It assumes the electron as a point particle, which leads to self-energy infinities. These issues were later resolved with the development of Quantum Electrodynamics (QED), which uses a field-theoretic approach incorporating the principles of the Dirac equation.
Lex TVN === Lex Internet
MicroStrategy Adopts Bitcoin as Primary Treasury Reserve Asset
TYSONS CORNER, Va.—(BUSINESS WIRE)—MicroStrategy® Incorporated (Nasdaq: MSTR), the largest independent publicly-traded business intelligence company, today announced that it has purchased 21,454 bitcoins at an aggregate purchase price of $250 million, inclusive of fees and expenses. The purchase of Bitcoin cryptocurrency was made pursuant to the two-pronged capital allocation strategy previously announced by the company when it released its second quarter 2020 financial results on July 28, 2020.
The company addressed the first prong, which called for returning a portion of its excess cash to shareholders, when it announced today that it had launched a cash tender offer for up to $250 million of MicroStrategy’s class A common stock via a modified Dutch Auction offer. By acquiring 21,454 bitcoins, MicroStrategy addressed the other prong of its capital allocation strategy, which called for investing up to $250 million in one or more alternative investments or assets.
“Our investment in Bitcoin is part of our new capital allocation strategy, which seeks to maximize long-term value for our shareholders,” said Michael J. Saylor, CEO, MicroStrategy Incorporated. “This investment reflects our belief that Bitcoin, as the world’s most widely-adopted cryptocurrency, is a dependable store of value and an attractive investment asset with more long-term appreciation potential than holding cash. Since its inception over a decade ago, Bitcoin has emerged as a significant addition to the global financial system, with characteristics that are useful to both individuals and institutions. MicroStrategy has recognized Bitcoin as a legitimate investment asset that can be superior to cash and accordingly has made Bitcoin the principal holding in its treasury reserve strategy.”
Mr. Saylor continued, “MicroStrategy spent months deliberating to determine our capital allocation strategy. Our decision to invest in Bitcoin at this time was driven in part by a confluence of macro factors affecting the economic and business landscape that we believe is creating long-term risks for our corporate treasury program ― risks that should be addressed proactively. Those macro factors include, among other things, the economic and public health crisis precipitated by COVID-19, unprecedented government financial stimulus measures including quantitative easing adopted around the world, and global political and economic uncertainty. We believe that, together, these and other factors may well have a significant depreciating effect on the long-term real value of fiat currencies and many other conventional asset types, including many of the assets traditionally held as part of corporate treasury operations.”
In considering various asset classes for potential investment, MicroStrategy observed distinctive properties of Bitcoin that led it to believe investing in the cryptocurrency would provide not only a reasonable hedge against inflation, but also the prospect of earning a higher return than other investments. Mr. Saylor articulated the opinion, “We find the global acceptance, brand recognition, ecosystem vitality, network dominance, architectural resilience, technical utility, and community ethos of Bitcoin to be persuasive evidence of its superiority as an asset class for those seeking a long-term store of value. Bitcoin is digital gold – harder, stronger, faster, and smarter than any money that has preceded it. We expect its value to accrete with advances in technology, expanding adoption, and the network effect that has fueled the rise of so many category killers in the modern era.”
A leader in the business intelligence space, MicroStrategy has a 30-year history of anticipating technology trends. MicroStrategy was one of the first companies in the enterprise business intelligence software sector. It was a pioneer in Relational Analytics, Web Intelligence, and Mobile Intelligence and has most recently invented HyperIntelligence® – zero click insights that can be embedded in applications to make them smarter, faster, and stronger.
In 2012, Mr. Saylor wrote “The Mobile Wave,” addressing the impact mobile computing would have on business, consumer, and political behavior and the implications of the rise of Apple, Google, Facebook, Amazon, and Twitter. MicroStrategy believes the world is entering “The Virtual Wave” – a rapid dematerialization of products, services, and processes enabled by advances in technology and catalyzed by the COVID crisis. MicroStrategy believes digital transformation has quickened amid rapidly shifting market requirements. These dynamics have many corporations rethinking their offerings, operations, and systems, as well as their balance sheets and financial strategies.
“MicroStrategy remains focused on its corporate strategy of operating a growing profitable business intelligence company, serving some of the largest most respected institutions worldwide. This strategy includes seeking to grow its revenue through its HyperIntelligence, Cloud Intelligence, and Embedded Intelligence offerings, a refreshed go-to-market focused on simplified products and pricing, and a cloud-first platform-as-a-service focus. MicroStrategy’s goal of generating long-term operating income and free cash flow has also led it to adopt a new capital allocation strategy. MicroStrategy believes that buying $250 million in Bitcoin will provide it the opportunity to earn better returns and preserve the value of our capital over time compared to holding cash. Our corporate strategy and two-pronged capital allocation strategy are designed to benefit shareholders, customers, partners, and employees,” said Phong Le, President & CFO, MicroStrategy Incorporated.
Amerykańskie przedsiębiorstwo software’owe Macromedia kupiło od przedsiębiorstwa FutureWave patent na animacje Flash.
Rozpoczęła się inwazja Armii Czerwonej na prefekturę Karafuto – należącą od 1905 roku do Japonii południową część Sachalinu.
Hedy Lamarr uzyskała patent dotyczący technologii bezkablowej komunikacji, wykorzystywany przez Aliantów podczas II Wojny Światowej. Później wynalazek stał się podstawą dla #wifi, #bluetooth i telefonii komórkowej. Hedy była też aktorką.
Ludowy Komisarz NKWD Nikołaj Jeżow wydał rozkaz rozpoczęcia „operacji polskiej”
Panika w 1857 roku, jeden z największych kryzysów ekonomicznych.
https://en.wikipedia.org/wiki/Pope_Alexander_VI - przekupny papież i kardynał
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