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🔗 Mathematics

The number e is a mathematical constant approximately equal to 2.71828 and is the base of the natural logarithm: the unique number whose natural logarithm is equal to one. It is the limit of (1 + 1/n)ⁿ as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series

${\displaystyle e=\sum \limits _{n=0}^{\infty }{\frac {1}{n!}}={\frac {1}{1}}+{\frac {1}{1}}+{\frac {1}{1\cdot 2}}+{\frac {1}{1\cdot 2\cdot 3}}+\cdots }$

The constant can be characterized in many different ways. For example, it can be defined as the unique positive number a such that the graph of the function y = a^x has unit slope at x = 0. The function f(x) = e^x is called the (natural) exponential function, and is the unique exponential function equal to its own derivative. The natural logarithm, or logarithm to base e, is the inverse function to the natural exponential function. The natural logarithm of a number k > 1 can be defined directly as the area under the curve y = 1/x between x = 1 and x = k, in which case e is the value of k for which this area equals one (see image). There are alternative characterizations.

e is sometimes called Euler's number after the Swiss mathematician Leonhard Euler (not to be confused with γ, the Euler–Mascheroni constant, sometimes called simply Euler's constant), or as Napier's constant. However, Euler's choice of the symbol e is said to have been retained in his honor. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.

The number e has eminent importance in mathematics, alongside 0, 1, π, and i. All five of these numbers play important and recurring roles across mathematics, and these five constants appear in one formulation of Euler's identity. Like the constant π, e is also irrational (i.e. it cannot be represented as ratio of integers) and transcendental (i.e. it is not a root of any non-zero polynomial with rational coefficients). The numerical value of e truncated to 50 decimal places is

🔗 Ukraine 🔗 Cities

New York or Niu-York is a rural settlement in Toretsk urban hromada, Bakhmut Raion, Donetsk Oblast, eastern Ukraine. It is located 37.9 kilometres (23.5 mi) north-northeast from the centre of the city of Donetsk. From 1951 to 2021, the settlement was named Novhorodske.

New York is administratively designated to Toretsk urban hromada, one of the hromadas of Ukraine with its center in the city of Toretsk, that is located about 10 kilometres (6.2 mi) north of New York. Population: 9,735 (2022 estimate).

🔗 Mathematics

In mathematics, Euler's identity (also known as Euler's equation) is the equality

${\displaystyle e^{i\pi }+1=0}$

where

e is Euler's number, the base of natural logarithms,

i is the imaginary unit, which by definition satisfies i² = −1, and

π is pi, the ratio of the circumference of a circle to its diameter.

Euler's identity is named after the Swiss mathematician Leonhard Euler. It is considered to be an exemplar of mathematical beauty as it shows a profound connection between the most fundamental numbers in mathematics.

🔗 Physics

In physics and cosmology, digital physics is a collection of theoretical perspectives based on the premise that the universe is describable by information. It is a form of digital ontology about the physical reality. According to this theory, the universe can be conceived of as either the output of a deterministic or probabilistic computer program, a vast, digital computation device, or mathematically isomorphic to such a device.

🔗 International relations 🔗 Iran 🔗 Syria 🔗 Sociology 🔗 Iraq 🔗 Arab world 🔗 Jewish history 🔗 Egypt 🔗 Israel 🔗 Israel Palestine Collaboration 🔗 Palestine

The Jewish exodus from Arab and Muslim countries, or Jewish exodus from Arab countries, was the departure, flight, expulsion, evacuation and migration of 850,000 Jews, primarily of Sephardi and Mizrahi background, from Arab countries and the Muslim world, mainly from 1948 to the early 1970s. The last major migration wave took place from Iran in 1979–80, as a consequence of the Iranian Revolution.

A number of small-scale Jewish exoduses began in many Middle Eastern countries early in the 20th century with the only substantial aliyah (immigration to the area today known as Israel) coming from Yemen and Syria. Very few Jews from Muslim countries immigrated during the period of Mandatory Palestine. Prior to the creation of Israel in 1948, approximately 800,000 Jews were living in lands that now make up the Arab world. Of these, just under two-thirds lived in the French and Italian-controlled North Africa, 15–20% in the Kingdom of Iraq, approximately 10% in the Kingdom of Egypt and approximately 7% in the Kingdom of Yemen. A further 200,000 lived in Pahlavi Iran and the Republic of Turkey.

The first large-scale exoduses took place in the late 1940s and early 1950s, primarily from Iraq, Yemen and Libya. In these cases over 90% of the Jewish population left, despite the necessity of leaving their property behind. Two hundred and sixty thousand Jews from Arab countries immigrated to Israel between 1948 and 1951, accounting for 56% of the total immigration to the newly founded state; this was the product of a policy change in favour of mass immigration focused on Jews from Arab and Muslim countries. The Israeli government's policy to accommodate 600,000 immigrants over four years, doubling the existing Jewish population, encountered mixed reactions in the Knesset; there were those within the Jewish Agency and government who opposed promoting a large-scale emigration movement among Jews whose lives were not in danger.

Later waves peaked at different times in different regions over the subsequent decades. The peak of the exodus from Egypt occurred in 1956 following the Suez Crisis. The exodus from the other North African Arab countries peaked in the 1960s. Lebanon was the only Arab country to see a temporary increase in its Jewish population during this period, due to an influx of Jews from other Arab countries, although by the mid-1970s the Jewish community of Lebanon had also dwindled. Six hundred thousand Jews from Arab and Muslim countries had reached Israel by 1972. In total, of the 900,000 Jews who left Arab and other Muslim countries, 600,000 settled in the new state of Israel, and 300,000 migrated to France and the United States. The descendants of the Jewish immigrants from the region, known as Mizrahi Jews ("Eastern Jews") and Sephardic Jews ("Spanish Jews"), currently constitute more than half of the total population of Israel, partially as a result of their higher fertility rate. In 2009, only 26,000 Jews remained in Arab countries and Iran. and 26,000 in Turkey.

The reasons for the exoduses are manifold, including push factors, such as persecution, antisemitism, political instability, poverty and expulsion, together with pull factors, such as the desire to fulfill Zionist yearnings or find a better economic status and a secure home in Europe or the Americas. The history of the exodus has been politicized, given its proposed relevance to the historical narrative of the Arab–Israeli conflict. When presenting the history, those who view the Jewish exodus as analogous to the 1948 Palestinian exodus generally emphasize the push factors and consider those who left as refugees, while those who do not, emphasize the pull factors and consider them willing immigrants.

🔗 Mathematics

Bellman's lost-in-a-forest problem is an unsolved minimization problem in geometry, originating in 1955 by the American applied mathematician Richard E. Bellman. The problem is often stated as follows: "A hiker is lost in a forest whose shape and dimensions are precisely known to him. What is the best path for him to follow to escape from the forest?" It is usually assumed that the hiker does not know the starting point or direction he is facing. The best path is taken to be the one that minimizes the worst-case distance to travel before reaching the edge of the forest. Other variations of the problem have been studied.

A proven solution is only known for a few shapes or classes of shape. A general solution would be in the form of a geometric algorithm which takes the shape of the forest as input and returns the optimal escape path as the output. Although real world applications are not apparent, the problem falls into a class of geometric optimization problems including search strategies that are of practical importance. A bigger motivation for study has been the connection to Moser's worm problem. It was included in a list of 12 problems described by the mathematician Scott W. Williams as "million buck problems" because he believed that the techniques involved in their resolution will be worth at least a million dollars to mathematics.

🔗 Computing 🔗 Computing/Computer hardware

Rambus DRAM (RDRAM), and its successors Concurrent Rambus DRAM (CRDRAM) and Direct Rambus DRAM (DRDRAM), are types of synchronous dynamic random-access memory (SDRAM) developed by Rambus from the 1990s through to the early 2000s. The third-generation of Rambus DRAM, DRDRAM was replaced by XDR DRAM. Rambus DRAM was developed for high-bandwidth applications and was positioned by Rambus as replacement for various types of contemporary memories, such as SDRAM. RDRAM is a serial memory bus.

DRDRAM was initially expected to become the standard in PC memory, especially after Intel agreed to license the Rambus technology for use with its future chipsets. Further, DRDRAM was expected to become a standard for graphics memory. However, RDRAM got embroiled in a standards war with an alternative technology—DDR SDRAM—and quickly lost out on grounds of price and, later, performance. By around 2003, DRDRAM was no longer supported in new personal computers.

🔗 Computing 🔗 Computing/Networking

The Network Control Program (NCP) provided the middle layers of the protocol stack running on host computers of the ARPANET, the predecessor to the modern Internet.

NCP preceded the Transmission Control Protocol (TCP) as a transport layer protocol used during the early ARPANET. NCP was a simplex protocol that utilized two port addresses, establishing two connections, for two-way communications. An odd and an even port were reserved for each application layer application or protocol. The standardization of TCP and UDP reduced the need for the use of two simplex ports for each application down to one duplex port.

🔗 Military history 🔗 Poland 🔗 Military history/World War II 🔗 Scotland 🔗 Zoo

Wojtek (1942 – 2 December 1963; Polish pronunciation: [ˈvɔjtɛk]; in English, sometimes spelled Voytek and pronounced as such) was a Syrian brown bear (Ursus arctos syriacus) bought, as a young cub, at a railway station in Hamadan, Iran, by Polish II Corps soldiers who had been evacuated from the Soviet Union. In order to provide for his rations and transportation, he was eventually enlisted officially as a soldier with the rank of private, and was subsequently promoted to corporal.

He accompanied the bulk of the II Corps to Italy, serving with the 22nd Artillery Supply Company. During the Battle of Monte Cassino, in Italy in 1944, Wojtek helped move crates of ammunition and became a celebrity with visiting Allied generals and statesmen. After the war, mustered out of the Polish Army, he was billeted and lived out the rest of his life at the Edinburgh Zoo in Scotland.

🔗 Shakespeare

The Shakespeare Programming Language (SPL) is an esoteric programming language designed by Jon Åslund and Karl Hasselström. Like the Chef programming language, it is designed to make programs appear to be something other than programs; in this case, Shakespearean plays.

A character list in the beginning of the program declares a number of stacks, naturally with names like "Romeo" and "Juliet". These characters enter into dialogue with each other in which they manipulate each other's topmost values, push and pop each other, and do I/O. The characters can also ask each other questions which behave as conditional statements. On the whole, the programming model is very similar to assembly language but much more verbose.