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🔗 Mathematics 🔗 Systems 🔗 Systems/Chaos theory

In mathematics, the Cantor function is an example of a function that is continuous, but not absolutely continuous. It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Though it is continuous everywhere and has zero derivative almost everywhere, its value still goes from 0 to 1 as its argument reaches from 0 to 1. Thus, in one sense the function seems very much like a constant one which cannot grow, and in another, it does indeed monotonically grow, by construction.

It is also referred to as the Cantor ternary function, the Lebesgue function, Lebesgue's singular function, the Cantor–Vitali function, the Devil's staircase, the Cantor staircase function, and the Cantor–Lebesgue function. Georg Cantor (1884) introduced the Cantor function and mentioned that Scheeffer pointed out that it was a counterexample to an extension of the fundamental theorem of calculus claimed by Harnack. The Cantor function was discussed and popularized by Scheeffer (1884), Lebesgue (1904) and Vitali (1905).

🔗 Statistics

The Erlang distribution is a two-parameter family of continuous probability distributions with support ${\displaystyle x\in [0,\infty )}$. The two parameters are:

• a positive integer ${\displaystyle k,}$ the "shape", and
• a positive real number ${\displaystyle \lambda ,}$ the "rate". The "scale", ${\displaystyle \mu ,}$ the reciprocal of the rate, is sometimes used instead.

The Erlang distribution with shape parameter ${\displaystyle k=1}$ simplifies to the exponential distribution. It is a special case of the gamma distribution. It is the distribution of a sum of ${\displaystyle k}$ independent exponential variables with mean ${\displaystyle 1/\lambda }$ each.

The Erlang distribution was developed by A. K. Erlang to examine the number of telephone calls which might be made at the same time to the operators of the switching stations. This work on telephone traffic engineering has been expanded to consider waiting times in queueing systems in general. The distribution is also used in the field of stochastic processes.

🔗 China 🔗 Languages 🔗 Hong Kong

"Add oil" is a Hong Kong English expression used as an encouragement and support to a person. Derived from the Chinese phrase Gayau (or Jiayou; Chinese: 加油), the expression is literally translated from the Cantonese phrase. It is originated in Hong Kong and is commonly used by bilingual Hong Kong speakers.

"Add oil" can be roughly translated as "Go for it". Though it is often described as "the hardest to translate well", the literal translation is the result of Chinglish and was added to the Oxford English Dictionary in 2018.

🔗 Computing 🔗 Computer Security 🔗 Computer Security/Computing 🔗 Computing/Software 🔗 Computing/Computer science 🔗 Cryptography 🔗 Cryptography/Computer science 🔗 Computing/Computer Security

Zooko's triangle is a trilemma of three properties that are generally considered desirable for names of participants in a network protocol:

• Human-meaningful: Meaningful and memorable (low-entropy) names are provided to the users.
• Secure: The amount of damage a malicious entity can inflict on the system should be as low as possible.
• Decentralized: Names correctly resolve to their respective entities without the use of a central authority or service.

🔗 Science

In combinatorial mathematics, an Aztec diamond of order n consists of all squares of a square lattice whose centers (x,y) satisfy |x| + |y| ≤ n. Here n is a fixed integer, and the square lattice consists of unit squares with the origin as a vertex of 4 of them, so that both x and y are half-integers.

The Aztec diamond theorem states that the number of domino tilings of the Aztec diamond of order n is 2^n(n+1)/2. The Arctic Circle theorem says that a random tiling of a large Aztec diamond tends to be frozen outside a certain circle.

It is common to color the tiles in the following fashion. First consider a checkerboard coloring of the diamond. Each tile will cover exactly one black square. Vertical tiles where the top square covers a black square, is colored in one color, and the other vertical tiles in a second. Similarly for horizontal tiles.

Knuth has also defined Aztec diamonds of order n + 1/2. They are identical with the polyominoes associated with the centered square numbers.

🔗 Physics

An electret (formed of as a portmanteau of electr- from "electricity" and -et from "magnet") is a dielectric material that has a quasi-permanent electric charge or dipole polarisation. An electret generates internal and external electric fields, and is the electrostatic equivalent of a permanent magnet. Although Oliver Heaviside coined this term in 1885, materials with electret properties were already known to science and had been studied since the early 1700s. One particular example is the electrophorus, a device consisting of a slab with electret properties and a separate metal plate. The electrophorus was originally invented by Johan Carl Wilcke in Sweden and again by Alessandro Volta in Italy.

The name derives from "electron" and "magnet"; drawing analogy to the formation of a magnet by alignment of magnetic domains in a piece of iron. Historically, electrets were made by first melting a suitable dielectric material such as a polymer or wax that contains polar molecules, and then allowing it to re-solidify in a powerful electrostatic field. The polar molecules of the dielectric align themselves to the direction of the electrostatic field, producing a dipole electret with a permanent electrostatic bias. Modern electrets are usually made by embedding excess charges into a highly insulating dielectric, e.g. by means of an electron beam, corona discharge, injection from an electron gun, electric breakdown across a gap, or a dielectric barrier.

🔗 Mathematics 🔗 Biology 🔗 Physics 🔗 Plants

Tendril perversion, often referred to in context as simply perversion, is a geometric phenomenon found in helical structures such as plant tendrils, in which a helical structure forms that is divided into two sections of opposite chirality, with a transition between the two in the middle. A similar phenomenon can often be observed in kinked helical cables such as telephone handset cords.

The phenomenon was known to Charles Darwin, who wrote in 1865,

A tendril ... invariably becomes twisted in one part in one direction, and in another part in the opposite direction... This curious and symmetrical structure has been noticed by several botanists, but has not been sufficiently explained.

The term "tendril perversion" was coined by Goriely and Tabor in 1998 based on the word perversion found in the 19th Century science literature. "Perversion" is a transition from one chirality to another and was known to James Clerk Maxwell, who attributed it to the topologist J. B. Listing.

Tendril perversion can be viewed as an example of spontaneous symmetry breaking, in which the strained structure of the tendril adopts a configuration of minimum energy while preserving zero overall twist.

Tendril perversion has been studied both experimentally and theoretically. Gerbode et al. have made experimental studies of the coiling of cucumber tendrils. A detailed study of a simple model of the physics of tendril perversion was made by MacMillen and Goriely in the early 2000s. Liu et al. showed in 2014 that "the transition from a helical to a hemihelical shape, as well as the number of perversions, depends on the height to width ratio of the strip's cross-section."

Generalized tendril perversions were put forward by Silva et al., to include perversions that can be intrinsically produced in elastic filaments, leading to a multiplicity of geometries and dynamical properties.

🔗 Business 🔗 Automobiles

The Toyota Way is a set of principles and behaviors that underlie the Toyota Motor Corporation's managerial approach and production system. Toyota first summed up its philosophy, values and manufacturing ideals in 2001, calling it "The Toyota Way 2001". It consists of principles in two key areas: continuous improvement, and respect for people.

🔗 Biography 🔗 France 🔗 Middle Ages 🔗 Middle Ages/History 🔗 Biography/arts and entertainment 🔗 Christianity 🔗 Catholicism 🔗 Middle Ages/Crusades 🔗 Military history/Crusades 🔗 Belgium 🔗 Christianity/Christianity in China

William of Rubruck (Dutch: Willem van Rubroeck, Latin: Gulielmus de Rubruquis; fl. 1248–1255) was a Flemish Franciscan missionary and explorer.

He is best known for his travels to various parts of the Middle East and Central Asia in the 13th century, including the Mongol Empire. His account of his travels is one of the masterpieces of medieval travel literature, comparable to those of Marco Polo and Ibn Battuta.

Rocky Mountain BASIC (also RMB or RM-BASIC) is a dialect of the BASIC programming language created by Hewlett-Packard. It was especially popular for control of automatic test equipment using GPIB. It has several features which are or were unusual in BASIC dialects, such as event-driven operation, extensive external I/O support, complex number support, and matrix manipulation functions. Today, RMB is mainly used in environments where an investment in RMB software, hardware, or expertise already exists.