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🔗 Mathematics

Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation operator D

${\displaystyle Df(x)={\frac {d}{dx}}f(x)\,,}$

and of the integration operator J

${\displaystyle Jf(x)=\int _{0}^{x}f(s)\,ds\,,}$

and developing a calculus for such operators generalizing the classical one.

In this context, the term powers refers to iterative application of a linear operator D to a function f, that is, repeatedly composing D with itself, as in ${\displaystyle D^{2}(f)=(D\circ D)(f)=D(D(f))}$.

For example, one may ask for a meaningful interpretation of:

${\displaystyle {\sqrt {D}}=D^{\frac {1}{2}}}$

as an analogue of the functional square root for the differentiation operator, that is, an expression for some linear operator that when applied twice to any function will have the same effect as differentiation. More generally, one can look at the question of defining a linear functional

${\displaystyle D^{a}}$

for every real-number a in such a way that, when a takes an integer value n ∈ ℤ, it coincides with the usual n-fold differentiation D if n > 0, and with the −nth power of J when n < 0.

One of the motivations behind the introduction and study of these sorts of extensions of the differentiation operator D is that the sets of operator powers { D^a |a ∈ ℝ } defined in this way are continuous semigroups with parameter a, of which the original discrete semigroup of { Dⁿ | n ∈ ℤ } for integer n is a denumerable subgroup: since continuous semigroups have a well developed mathematical theory, they can be applied to other branches of mathematics.

Fractional differential equations, also known as extraordinary differential equations, are a generalization of differential equations through the application of fractional calculus.

🔗 Judaism 🔗 Writing systems 🔗 Kabbalah

Gematria (; Hebrew: גמטריא or gimatria גימטריה, plural גמטראות or גימטריאות, gimatriot) is the practice of assigning a numerical value to a name, word or phrase by reading it as a number, or sometimes by using an alphanumerical cipher. The letters of the alphabets involved have standard numerical values, but a word can yield several values if a cipher is used.

According to Aristotle (384–322 BCE), isopsephy, based on the Milesian numbering of the Greek alphabet developed in the Greek city of Miletus, was part of the Pythagorean tradition, which originated in the 6th century BCE. The first evidence of use of Hebrew letters as numbers dates to 78 BCE; gematria is still used in Jewish culture. Similar systems have been used in other languages and cultures, derived from or inspired by either Greek isopsephy or Hebrew gematria, and include Arabic abjad numerals and English gematria.

The most common form of Hebrew gematria is used in the Talmud and Midrash, and elaborately by many post-Talmudic commentators. It involves reading words and sentences as numbers, assigning numerical instead of phonetic value to each letter of the Hebrew alphabet. When read as numbers, they can be compared and contrasted with other words or phrases – cf. the Hebrew proverb נכנס יין יצא סוד (nichnas yayin yatza sod, lit. 'wine entered, secret went out', i.e. "in vino veritas"). The gematric value of יין ('wine') is 70 (י=10; י=10; ן=50) and this is also the gematric value of סוד ('secret', ס=60; ו=6; ד=4)‎.

Although a type of gematria system ('Aru') was employed by the ancient Babylonian culture, their writing script was logographic, and the numerical assignments they made were to whole words. Aru was very different from the Milesian systems used by Greek and Hebrew cultures, which used alphabetic writing scripts. The value of words with Aru were assigned in an entirely arbitrary manner and correspondences were made through tables, and so cannot be considered a true form of gematria.

Gematria sums can involve single words, or a string of lengthy calculations. A short example of Hebrew numerology that uses gematria is the word חי (chai, lit. 'alive'), which is composed of two letters that (using the assignments in the mispar gadol table shown below) add up to 18. This has made 18 a "lucky number" among the Jewish people. Donations of money in multiples of 18 are very popular.

In early Jewish sources, the term can also refer to other forms of calculation or letter manipulation, for example atbash.

🔗 Apple Inc./Macintosh 🔗 Apple Inc. 🔗 Human–Computer Interaction 🔗 Industrial design 🔗 Apple Inc./iOS

A skeuomorph () is a derivative object that retains nonfunctional ornamental design cues (attributes) from structures that were inherent to the original. Examples include pottery embellished with imitation rivets reminiscent of similar pots made of metal and a software calendar that imitates the appearance of binding on a paper desk calendar.

🔗 Computing 🔗 Computer science 🔗 Brands

Cell is a multi-core microprocessor microarchitecture that combines a general-purpose PowerPC core of modest performance with streamlined coprocessing elements which greatly accelerate multimedia and vector processing applications, as well as many other forms of dedicated computation.

It was developed by Sony, Toshiba, and IBM, an alliance known as "STI". The architectural design and first implementation were carried out at the STI Design Center in Austin, Texas over a four-year period beginning March 2001 on a budget reported by Sony as approaching US$400 million. Cell is shorthand for Cell Broadband Engine Architecture, commonly abbreviated CBEA in full or Cell BE in part.

The first major commercial application of Cell was in Sony's PlayStation 3 game console, released in 2006. In May 2008, the Cell-based IBM Roadrunner supercomputer became the first TOP500 LINPACK sustained 1.0 petaflops system. Mercury Computer Systems also developed designs based on the Cell.

The Cell architecture includes a memory coherence architecture that emphasizes power efficiency, prioritizes bandwidth over low latency, and favors peak computational throughput over simplicity of program code. For these reasons, Cell is widely regarded as a challenging environment for software development. IBM provides a Linux-based development platform to help developers program for Cell chips.

🔗 India 🔗 India/Indian literature workgroup

The Shishupala Vadha (Sanskrit: शिशुपालवध, IAST: Śiśupāla-vadha, lit. "the slaying of Shishupala") is a work of classical Sanskrit poetry (kāvya) composed by Māgha in the 7th or 8th century. It is an epic poem in 20 sargas (cantos) of about 1800 highly ornate stanzas, and is considered one of the six Sanskrit mahakavyas, or "great epics". It is also known as the Māgha-kāvya after its author. Like other kavyas, it is admired more for its exquisite descriptions and lyrical quality than for any dramatic development of plot. Its 19th canto is noted for verbal gymnastics and wordplay; see the section on linguistic ingenuity below.

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

Pretty Good Privacy (PGP) is an encryption program that provides cryptographic privacy and authentication for data communication. PGP is used for signing, encrypting, and decrypting texts, e-mails, files, directories, and whole disk partitions and to increase the security of e-mail communications. Phil Zimmermann developed PGP in 1991.

PGP and similar software follow the OpenPGP, an open standard of PGP encryption software, standard (RFC 4880) for encrypting and decrypting data.

🔗 Constructed languages 🔗 Graphic design

Isotype (International System of Typographic Picture Education) is a method of showing social, technological, biological, and historical connections in pictorial form. It consists of a set of standardized and abstracted pictorial symbols to represent social-scientific data with specific guidelines on how to combine the identical figures using serial repetition. It was first known as the Vienna Method of Pictorial Statistics (Wiener Methode der Bildstatistik), due to its having been developed at the Gesellschafts- und Wirtschaftsmuseum in Wien (Social and Economic Museum of Vienna) between 1925 and 1934. The founding director of this museum, Otto Neurath, was the initiator and chief theorist of the Vienna Method. Gerd Arntz was the artist responsible for realising the graphics. The term Isotype was applied to the method around 1935, after its key practitioners were forced to leave Vienna by the rise of Austrian fascism.

🔗 Molecular Biology 🔗 Molecular Biology/Computational Biology

The Burrows–Wheeler transform (BWT, also called block-sorting compression) rearranges a character string into runs of similar characters. This is useful for compression, since it tends to be easy to compress a string that has runs of repeated characters by techniques such as move-to-front transform and run-length encoding. More importantly, the transformation is reversible, without needing to store any additional data except the position of the first original character. The BWT is thus a "free" method of improving the efficiency of text compression algorithms, costing only some extra computation. The Burrows–Wheeler transform is an algorithm used to prepare data for use with data compression techniques such as bzip2. It was invented by Michael Burrows and David Wheeler in 1994 while Burrows was working at DEC Systems Research Center in Palo Alto, California. It is based on a previously unpublished transformation discovered by Wheeler in 1983. The algorithm can be implemented efficiently using a suffix array thus reaching linear time complexity.

🔗 Mathematics

A squircle is a shape intermediate between a square and a circle. There are at least two definitions of "squircle" in use, the most common of which is based on the superellipse. The word "squircle" is a portmanteau of the words "square" and "circle". Squircles have been applied in design and optics.

🔗 Trains 🔗 Trains/UK Railways 🔗 Trains/Rail transport in Germany

Railway time was the standardised time arrangement first applied by the Great Western Railway in England in November 1840, the first recorded occasion when different local mean times were synchronised and a single standard time applied. The key goals behind introducing railway time were to overcome the confusion caused by having non-uniform local times in each town and station stop along the expanding railway network and to reduce the incidence of accidents and near misses, which were becoming more frequent as the number of train journeys increased.

Railway time was progressively taken up by all railway companies in Great Britain over the following seven years. The schedules by which trains were organised and the time station clocks displayed were brought in line with the local mean time for London or "London Time", the time set at Greenwich by the Royal Observatory, which was already widely known as Greenwich Mean Time (GMT).

The development of railway networks in North America in the 1850s, India in around 1860, and in Europe, prompted the introduction of standard time influenced by geography, industrial development, and political governance.

The railway companies sometimes faced concerted resistance from local people who refused to adjust their public clocks to bring them into line with London Time. As a consequence, two different times would be displayed in the town and in use, with the station clocks and the times published in train timetables differing by several minutes from that on other clocks. Despite this early reluctance, railway time rapidly became adopted as the default time across the whole of Great Britain, although it took until 1880 for the government to legislate on the establishment of a single standard time and a single time zone for the country.

Some contemporary commentators referred to the influence of railway time on encouraging greater precision in daily tasks and the demand for punctuality.