Falling and rising factorialsIn mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when These symbols are collectively called factorial powers. The Pochhammer symbol, introduced by Leo August Pochhammer, is the notation (x)_n , where n is a non-negative integer.
Real-time computingReal-time computing (RTC) is the computer science term for hardware and software systems subject to a "real-time constraint", for example from event to system response. Real-time programs must guarantee response within specified time constraints, often referred to as "deadlines". Real-time responses are often understood to be in the order of milliseconds, and sometimes microseconds. A system not specified as operating in real time cannot usually guarantee a response within any timeframe, although typical or expected response times may be given.
Bell polynomialsIn combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are used in the study of set partitions. They are related to Stirling and Bell numbers. They also occur in many applications, such as in the Faà di Bruno's formula. The partial or incomplete exponential Bell polynomials are a triangular array of polynomials given by where the sum is taken over all sequences j1, j2, j3, ..., jn−k+1 of non-negative integers such that these two conditions are satisfied: The sum is called the nth complete exponential Bell polynomial.
Binomial transformIn combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences. It is closely related to the Euler transform, which is the result of applying the binomial transform to the sequence associated with its ordinary generating function. The binomial transform, T, of a sequence, {an}, is the sequence {sn} defined by Formally, one may write for the transformation, where T is an infinite-dimensional operator with matrix elements Tnk.
Anoxygenic photosynthesisAnoxygenic photosynthesis is a special form of photosynthesis used by some bacteria and archaea, which differs from the better known oxygenic photosynthesis in plants in the reductant used (e.g. hydrogen sulfide instead of water) and the byproduct generated (e.g. elemental sulfur instead of molecular oxygen). Several groups of bacteria can conduct anoxygenic photosynthesis: green sulfur bacteria (GSB), red and green filamentous phototrophs (FAPs e.g. Chloroflexia), purple bacteria, acidobacteriota, and heliobacteria.
