Polynomial long divisionIn algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. Sometimes using a shorthand version called synthetic division is faster, with less writing and fewer calculations. Another abbreviated method is polynomial short division (Blomqvist's method).
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Bernstein polynomialIn the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial that is a linear combination of Bernstein basis polynomials. The idea is named after Sergei Natanovich Bernstein. A numerically stable way to evaluate polynomials in Bernstein form is de Casteljau's algorithm. Polynomials in Bernstein form were first used by Bernstein in a constructive proof for the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves.
Irreducible polynomialIn mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the field to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial x2 − 2 is a polynomial with integer coefficients, but, as every integer is also a real number, it is also a polynomial with real coefficients.
T helper cellThe T helper cells (Th cells), also known as CD4+ cells or CD4-positive cells, are a type of T cell that play an important role in the adaptive immune system. They aid the activity of other immune cells by releasing cytokines. They are considered essential in B cell antibody class switching, breaking cross-tolerance in dendritic cells, in the activation and growth of cytotoxic T cells, and in maximizing bactericidal activity of phagocytes such as macrophages and neutrophils.
Tomographic reconstructionTomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner.
Factorization of polynomials over finite fieldsIn mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.
Periodic summationIn mathematics, any integrable function can be made into a periodic function with period P by summing the translations of the function by integer multiples of P. This is called periodic summation: When is alternatively represented as a Fourier series, the Fourier coefficients are equal to the values of the continuous Fourier transform, at intervals of . That identity is a form of the Poisson summation formula. Similarly, a Fourier series whose coefficients are samples of at constant intervals (T) is equivalent to a periodic summation of which is known as a discrete-time Fourier transform.
T cellT cells are one of the important types of white blood cells of the immune system and play a central role in the adaptive immune response. T cells can be distinguished from other lymphocytes by the presence of a T-cell receptor (TCR) on their cell surface. T cells are born from hematopoietic stem cells, found in the bone marrow. Developing T cells then migrate to the thymus gland to develop (or mature). T cells derive their name from the thymus. After migration to the thymus, the precursor cells mature into several distinct types of T cells.
Test suiteIn software development, a test suite, less commonly known as a validation suite, is a collection of test cases that are intended to be used to test a software program to show that it has some specified set of behaviors. A test suite often contains detailed instructions or goals for each collection of test cases and information on the system configuration to be used during testing. A group of test cases may also contain prerequisite states or steps, and descriptions of the following tests.
