Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
Generic drugA generic drug is a pharmaceutical drug that contains the same chemical substance as a drug that was originally protected by chemical patents. Generic drugs are allowed for sale after the patents on the original drugs expire. Because the active chemical substance is the same, the medical profile of generics is equivalent in performance. A generic drug has the same active pharmaceutical ingredient (API) as the original, but it may differ in some characteristics such as the manufacturing process, formulation, excipients, color, taste, and packaging.
Mathematical statisticsMathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory. Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling.
Biological half-lifeBiological half-life (elimination half-life, pharmacological half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration (Cmax) to half of Cmax in the blood plasma. It is denoted by the abbreviation . This is used to measure the removal of things such as metabolites, drugs, and signalling molecules from the body. Typically, the biological half-life refers to the body's natural detoxification (cleansing) through liver metabolism and through the excretion of the measured substance through the kidneys and intestines.
EpirubicinEpirubicin is an anthracycline drug used for chemotherapy. It can be used in combination with other medications to treat breast cancer in patients who have had surgery to remove the tumor. It is marketed by Pfizer under the trade name Ellence in the US and Pharmorubicin or Epirubicin Ebewe elsewhere. Similarly to other anthracyclines, epirubicin acts by intercalating DNA strands. Intercalation results in complex formation which inhibits DNA and RNA synthesis.
Progressive rockProgressive rock (shortened as prog rock or simply prog) is a broad genre of rock music that primarily developed in the United Kingdom and United States through the mid- to late 1960s, peaking in the early 1970s. Initially termed "progressive pop", the style was an emergence of psychedelic bands who abandoned standard pop traditions in favour of instrumentation and compositional techniques more frequently associated with jazz, folk, or classical music.
DoxorubicinDoxorubicin, sold under the brand name Adriamycin among others, is a chemotherapy medication used to treat cancer. This includes breast cancer, bladder cancer, Kaposi's sarcoma, lymphoma, and acute lymphocytic leukemia. It is often used together with other chemotherapy agents. Doxorubicin is given by injection into a vein. Common side effects include hair loss, bone marrow suppression, vomiting, rash, and inflammation of the mouth.
Weierstrass functionIn mathematics, the Weierstrass function is an example of a real-valued function that is continuous everywhere but differentiable nowhere. It is an example of a fractal curve. It is named after its discoverer Karl Weierstrass. The Weierstrass function has historically served the role of a pathological function, being the first published example (1872) specifically concocted to challenge the notion that every continuous function is differentiable except on a set of isolated points.
