Abelian varietyIn mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry and indispensable tools for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field; the variety is then said to be defined over that field.
Algebraic varietyAlgebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition. Conventions regarding the definition of an algebraic variety differ slightly.
Projective varietyIn algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Equivalently, an algebraic variety is projective if it can be embedded as a Zariski closed subvariety of .
Selective progesterone receptor modulatorA selective progesterone receptor modulator (SPRM) is an agent that acts on the progesterone receptor (PR), the biological target of progestogens like progesterone. A characteristic that distinguishes such substances from full receptor agonists (e.g., progesterone, progestins) and full antagonists (e.g., aglepristone) is that their action differs in different tissues, i.e. agonist in some tissues while antagonist in others.
Chow varietyIn mathematics, particularly in the field of algebraic geometry, a Chow variety is an algebraic variety whose points correspond to effective algebraic cycles of fixed dimension and degree on a given projective space. More precisely, the Chow variety is the fine moduli variety parametrizing all effective algebraic cycles of dimension and degree in . The Chow variety may be constructed via a Chow embedding into a sufficiently large projective space.
Generalized flag varietyIn mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold. Flag varieties are naturally projective varieties. Flag varieties can be defined in various degrees of generality. A prototype is the variety of complete flags in a vector space V over a field F, which is a flag variety for the special linear group over F.
Selective glucocorticoid receptor modulatorSelective glucocorticoid receptor modulators (SEGRMs) and selective glucocorticoid receptor agonists (SEGRAs) formerly known as dissociated glucocorticoid receptor agonists (DIGRAs) are a class of experimental drugs designed to share many of the desirable anti-inflammatory, immunosuppressive, or anticancer properties of classical glucocorticoid drugs but with fewer side effects such as skin atrophy. Although preclinical evidence on SEGRAMs’ anti-inflammatory effects are culminating, currently, the efficacy of these SEGRAMs on cancer are largely unknown.
Affine varietyIn algebraic geometry, an affine algebraic set is the set of the common zeros over an algebraically closed field k of some family of polynomials in the polynomial ring An affine variety or affine algebraic variety, is an affine algebraic set such that the ideal generated by the defining polynomials is prime. Some texts call variety any algebraic set, and irreducible variety an algebraic set whose defining ideal is prime (affine variety in the above sense).
Selective estrogen receptor modulatorSelective estrogen receptor modulators (SERMs), also known as estrogen receptor agonist/antagonists (ERAAs), are a class of drugs that act on the estrogen receptor (ER). A characteristic that distinguishes these substances from pure ER agonists and antagonists (that is, full agonists and silent antagonists) is that their action is different in various tissues, thereby granting the possibility to selectively inhibit or stimulate estrogen-like action in various tissues.
DNA sequencingDNA sequencing is the process of determining the nucleic acid sequence – the order of nucleotides in DNA. It includes any method or technology that is used to determine the order of the four bases: adenine, guanine, cytosine, and thymine. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Knowledge of DNA sequences has become indispensable for basic biological research, DNA Genographic Projects and in numerous applied fields such as medical diagnosis, biotechnology, forensic biology, virology and biological systematics.
