Differentiable curveDifferential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential and integral calculus. Many specific curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus.
Conformal geometryIn mathematics, conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale.
Microbiological cultureA microbiological culture, or microbial culture, is a method of multiplying microbial organisms by letting them reproduce in predetermined culture medium under controlled laboratory conditions. Microbial cultures are foundational and basic diagnostic methods used as research tools in molecular biology. The term culture can also refer to the microorganisms being grown. Microbial cultures are used to determine the type of organism, its abundance in the sample being tested, or both.
Adipose tissueAdipose tissue, body fat, or simply fat is a loose connective tissue composed mostly of adipocytes. In addition to adipocytes, adipose tissue contains the stromal vascular fraction (SVF) of cells including preadipocytes, fibroblasts, vascular endothelial cells and a variety of immune cells such as adipose tissue macrophages. Adipose tissue is derived from preadipocytes. Its main role is to store energy in the form of lipids, although it also cushions and insulates the body.
Algebraic curveIn mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables. A projective algebraic plane curve is the zero set in a projective plane of a homogeneous polynomial in three variables. An affine algebraic plane curve can be completed in a projective algebraic plane curve by homogenizing its defining polynomial. Conversely, a projective algebraic plane curve of homogeneous equation h(x, y, t) = 0 can be restricted to the affine algebraic plane curve of equation h(x, y, 1) = 0.
Conformal groupIn mathematics, the conformal group of an inner product space is the group of transformations from the space to itself that preserve angles. More formally, it is the group of transformations that preserve the conformal geometry of the space. Several specific conformal groups are particularly important: The conformal orthogonal group. If V is a vector space with a quadratic form Q, then the conformal orthogonal group CO(V, Q) is the group of linear transformations T of V for which there exists a scalar λ such that for all x in V For a definite quadratic form, the conformal orthogonal group is equal to the orthogonal group times the group of dilations.
Aluminium oxideAluminium oxide (or Aluminium(III) oxide) is a chemical compound of aluminium and oxygen with the chemical formula . It is the most commonly occurring of several aluminium oxides, and specifically identified as aluminium oxide. It is commonly called alumina and may also be called aloxide, aloxite, or alundum in various forms and applications. It occurs naturally in its crystalline polymorphic phase α-Al2O3 as the mineral corundum, varieties of which form the precious gemstones ruby and sapphire.
Aluminium hydroxideAluminium hydroxide, , is found in nature as the mineral gibbsite (also known as hydrargillite) and its three much rarer polymorphs: bayerite, doyleite, and nordstrandite. Aluminium hydroxide is amphoteric, i.e., it has both basic and acidic properties. Closely related are aluminium oxide hydroxide, AlO(OH), and aluminium oxide or alumina (), the latter of which is also amphoteric. These compounds together are the major components of the aluminium ore bauxite. Aluminium hydroxide also forms a gelatinous precipitate in water.
SpectroscopySpectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO).
Electric arcAn electric arc (or arc discharge) is an electrical breakdown of a gas that produces a prolonged electrical discharge. The current through a normally nonconductive medium such as air produces a plasma, which may produce visible light. An arc discharge is initiated either by thermionic emission or by field emission. After initiation, the arc relies on thermionic emission of electrons from the electrodes supporting the arc. An arc discharge is characterized by a lower voltage than a glow discharge.
