Hilbert's basis theoremIn mathematics, specifically commutative algebra, Hilbert's basis theorem says that a polynomial ring over a Noetherian ring is Noetherian. If is a ring, let denote the ring of polynomials in the indeterminate over . Hilbert proved that if is "not too large", in the sense that if is Noetherian, the same must be true for . Formally, Hilbert's Basis Theorem. If is a Noetherian ring, then is a Noetherian ring. Corollary. If is a Noetherian ring, then is a Noetherian ring.
The Nature of the Firm"The Nature of the Firm" (1937) is an article by Ronald Coase. It offered an economic explanation of why individuals choose to form partnerships, companies, and other business entities rather than trading bilaterally through contracts on a market. The author was awarded the Nobel Memorial Prize in Economic Sciences in 1991 in part due to this paper. Despite the honor, the paper was written when Coase was an undergraduate and he described it later in life as "little more than an undergraduate essay.
Structural bioinformaticsStructural bioinformatics is the branch of bioinformatics that is related to the analysis and prediction of the three-dimensional structure of biological macromolecules such as proteins, RNA, and DNA. It deals with generalizations about macromolecular 3D structures such as comparisons of overall folds and local motifs, principles of molecular folding, evolution, binding interactions, and structure/function relationships, working both from experimentally solved structures and from computational models.
Structural alignmentStructural alignment attempts to establish homology between two or more polymer structures based on their shape and three-dimensional conformation. This process is usually applied to protein tertiary structures but can also be used for large RNA molecules. In contrast to simple structural superposition, where at least some equivalent residues of the two structures are known, structural alignment requires no a priori knowledge of equivalent positions.
Theory of the firmThe theory of the firm consists of a number of economic theories that explain and predict the nature of the firm, company, or corporation, including its existence, behaviour, structure, and relationship to the market. Firms are key drivers in economics, providing goods and services in return for monetary payments and rewards. Organisational structure, incentives, employee productivity, and information all influence the successful operation of a firm in the economy and within itself.
Productivity-improving technologiesThe productivity-improving technologies are the technological innovations that have historically increased productivity. Productivity is often measured as the ratio of (aggregate) output to (aggregate) input in the production of goods and services. Productivity is increased by lowering the amount of labor, capital, energy or materials that go into producing any given amount of economic goods and services. Increases in productivity are largely responsible for the increase in per capita living standards.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
Agricultural productivityAgricultural productivity is measured as the ratio of agricultural outputs to inputs. While individual products are usually measured by weight, which is known as crop yield, varying products make measuring overall agricultural output difficult. Therefore, agricultural productivity is usually measured as the market value of the final output. This productivity can be compared to many different types of inputs such as labour or land. Such comparisons are called partial measures of productivity.
