Cosmological constantIn cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.
Neighbourhood (graph theory)In graph theory, an adjacent vertex of a vertex v in a graph is a vertex that is connected to v by an edge. The neighbourhood of a vertex v in a graph G is the subgraph of G induced by all vertices adjacent to v, i.e., the graph composed of the vertices adjacent to v and all edges connecting vertices adjacent to v. The neighbourhood is often denoted N_G (v) or (when the graph is unambiguous) N(v). The same neighbourhood notation may also be used to refer to sets of adjacent vertices rather than the corresponding induced subgraphs.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
CountingCounting is the process of determining the number of elements of a finite set of objects; that is, determining the size of a set. The traditional way of counting consists of continually increasing a (mental or spoken) counter by a unit for every element of the set, in some order, while marking (or displacing) those elements to avoid visiting the same element more than once, until no unmarked elements are left; if the counter was set to one after the first object, the value after visiting the final object gives the desired number of elements.
Order theoryOrder theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.
Share (finance)In financial markets, a share (sometimes referred to as stock) is a unit of equity ownership in the capital stock of a corporation, and can refer to units of mutual funds, limited partnerships, and real estate investment trusts. Share capital refers to all of the shares of an enterprise. The owner of shares in a company is a shareholder (or stockholder) of the corporation. A share is an indivisible unit of capital, expressing the ownership relationship between the company and the shareholder.
Order of magnitudeAn order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is 10, the order of magnitude can be understood as the number of digits in the base-10 representation of the value.
Share priceA share price is the price of a single share of a number of saleable equity shares of a company. In layman's terms, the stock price is the highest amount someone is willing to pay for the stock, or the lowest amount that it can be bought for. In economics and financial theory, analysts use random walk techniques to model behavior of asset prices, in particular share prices on stock markets. This practice has its basis in the presumption that investors act rationally and without biases, and that at any moment they estimate the value of an asset based on future expectations.
Limiting magnitudeIn astronomy, limiting magnitude is the faintest apparent magnitude of a celestial body that is detectable or detected by a given instrument. In some cases, limiting magnitude refers to the upper threshold of detection. In more formal uses, limiting magnitude is specified along with the strength of the signal (e.g., "10th magnitude at 20 sigma"). Sometimes limiting magnitude is qualified by the purpose of the instrument (e.g., "10th magnitude for photometry") This statement recognizes that a photometric detector can detect light far fainter than it can reliably measure.
Photographic magnitudePhotographic magnitude (mph or mp ) is a measure of the relative brightness of a star or other astronomical object as imaged on a photographic film emulsion with a camera attached to a telescope. An object's apparent photographic magnitude depends on its intrinsic luminosity, its distance and any extinction of light by interstellar matter existing along the line of sight to the observer. Photographic observations have now been superseded by electronic photometry such as CCD charge-couple device cameras that convert the incoming light into an electric current by the photoelectric effect.
