Closure (topology)In topology, the closure of a subset S of points in a topological space consists of all points in S together with all limit points of S. The closure of S may equivalently be defined as the union of S and its boundary, and also as the intersection of all closed sets containing S. Intuitively, the closure can be thought of as all the points that are either in S or "very near" S. A point which is in the closure of S is a point of closure of S. The notion of closure is in many ways dual to the notion of interior.
P-adic analysisIn mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers. The theory of complex-valued numerical functions on the p-adic numbers is part of the theory of locally compact groups. The usual meaning taken for p-adic analysis is the theory of p-adic-valued functions on spaces of interest. Applications of p-adic analysis have mainly been in number theory, where it has a significant role in diophantine geometry and diophantine approximation.
NP-completenessIn computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.
Back painBack pain is pain felt in the back. It may be classified as neck pain (cervical), middle back pain (thoracic), lower back pain (lumbar) or coccydynia (tailbone or sacral pain) based on the segment affected. The lumbar area is the most common area affected. An episode of back pain may be acute, subacute or chronic depending on the duration. The pain may be characterized as a dull ache, shooting or piercing pain or a burning sensation. Discomfort can radiate to the arms and hands as well as the legs or feet, and may include numbness or weakness in the legs and arms.
Human backThe human back, also called the dorsum (: dorsa), is the large posterior area of the human body, rising from the top of the buttocks to the back of the neck. It is the surface of the body opposite from the chest and the abdomen. The vertebral column runs the length of the back and creates a central area of recession. The breadth of the back is created by the shoulders at the top and the pelvis at the bottom. Back pain is a common medical condition, generally benign in origin.
Valuation (finance)In finance, valuation is the process of determining the value of a (potential) investment, asset, or security. Generally, there are three approaches taken, namely discounted cashflow valuation, relative valuation, and contingent claim valuation. Valuations can be done for assets (for example, investments in marketable securities such as companies' shares and related rights, business enterprises, or intangible assets such as patents, data and trademarks) or for liabilities (e.g., bonds issued by a company).
CoefficientIn mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression. It may be a number (dimensionless), in which case it is known as a numerical factor. It may also be a constant with units of measurement, in which it is known as a constant multiplier. In general, coefficients may be any expression (including variables such as a, b and c). When the combination of variables and constants is not necessarily involved in a product, it may be called a parameter.
Complex numberIn mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; every complex number can be expressed in the form , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number , a is called the , and b is called the . The set of complex numbers is denoted by either of the symbols or C.
Business valuationBusiness valuation is a process and a set of procedures used to estimate the economic value of an owner's interest in a business. Here various valuation techniques are used by financial market participants to determine the price they are willing to pay or receive to effect a sale of the business.
P-completeIn computational complexity theory, a decision problem is P-complete (complete for the complexity class P) if it is in P and every problem in P can be reduced to it by an appropriate reduction. The notion of P-complete decision problems is useful in the analysis of: which problems are difficult to parallelize effectively, which problems are difficult to solve in limited space. specifically when stronger notions of reducibility than polytime-reducibility are considered.
Low back painLow back pain (LBP) or lumbago is a common disorder involving the muscles, nerves, and bones of the back, in between the lower edge of the ribs and the lower fold of the buttocks. Pain can vary from a dull constant ache to a sudden sharp feeling. Low back pain may be classified by duration as acute (pain lasting less than 6 weeks), sub-chronic (6 to 12 weeks), or chronic (more than 12 weeks). The condition may be further classified by the underlying cause as either mechanical, non-mechanical, or referred pain.
Complete latticeIn mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A lattice which satisfies at least one of these properties is known as a conditionally complete lattice. Specifically, every non-empty finite lattice is complete. Complete lattices appear in many applications in mathematics and computer science. Being a special instance of lattices, they are studied both in order theory and universal algebra.
