Z functionIn mathematics, the Z function is a function used for studying the Riemann zeta function along the critical line where the argument is one-half. It is also called the Riemann–Siegel Z function, the Riemann–Siegel zeta function, the Hardy function, the Hardy Z function and the Hardy zeta function. It can be defined in terms of the Riemann–Siegel theta function and the Riemann zeta function by It follows from the functional equation of the Riemann zeta function that the Z function is real for real values of t.
Network schedulerA network scheduler, also called packet scheduler, queueing discipline (qdisc) or queueing algorithm, is an arbiter on a node in a packet switching communication network. It manages the sequence of network packets in the transmit and receive queues of the protocol stack and network interface controller. There are several network schedulers available for the different operating systems, that implement many of the existing network scheduling algorithms. The network scheduler logic decides which network packet to forward next.
Lerch zeta functionIn mathematics, the Lerch zeta function, sometimes called the Hurwitz–Lerch zeta function, is a special function that generalizes the Hurwitz zeta function and the polylogarithm. It is named after Czech mathematician Mathias Lerch, who published a paper about the function in 1887. The Lerch zeta function is given by A related function, the Lerch transcendent, is given by The transcendent only converges for any real number , where: or and .
Mertens functionIn number theory, the Mertens function is defined for all positive integers n as where is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: Less formally, is the count of square-free integers up to x that have an even number of prime factors, minus the count of those that have an odd number.
Deep webThe deep web, invisible web, or hidden web are parts of the World Wide Web whose contents are not indexed by standard web search-engine programs. This is in contrast to the "surface web", which is accessible to anyone using the Internet. Computer scientist Michael K. Bergman is credited with inventing the term in 2001 as a search-indexing term. Deep web sites can be accessed by a direct URL or IP address, but may require entering a password or other security information to access actual content.
Bernoulli numberIn mathematics, the Bernoulli numbers Bn are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function. The values of the first 20 Bernoulli numbers are given in the adjacent table.
Hurwitz zeta functionIn mathematics, the Hurwitz zeta function is one of the many zeta functions. It is formally defined for complex variables s with Re(s) > 1 and a ≠ 0, −1, −2, ... by This series is absolutely convergent for the given values of s and a and can be extended to a meromorphic function defined for all s ≠ 1. The Riemann zeta function is ζ(s,1). The Hurwitz zeta function is named after Adolf Hurwitz, who introduced it in 1882. The Hurwitz zeta function has an integral representation for and (This integral can be viewed as a Mellin transform.
Mertens' theoremsIn analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens. In the following, let mean all primes not exceeding n. Mertens' first theorem is that does not exceed 2 in absolute value for any . () Mertens' second theorem is where M is the Meissel–Mertens constant (). More precisely, Mertens proves that the expression under the limit does not in absolute value exceed for any . The main step in the proof of Mertens' second theorem is where the last equality needs which follows from .
Web portalA web portal is a specially designed website that brings information from diverse sources, like emails, online fora and search engines, together in a uniform way. Usually, each information source gets its dedicated area on the page for displaying information (a portlet); often, the user can configure which ones to display. Variants of portals include mashups and intranet "dashboards" for executives and managers. The extent to which content is displayed in a "uniform way" may depend on the intended user and the intended purpose, as well as the diversity of the content.
Request for quotationA request for quotation (RfQ) is a business process in which a company or public entity requests a quote from a supplier for the purchase of specific products or services. RfQ generally means the same thing as Call for bids (CfB) and Invitation for bid (IfB). An RfQ typically involves more than the price per item. Information like payment terms, quality level per item or contract length may be requested during the bidding process.
