Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.

Multi-tiered structure for storing and displaying product and process variants

Abstract: A computer based system is provided that is capable of displaying component and process structures for configurable product classes stored in a data structure. Product classes in the data structure are represented by product nodes. Components, which are abstractions of concrete items used in the product, are represented by component nodes. Component nodes are mapped to each product class with which the component is associated, and are associated with one or more component variants, which are concrete items used in the manufacture of a particular product variant. Process nodes, which are abstractions of actual steps required to produce a product variant, known as process variants, are represented by process nodes. The computer based system can display several alternative views of the data structure. For example, upon receiving a selection for a particular product class, the computer based system converts and can graphically display all component and process nodes associated with that product class. Alternatively, the system can receive input of a product variant and display all component variants used in its production, which is its bill of materials.

Methods and system for utility network outage detection

Abstract: The present invention provides a system including a utility network including a product distribution pathway for delivering a product, a plurality of electronic utility devices associated with the utility network to monitor at least one parameter associated with the product distribution pathway, and a management processor in communication with the devices and operable to poll at least a subset of the electronic utility devices in response to an input to evaluate performance of one of the utility network and the system in response to information relating to the at least one parameter. The evaluation can include a rule-based analysis of one of the parameter and the information relating to the parameter.

Analysis of the asymmetric shortest queue problem

Abstract: In this paper we study a system consisting of two parallel servers withdifferent service rates. Jobs arrive according to a Poisson stream and generate an exponentially distributed workload. On arrival a job joins the shortest queue and in case both queues have equal lengths, he joins the first queue with probabilityq and the second one with probability 1 −q, whereq is an arbitrary number between 0 and 1. In a previous paper we showed for the symmetric problem, that is for equal service rates andq = 1/2, that the equilibrium distribution of the lengths of the two queues can be exactly represented by an infinite sum of product form solutions by using an elementary compensation procedure. The main purpose of the present paper is to prove a similar product form result for the asymmetric problem by using a generalization of the compensation procedure. Furthermore, it is shown that the product form representation leads to a numerically efficient algorithm. Essentially, the method exploits the convergence properties of the series of product forms. Because of the fast convergence an efficient method is obtained with upper and lower bounds for the exact solution. For states further away from the origin the convergence is faster. This aspect is also exploited in the paper.

Dct/idct processor and data processing method

Abstract: A one-dimensional discrete cosine transform processor of N (N: positive integer)-term input data X includes a preprocessing section for carrying out addition and subtraction of (i)th-term data x (i) and (N-i)th-term data x (N-1) of input data X, and a unit for performing a product sum operation for sets of intermediate data subjected to preprocessing by addition and sets of intermediate data subjected to preprocessing by subtraction, respectively. The product sum operation unit includes a data rearranging unit for outputting, in parallel and in order, bit data of the same figure of a set of data, a partial sum generator for generating a partial sum by using the parallel bit data as an address, and an accumulator for accumulating outputs of the partial sum generator. A one-dimensional inverse discrete cosine transform processor of N-term input data X includes a unit for performing a product sum operation of input data, and a postprocessing section for carrying out addition and subtraction of 2-term data in a predetermined combination of an output of the product sum operation unit. The number of times of multiplication is reduced by utilizing inherent characteristics of coefficients of DCT/IDCT processing. Since the product sum operation is performed by a ROM table and an adder, a faster multiplication is realized.