Division (mathematics)

About: Division (mathematics) is a research topic. Over the lifetime, 12717 publications have been published within this topic receiving 87814 citations.

Self-learning Monte Carlo method

Abstract: United States. Department of Energy. Office of Basic Energy Science. Division of Materials Sciences and Engineering. (award DE-SC0010526)

On-line algorithms for division and multiplication

Abstract: In this paper we are considering problems of division and multiplication in a computational environment in which all basic arithmetic algorithms satisfy "on-line" property: to generate jth digit of the result it is necessary and sufficient to have argument(s) available up to the (j+δ)th digit, where the index difference 6 is a small positive constant. Such an environment, due to its potential to perform a sequence of operations in an overlapped fashion, could conveniently speed up an arithmetic multiprocessor structure or it could be useful in certain real-time applications, with inherent on-line properties. The on-line property implies a left-to-right digit-by-digit type of algorithm and consequently, a redundant representation, at least, of the results. For addition and subtraction such algorithms, satisfying on-line property, can be easily specified. Multiplication requires a somewhat more elaborate approach and there are several possible ways of defining an on-line algorithm. However, the existence of an on-line division algorithm is not obvious and its analysis appears interesting.

Choice of Operation in Verbal Arithmetic Problems: The Effects of Number Size, Problem Structure and Context.

Abstract: 12-and 13-year-olds were tested with two types of tasks to test their understanding of applications of the multiplication and division of positive numbers: (i) writing down calculations required to solve verbal problems, and (ii) making up stories to fit given calculations. Selected pupils were interviewed to investigate further the thinking processes involved. The results indicate (a) the pervasive nature of certain numerical misconceptions, (b) the effects of structural differences among the items; particularly whether multiplication can be conceived as repeated addition or not, and whether division has the structure of partition, quotition or rate, (c) specific effects of context attributable to such aspects as relative familiarity, and (d) various interactions between these three sets of factors.

Packet network architecture for providing rapid response time

Abstract: A high capacity metropolitan area network (MAN) is described. Data traffic from users is connected to data concentrators at the edge of the network, and is transmitted over fiber optic data links to a hub where the data is switched. The hub includes a plurality of data switching modules, each having a control means, and each connected to a distributed control space division switch. Advantageously, the data switching modules, whose inputs are connected to the concentrators, perform all checking and routing functions, while the 1024×1024 maximum size space division switch, whose outputs are connected to the concentrators, provides a large fan-out distribution network for reaching many concentrators from each data switching module. Distributed control of the space division permits several million connection and disconnection actions to be performed each second, while the pipelined and parallel operation within the control means permits each of the 256 switching modules to process at least 50,000 transactions per second. The data switching modules chain groups of incoming packets destined for a common outlet of the space division switch so that only one connection in that switch is required for transmitting each group of chained packets from a data switching module to a concentrator. MAN provides security features including a port identification supplied by the data concentrators, and a check that each packet is from an authorized source user, transmitting on a port associated with that user, to an authorized destination use that is in the same group (virtual network) as the source user. Each packet has an associated high or low priority indication. Requests for connections in the space division switch for a chained group of packets whose first packet has a high priority indication are given priority.