Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the “Theory of Congruences” in Graph Theory. Thus he paved the way for the emergence of a new class of graphs, namely “Arithmetic Graphs”. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes a...

Let [Formula: see text] be the von Mangoldt function, let an integer and counting function for Goldbach numbers with summands in arithmetic progression modulo a common text]. We prove asymptotic formula weighted average, Cesàro weight of order text], this function. Our result is uniform suitable range

Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh’s extension principle, one can obtain a fuzzy extension of any objective function. Computing expensive multivariate functions of fuzzy numbers, however, often poses a difficult problem due to non-applicability of common fuzzy arithmetic algorithms, severe overestimation, or very high computat...

We present a general uni cation algorithm modulo Presburger Arithmetic for a restricted class of modularly speci ed theories where function symbols of the target theory have non arithmetic codomain sorts. Additionally, we comment on conditions guaranteeing decidability of matching and uni cation problems modulo more general theories than the arithmetic ones, which appear when automated deductio...

Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the “Theory of Congruences” in Graph Theory. Thus he paved the way for the emergence of a new class of graphs, namely “Arithmetic Graphs”. Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley graph becomes a...

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 Computer arithmetic and the MathCW library Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB Internet e-mail: [email protected] Salt Lake City, UT 84112-0090, USA URL: http://www.math.utah.edu/~beebe/ Abstract This talk describes the significance of specific features of integer and floating-point arithmetic for computation. It discusses the impact of the recent intro...

The Stanford Nanosecond Arithmetic Project is targeted at realizing an arithmetic processor with performance approximately an order of magnitude faster than currently available technology. The realization of SNAP is predicated on an interdisciplinary approach and effort spanning research in algorithms, data representation, CAD, circuits and devices, and packaging. SNAP is visualized as an arith...

Nathanson was the pioneer in introducing the concepts of Number Theory, particularly, the "Theory of Congruences" in Graph Theory, thus paving way for the emergence of a new class of graphs, namely "Arithmetic Graphs". Cayley graphs are another class of graphs associated with the elements of a group. If this group is associated with some arithmetic function then the Cayley g...

Let N0 be the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) is defined as an injective function f : V (G) → P(N0) such that the induced function f : E(G)→ P(N0) defined by f(uv) = f(u)+f(v) is also injective, where N0 is the set of all non-negative integers. A graph G which admits an IASI is called an IASI graph. An IASI of a graph G is said...

In recent work authors have proposed four new aggregation operators based on the arithmetic and geometric means of the Land Ror right side and left side apex angles for triangular [1] [2] and trapezoidal [3] [4] fuzzy numbers respectively. In this paper authors propose a new aggregation operator for TFNs in which the Land Rmembership function lines of the aggregate TFN have slopes which are the...