相关论文: Applicability of Partial Ternary Full Adder in Ter…

In this paper a low power and low area array multiplier with carry save adder is proposed. The proposed adder eliminates the final addition stage of the multiplier than the conventional parallel array multiplier. The conventional and…

We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neumann algebra $\mathcal{N}$ is never model complete if its…

We compare the implementation of a 8x8 bit multiplier with two different implementations of a 4x4 quaternary digit multiplier. Interfacing this binary multiplier with quaternary to binary decoders and binary to quaternary encoders leads to…

In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…

Standard numerical integrators suffer from an order reduction when applied to nonlinear Schr\"{o}dinger equations with low-regularity initial data. For example, standard Strang splitting requires the boundedness of the solution in $H^{r+4}$…

Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let $ m >2$ be a positive integer. For an odd prime $ p $, let $ r=p^m $ and…

We propose a new approach to extending the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on ternary associativity of the first and second kind. We propose a ternary commutator,…

The paper presents a systematic study and implementation of a reconfigurable combinatorial multi-operand adder for use in Deep Learning systems. The size of carry changes with the number of operands and hence a reliable algorithm to…

The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are…

Numerical monoids (cofinite, additive submonoids of the non-negative integers) arise frequently in additive combinatorics, and have recently been studied in the context of factorization theory. Arithmetical numerical monoids, which are…

We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…

Fix a commutative monoid $(T,+,0)$, a commutative monoid $(\Gamma,+,0_\Gamma)$, and a map \[ (a,\alpha,b,\beta,c)\longmapsto a\,\alpha\,b\,\beta\,c\in T \] which is additive in each variable and associative in the ternary sense. A left…

We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then…

A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…

Paul Erdos asked how frequently the ternary expansion of 2^n omits the digit 2. He conjectured this happens only for finitely many values of n. We generalize this question to consider iterates of two discrete dynamical systems. The first is…

This paper describes a new method of data encoding which may be used in various modern digital, computer and telecommunication systems and devices. The method permits the compression of data for storage or transmission, allowing the exact…

In truncated partial-wave analysis, one fits observables that are bilinear in the amplitudes rather than the amplitudes themselves. Truncation is therefore not merely a restriction of the amplitude basis, but of the bilinear interference…

Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To…

This paper investigates the algebraic structure of additive complementary pairs of cyclic codes over a finite commutative ring. We demonstrate that for every additive complementary pair of additive cyclic codes, both constituent codes are…

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime $p$, we present the explicit complete weight enumerator of a family of $p$-ary linear codes constructed with defining…