A density on a locally compact Abelian group G is a bounded system of compatible measures on the compact quotients of G. The notion of density arises naturally both in connection with the theory of uniform distribution and with the theory of almost periodic functions. Our main result effectively answers the question "when are all densities on G induced by measures on some compactification of G?...

In this note we communicate some important remarks about the concepts of almost periodic time scales and almost periodic functions on time scales that are proposed by Wang and Agarwal in their recent papers ( see [7]-[10]).

This paper presents a system for the automatic generation of Galois-field (GF) arithmetic circuits, named the GF Arithmetic Module Generator (GF-AMG). The proposed system employs a graph-based circuit description called the GF Arithmetic Circuit Graph (GF-ACG). First, we present an extension of the GF-ACG to handle GF(pm) (p ≥ 3) arithmetic circuits, which can be efficiently implemented by mult...

Multiplication is the dominant operation for many applications implemented on field-programmable gate arrays (FPGAs). Although most current FPGA families have embedded hard multipliers, soft multipliers using lookup tables (LUTs) in the logic fabric remain important. This paper presents a novel two-operand addition circuit (patent pending) that combines radix-4 partial-product generation with a...

This paper proposes novel algorithms for computing doublesize modular multiplications with few modulus-dependent precomputations. Low-end devices such as smartcards are usually equipped with hardware Montgomery multipliers. However, due to progresses of mathematical attacks, security institutions such as NIST have steadily demanded longer bit-lengths for public-key cryptography, making the mult...

In the article, we find new dilatation results on non-commutative $$L^p$$ spaces. We prove that any self-adjoint, unital, positive measurable Schur multiplier some $$B(L^2(\Sigma ))$$ admits, for all $$1\leqslant p<\infty $$ , an invertible isometric dilation -space. obtain a similar result completely Fourier VN(G), when G is unimodular locally compact group. Furthermore, establish multivariabl...

This Paper presents an efficient implementation of high speed multiplier using the shift and add method, Radix_2, Radix_4 modified Booth multiplier algorithm. In This paper we compare the working of the three multipliers by implementing each of them separately in FIR filter. The parallel multipliers like radix2 and radix4 modified booth multiplier does the computations using lesser adders and l...

In this paper, we use the frequency-response masking (FRM) approach to design prototype filters for cosine-modulated filter banks in the nearly-perfect reconstruction case. With such approach, it is possible to design a FRM filter with overall order almost equal to the direct-form FIR design, with only slight changes in the values of the inter-carrier and inter-symbol interferences and the atte...