PBW-Pairs of Varieties of Linear Algebras

The notion of a Poincaré–Birkhoff–Witt (PBW)-pair of varieties of linear algebras over a field is under consideration. Examples of PBW-pairs are given. We prove that if (𝒱, 𝒲) is a PBW-pair and the variety 𝒱 is homogeneous and Schreier, then so is 𝒲; the results similar to the Schreier property for PBW-pairs are also true for the Freiheitssatz and Word problem. In particular, it follows that the Freiheitssatz is true for the varieties of Akivis and Sabinin algebras. We give also examples of varieties that do not satisfy the Freiheitssatz. It is shown that an element u of a free algebra 𝒲[X] in a homogeneous Schreier variety of algebras 𝒲 satisfying the Freiheitssatz is a primitive element (a coordinate polynomial) if and only if the factor algebra of 𝒲[X] by the ideal generated by the element u is a free algebra in 𝒲. We consider also properties of primitive elements.     

Idealization and Theorems of D. D. Anderson II

In our recent work we investigated Anderson's theorems and gave a treatment of certain aspects of multiplication modules and cancellation-like modules via idealization. The purpose of this work is to continue our study and develop the tool of idealization of modules, particularly in the context of flat modules.     

Norms of multiplication operators on Hardy spaces and weighted composition operators from Hardy spaces to weighted-type spaces on bounded symmetric domains

Let D be a bounded symmetric domain. We calculate operator norm of the multiplication operator on the Hardy space H^p(D), as well as of the weighted composition operator from H^p(D) to a weighted-type space.     

Hardy-Orlicz Spaces and Their Multiplication Operators

In this paper some formulae on the relationship between Hardy and Hardy Orlicz spaces are presented, and multiplication operators on Hardy-Orlicz spaces are discussed.     

一种图像处理用的数字乘法器

本文提出一种图像处理用的数字乘法器电路方案,叙述了用PBOM进行乘法运算的原理,并提出了具体实施方案。     

On the possibilistic mean value and variance of multiplication of fuzzy numbers

In this paper, we introduce the definitions of the possibilistic mean, variance and covariance of multiplication of fuzzy numbers, and show some properties of these definitions. Then, we apply these definitions to build the possibilistic models of portfolio selection under the situations involving uncertainty over the time horizon, by considering the portfolio selection problem from the point of view of possibilistic analysis. Moreover, numerical experiments with real market data indicate that our approach results in better portfolio performance.     

Partial product reduction by using look-up tables for M×N multiplier

In this paper we present a new technique for partial product reduction in multiplication operations. The method is based on the construction of counter elements by means of look-up tables. The organization of these counters into reduction trees takes advantage of the inherent benefits of the integration of the memories and provides an alternative to classic operation methods. We show several reduction schemes that illustrate the proposed technique and describe hybrid examples that combine stored logic with classic combinational counters in order to adapt them better to each scheme. Our approach outperforms other schemes used for comparison. In this sense, not only an independent technology model has been established, but also an FPGA approximation has been implemented to measure such factors in a real-life technology platform.     

On the generalization of the Euler polynomials with the real parameters

In this study, we give multiplication formula for generalized Euler polynomials of order α and obtain some explicit recursive formulas. The multiple alternating sums with positive real parameters a and b are evaluated in terms of both generalized Euler and generalized Bernoulli polynomials of order α. Finally we obtained some interesting special cases.