We find that a compatible graded left-symmetric algebra structure on the Witt algebra induces an indecomposable module of the Witt algebra with 1-dimensional weight spaces by its left multiplication operators. From the classification of such modules of the Witt algebra, the compatible graded left-symmetric algebra structures on the Witt algebra are classified. All of them are simple and they in...

Consider the ring R := Q[τ, τ−1] of Laurent polynomials in the variable τ . The Artin’s Pure Braid Groups (or Generalized Pure Braid Groups) act over R, where the action of every standard generator is the multiplication by τ . In this paper we consider the cohomology of these groups with coefficients in the module R (it is well known that such cohomology is strictly related to the untwisted int...

High power problem become one of the most important bottleneck of the IC industry. FIR filter is a most basic element in a digital signal processing system. In this paper, we managed to design a new FIR filter that can have low power. We use a residue number system to design a FIR filter in order to reduce power. In our model, we designed a serial modulus adder and a new way to compute modulus ...

A CMOS four-quadrant analog multiplier circuit for neural networks integrated circuit implementation is presented. By applying differential balanced current mode signals (both for the input, output and weight signals) the multiplication function is easily implemented through two translinear loops. The multiplier exhibits low power consumption (the dc current is 250 nA under a differential power...

All rings are commutative with identity and all modules are unital. Let R be a ring, M an R-module and R(M), the idealization of M . Homogenous ideals of R(M) have the form I (+)N , where I is an ideal of R and N a submodule of M such that IM ⊆ N . A ring R (M) is called a homogeneous ring if every ideal of R (M) is homogeneous. In this paper we continue our recent work on the idealization of m...

Résumé. Soit p un nombre premier et K un corps de nombres. Soit ρE,p : GK −→ Aut(TpE) ∼= GL2(Zp) la représentation Galoisienne donnée par l’action du groupe de Galois sur le module de Tate p-adique d’une courbe elliptique E définie sur K. Serre a prouvé que l’image de ρE,p est ouverte si E n’a pas de multiplication complexe. Pour E une courbe elliptique définie sur K et dont l’invariant j n’app...

The free abelian group R(Q) on the set of indecomposable representations of a quiver Q, over a field K, has a ring structure where the multiplication is given by the tensor product. We show that if Q is a rooted tree (an oriented tree with a unique sink), then the ring R(Q)red is a finitely generated Z-module (here R(Q)red is the ring R(Q) modulo the ideal of all nilpotent elements). We will de...

Let H m be the reproducing kernel Hilbert space with the kernel function (z, w) ∈ B×B → (1− m ∑ i=1 ziw̄i) . We show that if θ : B → L(E , E∗) is a multiplier for which the corresponding multiplication operator Mθ ∈ L(H m ⊗ E , H 2 m ⊗ E∗) has closed range, then the quotient module Hθ, given by · · · −→ H m ⊗ E Mθ −→ H m ⊗ E∗ πθ −→ Hθ −→ 0, is similar to H m ⊗F for some Hilbert space F if and on...

---------------------------------------------------------------------***--------------------------------------------------------------------Abstract This paper proposes the computationally efficient, low power, high speed partial reconfigurable 9-tap FIR filter design using multiple constant multiplication technique. To reduce reconfiguration time dynamic partial reconfiguration is introduced. ...

Dual canonical bases of the quantum general linear supergroup are constructed which are invariant under the multiplication of the quantum Berezinian. By setting the quantum Berezinian to identity, we obtain dual canonical bases of the quantum special linear supergroup Oq(SLm|n). We apply the canonical bases to study invariant subalgebras of the quantum supergroups under left and right translati...