Definition 1.1. Given a ring R, a genus with values in R is a ring homomorphism, Ω ⊗Q→ R, where Ω is the G-bordism ring. For example, the Â-genus and L-genus are ring maps from Ω⊗Q→ Q. The Atiyah-Singer theorem shows that  can be refined to a genus Ω⊗Q→ Z. The L-genus (or signature) is defined on Ω⊗Q, and the Todd genus is defined on the complex cobordism category. We can define genera via mul...

In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ ove...

A ring R is called a left APP-ring if the left annihilator lR(Ra) is right s-unital as an ideal of R for any element a ∈ R. We consider left APP-property of the skew formal power series ring R[[x;α]] where α is a ring automorphism of R. It is shown that if R is a ring satisfying descending chain condition on right annihilators then R[[x;α]] is left APP if and only if for any sequence (b0, b1, ....

here, we propose an optical filter and an optical power splitter based on two-dimensionalphotonic crystal all circular ring resonators. these structures are made of a square lattice ofsilicon rods with the refractive index n1=3.464 surrounded by air (with refractive indexn2=1). first, we have designed the filter and by using that, we designed a power splitter. thetransmission efficiency and qua...

In modern VLSI circuits, a large number of clock buffers are inserted in clock distribution networks, which are significantly affected by process and power supply noise variations. The combined effect of process variations and power supply noise on clock skew and jitter is investigated in this paper. A statistical model of skitter, which consists of skew and jitter, is proposed. Clock paths wit...

In the following, we describe a way of factoring polynomials in Fq[X] with Drinfeld modules. We furthermore analyse the complexity of the algorithm and compare it to the well-known Cantor-Zassenhaus algorithm. 1. Defining Fq[X ]-module structures with Drinfeld modules Throughout this paper we will denote A = Fq[X ], where q is a power of some prime p, and N ∈ A for the polynomial which is to be...

Abstract. We give a polynomial-time algorithm of computing the classical Hurwitz numbers Hg,d, which were defined by Hurwitz 125 years ago. We show that the generating series of Hg,d for any fixed g > 2 lives in a certain subring of the ring of formal power series that we call the Lambert ring. We then define some analogous numbers appearing in enumerations of graphs, ribbon graphs, and in the ...