By using gauge transformations, we manage to obtain new solutions of (2+1)-dimensional Kadomtsev-Petviashvili(KP), Kaup-Kuperschmidt(KK) and Sawada-Kotera(SK) equations from non-zero seeds. For each the preceding equations, a Galilean type transformation between these $u_2$ previously known $u_2^{\prime}$ generated zero seed is given. We present several explicit formulas single-soliton for $u_2...

This paper introduces the notion of zero ring graphs. Basic properties of the zero ring graphs are investigated and characterization results regarding connectedness and planarity are given. Further, we determine the chromatic number for ΓM 2 (Zp[x]/〈x〉), where p is a prime, k > 1 and it is shown that an isomorphism exists among the zero ring graphs ΓM 2 (Zpk), ΓM 2 (Zp[x]/〈x〉) and ΓM 2 (Fpk).

We make a systematic study of groups of deeciency zero, concentrating on groups of prime-power order. We prove that a number of p-groups have deeciency zero and give explicit balanced presentations for them. This signiicantly increases the number of such groups known. We describe a reasonably general computational approach which leads to these results. We also list some other nite groups of dee...

ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...

‎let $r$ be a $*$-prime ring with center‎ ‎$z(r)$‎, ‎$d$ a non-zero $(sigma,tau)$-derivation of $r$ with associated‎ ‎automorphisms $sigma$ and $tau$ of $r$‎, ‎such that $sigma$‎, ‎$tau$‎ ‎and $d$ commute with $'*'$‎. ‎suppose that $u$ is an ideal of $r$ such that $u^*=u$‎, ‎and $c_{sigma,tau}={cin‎ ‎r~|~csigma(x)=tau(x)c~mbox{for~all}~xin r}.$ in the present paper‎, ‎it is shown that...

This paper develops a prime radix transform algorithm that can be used to calculate the discrete Fourier transform (DFT) of a data block of length P, a prime, using fixed coefficient second order recursive filter sections: this simple hardware structure allows compact, high performance DFT processors to be developed. Further “massaging” of the prime radix algorithm produces the zero factor tran...

Let $mathcal{A}$ and $mathcal{B}$ be two $C^{*}$-algebras such that $mathcal{B}$ is prime. In this paper, we investigate the additivity of maps $Phi$ from $mathcal{A}$ onto $mathcal{B}$ that are bijective, unital and satisfy $Phi(AP+eta PA^{*})=Phi(A)Phi(P)+eta Phi(P)Phi(A)^{*},$ for all $Ainmathcal{A}$ and $Pin{P_{1},I_{mathcal{A}}-P_{1}}$ where $P_{1}$ is a nontrivial projection in $mathcal{A...

A ring is called a Gelfand ring (pm ring ) if each prime ideal is contained in a unique maximal ideal. For a Gelfand ring R with Jacobson radical zero, we show that the following are equivalent: (1) R is Artinian; (2) R is Noetherian; (3) R has a finite Goldie dimension; (4) Every maximal ideal is generated by an idempotent; (5) Max (R) is finite. We also give the following resu1ts:an ideal...

Models of bipedal robots in motion are fundamentally hybrid due to the presence of continuous phases, discrete transitions, and unilateral constraints arising from the contact forces between the robot and the ground. A major challenge in the control of bipedal robots has been to create a feedback theory that provides systematic synthesis methods, provable correctness and computational tools for...