Modal analysis and cutoff frequencies of a doubly clad plasma loaded waveguide having a lemniscates of Bernoulli-type core cross-section

The modal dispersion characteristics of EM waves in a new unconventional plasma loaded doubly clad waveguide having a shape of the lemniscates of Bernoulli-type core cross-section have been studied analytically. The proposed waveguide has three parts namely the core with slighter high index, the inner cladding with plasma and the outer cladding with air. Now using the necessary orthogonal coordinates for the proposed structure and imposing the boundary conditions under the weak guidance condition, the modal characteristics equation has been obtained considering variations in plasma width and plasma frequency, the dispersion curves and cutoff frequencies have been obtained and presented in this paper. It is noted that as the width of plasma layer increases, the cutoff frequency also increases considerably in all considered cases. This shows that using plasma width as a new parameter we can control any particular mode on our wish.     

Analytic invariant curves for an iterative equation related to mosquito model

In this paper, we study the existence of analytic invariant curves of a iterative equation which from mosquito model. By constructing an invertible analytic solution g(x) of an auxiliary equation of the form invertible analytic solutions of the form g(αg ^{? 1}(x)) for the original iterative functional equation are obtained. Besides the hyperbolic case 0 < | α | < 1, we focus on those α on the unit circle S¹, that is, | α | = 1. We discuss not only those α at resonance, that is at a root of the unity, but also those α near resonance under the Brjuno condition. Copyright © 2013 John Wiley & Sons, Ltd.     

The Landau–Hall problem on canal surfaces

In this note we study the Landau–Hall problem on a generalized canal surface and classify all uniform magnetic trajectories of a charged particle moving on such a surface under the action of a uniform magnetic field.     

Analytic moduli spaces of simple sheaves on families of integral curves

We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, which we provide.     

A note on finding clothoids

The clothoid is a spiral that is used as transition curve in highway and railway route design. Although its defining formulas are transcendental functions, recent work has shown that it can be used fairly easily on small computers. A single nonlinear equation must be solved in each of four common arrangements of the clothoid. The purpose of this work is to give starting intervals for which Newton's root finding method applied to those equations is guaranteed to converge.     

Iwasawa theory of quadratic twists of <Emphasis Type="Italic">X</Emphasis><Subscript>0</Subscript>(49)

The field \(K = \mathbb{Q}\left( {\sqrt { - 7} } \right)\) is the only imaginary quadratic field with class number 1, in which the prime 2 splits, and we fix one of the primes p of K lying above 2. The modular elliptic curve X ₀(49) has complex multiplication by the maximal order O of K, and we let E be the twist of X ₀(49) by the quadratic extension \(KK(\sqrt M )/K\), where M is any square free element of O with M ≡ 1 mod 4 and (M,7) = 1. In the present note, we use surprisingly simple algebraic arguments to prove a sharp estimate for the rank of the Mordell-Weil group modulo torsion of E over the field F _∞ = K(E _p∞), where E _p∞ denotes the group of p^∞-division points on E. Moreover, writing B for the twist of X ₀(49) by \(K(\sqrt[4]{{ - 7}})/K\), our Iwasawa-theoretic arguments also show that the weak form of the conjecture of Birch and Swinnerton-Dyer implies the non-vanishing at s = 1 of the complex L-series of B over every finite layer of the unique Z₂-extension of K unramified outside p. We hope to give a proof of this last non-vanishing assertion in a subsequent paper.     

Degradation Kinetics of an Epoxy/Cycloaliphatic Amine Resin Under Isothermal and Non-isothermal Conditions

A study of an epoxy-cycloaliphatic amine system has been realized using a thermogravimetric technique (TG). Isothermal and non-isothermal (dynamic) methods were employed to determine the kinetic data of this system. Five methods were used for determining the activation energies of this system in the dynamic heating experiments. In two of them (Flynn-Wall-Ozawa, and Kissinger) it is not necessary to have a prior knowledge of the reaction mechanism of the degradation behaviour for this system. In the other ones (Coats and Redfern, Horowitz and Metzger, and Van Krevelen et al.) it is necessary to know this reaction mechanism, besides Criado et al. method was used for determining it. The results have shown that good agreement between the activation energies obtained from all methods can be achieved if it is assumed that the degradation behaviour of this system is of sigmoidal-rate type. This revised version was published online in August 2006 with corrections to the Cover Date.     

关于Goppa 几何码最小距离的一个新方法

引进一个关于Goppa几何码(代数几何码)最小距离界的一个新方法.应用Maharaj的思想(即用显示基来近似表达Riemann-Roch空间)到Goppa几何码的最小距离的界上去.通过厄米特曲线上的代数几何码的一类例子,来证明标准的几何码的下界在某些情形下可以被显著地改进.进一步地,我们给出了这些码的最小距离上界,并说明了我们的下界非常接近这个上界.     

Elliptic Curves Suitable for Pairing Based Cryptography

For pairing based cryptography we need elliptic curves defined over finite fields whose group order is divisible by some prime with where k is relatively small. In Barreto et al. and Dupont et al. [Proceedings of the Third Workshop on Security in Communication Networks (SCN 2002), LNCS, 2576, 2003; Building curves with arbitrary small Mov degree over finite fields, Preprint, 2002], algorithms for the construction of ordinary elliptic curves over prime fields with arbitrary embedding degree k are given. Unfortunately, p is of size .We give a method to generate ordinary elliptic curves over prime fields with p significantly less than which also works for arbitrary k. For a fixed embedding degree k, the new algorithm yields curves with where or depending on k. For special values of k even better results are obtained.We present several examples. In particular, we found some curves where is a prime of small Hamming weight resp. with a small addition chain.AMS classification: 14H52, 14G50