A probabilistic property of Katsuura's continuous nowhere differentiable function

Katsuura's example of a continuous nowhere differentiable function is based on a fixed-point method. In this paper we use probability theory to study the increments of Katsuura's function.     

Addition law structure of elliptic curves

The study of alternative models for elliptic curves has found recent interest from cryptographic applications, after it was recognized that such models provide more efficiently computable algorithms for the group law than the standard Weierstrass model. Examples of such models arise via symmetries induced by a rational torsion structure. We analyze the module structure of the space of sections of the addition morphisms, determine explicit dimension formulas for the spaces of sections and their eigenspaces under the action of torsion groups, and apply this to specific models of elliptic curves with parametrized torsion subgroups.     

Finding composite order ordinary elliptic curves using the Cocks-Pinch method

We apply the Cocks-Pinch method to obtain pairing-friendly composite order groups with prescribed embedding degree associated to ordinary elliptic curves, and we show that new security issues arise in the composite order setting.     

Asymptotic zero distribution of a class of 3F2 hypergeometric functions

We study the asymptotic behavior of the zeros of certain families of ₃F₂ functions. Classical tools are used to analyse the asymptotic behavior of the zeros of the polynomial In addition, families of ₃F₂ functions that are connected in a formulaic sense with Gauss hypergeometric polynomials of the form and are investigated. Numerical evidence of the clustering o zeros on certain curves is generated by Mathematica.     

Static and dynamic properties of KCN<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Cl<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>

An extended three-body force shell model (ETSM) has been applied to investigate the static and dynamic properties of KCN _x Cl_1−x for the compositionx = 0.56 and 1.0 at 300 K. The phonon dispersion curves computed by us are compared with the single crystal neutron diffraction data. The unusual features of these curves are the upward curvature seen in some of the acoustic branches. This is a result ofK-dependent softening of the phonon due to translation-rotation coupling. The transverse acoustic branch is more soft near the zone centre.     

Variations of Robin capacity and applications

We obtain some estimates for the distortions of the moduli of quadrilaterals, the reduced moduli, and Robin capacities depending on the variation of the boundary of a domain. We show that for sufficiently smooth variations of the boundary the corresponding variations of the moduli and capacities are proportional to the area of the variable part of the domain in some extremal metric. We apply these results to studying the generalized Lavrent’ev problem of finding the shape of an infinitely thin airfoil of given length with the maximal aerodynamical lift under some restriction on the curvature of the airfoil.     

Weierstrass points on X 0(p ℓ) and arithmetic properties of Fourier coefficients of cusp forms

Generally it is unknown, whether or not ∞ is a Weierstrass point on the modular curve X ₀(N) if N is squarefree. A classical result of Atkin and Ogg states that ∞ is not a Weierstrass point on X ₀(N), if N=pM with p prime, p ∤ M and the genus of X ₀(M) zero. We use results of Kohnen and Weissauer to show that there is a connection between this question and the p-adic valuation of cusp forms under the Atkin–Lehner involution. This gives, in a sense, a generalization of Ogg’s Theorem in some cases.      

局部形状可调整的三次有理B样条插值曲线

利用三次非均匀有理B样条,给出了一种构造局部插值曲线的方法,生成的插值曲线是C2连续的.曲线表示式中带有一个局部形状参数,随着一个局部形状参数值的增大,所给曲线将局部地接近插值点构成的控制多边形.基于三次非均匀有理B样条函数的局部单调性和一种保单调性的准则,给出了所给插值曲线的保单调性的条件.     

曲线族的模不等式

研究了曲线族的模 ,得到了 :1 )设Γ是 Rn 中连结不相交的曲线α1 与α2 的曲线族 ,若d(α1 ,α2 )≥ r,minj=1 ,2 dia(αj)≤ s,则 M(Γ )≤ 1 +srnΩn. 2 )设Γ是连结 Rn 中的闭连集 F1 与 F2 的曲线族 ,若minj=1 ,2 dia( Fj)≥ ad( F1 ,F2 ) ,则 M( Γ)≥ C( n,a) . 3 )设 R=R( C,C0 )是 R2 中的环 ,D表示 R2 \C中含 R的一个分支 ,α,β是 C上两条不相交的子曲线 .若 ΓR,ΓD 分别是 R与 D中连结 α和 β的曲线族 ,则 M( ΓR)≤ M( ΓD)≤φ( mod R) M(ΓR)     

Radial Quantization in Rotating Space–Times

We examine the time discontinuity in rotating space–times for which the topology of time is S¹. A kinematic restriction is enforced that requires the discontinuity to be an integral number of the periodicity of time. Quantized radii emerge for which the associated tangential velocities are less than the speed of light. Using the de Broglie relationship, we show that quantum theory may determine the periodicity of time. A rotating Kerr–Newman black hole and a rigidly rotating disk of dust are also considered; we find that the quantized radii do not lie in the regions that possess CTCs.