Order and Canonical Product of the Weierstrass R-Integral

Ukrainian Mathematical Journal - The order of the R-integral is specified and its representation in the form of the canonical Weierstrass product is found.     

Torsion Zero-Cycles on a Product of Canonical Lifts of Elliptic Curves

Let X be a surface over a p-adic field with good reduction and let Y be its special fiber. We write T(X) and T(Y) for the kernels of the Albanese maps of X and Y, respectively. Then, F(X) = T(X)/T(X)_div is conjectured to be finite, where T(X)_div is the maximal divisible subgroup of T(X). Furthermore, F(X) is conjectured to be isomorphic to T(Y) modulo p-primary torsion. We show that the p-primary torsion subgroup of F(X) can be arbitrary large even though we fix the special fiber Y.     

具有奇素典范指标的一般型三维簇的典范稳定性

主要研究具有奇指标的一般型光滑射影三维簇的典范映射,称φm是典范稳定的,如果对于所有的m≥m(r),φm是双有理的.证明了m(3)=13,m(5)=15,m(7)=18以及m(r)=2r对于所有的r≥11.     

一类函数方程的稳定性及微商配置解

本文对一类重要的函数方程建立解稳定性定理,提出微商配置解,证明了收敛性.     

多目标最优化问题相依导数的灵敏性与稳定性(英)

设Y（u）是可行域在目标空间的像，W（u）＝minpY（u）是有效集和N（u）＝W－minDDY是弱有效集．在适当条件下，本文证明了DNW－minpY和W－minDDY＝DW＝DN．本文也讨论了边缘映射导数的连续性．     

On the Rational Canonical Form of a Matrix

Let L be a linear map on the space of n×n matrices over a field. We determine the structure of the maps L that preserve commutativity. We also determine the structure of all linear maps on complex matrices that preserve the higher numerical range. The main tool is the Fundamental Theorem of Projective Geometry.     

Canonical variation of a Lorentzian metric

Given a Lorentzian manifold (M,_gL)$(M,g_L)$ and a timelike unitary vector field E  , we can construct the Riemannian metric _gR=_gL+2ω⊗ω$g_R=g_L+2\omega \otimes \omega$, ω being the metrically equivalent one form to E. We relate the curvature of both metrics, especially in the case of E   being Killing or closed, and we use the relations obtained to give some results about (M,_gL)$(M,g_L)$.     

The Canonical Decomposition of the Poset of a Hammock

In the Auslander-Reiten quiver of a representation-directedalgebra several hammocks occur naturally; they begin at theprojective cover of a simple module E and end in the correspondinginjective hull. It is known that hammocks are Auslander-Reitenquivers of posets, so there is a poset corresponding to eachsimple module; it describes the set of modules having E as acomposition factor. In this paper we show that this poset Sdecomposes canonically into a coideal S⁺ and an ideal S^–which can easily be described by vectorspace-categories correspondingto a one-point extension or a one-point coextension, respectively.In addition, we describe the simple modules for which S⁺ andS^– are not comparable, and also those for which S⁺ S^–. We also show how to use the results in order to prove for certainposets that they do not occur as posets corresponding to simplemodules.     

Stability and Convergence of Product Formulas for Operator Matrices

We present easy to verify conditions implying stability estimates for operator matrix splittings which ensure convergence of the associated Trotter, Strang and weighted product formulas. The results are applied to inhomogeneous abstract Cauchy problems and to boundary feedback systems.     

基于Caputo导数的Miller-Ross序列导数微分方程的稳定性分析

讨论了基于Caputo导数的Miller-Ross序列导数的分数阶微分方程的稳定性.根据Laplace变换,得到分数阶微分方程的解;应用Mittag-Leffler函数的渐近展开,讨论了方程的稳定性.分两部分:齐次方程与非齐次方程.     

Canonical form of a nonlinear monetary system

This paper addresses an autonomous system of quadratic ordinary differential equations, which describes a monetary system involving interest rate, investment demand and price index. The canonical form of this system is derived, which is dependent on a single parameter. On this basis, it is proved that this system is not smoothly equivalent to the generalized Lorenz canonical form.     

Canonical form of a two-dimensional Riemann manifold

A proof of the existence on a Riemann manifold of a system of canonical cuts such that the canonical form of the manifold will be a convex region with the minimum number of sides.Translated from Matematicheskie Zametki, Vol. 9, No. 1, pp. 67–70, January, 1971.The author wishes to thank É. B. Vinberg for suggesting the problem, and A. B. Katk and G. A. Margulis for their comments on the work.     

Canonical frame of a curve on a conformal plane

We show how differential geometry of smooth curves on the conformal plane can be studied by Élie Cartan’s method of exterior forms and moving frames. We find the canonical form of the derivation equations of a curve (which is not a circle) in the case of a semi-isotropic frame. We give a new proof of the theorem that states that curves of constant (in particular, zero) conformal curvature are loxodromes. We integrate the system of structure equations of the isotropy subgroup of a point.     

Inequalities for the Polar Derivative of a Polynomial

Let P(z) be a polynomial of degree at most n. We consider an operator D _?? which maps a polynomial P(z) into D _?? P(z) :=?nP(z)?+?(?? ? z)P??(z) and prove results concerning the estimates of |D _?? P(z)| on the disk |z|?=?R??? 1, and thereby obtain extensions and generalizations of a number of well-known polynomial inequalities.     

Canonical formulas for a paraconsistent analog of the Scott logic

We explore how the technique of canonical formulas can be applied in studying a paraconsistent analog Ls of the known intermediate Scott logic SL. Canonical formulas are defined which axiomatize Ls relative to minimal logic and allow us to describe all countermodels of the logic in question.     

Jordan Canonical Form of a Matrix over the Quaternion Field

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Numerical Determination of a Canonical Form of a Symplectic Matrix

We propose an algorithm that transforms a real symplectic matrix with a stable structure to a block diagonal form composed of three main blocks. The two extreme blocks of the same size are associated respectively with the eigenvalues outside and inside the unit circle. Moreover, these eigenvalues are symmetric with respect to the unit circle. The central block is in turn composed of several diagonal blocks whose eigenvalues are on the unit circle and satisfy a modification of the Krein-Gelfand-Lidskii criterion. The proposed algorithm also gives a qualitative criterion for structural stability.     

Global Integrability of the Derivative of a Quasiconformal Mapping

We establish an essentially sharp growth condition on the quasihyperbolic metric of a domain sufficient for the global higher integrability of the derivative of a quasiconformal mapping.     

Some Results on the Polar Derivative of a Polynomial

Let P(z) be a polynomial of degree n and for any complex number α, let Dα P(z) = n P(z)+(α-z)P′(z) denote the polar derivative of P(z) with respect to α. In this paper, we obtain certain inequalities for the polar derivative of a polynomial with restricted zeros. Our results generalize and sharpen some well-known polynomial inequalities.