Adsorption-energetic and IR spectroscopic studies of NH4 natrolite

The ammonium form of natural zeolite, natrolite, obtained by vapor phase ion exchange is similar to calcium-containing zeolites of the natrolite group in its de- and rehydration characteristics and the heats of immersion in water. The adsorption capacity and the heat of immersion in water are maximum after evacuation of the zeolite at 200 °C. The irreversible sintering of NH₄ natrolite occurs above 200 °C (up to 45% at 500 °C), accompanied by the formation of hydroxyl groups. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 359–361, February, 1998.     

Finite-dimensional crystals B 2,s for quantum affine algebras of type D (1) n

The Kirillov–Reshetikhin modules W^r,s are finite-dimensional representations of quantum affine algebras U’_q labeled by a Dynkin node r of the affine Kac–Moody algebra and a positive integer s. In this paper we study the combinatorial structure of the crystal basis B^2,s corresponding to W^2,s for the algebra of type D⁽¹⁾_n. 2000 Mathematics Subject Classification Primary—17B37; Secondary—81R10 Supported in part by the NSF grants DMS-0135345 and DMS-0200774.     

The illumination conjecture and its extensions

Summary The Illumination Conjecture was raised independently by Boltyanski and Hadwiger in 1960. According to this conjecture any <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>d$-dimensional convex body can be illuminated by at most $2^d$ light sources. This is an important fundamental problem. The paper surveys the state of the art of the Illumination Conjecture.     

Invariants of Multi-Component Ermakov Systems

It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants. This extends the result to the two-component Ermakov system.     

Electrochemical behaviors of the magnesium alloy substrates in various pretreatment solutions

Interface reactions and film features of AZ91D magnesium alloy in pickling, activation and zinc immersion solutions have been investigated. The surface morphologies of the specimens were observed with scanning electron microscope (SEM). Electrochemical behaviors of AZ91D magnesium alloy in the baths of pickling, activation and zinc immersion were analyzed based on the open circuit potential (OCP) - time curves in various solutions. The results show that the corrosive rate in HNO₃ + CrO₃ or HNO₃ + H₃PO₄ pickling solution was more rapid than in KMnO₄ pickling-activation solution. Both α phase and β phase of the substrates were uniformly corroded in HNO₃ + CrO₃ or HNO₃ + H₃PO₄ pickling solution, the coarse surface can augment the mechanical occlusive force between the subsequent coatings and the substrates, so coatings with good adhesion can be obtained. In HF activation solution, the chromic compound formed via HNO₃ + CrO₃ pickling was removed and a compact MgF₂ film was formed on the substrate surface. In K₄P₂O₇ activation solution, the corrosion products formed via HNO₃ + H₃PO₄ pickling were removed, a new thin film of oxides and hydroxides was formed on the substrate surface. In KMnO₄ pickling-activation solution, a film of manganic oxides and phosphates was adhered on the substrate surface. Zinc film was symmetrically produced via K₄P₂O₇ activation or KMnO₄ pickling-activation, so it was good interlayer for Ni or Cu electroplating. Asymmetrical zinc film was produced because the MgF₂ film obtained in the HF activation solution had strong adhesive attraction and it was not suitable for interlayer for electroplating. However, the substrate containing compact MgF₂ film without zinc immersion was fit for direct electroless Ni-P plating.     

Affine Weyl group symmetries of Frobenius Painlevé equations

In this paper, we introduce a Frobenius Painlevé IV equation and the corresponding Hamilton system, and we give the symmetric form of the Frobenius Painlevé IV equation. Then, we construct the Lax pair of the Frobenius Painlevé IV equation. Furthermore, we recall the Frobenius modified KP hierarchy and the Frobenius KP hierarchy by bilinear equations, then we show how to get Frobenius Painlevé IV equation from the Frobenius modified KP hierarchy. In order to study the different aspects of the Frobenius Painlevé IV equation, we give the similarity reduction and affine Weyl group symmetry of the equation. Similarly, we introduce a Frobenius Painlevé II equation and show the connection between the Frobenius modified KP hierarchy and the Frobenius Painlevé II equation.     

A systematization of convexity and quasiconvexity concepts for set-valued maps,defined by l-type and u-type preorder relations

Abstract

In this paper, we study different classes of generalized convex/quasiconvex set-valued maps, defined by means of the l-type and u-type preorder relations, currently used in set-valued optimization. In particular, we identify those classes of set-valued maps for which it is possible to extend the classical characterization of convex real-valued functions by quasiconvexity of their affine perturbations.     

The argument shift method and the Gaudin model

We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U ( ) of a semisimple Lie algebra . This family is parameterized by finite sequences μ, z ₁, ..., z _n , where μ ∈ ^* and z _i ∈ ℂ. The construction presented here generalizes the famous construction of the higher Gaudin Hamiltonians due to Feigin, Frenkel, and Reshetikhin. For n = 1, the corresponding commutative subalgebras in the Poisson algebra S( ) were obtained by Mishchenko and Fomenko with the help of the argument shift method. For commutative algebras of our family, we establish a connection between their representations in the tensor products of finite-dimensional -modules and the Gaudin model. __________ Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 3, pp. 30–43, 2006 Original Russian Text Copyright ? by L. G. Rybnikov     

F_2~n上4次正形置换多项式的形式与计数

分组密码是现代密码学中一个重要的研究分支,而置换理论在分组密码中有重要的地位.1995年,美国Teledyne电子技术公司的Lothrop Mittenthal博士提出了一种置换,即正形置换.正形置换是一类完全映射,完全映射是由Mann在1942年研究正交拉丁方的构造时引入的,其具有良好的密码学性质(良好的扩散性和完全平衡性),因此,正形置换常用来构造密码系统的算法,研究正形置换也就非常有必要.本文根据文章[1]的方法讨论了F2n(n=4,5)上的4次正形置换多项式的形式与计数,至于n5的情形我们将在以后的篇章中继续讨论.     

The Core of a Locally Extended Affine Lie Algebra

Locally extended affine Lie algebras are a general version of extended affine Lie algebras. In this article, we completely describe the structure of the core of a locally extended affine Lie algebra. We prove that the core of a locally extended affine Lie algebra is a direct limit of Lie tori.