Banach-stone theorems and separating maps

LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH ⁻¹ are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries 4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex. Research supported by the Fundació Caixa Castelló, MI/25.043/92     

Dupin hypersurfaces with four principal Curvatures,II

If M is an isoparametric hypersurface in a sphere S ⁿ with four distinct principal curvatures, then the principal curvatures κ₁, . . . , κ₄ can be ordered so that their multiplicities satisfy m ₁ = m ₂ and m ₃ = m ₄, and the cross-ratio r of the principal curvatures (the Lie curvature) equals −1. In this paper, we prove that if M is an irreducible connected proper Dupin hypersurface in R ⁿ (or S ⁿ ) with four distinct principal curvatures with multiplicities m ₁ = m ₂ ≥ 1 and m ₃ = m ₄ = 1, and constant Lie curvature r = −1, then M is equivalent by Lie sphere transformation to an isoparametric hypersurface in a sphere. This result remains true if the assumption of irreducibility is replaced by compactness and r is merely assumed to be constant.      

Towards a normative model for inventory cost management in a generalized ABC classification system

This paper establishes a general ABC inventory classification system as the foundation for a normative model of the maintenance cost structure and stock turnover characteristics of a large, multi-item inventory system with constant demand. For any specified number of inventory classes, the model allows expression of the overall system combined ordering and holding cost in terms of (i) the re-ordering frequencies for the items in each inventory class and (ii) the inventory class structure, that is, the proportion of the total system's items that are in each inventory class. The model yields a minimum total maintenance cost function, which reflects the effect of class structure on inventory maintenance costs and turnover. If the Pareto curve (a.k.a. Distribution-by-value function) for the inventory system can be expressed (or approximated) analytically, the model can also be used to determine an optimal class structure, as well as an appropriate number of inventory classes. A special case of the model produces a simply structured, class-based ordering policy for minimizing total inventory maintenance costs. Using real data, the cost characteristics of this policy are compared to those of a heuristic, commonly used by managers of multi-item inventory systems. This cost comparison, expressed graphically, underscores the need for normative modelling approaches to the problem of inventory cost management in large, multi-item systems.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop. Original Russian Text ? A.Yu. Kolesov, E.F. Mishchenko, N.Kh. Rozov, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 259, pp. 106–133.     

Lagrangian Duality in Set-Valued Optimization

In this paper, we study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets (Kuroiwa, D. in Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, pp. 221–228, 1999). We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given. The authors thank the two referees for valuable comments and suggestions on early versions of the paper. The research of the first author was partially supported by Ministerio de Educación y Ciencia (Spain) Project MTM2006-02629 and by Junta de Castilla y León (Spain) Project VA027B06.     

Automorphisms of the semigroup of invertible matrices with nonnegative elements

In this paper, we prove that every automorphism of the semigroup of invertible matrices with nonnegative elements over a linearly ordered associative ring on some specially defined subgroup coincides with the composition of an inner automorphism of the semigroup, an order-preserving automorphism of the ring, and a central homothety. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 3–23, 2005.     

Electrodynamic properties of nanoporous silicon in the range from terahertz to infrared frequencies

The dielectric response (conductivity and permittivity) spectra of a series of nanoporous silicon samples prepared by anodization of low-resistivity single-crystal silicon are measured, for the first time, using terahertz and IR spectroscopy in the frequency range 7–4000 cm^?1 at room temperature. The spectra obtained are analyzed in terms of the effective medium theory with a size-dependent dielectric response function of nanoinclusions and averaged dielectric characteristics of the surrounding medium. The geometric and dielectric characteristics of silicon nanoinclusions are determined. The dielectric properties of inclusions are found to be affected by nanosize effects, namely, carrier scattering at crystallite boundaries and a broadening of the band gap due to quantum confinement. The spectra of the samples prepared by adding iodine to the electrolyte exhibit a resonance at frequencies of 150–300 cm^?1. The nature of the resonance can be associated with the presence of chemisorbed iodine on the surface of porous silicon. Possible mechanisms responsible for the changes in broadband conductivity and permittivity spectra of single-crystal silicon upon transformation into a nanoporous structure are discussed.     

Change in the magnetic state of a surface upon formation of hydrogen bonds during adsorption

It is established that reversible adsorption of water and methyl alcohol molecules, occurring via formation of hydrogen bonds, changes the dynamic properties of domain walls in the surface region of soft ferromagnets, as well as their initial static magnetic susceptibility. A mechanism is proposed for the effects revealed.     

Magnetic structure and transport properties of atomically disordered crystals of two-dimensional manganites La2−2x Sr1+2x Mn2O7

The magnetic structure and transport properties of partially disordered crystals of two-dimensional manganites La_2?2x Sr_1+2x Mn₂O₇ (x = 0.3, 0.4) are studied over a wide range of temperatures. The crystals are transformed into an atomically disordered state under irradiation with fast neutrons at a dose of 2 × 10¹⁹ cm^?2. The average concentration of substitutional defects in the crystal is ≈4%. It is found that substitutional defects are responsible for the transition of these manganites from the ferromagnetic metal state to the insulator state with a spin glass structure. The results obtained are discussed in terms of the ratio between the kinetic energy of charge carriers and the exchange energy of localized spins.     

A change in the physical state of a nonequilibrium blood plasma protein film in patients with carcinoma

Pronounced changes in the physical phase and in the phase transition dynamics of proteins in drying blood plasma are observed. The morphologies (topologies) of these nonequilibrium films in donors and in patients with various types of metastatic carcinoma qualitatively differ by the process of protein film self-assembly and by symmetry type. New types of defects and solid crystals appear, liquid crystals persist for a long time, etc. The microscopic examination of the drying protein plasma topology can be used for diagnosing metastatic carcinoma.