Fixed point theorems for multivalued nonexpansive mappings satisfying inwardness conditions

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(X) the family of all compact convex subsets of X and T a nonexpansive mapping from C into KC(X) with bounded range. We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is an 1-χ-contractive mapping.     

Little Grothendieck's theorem for sublinear operators

Let SB(X,Y) be the set of the bounded sublinear operators from a Banach space X into a Banach lattice Y. Consider π₂(X,Y) the set of 2-summing sublinear operators. We study in this paper a variation of Grothendieck's theorem in the sublinear operators case. We prove under some conditions that every operator in SB(C(K),H) is in π₂(C(K),H) for any compact K and any Hilbert H. In the noncommutative case the problem is still open.     

Conic Formulation for l p -Norm Optimization

In this paper, we formulate the l _p -norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers.     

Parametric Quintic-Spline Approach to the Solution of a System of Fourth-Order Boundary-Value Problems

In this paper, we use parametric quintic splines to derive some consistency relations which are then used to develop a numerical method for computing the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is known that a class of variational inequalities related to contact problems in elastostatics can be characterized by a sequence of variational inequations, which are solved using some numerical method. Numerical evidence is presented to show the applicability and superiority of the new method over other collocation, finite difference, and spline methods.     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Influence of the Interaction between Two Neighboring Periodically Curved Fibers on the Stress Distribution in a Composite Material

A method is developed for a stress analysis in an infinite elastic body containing two neighboring periodically cophasaly curved fibers located along two parallel lines. The stress distribution is studied when the body is loaded at infinity by uniformly distributed normal forces in the fiber direction. The investigation is carried out within the framework of a piecewise homogeneous body model with the use of exact three-dimensional equations of elasticity theory. Numerical results related to the stress distribution considered and the influence of interaction between the fibers on this distribution are given.     

Billiards and Teichmüller curves on Hilbert modular surfaces

This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.

     

Variety of LaSrMnO structures induced by growth conditions and laser irradiation

Crystallographic phase transitions in perovskite-like LaSrMnO metallic oxides are studied. The transitions are induced when internal stresses generated during film synthesis (at temperatures between 450 and 730°C) vary (decrease or increase) upon subsequent irradiation by a KrF laser emitting in the UV range. As the synthesis temperature T _s grows, the rhombohedral-to-orthorhombic phase transition occurs at 650–670°C. The resistivity is shown to be either temperature-independent, ρ(T)=const, at T<T _crit, or varies and reaches a maximum, ρ(T)=ρ_max, at the Curie temperature T _c. Optical transmission spectra taken at photon energies ℏω=0.5–2.5 eV exhibit both a high (0.8–0.9) and low (0.1–0.3) transmission coefficient t, depending on the synthesis temperature. As follows from X-ray diffraction data, the laser irradiation causes a phase transition only in LaSrMnO films grown at T _s<650°C. Phases of different size scales appear: the long-range-order orthorhombic matrix and mesoscopic-range-order rhombohedral clusters are observed in the films grown at T _s=450–550°C and the rhombohedral matrix with orthorhombic clusters, in the films grown at T _s=550–650°C.     

Many body effects and internal transitions of confined excitons in GaAs and CdTe quantum wells

Many body effects contribute significantly to the energy states of electron-hole pairs confined in quantum wells in the presence of excess electrons. We present results of optically detected resonance spectroscopy of the internal transitions of photo-excited electron-hole pairs in the presence of excess electrons for GaAs QWs and CdTe QWs. Compared to the case of isolated negatively charged excitons, excess electrons produce a large blue shift of the internal transitions in modulation-doped GaAs quantum wells (QWs) for filling factor <2, and similar effects are found in CdTe QWs. For filling factor >2 no internal transitions are observed. These measurements demonstrate the strong effects of electron-electron correlations on the internal transitions of charged excitons in these quasi-2D systems and the importance of magnetic translation invariance. In the presence of excess electrons, the observed internal transitions are those of a magnetoplasmon bound to a mobile valence band hole.     

Broadening the scope of 1,2,4-triazine synthesis by the application of microwave technology

By the application of microwave technology, a general protocol has been developed for the rapid synthesis of diverse 3,5,6-trisubstituted 1,2,4-triazines in excellent yield and purity, including many previously unknown 3-heterocyclic-1,2,4-triazines.