Solving the heat equation on the unit sphere via Laplace transforms and radial basis functions

We propose a method to construct numerical solutions of parabolic equations on the unit sphere. The time discretization uses Laplace transforms and quadrature. The spatial approximation of the solution employs radial basis functions restricted to the sphere. The method allows us to construct high accuracy numerical solutions in parallel. We establish L ₂ error estimates for smooth and nonsmooth initial data, and describe some numerical experiments.     

General Versions of the Ekeland Variational Principle: Ekeland Points and Stop and Go Dynamics

Journal of Optimization Theory and Applications - We establish general versions of the Ekeland variational principle (EVP), where we include two perturbation bifunctions to discuss and obtain...     

Levitin–Polyak well-posedness for set optimization problems involving set order relations

Positivity - In this paper set optimization problems with three types of set order relations are concerned. We introduce various types of Levitin–Polyak (LP) well-posedness for set...     

Higher-order optimality conditions for proper efficiency in nonsmooth vector optimization using radial sets and radial derivatives

We establish both necessary and sufficient optimality conditions of higher orders for various kinds of proper solutions to nonsmooth vector optimization in terms of higher-order radial sets and radial derivatives. These conditions are for global solutions and do not require continuity and convexity assumptions. Examples are provided to show advantages of the results over existing ones in a number of cases.     

Preparation of hydrogenated natural rubber with nanomatrix structure

Hydrogenated deproteinized natural rubber (HDPNR) with nanomatrix structure was prepared through graft‐copolymerization of acrylonitrile and styrene onto HDPNR particle in latex stage. Structural characterization of the resulting materials through nuclear magnetic resonance and Fourier‐transform infrared spectroscopy confirmed that acrylonitrile and styrene were grafted onto HDPNR. The weather resistance, thermal properties, mechanical properties, storage modulus, and morphology of the resulting materials were investigated in comparison with those of HDPNR. The obtained result indicated that the graft‐copolymerization of HDPNR with hydrogenation conversion of 60 mol% attained the highest grafting efficiency. Thermal resistance and storage modulus of HDPNR‐graft‐poly (styrene‐co‐acrylonitrile) (HDPNR‐g‐SAN) were superior compared with those of HDPNR and deproteinized natural rubber. This was attributed to the nanomatrix formed in HDPNR‐g‐SAN, which was confirmed through a transmission electron microscope. Ribbed smoked sheet natural rubber exhibited the outstanding mechanical properties and weather resistance when it was mixed with HDPNR‐g‐SAN.     

On a class of degenerate and singular elliptic systems in bounded domains

This paper deals with the nonexistence and multiplicity of nonnegative, nontrivial solutions to a class of degenerate and singular elliptic systems of the form

where Ω is a bounded domain with smooth boundary ∂Ω in , N2, and , , h_i (i=1,2) are allowed to have “essential” zeroes at some points in Ω, (F_u,F_v)=F, and λ is a positive parameter. Our proofs rely essentially on the critical point theory tools combined with a variant of the Caffarelli–Kohn–Nirenberg inequality in [P. Caldiroli, R. Musina, On a variational degenerate elliptic problem, NoDEA Nonlinear Differential Equations Appl. 7 (2000) 189–199].     

Acousto-optical tweezers for stretch of DNA molecule

The appearance of microlenses in the amorphous crystal Ge₃₃As₁₂Se₃₃ modulated by the acoustic waves with intensity of 10⁷ W/m² and frequency of (200–400) MHz is presented. The flexibility of microlens, i.e. the dependence of its focal point in 3D space on the parameters of acoustic wave is studied. Basing on flexibility of microlens, a model of acousto-optical tweezers to stretch the λ-phage WLC DNA molecule is proposed. And then the control process of stretched length of DNA molecule in 3D space of the water (fluid) by calibration of the acoustic frequency is numerically observed and discussed. The obtained results show the possibility to use the acousto-optical tweezers to control the stretched length of WLC DNA molecule with high fineness.     

Local rules for quasiperiodic tilings of quadratic 2-planes inR 4

We prove that quasiperiodic tilings of the plane, appearing in the strip projection method always admit local rules, when the linear embedding ofR ² inR ⁴ has quadratic coefficients. These local rules are constructed and studied. The connection between Novikov quasicrystallographic groups and the quasiperiodic tilings of Euclidean space is explained. All the point groups in Novikov's sense, compatible with these local rules, are enlisted. The two-dimensional quasicrystals with infinite-fold rotational symmetry are constructed and studied.Address after September 1, 1992: Dept. of Physics, Harvard University, Cambridge, MA 02138, USA