Products of projective S-Systems

The tree main results of this paper deal with the generating vectors of simple infinite and finite dimesional modules arising as composition factors of the Kac modules K↓ G ₀ and K of the Lie superalgebra sl(m/n).     

A New Class of Kernels Leading to an Arbitrary Decay in Viscoelasticity

A new assumption on the relaxation in a viscoelastic problem ensuring uniform stability in an arbitrary rate is established. This assumption replaces a usual condition and allows for a much wider class of kernels. As consequences several earlier results are extended and improved.     

Maximum spin aligned states in 98 47Ag51

New excited states have been observed in the neutron deficient isotope ⁹⁸Ag following the ⁵⁸Ni+⁵⁰Cr →¹⁰⁸Te^* heavy–ion reaction. One of these states may be interpreted as a maximum spin aligned state of the πg_9/2 ⁻³νg_7/2 configuration. Other possible interpretations within the nuclear shell model are discussed as well. Received: 24 October 1997     

On toric h-vectors of centrally symmetric polytopes

We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational. Received: 24 March 2004     

Fabrication of solid‐state nanopores and its perspectives

Nanofluidics is becoming an extensively developing technique in the field of bioanalytical chemistry. Nanoscale hole embed in an insulating membrane is employed in a vast variety of sensing platforms and applications. Although, biological nanopores have several attractive characteristics, in this paper, we focused on the solid‐state nanopores due to their advantages as high stability, possibility of diameter control, and ease of surface functionalizing. A detection method, based on the translocation of analyzed molecules through nanochannels under applied voltage bias and resistive pulse sensing, is well established. Nevertheless, it seems that the new detection methods like measuring of transverse electron tunneling using nanogap electrodes or optical detection can offer significant additional advantages. The aim of this review is not to cite all related articles, but highlight the steps, which in our opinion, meant important progresses in solid‐state nanopore analysis.     

Classification of Toeplitz operators on hardy spaces of bounded domains in the plane

We construct an orthonormal basis for the class of square integrable functions on bounded domains in the plane in terms of the classical kernel functions in potential theory. Then we generalize the results of Brown and Halmos about algebraic properties of Toeplitz operators and Laurent operators on the unit disc to general bounded domains. This is a complete classification of Laurent operators and Toeplitz operators for bounded domains.     

Instabilities in two-liquid layers subject to a horizontal temperature gradient

We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B₂O₃, a configuration of considerable technological importance. Four different flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscillatory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques. PACS 47.20.Dz, 47.20.Bp, 47.54.+r, 47.27.Te, 44.25.+f, 47.20.Ma     

A spectral element method using the modal basis and its application in solving second‐order nonlinear partial differential equations

We present a high‐order spectral element method (SEM) using modal (or hierarchical) basis for modeling of some nonlinear second‐order partial differential equations in two‐dimensional spatial space. The discretization is based on the conforming spectral element technique in space and the semi‐implicit or the explicit finite difference formula in time. Unlike the nodal SEM, which is based on the Lagrange polynomials associated with the Gauss–Lobatto–Legendre or Chebyshev quadrature nodes, the Lobatto polynomials are used in this paper as modal basis. Using modal bases due to their orthogonal properties enables us to exactly obtain the elemental matrices provided that the element‐wise mapping has the constant Jacobian. The difficulty of implementation of modal approximations for nonlinear problems is treated in this paper by expanding the nonlinear terms in the weak form of differential equations in terms of the Lobatto polynomials on each element using the fast Fourier transform (FFT). Utilization of the Fourier interpolation on equidistant points in the FFT algorithm and the enough polynomial order of approximation of the nonlinear terms can lead to minimize the aliasing error. Also, this approach leads to finding numerical solution of a nonlinear differential equation through solving a system of linear algebraic equations. Numerical results for some famous nonlinear equations illustrate efficiency, stability and convergence properties of the approximation scheme, which is exponential in space and up to third‐order in time. Copyright © 2014 John Wiley & Sons, Ltd.     

Local orbitals by minimizing powers of the orbital variance

It is demonstrated that a set of local orthonormal Hartree-Fock (HF) molecular orbitals can be obtained for both the occupied and virtual orbital spaces by minimizing powers of the orbital variance using the trust-region algorithm. For a power exponent equal to one, the Boys localization function is obtained. For increasing power exponents, the penalty for delocalized orbitals is increased and smaller maximum orbital spreads are encountered. Calculations on superbenzene, C(60), and a fragment of the titin protein show that for a power exponent equal to one, delocalized outlier orbitals may be encountered. These disappear when the exponent is larger than one. For a small penalty, the occupied orbitals are more local than the virtual ones. When the penalty is increased, the locality of the occupied and virtual orbitals becomes similar. In fact, when increasing the cardinal number for Dunning's correlation consistent basis sets, it is seen that for larger penalties, the virtual orbitals become more local than the occupied ones. We also show that the local virtual HF orbitals are significantly more local than the redundant projected atomic orbitals, which often have been used to span the virtual orbital space in local correlated wave function calculations. Our local molecular orbitals thus appear to be a good candidate for local correlation methods.     

Strict Monotonicity of Eigenvalues and Unique Continuation

In this paper, we show that the strict mononicity of the eigen-values of an uniformly elliptic operator of second order is equivalent to a unique continuation property.