On a Boundary Value Problem for a Polynomial Pencil of the Sturm-Liouville Equation with Spectral Parameter in Boundary Conditions

The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.

Spectral Decomposition of Weighted Shift Operators

The reseearch on the relation between weighted shift operators on Hilbert spaces and other important class of operators attracted the attention of some mathematicians. For example, the relation between weighted shift operators and subnormal operators has been thoroughly studied by J. Stampfli, R. Gellar and D. A. Herrero, etc. (see reference [1]) But the decomposability of weighted shift operators has not yet attracted enough attention up to now. We made initial research

SYSTEMATIC FORECAST ERROR IN U.S.NMC OPERATIONAL SPECTRAL MODEL

The distribution of monthly mean error of NMC model forecasts and its seasonal variation are investi- gated.The ratio of monthly mean error to standard deviation is used here to find out that the region where a correction of systematic error is needed and appropriate is mainly in low latitudes.The improvement,after the model's vertical resolution and some physical parameters were changed from April 1985,is investigated,and the NMC operational model forecasts have also compared with those of ECMWF.

Integral domains with finitely many spectral semistar operations

Let D be a finite-dimensional integral domain, Spec（D） be the set of prime ideals of D, and SpSS（D） be the set of spectral semistar operations on D. Mimouni gave a complete description for the prime ideal structure of D with ｜SpSS（D）｜ = n ＋ dim（D） for 1 ≤ n ≤5 except for the quasi-local cases of n = 4, 5. In this paper, we show that there is an integral domain D such that ｜SpSS（D） ｜ = n＋dim（D） for all positive integers n with n ≠ 2. As corollaries, we completely characterize the quasi-local domains D with ｜SpSS（D）｜= n＋dim（D） for n = 4, 5. Furthermore, we also present the lower and upper bounds of ISpSS（D）I when Spee（D） is a finite tree.

POSITIVE SOLUTIONS TO SECOND-ORDER SINGULAR NEUMANN BOUNDARY VALUE PROBLEM WITH PARAMETERS IN THE BOUNDARY CONDITIONS

In this paper, we consider a class of nonlinear second-order singular Neumann boundary value problem with parameters in the boundary conditions. By the fixed point index, spectral theory of the linear operators, and lower and upper solutions method, we prove that there exists a constant λ* > 0 such that for λ ∈ (0, λ * ), NBVP has at least two positive solutions; for λ = λ* , NBVP has at least one positive solution; for λ > λ* , NBVP has no solution.

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous Hoolder-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters（the hadronic mass and width etc.）. We test the new approach in the ρ meson channel with re-examination and inclusion of αs corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.