Chebyshev polynomials on symmetric matrices

In this paper we evaluate Chebyshev polynomials of the second kind on a class of symmetric integer matrices, namely on adjacency matrices of simply laced Dynkin and extended Dynkin diagrams. As an application of these results we explicitly calculate minimal projective resolutions of simple modules of symmetric algebras with radical cube zero that are of finite and tame representation type.     

Square integrability of representations on p-adic symmetric spaces

A symmetric space analogue of Casselman's criterion for square integrability of representations of a p-adic group is established. It is described in terms of exponents of Jacquet modules along parabolic subgroups associated to the symmetric space.     

Closedness of the solution map for parametric weak vector equilibrium problems

In this paper we introduced a new definition of vector topological pseudomonotonicity to study the parametric weak vector equilibrium problems. The main result gives sufficient conditions for closedness of the solution map defined on the set of parameters.     

Beta decay of nuclide 56Fe,56Co,56Ni,56Mn,56Cr and 56V due to strong electron screening in stellar interiors

According to a new electron screening theory,we discuss the beta decay rates of nuclide 56Fe,56Co,56Ni,56Mn,56Cr and 56V with and without strong electron screening (SES).The results show that SES has only a slight effect on the beta decay rates for ρ/μe 108 g/cm3.However the beta decay rates would be influenced greatly for ρ/μe 108 g/cm3.Due to SES,the maximum values of the C-factor (in %) on beta decay rates of 56Fe,56Co,56Ni,56Mn,56Cr and 56V is of the order of 95.03%,35.02%,98.05%,80.33%,98.30% and 98.71% at T9 = 4.0 and 98.83%,98.89%,99.65%,10.32%,4.10% and 40.21% at T9 = 7.0,respectively.     

工程测量中光波干涉必须满足的几个条件

讨论了两列光波发生干涉现象的理想化条件和在实验中能否观察到干涉现象发生的操作性条件，推导了各种情况下的理论公式。从工程应用的角度出发，研究了检测仪器的响应时间T和光强分辨能力对观察光的干涉现象的影响，提出了观察光的干涉现象的第四个必要条件，对在各种情况下应用光的干涉现象有一定的指导作用。     

A Response to “On method overfitting”

If special-purpose methods can be overfitted to benchmarks, so can general methods.     

A note on anisotropic,inhomogeneous, poro‐elastic media

A modification of the material law associated with the well‐known Biot system as suggested by Murad and Cushman (Int. J. Eng. Sci. 1996; 34(3):313–338) and first investigated by Showalter (J. Math. Anal. Appl. 2000; 251(1):310–340) is reconsidered, generalized and analysed in the light of a new approach to a comprehensive class of evolutionary problems. The framework allows a uniform approach to problems involving general anisotropic, inhomogeneous, non‐smooth media thus covering, for example, transmission problems in layered materials. Copyright © 2009 John Wiley & Sons, Ltd.     

A simple finite volume method for the shallow water equations

We present a new finite volume method for the numerical solution of shallow water equations for either flat or non-flat topography. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and a corrector stage. The predictor stage uses the method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. The proposed finite volume method is well balanced, conservative, non-oscillatory and suitable for shallow water equations for which Riemann problems are difficult to solve. The proposed finite volume method is verified against several benchmark tests and shows good agreement with analytical solutions.     

An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

In this paper, we investigate the positivity property for a class of 2-stage explicit Runge-Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.