ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.     

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

On a family of vector space categories

In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.     

Cartan matrices of selfinjective algebras of tubular type

The Cartan matrix of a finite dimensional algebra A is an important combinatorial invariant reflecting frequently structural properties of the algebra and its module category. For example, one of the important features of the modular representation theory of finite groups is the nonsingularity of Cartan matrices of the associated group algebras (Brauer’s theorem). Recently, the class of all tame selfinjective algebras having simply connected Galois coverings and the stable Auslander-Reiten quiver consisting only of stable tubes has been shown to be the class of selfinjective algebras of tubular type, that is, the orbit algebras /G of the repetitive algebras of tubular algebras B with respect to the actions of admissible groups G of automorphisms of . The aim of the paper is to describe the determinants of the Cartan matrices of selfinjective algebras of tubular type and derive some consequences.     

The use of phase portraits to visualize and investigate isolated singular points of complex functions

ABSTRACT

Undergraduate students usually study Laurent series in a standard course of Complex Analysis. One of the major applications of Laurent series is the classification of isolated singular points of complex functions. Although students are able to find series representations of functions, they may struggle to understand the meaning of the behaviour of the function near isolated singularities. In this paper, I briefly describe the method of domain colouring to create enhanced phase portraits to visualize and study isolated singularities of complex functions. Ultimately this method for plotting complex functions might help to enhance students' insight, in the spirit of learning by experimentation. By analysing the representations of singularities and the behaviour of the functions near their singularities, students can make conjectures and test them mathematically, which can help to create significant connections between visual representations, algebraic calculations and abstract mathematical concepts.     

关于药物对小鼠肝脏细胞色素P-450含量的影响实验结果的分析

肝药酶诱导剂苯巴比妥能诱导细胞色素P-450的合成,而肝药酶抑制剂放线菌素D能抑制细胞色素P-450的合成,本实验应用示差光谱法对P-450含量加以测定.本文改进了传统的计算药后诱导组和抑制组P-450含量增加或减少的百分比来评价药物的方法,在M athem atica数学软件环境下,对数据进行方差分析和t检验,提高了数据处理精度和可信度.并对原方法表示怀疑.     

Comparison principle and analogues of the phragmen—lindelöf theorem for solutions of parabolic inequalities

It is well known that a Monotonicity Condition and a Coerciveness Condition principally lie in the basis of most results of the Theory of PDE's. The necessity of these important assumptions for the validity of a comparison principle and analogues of the Phragmen-Lindelöf theorem for solutions of quasilinear parabolic inequalities is discussed in the paper. In the first part of the work we introduce a new concept of monotonicity for nonlinear differential operators-nonlinear monotonicity concept-and on its basis we obtain new phenomena for solutions, subsolutions and supersolutions of the well-known quasilinear differential equations. In the second part we omit the current coerciveness condition and change it by a weaker one. In spite of this we obtain a series of new qualitative properties of solutions for wide classes of quasilinear parabolic inequalities. Most of these properties are also new for solutions of the well-known equations, which we consider in the paper.     

Bounds of the Hausdorff Measure of Sierpinski carpet

By means of the idea of [2]（Jia Baoguo,J.Math.Anal.Appl.In press） and the self.similarity of Sierpinski carpet, we obtain the lower and upper bounds of the Hausdorff Measure of Sierpinski carpet, which can approach the Hausdorff Measure of Sierpinski carpet infinitely.     

Existence and nonexistence results for reaction-diffusion equations in product of cones

Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.