The tanh method for travelling wave solutions to the Zhiber–Shabat equation and other related equations

The tanh method and the extended tanh method are used for handling the Zhiber–Shabat equation and the related equations: Liouville equation, sinh-Gordon equation, Dodd–Bullough–Mikhailov (DBM) equation, and Tzitzeica–Dodd–Bullough equation. Travelling wave solutions of different physical structures are formally derived for each equation.     

Conservation laws of second order for the Born-Infeld equation and other related equations

We describe a class of quasilinear partial differential equations of second order with two independent variables in the general case of mixed type for which we construct conservation laws of second order which are quadratic with respect to the second derivatives. As examples, we present similar conservation laws for the Born-Infeld equation, for the equations of minimal and maximal surfaces in Minkowski space, and for the classical equation of minimal surfaces.     

On the zeros of functions in Bergman spaces and in some other related classes of functions

A well-known theorem of H.S. Shapiro and A.L. Shields implies that if f?0 is a function which belongs to the Bergman space Ap (0<p<∞) and {zk} is a sequence of zeros of f which is contained in a Stolz angle, then {zk} satisfies the Blaschke condition. In this paper we improve this result. We consider a large class of regions contained in the unit disc D which touch ∂D at a point ξ tangentially and we prove that the mentioned result remains true if we substitute a Stolz angle by any of these regions of tangential approach.     

On the exact location of the zeros of certain families of rational period functions and other related rational functions

The classification of Rational Period Functions on the modular group has been of some interest recently, and was accomplished by studying the pole sets of these rational functions. We take a complex analytic point of view and begin an investigation into the location of zeros of certain families of rational period functions.

     

The chromatic number and other functions of the lexicographic product

The values of the chromatic and achromatic number, point- and line-connectivity, and point independence number of the lexicographic product of two graphs are examined in relation to the values of the respective parameters on the factor graphs.     

The blue and minque in Gauss-Markoff model with linear transformation of the observable variables

For a singular linear model A = (y, Xβ, σ2 V) and its transformed model AF = (Fy, FXβ, σ2FVF'), where V is nonnegative definite and X can be rank-deficient,the expressions for the differences of the estimates for the vector of FXβ and the variance factor σ2 are given. Moreover, the necessary and sufficient conditions for the equalities of the estimates for the vector of FXβ and the variance factor σ2 are also established. In the meantime, works in Baksalary and Kala (1981) are strengthened and consequences in Puntanen and Nurhonen (1992), and Puntanen (1996) are extended.     

房颤复律前后血BNP水平变化及复发的相关因素

目的探讨房颤对血脑利钠肽(BNP)水平的影响及房颤复发的相关因素.方法选择阵发性或持续性房颤非心衰患者49例(房颤组),另择同期类似疾病窦性心律患者50例作为对照组.检测对照组及房颤组复律前的血BNP水平.房颤组患者使用胺碘酮药物复律,在复律后24h检测血BNP水平,并随访观察6个月.比较分析6个月内房颤组复发与未复发患者的血BNP水平及临床特征.结果复律前房颤组血BNP水平显著高于对照组(P<0.01);房颤组复律后血BNP水平显著低于复律前(P<0.01),与对照组比较差异无统计学意义(P>0.05).随访期间房颤组31例未复发,18例复发;复律前后复发者血BNP水平均显著高于未复发者(均P<0.01);复发者与未复发者仅左房内径、病程、束支传导阻滞、二尖瓣反流等临床特征的差异具有统计学意义(P<0.05或0.01).结论房颤患者血BNP水平升高,并在复律时降低.血BNP水平、左房内径、房颤病程、束支传导阻滞、二尖瓣反流等特征可能与房颤复发有关.     

The stability of the Rogers-Shephard inequality and of some related inequalities

An essentially optimal stability version of the Rogers-Shephard inequality and stability versions of some other related affine invariant inequalities are verified. The characteristic feature of all these inequalities is that simplices provide the equality case.     

The Relative Sizes of the Terms in Chebyshev and other Ultraspherical Expansions

Lanczos (1952) claims that expansion of a function in a seriesof Chebyshev polynomials is usually superior to expansion ina series of ultraspherical polynomials for any possible non-zerovalue of the parameter . We look for conditions on the functionunder which this superiority can be proved and measured; weachieve some success on the assumption that is positive, butthe results for negative are less satisfactory.     

The Haruki-Rassias and related integral representations of the Bernoulli and Euler polynomials

Haruki and Rassias [H. Haruki, T.M. Rassias, New integral representations for Bernoulli and Euler polynomials, J. Math. Anal. Appl. 175 (1993) 81-90] found the integral representations of the classical Bernoulli and Euler polynomials and proved them by making use of the properties of certain functional equation. In this sequel, we rederive, in a completely different way, the results of Haruki and Rassias and deduce related and new integral representations. Our proofs are quite simple and remarkably elementary.     

The sojourn time and related characteristics of the age-dependent branching process

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival ofall the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in timet and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter-relationships are found among the means of (i) the total number of cells which die in timet (ii) the total sojourn time of all cells in the system upto timet and (iii) the number of living cells at timet. Some of the existing results are deduced as special cases for related processes.     

The Demyanov metric and some other metrics in the family of convex sets

We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.     

The nullcone in the multi-vector representation of the symplectic group and related combinatorics

We study the nullcone in the multi-vector representation of the symplectic group with respect to a joint action of the general linear group and the symplectic group. By extracting an algebra over a distributive lattice structure from the coordinate ring of the nullcone, we describe a toric degeneration and standard monomial theory of the nullcone in terms of double tableaux and integral points in a convex polyhedral cone.     

The dynamical behavior of the discontinuous Galerkin method and related difference schemes

We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions which guarantee that the continuous problem defines a dissipative dynamical system. We show that, under certain conditions, the discontinuous Galerkin approximation also defines a dissipative dynamical system and we study the approximation properties of the associated discrete dynamical system. We also study the behavior of difference schemes obtained by applying a quadrature formula to the integrals defining the discontinuous Galerkin approximation and construct two kinds of discrete finite element approximations that share the dissipativity properties of the original method.

     

The propagation of non-Lefschetz type, the Gottlieb group and related questions

This is a brief note which indicates how the property of being non-Lefschetz may be propagated by equivariant symplectic maps. We also discuss some questions related to the Gottlieb group and nilpotency of symplectic manifolds. To Vladimir Arnold, who taught me symplectic geometry without knowing it     

The economics of water resources for the generation of electricity and other uses

An optimal control approach is used to analyze the tradeoff between the use of water resources for electricity generation versus other economic uses (irrigation, industry, etc.). For that purpose, a dynamic model is presented which establishes relationships between economic growth, water resources management, and energy policy in the context of the aforementioned tradeoff, in an economy whose energy matrix is heavily dependent upon hydroelectric power. Among other results, the analysis establishes that in the market, the price of water for non-energy uses should be twice the price of the energy goods, indicating the necessity of substituting other sources of energy for hydroelectric power.     

The mapping class group of powers of the long ray and other non-metrisable spaces

We identify the mapping class group, i.e. the space of homeomorphisms modulo isotopy, of powers of the long ray and long line as well as generalisations of the long plane obtained by taking copies of the first octant of the long plane and identifying them along their boundaries. We show that every countable group is the mapping class group of such a space. We also consider homotopy classes of continuous functions between these spaces.