Conservation laws for some compacton equations using the multiplier approach

This paper is an application of the variational derivative method to the derivation of the conservation laws for partial differential equations. The conservation laws for (1+1) dimensional compacton k(2,2) and compacton k(3,3) equations are studied via multiplier approach. Also the conservation laws for (2+1) dimensional compacton Zk(2,2) equation are established by first computing the multipliers.     

Common fixed point theorem for hybrid generalized multi-valued contraction mappings

In this paper, we introduce the notion of a hybrid generalized multi-valued contraction mapping and establish the common fixed point theorem for this mapping. Our results generalize, unify, extend and complement several common fixed point theorems of many authors in the literature.     

Comment on “On the original proof by reductio ad absurdum of the Hohenberg–Kohn theorem for many‐electron Coulomb systems”

We argue with Kryachko's criticism [Int J Quantum Chem 2005, 103, 818] of the original proof of the second Hohenberg‐Kohn theorem. The Kato cusp condition can be used to refute a “to‐be‐refuted” statement as an alternative to the original proof by Hohenberg and Kohn applicable for Coulombic systems. Since alternative ways to prove falseness of the “to‐be‐refuted” statement in a reduction ad absurdum proof do not exclude each other, Kryachko's criticism is not justified. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Variability of scaling parameters in non-conservative systems: Geophysical aspect

Newly obtained data on the critical dynamics of the drifting/fracturing sea ice in the Arctic Ocean were analyzed and compared with published data on the dynamic processes in the Earth’s crust. Substantial similarities were found in the scaling behavior of both geophysical systems; the most important of them is the b-value space/time variability including a pre-failure drop of this parameter. The b-value pattern of the ensemble of drifting ice floes is an analogue of the b-value distribution over areas and depths in tectonic structures. A common feature of the pre-failure state in the cryosphere and in the Earth’s crust is the increased degree of the energy conservation that manifests itself both in the sea ice consolidation prior to basin-wide ice pack fragmentations, and in involving harder geological formations in the fracture process before earthquakes, respectively. From the viewpoint of the conservative SOC concept, this relation between the system’s conservativity and the occurrence of large-scale fracture events means that the expected scale level of failure is determined by the system’s closeness to “true” SOC behavior.     

Super-vertex-antimagic total labelings of disconnected graphs

Let G=(V,E) be a finite, simple and non-empty (p,q)-graph of order p and size q. An (a,d)-vertex-antimagic total labeling is a bijection f from V(G)∪E(G) onto the set of consecutive integers 1,2,…,p+q, such that the vertex-weights form an arithmetic progression with the initial term a and the common difference d, where the vertex-weight of x is the sum of values f(xy) assigned to all edges xy incident to vertex x together with the value assigned to x itself, i.e. f(x). Such a labeling is called super if the smallest possible labels appear on the vertices.In this paper, we will study the properties of such labelings and examine their existence for disconnected graphs.     

Pair lengths of product graphs

The pair length of a graph G is the maximum positive integer k, such that the vertex set of G can be partitioned into disjoint pairs {x,x^′}, such that d(x,x^′)?k for every x∈V(G) and x^′y^′ is an edge of G whenever xy is an edge. Chen asked whether the pair length of the cartesian product of two graphs is equal to the sum of their pair lengths. Our aim in this short note is to prove this result.     

Uniform asymptotics of some q-orthogonal polynomials

Uniform asymptotic formulas are obtained for the Stieltjes-Wigert polynomial, the q⁻¹-Hermite polynomial and the q-Laguerre polynomial as the degree of the polynomial tends to infinity. In these formulas, the q-Airy polynomial, defined by truncating the q-Airy function, plays a significant role. While the standard Airy function, used frequently in the uniform asymptotic formulas for classical orthogonal polynomials, behaves like the exponential function on one side and the trigonometric functions on the other side of an extreme zero, the q-Airy polynomial behaves like the q-Airy function on one side and the q-Theta function on the other side. The last two special functions are involved in the local asymptotic formulas of the q-orthogonal polynomials. It seems therefore reasonable to expect that the q-Airy polynomial will play an important role in the asymptotic theory of the q-orthogonal polynomials.     

Pt及其修饰电极上甲醇吸附和氧化的CV和EQCM研究

运用电化学循环伏安和石英晶体微天平 (EQCM )研究了 0 .1mol·L- 1H2 SO4 溶液中甲醇在Pt电极和以Sb ,S不可逆吸附原子修饰的Pt(Pt/Sbad和Pt/Sad)电极上的吸附和氧化过程 .结果表明甲醇的氧化与电极表面氧物种有着极其密切的关系 .Pt电极表面Sb吸附原子能在较低的电位下吸附氧 ,可显著提高甲醇电催化氧化活性 .与Pt电极相比较 ,Sb吸附原子修饰的Pt电极使甲醇氧化的峰电位负移了 0 .13V .相反 ,Pt电极表面S吸附原子的氧化会消耗表面氧物种 ,抑制了甲醇的电氧化 .本文从表面质量变化提供了吸附原子电催化作用的新数据     

考虑最优广告费用及数量折扣的供应链企业间的博弈分析

主要研究由一个制造商和一个销售商组成的二级供应链系统,在随机需求下,考虑广告促销及数量折扣前后,双方如何博弈,如何决策的问题.在制造商Stackelberg策略下,对供应链协调价进行了分析,提供了制造商制定数量折扣策略的思路.