A Unified Fixed Point Theory in Generalized Convex Spaces

Let B be the class of ＇better＇ admissible multimaps due to the author. We introduce new concepts of admissibility （in the sense of Klee） and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added.     

一类抽象动力系统的C0群性质及其在迁移理论中的应用

本文研究一类抽象动力系统的性质.使用Hilbert空间的分解方法,获得了主算子的谱和相应的群的表示;使用有界线性算子的扰动理论,获得了抽象动力算子的谱分解.作为应用,研究了迁移理论中的一类积-微分方程.     

Characterizations of linear Volterra integral equations with nonnegative kernels

We first introduce the notion of positive linear Volterra integral equations. Then, we offer a criterion for positive equations in terms of the resolvent. In particular, equations with nonnegative kernels are positive. Next, we obtain a variant of the Paley-Wiener theorem for equations of this class and its extension to perturbed equations. Furthermore, we get a Perron-Frobenius type theorem for linear Volterra integral equations with nonnegative kernels. Finally, we give a criterion for positivity of the initial function semigroup of linear Volterra integral equations and provide a necessary and sufficient condition for exponential stability of the semigroups.     

The Koszul dual of a weakly Koszul module

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.     

Elliptic enumeration of nonintersecting lattice paths

We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given starting point to a given end point evaluates to an elliptic generalization of the binomial coefficient. Convolution gives an identity equivalent to Frenkel and Turaev's 0" style="vertical-align:bottom" width="30" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si1.gif"> summation. This appears to be the first combinatorial proof of the latter, and at the same time of some important degenerate cases including Jackson's 0" style="vertical-align:bottom" width="23" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si2.gif"> and Dougall's 0" style="vertical-align:bottom" width="25" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si3.gif"> summation. By considering nonintersecting lattice paths we are led to a multivariate extension of the 0" style="vertical-align:bottom" width="30" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0097316506001178-si4.gif"> summation which turns out to be a special case of an identity originally conjectured by Warnaar, later proved by Rosengren. We conclude with discussing some future perspectives.     

Controllability of Linear Systems in Non Reflexive Banch Spaces

§ 1.Introduction　 Let Xand Ube Banch spaces,S(t) a C0 semi-group in X,A the infinitesimal gen-erator of S(t) ,and B∈L(U,X) .Consider the systemΣP:x(t) =Ax(t) + Bu(t) ,　 t≥ 0 ,(1 .1 )where u∈ Lploc([0 ,∞ ) ,U) ,1≤p<∞ .　 The problem of controllability of linear systems in Banch spaces has been studied bymany authors.In [1 ] ,the weak and strong reachability and controllability of infinite di-mensional linear systems were investigated.In[2 ,3 ,4 ] ,the controllability of infi…     

Multi-wavelength operation of LD side-pumped Nd:YAG laser

A dual-wavelength laser at 1064 0;nm and 1319 0;nm is obtained by a single Nd:YAG crystal rod. On the basis of 1064 0;nm and 1319 0;nm dual-wavelength laser installation, the second harmonic waves at 532 0;nm and 660 0;nm can be achieved by using non-linear frequency conversion technology. When 1064 0;nm and 1319 0;nm lasers oscillate simultaneously, the maximum output power is 30.5 0;W and 8.78 0;W, respectively. When the 1319 0;nm laser is restrained, we obtain a 35.6 0;W maximum output power at 1064 0;nm and by contrary 11.2 0;W at 1319 0;nm. The maximum output powers of 532 0;nm and 660 0;nm lasers are 5.34 0;W and 1.353 0;W when oscillating simultaneously. With one of them restrained, the maximum output power is 6.72 0;W at 532 0;nm and 1.90 0;W at 660 0;nm. The optimum repetition rate of the acousto-optic Q-switch is 10.5 0;KHz and 20.5 0;KHz for 532 0;nm and 660 0;nm lasers, respectively. The optical-to-optical conversion efficiency from the fundamental waves to the harmonic waves is 17.5% and 15.4%. The instability is less than 2%.     

A first-principles study of C + O reaction on NiCo(1 1 1) surface

A density-functional theory method has been conducted to investigate the association of C 0;+ 0;O on (1 0;1 0;1) facets of ordered NiCo alloy and the results have been compared with those obtained on pure Ni(1 0;1 0;1) surface. In reaction of C 0;+ 0;O, the favorable reaction path is that C adsorbed on HCP-1 site moves to the nearest Ni-Co bridge site, and associates with O migrating from FCC-1 site to result in CO adsorbed on the bridge site of Ni-Co. However, the reaction barrier is higher by 0.35 0;eV than that on pure Ni(1 0;1 0;1), which indicates that the incorporation of Co into the Ni crystal is not in favor of the reaction of carbon delimination.     

A Class of k-Quantum Nonlinear Coherent States and Some of Their Properties

A class of k-quantum nonlinear coherent states, i.e., the k eigenstates of the powers B ^k (k 0w7lj21488w43/xxlarge8805.gif" alt="ge" align="MIDDLE" BORDER="0"> 3) of the annihilation operator 0w7lj21488w43/10773_2004_Article_496715_TeX2GIFIE1.gif" alt=" $$B = a\frac{1}{{f(N)}}$$ " align="middle" border="0"> of f-oscillators, is obtained and its completeness is investigated. An alternative method to construct them is proposed. We introduce a new kind of higher-order squeezing and sub-Poissonian distribution. The quantum statistical properties of the k states are studied. The result shows that all of the eigenstates can be generated by a linear superposition of k Roy-type nonlinear coherent states. These states may form a complete Hilbert space, and the M-th order [M = (n + 1/2)k; n = 0,1, ...] squeezing effects exist in all of the k states when k is even. There is the sub-Poissonian distribution in all of the states.     

Measurement of the G asymmetry for the γp↦Nπ channels in the Δ(1232) resonance region

The G asymmetry of the γp↦N`0; reaction has been measured for the first time for E<sub>γ</sub> = 340±14 MeV. This observable, for which very scarce published data exist, plays an important role to disentangle the contributions of the various nucleon resonances. The experiment, performed at the Mainz microtron MAMI, used a 4`0;-detector system, a linearly polarized, tagged photon beam, and a longitudinally polarized proton target.