Apparent molar heat capacities and volumes of electrolytes and ions int-butanol-water mixtures

The apparent molar volumes V and heat capacities C _p, of NaCl, LiCl, NaF, KI, NaBPh₄ and Ph₄PCl have been determined in solutions of H₂O containing up to 40 mass% t-butyl alcohol (TBA) by flow densitometry and flow microcalorimetry. Combination of these results with literature data allows calculation of V and C _p, for 16 ions in these mixtures using the assumption that _tX(Ph₄P⁺) = _tX(BPh ₄ ^– ) where X=V or C _p and _tX is the change in X for a species on transfer from H₂O to TBA-H₂O mixtures. These are the first reported single ion values for C _p, in a mixed solvent. While whole electrolyte volumes and heat capacities show relatively smooth changes with solvent composition, _tX(ion) exhibit two well-developed extrema at around 10 and 25 mass% TBA. The shape of the _tX(ion) curves shows considerable uniformity among the alkali metal cations and the halide ions but the extrema become more pronounced with increasing size among the tetraalkylammonium ions. These extrema are analogous to those observed in aqueous organic mixtures of surfactants and are probably indicative of microphase transitions in these strongly interacting solvent mixtures.     

XTR-Kurosawa-Desmedt Scheme

This paper proposes an XTR version of the Kurosawa-Desmedt scheme. Our scheme is secure against adaptive chosen-ciphertext attack under the XTR version of the Decisional Diffie-Hellman assumption in the standard model. Comparing efficiency between the Kurosawa-Desmedt scheme and the proposed XTR-Kurosawa-Desmedt scheme, we find that the proposed scheme is more efficient than the Kurosawa-Desmedt scheme both in communication and computation without compromising security.     

On the generic properties of convex optimization problems in conic form

We prove that strict complementarity, primal and dual nondegeneracy of optimal solutions of convex optimization problems in conic form are generic properties. In this paper, we say generic to mean that the set of data possessing the desired property (or properties) has strictly larger Hausdorff dimension than the set of data that does not. Our proof is elementary and it employs an important result due to Larman [7] on the boundary structure of convex bodies. Received: September 1997 / Accepted: May 2000?Published online November 17, 2000     

A fair sampling test for EPR-Bell experiments

The low efficiency of detectors in all EPR experiments with optical photons makes the use of the fair sampling assumption unavoidable. This assumption is reputed to be both reasonable and impossible to test experimentally. We argue that there is, in fact, little evidence supporting the fair sampling assumption, and we propose an experiment capable of putting this crucial hypothesis to a test.     

一类三元共聚反应的拟二元化处理方法和简单稳态假定下的三元共聚的可拟二元化特性

对一类两种主单体比例保持恒定,微量或少量第三单体参与的改性三元共聚体系,采用了将两种主单体视为一种单体,微(少)量第三单体与此"主单体"进行拟二元共聚的处理方式,分别用动力学概念推导法和从三元共聚简易组成式直接导出法,推得拟二元共聚等效竞聚率计算式,两种方法所得结果一致.对文献报道的一些三元共聚实例进行了计算,证实了本...     

On the local representation of piecewise smooth equations as a Lipschitz manifold

We study systems of equations, F(x)=0$F(x)=0$, given by piecewise differentiable functions F:Rⁿ→R^k$F:{\mathbb{R}}^n\to {\mathbb{R}}^k$, k?n$k?n$. The focus is on the representability of the solution set locally as an (n−k)$(n-k)$-dimensional Lipschitz manifold. For that, nonsmooth versions of inverse function theorems are applied. It turns out that their applicability depends on the choice of a particular basis. To overcome this obstacle we introduce a strong full-rank assumption (SFRA) in terms of Clarke?s generalized Jacobians. The SFRA claims the existence of a basis in which Clarke?s inverse function theorem can be applied. Aiming at a characterization of SFRA, we consider also a full-rank assumption (FRA). The FRA insures the full rank of all matrices from the Clarke?s generalized Jacobian. The article is devoted to the conjectured equivalence of SFRA and FRA. For min-type functions, we give reformulations of SFRA and FRA using orthogonal projections, basis enlargements, cross products, dual variables, as well as via exponentially many convex cones. The equivalence of SFRA and FRA is shown to be true for min-type functions in the new case k=3$k=3$.     

Solvability of the boundary-value problem for a variable-order differential equation on a geometric graph

The solvability of the boundary-value problem for a string-beam model is studied. The model is described by an equation of orders 2 or 4 on dirrerent edges of an arbitrary graph. Criteria for the problem to be degenerate and nondegenerate are obtained; in particular, it is proved that the nondegeneracy of the problem is equivalent to the maximum principle.     

Nondegeneracy of Polyhedra and Linear Programs

This paper deals with nondegeneracy of polyhedra andlinear programming (LP) problems. We allow for the possibilitythat the polyhedra and the feasible polyhedra of the LPproblems under consideration be non-pointed.(A polyhedron is pointed if it has a vertex.) With respect to a given polyhedron, we consider two notions ofnondegeneracy and then provide several equivalent characterizationsfor each of them. With respect to LP problems, we study thenotion of constant cost nondegeneracy first introduced byTsuchiya [25] under a different name, namelydual nondegeneracy. (We do not follow this terminology sincethe term dual nondegeneracy is already used to refer to a relatedbut different type of nondegeneracy.) We show two main results about constant cost nondegeneracy of an LP problem.The first one shows that constant cost nondegeneracy of an LPproblem is equivalent to the condition that the union of all minimal faces of the feasible polyhedron be equal to the set of feasible points satisfying a certain generalized strict complementarity condition.When the feasible polyhedron of an LP is nondegenerate,the second result showsthat constant cost nondegeneracy is equivalent to the conditionthat the set of feasible points satisfying the generalizedcondition be equal to the set of feasible points satisfyingthe same complementarity condition strictly.For the purpose of giving a preview of the paper,the above results specialized to the context of polyhedra and LP problems in standard form are described in the introduction.     

A Robust SQP Method for Mathematical Programs with Linear Complementarity Constraints

The relationship between the mathematical program with linear complementarity constraints (MPLCC) and its inequality relaxation is studied. Based on this relationship, a new sequential quadratic programming (SQP) method is presented for solving the MPLCC. A certain SQP technique is introduced to deal with the possible infeasibility of quadratic programming subproblems. Global convergence results are derived without assuming the linear independence constraint qualification for MPEC, the nondegeneracy condition, and any feasibility condition of the quadratic programming subproblems. Preliminary numerical results are reported. Research is partially supported by Singapore-MIT Alliance and School of Business, National University of Singapore.     

空间均匀Boltzmann方程的唯一性

本文讨论空间均匀的Boltzmann方程的唯一性.当碰撞核满足Grad假设且对某s>2初始值f0∈Ls1(R3) ∩L1logL1时,我们证明了该方程守恒解是唯一的.