Protonation equilibria in aqueous solutions of the hydrolysed copolymer of maleic anhydride with cyclopentene

The thermodynamics of proton dissociation of the hydrolysed 1:1 copolymer of maleic anhydride with cyclopentene in aqueous solution has been investigated. Potentiometric, microcalorimetric and dilatometric measurements on the copolymer solutions indicate that the two acidic functions are quite strong and not very different. Relatively poor solvation of vicinal carboxyl groups could account for the behaviour of the copolymer; it could stem from steric hindrances imposed by the cyclopentene residues.     

On the optimal controls of a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions

Summary In this paper we consider the question of existence of optimal controls for a class of systems governed by second order parabolic partial delay-differential equations with first boundary conditions and with controls appearing in the coefficients. In Theorems2.2 and2.3 we present existence and uniqueness of solutions of the first boundary problems. In Theorems3.1 and3.2 we prove that whenever the coefficients of the system converge in the w*-topology (L¹ topology on L^∞) the corresponding solutions converge weakly in an appropriate Sobolev space. Using these basic results we present two theorems (Theorems4.1 and4.2) on the existence of optimal controls. Entrata in Redazione il 21 gennaio 1978.     

Cycles with a chord are graceful

In this paper, we prove that every cycle plus a chord is graceful, thus answering a conjecture of R. Bodendiek, H. Schumacher, and H. Wegner.     

A fast Fourier transform on multipoles (FFTM) algorithm for solving Helmholtz equation in acoustics analysis

This article presents a fast algorithm for the efficient solution of the Helmholtz equation. The method is based on the translation theory of the multipole expansions. Here, the speedup comes from the convolution nature of the translation operators, which can be evaluated rapidly using fast Fourier transform algorithms. Also, the computations of the translation operators are accelerated by using the recursive formulas developed recently by Gumerov and Duraiswami [SIAM J. Sci. Comput. 25, 1344-1381(2003)]. It is demonstrated that the algorithm can produce good accuracy with a relatively low order of expansion. Efficiency analyses of the algorithm reveal that it has computational complexities of O(Na), where a ranges from 1.05 to 1.24. However, this method requires substantially more memory to store the translation operators as compared to the fast multipole method. Hence, despite its simplicity in implementation, this memory requirement issue may limit the application of this algorithm to solving very large-scale problems.     

Multivariate Polynomial Minimization and Its Application in Signal Processing

We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n ^r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2^r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open.     

Product measurements and fully symmetric measurements in qubit-pair tomography: A numerical study

State tomography on qubit pairs is routinely carried out by measuring the two qubits separately, while one expects a higher efficiency from tomography with highly symmetric joint measurements of both qubits. Our numerical study of simulated experiments does not support such expectations.     

New Generalized Second-Order Contingent Epiderivatives and Set-Valued Optimization Problems

In this paper, we introduce the concept of a generalized second-order composed contingent epiderivative for set-valued maps and discuss its relationship to the generalized second-order contingent epiderivative. We also investigate some of its properties. Then, by virtue of the generalized second-order composed contingent epiderivative, we establish a unified second-order sufficient and necessary optimality condition for set-valued optimization problems, which is a generalization of the corresponding results in the literature.     

GENERAL INFORMATION

In this note, we obtain a sufficient and necessary condition for a point to be a local minimizer of a continuous optimization problem with maximin constraints via the local minimizers of its transformed standard nonlinear optimization problem.