Geometrical and Topological Properties of Real Polynomial Fibres

We establish a Gauss—Bonnet type formula for a smooth fibre of a nonproper real polynomial of ⁿ . For this we need to study topological properties of a generic hyperplane section of this fibre.     

Early Gravity-Wave Detection Experiments, 1960-1975

I discuss the experiments of Joseph Weber (1919-2000) of the University of Maryland between 1960 and 1973 that were aimed at the detection of gravity waves. He used throughout a quadratic detector to demodulate his antenna signal, which I analyze and compare to a linear detector.The latter was used by all of the other groups that entered the field. Of these, Richard Garwin and I at IBM were one of the first groups to publish, and I discuss in detail our experiments between 1973 and 1975. I then discuss the experiments that were carried out at Bell Labs-Rochester, Glasgow, Munich-Frascati,Moscow, and Tokyo. I compare the results, all of which were negative, with Webers claimed detection of large numbers of gravity-wave events, as many as seven per day. I conclude that these were not in fact gravity waves, but artifacts of his extremely hands-on data-analysis procedures, which I discuss in detail. Finally, I speculate on how this came about.     

Determination of mimosine by a sensitive indirect spectrophotometric method

A simple and sensitive indirect spectrophotometric method is described for the determination of mimosine based on its reaction with diazotized sulfanilamide (DZSAM). DZSAM couples with N-(1-naphthyl)ethylenediamine (NEDA) forming a pink colored azodye, absorbing maximally at 540 nm (ε_max=27 mM⁻¹ cm⁻¹). In the present method, mimosine was first reacted with known excess of DZSAM and the unreacted DZSAM was determined by coupling with NEDA. The reaction of mimosine with DZSAM proceeded optimally at neutral pH. The decrease in absorbance of the DZSAM-NEDA-coupled product obeyed Beer’s law in the concentration range of 0.005-0.15 μg ml⁻¹ of mimosine. The present method was applied to estimate mimosine in plant extracts containing lesser than 0.05 μg ml⁻¹ with recovery at 99±0.41%. The method described is superior to other reported methods in terms of ease of adaptability and sensitivity.     

On the existence of solutions of variational inequalities in Banach spaces

In this paper, we study the existence of the solution of the variational inequality 〈Tx−ξ,y−x〉?0 by applying the generalized projection operator , where B is a Banach space with dual space B∗ and by using the well-known FanKKM Theorem.     

Bell's Inequality for Two-Particle Mixed Spin States

We derive the Bell–Clauser–Horne–Shimony–Holt inequalities for two-particle mixed spin states both in the conventional quantum mechanics and in the hidden-variables theory. We consider two cases for the vectors , and specifying the axes onto which the particle spins of a correlated pair are projected. In the first case, all four vectors lie in the same plane, and in the second case, they are oriented arbitrarily. We compare the obtained inequalities and show that the difference between the predictions of the two theories is less for mixed states than for pure states. We find that the inequalities obtained in quantum mechanics and the hidden-variables theory coincide for some special states, in particular, for the mixed states formed by pure factorable states. We discuss the points of similarity and difference between the uncertainty relations and Bell's inequalities. We list all the states for which the right-hand side of the Bell–Clauser–Horne–Shimony–Holt inequality is identically equal to zero.     

Inequalities of Hadamard Type for r-Convex Functions in Carnot Groups

For a Carnot group G,we establish the relationship between extended mean values and r-convexfunctions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convexfunction on G.     

Stabilization and H{infty} control of two-dimensional Markovian jump systems

This paper extends the results obtained for one-dimensionalMarkovian jump systems, to investigate the problems of stochasticstabilization and H control of two-dimensional (2D) systemswith Markovian jump parameters. The mathematical model of 2Djump systems is established upon the well-known Roesser model,and sufficient conditions are obtained for the existence ofdesired controllers in terms of linear matrix inequalities,which can be readily solved by available numerical software.These obtained results are further extended to more generalcases whose system matrices also contain parameter uncertaintiesrepresented by either polytopic or norm-bounded approaches.A numerical example is provided to show the applicability ofthe proposed theories.     

Computing Eigenelements of Real Symmetric Matrices via Optimization

In certain circumstances, it is advantageous to use an optimization approach in order to solve the generalized eigenproblem, Ax = Bx, where A and B are real symmetric matrices and B is positive definite. In particular, this is the case when the matrices A and B are very large the computational cost, prohibitive, of solving, with high accuracy, systems of equations involving these matrices. Usually, the optimization approach involves optimizing the Rayleigh quotient.We first propose alternative objective functions to solve the (generalized) eigenproblem via (unconstrained) optimization, and we describe the variational properties of these functions.We then introduce some optimization algorithms (based on one of these formulations) designed to compute the largest eigenpair. According to preliminary numerical experiments, this work could lead the way to practical methods for computing the largest eigenpair of a (very) large symmetric matrix (pair).