Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies

This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of the equations of motion, viewing motion as a curve in an infinite-dimensional Banach manifold of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies, where the residual stresses result from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two-dimensional curved annulus embedded in a sphere.     

The Cross-Entropy Method for Combinatorial and Continuous Optimization

We present a new and fast method, called the cross-entropy method, for finding the optimal solution of combinatorial and continuous nonconvex optimization problems with convex bounded domains. To find the optimal solution we solve a sequence of simple auxiliary smooth optimization problems based on Kullback-Leibler cross-entropy, importance sampling, Markov chain and Boltzmann distribution. We use importance sampling as an important ingredient for adaptive adjustment of the temperature in the Boltzmann distribution and use Kullback-Leibler cross-entropy to find the optimal solution. In fact, we use the mode of a unimodal importance sampling distribution, like the mode of beta distribution, as an estimate of the optimal solution for continuous optimization and Markov chains approach for combinatorial optimization. In the later case we show almost surely convergence of our algorithm to the optimal solution. Supporting numerical results for both continuous and combinatorial optimization problems are given as well. Our empirical studies suggest that the cross-entropy method has polynomial in the size of the problem running time complexity.     

A Tutorial on the Cross-Entropy Method

The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning.     

On the initial-occupancy dependence of some luminescence phenomena under the one-trap-one-recombination-center (OTOR) model

We discuss the expected dependence of the maximum signal of a number of luminescence phenomena, used in dosimetry and archaeological and geological dating, on the initial occupancy of the relevant traps, n₀, within the OTOR (also called General One Trap (GOT)) model. This, in turn, has important bearing on the dose dependence of these phenomena. We discuss the dependence of the linearly-modulated optically-stimulated-luminescence (LM-OSL) as well as the non-linear optical stimulation (NL-OSL) on the initial concentration n₀ of trapped carriers. We also consider the behavior of CW-OSL and phosphorescence in a transformed form, as well as TL measured under hyperbolic and linear heating rates. Using an appropriate presentation, the maximum of the signal is seen to depend nearly linearly on n₀, which in many cases means nearly linear dependence on the dose, a property important for dosimetry and dating.     

A new look at the linear-modulated optically stimulated luminescence (LM-OSL) as a tool for dating and dosimetry

Optically stimulated luminescence (OSL) has been in use for dosimetry and dating in the last two decades. Since the OSL dependence on time is a featureless decaying function, a linear-modulation of the stimulating-light intensity has been suggested [Bulur, E., 1996. An alternative technique for optically stimulated luminescence. Radiat. Meas. 26, 701–709.], which resulted in a peak-shaped curve. The properties of this curve have been studied, assuming first-, second- and general-order kinetics. In a recent paper we have shown [Chen, R., Pagonis, V., 2008. A unified presentation of thermoluminescence (TL), phosphorescence and linear-modulated OSL (LM-OSL). J. Phys. D: Appl. Phys. 41, 035102 (1–6).] that for general-order curves, the peak maximum cannot be expected to depend linearly on the dose of excitation. A new presentation of the LM-OSL has been suggested, in which the peak maximum is linear with the filling of trapping states, which, in turn, may be expected to be linear with the dose under appropriate conditions. In the present work, we report on results of numerical simulation of the LM-OSL using the one trap-one recombination center (OTOR) model, dealing with the traffic of carriers between one trapping state, one kind of recombination center and the conduction and valence bands during excitation and read-out, and without making any simplifying assumptions. The process during optical read-out has been followed in the simulation that consisted of the numerical solution of the relevant sets of coupled differential equations, and also by analytical treatment. Sets of parameters leading to approximately first- and second-order kinetics, and to intermediate cases, have been used and the results presented in the original and the new ways are shown. The consequences concerning dating and dosimetry are discussed.     

Synthesis of Enantiomeric Aminoalkylcarbamoylphosphonates and Their Evaluation as Dual‐Action Anticancer MMP and Carbonic Anhydrase Inhibitors

Carbamoylphosphonates (CPOs) have recently been identified as extracellular in vivo active inhibitors of the cancer and metastasis‐promoting extracellular enzymes, carbonic anhydrases (CAs) IX and XII, and matrix metalloproteinase‐2 (MMP‐2). This article describes the stereoselective synthesis and the evaluation of the biological properties of a pair of enantiomeric aminoalkylcarbamoylphosphonates, which have been enantioselectively synthesized from l ‐serine, using functional group‐transformations. The structures of the enantiomeric products have been determined by X‐ray crystallography. The enantiomeric purities of compounds have been confirmed by chiral shift reagent NMR experiments and by circular dichroism. In vitro evaluation of the CPOs synthesized revealed that they possess micromolar IC₅₀ inhibitory action against CAIX and CAXII. The two enantiomers as well as the racemic or optically inactive ones do not differ by any significant extent from previously reported CPOs’ CA inhibitory values. On the other hand, MMPs inhibitory activities are rather weak; only MMP‐2 showed a notable IC₅₀ value.     

Using Homogeneous Weights for Approximating the Partial Cover Problem

In this paper we consider the natural generalizations of two fundamental problems, the Set-Cover problem and the Min-Knapsack problem. We are given a hypergraph, each vertex of which has a nonnegative weight, and each edge of which has a nonnegative length. For a given threshold , our objective is to find a subset of the vertices with minimum total cost, such that at least a length of of the edges is covered. This problem is called the partial set cover problem. We present an O(|V|² + |H|)-time, Δ_E-approximation algorithm for this problem, where Δ_E ≥ 2 is an upper bound on the edge cardinality of the hypergraph and |H| is the size of the hypergraph (i.e., the sum of all its edges cardinalities). The special case where Δ_E = 2 is called the partial vertex cover problem. For this problem a 2-approximation was previously known, however, the time complexity of our solution, i.e., O(|V|²), is a dramatic improvement.We show that if the weights are homogeneous (i.e., proportional to the potential coverage of the sets) then any minimal cover is a good approximation. Now, using the local-ratio technique, it is sufficient to repeatedly subtract a homogeneous weight function from the given weight function.     

Locally convex functions and the Schwarzian derivative

In this paper we study various classes of locally convex analytic functions in the unit disc, which are invariant under the group of M?bius automorphisms of the unit disc. Bounds for the Schwarzian derivative of functions in these classes are achieved and used to obtain estimates for the uniform hyperbolic radius of univalence in these classes.     

Analysis of wave fluctuation phenomena in random media in presence of a reflecting boundary

Modelling of wave propagation for modern high-frequency radio links must take into account the fluctuation phenomena caused by random changes of the medium's parameters. There are two factors that cause signals from transmitter to receiver to arrive via multiple random paths. The first is a result of scattering by boundaries and various obstacles, while the second is related to random changes in the refractive index of the medium. Similar phenomena are observed in underwater acoustic propagation. In this work the influence of both factors is demonstrated in a simple example when the propagation takes place above a perfectly reflecting surface in the presence of a randomly fluctuating medium.     

The Geometry of Cauchy's Fluxes

A formulation of the Cauchy theory for balance laws of scalar valued quantities is considered from a general geometric point of view. It is assumed only that the ambient space is an orientable m-dimensional manifold. The analog of the usual flux vector field is an (m−1)-differential form. Both the Cauchy theorem and differential version of the balance laws are formulated in this context. Accepted December 9, 1999?Published online July 12, 2000