Global Solution of Optimization Problems with Parameter-Embedded Linear Dynamic Systems

This paper develops a theory for the global solution of nonconvex optimization problems with parameter-embedded linear dynamic systems. A quite general problem formulation is introduced and a solution is shown to exists. A convexity theory for integrals is then developed to construct convex relaxations for utilization in a branch-and-bound framework to calculate a global minimum. Interval analysis is employed to generate bounds on the state variables implied by the bounds on the embedded parameters. These bounds, along with basic integration theory, are used to prove convergence of the branch-and-bound algorithm to the global minimum of the optimization problem. The implementation of the algorithm is then considered and several numerical case studies are examined thoroughly     

Exploring Little Higgs models with ATLAS at the LHC-

The European Physical Journal C - We discuss possible searches for the new particles predicted by Little Higgs Models at the LHC. By using a simulation of the ATLAS detector, we demonstrate how the...     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

Effects of Polymer Bridging and Electrostatics on the Rheological Behavior of Aqueous Colloidal Dispersions†

Effects of a low molecular weight physically adsorbed polyethylene oxide (PEO) and the range of the electrostatic repulsion on the rheological behavior of silica dispersions (as a model system) has been investigated. Particular attention is given to the evolution of the rheological behavior with increasing the polymer concentration in the system and also effectiveness of the polymer as a dispersant under extreme conditions (high ionic strength). Results indicate that at small separation distances and low polymer coverage, the polymer chains are long enough to adsorb on the surface of two particles simultaneously causing bridging flocculation in the system and hence increasing the viscosity and linear viscoelastic functions of the dispersion. A significant increase was observed in the viscosity of the dispersion at salt concentrations high enough to eliminate electrostatics between the particles. Under these conditions,the viscosity of the system increased significantly when PEO was added to the dispersion showing that at high electrolyte concentrations, a neutral polymer such as PEO is not able to stabilize the system.     

Solving of second order nonlinear PDE problems by using artificial controls with controlled error

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region inR ². We transfer this problem to a new problem of second order nonlinear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error inL ₁ is controlled.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics

We present a short survey on the biological modeling, dynamics analysis, and numerical simulation of nonlocal spatial effects, induced by time delays, in diffusion models for a single species confined to either a finite or an infinite domain. The nonlocality, a weighted average in space, arises when account is taken of the fact that individuals have been at different points in space at previous times. We discuss and compare two existing approaches to correctly derive the spatial averaging kernels, and we summarize some of the recent developments in both qualitative and numerical analysis of the nonlinear dynamics, including the existence, uniqueness (up to a translation), and stability of traveling wave fronts and periodic spatio-temporal patterns of the model equations in unbounded domains and the linear stability, boundedness, global convergence of solutions and bifurcations of the model equations in finite domains.     

On p-Extensions of Fields of Characteristic p

It is proved that a Galois extension of a field of characteristic p is completely determined by its Galois group and the endomorphism of the additive group of the group algebra that corresponds to the raising to the power p.