Minimum weight design of symmetrically stiffened orthotropic cylinders under axial compression

Minimum weight design of symmetrically stiffened orthotropic cylinders under axial compressio

Minimum weight design aspects of stiffened cylinders under compression

Survey on minimum weight design aspects of stiffened cylinders under compressio

Structural design synthesis approach to filamentary composites

Structural design methods for analysis of multilayer or laminated filamentary composite

The Natural Logarithm on Time Scales

We define an appropriate logarithm function on time scales and present its main properties. This gives answer to a question posed by M. Bohner in [J. Difference Equ. Appl. {\bf 11} (2005), no. 15, 1305--1306].Comment: 6 page

On approximate solutions of semilinear evolution equations

A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer from an approximate solution the existence of an exact solution. According to this theorem, the interval of existence of the exact solution and the distance of the latter from the approximate solution can be evaluated solving a one-dimensional "control" integral equation, where the unknown gives a bound on the previous distance as a function of time. For example, the control equation can be applied to the approximation methods based on the reduction of the evolution equation to finite-dimensional manifolds: among them, the Galerkin method is discussed in detail. To illustrate this framework, the nonlinear heat equation is considered. In this case the control equation is used to evaluate the error of the Galerkin approximation; depending on the initial datum, this approach either grants global existence of the solution or gives fairly accurate bounds on the blow up time.Comment: 33 pages, 10 figures. To appear in Rev. Math. Phys. (Shortened version; the proof of Prop. 3.4. has been simplified

The Effect of Indole-3-Acetic Acid (IAA) on the Activity Levels of Dehydrogenases in the Silkgland of Silkworm, Bombyx Mori L

The effect of indole-3-acetic acid (IAA) on the glucose-6-phosphate dehydrogenase (G-6-PDH),lactate dehydrogenase (LDH), glutamate dehydrogenase (GDH), iso-citrate dehydrogenase (ICDH), succinate dehydrogenase (SDH) and malate dehydrogenase (MDH) were studied The stimulation of G-6-PDH activity in the silk gland of experimental larva indicates increased oxidation of glucose resulting in higher levels of NADPH. Increased G-6-PDH activity in the present study suggests this as compensatory mechanism to maintain the structural complexity, functional integrity and metabolic centrality of the cells The activity of LDH, ICDH, MDH and SDH were increased in the silk gland of IAA treated larvae. The increased activity of the dehydrogenases may be attributed to increased turnover of aminoacids and oxidative metabolism in the silk gland. The activity level of GDH was increased in silk gland which indicates the increased oxidation of glutamate

A generalization of Ostrowski inequality on time scales for k points

In this paper we first generalize the Ostrowski inequality on time scales for k points and then unify corresponding continuous and discrete versions. We also point out some particular Ostrowski type inequalities on time scales as special cases.Comment: 10 page

Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set

A General Backwards Calculus of Variations via Duality

We prove Euler-Lagrange and natural boundary necessary optimality conditions for problems of the calculus of variations which are given by a composition of nabla integrals on an arbitrary time scale. As an application, we get optimality conditions for the product and the quotient of nabla variational functionals.Comment: Submitted to Optimization Letters 03-June-2010; revised 01-July-2010; accepted for publication 08-July-201

Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations

The aim of the paper is to present a nontrivial and natural extension of the comparison result and the monotone iterative procedure based on upper and lower solutions, which were recently established in (Wang et al. in Appl. Math. Lett. 25:1019-1024, 2012), to the case of any finite number of nonlinear fractional differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This article was financially supported by University of Łódź as a part of donation for the research activities aimed at the development of young scientists, grant no. 545/1117