Noise in a Small Genetic Circuit that Undergoes Bifurcation

Based on the consideration of Boolean dynamics, it has been hypothesized that cell types may correspond to alternative attractors of a gene regulatory network. Recent stochastic Boolean network analysis, however, raised the important question concerning the stability of such attractors. In this paper a detailed numerical analysis is performed within the framework of Langevin dynamics. While the present results confirm that the noise is indeed an important dynamical element, the cell type as represented by attractors can still be a viable hypothesis. It is found that the stability of an attractor depends on the strength of noise related to the distance of the system to the bifurcation point and it can be exponentially stable depending on biological parameters.     

Numerical Approximation of the Spectra of Phan-Thien Tanner Liquids

The linear stability of the linear Phan-Thien Tanner (PTT) fluid model is investigated for plane Poiseuille flow. The PTT model involves parameters that can be used to fit shear and extensional data, which makes it suitable for describing both polymer solutions and melts. The base flow is determined using a Chebyshev-tau method. The linear stability equations are also discretized using Chebyshev approximations to furnish a generalized eigenvalue problem. The spectrum is shown to comprise a continuous part and a discrete part. The theoretical and numerical results are validated for the UCM and Oldroyd-B models, which are special cases of the PTT model, by comparing with results in the literature. It is demonstrated that the linear PTT fluid is stable to infinitesimal disturbances with respect to the range of shear-thinning, extensional and elasticity parameters considered. The computational efficiency and accuracy of the numerical method are also investigated.     

Factors affecting the demand for softwood lumber in the united states

This study sets out to examine whether the demand for softwood lumber in the United States is responsive to various market factors including the price of softwood lumber, the price of other building materials, and the level of economic activity (e.g. housing starts). Concern in the analysis is focused on overcoming some of the methodological shortcomings found in previous studies of this issue. The results are conclusive. The quantity of softwood lumber demanded does respond to the various economic factors considered. Moreover, when the structural stability of the estimated relationships is investigated, the results suggest that the demand for softwood lumber regionally in the United States has remained unaltered over the sample period (1950–1985).     

Epidemic dynamics in a heterogeneous incompletely isolated population with allowance for seasonal variations in the infection rate

Mathematical parasite-host models are generalized to the case when the population members differ in susceptibility and contagiousness, there is an external source of infection, and the model parameters depend periodically (seasonally) on time. The model is proved to have a periodic solution that is unique and exponentially stable for sufficiently small periodic oscillations of the coefficients.     

Stability of some low‐order approximations for the Stokes problem

Two‐level low‐order finite element approximations are considered for the inhomogeneous Stokes equations. The elements introduced are attractive because of their simplicity and computational efficiency. In this paper, the stability of a Q₁(h)–Q₁(2h) approximation is analysed for general geometries. Using the macroelement technique, we prove the stability condition for both two‐ and three‐dimensional problems. As a result, optimal rates of convergence are found for the velocity and pressure approximations. Numerical results for three test problems are presented. We observe that for the computed examples, the accuracy of the two‐level bilinear approximation is compared favourably with some standard finite elements. Copyright © 2007 John Wiley & Sons, Ltd.     

STABILITY OF DELAY DIFFERENTIAL SYSTEMS BY SEVERAL LIAPUNOV FUNCTIONS

1 IntroductionConsider the functional differential equations (FDE's) with finite delay ofthe form:where x,(0) = x(t 0) for --r 5 0 5 0 with some r 2 0 and f: [T, co] x C RI with C = C([--r, 0], R') the space of continuous functions mapping [--r, 0]into l-dimensional real space RI. For any yi E C we define the norm of yi as:where l' I is any norm in RI.Inspired by the ideas in [l--3], we develop a new technique in this work tostudy the stability of FDE's, where the components xl) xZt…     

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通过对拉压杆概念的回顾以及出现在教科书中几个实例的分析，一方面 说明规范化载荷平衡分析的必要性，另一方面展示杆件分析类型的标准与意义.     

Problem of determining the nonstationary potential in a hyperbolic-type equation

We solve the problem of determining the hyperbolic equation coefficient depending on two variables. Some additional information is given by the trace of the direct problem solution on the hyperplane x = 0. We estimate the stability of the solution of the inverse problem under study and prove the uniqueness theorem. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 2, pp. 220–225, August, 2008.     

Combining atom‐transfer radical polymerization and ring‐opening polymerization through bifunctional initiators derived from hydroxy benzyl alcohol—Preparation and characterization of initiators,macroinitiators, and block copolymers

A simple, one‐step procedure has been developed for the preparation of bifunctional initiators capable of polymerizing monomers suitable for atom‐transfer radical polymerization (ATRP) and ring‐opening polymerization (ROP). These bifunctional initiators were employed for making narrow disperse poly(styrene) macroinitiators, which were subsequently used for the ROP of various lactides to yield poly(styrene‐block‐lactide) copolymers. Thermogravimetric analysis (TGA) of these block copolymers are interesting in that it shows a two‐step degradation curve with the first step corresponding to the degradation of poly(lactide) segment and the second step associated with the poly(styrene) segment of the block copolymer. This nature of the block copolymer makes it possible to estimate the block copolymer content by TGA in addition to the ¹H NMR spectroscopic analysis. Thus, this study for the first time highlights the possibility of making porous materials by thermal means which are otherwise obtained by base hydrolysis. The bifunctional initiators were prepared by the esterification of 3‐hydroxy, 4‐hydroxy, and 3,5‐dihydroxy benzyl alcohols with α‐bromoisobutyryl bromide and 2‐bromobutyryl bromide. A mixture of products was obtained, which were purified by column chromatography. The esterified benzyl alcohols were employed in the polymerization of styrene under copper (Cu)‐catalyzed ATRP conditions to yield macroinitiators with low polydispersity. These macroinitiators were subsequently used in the ROP of L ‐, DL ‐, and mixture of lactides. The formation of block copolymers was confirmed by gel permeation chromatography (GPC), spectroscopic and thermal characterizations. The molecular weight of the block copolymers was always higher than the macroinitiator, and the GPC chromatogram was symmetrical indicating the uniform initiation of ROP by the macroinitiators. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 102–116, 2008     

A Reader's Guide to Gacs's “Positive Rates” Paper

Peter Gacs's monograph, which follows this article, provides a counterexample to the important Positive Rates Conjecture. This conjecture, which arose in the late 1960's, was based on very plausible arguments, some of which come from statistical mechanics. During the long gestation period of the Gacs example, there has been a great deal of skepticism about the validity of his work. The construction and verification of Gacs's counterexample are unavoidably complex, and as a consequence, his paper is quite lengthy. But because of the novelty of the techniques and the significance of the result, his work deserves to become widely known. This reader's guide is intended both as a cheap substitute for reading the whole thing, as well as a warm-up for those who want to plumb its depths.