A System of Reaction-Diffusion Equations in the Unstirred Chemostat With an Inhibitor

1 Introduction This paper is concerned with competition of two organisms in an un-stirred chemostat-typesystem in the presence of an inhibitor. The basic assumption is that the inhibitor is from anexternal source and is lethal to one competitor but not to the other competitor which can takeit up harmlessly. The pioneering work in this direction is that of Lenski and Hattingh. Theyconsidered the effect of the inhibitor on populations of the two organisms in a "well-stirred" bio-     

THE BROADCAST FUNCTION VALUE B(23) IS 33 OR 34

1. IntroductionLet G be a connected network of order n. Broadcasting is the process of distributinginformation from an originator to all other nodes of a communication network. The problemaddressed in this paper is under the assumption that only one piece information is to bedistributed, each communication involves exactly two adjacent nodes and takes one unit oftime, and no node is involved into two or more simultaneous communications. Given a nodex as originator, we define the broadcast tim…     

Modeling and targeting an essential metabolic pathway of Plasmodium falciparum in apicoplast using Petri nets

Petri net(PN) is one of the promising computational and mathematical formalisms used to represent and study the behavior of complex metabolic networks. The various available analysis techniques of PN could be used to validate and analyze the network in different scenarios. Plasmodium falciparum is one of the threatening parasites which causes malaria, a deadly disease affecting a large number of today’s world population. The development of antimalarial drug resistance is an emerging global threat, highlighting the need to discover novel antimalarial targets. The fatty acid biosynthesis of malarial parasite is one of the essential metabolic pathways required for its growth and is present in apicoplast, a non-photosynthetic plastid. The malarial parasite obtains fatty acids by using type two fatty acid synthase(FAS II) enzyme,which is different from type one enzyme used by human host, making it an ideal drug target.This article proposes and studies the PN model of the parasite’s FAS II pathway to analyze the mechanism of potential drug targets in this pathway. The proposed PN model can serve as a base for further findings in the field of antimalarial drug targets to decrease the malaria mortality rate.     

A variational inequality arising from European option pricing with transaction costs

In this paper we present a method which can transform a variational inequality with gradient constraints into a usual two obstacles problem in one dimensional case.The prototype of the problem is a parabolic variational inequality with the constraints of two first order differential inequalities arising from a two-dimensional model of European call option pricing with transaction costs.We obtain the monotonicity and smoothness of two free boundaries.     

Steiner Minimal Trees in Rectilinear and Octilinear Planes

This paper considers the Steiner Minimal Tree （SMT） problem in the rectilinear and octilinear planes. The study is motivated by the physical design of VLSI： The rectilinear case corresponds to the currently used M-architecture, which uses either horizontal or vertical routing, while the octilinear case corresponds to a new routing technique, X-architecture, that is based on the pervasive use of diagonal directions. The experimental studies show that the X-architecture demonstrates a length reduction of more than 10-20%. In this paper, we make a theoretical study on the lengths of SMTs in these two planes. Our mathematical analysis confirms that the length reduction is significant as the previous experimental studies claimed, but the reduction for three points is not as significant as for two points. We also obtain the lower and upper bounds on the expected lengths of SMTs in these two planes for arbitrary number of points.     

A new two-part test based on density ratio model for zero-inflated continuous distributions

In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a χ~2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.     

LINEAR SEARCH FOR A BROWNIAN TARGET MOTION

A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point.The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite,and to show the existence of a search plan which made this expected value minimum.     

Bifurcation of limit cycles in small perturbations of a hyper-elliptic Hamiltonian system with two nilpotent saddles

In this paper we study the first-order Melnikov function for a planar near-Hamiltonian system near a heteroclinic loop connecting two nilpotent saddles. The asymptotic expansion of this Melnikov function and formulas for the first seven coefficients are given. Next, we consider the bifurcation of limit cycles in a class of hyper-elliptic Hamiltonian systems which has a heteroclinic loop connecting two nilpotent saddles. It is shown that this system can undergo a degenerate Hopf bifurcation and Poincarè bifurcation, which emerges at most four limit cycles in the plane for sufficiently small positive ε. The number of limit cycles which appear near the heteroclinic loop is discussed by using the asymptotic expansion of the first-order Melnikov function. Further more we give all possible distribution of limit cycles bifurcated from the period annulus.     

Scale and time effects on mathematical models for transport in the environment

The purpose of this paper is to analyse mathematical models used in environmental modelling.Following a brief survey of the development in modelling scale-and time-dependent dispersion processes in the environment,this paper compares three similarity solutions,one of which is a solution of the generalized Feller equation(GF)with fractal parameters,and the other two for the newly-developed generalized Fokker-Planck equation(GFP).The three solutions are derived with parameters having physical significance.Data from field experiments are used to verify the solutions.The analyses indicate that the solutions of both GF and GFP represent the physically meaningful natural processes,and simulate the realistic shapes of tracer breakthrough curves.     

LOCAL CLASSICAL SOLUTION OF FREE BOUNDARY PROBLEM FOR A COUPLED SYSTEM

This paper considers a two-phase free boundary problem for coupled system including one parabolic equation and two elliptic equations. The problem comes from the discussion of a growth model of self-lnaintaining protocell in multidimensional case. The local classical solution of the problem with free boundary F : y = g(x,t) between two domains is being seeked. The local existence and uniqueness of the problem will be proved in multidimensional case.     

The Validity of the Multifractal Formalism: Results and Examples

By obtaining a new sufficient condition for a valid multifractal formalism, we improve in this paper a result developed by L. Olsen (1995, Adv. Math.116, 82-196). In particular, we describe a large class of measures satisfying the multifractal formalism and for which the construction of Gibbs measures is not possible. Some of these measures are not unidimensional but have a nontrivial multifractal spectrum, giving a negative answer to a question asked by S. J. Taylor (1995, J. Fourier Anal. Appl., special issue). We also describe a necessary condition of validity for the formalism which is very close to the sufficient one. This necessary condition allows us to describe a measure μ for which the multifractal packing dimension function B_μ(q) is a nontrivial real analytic function but the multifractal formalism is nowhere satisfied. This example gives also a solution to a problem posed by Taylor (cited above).     

广义度量方程的改进及其应用(I)

众所周知, 度量方程作为距离几何的基本内容和工具之一,在几何约束求解中扮演着主要的角色.改进了杨定华关于$n$维欧氏空间中两个等数量有限基本元素构成集合的广义度量方程, 建立了更为一般意义的、应用方便的广义度量方程,作为其初步应用,导出了两个单形之间的一些有趣的矩阵恒等式关系.特别地,将其两边取行列式,可以简洁得到关于联系两个单形的几何恒等式.     

Cotorsion Dimension of Unbounded Complexes

We extend the cotorsion dimension of R-modules to unbounded R-complexes by applying the flat model structure on Ch(R) proposed by J. Gillespie. This is not natural because there has been no sufficiently general result available for the existence of proper “cotorsion” resolutions of unbounded complexes, for which one would be able to define the derived functors. The global cotorsion dimension of ring is discussed in our present framework, and the relations between it and other dimensions are investigated as well. Some rings are characterized and some known results are extended.     

A weighted least squaes study of robustness in interior point linear programming

This paper studies the robustness of interior point linear programming algorthims with respect to initial iterates that are too close to the boundary. Weighted least squares analysis is used in studying the near-boundary behavior of the affine scaling and Newton centering directions, which are often combined by interior point methods. This analysis leads to the develoment of a modified Newton centering direction exhibiting better near-boundary behavior than the two directions. Theoretical and computational results from the NETLIB test set are presented indicating that an approach which uses the modified newton direction is more robust than both the pure affine scaling approach and one which uses the Newton direction as the centering direction.     

Canonical maps to twisted rings

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring , which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent interest. D. Rogalski was partially supported by NSF grant DMS-0202479. J. J. Zhang was partially supported by NSF grant DMS-0245420 and Leverhulme Research Interchange Grant F/00158/X (UK).     

Conditions at infinity for boltzmann's equation.

We consider here realistic conditions at infinity for solutions of the Boltzmann's equation, such as a pure Maxwellian equilibrium at infinity possibly with suitable boundary conditions on an exterior domain, different Maxwellian equilibria at +∞ and -;∞ in a tube-like situation and more generally conditions at infinity obtained from a fixed solution. In order to adapt the recent global existence and compactness results due to R.J. DiPerna and the author, we have to obtain some local a priori estimates on the mass, kinetic energy and entropy. And this is precisely what we achieve here by two different and new methods. The first one consists in using the relative entropy of solutions with respect to a fixed, possibly local, Maxwellian. This method allows to treat general collision kernels with angular cut-off and some of the conditions at infinity mentioned above. The second method is based upon a L¹ estimate and an extension of the entropy identity which uses a truncated H-functional. This method requires a “uniform integrability” condition on the collision kernel but allows to consider the most general conditions at infinity.     

企业战略对并购行为的影响和潜在机制

为探究企业战略风险度和偏离度对并购行为的影响,本文以沪深A股2010~2017为样本数据,基于Logit和Possion模型对企业战略与并购行为的影响机制进行实证检验。结果显示:企业战略风险度与并购行为显著正相关,表明企业战略越是风险偏好型的企业,其并购倾向越高,并购次数越多;企业战略偏离度与并购行为显著负相关,表明企业战略越是偏离同行常规战略的企业,其并购倾向越低,并购次数越少。进一步研究表明,完善的内部控制、较高的薪酬激励和聘请稳健的高管能够有效约束由企业战略引起的过度并购和并购不足行为,促进并购行为合理化。本文基于企业战略视角研究并购倾向和并购次数,有助于理解并购行为形成的内在机制,同时,对上市公司并购行为的治理和风险管控亦提供了新的线索和证据。     

Gorenstein代数上的Hopf代数作用

令H是有限维Hopf代数，A是左H-模代数。本文证明了A是Gorenstein代数的充分必要条件。A^H也是Gorenstein代数的条件。它是Enochs EE,GarciaJJ和del RioA关于群作用相应的理论的推广，同时给出A/A^H是Frobenius扩张的条件。     

Injective dimension of Weyl algebras over affine coefficient rings

The concern of this paper is to derive formulas for the injective dimension of then- th Weyl algebraA _n (R) in casek is a field of characteristic zero andR is a commutative affinek-algebra of finite injective dimension. For the casen=1 we prove a more general result from which the above result follows. Such formulas can be viewed as generalizations of the corresponding results given by J. C. McConnell in the caseR has finite global dimension.Project supported in part by the National Natural Science Foundation for Youth