Shadowing in a neighborhood of a separatrix

We consider a model example of a diffeomorphism of a two-dimensional manifold with two hyperbolic fixed points joined by a separatrix. We show that, in a tubular neighborhood of the separatrix, every pseudotrajectory satisfying an additional error smallness condition is shadowed by an exact trajectory.     

On a mapping of a projective space into a sphere

We obtain an exact estimate for the minimum multiplicity of a continuous finite-to-one mapping of a projective space into a sphere for all dimensions. For finite-to-one mappings of a projective space into a Euclidean space, we obtain an exact estimate for this multiplicity for n = 2, 3. For n ≥ 4, we prove that this estimate does not exceed 4. Several open questions are formulated.     

Equivalence of a Scalar and a Vector Equilibrium Problem for a Pair of Functions Forming a Nikishin System

Mathematical Notes - We prove the equivalence of a vector and a scalar equilibrium problem that naturally arise when studying the limit distribution of zeros of type I Hermite–Padé...     

Two equivalent definitions of a congruence on a finitary model in a quasivariety

LetL be a finitary language and letK be a subcategory of the category of allL-models andL-morphisms. For aK-objectA we consider two definitions of aK-congruence relation onA: that given by Rosenberg and Sturm [2], and that given by Adámek [1]. Both definitions are external definitions in the sense that they depend on the otherK-objects. IfK is a full subcategory, such that theK-objects form a quasivariety, then it is shown that the definitions ofK-congruence are equivalent and a purely internal characterisation is given.Presented by I. Rosenberg.I am indebted to Professor Teo Sturm as this paper originated from his seminar series on Algebraic Structures.     

Generalization of a theorem on the quasi-analyticity of a function

It is a known fact that if a function, together with all of its derivatives, vanishes at a point, then the function will be zero in a neighborhood of the point if its successive derivatives satisfy certain estimates. We show that even if the function does not have a priori all of its derivatives but is such that its first derivative has a special sequence of majorizing functions, then in this case also the function will be equal to zero. We use our results to obtain theorems concerning the uniqueness of the solution of an abstract Cauchy problem.     

Octahedral Projections of a Point onto a Polyhedron

In computational methods and mathematical modeling, it is often required to find vectors of a linear manifold or a polyhedron that are closest to a given point. The “closeness” can be understood in different ways. In particular, the distances generated by octahedral, Euclidean, and Hölder norms can be used. In these norms, weight coefficients can also be introduced and varied. This paper presents the results on the properties of a set of octahedral projections of the origin of coordinates onto a polyhedron. In particular, it is established that any Euclidean and Hölder projection can be obtained as an octahedral projection due to the choice of weights in the octahedral norm. It is proven that the set of octahedral projections of the origin of coordinates onto a polyhedron coincides with the set of Pareto-optimal solutions of the multicriterion problem of minimizing the absolute values of all components.     

Properties of a matrix with a very ill-conditioned eigenproblem

It is proved that a matrix that has a very ill-conditioned eigenvector matrix is close to one that has multiple eigenvalues, and an estimate of this distance is given, measured in the Euclidean matrix norm.     

The stability of the steady motion of a gyrostat with a liquid in a cavity

A symmetrical rigid body with a spherical base, carrying a rotor and having a cavity in the shape of an ellipsoid of revolution, completely filled with an ideal incompressible liquid in uniform vortex motion, is moving along an absolutely rough plane. It is shown that this system admits of an energy integral, Jellett's integral, the integral of constant vorticity and a geometric integral. The construction of a Lyapunov function as a linear combination of first integrals [1] yields the sufficient conditions for the rotation of the gyrostat about the vertically positioned axis of symmetry to be stable. The conditions for the gyrostat's rotation to be unstable are found. It is shown that the rotor may prove to have either a stabilizing or destabilizing effect on the system and that the gyrostat admits of motions of the type of regular precession. The sufficient conditions for the stability of these motions are obtained.     

Excitation of a tube wave in a borehole by a slow wave propagating in a fluid layer

Conversion of a slow wave propagating in a fluid layer inside an elastic medium into a tube wave propagating in a borehole that intersects this layer is considered. It is shown that the total field of the latter wave consists of three summands of different physical nature. Seismograms of the slow and tube waves are presented. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 115–124. Translated by P. V. Krauklis.     

An analysis of the a priori and a posteriori

I present and defend a unified, non-reductive analysis of the a priori and a posteriori. It is a mistake to remove all epistemic conditions from the analysis of the a priori (as, for example, Alvin Goldman has recently suggested doing). We can keep epistemic conditions (like unrevisability) in the analysis as long as we insist that a priori and a posteriori justification admit of degrees. I recommend making the degree to which a belief’s justification is a priori or a posteriori solely dependent on the revisability relations that obtain among the faculties that deliver the belief and all other faculties.     

Eigenfrequencies of a tube bundle immersed in a fluid

In this paper we study a simplified version of a mathematical model that describes the eigenfrequencies and eigenmotions of a coupled system consisting of a set of tubes (or a tube bundle) immersed in an incompressible perfect fluid. The fluid is assumed to be contained in a rectangular cavity, and the tubes are assumed to be identical, and periodically distributed in the cavity. The mathematical model that governs this physical problem is an elliptic differential eigenvalue problem consisting of the Laplace equation with a nonlocal boundary condition on the holes, and a homogeneous Neumann boundary condition on the boundary of the cavity. In the simplified model that we study in this paper, the Neumann condition is replaced by a periodic boundary condition. Our goal in studying this simple version is to derive some basic properties of the problem that could serve as a guide to envisage similar properties for the original model. In practical situations, this kind of problem needs to be solved for tube bundles containing a very large number of tubes. Then the numerical analysis of these problems is in practice very expensive. Several approaches to overcome this difficulty have been proposed in the last years using homogenization techniques. Alternatively, we propose in this paper an approach that consists in obtaining an explicit decomposition of the problem into a finite family of subproblems, which can be easily solved numerically. Our study is based on a generalized notion of periodic function, and on a decomposition theorem for periodic functions that we introduce in the paper. Our results rely on the theory of almost periodic functions, and they provide a simple numerical method for obtaining approximations of all the eigenvalues of the problem for any number of tubes in the cavity. We also discuss a numerical example.     

On a matrix-based measure of the degree of coreness of a node in a network

The paper focuses on the right and left eigenvectors of a network matrix that belong to the largest eigenvalue. It is shown that each of vector entries measures the walk centrality of the corresponding node’s position in the network’s link structure and of the positions of the node’s adjacent nodes; as a result, it indicates to which degree the node can be associated with the structure’s core, i.e., the structural coreness of the node. The relationship between the vectors’ coordinates and the position of the nodes, as well as the actual computation of the coordinates, is based on an iterative computational scheme known as the power method. The paper studies the method’s convergence for networks of different structure. Some possible applications are discussed. The paper also includes a numerical example dealing with a real network of 197 nodes and 780 links.     

关于一个素数和一个素数的k次方和问题

设k≥2,且Hk表示一个正整数n的集合,使得该集合中的元素满足a+bk≡n(modq)对任意的q,在模q的既约剩余系中有解,令Dk(N)表示所有的n≤N,且n∈Hk且不能表成p1+p2k=n形式的整数.那么在GRH下, Dk(N)相似文献   

一个素数和一个素数的平方和问题

H表示一个正整数N的集合,使对任意的正整数q,同余方程a+b~2≡N(mod q)在模q的既约剩余系中有解a;b.E(x)表示N≤x,N∈H,但不能表成p_1+p_2~2=N的数的个数,其中p_1,p_2个表示素数,则E(x)<相似文献   

Resolution of a scheduling problem in a flowshop robotic cell

We develop in this paper a generic and precise identification of a scheduling problem in a flexible manufacturing system. We consider a flowshop robotic cell that processes several jobs. We assume that there is no intermediate buffer between machines. So, jobs may be blocked when downstream machines are busy. We present an integer programming model to determine the sequence of jobs that minimizes the makespan criterion. In order to solve large size problems, we propose a genetic algorithm (GA). Finally, computational experiments are proposed in order to compare the makespan returned by the GA to a lower bound.     

Phenomenological model of interaction of a plate with a flow

In the present paper, a finite-dimensional phenomenological model of unsteady interaction of a rigid plate with a flow is proposed. It is assumed that the plate performs translational motion across the flow. The internal dynamics of the flow is modeled by the attached second order dynamical system. It is shown that the model allows satisfactory agreement with experimental data. With the developed model an inverse problem of dynamics is examined for the situation where the plate performing uniform translational motion at some moment begins uniform deceleration and finally stops. It is shown that for sufficiently large values of the plate acceleration for some time range the flow does not resist the motion of the plate but “accelerates” it. It is shown also that the equations of motion in the context of the proposed model can be reduced to the integro-differential form, and comparison with the known model of S. M. Belotserkovsky is performed. The structural resemblance of the motion equations for a body in flow in both models is noted. The domain of applicability of the quasi-stationary model is examined. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 43–62, 2005.     

Global existence of a restoring force realizing a prescribed half-period

We consider an inverse problem to determine a nonlinearity of an autonomous differential equation so that each solution of the equation has a half-period that is a prescribed function of a half-amplitude of the solution. A global existence of the nonlinearity is proved under the assumption that the prescribed function is Lipschitz continuous. A reconstructive way of the nonlinearity is also given.     

The quasistatic motions of a three-body system on a plane

A controlled three-body system on a horizontal plane with dry friction is considered. The interaction forces between each pair of bodies are controls that are not subject to prior constraints but must be chosen in such a way that the motions of the system generated by them are quasistatic, that is, the total force acting on each of the bodies must be close to zero. All motions in which one body moves and the other two are fixed are found in the class of quasistatic motions. The problem of the optimal displacement of a moving body between two specified positions on a plane such that the absolute magnitude of the work of the friction forces along the trajectory is a minimum is solved. The quasistatic controllability of a three-body system is demonstrated and algorithms for bringing it into a specified position are discussed. The system considered simulates a mobile robot consisting of three bodies between which control forces act that can be realized by linear motors. The sizes of the bodies are assumed to be negligibly small compared with the distances between them so that the bodies are treated as particles.     

On a Γ-limit of a family of anisotropic singular perturbations

We construct an example confirming that the interfacial energy density of the Γ-limit of a family of nonconvex functionals, cannot be computed, in general, by assuming that the local behavior of a sequence of vector-valued minimizers near the interface is unidirectional.     

Interaction of a granular flow with a rectangular obstacle

In this work we studied the cluster formation of particles flowing between two parallel plates hitting a rectangular obstacle. After a short time a cluster is formed on top of the obstacle. Quantification of the cluster formation, shows that the number of clusters decrease with time, whereas the mean and maximum cluster size grow during the simulation. Our results indicate that for the development of clusters the value of the restitution coefficient for particle–particle collisions is most important parameter for this formation process. We found that changes in the value of the restitution parameters for particle–obstacle and particle–wall did not show significant changes in the cluster development.