Integral properties of flows satisfying mixed no-slip and no-shear conditions

Summary Total momentum flux considerations lead simply to integral properties of five examples of viscous flows satisfying mixed no-slip and no-shear conditions. The integral results may be inferred from the velocity distributions at the slots only. This simplicity of integral properties holds for a wider class of flows subject to mixed conditions: the no-shear slots may be distributed irregularly and may occur in two separate surfaces (parallel plates or concentric tubes). It carries over also to analogous slow flows with arbitrary distributions of no-shear patches in the boundaries. The work yields a number of definite integrals.

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Zusammenfassung Betrachtung des Gesamt-Impulses gibt Integral-Eigenschaften von zähen Strömungen an fünf Beispielen mit gemischten Randbedingungen (Haften und Gleiten). Die Integrale können von der Geschwindigkeitsverteilung an den Schlitzen allein (Gleiten) abgeleitet werden. Diese einfachen Integral-Eigenschaften gelten für eine weite Klasse von Strömungen mit gemischten Randbedingungen; die Schlitze können beliebig verteilt sein und sich auf verschiedenen Flächen befinden. Resultate können auf langsame Strömungen mit beliebigen Schlitzen der Begrenzung übertragen werden. Die Verallgemeinerung zur Strömung zwischen konzentrischen Rohren mit einem oder mehreren Längs-Schlitzen wird angegeben.

     

Interpolation by splines satisfying mixed boundary conditions

We consider interpolation of Hermite data by splines of degreen withk given knots, satisfying boundary conditions which may involve derivatives at both end points (e.g., a periodicity condition). It is shown that, for a certain class of boundary conditions, a necessary and sufficient condition for the existence of a unique solution is that the data points and knots interlace properly and that there does not exist a polynomial solution of degreen?k. The method of proof is to show that any spline interpolating zero data vanishes identically, rather than the usual determinantal approach.     

On barotropic trapped wave solutions with no-slip boundary conditions

Barotropic trapped wave solutions of a linearized system of the ocean dynamics equations are described for a semi-infinite, f-plane model basin of constant depth bordering a straight, vertical coast, for some “typical” values of the model parameters. No-slip boundary conditions are considered. When the wave length is shorter than the Rossby deformation radius, the main features of the wave solutions are as follows: the Kelvin wave exponential offshore decay scale essentially decreases as the wave length decreases, and an additional wave solution propagating in the opposite direction appears.     

On elliptic problems satisfying Landesman-Laser conditions

In this paper we consider two elliptic problems. The first one is a Dirichlet problem while the second is Neumann. We extend all the known results concerning Landesman-Laser conditions by using the Mountain-Pass theorem with the Cerami (PS) condition.     

Compositions of n satisfying some coprimality conditions

An ?-composition of n is a sequence of length ? of positive integers summing up to n. In this paper, we investigate the number of ?-compositions of n satisfying two natural coprimality conditions. Namely, we first give an exact asymptotic formula for the number of ?-compositions having the first summand coprime to the others. Then, we estimate the number of ?-compositions whose summands are all pairwise coprime.     

Additive mappings satisfying algebraic conditions in rings

Let \(R\) be any \((n+1)!\) -torsion free ring and \(F,D: R\rightarrow R\) be additive mappings satisfying \(F(x^{n+1})=(\alpha (x))^nF(x)+\sum \nolimits _{i=1}^n (\alpha (x))^{n-i}(\beta (x))^iD(x)\) for all \(x\in R\) , where \(n\) is a fixed integer and \(\alpha \) , \(\beta \) are automorphisms of \(R\) . Then, \(D\) is Jordan left \((\alpha , \beta )\) -derivation and \(F\) is generalized Jordan left \((\alpha , \beta )\) -derivation on \(R\) and if additive mappings \(F\) and \(D\) satisfying \(F(x^{n+1})=F(x)(\alpha (x))^n+\sum \nolimits _{i=1}^n (\beta (x))^iD(x)(\alpha (x))^{n-i}\) for all \(x\in R\) . Then, \(D\) is Jordan \((\alpha , \beta )\) -derivation and \(F\) is generalized Jordan \((\alpha , \beta )\) -derivation on \(R\) . At last some immediate consequences of the above theorems have been given.     

On harmonic functions satisfying nonlocal boundary conditions

We study functions that are harmonic on a strip and satisfy nonlocal boundary conditions, establish constraints that should be imposed on the coefficients in the boundary conditions to guarantee the uniqueness of nonnegative solutions, and present examples when the uniqueness theorems are not true.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 462–467, April, 1994.     

Sperner families satisfying additional conditions and their convex hulls

The profile of a hypergraph onn vertices is (f ₀,...,f _n ) wheref _i denotes the number ofi-element edges. The extreme points of the set of the profiles are determined for Sperner hypergraphs satisfying some additional conditions. The results contain some old theorems of extremal set theory as particular cases.     

Flows over edge-disjoint mixed multipaths and applications

For improving reliability of communication in communication networks, where edges are subject to failure, Kishimoto [Reliable flow with failures in a network, IEEE Trans. Reliability, 46 (1997) 308-315] defined a δ-reliable flow, for a given source-sink pair of nodes, in a network for δ∈(0,1], where no edge carries a flow more than a fraction δ of the total flow in the network, and proved a max-flow min-cut theorem with cut-capacites defined suitably. Kishimoto and Takeuchi in [A method for obtaining δ-reliable flow in a network, IECCE Fundamentals E-81A (1998) 776-783] provided an efficient algorithm for finding such a flow.When (1/δ) is an integer, say q, Kishimoto and Takeuchi [On m-route flows in a network, IEICE Trans. J-76-A (1993) 1185-1200 (in Japanese)] introduced the notion of a q-path flow. Kishimoto [A method for obtaining the maximum multi-route flows in a network, Networks 27 (1996) 279-291] proved a max-flow min-cut theorem for q-path flow between a given source-sink pair (s,t) of nodes and provided a strongly polynomial algorithm for finding a q-path flow from s to t of maximum flow-value.In this paper, we extend the concept of q-path flow to any real number q?1. When q(=1/δ) is fractional, we show that this general q-path flow can be viewed as a sum of some ⌈q⌉-path flow and some ⌊q⌋-path flow. We discuss several applications of this results, which include a simpler proof and generalization of a known result on wavelength division multiplexing problem.Finally we present a strongly polynomial, combinatorial algorithm for synthesizing an undirected network with minimum sum of edge capacities that satisfies (non-simultaneously) specified minimum requirements of q-path flow-values between all pairs of nodes, for a given real number q?1.     

Groups satisfying weak chain conditions on non-modular subgroups

In this paper (generalized) soluble groups for which the set of all non-modular subgroups satisfies some weak chain condition are described. Groups satisfying weak chain conditions on non-permutable subgroups are also considered.     

Bases of spaces of matrices satisfying rank conditions

Motivated by the problem concerning the existence of non-singular bilinear maps, vector spaces of matrices consisting of matrices with rank bounded below are investigated. It is shown that bases for such spaces of maximum dimension can be chosen in such a way to consist of matrices of the minimal rank. An estimate of the ranks of matrices in particular types of bases for maximal such spaces is also given. This extends previously known results which were valid only in the case of spaces consisting of matrices of rank not equal to one.