不可压缩理想势流绕两平行平板间圆柱流动的新的近似解析解

文献[1]得到了不可压缩理想势流绕两平行平板间圆柱流动的近似分析解.本文指出,用М.Е.Швец法[2]亦可得到与文献[1]完全相同的结果.如果用本文作者新提出的改进了的М.Е.Швец法[2]则可得到比文献[1]更加精确的结果.有算例.     

Holonomy and Parallel Transport for Abelian Gerbes

In this paper, we establish a one-to-one correspondence between U(1)-gerbes with connections, on the one hand, and their holonomies, for simply connected manifolds, or their parallel transports, in the general case, on the other hand. This result is a higher-order analogue of the familiar equivalence between bundles with connections and their holonomies for connected manifolds. The holonomy of a gerbe with group U(1) on a simply connected manifold M is a group morphism from the thin second homotopy group to U(1), satisfying a smoothness condition, where a homotopy between maps from [0,1]² to M is thin when its derivative is of rank 2. For the non-simply connected case, holonomy is replaced by a parallel transport functor between two special Lie groupoids, which we call Lie 2-groups. The reconstruction of the gerbe and connection from its holonomy is carried out in detail for the simply connected case.     

Graphs with two isomorphism classes of spanning unicyclic subgraphs

The graphs whose spanning unicyclic subgraphs partition into exactly two isomorphism classes are characterized.This work is a continuation of [6] where graphs with one isomorphism class of spanning unicyclic graphs are characterized. The analogous question for spanning trees was posed in [10] and graphs with one isomorphism class of spanning trees were characterized in [2], [3], [4], [7], [11] while graphs with two isomorphism classes of spanning trees were characterized in [4], [5]. Related topics are treated in [1], [8], [9].     

Majorizing functions and two-point Newton-type methods

The semi-local convergence of a Newton-type method used to solve nonlinear equations in a Banach space is studied. We also give, as two important applications, convergence analyses of two classes of two-point Newton-type methods including a method mentioned in [5] and the midpoint method studied in [1], [2] and [12]. Recently, interest has been shown in such methods [3] and [4].     

Shannon switching games without terminals III

Shannon switching game has been analyzed by Lehman [3] in matroid theory. Kano [2] has studied games with many terminals where Short intends to connect at least two of them. This result is included in [6] and [7], where the games are described on graphs with group action. These results will be generalized in this paper which deals with games on a finite set with two matroid structures. Our new theory can be applied to the game where Short's purpose is to connect all the given pairs of terminals and to the game where Short's purpose is to connect at least one of given two pairs of terminals. On the other hand, the game is not reversible (see [9]) if Short's purpose is to connect at least one of given three pairs of terminals.     

Determination of the underground contour of a submerged apron with a region of constant velocity when there is a salt backwater

Within the framework of two-dimensional seepage theory, the underground contour of a submerged apron with a region of constant velocity in the case where there is a layer of stagnant salt water under the apron is constructed. The solution of the corresponding boundary-value problem is found by Polubarinova-Kochina's method [1] using the results obtained in [2]. The results of numerical calculations are given and the influence of the fundamental defining parameters of the model on the shape and size of the underground contour of the apron is analysed. Mention is made of special and limiting cases: a scheme with a water-confining stratum [3], an unsubmerged apron [2] and flow around a tongue [4,5].     

On the reflexive class group

In [13] S. Yuan introduced the so-called reflexive class group of an integrally closed noetherian domain, which is isomorphic to the usual class group. This construction was generalized afterwards by M. Orzech to arbitrary Krull domains, cf. [7]. On the other hand in [10] the author studied the relative Picard group with respect to an arbitrary idempotent kernel functor a. In this note we show that if a is the idempotent kernel functor associated to the prime ideals of height one, then both notions coincide. Some easy applications are included.     

Polyhomogeneous maps and best local approximations of degree α

Contemporary investigations in the theory of nonlinear integral operators ([9], [10]) and in the differential calculus ([5], [11]) have led to generalizations of the notion of a polynomial map between two vector spaces. This article studies basic properties of such so-called polyhomogeneous maps. Our initial point of reference is the recent study of polynomial maps by Bochnak and Siciak [2]. Our examination of continuity properties leads to new characterizations of braked spaces and sequential spaces. Then, we turn to the polyhomogeneous approximating maps studied by Melamed and Perov [9] and Moore and Nashed [10]. We present some generalizations of the results of [9] and [10] and then go on to study permanence properties of such approximations.     

The integration of certain products of the multivariableH-function with a general class of polynomials

The authors present six general integral formulas (four definite integrals and two contour inegrals) for theH-function of several complex variables, which was introduced and studied in a series of earlier papers by H. M. Srivastava and R. Panda (cf., e.g., [25] through [29]; see also [14] through [18], [20], [24], [32], [34], [35], [37], and [38]). Each of these integral formulas involves a product of the multivariableH-function and a general class of polynomials with essentially arbitrary coefficients which were considered elsewhere by H. M. Srivastava [21]. By assigning suiatble special values to these coefficients, the main results (contained in Theorems 1, 2 and 3 below) can be reduced to integrals involving the classical orthogonal polynomials including, for example, Hermite, Jacobi [and, of course, Gegenbauer (or ultraspherical), Legendre, and Tchebycheff], and Laguerre polynomials, the Bessel polynomials considered by H. L. Krall and O. Frink [9], and such other classes of generalized hypergeometric polynomials as those studied earlier by F. Brafman [3] and by H. W. Gould and A. T. Hopper [8]. On the other hand, the multivariableH-functions occurring in each of our main results can be reduced, under various special cases, to such simpler functions as the generalized Lauricella hypergeometric functions of several complex variables [due to H. M. Srivastava and M. C. Daoust (cf. [22] and [23])] which indeed include a great many of the useful functions (or the products of several such functions) of hypergeometric type (in one and more variables) as their particular cases (see,e. g., [1], [10] and [39]). Many of the aforementioned applications of our integral formulas (contained in Theorems 1, 2 and 3 below) are considered briefly. Further usefulness of some of these consequences of Theorems 1 and 2 in terms of the classical orthogonal polynomials is illustrated by considering a simple problem involving the orthogonal expansion of the multivariableH-function in series of Jacobi polynomials. It is also shown how these general integrals are related to a number of results scattered in the literature. 0261 0262 V     

Parallel linear multigrid by agglomeration for the acceleration of 3D compressible flow calculations on unstructured meshes

In this paper, we report on our recent efforts concerning the design of parallel linear multigrid algorithms for the acceleration of 3-dimensional compressible flow calculations. The multigrid strategy adopted in this study relies on a volume agglomeration principle for the construction of the coarse grids starting from a fine discretization of the computational domain. In the past, this strategy has mainly been studied in the 2-dimensional case for the solution of the Euler equations (see Lallemand et al. [6]), the laminar Navier–Stokes equations (see Mavriplis and Venkatakrishnan [12]) and the turbulent Navier–Stokes equations (see Carré [1], Mavriplis [10] and Francescatto and Dervieux [4]). A first extension to the 3-dimensional case is presented by Mavriplis and Venkatakrishnan in [13] and more recently in Mavriplis and Pirzadeh [11]. The main contribution of the present work is twofold: on the one hand, we demonstrate the successful extension and application of the multigrid by a volume agglomeration principle to the acceleration of complex 3-dimensional flow calculations on unstructured tetrahedral meshes and, on the other hand, we enhance further the efficiency of the methodology through its adaptation to parallel architectures. Moreover, a nontrivial aspect of this work is that the corresponding software developments are taking place in an existing industrial flow solver. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Method for Global Approximation of the Initial Value Problem

For the numerical solution of the initial value problem a parallel, global integration method is derived and studied. It is a collocation method. If f(x,y)f(x) the method coincides with the Filippi's modified Clenshaw–Curtis quadrature [11]. Two numerical algorithms are considered and implemented, one of which is the application of the new method to Picard iterations, so it is a waveform relaxation technique [3]. Numerical experiments are favourably compared with the ones given by the known GAM [2], GBS [14] and Sarafyan [18] methods.     

On function classes in P 3 precomplete with respect to a strengthened closure operator

A classical theorem of Post [1] describes five precomplete classes in the set of Boolean functions. In [2], it was shown that there exist 18 precomplete classes of functions of three-valued logic. In [1, 2], the closure of sets of functions with respect to the substitution operator was studied. We consider two closure operators on functions of three-valued logic, which are obtained by supplementing the substitution operator by closures with respect to two identifications of function values, and prove the existence of three precomplete classes for one of these operators and five precomplete classes for the other.     

Large normal ideals concentrating on a fixed small cardinality

The property on the filter in Definition 1, a kind of large cardinal property, suffices for the proof in Liu Shelah [LiSh484] and is proved consistent as required there (see Conclusion 6). A natural property which looks better, not only is not obtained here, but is shown to be false (in Claim 7). On earlier related theorems see Gitik Shelah [GiSh310]. On such games see e.g. [Je], [Sh-b], [Sh-f]. Received June 27, 1994     

Linear congruence relations for 2-adic L-series at integers

In the paper we find a further generalization of congruences of the K. Hardy and K. S. Williams [5] type which seems to be a full generalization of congruences of G. Gras [4]. Moreover we extend results of [5], [7], [8], [9] and in part of [6]. We apply ideas and methods of [2], [7] and [9].     

Steady convection in the presence of an external magnetic field

The problem of the equilibrium of a liquid enclosed in a vessel heated from below has been considered by Sorokin [1], Iudovich and Ukhovskii [2] and Velt [3]. It has been established that if the Rayleigh number λ exceeds a certain critical value λ₀, then secondary steady flows arise in the liquid.

The stability of a conductive liquid heated from below has been studied by many authors. The most complete and general studies are those of Sorokin and Sushkin [4], whose paper contains the appropriate bibliography, and that of Shliomis [5]. The results of [4 and 5] make clear the physical picture of the phenomena associated with the heating of a conductive fluid and indicate the possible existence of secondary steady and periodic flows.

The existence of steady convective flows in a conductive liquid are proved below. Our study is based on the procedure set forth in [2].     

ALTERNATING BAND CRANK-NICOLSON METHOD FOR δu／δt=δ^2u／δx^2＋δ^2u／δy^2

the Alternating Segment Crank-Nicolson scheme for one-dimensional diffusion equation has been developed in [1],and the Alternating Block Crank-Nicolson method for two-dimensional problem in [2].The methods have the advantages of parallel computing,stability and good accuracy.In this paper for the two-dimensional diffusion equation,the net region is divided into bands,a special kind of block.This method is called the alternating Band Crank-Nicolson method.     

ALTERNATING BAND CRANK-NICOLSON METHOD FOR

The Alternating Segment Crank-Nicolson scheme for one-dimensional diffusion equation has been developed in [ 1 ], and the Alternating Block Crank-Nicolson method for two-dimensional problem in [2]. The methods have the advantages of parallel computing, stability and good accuracy. Tn this paper for the two-dimensional diffusion equation, the net region is divided into bands, a special kind of block. This method is called the alternating Band Crank-Nicolson method.     

Drinfeld–Sokolov reduction for quantum groups and deformations of W-algebras

We define deformations of W-algebras associated to comple semisimple Lie algebras by means of quantum Drinfeld-Sokolov reduction procedure for affine quantum groups. We also introduce Wakimoto modules for arbitrary affine quantum groups and construct free field resolutions and screening operators for the deformed W-algebras. We compare our results with earlier definitions of q-W-algebras and of the deformed screening operators due to Awata, Kubo, Odake, Shiraishi [60],[6], [7], Feigin, E. Frenkel [22] and E. Frenkel, Reshetikhin [34]. The screening operator and the free field resolution for the deformed W-algebra associated to the simple Lie algebra sl₂ coincide with those for the deformed Virasoro algebra introduced in [60]. The author is supported by the Swiss National Science Foundation.     

On General Transport Equations with Abstract Boundary Conditions. The Case of Divergence Free Force Field

This work is a continuation of our previous paper [8]. We investigate well-posedness (in the semigroup theory sense) of transport equations with general external fields and general measures associated to boundary conditions modeled by abstract boundary operators H. Fine properties of the traces are investigated, extending well-known results by M. Cessenat [15]. For dissipative boundary conditions, we revisit and generalize results from [12, 17] while, for multiplicative boundary conditions we extend techniques from [25]. Finally, we also investigate the case of boundary conditions associated to a boundary operator of norm one, extending the recent results of [6, 27] to more general fields and measures.     

Pathwidth of outerplanar graphs

We are interested in the relation between the pathwidth of a biconnected outerplanar graph and the pathwidth of its (geometric) dual. Bodlaender and Fomin [3], after having proved that the pathwidth of every biconnected outerplanar graph is always at most twice the pathwidth of its (geometric) dual plus two, conjectured that there exists a constant c such that the pathwidth of every biconnected outerplanar graph is at most c plus the pathwidth of its dual. They also conjectured that this was actually true with c being one for every biconnected planar graph. Fomin [10] proved that the second conjecture is true for all planar triangulations. First, we construct for each p ≥ 1, a biconnected outerplanar graph of pathwidth 2p + 1 whose (geometric) dual has pathwidth p + 1, thereby disproving both conjectures. Next, we also disprove two other conjectures (one of Bodlaender and Fomin [3], implied by one of Fomin [10]. Finally we prove, in an algorithmic way, that the pathwidth of every biconnected outerplanar graph is at most twice the pathwidth of its (geometric) dual minus one. A tight interval for the studied relation is therefore obtained, and we show that all cases in the interval happen. © 2006 Wiley Periodicals, Inc. J Graph Theory 55: 27–41, 2007