Nowhere‐zero 3‐flows in locally connected graphs

Let G be a graph. For each vertex v ∈V(G), N_v denotes the subgraph induces by the vertices adjacent to v in G. The graph G is locally k‐edge‐connected if for each vertex v ∈V(G), N_v is k‐edge‐connected. In this paper we study the existence of nowhere‐zero 3‐flows in locally k‐edge‐connected graphs. In particular, we show that every 2‐edge‐connected, locally 3‐edge‐connected graph admits a nowhere‐zero 3‐flow. This result is best possible in the sense that there exists an infinite family of 2‐edge‐connected, locally 2‐edge‐connected graphs each of which does not have a 3‐NZF. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 211–219, 2003     

Arc‐Disjoint In‐ and Out‐Branchings With the Same Root in Locally Semicomplete Digraphs

Deciding whether a digraph contains a pair of arc‐disjoint in‐ and out‐branchings rooted at a specified vertex is a well‐known NP‐complete problem (as proved by Thomassen, see 2 ). This problem has been shown to be polynomial time solvable for semicomplete digraphs 2 and for quasi‐transitive digraphs 6 . In this article, we study the problem for locally semicomplete digraphs. We characterize locally semicomplete digraphs that contain a pair of arc‐disjoint in‐ and out‐branchings rooted at a specified vertex. Our proofs are constructive and imply the existence of a polynomial time algorithm for finding the desired branchings when they exist. Our results generalizes those from 2 for semicomplete digraphs and solves an open problem from 4 .     

On C*‐Like Locally Convex ∗︁‐Algebras

The main purpose of this paper is to define the notion of C*‐like locally convex∗︁‐algebras and to study the structure of such ∗︁‐algebras.     

On the hamiltonicity of line graphs of locally finite, 6‐edge‐connected graphs

The topological approach to the study of infinite graphs of Diestel and KÜhn has enabled several results on Hamilton cycles in finite graphs to be extended to locally finite graphs. We consider the result that the line graph of a finite 4‐edge‐connected graph is hamiltonian. We prove a weaker version of this result for infinite graphs: The line graph of locally finite, 6‐edge‐connected graph with a finite number of ends, each of which is thin, is hamiltonian.     

On C‐Suslin spaces

We prove a closed graph theorem for Baire locally convex spaces (for Baire linear topological spaces) in the domain and weakly C‐Suslin locally convex spaces (respectively, for C‐Suslin linear topological spaces) in the range which improves some classic closed graph theorems and other, more recent, related results.     

Locally boundedly A‐p‐convex algebras

We consider locally p‐convex algebras the bornologies of which coincide with the ones of p‐normed or multiplicatively p‐convex topologies. Two new classes of these algebras are introduced here. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic homogenization of Hamilton‐Jacobi‐Bellman equations

We study the homogenization of some Hamilton‐Jacobi‐Bellman equations with a vanishing second‐order term in a stationary ergodic random medium under the hyperbolic scaling of time and space. Imposing certain convexity, growth, and regularity assumptions on the Hamiltonian, we show the locally uniform convergence of solutions of such equations to the solution of a deterministic “effective” first‐order Hamilton‐Jacobi equation. The effective Hamiltonian is obtained from the original stochastic Hamiltonian by a minimax formula. Our homogenization results have a large‐deviations interpretation for a diffusion in a random environment. © 2005 Wiley Periodicals, Inc.     

An interior point Newton‐like method for non‐negative least‐squares problems with degenerate solution

An interior point approach for medium and large non‐negative linear least‐squares problems is proposed. Global and locally quadratic convergence is shown even if a degenerate solution is approached. Viable approaches for implementation are discussed and numerical results are provided. Copyright © 2006 John Wiley & Sons, Ltd.     

Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005     

Length‐preserving evolution of non‐simple symmetric plane curves

The length‐preserving nonlocal flow in the plane is investigated for locally convex closed curves, which may be non‐simple. It turns out that for certain classes of symmetric curves, the flows converge to m‐fold circles. Copyright © 2013 John Wiley & Sons, Ltd.     

Locally 3‐Transitive Graphs of Girth 4

A natural topic of algebraic graph theory is the study of vertex transitive graphs. In the present article, we investigate locally 3‐transitive graphs of girth 4. Taking our former results on locally symmetric graphs of girth 4 as a starting point, we show what properties are retained if we weaken the requirement of local symmetry to local 3‐transitivity.     

The locally uniformly non‐square points of Orlicz–Bochner sequence spaces

In this paper, we investigate the locally uniformly non‐square point of Orlicz–Bochner sequence spaces endowed with Luxemburg norm. Analysing and combining the generating function M and properties of the real Banach space X , we get sufficient and necessary conditions of locally uniformly non‐square point, which contributes to criteria for locally uniform non‐squareness in Orlicz–Bochner sequence spaces. The results generalize the corresponding results in the classical Orlicz sequence spaces.     

On local non‐compactness in recursive mathematics

A metric space is said to be locally non‐compact if every neighborhood contains a sequence that is eventually bounded away from every element of the space, hence contains no accumulation point. We show within recursive mathematics that a nonvoid complete metric space is locally non‐compact iff it is without isolated points. The result has an interesting consequence in computable analysis: If a complete metric space has a computable witness that it is without isolated points, then every neighborhood contains a computable sequence that is eventually computably bounded away from every computable element of the space. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantifier‐eliminable locally finite graphs

We identify the locally finite graphs that are quantifier‐eliminable and their first order theories in the signature of distance predicates. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

OPTIMAL CHOICE BETWEEN EVEN‐ AND UNEVEN‐AGED FORESTRY

Abstract Existing optimal rotation models include even‐aged management exogenously into the model structure. As an economic model, this Faustmann framework is restrictive, and a more general model should not include any such preconditions. Even‐aged management should follow endogenously as an optimal solution if it proves out to be superior to other systems, such as uneven‐aged management. Without such a general model, the economically optimal choice between even‐aged and uneven‐aged forestry remains somewhat arbitrary. This study specifies such a model and shows how even‐aged management follows endogenously and reveals what factors work in favor of each management alternative. Numerical analysis shows that even‐ and uneven‐aged systems may represent locally optimal solutions and may yield equal economic outcomes. Instead of the usual comparative statics results of the Faustmann model, changes in the rate of discount, timber price, or planting cost may imply that the optimal solution shifts from even‐ to uneven‐aged management.     

Bounded approximation properties in non‐archimedean Banach spaces

Some non‐archimedean bounded approximation properties are introduced and studied in this paper. As an application, an affirmative answer is given, for non‐spherically complete base fields, to the following problem, posed in 13 , p. 95: Does there exist an absolutely convex edged set B in a non‐archimedean locally convex space such that its closure $\overline{B}Some non‐archimedean bounded approximation properties are introduced and studied in this paper. As an application, an affirmative answer is given, for non‐spherically complete base fields, to the following problem, posed in 13 , p. 95: Does there exist an absolutely convex edged set B in a non‐archimedean locally convex space such that its closure $\overline{B}$ is not edged?     

A monotone conservative Eulerian–Lagrangian scheme for reaction‐diffusion‐convection equations modeling chemotaxis

A numerical method for convection dominated diffusion problems, that exploits the use of characteristics, is derived and analyzed. It is shown to preserve positivity of solutions and be locally mass conserving. Stability, consistency and order one convergence are verified. Because of the way in which it determines characteristic pre‐images of grid cells, the method can be easily implemented for 1‐, 2‐, or 3‐dimensional problems on rectangular grids.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

A locally conservative Eulerian‐Lagrangian control‐volume method for transient advection‐diffusion equations

Characteristic methods generally generate accurate numerical solutions and greatly reduce grid orientation effects for transient advection‐diffusion equations. Nevertheless, they raise additional numerical difficulties. For instance, the accuracy of the numerical solutions and the property of local mass balance of these methods depend heavily on the accuracy of characteristics tracking and the evaluation of integrals of piecewise polynomials on some deformed elements generally with curved boundaries, which turns out to be numerically difficult to handle. In this article we adopt an alternative approach to develop an Eulerian‐Lagrangian control‐volume method (ELCVM) for transient advection‐diffusion equations. The ELCVM is locally conservative and maintains the accuracy of characteristic methods even if a very simple tracking is used, while retaining the advantages of characteristic methods in general. Numerical experiments show that the ELCVM is favorably comparable with well‐regarded Eulerian‐Lagrangian methods, which were previously shown to be very competitive with many well‐perceived methods. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Multiple solutions for a Robin‐type differential inclusion problem involving the p(x)‐Laplacian

In this paper, we obtain the existence of at least two nontrivial solutions for a Robin‐type differential inclusion problem involving p(x)‐Laplacian type operator and nonsmooth potentials. Our approach is variational, and it is based on the nonsmooth critical point theory for locally Lipschitz functions. Copyright © 2013 John Wiley & Sons, Ltd.