A theorem on integer flows on cartesian products of graphs

It is shown that the Cartesian product of two nontrivial connected graphs admits a nowhere‐zero 4‐flow. If both factors are bipartite, then the product admits a nowhere‐zero 3‐flow. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 93–98, 2003     

The effect of gossip on social networks

In this article, we develop a simple model for the effect of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A‐B and weakens both B‐C and A‐C. We find, in both an analytic derivation and model simulations, that if gossip does not spread beyond simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. Additionally, our simulations show that the effect of gossip on network metrics (clustering coefficient, average‐path‐length, and sum‐of‐strengths) varies with network structure and average‐node‐degree. © 2010 Wiley Periodicals, Inc. Complexity 16: 39‐47, 2011     

Minimality conditions on circularly ordered structures

We explore analogues of o‐minimality and weak o‐minimality for circularly ordered sets. Much of the theory goes through almost unchanged, since over a parameter the circular order yields a definable linear order. Working over ?? there are differences. Our main result is a structure theory (with infinitely many doubly transitive examples related to Jordan permutation groups) for ?₀‐categorical weakly circularly minimal structures. There is a 5‐homogeneous (or ‘5‐indiscernible’) example which is not 6‐homogeneous, but any example which is k‐homogeneous for some k ≥ 6 is k‐homogeneous for all k. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nowhere‐Zero Flows on Signed Complete and Complete Bipartite Graphs

Bouchet's conjecture asserts that each signed graph which admits a nowhere‐zero flow has a nowhere‐zero 6‐flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow‐admissible graph admits a nowhere‐zero 4‐flow and we characterise those which have a nowhere‐zero 2‐flow and a nowhere‐zero 3‐flow.     

Unilateral Constrained Bending Vibrations on a Torsional String

Vibrations in long torsional strings result in spatio‐temporal dynamics. In order to actively damp these vibrations the system has to be analysed analytically, numerically and experimentally. Stick‐slip‐effects result in torsional selfexcited vibrations of the string. These vibrations are coupled with bending vibrations which are constrained by the borehole. The straight string was modelled in an experimental setup. The control of the straight string and the unilateral constrained bending vibrations were treated seperately. The dynamics of straight strings were controlled using three different approaches: firstly, a simple PD‐controller with the parameters calculated based on a one‐degree‐of‐freedom oscillator, secondly, the parameters were optimized using a simplex‐method, thirdly, the Karhunen‐Loeve‐transformation was used in order to reduce the dimension of the system. A controller based on the reduced system was implemented and the parameters were optimized with the same simplex algorithm. The unilateral constrained bending motion were examined at a cantilever beam which was assumed to be constrained in one direction in the middle of the beam. First, the beam was modelled analytically as a continuous system. The two states (contact and no contact) were described separately. The transition between these states were modelled with energy assumptions. Second, the beam was modelled as a Finite‐Element‐System. The numerical results of both methods were compared with experimental data.     

Variation on a theme of Schütte

Let ? be a primitive recursive well‐ordering on the natural numbers and assume that its order‐type is greater than or equal to the proof‐theoretic ordinal of the theory T. We show that the proof‐theoretic strength of T is not increased if we add the negation of the statement which formalizes transfinite induction along ?. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar

We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd.     

Coloring Graphs with Constraints on Connectivity

A graph G has maximal local edge‐connectivity k if the maximum number of edge‐disjoint paths between every pair of distinct vertices x and y is at most k. We prove Brooks‐type theorems for k‐connected graphs with maximal local edge‐connectivity k, and for any graph with maximal local edge‐connectivity 3. We also consider several related graph classes defined by constraints on connectivity. In particular, we show that there is a polynomial‐time algorithm that, given a 3‐connected graph G with maximal local connectivity 3, outputs an optimal coloring for G. On the other hand, we prove, for , that k‐colorability is NP‐complete when restricted to minimally k‐connected graphs, and 3‐colorability is NP‐complete when restricted to ‐connected graphs with maximal local connectivity k. Finally, we consider a parameterization of k‐colorability based on the number of vertices of degree at least , and prove that, even when k is part of the input, the corresponding parameterized problem is FPT.     

Forcing operators on MTL‐algebras

We study the forcing operators on MTL‐algebras, an algebraic notion inspired by the Kripke semantics of the monoidal t ‐norm based logic (MTL). At logical level, they provide the notion of the forcing value of an MTL‐formula. We characterize the forcing operators in terms of some MTL‐algebras morphisms. From this result we derive the equality of the forcing value and the truth value of an MTL‐formula (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gliding motion of bacteria on power‐law slime

The present investigation deals with an undulating surface model for the motility of bacteria gliding on a layer of non‐Newtonian slime. The slime being the viscoelastic material is considered as a power‐law fluid. A hydrodynamical model of motility involving an undulating cell surface which transmits stresses through a layer of exuded slime to the substratum is examined. The non‐linear differential equation resulting from the balance of momentum and mass is solved numerically by a finite difference method with an iteration technique. The manner in which the various exponent values of the power‐law flow affect the structure of the boundary layer is delineated. A comparison is made of the power‐law fluid with the Newtonian fluid. For the power‐law fluid with respect to different power‐law exponent values, shear‐thinning and shear‐thickening effects can be observed, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

A preliminary investigation on an ELLAM scheme for linear transport equations

We present an Eulerian‐Lagrangian localized adjoint method (ELLAM) for linear advection‐reaction partial differential equations in multiple space dimensions. We carry out numerical experiments to investigate the performance of the ELLAM scheme with a range of well‐perceived and widely used methods in fluid dynamics including the monotonic upstream‐centered scheme for conservation laws (MUSCL), the minmod method, the flux‐corrected transport method (FCT), and the essentially non‐oscillatory (ENO) schemes and weighted essentially non‐oscillatory (WENO) schemes. These experiments show that the ELLAM scheme is very competitive with these methods in the context of linear transport PDEs, and suggest/justify the development of ELLAM‐based simulators for subsurface porous medium flows and other applications. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 22–43, 2003     

Concentrated portfolio selection models based on historical data

A new risk measure fully based on historical data is proposed, from which we can naturally derive concentrated optimal portfolios rather than imposing cardinality constraints. The new risk measure can be expressed as a quadratics of the introduced greedy matrix, which takes investors' joint behavior into account. We construct distribution‐free portfolio selection models in simple case and realistic case, respectively. The latest techniques for describing transaction cost constraints and solving nonconvex quadratic programs are utilized to obtain the optimal portfolio efficiently. In order to show the practicality, efficiency, and robustness of our new risk measure and corresponding portfolio selection models, a series of empirical studies are carried out with trading data from advanced stock markets and emerging stock markets. Different performance indicators are adopted to comprehensively compare results obtained under our new models with those obtained under the mean‐variance, mean‐semivariance, and mean‐conditional value‐at‐risk models. Out‐of‐sample results sufficiently show that our models outperform the others and provide a simple and practical approach for choosing concentrated, efficient, and robust portfolios. Copyright © 2014 John Wiley & Sons, Ltd.     

Square function estimates on layer potentials for higher‐order elliptic equations

In this paper we establish square‐function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m , with variable t‐independent coefficients in the upper half‐space. This generalizes known results for variable‐coefficient second‐order operators, and also for constant‐coefficient higher‐order operators.     

Heat Flow on Alexandrov Spaces

We prove that on compact Alexandrov spaces with curvature bounded below the gradient flow of the Dirichlet energy in the \begin{align*}L^2\end{align*}‐space produces the same evolution as the gradient flow of the relative entropy in the \begin{align*}L^2\end{align*}‐Wasserstein space. This means that the heat flow is well‐defined by either one of the two gradient flows. Combining properties of these flows, we are able to deduce the Lipschitz continuity of the heat kernel as well as Bakry‐Émery gradient estimates and the \begin{align*}\Gamma_2\end{align*}‐condition. Our identification is established by purely metric means, unlike preceding results relying on PDE techniques. Our approach generalizes to the case of heat flow with drift. © 2012 Wiley Periodicals, Inc.     

More on foxes

An edge in a k‐connected graph G is called k‐contractible if the graph obtained from G by contracting e is k‐connected. Generalizing earlier results on 3‐contractible edges in spanning trees of 3‐connected graphs, we prove that (except for the graphs if ) (a) every spanning tree of a k‐connected triangle free graph has two k‐contractible edges, (b) every spanning tree of a k‐connected graph of minimum degree at least has two k‐contractible edges, (c) for , every DFS tree of a k‐connected graph of minimum degree at least has two k‐contractible edges, (d) every spanning tree of a cubic 3‐connected graph nonisomorphic to K₄ has at least many 3‐contractible edges, and (e) every DFS tree of a 3‐connected graph nonisomorphic to K₄, the prism, or the prism plus a single edge has two 3‐contractible edges. We also discuss in which sense these theorems are best possible.     

Discretization effects on approximate deconvolution modeling for LES

We study the applicability of low‐order schemes with the approximate deconvolution model (ADM) for large‐eddy simulation. As a test case compressible decaying isotropic turbulence is considered. Results obtained with low‐order finite difference schemes and a pseudospectral scheme are compared with filtered well‐resolved direct numerical simulation (DNS) data. It is found that even for low‐order schemes very good results can be obtained if the cutoff wavenumber of the filter is adjusted to the modified wavenumber of the differentiation scheme.     

Influence of the rail pad on a vehicle travelling on a straight track

In the following text, the influence of the stiffness of rail fastening systems of high‐speed railway lines on the dynamic stability of a vehicle travelling along a straight track is investigated. The dynamic behaviour of the rail head in lateral direction is incorporated in the model by means of mechanical models derivedfrom a preceding frequency analysis of the track. For the wheel‐rail interface, linear contact mechanics and kinematic relations are applied. The investigation leads to the conclusion that on high‐speed lines the critical velocity of vehicles is reduced as a result of the increased elasticity of the rail pads. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on constraint preconditioners for nonsymmetric saddle point problems

A class of constraint preconditioners for solving two‐by‐two block linear equations with the (1,2)‐block being the transpose of the (2,1)‐block and the (2,2)‐block being zero was investigated in a recent paper of Cao (Numer. Math. 2006; 103 :47–61). In this short note, we extend his idea by allowing the (1,2)‐block to be not equal to the transpose of the (2,1)‐block. Results concerning the spectrum, the form of the eigenvectors and the convergence behaviour of a Krylov subspace method, such as GMRES are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

A note on Prandtl boundary layers

This note concerns nonlinear ill‐posedness of the Prandtl equation and an invalidity of asymptotic boundary layer expansions of incompressible fluid flows near a solid boundary. Our analysis is built upon recent remarkable linear illposedness results established by Gérard‐Varet and Dormy and an analysis by Guo and Tice. We show that the asymptotic boundary layer expansion is not valid for nonmonotonic shear layer flows in Sobolev spaces. We also introduce a notion of weak well‐posedness and prove that the nonlinear Prandtl equation is not well‐posed in this sense near nonstationary and nonmonotonic shear flows. On the other hand, we are able to verify that Oleinik's monotonic solutions are well‐posed. © 2011 Wiley Periodicals, Inc.     

Remark on energy‐critical NLS in 5D

We reprove global well‐posedness and scattering for the defocusing energy‐critical nonlinear Schrödinger equation in five dimensions. Inspired by the recent work of Killip and Visan, we adapt the Dodson's strategy ‘long‐time Strichartz estimate’ used in the work on mass‐critical nonlinear Schrödinger equation sets. Copyright © 2015 John Wiley & Sons, Ltd.