Global solvability of the Navier–Stokes equations with a free surface in the maximal Lp-Lq regularity class

We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the N-dimensional Euclidean space for $N\ge 2$. The aim of this paper is to show the global solvability of the Navier–Stokes equations with a free surface, describing the above-mentioned motion, in the maximal $L_p\text{-}{L}_q$ regularity class. Our approach is based on the maximal $L_p\text{-}{L}_q$ regularity with exponential stability for the linearized equations, and also it is proved that solutions to the original nonlinear problem are exponentially stable.     

On the nonlinear wave equation Utt−B(t,‖Ux‖)Uxx=f(x,t,U,Ux,Ut) associated with the mixed homogeneous conditions

In this paper we consider the following nonlinear wave equation

(1)     

Does the location and the institutional background matter in convergence modelling of the EU regions?

Central European Journal of Operations Research - The paper focuses on the testing of regional income convergence of NUTS2 EU regions during the 2000–2011 period with the emphasis on...     

Isoperimetric regions in spherical cones and Yamabe constants of M ×?S1

We study isoperimetric regions on Riemannian manifolds of the form (M ⁿ × (0, π), sin²(t)g + dt ²) where g is a metric of positive Ricci curvature ≥ n − 1. When g is an Einstein metric we use this to compute the Yamabe constant of (M ×\mathbbR, g+ dt² ){(M \times \mathbb{R}, g+ dt^2 )} and so to obtain lower bounds for the Yamabe invariant of M × S ¹.     

Algebras almost commuting with Clifford algebras in a II∞ factor

We are concerned here with certain Banach algebras of operators contained within a fixed II factor N. These algebras may be thought of as noncommutative classifying spaces for the functor Ext _* ^N The basic objects of study are the algebras A _kN (for n=1, 2,...). Here, we are given an essentially unique representation of the complex Clifford algebra C _k N and the elements of A _k are those operators in N which exactly commute with the first k–1 generators of C _k and also commute with the kth generator modulo a symmetric ideal N. Up to isomorphism, these algebras are periodic with period 2.We determine completely the homotopy types of A ₁ ^–1 and A ₂ ^–1 Here, A ₁ ^–1 is homotopy equivalent to the space of (Breuer) Fredholm operators in N, while A ₂ ^–1 is homotopy equivalent to the group K _N ^–1 ={x N^–1¦ x=1+k, k K_N}. We use these results to compute the K-theory of A ₁ and A ₂.For a fixed C ^*-algebra A, we define abelian groups G _k,N(A) of equivalence classes of homomorphisms AA _k. Letting N = M (H) for a II₁ factor M we define similar abelian groups G _k(A, M) where we replace N by L(E) for countably generated right Hilbert M-modules E with (left) actions C _k L(E). Using ideas of Skandalis, we show that G _k,NG_k(A, M) so that the G _k,N are stable half-exact homotopy functors because the G _k(·, M) are such.In general, we show that G _k(A, M)KK ^k(A, M) and so our theory fits neatly into Kasparov KK-theory. We investigate many interesting examples from our point of view.     

Counting derangements, involutions and unimodal elements in the wreath product Cr ? Sn

We count derangements, involutions and unimodal elements in the wreath product C _r ≀ S _n by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric group S _n and on the hyperoctahedral group B _n when r = 1, 2, respectively.     

The correct proofs for the optimal ordering policy with?trade credit under two different payment methods in?a?supply chain system

Cheng et al. (Top, 2010. doi:10.1007/s11750-08-0062-3) consider the optimal ordering policy with trade credit under two different payment methods. Under Assumption (5) by Cheng et al., the annual total relevant cost TRC(T) is only defined on a finite interval. However, Cheng et al. treat the domain of TRC(T) to be the set of all positive numbers such that the formulation and optimal solution of TRC(T) cause some errors. So, the main purpose of this paper not only removes those shortcomings by Cheng et al. but also presents the correct proofs for Theorems?1 and?2 of Cheng et?al.     

Massless excitations of long strings in AdS4 × ?P3

We consider the AdS₄ × ℂℙ³ IIA superstring sigma model in the background of a “spinning string” classical solution with two charges. In the limit when one of the spins is infinite, there are massless excitations which govern the long-range worldsheet properties of the model. We obtain a sigma model of ℂℙ³ with fermions which describes the dynamics of these massless modes.     

Concentrated monotone measures with non-unique tangential behavior in ?3

We show that for every ɛ > 0 there is a set A ⊂ ℝ³ such that H ¹ ⌞A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and H ¹ ⌞A has the 1-dimensional density between 1 and 2+ɛ everywhere in the support.     

Torsion in K‐Theory for Boundary Actions on Affine Buildings of Type ?n

Let be a torsionfree lattice in G=PGL(n+1, , where n 1 and is a nonArchimedean local field. Then acts on the Furstenberg boundary G/P, where P is a minimal parabolic subgroup of G. The identity element I in the crossedproduct C ^*algebra C(G/P) generates a class [I] in the K ₀ group of C(G/P) . It is shown that [I] is a torsion element of K ₀ and there is an explicit bound for the order of [I]. The result is proved more generally for groups acting on affine buildings of type à _n. For n=1, 2 the Euler–Poincaré characteristic () annihilates the class [I].     

Vector subdivision schemes in (Lp(?s))r(1?p?∞) spaces

The purpose of this paper is to investigate the refinement equations of the form

How do changes in risk and risk aversion affect self-protection with Selden/Kreps–Porteus preferences?

This paper examines the determinants of optimal effort in an intertemporal self-protection model. We separate attitude toward risk and attitude toward intertemporal substitution by adopting Selden/Kreps–Porteus preferences. We not only explore the sufficient conditions on risk preferences for guaranteeing the unambiguous effects of changes in risk on the optimal effort level but also show how a change in risk aversion alone affects the optimal effort level.     

The sharp Jackson inequality in the space L2 on the segment [?1, 1] with the power weight

In the space L ₂ on the segment [−1, 1] with the power weight |x|^2λ+1, λ ≥ −1/2, we define a complete orthogonal system, the value of the best approximation with respect to this system, the operator of generalized shift, and the modulus of continuity and prove the sharp Jackson inequality.     

Curves with Many Points and Multiplication Complexity in Any Extension of q

From the existence of algebraic function fields having some good properties, we obtain some new upper bounds on the bilinear complexity of multiplication in all extensions of the finite field _q, where q is an arbitrary prime power. So we prove that the bilinear complexity of multiplication in the finite fields _qⁿ is linear uniformly in q with respect to the degree n.     

Finite Interpolation with Minimum Uniform Norm in

Given a finite sequence a{a₁, …, a_N} in a domain Ω ⁿ, and complex scalars v{v₁, …, v_N}, consider the classical extremal problem of finding the smallest uniform norm of a holomorphic function verifying f(a_j)=v_j for all j. We show that the modulus of the solutions to this problem must approach its least upper bound along a subset of the boundary of the domain large enough so that its A(Ω)-hull contains a subset of the original a large enough to force the same minimum norm. Furthermore, all the solutions must agree on a variety which contains the hull (in an appropriate, weaker, sense) of a measure supported on the maximum modulus set. An example is given to show that the inclusions can be strict.     

Approximation in Lp( ) from Spaces Spanned by the Perturbed Integer Translates of a Radial Function

The problem of approximating smooth L_p-functions from spaces spanned by the integer translates of a radially symmetric function φ is very well understood. In case the points of translation, Ξ, are scattered throughout ^d, the approximation problem is only well understood in the “stationary” setting. In this work, we provide lower bounds on the obtainable approximation orders in the “non-stationary” setting under the assumption that Ξ is a small perturbation of ^d. The functions which we can approximate belong to certain Besov spaces. Our results, which are similar in many respects to the known results for the case Ξ= ^d, apply specifically to the examples of the Gauss kernel and the generalized multiquadric.     

Splitting extrapolation for solving second order elliptic systems with curved boundary in by using d-quadratic isoparametric finite element

Splitting extrapolation for solving second order elliptic systems with curved boundary in by using isoparametric d-quadratic element Q₂ is presented, which is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem with curved boundary is turned into many discrete problems involving several grid parameters. The multivariate asymptotic expansions of isoparametric d-quadratic Q₂ finite element errors with respect to independent grid parameters are proved for second order elliptic systems. Therefore after solving smaller problems with similar sizes in parallel, a global fine grid approximation with higher accuracy is computed by the splitting extrapolation method.