Irreducible projective representations of finite groups

The purpose of this paper is to prove a result on the number of irreducible projective representations of a finite group with respect to a given factor set and a group of linear characters acting on them. It includes a determination of the number of classes of projectively equivalent representations as well as a result of M. Osima on the classes of linearly equivalent representations. Osima proved his result by defining and calculating on irreducible projective Brauer characters, whereas the method used here is based on Brauer's well-known result for the linear modular representations and an induction argument on suitable coverings.     

A polynomial Hutton theorem with applications

Extending a classical linear result due to Hutton to a nonlinear setting, we prove that a continuous homogeneous polynomial between Banach spaces can be approximated by finite rank polynomials if and only if its adjoint can be approximated by finite rank linear operators. Among other consequences, we apply this result to generalize a classical result due to Aron and Schottenloher about the approximation property on spaces of polynomials and a recent result due to Çaliskan and Rueda about the quasi-approximation property on projective symmetric tensor products.     

A local finiteness theorem for corings over semihereditary rings

The fundamental theorem on coalgebras asserts that coalgebras are locally finite in the case where the ground ring is a field. We prove the local finiteness theorem of corings under the semihereditarity condition on the base algebra and the projectivity condition on a coring. This result generalizes not only the fundamental theorem on coalgebras but also Hazewinkel’s result on the local finiteness of coalgebras over a principal ideal domain and Bergman’s unpublished result on the local finiteness of corings over a semisimple Artinian ring.     

An extension of Peleg's inequality

In this note, we prove an extension of a remarkable result due to B. Peleg. Peleg's result concerns the simultaneous validity of a set of inequalities for families of functions defined on a finite product of standard simplices in finite-dimensional spaces. The main result we prove here provides an extension of that result to the case of functions defined on a rather general product of simplices. Some topological requirements lead us to deal with this problem from a functional point of view.     

Spectral approximation in L(H)

We introduce the concept of numerical range approximant which is related to that of a spectral approximant. We obtain a variant of Bouldin result on spectral approximation of normal operators [3] and an analogous result for numerical range approximation . We also extend Maher's result on partially isometric approximation [9] and Halmos' on positive approximation [6].     

On existence and asymptotic behaviour of solutions of a functional integral equation

The paper contains a result on the existence and asymptotic behaviour of solutions of a functional integral equation. That result is proved under rather general hypotheses. The main tools used in our considerations are the concept of a measure of noncompactness and the classical Schauder fixed point principle. The investigations of the paper are placed in the space of continuous and tempered functions on the real half-line. We prove an existence result which generalizes several ones concerning functional integral equations and obtained earlier by other authors. The applicability of our result is illustrated by some examples.     

Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces

First, we consider a strongly continuous semigroup of nonexpansive mappings defined on a closed convex subset of a complete CAT(0) space and prove a convergence of a Mann iteration to a common fixed point of the mappings. This result is motivated by a result of Kirk (2002) and of Suzuki (2002). Second, we obtain a result on limits of subsequences of Mann iterations of multivalued nonexpansive mappings on metric spaces of hyperbolic type, which leads to a convergence theorem for nonexpansive mappings on these spaces.     

Unified approach to some geometric results in variational analysis

Based on a study of a minimization problem, we present the following results applicable to possibly nonconvex sets in a Banach space: an approximate projection result, an extended extremal principle, a nonconvex separation theorem, a generalized Bishop-Phelps theorem and a separable point result. The classical result of Dieudonné (on separation of two convex sets in a finite-dimensional space) is also extended to a nonconvex setting.     

Multipermutation-Based Intersection Theorem and Its Applications

In this paper, we introduce a multipermutation-based intersection theorem on the product space of several unit simplices, called the simplotope. This theorem gives a substantial generalization of an intersection result of Scarf on the unit simplex (Ref. 1). By using this new result, we also obtain a multipermutation-based generalization of the Brouwer fixed-point theorem on the simplotope. Furthermore, we apply this new result to an economic equilibrium model with indivisibilities and obtain an equilibrium existence theorem.     

Conditions on subgraphs,degrees, and domination for hamiltonian properties of graphs

Motivated by a hamiltonicity result due to Ageev, involving claw-free graphs with a small domination number, we study analogous conditions that guarantee different types of hamiltonian properties. In our first main result we relax the condition on claw-freeness and obtain a common generalization of the result of Ageev and a recent result due to Cai. Our other results deal with similar conditions that guarantee traceability, pancyclicity and hamiltonian-connectivity. We also leave some open problems.     

An acceleration property of theE-algorithm for alternate sequences

We prove a convergence acceleration result by theE-algorithm for sequences whose error has an asymptotic expansion on the scale of comparison for which a determinantal relation holds. This result is generalized to the vector case. Moreover we prove a result which contains an acceleration property for columns and diagonals of theE array. This result is applied to some alternating series.     

Stability of complex hyperbolic space under curvature-normalized Ricci flow

Using the maximal regularity theory for quasilinear parabolic systems, we prove two stability results of complex hyperbolic space under the curvature-normalized Ricci flow in complex dimensions two and higher. The first result is on a closed manifold. The second result is on a complete noncompact manifold. To prove both results, we fully analyze the structure of the Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result, we also define suitably weighted little Hölder spaces on a complete noncompact manifold and establish their interpolation properties.     

Effective stability for slow time-dependent near-integrable Hamiltonians and application

The aim of this note is to prove a result of effective stability for a non-autonomous perturbation of an integrable Hamiltonian system, provided that the perturbation depends slowly on time. Then we use this result to clarify and extend a stability result of Giorgilli and Zehnder for a mechanical system with an arbitrary time-dependent potential.     

Homotopical Stability of Isolated Critical Points of Continuous Functionals

We give a simple proof of the so-called Potential well theorem of Ioffe and Schwartzman, estimating the size of the potential well associated with a local minimum of a continuous functional defined on a complete metric space. Applications to the homotopical stability of an isolated local minimum and to an abstract bifurcation result, as in Ioffe and Schwartzman, are described. We also establish a result on homotopical stability of arbitrary isolated critical points of continuous functionals, thus extending a result of Chang.     

An extension criterion for the local in time solution of the chemotaxis Navier–Stokes equations in the critical Besov spaces

We consider the Keller–Segel model coupled with the incompressible Navier–Stokes equations in the dimension three. Based on the wellposedness result in the critical Besov spaces, we present a result on the extension criterion for the local in time solution in the same functional setting, which is a new result for the model.     

On the fundamental group of hyperelliptic fibrations and some applications

We prove that for a hyperelliptic fibration on a surface of general type with irreducible fibers over a (possibly) non-complete curve, the image of the fundamental group of a general fiber in the fundamental group of the surface is finite. Examples show that the result is optimal. As a corollary of this result we prove two conjectures; the Shafarevich conjecture on holomorphic convexity for the universal cover of these surfaces, and a conjecture of Nori on the finiteness of the fundamental groups of some surfaces. We also prove a striking general result about the multiplicities of multiple fibers of a hyperelliptic fibration on a smooth, projective surface.     

Well-posedness and stability for a mixed order system arising in thin film equations with surfactant

The objective of the present work is to provide a well-posedness result for a capillary driven thin film equation with insoluble surfactant. The resulting parabolic system of evolution equations is not only strongly coupled and degenerated, but also of mixed orders. To the best of our knowledge the only well-posedness result for a capillary driven thin film with surfactant is provided in [4] by the same author, where a severe smallness condition on the surfactant concentration is assumed to prove the result. Thus, in spite of an intensive analytical study of thin film equations with surfactant during the last decade, a proper well-posedness result is still missing in the literature. It is the aim of the present paper to fill this gap. Furthermore, we apply a recently established result on asymptotic stability in interpolation spaces [15] to prove that the flat equilibrium of our system is asymptotically stable.     

Multiplicity result for a double eigenvalue quasilinear problem on unbounded domain

In this paper we prove a multiplicity result for a double eigenvalue quasilinear problem on unbounded domain with nonlinear boundary conditions. We use a recent Ricceri-type result of Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Anal. TMA 54 (2003) 651–665]. This result completes some recent results obtained in this direction.     

Well-Posedness of A Compressible Gas-Liquid Model for Deepwater Oil Well Operations

The main purpose of this paper is two-fold: (i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 (2011), pp. 2014–2047]; (ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 (2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.     

Dilation of generalized Toeplitz kernels on ordered groups

We introduce the concept of Toeplitz-Kre?n-Cotlar triplet on ordered groups and we prove a general dilation result and a general representation result for the positive definite case.This general result includes and extends previous generalizations of the Kre?n extension theorem, the Sz.-Nagy and Foias commutant lifting theorem and the generalized Herglotz-Bochner-Weil theorem.