bluuebunny/crossref_metadata_2025 huggingface dataset:
Torsion in K0 of unit-regular rings
Authors: Goodearl K. R.
Published: December 2008

We construct examples of unit-regular rings R for which K0(R) has torsion, thus answering a longstanding open question in the negative. In fact, arbitrary countable torsion abelian groups are embedded in K0 of simple unit-regular algebras over arbitrary countable fields. In contrast, in all these examples K0(R) is strictly unperforated.
On quasi-F-orthodox semigroups
Authors: Billhardt Bernd , Szendrei Mária B.
Published: December 2008

An orthodox semigroup S is termed quasi-F-orthodox if the greatest inverse semigroup homomorphic image of S1 is F-inverse. In this paper we show that each quasi-F-orthodox semigroup is embeddable into a semidirect product of a band by a group. Furthermore, we present a subclass in the class of quasi-F-orthodox semigroups whose members S are embeddable into a semidirect product of a band B by a group in such a way that B belongs to the band variety generated by the band of idempotents in S. In particular, this subclass contains the F-orthodox semigroups and the idempotent pure homomorphic images of the bifree orthodox semigroups.
On discrete generalised triangle groups
Authors: Hagelberg M. , MacLachlan C. , Rosenberger G.
Published: December 2008

A generalised triangle group has a presentation of the form

whereRis a cyclically reduced word involving bothxandy. WhenR=xy, these classical triangle groups have representations as discrete groups of isometrics ofS2,R2,H2depending on

In this paper, for other wordsR, faithful discrete representations of these groups in Isom+H3=PSL(2,C) are considered with particular emphasis on the caseR= [x, y] and also on the relationship between the Euler characteristic χ and finite covolume representations.
Existence theory for nonresonant singular boundary value problems
Authors: O'Regan Donal
Published: December 2008

We present some existence results for the “nonresonant” singular boundary value problem a.e. on [0, 1] with Here μ is such that a.e. on [0, 1] with has only the trivial solution.
On the foundations of inverse monoids and inverse algebras
Authors: Leech Jonathan
Published: December 2008

Symmetric inverse monoids of objects in arbitrary categories are studied. Necessary and sufficient conditions are given for such monoids to be E-unitary or else form (complete) inverse algebras. Particular attention is given to symmetric inverse monoids of objects in free categories.
Construction of Schauder decomposition on banach spaces of periodic functions
Authors: Goh Say Song , Lee S. L. , Shen Zuowei , Tang W. S.
Published: December 2008

This paper deals with Schauder decompositions of Banach spaces X2π of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,…, which form a multiresolution of X2π,. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space on one hand and by interpolatory projections in the Banach space C2π on the other. The approach, using “orthogonal splines”, is constructive and leads to the construction of a Schauder decomposition of X2π and a biorthogonal system for X2π, and its dual X2π. Decomposition and reconstruction algorithms are derived from the construction.
On some “stability” properties of the full C*-algebra associated to the free group F∞
Authors: Harcharras Asma
Published: December 2008

Let C*(F∞) be the full C*-algebra associated to the free group of countably many generators and SnC*(F∞) be the class of all n-dimensional operator subspaces of C*(F∞). In this paper, we study some stability properties of SnC*(F∞). More precisely, we will prove that for any E0, E1 in SnC*(F∞), the Haagerup tensor product E0⊗hE1 and the operator space obtained by complex interpolation Eθ are (1 + ∈)-contained in C*(F∞) for arbitrary ∈>0. On the other hand, we will show an extension property for WEPC*-algebras.
Nonlinear periodic parabolic problems with nonmonotone discontinuities
Authors: Kandilakis Dimitrios A. , Papageorgiou Nikolaos S.
Published: December 2008

In this paper we consider a nonlinear periodic parabolic boundary value problem with a discontinuous nonmonotone nonlinearity. Using a lifting result for operators of type (S+), a general surjectivity theorem for operators of monotone type and an auxiliary problem defined by truncation and penalization we prove the existence of a solution in the order interval formed by an upper and lower solution. Moreover we show that the set of all such solutions is compact in Lp(T, (Z)).
Geometrically finite kleinian groups and parabolic elements
Authors: Ohshika Ken'ichi
Published: December 2008

Let Γ be a torsion-free geometrically finite Kleinian group. In this paper, we investigate which systems of loxodromic conjugacy classes of Γ can be simultaneously made parabolic in a group on the boundary of the quasi-conformal deformation space of Γ. We shall prove that for this, it is sufficient that the classes of the system are represented by disjoint primitive simple closed curves on the ideal boundary of H3/Γ.
Generalized blocked triangular matrix rings associated with finite abelian centralizer near-rings
Authors: Smith Kirby C. , Van Wyk Leon
Published: December 2008

ForNany member of a large class of finite abelian right centralizer near-rings, the subring of the ring End(N) of endomorphisms of (N, +) generated by the set of right multiplication maps onNis explicitly described as a generalized blocked triangular matrix ring, which in some cases turns out to be a structural matrix ring.
Rank and abelian rank of systems of equations over the free group
Authors: Lawrence John
Published: December 2008

Given a finite irredundant system of equations to be solved over the free group, one has four non-negative integers: the number of equations, the number of indeterminants, the rank of the system and the Abelian rank of the system. We show which four-tuples can actually occur.
On the Ganea strong category in proper homotopy
Authors: Ayala R. , Quintero A.
Published: December 2008

This paper contains some basic relations between Ganea strong category and Lusternik Schnirelmann category in proper homotopy theory. We focus our interest on the case of category 2 in order to show that ℚn is the unique open n-manifold with proper Lusternik-Schnirelmann category 2 (n ≠ 3).
Infinite Coxeter groups are virtually indicarle
Authors: Cooper D. , Long D. D. , Reid A. W.
Published: December 2008

We prove that any infinite Coxeter group has a finite index subgroup which surjects ℤ.
A class of nonlinear elliptic problems with nonconvex constraints and applications
Authors: Chemetov N. , Rodrigues J. F.
Published: December 2008

Conditions for the existence of solutions of a class of elliptic problems with nonconvex constraints are given in the general framework of pseudo-monotone operators. Applications are considered in unilateral problems of free boundary type, yielding the solvability of a Reynold's lubrication model and of a biological population problem with nonlocal terms and global constraints.
The global dimension theorem for weighted convolution algebras
Authors: Ghahramani F. , Selivanov Yu. V.
Published: December 2008

We show that the global dimension, dgA, of every commutative Banach algebra A whose radical is a weighted convolution algebra is strictly greater than one. As an application, we see that in this case H2(A, X) ≠ 0 for some Banach A-bimodule X and thus there exists an unsplittable singular extension of the algebra A.
Excision in Banach simplicial and cyclic cohomology
Authors: Lykova Zinaida A.
Published: December 2008

We prove that, for every extension of Banach algebras 0 → B →A → D → 0 such that B has a left or right bounded approximate identity, the existence of an associated long exact sequence of Banach simplicial or cyclic cohomology groups is equivalent to the existence of one for homology groups. It follows from the continuous version of a result of Wodzicki that associated long exact sequences exist. In particular, they exist for every extension of C*-algebras.
Concentration of the error between a function and its polynomial of best uniform approximation
Authors: Hasson Maurice
Published: December 2008

Let f be a continuous real valued function defined on [−1, 1] and let En(f) denote the degree of best uniform approximation to f by algebraic polynomial of degree at most n. The supremum norm on [a, b] is denoted by ∥.∥[a, b] and the polynomial of degree n of best uniform approximation is denoted by Pn. We find a class of functions f such that there exists a fixed a ∈(−1, 1) with the following property

for some positive constants C and N independent of n. Moreover the sequence is optimal in the sense that if is replaced by then the above inequality need not hold no matter how small C > 0 is chosen.

We also find another, more general class a functions f for which

infinitely often.
Fractional part sums and lattice points
Authors: Nowak Werner Georg
Published: December 2008

The objective of this article are sumsS(M)=∑n;ψ(Mf(n/M)) where ψdenotes essentially the fractional part minus ½,fis aC4-function withfnnonvanishing, and summation is extended over an interval of orderM. ForS(M) an Ω-estimate and a mean-square bound is obtained. Applications to problems concerning the number of lattice points in large planar domains are discussed.
A Prüfer approach to half-linear Sturm-Liouville problems
Authors: Browne Patrick J.
Published: December 2008

We consider the half linear Sturm-Liouville problem

on the interval [0,1] subject to separated boundary conditions (which may be eigenparameter dependent at x = 1) and use Prüfer techniques to produce an oscillation theory for this problem. Both right definite (r > 0) and left definite (r of both signs) cases are discussed.
Canonical bases and standard monomials
Authors: Marsh R. J.
Published: December 2008

Let U be the quantized enveloping algebra associated to a simple Lie algebra g by Drinfel'd and Jimbo. Let λ be a classical fundamental weight for g, and ⋯(λ) the irreducible, finite-dimensional type 1 highest weight U-module with highest weight λ. We show that the canonical basis for ⋯(λ) (see Kashiwara [6, §0] and Lusztig [18, 14.4.12]) and the standard monomial basis (see [11, §§2.4 and 2.5]) for ⋯(λ) coincide.
On duality between K- and J-spaces
Authors: Cobos Fernando , Fernández-Martínez Pedro , Martínez Antón , Raynaud Yves
Published: December 2008

We study the relationship between the dual of the K-space defined by means of a polygon and the J-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is formed by Banach lattices
Extensions of AH algebras with the ideal property
Authors: Pasnicu Cornel
Published: December 2008

In this note we show that if we have an exact sequence of AH algebras (AH stands for “approximately homogeneous”) 0 → I → A → B → 0, then A has the ideal property (i.e., any ideal is generated by its projections) if and only if I and B have the ideal property. Also, we prove that an extension of two AT algebras (AT stands for “approximately circle”) with the ideal property is an AT algebra with the ideal property if and only if the extension is quasidiagonal.
Unique continuation at infinity of solutions to Schrödinger equations with complex-valued potentials
Authors: Cruz-Sampedro J.
Published: December 2008

We obtain optimal L2-lower bounds for nonzero solutions to – ΔΨ + VΔ = EΨ in Rn, n ≥ 2, E ∈ R where V is a measurable complex-valued potential with V(x) = 0(|x|-c) as |x|→∞, for some ε∈ R. We show that if 3δ = max{0, 1 – 2ε} and exp (τ|x|1+δ)Ψ ∈ L2(Rn)for all τ > 0, then Ψ; has compact support. This result is new for 0 < ε ½ and generalizes similar results obtained by Meshkov for = 0, and by Froese, Herbst, M. Hoffmann-Ostenhof, and T. Hoffmann-Ostenhof for both ε≤O and ε≥½. These L2-lower bounds are well known to be optimal for ε ≥ ½ while for ε < ½ this last is only known for ε = O in view of an example of Meshkov. We generalize Meshkov's example for ε< ½ and thus show that for complex-valued potentials our result is optimal for all ε ∈ R.
H2(T, G, ∂) and central extensions for crossed modules
Authors: Grandjean A. R.- , Ladra M.
Published: December 2008

We prove in this paper that if (T, G, ∂) is a perfect and aspherical (Ker ∂ = 1) crossed module, then it admits a universal central extension, whose kernel is the invariant H2(T, G, ∂), that we introduced in [9].
Period polynomials and congruences for Hecke algebras
Authors: Hohnen Winfried
Published: December 2008

Using the Eichler-Shimura isomorphism and the action of the Hecke operator T2 on period polynomials, we shall give a simple and new proof of the following result (implicitly contained in the literature): let f be a normalized Hecke eigenform of weight k with respect to the full modular group with eigenvalues λp under the usual Hecke operators Tp (p a prime). Let Kf be the field generated over Q by the λp for all p. Let p be a prime of Kf lying above 5. Then
The “maximal” tensor product of operator spaces
Authors: Oikhberg Timur , Pisier Gilles
Published: December 2008

In analogy with the maximal tensor product of C*-algebras, we define the “maximal” tensor product E1⊗μE2 of two operator spaces E1 and E2 and we show that it can be identified completely isometrically with the sum of the two Haagerup tensor products: E1⊗hE2 + E2⊗hE1. We also study the extension to more than two factors. Let E be an n-dimensional operator space. As an application, we show that the equality E*⊗μE = E*⊗min E holds isometrically iff E = Rn or E = Cn (the row or column n-dimensional Hilbert spaces). Moreover, we show that if an operator space E is such that, for any operator space F, we have F ⊗min E = F⊗μ E isomorphically, then E is completely isomorphic to either a row or a column Hilbert space.
Real interpolation for divisible cones
Authors: Carro María J. , Ericsson Stefan , Persson Lars-Erik
Published: December 2008

We give necessary and sufficient conditions on a general cone of positive functions to satisfy the Decomposition Property (DP) introduced in [5] and connect the results with the theory of interpolation of cones introduced by Sagher [9]. One of our main result states that ifQsatisfies DP or equivalently is divisible, then for the quasi-normed spacesE0andE1,

According to this formula, it yields that the interpolation theory for divisible cones can be easily obtained from the classical theory.
C*-ideals generated by polynomials
Authors: Tapper Paul
Published: December 2008

The *-algebra A1 is defined to be the free unital *-algebra with one generator x. A *-ideal I of A1 is defined to be a C*-ideal if A1/I may be embedded into a C*-algebra. It is proved that if I is a *-ideal of A1 generated by polynomials in A1, then I is a C*-ideal. This is not true for general *-ideals of A1.
Interaction of some meromorphic solutions of the KdV equation
Authors: Kovalyov M. , Lee K. M.
Published: December 2008

A necessary and sufficient condition for confluence of two poles of a class of meromorphic solutions of the KdV equation is introduced and proved.
A generalization of the Bernstein polynomials
Authors: Oruç Haul , Phillips George M. , Davis Philip J.
Published: December 2008

This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that, when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.
Uniqueness in the Cauchy problem for the heat equation
Authors: Chung Soon-Yeong
Published: December 2008

We relax the growth condition in time for uniqueness of solutions of the Cauchy problem for the heat equation as follows: Let u(x, t) be a continuous function on ℝn × [0, T] satisfying the heat equation in ℝn × (0, t) and the following:

(i) There exist constants a > 0, 0 < α < 1, and C > 0 such that

(ii) u(x, 0) = 0 for x ∈ ℝn.

Then u(x, t)≡ 0 on ℝn × [0, T]

We also prove that the condition 0 < α < 1 is optimal.
Some results on test elements
Authors: Aberbach Ian M. , Maccrimmon Brian
Published: December 2008

Let (R, m) be a Noetherian local reduced ring of positive prime characteristic. We show that if R is ℚ-Gorenstein then the test ideal of R localizes, which extends a result of K. E. Smith. We also show that if Rc, is weakly F-regular and ℚ-Gorenstein, then c has a power which is a completely stable test element. This extends results of Höchster and Huneke.
On products of all elements of a finite semigroup
Authors: Hermann P. Z. , Robertson E. F. , Ruškuc N.
Published: December 2008

LetSbe a finite semigroup. Consider the setp(S)of all elements ofSwhich can be represented as a product of all the elements ofSin some order. It is shown thatp(S)is contained in the minimal idealMofSand intersects each maximal subgroupHofMin essentially the same way. The main result shows thatp(S)intersectsHin a union of cosets ofH′.
On the cyclic coverings of the knot 52
Authors: Bandieri P. , Kim A. C. , Mulazzani M.
Published: December 2008

We construct a family of hyperbolic 3-manifolds whose fundamental groups admit a cyclic presentation. We prove that all these manifolds are cyclic branched coverings of S3 over the knot 52 and we compute their homology groups. Moreover, we show that thecyclic presentations correspond to spines of the manifolds.
On the approximation of Finsler metrics on Euclidean domains
Authors: Barbatis G.
Published: December 2008

We prove that Finsler metrics on Euclidean domains can be approximated in a certain sense by so-called Finsler-type metrics. As an application we improve upon previous estimates on the fundamental solution of higher order parabolic equations.
Composition algebras of degree two
Authors: Elduque Alberto , Pérez-izquierdo José M.
Published: December 2008

Composition algebras in which the subalgebra generated by any element has dimension at most two are classified over fields of characteristic ≠2,3. They include, besides the classical unital composition algebras, some closely related algebras and all the composition algebras with invariant quadratic norm.
On the complex oscillation for a class of homogeneous linear differential equations
Authors: Shi-An Gao
Published: December 2008

Using a combined dominant condition, we obtain general results concerning the complex oscillation for a class of homogeneous linear differential equations w(k) + + … + A1w′ + (A0 + A)w = 0 with k ≥ 2, which has been investigated by many authors. In particular, we discover that there exists a unique case that possesses k linearly independent zero-free solutions for these equations, and we resolve an open problem and simultaneously answer a question of Bank.
Maximal functions and transference for groups of operators
Authors: Blower Gordon
Published: December 2008

Let Δ be the Laplace operator on ℝd and 1 < δ < 2. Using transference methods we show that, for max {q, q/(q – 1)} < 4d/(2d + 1 – δ), the maximal function for the Schrödinger group is in Lq, for f ∈ Lq with Δδ/2f ∈Lq. We obtain a similar result for the Airy group exp it Δ3/2. An abstract version of these results is obtained for bounded C0-groups eitL on subspaces of Lp spaces. Certain results extend to maximal functions defined for functions with values in U M D Banach spaces.
Summability of alternating gap series
Authors: Keating J. P. , Reade J. B.
Published: December 2008

The Abel and Cesàro summabilities of two alternating gap series are investigated. We prove that the series is summable at x = 1 (in both senses), but that is not. In 1907, Hardy obtained essentially the same result for the latter series; our proof is shorter and more elementary: we use the Poisson summation formula to derive an explicit estimate for the size of the oscillations as x → 1_. This represents an example of a general method for determining the Abel summability of similar series.
On the solvability of semilinear differential equations at resonance
Authors: Kuo Chung-Cheng
Published: December 2008

In this paper we use the Leray–Schauder continuation method to study the existence of solutions for semilinear differential equations Lu + g(x, u) = h, in which the linear operator L on L2(Ω) may be non-self-adjoint, the L2(Ω)-function h belongs to N⊥(L), the nonlinear term g(x, u) ∈ O(|u|α) as |u| → ∞ for some 0 ≤ α < 1 and satisfies

for all v ∈ N(L) – {0}, where and
Linear isometries on subalgebras of uniformly continuous functions
Authors: Araujo Jesús , Font Juan J.
Published: December 2008

We describe the linear surjective isometries between various subalgebras of uniformly continuous bounded functions defined on closed subsets of Banach spaces.
Discrete focal boundary-value problems
Authors: Agarwal Ravi P. , O'Regan Donal
Published: December 2008

In this paper we shall employ the nonlinear alternative of Leray–Schauder and known sign properties of a related Green's function to establish the existence results for the nth-order discrete focal boundary-value problem. Both the singular and non-singular cases will be discussed.
Subgroups of finite index in groups with finite complete rewriting systems
Authors: Pride S. J. , Wang Jing
Published: December 2008

We show that if a group G has a finite complete rewriting system, and if H is a subgroup of G with |G : H| = n, then H * Fn–1 also has a finite complete rewriting system (where Fn–1 is the free group of rank n – 1).
Operators having the symmetrized bidisc as a spectral set
Authors: Agler J. , Young N. J.
Published: December 2008

We characterize those commuting pairs of operators on Hubert space that have the symmetrized bidisc as a spectral set in terms of the positivity of a hermitian operator pencil (without any assumption about the joint spectrum of the pair). Further equivalent conditions are that the pair has a normal dilation to the distinguished boundary of the symmetrized bidisc, and that the pair has the symmetrized bidisc as a complete spectral set. A consequence is that every contractive representation of the operator algebra A(Γ) of continuous functions on the symmetrized bidisc analytic in the interior is completely contractive. The proofs depend on a polynomial identity that is derived with the aid of a realization formula for doubly symmetric hereditary polynomials, which are positive on commuting pairs of contractions.
2-groups with few conjugacy classes
Authors: Boston Nigel , Walker Judy L.
Published: December 2008

An old question of Brauer that asks how fast numbers of conjugacy classes grow is investigated by considering the least number cn of conjugacy classes in a group of order 2n. The numbers cn are computed for n ≤ 14 and a lower bound is given for c15. It is observed that cn grows very slowly except for occasional large jumps corresponding to an increase in coclass of the minimal groups Gn. Restricting to groups that are 2-generated or have coclass at most 3 allows us to extend these computations.
Optimal control of a nonlinear elliptic population system
Authors: Arino Ovide , Montero-Sánchez Juan-Aurelio
Published: December 2008

An optimal control for a nonlinear system is considered. The existence of an optimal-control pair, the characterization of the optimal control in terms of the optimal system and the uniqueness of solutions for the control problem are established. The uniqueness requires smallness assumptions on parameters in the functional.
Normal-equivalent operators and operators with dual of scalar-type
Authors: Ghaemi M. B.
Published: December 2008

If T ∈ L(X) is such that T′ is a scalar-type prespectral operator, then Re T′ and Im T′ are both dual operators. It is shown that that the possession of a functional calculus for the continuous functions on the spectrum of T is equivalent to T′ being scalar-type prespectral of class X, thus answering a question of Berkson and Gillespie.
Growth and oscillation theory of non-homogeneous linear differential equations
Authors: Gundersen Gary G. , Steinbart Enid M. , Wang Shupei
Published: December 2008

We investigate the growth and the frequency of zeros of the solutions of the differential equation f(n) + Pn–1 (z) f(n–1) + … + P0 (z) f = H (z), where P0 (z), P1(z), …, Pn–1(z) are polynomials with P0 (z) ≢ 0, and H (z) ≢ 0 is an entire function of finite order.
On quotients of tensor algebras and their C*-envelopes
Authors: Muhly Paul S. , Solel Baruch
Published: December 2008

We identify the C*-envelopes of certain quotients of tensor algebras over C*-correspondences.
On Turnbull identity for skew-symmetric matrices
Authors: Umeda Tôru , Hirai Takeshi
Published: December 2008

In the last six lines of Turnbull's 1948 paper, he left an enigmatic statement on a Capelli-type identity for skew-symmetric matrix spaces. In the present paper, on Turnbull's suggestion, we show that certain Capelli-type identities hold for this case. Our formulae connect explicitly the central elements inU(gln) to the invariant differential operators, both of which are expressed with permanent. This also clarifies the meaning of Turnbull's statement from the Lie-theoretic point of view.
Heisenberg-invariant kummer surfaces
Authors: Hulek K. , Nieto I. , Sankaran G. K.
Published: December 2008

We study, from the point of view of abelian and Kummer surfaces and their moduli, the special quintic threefold known as Nieto's quintic. It is, in some ways, analogous to the Segre cubic and the Burkhardt quartic and can be interpreted as a moduli space of certain Kummer surfaces. It contains 30 planes and has 10 singular points: we describe how some of these arise from bielliptic and product abelian surfaces and their Kummer surfaces.
Derivations of 2-subhomogeneous C*-algebras
Authors: Somerset D. W. B.
Published: December 2008

A characterization is given of those unital, 2-subhomogeneous, Fell C*-algebras which have only inner derivations. This proves Sproston and Strauss's conjecture from 1992. Various examples are given of phenomena which cannot occur for separable C*-algebras. In particular, an example is given of a C*-algebra with only inner derivations which has a quotient algebra admitting outer derivations. This answers a question of Akemann, Elliott, Pedersen and Tomiyama from 1976.
On the solution sets to differential inclusions on an unbounded interval
Authors: Staicu Vasile
Published: December 2008

We prove that for F: [0,∞) × ℝn → K (ℝn) a Lipschitzian multifunction with compact values, the set of derivatives of solutions of the Cauchy problem

is a retract of
On the essential spectrum of Banach-space operators
Authors: Eschmeier Jörg
Published: December 2008

LetTandSbe quasisimilar operators on a Banach spaceX. A well-known result of Herrero shows that each component of the essential spectrum ofTmeets the essential spectrum ofS. Herrero used that, for ann-multicyclic operator, the components of the essential resolvent set with maximal negative index are simply connected. We give new and conceptually simpler proofs for both of Herrero's results based on the observation that on the essential resolvent set ofTthe section spaces of the sheaves

are complete nuclear spaces that are topologically dual to each other. Other concrete applications of this result are given.
Rank properties in finite inverse semigroups
Authors: Isabel Maria , Ribeiro Marques
Published: December 2008

Two possible concepts of rank in inverse semigroup theory, the intermediateI-rank and the upperI-rank, are investigated for the finite aperiodic Brandt semigroup. The so-called largeI-rank is found for an arbitrary finite Brandt semigroup, and the result is used to obtain the large rank of the inverse semigroup of all proper subpermutations of a finite set.
Some examples of critical points for the total mean curvature functional
Authors: Arroyo Josu , Barros Manuel , Garay Oscar J.
Published: December 2008

We study the following problem: establish existence and classification of closed curves which are critical points for the total curvature functional, defined on spaces of curves in a Riemannian manifold. This problem is completely solved in a real space form. Next, we give examples of critical points for this functional in a class of metrics with constant scalar curvature on the three sphere. Also, we obtain a rational one-parameter family of closed helices which are critical points for that functional in ℂℙ2 (4) when it is endowed with its usual Kaehlerian structure. Finally, we use the principle of symmetric criticality to get equivariant submanifolds, constructed on the above curves, which are critical points for the total mean curvature functional.
Jacobians of singular spectral curves and completely integrable systems
Authors: Vivolo Olivier
Published: December 2008

Consider an isospectral manifold formed by matrices M ∈ glr(ℂ)[x] with a fixed leading term. The description of such a manifold is well known in the case of a diagonal leading term with different eigenvalues. On the other hand, there are many important systems where this term has multiple eigenvalues. One approach is to impose conditions in the sub-leading term. The result is that the isospectral set is a smooth manifold, bi-holomorphic to a Zariski open subset of the generalized Jacobian of a singular curve.
Prime ideals and radicals in semigroup-graded rings
Authors: Bell Allen D. , Stalder Shubhangi S. , Teply Mark L.
Published: December 2008

In this paper we study the ideal structure of the direct limit and direct sum (with a special multiplication) of a directed system of rings; this enables us to give descriptions of the prime ideals and radicals of semigroup rings and semigroup-graded rings.

We show that the ideals in the direct limit correspond to certain families of ideals from the original rings, with prime ideals corresponding to “prime” families. We then assume the indexing set is a semigroup ft with preorder defined by α≺β if β is in the ideal generated by α, and we use the direct sum to construct an Ω-graded ring; this construction generalizes the concept of a strong supplementary semilattice sum of rings. We show the prime ideals in this direct sum correspond to prime ideals in the direct limits taken over complements of prime ideals in Ω when two conditions are satisfied; one consequence is that when these conditions are satisfied, the prime ideals in the semigroup ringS[ft] correspond bijectively to pairs (Φ,Q) with Φ a prime ideal of Ω andQa prime ideal ofS. The two conditions are satisfied in many bands and in any commutative semigroup in which the powers of every element become stationary. However, we show that the above correspondence fails when Ω is an infinite free band, by showing thatS[Ω] is prime wheneverSis.

When Ω satisfies the above-mentioned conditions, or is an arbitrary band, we give a description of the radical of the direct sum of a system in terms of the radicals of the component rings for a class of radicals which includes the Jacobson radical and the upper nil radical. We do this by relating the semigroup-graded direct sum to a direct sum indexed by the largest semilattice quotient of Ω, and also to the direct product of the component rings.
Existence theorems on the Dirichlet problem for the equation Δu + f(x, u)=0
Authors: Bonanno Gabriele
Published: December 2008

In this note we consider the Dirichlet problem Δu + f(x, u)=0 in Ω, u = 0 on ∂Ω here Ω is a bounded domain in ℝn(n≧3), with smooth boundary ∂Ω. We prove the existence of strong solutions to the previous problem, which are positive if f satisfies a suitable condition. As a consequence we find that the problem with , may have positive solutions even if g is not a lower-order perturbation of Next We examine the case .
Submodules of Specht modules for Weyl groups
Authors: Halicioğlu Saіt
Published: December 2008

The construction of all irreducible modules of the symmetric groups over an arbitrary field which reduce to Specht modules in the case of fields of characteristic zero is given by G. D. James. Halicioğlu and Morris describe a possible extension of James' work for Weyl groups in general, where Young tableux are interpreted in terms of root systems. In this paper we show how to construct submodules of Specht modules for Weyl groups.
Congruence coherent distributive doublep-algebras
Authors: Adams M. E. , Atallah M. , Beazer R.
Published: December 2008

For distributive doublep-algebras, a close connection is established between being congruence coherent and congruence regular. Every congruence regular distributive doublep-algebra is congruence coherent. Even though every congruence coherent distributive doublep-algebra that has either a non-empty core or finite range is congruence regular, an example is given that is congruence coherent but not congruence regular.
Asymptotic behaviour and blow-up of some unbounded solutions for a semilinear heat equation
Authors: Tzanetis D. E.
Published: December 2008

The initial-boundary value problem for the nonlinear heat equation u1 = Δu + λf(u) might possibly have global classical unbounded solutions, for some “critical” initial data . The asymptotic behaviour of such solutions is studied, when there exists a unique bounded steady state w(x;λ) for some values of λ We find, for radial symmetric solutions, that u*(r, t)→w(r) for any 0<r≤l but supu*(·, t) = u*(0, t)→∞, as t→∞. Furthermore, if , where is some such critical initial data, then û = u(x, t; û0) blows up in finite time provided that f grows sufficiently fast.
The decomposition of artinian modules over hyper-(cyclic or finite) groups
Authors: Qin Y. B.
Published: December 2008

If G is a hyperfinite locally soluble group and A an artinian ZG-module then Zaĭcev proved that A has an f-decomposition. For G being a hyper-(cyclic or finite) locally soluble group, Z. Y. Duan has shown that any periodic artinian ZG-module A has an f-decomposition. Here we prove that: if G is a hyper-(cyclic or finite) group, then any artinian ZG-module A has an f-decomposition.
A mixed dirichlet-neumann problem for a nonlinear reynolds equation in elastohydrodynamic piezoviscous lubrication
Authors: Durany J. , García G. , Vázquez C.
Published: December 2008

The aim of this work is to study the existence of solutions for a mathematical model of the displacement of a piezoviscous lubricant between two elastic surfaces. As we deal with a rolling ball contact problem, the deformations are modelled by the linear Hertzian theory. The fluid pressure behaviour is governed by the classical Reynolds equation for thin film displacement. The relevant aspect of cavitation in lubrication is described by means of the Elrod Adams model which leads to a mathematical free boundary problem.

The two main original features of the model problem in relation to previous works are: the supply of lubricant coming from a groove that is transversal to the direction of fluid displacement and the consideration of a piezoviscous law of Barus. Mathematically, the first one leads to a mixed Dirichlet-Neumann problem for the Reynolds equation and the second one involves an additional nonlinearity in a diffusion type term.
Lattice packing of nearly-euclidean balls in spaces of even dimension
Authors: Rush J. A.
Published: December 2008

We consider nearly-Euclidean balls of the shape

where ε is a small positive number, and n is even. If ε is small enough, then the maximum lattice-packing density of this body is essentially greater than the Minkowski-Hlawka bound for large n.
The solution via monotonicity methods of some nonscalar reaction-diffusion problems
Authors: Delgado Manuel
Published: December 2008

We present some applications of monotonicity methods to the solution of certain nonscalar reaction-diffusion problems. In particular we prove existence under appropriate conditions and we introduce a convergent algorithm.
Minimal permutation representations of the two double covers ofSn
Authors: Brinkman John
Published: December 2008

Let G be a finite group and denote by µ(G) (see [2]) the least positive integermsuch that G has a faithful permutation representation in the symmetric group of degreem. This note considers the value of µ(G) when G is a double cover of the symmetric group.
Biorthogonality in the banach spaces ℓp(n)
Authors: Felton Anthony J. , Rogosinski H. P.
Published: December 2008

We consider the finite-dimensional Banach spaces ℓp(n), where p>l. On these spaces there is a unique homogeneous semi-inner-product [.,.] consistent with the norm. If p≠2 this semi-inner product is not symmetric. We define a pair of vectors x and y to be biorthogonal if [x, y] = [y, x] = 0. For a given non-zero x, let τ(X) be the number of elements in a maximal linearly independent set of vectors biorthogonal to x. If p = 2 it is well-known that this number is n–1. The aim of this paper is to find τ(X) when p≠2. Our investigation shows that the situation differs from the Euclidean case in that the value of τ(X) can be either n–l or n –2. The ‘exceptional’ vectors x for which τ(x) = n –2 are characterised.
Normalizers of finite multiplicity nests
Authors: Davidson Kenneth R.
Published: December 2008

We show that every continuous nest of bounded multiplicity is unitarily equivalent to itself in a non-trivial way. Along the way, it is shown that no finite (measurable) partition of the unit interval can separate absolutely continuous homeomorphisms.
Direct finiteness of certain monoid algebras
Authors: Munn W. D.
Published: December 2008

A semigroup is said to be completely regular if and only if each of its elements lies in a subgroup. It is shown that the algebra of a completely regular monoid (semigroup with identity) over a field of characteristic zero is directly finite.
Distance between Hermitian operators in Schatten classes
Authors: Bhatia Rajendra , Šemrl Peter
Published: December 2008

We consider the distance between a fixed Hermitian operator B and the unitary orbit of another Hermitian operator A and show that in each Schatten p-class, 1<p<∞, critical points of this distance function are at operators commuting with B. As a consequence we obtain a perturbation bound for the eigenvalues of Hermitian operators in these Schatten classes.
Boundary value problems singular in the solution variable with nonlinear boundary data
Authors: O'Regan Donal
Published: December 2008

Existence results are established for the equationy″ +f(t, y) = 0, 0<t<1. Herefmay be singular inyandfis allowed to change sign. Our boundary data includey(0) =y′(1) +ky(1) = 0,k> – 1 andy(0) =y′(1) +cy4(1) = 0,c>0.
Oscillatory and asymptotic behaviour of second order nonlinear difference equations
Authors: Liu Bing , Yan Jurang
Published: December 2008

In this paper we are dealing with oscillatory and asymptotic behaviour of solutions of second order nonlinear difference equations of the form

Some sufficient conditions for all solutions of (E) to be oscillatory are obtained. Asymptotic behaviour of nonoscillatory solutions of (E) is considered also.
On the dynamic scaling behaviour of solutions to the discrete smoluchowski equations
Authors: Da Costa F. P.
Published: December 2008

In this paper we generalize recent results of Kreer and Penrose by showing that solutions to the discrete Smoluchowski equations

with general exponentially decreasing initial data, with density p, have the following asymptotic behaviour

where J = {j: cj(t)>0, t>0} and q = gcd{j: cj(0)>0}.
Proof of a conjecture of Heath-Brown concerning quadratic residues
Authors: Hall R. R.
Published: December 2008

The conjecture in question is that the proportion of the first n positive integers which are quadratic residues of an arbitrary prime p is bounded below by a positive. δ. This is established here as a corollary of a more general result concerning multiplicative functions; the problem of the sharp δ is left open.
Effective computation of the Gelfand-Kirillov dimension
Authors: Bueso José L. , Jiménez F. J. Castro , Jara Pascual
Published: December 2008

In this note we propose an effective method based on the computation of a Gröbner basis of a left ideal to calculate the Gelfand-Kirillov dimension of modules.
The Bourgain algebra of a nest algebra
Authors: Feeman Timothy G.
Published: December 2008

In analogy with a construction from function theory, we herein define right, left, and two-sided Bourgain algebras associated with an operator algebra A. These algebras are defined initially in Banach space terms, using the weak-* topology on A, and our main result is to give a completely algebraic characterization of them in the case where A is a nest algebra. Specifically, if A = alg N is a nest algebra, we show that each of the Bourgain algebras defined has the form A + K ∩ B, where B is the nest algebra corresponding to a certain subnest of N. We also characterize algebraically the second-order (and higher) Bourgain algebras of a nest algebra, showing for instance that the second-order two-sided Bourgain algebra coincides with the two-sided Bourgain algebra itself in this case.
Essentially defined derivations on semisimple Banach algebras
Authors: Villena A. R.
Published: December 2008

We prove that every partially defined derivation on a semisimple complex Banach algebra whose domain is a (non necessarily closed) essential ideal is closable. In particular, we show that every derivation defined on any nonzero ideal of a prime C*-algebra is continuous.
A note on weighted maximal inequalities
Authors: Lai Qinsheng
Published: December 2008

In this paper, we obtain some characterizations for the weighted weak type (1, q) inequality to hold for the Hardy-Littlewood maximal operator in the case 0<q<1; prove that there is no nontrivial weight satisfying one-weight weak type (p, q) inequalities when 0<p≠q< ∞, and discuss the equivalence between the weak type (p, q) inequality and the strong type (p, q) inequality when p≠q.
Centralizers of abelian subgroups in locally finite simple groups
Authors: Kuzucuoǧlu M.
Published: December 2008

It is shown that, if a non-linear locally finite simple group is a union of finite simple groups, then the centralizer of every element of odd order has a series of finite length with factors which are either locally solvable or non-abelian simple. Moreover, at least one of the factors is non-linear simple. This is also extended to abelian subgroup of odd orders.
A remark on the C-normality of maximal subgroups of finite groups
Authors: Wang Yanming
Published: December 2008

A subgroup H is called c-normal in a group G if there exists a normal subgroup N of G such that HN = G and H∩N ≤ HG, where HG =: Core(H) = ∩g∈GHg is the maximal normal subgroup of G which is contained in H. We use a result on primitive groups and the c-normality of maximal subgroups of a finite group G to obtain results about the influence of the set of maximal subgroups on the structure of G.
Completely bounded Banach-Mazur distance
Authors: Zhang Chun
Published: December 2008

Analogous to the Banach-Mazur distance between Banach spaces, we study the completely bounded Banach-Mazur distance between operator spaces.

In many cases of Banach spaces and Hilbert spaces we show that the infimum is attained when T is the identity map, and X, Y have the same base space. This provides a machinery to compute and estimate dcb(X, Y). Later, using symmetric norming functions we construct counterexamples to show that distinct infinite dimensional homogeneous operator spaces may have finite cb-distance, and that two homogeneous Hilbertian operator spaces may not coincide even if they coincide over all 2-dimensional subspaces.
An approach to Boyle's conjecture
Authors: van Huynh Dinh , Rizvi S. Tariq
Published: December 2008

A ring R is called a right QI-ring if every quasi-injective right R-module is injective. The well-known Boyle's Conjecture states that any right QI-ring is right hereditary. In this paper we show that if every continuous right module over a ring R is injective, then R is semisimple artinian. In fact, if every singular continuous right R-module satisfying the restricted semisimple condition is injective, then R is right hereditary. Moreover, in this case, every singular right R-module is injective.
A reaction infiltration problem: classical solutions
Authors: Chadam John , Chen Xinfu , Gianni Roberto , Ricci Riccardo
Published: December 2008

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.
Biorthogonality in the real sequence spaces ℓp
Authors: Felton Anthony J. , Rogosinski H. P.
Published: December 2008

In this paper we generalise some of the results obtained in [1] for the n-dimensional real spaces ℓp(n) to the infinite dimensional real spaces ℓp. Let p >1 with p ≠ 2, and let x be a non-zero real sequence in ℓp. Let ε(x) denote the closed linear subspace spanned by the set of all those sequences in ℓp which are biorthogonal to x with respect to the unique semi-inner-product on ℓp consistent with the norm on ℓp. In this paper we show that codim ε(x)=1 unless either x has exactly two non-zero coordinates which are equal in modulus, or x has exactly three non-zero coordinates α, β, γ with |α| ≥ |β| ≥ |γ| and |α|p > |β|p + |γ|p. In these exceptional cases codim ε(x) = 2. We show that is a linear subspace if, and only if, x has either at most two non-zero coordinates or x has exactly three non-zero coordinates which satisfy the inequalities stated above.
Positive definite kernels and Hilbert C*-modules
Authors: Murphy Gerard J.
Published: December 2008

A theory of positive definite kernels in the context of Hilbert C*-modules is presented. Applications are given, including a representation of a Hilbert C*-module as a concrete space of operators and a construction of the exterior tensor product of two Hilbert C*-modules.
A remark on the tensor product of two maximal operator spaces
Authors: Le Merdy Christian
Published: December 2008

Given a Banach space E, let us denote by Max(E) the largest operator space structure on E. Recently Paulsen-Pisier and, independently, Junge proved that for any Banach spaces E, F, isomorphically where and respectively denote the Haagerup tensor product and the spatial tensor product of operator spaces. In this paper we show that, in general, this equality does not hold completely isomorphically.
Families of SU(2) representations for mapping cylinders of periodic monodromy
Authors: Daskalopoulos G. , Dostoglou S. , Wentworth R.
Published: December 2008

We examine the action of diffeomorphisms of an oriented surface with boundary on the space of conjugacy classes of SU(2) representations of the fundamental group and prove that in the case of a single periodic diffeomorphism the induced action always has fixed points. For the corresponding 3-dimensional mapping cylinders we obtain families of representations parametrized by their value on the longitude of the torus boundary.
The profile near quenching time for the solution of a singular semilinear heat equation
Authors: Guo Jong-Shenq , Hu Bei
Published: December 2008

We study the profile near quenching time for the solutions of the first and second initial boundary value problems (IBVP) for a semilinear heat equation. Under certain conditions, one-point quenching occurs for both first and second IBVPs. Furthermore, we derive the asymptotic self-similar quenching rate for both problems.
A special sublattice of the congruence lattice of a regular semigroup
Authors: Petrich Mario
Published: December 2008

Let S be a regular semigroup and be its congruence lattice. For ρ ∈ , we consider the sublattice Lρ of generated by the congruences pw where w ∈ {K, k, T, t}* and w has no subword of the form KT, TK, kt, tk. Here K, k, T, t are the operators on induced by the kernel and the trace relations on . We find explicitly the least lattice L whose homomorphic image is Lρ for all ρ ∈ and represent it as a distributive lattice in terms of generators and relations. We also consider special cases: bands of groups, E-unitary regular semigroups, completely simple semigroups, rectangular groups as well as varieties of completely regular semigroups.