bluuebunny/crossref_metadata_2025_split huggingface dataset:
Asymptotic equivalence of a linear and nonlinear system with impulse effect
Authors: Simeonov P. S. , Bainov D. D. 
Published: December 2008

The present paper deals with the problem of asymptotic equivalence of the system with impulse effectandwhere x, y:I→Rn; g:I→Rn; f:I × Rn→Rn; bk:Rn→Rn; I = [0, ∞); Rn is the n-dimensional Euclidean space with a norm |·|; A and B are constant matrices; the moments {tk} constitute an increasing sequence 0 < t1 < … < tk < …, limk→∞tk = ∞.
A version of Runge's theorem for the Helmholtz equation with applications to scattering theory
Authors: Ochs R. L. 
Published: December 2008

Let D be a bounded, simply connected domain in the plane R2 that is starlike with respect to the origin and has C2, α boundary, ∂D, described by the equation in polar coordinateswhere C2, α denotes the space of twice Hölder continuously differentiable functions of index α. In this paper, it is shown that any solution of the Helmholtz equationin D can be approximated in the space by an entire Herglotz wave functionwith kernel g ∈ L2[0,2π] having support in an interval [0, η] with η chosen arbitrarily in 0 > η < 2π.
On the non-vanishing of Poincaré series
Authors: Mozzochi C. J. 
Published: December 2008

R. A. Rankin [2] and J. Lehner [1] considered the non-vanishing of Poincaré series for the classical modular matrix group and for an arbitrary fuchsian group, respectively.In this paper we consider the non-vanishing of Poincaré series for the congruence group
An upper bound for λ1 for Γ(q) and Γ0(q)
Authors: Mozzochi C. J. 
Published: December 2008

Under the assumption of the Selberg conjecture I establish by means of the Selberg trace formula the following:Theorem. Let Γ denote Γ(q) or Γ0(q), q square-free. Let Δq denote the Laplace operator on L2(Γ\H), and let Σq denote its discrete spectrum. Then there exists an absolute positive constant A such that for q≧A
Monoids over which all weakly flat acts are flat
Authors: Bulman-Fleming Sydney , McDowell Kenneth 
Published: December 2008

If R is a ring with identity and M is a left R-module then it is well known that the following statements are equivalent:(1) M is flat.(2) The functor −⊗M preserves embeddings of right ideals into R.This paper investigates situations in which the analogous statements are equivalent in the context of S-sets over a monoid S.
Injectively immersed tori in branched covers over the figure eight knot
Authors: Jones Kerry N. 
Published: December 2008

An algorithm is given for determining presence or absence of injectively (at the fundamental group level) immersed tori (and constructing them, if present) in a branched cover of S3, branched over the figure eight knot, with all branching indices greater than 2. Such tori are important for understanding the topology of 3-manifolds in light of (for example) the Jaco-Shalen–Johannson torus decomposition theorem and the fact that the figure eight knot is universal, i.e., that all 3-manifolds are representable as branched covers of S3, branched over the figure eight knot.The algorithm is principally geometric in its derivation and graph-theoretic in its operation. It is applied to two examples, one of which has an incompressible torus and the other of which is atoroidal.
Existence of solutions in a singular biharmonic nonlinear problem
Authors: Hernandez Gaston L. , Choi Y. 
Published: December 2008

In this work we prove the existence and uniqueness of positive solutions of the nonlinear singular boundary value problemwhere 0<σ<1.Extensions of the above results to the case of Δ2u−f(x, u) = 0 with appropriate singularity built into f are also given.
Radial growth and exceptional sets for Cauchy–Stieltjes integrals
Authors: Hallenbeck D. J. , MacGregor T. H. 
Published: December 2008

This paper considers the radial and nontangential growth of a function f given bywhere α>0 and μ is a complex-valued Borel measure on the unit circle. The main theorem shows how certain local conditions on μ near eiθ affect the growth of f(z) as z→eiθ in Stolz angles. This result leads to estimates on the nontangential growth of f where exceptional sets occur having zero β-capacity.
On discrete generalised triangle groups
Authors: Hagelberg M. , MacLachlan C. , Rosenberger G. 
Published: December 2008

A generalised triangle group has a presentation of the formwhereRis a cyclically reduced word involving bothxandy. WhenR=xy, these classical triangle groups have representations as discrete groups of isometrics ofS2,R2,H2depending onIn 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.
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 propertyfor 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 whichinfinitely often.
A Prüfer approach to half-linear Sturm-Liouville problems
Authors: Browne Patrick J. 
Published: December 2008

We consider the half linear Sturm-Liouville problemon 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.
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.
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.
On the complex oscillation for a class of homogeneous linear differential equations
Authors: Shi-An Gao 
Published: December 2008

AbstractUsing 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

AbstractLet 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

AbstractThe 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

AbstractIn 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 satisfiesfor all v ∈ N(L) – {0}, where and
Subgroups of finite index in groups with finite complete rewriting systems
Authors: Pride S. J. , Wang Jing 
Published: December 2008

AbstractWe 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

AbstractWe 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

AbstractAn 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

AbstractAn 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

AbstractIf 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

AbstractWe 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 Turnbull identity for skew-symmetric matrices
Authors: Umeda Tôru , Hirai Takeshi 
Published: December 2008

AbstractIn 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

AbstractWe 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

AbstractA 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 essential spectrum of Banach-space operators
Authors: Eschmeier Jörg 
Published: December 2008

AbstractLetTandSbe 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 sheavesare 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

AbstractTwo 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

AbstractWe 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

AbstractConsider 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.
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.
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 formSome 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 equationswith general exponentially decreasing initial data, with density p, have the following asymptotic behaviourwhere J = {j: cj(t)>0, t>0} and q = gcd{j: cj(0)>0}.
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.
The isomorphism problem for a class of para-free groups
Authors: Fine Benjamin , Rosenberger Gerhard , Stille Michael 
Published: December 2008

In 1962 Gilbert Baumslag introduced the class of groups Gi, j for natural numbers i, j, defined by the presentations Gi, j = < a, b, t; a−1 = [bi, a] [bj, t] >. This class is of special interest since the groups are para-free, that is they share many properties with the free group F of rank 2.Magnus and Chandler in their History of Combinatorial Group Theory mention the class Gi, j to demonstrate the difficulty of the isomorphism problem for torsion-free one-relator groups. They remark that as of 1980 there was no proof showing that any of the groups Gi, j are non-isomorphic. S. Liriano in 1993 using representations of Gi, j into PSL(2, pk), k ∈ ℕ, showed that G1,1 and G30,30 are non-isomorphic. In this paper we extend these results to prove that the isomorphism problem for Gi, 1, i ∈ ℕ is solvable, that is it can be decided algorithmically in finitely many steps whether or not an arbitrary one-relator group is isomorphic to Gi, 1. Further we show that Gi, 1 ≇ G1, 1 for all i > 1 and if i, k are primes then Gi, 1 ≅ Gk, 1 if and only if i = k.
A counterexample of hermitian liftings
Authors: Lin Pei-Kee 
Published: December 2008

Let X be a complex Banach space, and let and denote respectively the algebras of bounded and compact operators on X. The quotient algebra is called the Calkin algebra associated with X. It is known that both and are complex Banach algebras with unit e. For such unital Banach algebras B, setand define the numerical range of x ∈ B asx is said to be hermitian if W(x)⊆R. It is known thatFact 1. ([4 vol. I, p. 46]) x is hermitian if and only if ‖eiαx‖ = (or ≦)1 for all α ∈ R, where ex is defined by
Positive multipoint Padé continued fractions
Authors: Hendriksen Erik , Njåstad Olav 
Published: December 2008

Multipoint Padé fractions were introduced in [2]. They are continued fractions defined in the following way:Let {a1,a2,…,ap} be given fixed points in the complex plane. For each n ≧1 let an = am where 1≦m≦p and n≡m (mod p).