bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic behaviour of ideals relative to injective modules over commutative Noetherian rings
Authors: Toroghy H. Ansari , Sharp R. Y.
Published: December 2008

LetEbe an injective module over the commutative Noetherian ringA, and letabe an ideal ofA. TheA-module (0:Eα) has a secondary representation, and the finite set AttA(0:Eα) of its attached prime ideals can be formed. One of the main results of this note is that the sequence of sets (AttA(0:Eαn))n∈Nis ultimately constant. This result is analogous to a theorem of M. Brodmann that, ifMis a finitely generatedA-module, then the sequence of sets (AssA(M/αnM))n∈Nis ultimately constant.
An algebraic link concordance group for (p, 2p−1)-links in S2p+1
Authors: Gilmer Pat , Livingston Charles
Published: December 2008

A concordance classification of links of , p < 1, is given in terms of an algebraically defined group, Φ±, which is closely related to Levine's algebraic knot concordance group. For p=1,Φ_ captures certain obstructions to two component links in S3 being concordant to boundary links, the generalized Sato-Levine invariants defined by Cochran. As a result, purely algebraic proofs of properties of these invariants are derived.
On accessible subrings of associative rings
Authors: Andruszkiewicz R. R.
Published: December 2008

We describe for every naturalnthe class of ringsRsuch that ifRis an accessible (left accessible) subring of a ring thenRis ann-accessible (n-left-accessible) subring of the ring. This is connected with the problem of the termination of Kurosh's construction of the lower (lower strong) radical. The result forn= 2 was obtained by Sands in a connection with some other questions.
Annihilators in semiprime right Goldie rings
Authors: Hajarnavis C. R.
Published: December 2008

(i) Let R be a semiprime right Goldie ring with dim R = n. Then a maximal chain of right annihilators in R has exactly n terms, (ii) A semiprime locally right Goldie ring with ACC and DCC on right annihilators is a right Goldie ring.
Normal -Fitting classes
Authors: Beidleman J. C. , Tomkinson M. J.
Published: December 2008

The authors together with M. J. Karbe [Ill. J. Math.33 (1989) 333–359] have considered Fitting classesof-groups and, under some rather strong restrictions, obtained an existence and conjugacy theorem for-injectors. Results of Menegazzo and Newell show that these restrictions are, in fact, necessary.

The Fitting classisnormalif, for eachis the unique-injector ofG.isabelian normal if, for each. For finite soluble groups these two concepts coincide but the class of Černikov-by-nilpotent-groups is an example of a nonabelian normal Fitting class of-groups. In all known examples in which-injectors existis closely associated with some normal Fitting class (the Černikov-by-nilpotent groups arise from studying the locally nilpotent injectors).

Here we investigate normal Fitting classes further, paying particular attention to the distinctions between abelian and nonabelian normal Fitting classes. Products and intersections with (abelian) normal Fitting classes lead to further examples of Fitting classes satisfying the conditions of the existence and conjugacy theorem.
Existentially closed locally cofinite groups
Authors: Leinen Felix
Published: December 2008

Let be a class of finite groups. Then a c-group shall be a topological group which has a fundamental system of open neighbourhoods of the identity consisting of normal subgroups with -factor groups and trivial intersection. In this note we study groups which are existentially closed (e.c.) with respect to the class Lc of all direct limits of c-groups (where satisfies certain closure properties). We show that the so-called locally closed normal subgroups of an e.c. Lc-group are totally ordered via inclusion. Moreover it turns out that every ∀2-sentence, which is true for countable e.c. L-groups, also holds for e.c. Lc-groups. This allows it to transfer many known properties from e.c. L-groups to e.c. Lc-groups.
Countable periodic CC-groups as automorphism groups
Authors: Dixon Martyn R.
Published: December 2008

It is shown that if G is a group and Aut G is a countable periodic CC-group then Aut G is FC.
Distributivep-algebras and doublep-algebras havingn-permutable congruences
Authors: Beazer R.
Published: December 2008

Recent research on aspects of distributive lattices,p-algebras, doublep-algebras and de-Morgan algebras (see [2] and the references therein) has led to the consideration of the classes(n≧1) of distributive lattices having non+ 1-element chain in their poset of prime ideals. In [1] we were obliged to characterize the members ofby a sentence in the first-order theory of distributive lattices. Subsequently (see [2]), it was realised thatcoincides with the class of distributive lattices havingn+1-permutable congruences. This result is hereby employed to describe those distributivep-algebras and doublep-algebras havingn-permutable congruences. As an application, new characterizations of those distributivep-algebras and doublep-algebras having the property that their compact congruences are principal are obtained. In addition, those varieties of distributivep-algebras and doublep-algebras havingn-permutable congruences are announced.
Sur les algebres de Bernstein V: Les algebres de Bernstein Jordan faibles
Authors: Labra Alicia , Mallol Cristian , Micali Artibano , Varro Richard
Published: December 2008

Nous Présentons ici l'étude, dans l'optique exhibée dans [7], d'une catégorie d'algèbres à idempotents, commutatives, non associatives, définies par des relations. On y trouve une structure qui n'est en général ni pondérée ni de Jordan et où, cependant, ces conditions sont équivalentes.

Following a previous paper, we study here a class of commutative and non associative algebras with idempotents and defined by relations. We find a structure which is not, in general, baric or Jordan but where these notions are equivalent.
Modular correspondences on X(11)
Authors: Adler Allan
Published: December 2008

In this paper, we show how to give a geometric interpretation of the modular correspondence T3 on the modular curve X(11) of level 11 using projective geometry. We use Klein's theorem that X(11) is isomorphic to the nodal curve of the Hessian of the cubic threefold Λ defined by V2W + W2X + X2Y + Y2Z + Z2V = 0 in P4(C) and geometry which we learned from a paper of W. L. Edge. We show that the correspondence T3 is essentially the correspondence which associates to a point p of the curve X(11) the four points where the singular locus of the polar quadric of p with respect to Λ meets X(11). Our control of the geometry is good enough to enable us to compute the eigenvalues of T3 acting on the cohomology of X(11). This is the first example of an explicit geometric description of a modular correspondence without valence. The results of this article will be used in subsequent articles to associate two new abelian varieties to a cubic threefold, to desingularize the Hessian of a cubic threefold and to study self-conjugate polygons formed by the quadrisecants of the nodal curve of the Hessian.
Products of idempotent endomorphisms of an independence algebra of finite rank
Authors: Fountain John , Lewin Andrew
Published: December 2008

Products of idempotents are investigated in the endomorphism monoid of an algebra belonging to a class of algebras which includes finite sets and finite dimensional vector spaces as special cases. It is shown that every endomorphism which is not an automorphism is a product of idempotent endomorphisms. This provides a common generalisation of earlier results of Howie and Erdos for the cases when the algebra is a set or vector space respectively.
Elements of finite order in Stone-Čech compactifications
Authors: Baker John , Hindman Neil , Pym John
Published: December 2008

LetSbe a free semigroup (on any set of generators). WhenSis given the discrete topology, its Stone-Čech compactification has a natural semigroup structure. We give two results about elementspof finite order inβS. The first is that any continuous homomorphism ofβSinto any compact group must sendpto the identity. The second shows that natural extensions, to elements of finite order, of relationships between idempotents and sequences with distinct finite sums, do not hold.
On the deficiencies of composite entire functions
Authors: Langley J. K.
Published: December 2008

For any sequence (aj) of complex numbers and for any ρ > ½, we construct an entire function F with the following properties. F has order ρ, mean type, each aj is a deficient value of F, and F is given by F(z)=f(g(z)), where f and g are transcendental entire functions. This complements a result of Goldstein. We also construct, for any ρ>½, an entire function G of order p, mean type, such that liminf,→ ∞ T(r, G)/T(r, G′)>1.
Congruence permutable extensions of distributive doublep-algebras
Authors: Beazer R. , Sichler J.
Published: December 2008

Every distributive doublep-algebraLis shown to have a congruence permutable extensionKsuch that every congruence ofLhas a unique extension toK.
Group rings whose torsion units form a subgroup
Authors: Coelho Sônia P. , Milies C. Polcino
Published: December 2008

In this note, we determine fields K and groups G that are either nilpotent or FC and such that the set of torsion elements of the group ring KG forms a subgroup.
A simple proof of Arazy's theorem
Authors: Erdos J. A.
Published: December 2008

Arazy has characterized the isometries of p, (0 < p ≦ ∞, p ≠ 2) onto itself as all maps of the form X↦UXV where U and V are either both unitary or both anti-unitary. A simple proof of this result is given.
Multiresolution and wavelets
Authors: Jia Rong-Qing , Shen Zuowei
Published: December 2008

Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspaceSofL2(ℝd), letSkbe the 2k-dilate ofS(k∈ℤ). A necessary and sufficient condition is given for the sequence {Sk}k∈ℤto fom a multiresolution ofL2(ℝd). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable properties. With the aid of the general theory of vector fields on spheres, it is demonstrated that the intrinsic properties of the scaling function must be used in constructing orthogonal wavelets with a certain decay rate. When the scaling function is skew-symmetric about some point, orthogonal wavelets and prewavelets are constructed in such a way that they possess certain attractive properties. Several examples are provided to illustrate the general theory.
A further necessary and sufficient condition for strong convergence of nonlinear contraction semigroups and of iterative methods for accretive operators in Banach spaces
Authors: Xu Zong-Ben , Jiang Yao-Lin , Roach G. F.
Published: December 2008

Let A be a quasi-accretive operator defined in a uniformly smooth Banach space. We present a necessary and sufficient condition for the strong convergence of the semigroups generated by – A and of the steepest descent methods to a zero of A.
The f-decomposition of Artinian modules over hyperfinite groups
Authors: Duan Z. Y.
Published: December 2008

A ℤG-module A is said to have an f-decomposition if in which A∫ is a ℤG-submodule of A such that each irreducible ℤG-factor of A∫ as an abelian group is finite and the ℤG-submodule A∫ has no finite irreducible ℤG-factors. In this paper, we prove that: if G is a hyperfinite group then any artinian ℤG-module A has an f-decomposition, which gives a positive answer to the question raised by D.I. Zaitzev in 1986.
The co-localization of an Artinian module
Authors: Melkersson Leif , Schenzel Peter
Published: December 2008

For a multiplicative set S of a commutative ring R we define the co-localization functor HomR(Rs,⋅). It is a functor on the category of R-modules to the category of Rs-modules. It is shown to be exact on the category of Artinian R-modules. While the co-localization of an Artinian module is almost never an Artinian Rs-module it inherits many good properties of A, e.g. it has a secondary representation. The construction is applied to the dual of a result of Bourbaki, a description of asymptotic prime divisors and the co-support of an Artinian module.
Open surfaces with congruent geodesics
Authors: Charitos Charlambos
Published: December 2008

The aim of this paper is to prove the Theorem: Let M be a complete non compact surface without boundary in the euclidean space 3. We suppose that all geodesies of M are congruent. Then M is an affine plane in 3.
Microlocal regularity on step two nilpotent Lie groups
Authors: Miller Kenneth G.
Published: December 2008

A necessary and sufficient condition for a homogeneous left invariant partial differential operator P on a nilpotent Lie group G to be hypoelliptic is that π(P) be injective in π for every nontrivial irreducible unitary representation π of G. This was conjectured by Rockland in [18], where it was also proved in the case of the Heisenberg group. The necessity of the condition in the general case was proved by Beals [2] and the sufficiency by Helffer and Nourrigat [4]. In this paper we present a microlocal version of this theorem when G is step two nilpotent. The operator may be homogeneous with respect to any family of dilations on G, not just the natural dilations. We may also consider pseudodifferential operators as well as partial differential operators.
Cohomology of induced modules in rings of differential operators
Authors: Brown Kenneth A. , Levasseur Thierry
Published: December 2008

Let K be a field of characteristic zero and let Δ ={δ1,…,δn} be a set of commuting K-derivations of the commutative Noetherian K-algebra R. Let S = R[X1,…,Xn] be the corresponding ring of differential operators, so [Xi, r] = Xir − rXi=δi(r and [Xi, Xj]=0, for 1≦i, j≦n. Let M be a maximal ideal of R with R/M of finite dimension over K. The purpose of this note is to describe the groups
Almost Hermitian homogeneous structures
Authors: Abbena Elsa , Garbiero Sergio
Published: December 2008

Let (M, g, J) be an almost Hermitian manifold. More precisely, M is a ∞ differentiable manifold of dimension 2n, J is an almost complex structure on M, i.e. it is a tensor field of type (1, 1) such that

for any X∈(M), ((M) is the Lie algebra of ∞ vector fields on M), and g is a Riemannian metric compatible with J, i.e.
Torsion-free pre-images of modules of finite length
Authors: O'Carroll L.
Published: December 2008

The purpose of this note is to provide a simplified proof of the following result due to Crawley-Boevey, Kropholler and Linnell.
An iteration method for the determination of an unknown boundary condition in a parabolic initial-boundary value problem
Authors: Pilant Michael , Rundell William
Published: December 2008

Consider the initial boundary value problem

In the context of the heat conduction problem, this models the case where the heat flux across the ends at the rod is a function of the temperature. If the heat exchange between the rod and its surroundings is purely by convection, then one commonly assumes that f is a linear function of the difference in temperatures between the ends of the rod and that of the surroundings, (Newton's law of cooling). For the case of purely radiative transfer of energy a fourth power law for the function f is usual, (Stefan's law).
Endomorphisms of fibred groups
Authors: Maxson Carlton J. , Pilz Gunter F.
Published: December 2008

A collection = {Gα|α∈A} of proper subgroups Gα of a group G is a fibration of G if

It is of geometric interest to associate two semigroups to a group G with fibration :
On extensions of valuations to simple transcendental extensions
Authors: Khanduja Sudesh K. , Garg Usha
Published: December 2008

Let ν0 be a valuation of a field K0 with residue field k0 and value group Z, the group of rational integers. Let K0(x) be a simple transcendental extension of K0. In 1936, Maclane [3] gave a method to determine all real valuations V of K0(x) which are extensions of ν0. But his method does not seem to give an explicit construction of these valuations. In the present paper, assuming K0 to be a complete field with respect to ν0, we explicitly determine all extensions of ν0 to K0(x) which have Z as the value group and a simple transcendental extension of k0 as the residue field. If V is any extension of ν0 to K0(x) having Z as the value group and a transcendental extension of k0 as the residue field, then using the Ruled Residue theorem [4, 2, 5], we give a method which explicitly determines V on a subfield of K0(x) properly containing K0.
On the projective tensor product of Fréchet spaces
Authors: Díaz Juan C. , Molina Juan A. López
Published: December 2008

We are concerned with the following problem. Let F be a Fréchet Montel space and let E be a Fréchet space with a certain property (P). When does it follow that the complete projective tensor product has the property (P)? (We consider the following properties: being Montel, reflexive, satisfying the density condition.) In this paper we provide a positive answer if F is a Montel generalized Dubinsky sequence space with decreasing steps.
Congruence lattices of regular semigroups related to kernels and traces
Authors: Petrich Mario
Published: December 2008

The kernel–trace approach to congruences on a regular semigroupScan be refined by introducing the left and right traces. This induces eight operators on the lattice of congruences onS:t1,k, tr,;Tt,K,Tr;t,T. We describe the lattice of congruences onSgenerated by six 3-element subsets of the set {ωt1, ωk, ωtr, εTt, εK, εTr} where ω and ε denote the universal and the equality relations. This is effected by means of a diagram and in terms of generators and relations on a free distributive lattice, or a homomorphic image thereof. We perform the same analysis for the lattice of congruences onSgenerated by the set {εK, ωk, εT, ωt}.
An injective far-field pattern operator and inverse scattering problem in a finite depth ocean
Authors: Xu Yongzhi
Published: December 2008

The inverse scattering problem for acoustic waves in shallow oceans are different from that in the spaces of R2 and R3 in the way that the “propagating” far-field pattern can only carry the information from the N +1 propagating modes. This loss of information leads to the fact that the far-field pattern operator is not injective. In this paper, we will present some properties of the far-field pattern operator and use this information to construct an injective far-field pattern operator in a suitable subspace of L2(∂Ω). Based on this construction an optimal scheme for solving the inverse scattering problem is presented using the minimizing Tikhonov functional.
Invariants and examples of group actions on trees and length functions
Authors: Wilkens David L.
Published: December 2008

An action of a group G on a tree, and an associated Lyndon length function l, give rise to a hyperbolic length function L and a normal subgroup K having bounded action. The Theorem in Section 1 shows that for two Lyndon length functions l, l′ to arise from the same action of G on some tree, L = L′ and K = K′. Moreover for L non-abelian L = L′ implies K = K′. That this is not so for abelian L is shown in Section 2 where two examples of Lyndon length functions l, l′ on an H.N.N. group are given, with their associated actions on trees, for which L = L′ is abelian but K≠K′.
On the semiprimitivity of skew polynomial rings
Authors: Moussavi A.
Published: December 2008

Let R be a left Noetherian ring with the ascending chain condition on right annihilators, let α be a ring monomorphism of R and δ an α-derivation of R. We prove that, if R is semiprime or α-prime, then R[X;α, δ] is semiprimitive (and left Goldie), and that J(R[X;α]) equals N(R)[X;α].
DenseQ-subalgebras of Banach andC*-algebras and unbounded derivations of Banach andC*-algebras
Authors: Kissin E. , Shulman V. S.
Published: December 2008

The paper studies denseQ-subalgebras of Banach andC*-algebras. It proves that the domainD(δ) of a closed unbounded derivation δ of a Banach unital algebraAautomatically contains the identity and is aQ-subalgebra ofA, so thatSpA(x) =SpD(δ)(x) for allx∈D(δ). The paper shows that every finite-dimensional semisimple representation of aQ-subalgebra is continuous. It also shows that if π is an injective *-homomorphism of a dense locally normalQ*-subalgebraBof aC*-algebra, then ‖x‖≦‖π(x)‖ for allx∈B. The paper studies the link between closed ideals of a Banach algebraAand of its dense subalgebraB. In particular, ifAis aC*-algebra andBis a locally normal *-subalgebra ofA, thenI→I∩Bis a one-to-one mapping of the set of all closed two-sided ideals inAonto the set of all closed two-sided ideals inBand.
On the semilattice of idempotents of a free inverse monoid
Authors: Silva Pedro V.
Published: December 2008

Some new concepts are introduced, in particular that of a unique factorization semilattice. Necessary and sufficient conditions are given for two principal ideals of the semilattice of idempotents of a free inverse monoidFIM(X) to be isomorphic and some properties of the Munn semigroup ofE[FIM(X)] are obtained. Some results on the embedding of semilattices inE[FIM(X)] are also obtained.
Lacunary Müntz systems
Authors: Borwein Peter , Erdélyi Tamás
Published: December 2008

The classical theorem of Müntz and Szász says that the span of

is dense in C[0,1] in the uniform norm if and only if . We prove that, if {λi} is lacunary, we can replace the underlying interval [0,1] by any set of positive measure. The key to the proof is the establishment of a bounded Remez-type inequality for lacunary Müntz systems. Namely if A ⊆ [0,1] and its Lebesgue measure µ(A) is at least ε > 0 then

where c depends only on ε and Λ (not on n and A) and where Λ:=infiλi+1/λi>1.
Asymptotic estimates for eigenvalues of right definite two parameter Sturm–Liouville problems
Authors: Browne Patrick J. , Sleeman B. D.
Published: December 2008

Precise asymptotic estimates for the eigenvalues of a uniformly right definite two parameter system of Sturm–Liouville problems are developed. The work extends recent results of B. P. Rynne.
Rings of differential operators on toric varieties
Authors: Jones A. G.
Published: December 2008

Let be a finite dimensional toric variety over an algebraically closed field of characteristic zero, k. Let be the sheaf of differential operators on . We show that the ring of global sections, is a finitely generated Noetherian k-algebra and that its generators can be explicitly found. We prove a similar result for the sheaf of differential operators with coefficients in a line bundle.
Sn-normal semigroups
Authors: Levi I. , McFadden R. B.
Published: December 2008

Certain subsemigroups of the full transformation semigroup Tn on a finite set of cardinality n are investigated, namely those subsemigroups S of Tn, which are normalised by the symmetric group on n elements, the group of units of Tn. The Sn-normal closure of an element of Tn is determined, and the structure of the Sn-normal ideals consisting of the members of Tn whose image contains at most r elements is studied.
Wavelet bases for a unitary operator
Authors: Lee S. L. , Tan H. H. , Tang W. S.
Published: December 2008

Let T be a unitary operator on a complex Hilbert space ℋ, and X, Y be finite subsets of ℋ. We give a necessary and sufficient condition for TZ(X): {Tnx: n ∈ Z, x ∈ X} to be a Riesz basis of its closed linear span 〈TZ(X)〉. If TZ(X) and TZ(Y) are Riesz bases, and 〈TZ(X)〉⊂〈TZ(Y)〉, then X is extendable to X′ such that TZ(X′) is a Riesz basis of TZ(Y) The proof provides an algorithm for the construction of Riesz bases for the orthogonal complement of 〈TZ(X)〉 in 〈TZ(Y)〉. In the case X consists of a single B-spline, the algorithm gives a natural and quick construction of the spline wavelets of Chui and Wang [2, 3]. Further, the duality principle of Chui and Wang in [3] and [4] is put in the general setting of biorthogonal Riesz bases in Hilbert space.
On fractional integration of generalized functions on a half-line
Authors: Rubin B.
Published: December 2008

A new approach to fractional integrals of distributions on a half-line is suggested. The results admit an extension to a large class of Mellin convolutions.
Finite type immersions of flat tori into Euclidean spaces
Authors: Baikoussis Christos , Defever Filip , Koufogiorgos Themis , Verstraelen Leopold
Published: December 2008

We prove the existence of nontrivial k-type surfaces by constructing k-type immersions of flat tori in 6 which are not product immersions.
On groups with a triple factorisation
Authors: Fransman Andrew
Published: December 2008

The aim of this paper is to discuss groups G=HK=HA=KA with a triple factorisation as a product of two subgroups H and K and a nilpotent normal subgroup A. It is of interest to know whether such a group G satisfies some nilpotency or supersolubility condition if H and K satisfy the same condition. A positive answer to this problem is given for certain group classes under the hypothesis that A is prefactorised in G = HK. Some applications of the main theorem are also mentioned.
Matrix and vector sequence transformations revisited
Authors: Brezinski C. , Salam A.
Published: December 2008

Sequence transformations are extrapolation methods. They are used for the purpose of convergence acceleration. In the scalar case, such algorithms can be obtained by two different approaches which are equivalent. The first one is an elimination approach based on the solution of a system of linear equations and it makes use of determinants. The second approach is based on the notion of annihilation difference operators. In this paper, these two approaches are generalized to the matrix and the vector cases.
The Cartan determinant and generalizations of quasihereditary rings
Authors: Burgess W. D. , Fuller K. R.
Published: December 2008

The Cartan determinant conjecture for left artinian rings was verified for quasihereditary rings showing detC(R) = detC(R/I), where I is a protective ideal generated by a primitive idempotent. This article identifies classes of rings generalizing the quasihereditary ones, first by relaxing the “projective” condition on heredity ideals. These rings, called left k-hereditary are all of finite global dimension. Next a class of rings is defined which includes left serial rings of finite global dimension, quasihereditary and left 1-hereditary rings, but also rings of infinite global dimension. For such rings, the Cartan determinant conjecture is true, as is its converse. This is shown by matrix reduction. Examples compare and contrast these rings with other known families and a recipe is given for constructing them.
The spectra of Toeplitz operators with unimodular symbols
Authors: Nakazi Takahiko
Published: December 2008

The spectrum σ(Tφ) of a Toeplitz operator Tφ on the open unit disc D for a unimodular symbol φ is studied and many sufficient conditions for σ(Tφ)⊆∂D or σ(Tφ) = are given. In particular if φ is a unimodular function in H∞ + C, then σ(Tφ)⊆∂D or σ(Tφ) =
On the capability of groups
Authors: Ellis Graham
Published: December 2008

We show how the third integral homology of a group plays a role in determining whether a given group is isomorphic to an inner automorphism group. Various necessary conditions, and sufficient conditions, for the existence of such an isomorphism are obtained.
On Cohen-Macaulay and Gorenstein simplicial affine semigroups
Authors: Rosales J. C. , García-Sánchez Pedro A.
Published: December 2008

We give arithmetic characterizations which allow us to determine algorithmically when the semigroup ring associated to a simplicial affine semigroup is Cohen-Macaulay and/or Gorenstein. These characterizations are then used to provide information about presentations of this kind of semigroup and, in particular, to obtain bounds for the cardinality of their minimal presentations. Finally, we show that these bounds are reached for semigroups with maximal codimension.
Finite groups which are products of pairwise totally permutable subgroups
Authors: Ballester-Bolinches A. , Pedraza-Aguilera M. C. , Pérez-Ramos M. D.
Published: December 2008

Finite groups which are products of pairwise totally permutable subgroups are studied in this paper. The -residual, -projectors and -normalizers in such groups are obtained from the corresponding subgroups of the factor subgroups under suitable hypotheses.
Finite travelling waves for semilinear parabolic systems
Authors: Wang Ming-Xin
Published: December 2008

In this paper, finite travelling waves for the semilinear parabolic systems

are studied, where di > 0, ei > 0, mij ≥ 0 for all 1 ≤ i,j ≤ n, and for all 1 ≤ i ≤ n. Let M = (mij)n × n and A = I – M. It will be proved that (*) has finite travelling waves if and only if all principal minors of A are positive. Moreover, some asymptotic behaviours of finite travelling waves will be obtained.
Bounds for the size of integral solutions to Ym = f(X)
Authors: Poulakis Dimitrios
Published: December 2008

Let K be an algebraic number field with ring of integers OK and f(X) ∈ OK[X]. In this paper we establish improved explicit upper bounds for the size of solutions in OK, of diophantine equations Y2 = f(X), where f(X) has at least three roots of odd order, and Ym = f(X), where m is an integer ≥ 3 and f(X) has at least two roots of order prime to m.
Gelfand-Kirillov dimension of multi-filtered algebras
Authors: Torrecillas José Gómez
Published: December 2008

We consider associative algebras filtered by the additive monoid ℕp. We prove that, under quite general conditions, the study of Gelfand-Kirillov dimension of modules over a multi-filtered algebra R can be reduced to the associated ℕp-graded algebra G(R). As a consequence, we show the exactness of the Gelfand-Kirillov dimension when the multi-filtration is finite-dimensional and G(R) is a finitely generated noetherian algebra. Our methods apply to examples like iterated Ore extensions with arbitrary derivations and “homothetic” automorphisms (e.g. quantum matrices, quantum Weyl algebras) and the quantum enveloping algebra of sl(v + 1)
Convexity and generalized Bernstein polynomials
Authors: Goodman Tim N. T. , Oruç Halil , Phillips George M.
Published: December 2008

In a recent generalization of the Bernstein polynomials, the approximated function f is evaluated at points spaced at intervals which are in geometric progression on [0, 1], instead of at equally spaced points. For each positive integer n, this replaces the single polynomial Bnf by a one-parameter family of polynomials , where 0 < q ≤ 1. This paper summarizes briefly the previously known results concerning these generalized Bernstein polynomials and gives new results concerning when f is a monomial. The main results of the paper are obtained by using the concept of total positivity. It is shown that if f is increasing then is increasing, and if f is convex then is convex, generalizing well known results when q = 1. It is also shown that if f is convex then, for any positive integer n This supplements the well known classical result that when f is convex.
Some natural subgroups of the Nottingham group
Authors: Camina Rachel
Published: December 2008

The Nottingham group can be described as the group of normalized automorphisms of the ring Fp[[t]], namely, those automorphisms acting trivially on tFp[[t]]/t2Fp[[t]]. In this paper we consider certain proper subgroups of the Nottingham group. We prove that these subgroups are identical to their normalizers and that some of them are isomorphic to the Nottingham group.
A criterion for hyperbolicity
Authors: Batty Michael
Published: December 2008

The usual definition of hyperbolicity of a group G demands that all geodesic triangles in the Cayley graph of G should be thin. Using the theorem that a susbquadratic isoperimetric inequality implies a linear one, we show that it is in fact only necessary for all triangles from a given combing to be thin, thus giving a new criterion for hyperbolicity of finitely presented groups.
The Structure of 0-E-unitary inverse semigroups I: the monoid case
Authors: Lawson Mark V.
Published: December 2008

This is the first of three papers in which we generalise the classical McAlister structure theory for E-unitary inverse semigroups to those 0-E-unitary inverse semigroups which admit a 0-restricted, idempotent pure prehomomorphism to a primitive inverse semigroup. In this paper, we concentrate on finding necessary and sufficient conditions for the existence of such prehomomorphisms in the case of 0-E-unitary inverse monoids. A class of inverse monoids which satisfy our conditions automatically are those which are unambiguous except at zero, such as the polycyclic monoids.
Faithful, irreducible *-representations for group algebras of free products
Authors: Crabb M. J. , McGregor C. M.
Published: December 2008

Let G be the free product of groups A and B, where |A|≥3 and |B|≥2. We construct faithful, irreducible *-representations for the group algebras ℂ[G] and ℓ1(G). The construction gives a faithful, irreducible representation for F[G] when the field F does not have characteristic 2.
On a question of Milnor concerning singularities of maps
Authors: Rees Elmer G.
Published: December 2008

Restrictions are given on the dimensions m and k for which there is a map f: ℝ m → ℝk whose Jacobian has rank k in a neighbourhood of a singular point if f is either quadratic or even. The restrictions are shown to be best possible in the quadratic case.
Combinatorial L2-determinants
Authors: Deitmar Anton
Published: December 2008

We show that the zeta function of a regular graph admits a representation as a quotient of a determinant over a L2-determinant of the combinatorial Laplacian.
Equations with torsion-free coefficients
Authors: Clifford Andrew , Goldstein Richard Z.
Published: December 2008

In this paper we generalize techniques used by Klyachko and the authors to prove some tessellation results about S2. These results are applied to prove the solvability of certain equations with torsion-free coefficients.
The asymptotic behaviour of the mean-square of fractional part sums
Authors: Kühleitner Manfred , Nowak Werner Georg
Published: December 2008

In this article we consider sumsS(t) = Σnψ(tf(n/t)), where ψ denotes, essentially, the fractional part minus ½fis aC4-function withf″ non-vanishing, and summation is extended over an interval of ordert. For the mean-square ofS(t), an asymptotic formula is established. Iffis algebraic this can be sharpened by the indication of an error term.
The efficiency of standard wreath product
Authors: Çevik A. Sinan
Published: December 2008

Let ξ be the set of all finite groups that have efficient presentations. In this paper we give sufficient conditions for the standard wreath product of two ξ-groups to be a ξ-group.
On a quartic diophantine equation
Authors: Stroeker R. J. , De Weger B. M. M.
Published: December 2008

In this paper we consider the quartic diophantine equation 3(y2 – 1) = 2x2(x2 – 1) in integers x and y. We show that this equation does not have any other solutions (x, y) with x≧0 than those given by x = 0,1,2,3,6,91. Two approaches are emphasized, one based on diophantine approximation techniques, the other depends on the structure of certain quartic number fields.
A lower bound for the number of zeros of a meromorphic function and its second derivative
Authors: Langley J. K.
Published: December 2008

We prove that for a function f(z) transcendental and meromorphic in the plane and not of the form exp(az + b), we have either N(r, 1/ff″)≠0(T(r, f′/f)) or .
A mathematician among the molasses barrels: Maclaurin's unpublished memoir on volumes Introduction: Maclaurin's memoir and its place in eighteenth-century Scotland
Authors: Grabiner Judith V.
Published: December 2008

Suppose we are given a solid of revolution generated by a conic section. Slice out a frustum of the solid [14, diagrams pp. 77, 80]. Then, construct a cylinder, with the same height as the frustum, whose diameter coincides with the diameter of the frustum at the midpoint of its height. What is the difference between the volume of the frustum and the volume of this cylinder? Does this difference depend on where in the solid the frustum is taken?

The beautiful theorems which answer these questions first appear in a 1735 manuscript by Colin Maclaurin (1698–1746). This manuscript [14], the only original mathematical work by Maclaurin not previously printed, is published here for the first time, with the permission of the Trustees of the National Library of Scotland. (An almost identical copy [15] exists in the Edinburgh University Library.) In this work, Maclaurin proved that the difference between the cylinder constructed as above and the frustum of the given solid depends only on the height of the frustum, not the position of the frustum in the solid. When the solid is a cone, Maclaurin showed that its frustum exceeds the corresponding cylinder by one fourth the volume of a similar cone with the same height. For a sphere, the cylinder exceeds the frustum by one half the volume of the sphere whose diameter is equal to the height of the frustum; this holds, he observed, for all spheres. He derived analogous results for the ellipsoid and hyperboloid of revolution. Finally, for the paraboloid of revolution, he proved that the cylinder is precisely equal to the frustum.
On semi-artinian modules and injectivity conditions
Authors: Clark J. , Smith P. F.
Published: December 2008

It is well known that a module M has finite length if and only if it is semi-artinian and Noetherian or, equivalently, semi-noetherian and artinian. Our main result shows that finite length is often achieved by just assuming that M is semi-artinian, semi-noetherian and has finitely generated socle.
Compact subsemigroups of (βℕ, +) containing the idempotents
Authors: Hindman Neil , Strauss Dona
Published: December 2008

The space βℕ is the Stone-Čech compactification of the discrete space of positive integers. The set of elements of βℕ which are in the kernel of every continuous homomorpnism from βℕ to a topological group is a compact semigroup containing the idempotents. At first glance it would seem a good candidate for the smallest such semigroup. We produce an infinite nested sequence of smaller such semigroups all defined naturally in terms of addition on ℕ.
The maximal operator space of a normed space
Authors: Paulsen Vern I.
Published: December 2008

We obtain some new results about the maximal operator space structure which can be put on a normed space. These results are used to prove some dilation results for contractive linear maps from a normed space into B(H). Finally, we prove CB(MIN(X), MAX(y)) = Γ2(X, Y) and apply this result to prove some new Grothendieck-type inequalities and some new estimates on spans of “free” unitaries.
Upper bounds for the separation of real zeros of polynomials
Authors: Walker Peter
Published: December 2008

Let be a polynomial with distinct real zeros whose separation is defined by δ(f) = min i≠j(ai-aj ). We establish upper estimates for δ(f′-kf) in terms of n, k, and δ(f). The results give sufficient conditions for the inverse operator (D – kl)−1 to preserve the reality of the zeros of a polynomial.
Homogeneous structures on Kähler submanifolds of complex projective spaces
Authors: Console Sergio , Fino Anna
Published: December 2008

In this paper we give a differential characterization of homogeneous Kähler submanifolds of complex projective spaces in terms of the existence of a tensor field, the homogeneous structureS. We show that for any m∈M, Smdetermines a unitary representation whose orbit atmis a compact, complete Kähler submanifold which extendsM. We consider the U(n) × U(N ~ n) (n = dimℂM) module of the space of these tensors and we find its irreducible factors.
A time-like surface in Minkowski 3-space which contains pseudocircles
Authors: Izumiya Shyuichi , Takiyama Akihiro
Published: December 2008

Simple characterizations of a pseudosphere or a plane in Minkowski 3-space by the existence of pseudocircles are given.
A note on the Gaussian cardinal-interpolation operator
Authors: Sivakumar N.
Published: December 2008

Suppose λ is a positive number, and let , x∈Rd, denote the d-dimensional Gaussian. Basic theory of cardinal interpolation asserts the existence of a unique function , x∈Rd, satisfying the interpolatory conditions , k∈Zd, and decaying exponentially for large argument. In particular, the Gaussian cardinal-interpolation operator, given by , x∈Rd, , is a well-defīned linear map from ℓ2(Zd) into L2(Rd). It is shown here that its associated operator-norm is , implying, in particular, that is contractive. Some sidelights are also presented.
Comments on some inequalities of Pearce and Pečarić
Authors: Alzer Horst
Published: December 2008

We prove inequalities for convex functions, Lp norms, and sums of powers. Our results sharpen recently published inequalities of C. E. M. Pearce and J. E. Pečarić.
A comparison theorem on magnetic jacobi fields
Authors: Adachi Toshiaki
Published: December 2008

A scalar multiple of the Kähler form of a Kähler manifold is called a Kähler magnetic field. We are focused on trajectories of charged particles under this action. As a variation of trajectories we define a magnetic Jacobi field. In this paper we discuss a comparison theorem on magnetic Jacobi fields, which corresponds to the Rauch's comparison theorem.
A new proof of N. J. Young's theorem on the orbits of the action of the symplectic group
Authors: Timotin Dan
Published: December 2008

The group of symplectic transformations acts on the unit ball of a Hilbert space. The structure of the orbits has been determined by N. J. Young in [8]. We provide a new proof of this theorem; it is slightly simpler than the original one, and does not involve Brown–Douglas–Fillmore theory. Moreover, the steps followed hopefully throw some additional light on the subject. We rely heavily on previous work of Khatskevich, Shmulyan and Shulman ([5, 6, 7[); the proofs of the results used are included for completeness.
Box dimension for graphs of fractal functions
Authors: Brown Gavin , Yin Qinghe
Published: December 2008

We calculate the box-dimension for a class of nowhere differentiable curves defined by Markov attractors of certain iterated function systems of affine maps.
The different and differentials of local fields with imperfect residue fields
Authors: de Smit Bart
Published: December 2008

Let K be a complete field with respect to a discrete valuation and let L be a finite Galois extension of K. If the residue field extension is separable then the different of L/K can be expressed in terms of the ramification groups by a well-known formula of Hilbert. We will identify the necessary correction term in the general case, and we give inequalities for ramification groups of subextensions L′/K in terms of those of L/K. A question of Krasner in this context is settled with a counterexample. These ramification phenomena can be related to the structure of the module of differentials of the extension of valuation rings. For the case that [L: K] = p2, where p is the residue characteristic, this module is shown to determine the correction term in Hilbert's formula.
Some integer-valued trigonometric sums
Authors: Byrne Graeme J. , Smith Simon J.
Published: December 2008

It is shown that for m = 1,2,3,…, the trigonometric sums and can be represented as integer-valued polynomials in n of degrees 2m – 1 and 2m, respectively. Properties of these polynomials are discussed, and recurrence relations for the coefficients are obtained. The proofs of the results depend on the representations of particular polynomials of degree n – 1 or less as their own Lagrange interpolation polynomials based on the zeros of the nth Chebyshev polynomial Tn(x) = cos(narccos x), -1≤x≤1.
Dickson–Stirling numbers
Authors: Hsu L. C. , Mullen Gary L. , Shiue Peter Jau-Shyong
Published: December 2008

The Dickson polynomialDn, (x,a) of degreenis defined bydenotes the greatest integer function. In particular, we defineD0(x,a) = 2 for all realxanda. By using Dickson polynomials we present new types of generalized Stirling numbers of the first and second kinds. Some basic properties of these numbers and a combinatorial application to the enumeration of functions on finite sets in terms of their range values is also given.
E-Ideals in baric algebras: basic properties
Authors: Catalan A. , Mallol C. , Costa R.
Published: December 2008

In this work we introduce the notion of E-ideal, generalizing I. M. H. Etherington's idea. We study the general characteristics of the lattice of E-ideals in baric algebras, and some properties inherited from an arithmetic of train polynomials.
On quasi-orthodox semigroups with inverse transversals
Authors: Blyth T. S. , Santos M. H. Almeida
Published: December 2008

An inverse transversal of a regular semigroup S is an inverse subsemigroup So that contains precisely one inverse of each element of S. Here we consider the case where S is quasi-orthodox. We give natural characterisations of such semigroups and consider various properties of congruences.
Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space
Authors: Hayashi Nakao , Hirata Hitoshi
Published: December 2008

We study the initial value problem to the Davey-Stewartson system for the elliptic-hyperbolic case in the usual Sobolev space. We prove local existence and uniquenessH5/2with a condition such that theL2norm of the data is sufficiently small.
On the structure of an endomorphism near-ring
Authors: Peterson Gary L.
Published: December 2008

If G is an additive (but not necessarily abelian) group and S is a semigroup of endomorphisms of G, the endomorphism near-ring R of G generated by S consists of all the expressions of the form ɛ1s1+…+ɛnsnwhere ɛi=±1 and si∈S for each i. When functions are written on the right, R forms a distributively generated left near-ring under pointwise addition and composition of functions. A basic reference on near-rings which has a substantial treatment of endomorphism near-rings is [6].
Limits of pure states
Authors: Archbold R. J.
Published: December 2008

In [7, Section 5], Glimm showed that if φ and ψ are inequivalent pure states of a liminal C*-algebra A such that the Gelfand-Naimark-Segal (GNS) representations πφ and πψ cannot be separated by disjoint open subsets of the spectrum Â then ½ (φ+ψ) is a weak*-limit of pure states. We extend this to arbitrary C*-algebras (and more general convex combinations) by means of what we hope will be regarded as a transparent proof based on the notion of transition probabilities. As an application, we show that if J is a proper primal ideal of a separable C*-algebra A then there exists a state φ in (the pure state space) such that J=ker πφ (Theorem 3). The significance of this is discussed below after the introduction of further notation and terminology.
Finite groups of deficiency zero involving the Lucas numbers
Authors: Campbell C. M. , Robertson E. F. , Thomas R. M.
Published: December 2008

In this paper, we investigate a class of 2-generator 2-relator groups G(n) related to the Fibonacci groups F(2,n), each of the groups in this new class also being defined by a single parameter n, though here n can take negative, as well as positive, values. If n is odd, we show that G(n) is a finite soluble group of derived length 2 (if n is coprime to 3) or 3 (otherwise), and order |2n(n + 2)gnf(n, 3)|, where fn is the Fibonacci number defined by f0=0,f1=1,fn+2=fn+fn+1 and gn is the Lucas number defined by g0 = 2, g1 = 1, gn+2 = gn + gn+1 for n≧0. On the other hand, if n is even then, with three exceptions, namely the cases n = 2,4 or –4, G(n) is infinite; the groups G(2), G(4) and G(–4) have orders 16, 240 and 80 respectively.
Principal train algebras of rank 3 and dimensions≦5
Authors: Costa R.
Published: December 2008

A commutative algebra A over the field F, endowed with a non-zero homorphism ω:A →F is principal train if it satisfies the identity xr+y1ω(x)xr−1 +… +yr−1ω(x)r−1x=0 where y1,…,yr−1 are fixed elements in F. We present in this paper, after the introduction of the concept of “type” of A, some results concerning the classification in the case r = 3. In particular we describe all these algebras of dimension≦5.