bluuebunny/crossref_metadata_2025 huggingface dataset:
Note on a paper of P. M. Cohn
Authors: Singh Surjit
Published: November 2008

P. M. Cohn has given a characterization of pseudovaluation on a field in (1). There he defines the notion of an integral element over a multiplicatively closed set and states that the association of the set A to the set A* of all elements that are integral over it is a closure operator. There is an error in the statement that A* = (A*)*. In this note we show, by an example, that A* and (A*)* are not equal in general. We also give an example to show that even for the special type of sets that Cohn needs, namely the gauge sets, this property fails to hold. However, since the other conditions for a closure operator (A ⊆ A* and A ⊆ B implies A* ⊆ B*) are satisfied, one obtains a Kuratowski closure operator by iterating *. If we denote by Ā the closure of A by iterating * then theorem 10·3, its corollary and theorem 10·4 in (1) that have a bearing on this error, are valid as stated with the same proof replacing only K* by . Further theorem 13·3 is valid without modification since Cohn considers only a special class of pseudovaluations namely regular pseudo valuations for which K* = .
Rado's theorem for polymatroids
Authors: McDiarmid Colin J. H.
Published: November 2008

The theorem of R. Rado (12) to which I refer by the name ‘Rado's theorem for matroids’ gives necessary and sufficient conditions for a family of subsets of a finite setYto have a transversal independent in a given matroid onY. This theorem is of fundamental importance in both transversal theory and matroid theory (see, for example, (11)). In (3) J. Edmonds introduced and studied ‘polymatroids’ as a sort of continuous analogue of a matroid. I start this paper with a brief introduction to polymatroids, emphasizing the role of the ‘ground-set rank function’. The main result is an analogue for polymatroids of Rado's theorem for matroids, which I call not unnaturally ‘Rado's theorem for polymatroids’.
Hilbert space methods in the theory of Jordan algebras. I
Authors: Devapakkiam C. Viola
Published: November 2008

In this paper, we study the structure of certain infinite-dimensional Jordan algebras admitting an inner product. These algebras, called J*-algebras in the sequel, have already been considered in (4) in connexion with the norm uniqueness problem for non-associative algebras. We deal here with the structure and classification of these algebras. Existence of self-adjoint idempotents plays a central role in the classification problem.
Representation of systems of measurable sets
Authors: Bollobás B. , Varopoulos N. Th.
Published: November 2008

The aim of this note is to prove an analogue of P. Hall's theorem on distinct representatives (1) for a family of measurable sets.
Positive-moment problems in abstract measure spaces
Authors: Rogosinski H. P.
Published: November 2008

In this paper we continue the investigation of positive-moment problems, begun in (4). For an arbitrary index set A we consider a family (fα)α ∈ A of measurable real-valued functions on a measure-space (X, µ). We suppose throughout that

where (Xm) is an increasing sequence of measurable subsets of X and where, for each α in A and each m, fα is µ-integrable over Xm. Let (сα)α ∈ A be a given family of real numbers. We consider the following restricted positive-moment problem: does there exist a measurable function g on X such that 0 ≤° g ≤° 1 and such that

for every α in A? (Here the symbol ‘≤°’ indicates that the relation ≤ holds almost everywhere with respect to µ on X. Symbols ‘ = °, <°, …’ are used similarly.) If such a g exists we call (сα)α ∈ A a moment family for the problem:
On the Lusternik–Schnirelmann category of Grassmannians
Authors: Berstein Israel
Published: November 2008

This note contains a partial generalization of the results of (3). We extend to arbitrary n and k the complete determination of the cases in which cup length is strictly less than the maximum possible value dim Gn, k(R) = nk. We also show that the Lusternik–Schnirelmann category cat Gn, k(R) < nk in the same cases.
The supersolvable residual of an -group
Authors: Brewster Ben , Ottaway Malcolm
Published: November 2008

Let be the class of groups possessing a subgroup of index n for each divisor n of the group order. McLain (7) initiated the formal investigation of and observed that every solvable group is a direct factor of an -group. However, subclasses of provide some interesting problems. Various subclasses of which satisfy other properties were studied by McLain; the upshot being that these classes approach supersolvability. This program was pursued by Humphreys (3) and Humphreys and Johnson (4), among others. In particular, , the largest quotient closed subclass of , was considered in (3) and (4). Humphreys (3) has shown an odd order -group is supersolvable, but provides some non-supersolvable groups. Our motivation is that if S ∈ QR0(S3), the formation generated by S3, and V is a faithful irreducible GF(2) [S]-module, the semidirect product VS ∈ .
Vector lattices freely generated by distributive lattices
Authors: Beynon W. M.
Published: November 2008

In this paper, the duality theory for vector lattices developed by the author in (2) is applied to the study of vector lattices freely generated by distributive lattices.

If L is a finite distributive lattice defined by a set of generators X, subject to a finite set of relations R, then the vector lattice FVL(L) freely generated by the elements of L subject to the relations governing intersection and union in L is a finitely generated projective vector lattice, being a quotient of the vector lattice freely generated by elements of X by the principal ideal generated by the relations R. Thus, there is a polyhedron Q, such that FVL(L) is isomorphic with the vector lattice of real valued polyhedral functions on Q, under pointwise operations, and the isomorphism class of FVL(L) determines and is determined by the polyhedral type of Q. The principal result of this paper shows that the polyhedral class to which Q belongs can be simply characterised in terms of the nerve of the poset P of join-irreducible elements of L. Explicitly, up to polyhedral equivalence, Q is a suspension of the nerve of P.
On null cone preserving mappings
Authors: Lester J. A. , McKiernan M. A.
Published: November 2008

Alexandrov (1), Zeeman (3) and others after them have investigated at length the problem of characterizing as Lorentz transformations those mappings f of Minkowski space M which ‘preserve cones’, i.e. if C(a) denotes the null-cone in M with vertex a ∈ M, then

for all a ∈ M.
Some unexpectedly non-singular orbit spaces
Authors: Morton H. R.
Published: November 2008

The orbit space of a manifold under the smooth action of a compact Lie group is typically a ‘manifold with singularities’. The orbits of a given type each form a mani-fold, but these ‘strata’ generally do not give a manifold when pieced together. For example, the orbit space of S3 under the action of given by the matrix.

is the suspension of P(2), which fails to be a manifold at the suspension points.

In this paper I shall give examples where, in spite of having many orbit types, the orbit space is a manifold, with or without boundary.
Bounds for the solution of a non-linear parabolic initial-boundary value problem
Authors: Carter M. R.
Published: November 2008

A number of papers have appeared over the past decade or so which study questions of the existence and stability of positive steady-state solutions for parabolic initial-boundary value problems of the general form
Primitive irreducible representations of nilpotent groups
Authors: Harper D. L.
Published: November 2008

Here we answer a question raised by Zaleskii (5) and reiterated by Segal (3) of whether a finitely generated nilpotent group can have primitive irreducible representations.
Chain conditions and the existence of delta-families
Authors: Williams N. H.
Published: November 2008

Let = (Ai;i ∈ I) be an indexed family of sets. The family is said to contain the family = (Bj;j ∈ J) if there is a one-to-one map f from J into I such that Bj = Af(i) for all j in J. The indexed family = (Ai;i ∈ I) is said to be a Δ (λ)-family if |I| = λ and Ai ∩ Aj = Ak ∩ Ai for all pairs i, j and k, l from I. The family is said to be a (λ, k)-family if |I| = λ and |Ai| = k for all Ai.
On Legendre transformations and umbilic catastrophes
Authors: Sewell M. J.
Published: November 2008

In a previous paper this author used elementary mathematics to describe some simple connexions between multi-valued Legendre transformations and those elementary catastrophes having one ‘behaviour’ variable, which belong to a family of polynomials called cuspoids (see Sewell (13)). The Legendre singularities permitted there are isolated and of dimension one, i.e. they exist where a Hessian matrix exceptionally has co-rank one (not more) and elsewhere has full rank (co-rank zero).
The word problem for semigroups satisfying x3 = x
Authors: Gerhard J. A.
Published: November 2008

In the paper (4) of Green and Rees it was established that the finiteness of finitely generated semigroups satisfying xr = x is equivalent to the finiteness of finitely generated groups satisfying xr−1 = 1 (Burnside's Problem). A group satisfying x2 = 1 is abelian and if it is generated by n elements, it has at most 2n elements. The free finitely generated semigroups satisfying x3 = x are thus established to be finite, and in fact the connexion with the corresponding problem for groups can be used to give an upper bound on the size of these semigroups. This is a long way from an algorithm for a solution of the word problem however, and providing such an algorithm is the purpose of the present paper. The case x = x3 is of interest since the corresponding result for x = x2 was done by Green and Rees (4) and independently by McLean(6).
Martingale convergence in von Neumann algebras
Authors: Lance E. Christopher
Published: November 2008

Let N be a von Neumann subalgebra of a von Neumann algebra M. A linear mapping π: M → N is called a retraction if it is idempotent and has norm one. By a result of Tomiyama(15) a retraction is a positive mapping and is a module homo-morphism over N. A retraction is normal if it is ultraweakly continuous, and faithful if it does not annihilate any nonzero positive element of M. Suppose that (Nn)n≥1 is an increasing sequence of von Neumann subalgebras of M whose union is weakly dense in M and that, for each n, πn: M → Nn is a faithful normal retraction. The sequence (πn) is called a martingale if, whenever m ≥ n,
The topological s-cobordism theorem fails in dimension 4 or 5
Authors: Matumoto T. , Siebenmann L.
Published: November 2008

Although examples have been known since 1969 [Si], which reveal a quite similar failure of the differentiable and piecewise-linear s-cobordism theorems, these did not immediately suggest any topological failure.
On nonlinear perturbations of linear second order elliptic boundary value problems
Authors: Fitzpatrick P. M.
Published: November 2008

Let Ω ⊆ n be open and bounded, with ∂Ω smooth. Sufficient conditions on f are given in order that for p > n, the equation

has a solution for every h ∈ Lp; L is a second order symmetric elliptic operator and B represents either the first, second or third boundary value problems. These conditions are in terms of the asymptotic behaviour of f, in its second variable, in relation to those λ for which there is a nontrivial solution of
Some cubic surfaces with no rational points
Authors: Bremner Andrew
Published: November 2008

Selmer(1) conjectured that the Hasse principle holds for all cubic surfaces of the type

that is, such a surface has a rational point whenever it has points defined over every p-adic field Qp; and he proved this assertion in the case that ab = cd.
On polycyclic groups with isomorphic finite quotients
Authors: Grunewald Fritz , Segal Daniel
Published: November 2008

Following P. F. Pickel (5) we write (G) for the set of isomorphism classes of finite quotients of a group G. One of the outstanding problems in the theory of polycyclic groups is to determine whether there can be infinitely many non-isomorphic polycyclic groups G with a given (G). We solve a special case of this problem with our first main result:

Theorem 1. Let G be an abelian-by-cyclic polycyclic group. Then the polycyclic-by-finite groups H withlie in only finitely many isomorphism classes.
Path node-covering constants for certain families of trees
Authors: Meir A. , Moon J. W.
Published: November 2008

1. introduction. A set P of disjoint paths in a graph G is a node-covering of G if every node of G is in a path in P. (For definitions not given here see (5) or (11).) The path (node-covering) number of G is the smallest possible number p(G) of paths in such a node-covering of G. The problem of determining the path number of a graph was considered in (1) and (4) for undirected graphs and in (2) for directed graphs. In particular, an algorithm for determining the path number of a tree was given in (1) and (4). If ℱ denotes some family of trees, let μ(n) = μℱ(n) denote the average value of p(T) over all trees T in ℱ with n nodes. Our object here is to show the existence and to determine the value of the path (node-covering) constant

for certain families ℱ of trees. The arguments are similar to those used in (7), (8), and (9), where some other parameters, associated with families of trees, were investigated.
On dichotomy of Riesz products
Authors: Ritter G.
Published: November 2008

Background. Riesz products are very useful for the construction of singular measures on compact, Abelian groups. Under some circumstances, two Riesz products are either equivalent or singular in the measure-theoretic sense. Exact knowledge of these circumstances has been of major interest ever since the 1930s, when Riesz's famous example (8) was recognized as a fertile source of examples of singular continuous measures. Zygmund(11) showed that any Riesz product over a Hadamard dissociate subset of ℕ is either a square integrable function or singular with respect to Lebesgue measure. Hewitt–Zuckerman(4) generalized these products to all compact, Abelian groups, introducing the notion of a dissociate subset. They extended Zygmund's result in certain cases. The next major step was taken by Brown–Moran(3) and Peyrière(6), (7), who showed that two Riesz products

are mutually singular if

The author (9) has improved another result of Brown–Moran (3) by showing that µa and µb are equivalent if
Remarks on generalized analytic independence
Authors: Valla Giuseppe
Published: November 2008

This paper is concerned with the notion of independence relating sets of elements in a ring A to a proper ideal a of A. A set of elements a1, …, an ∈A is called a-independent if every form in A[X1, …, Xn] vanishing at a1,…, an has all its coefficients in a. This notion leads to many questions (cf. (2) and (12)), which are of some interest in their own right, several of which are considered here. On the other hand, this independence is related to the structure of the graded ring associated to the ideal generated by the set of elements, hence is often relevant to some problems concerning regular sequences and complex.
Groups with many characteristically simple subgroups
Authors: Wilson J. S.
Published: November 2008

1. A group G is called characteristically simple if it has no proper non-trivial subgroups which are invariant under all automorphisms of G. It is known that if G is characteristically simple then each countable subgroup lies in a countable characteristically simple subgroup of G. A similar assertion holds for simple groups. These results were proved by Philip Hall in lectures in 1966, and further proofs appear in (4) and (6). For simple groups there is a well known and elementary result in the other direction: if every two-generator subgroup of a group G lies in a simple subgroup, then G is simple. These considerations prompt the question (first raised, I believe, by Philip Hall) whether a group G is necessarily characteristically simple if each countable subgroup lies in a characteristically simple subgroup.
Subrings of the first neighbourhood ring
Authors: Kirby D.
Published: November 2008

1. Introduction. In (2) we associated with a commutative ring R with identity the lattice ℒ(R) of rings S which satisfy (i) R ⊆ S ⊆ T, where T is the total quotient ring of R, and (ii) dS ⊆ R for some d ∈ R which is not a zero-divisor. The rings of ℒ(R) can be constructed by blowing up ideals of the set of ideals A of R which satisfy (i) 0: A = 0, and (ii) there exist integers m1n ≥ 1 and α ∈ An such that αAm = Am+n (see Propositions 2·3 and 2·5 of (2)).
Multiple points of codimension one immersions of oriented manifolds
Authors: Eccles Peter John
Published: November 2008

Work by L.S.Pontrjagin(18) and M.W.Hirsch(7) allows us to identify the stablen-stemwith the bordism group of oriented compact closed smoothn-manifolds immersed in ℝn+1. In a recent paper (11), U. Koschorke discusses invariants thereby defined onby analysing the self-intersections of immersed manifolds. In particular he discusses the homomorphism

defined by assigning to a generic immersionMn→ ℝn+1number (modulo 2) of its (n+ 1)-fold points.
The Hughes problem for exponent nine
Authors: Laffey Thomas J.
Published: November 2008

Let G be a finite group and n a natural number. Set Hn(G) = ≺g ∈ G|gn ≠ 1≻. The aim of this paper is to prove the following result.
Galerkin approximations in several parameter bifurcation problems
Authors: Alexander J. C. , Fitzpatrick P. M.
Published: November 2008

The purpose of this paper is to prove a theorem giving conditions yielding global bifurcation of the solutions of a family of parameterized nonlinear equations, the domain and the range of which lie in Banach spaces, where the parameter is allowed to be a vector in , k a positive integer. The basic contribution is that the parameter is vector valued and that the nonlinearities allowed are very general; however, even for scalar parameters, our results extend those of previous authors.
Conditions for the local existence of metric in a generic affine manifold
Authors: Cheng Kuo-Shung , Ni Wei-Tou
Published: November 2008

For a manifold with a generic symmetric affine connection, explicit necessary and sufficient conditions for the local existence of metric compatible with the connection are obtained in terms of the Riemann tensor and its first-order covariant derivatives. If these conditions are satisfied, the solutions for metric are unique up to a constant scale factor and the absolute value of the signature is uniquely determined. Explicit formulae for the solutions are given in terms of integrals.
A generalization of the Sα-summation method
Authors: Meir A. , Sharma A.
Published: November 2008

In 1949, Meyer-König (5) introduced the so-called Sα-method of summability which is one of a family of transformations including the Euler, Borel and Taylor methods. Later in 1959, Jakimowski (3) defined the [F, dn] transformation which includes the Euler method as a special case. If {dn} is given infinite sequence and E denotes the displacement operator (i.e. Eks0 = sk), then the [F, dn] transformation of {sn} is given by {tn} where
Diffusion and convection of heat in a dipole convection field
Authors: Norminton E. J.
Published: November 2008

The problem of the diffusion and convection of heat from an arbitrarily placed source in the convection field due to a fluid producing dipole is considered. The solution for the temperature at any point in the fluid is found analytically. The isotherms and lines of constant flux are plotted.
Primitivity in representations of polycyclic groups
Authors: Harper D. L.
Published: November 2008

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?
Weak convergence of sequences of random elements with random indices
Authors: Csörgő M. , Rychlik Z.
Published: November 2008

Let (S, d) be a separable metric space equipped with its Borel σ field . Let {Yn, n ≥ 1} be a sequence of S-valued random elements defined on a probability space (Ω, , p). Assume Yn ⇒ Y converges weakly to an S-valued random element Y. Let {Nn, n ≥ 1} be a sequence of positive integer-valued random variables defined on the same probability space (Ω, , p).
Completeness properties inL2of the eigenfunctions of two semi-linear differential operators
Authors: Fraenkel L. E.
Published: November 2008

This paper concerns the boundary-value problems

in which λ is a real parameter,uis to be a real-valued function inC2[0, 1], and problem (I) is that with the minus sign. (The differential operatorsare called semi-linear because the non-linearity is only in undifferentiated terms.) If we linearize the equations (for ‘ small’ solutionsu) by neglecting, there result the eigenvalues λ =n2π2(withn= 1,2,…) and corresponding normalized eigenfunctions

and it is well known ((2), p. 186) that the sequence {en} iscompletein that it is an orthonormal basis for the real Hilbert spaceL2(0, 1). We shall be concerned with possible extensions of this result to the non-linear problems (I) and (II), for which non-trivial solutions (λ,u) bifurcate from the trivial solution (λ, 0) at the points {n2π2,0) in the product space×L2(0, 1). (Heredenotes the real line.)
Lomonosov's hyperinvariant subspace theorem for real spaces
Authors: Hooker N. D.
Published: November 2008

In 1973, V.I.Lomonosov introduced a new technique for finding invariant and hyperinvariant subspaces for certain classes of (continuous, linear) operators on complex Banach spaces. Recall that a closed subspace M of the Banach space X is called hyperinvariant for the operator T if S(M) ⊂ M for every operator S which commutes with T.
Normal modes for Green's functions and the method of theta functions
Authors: Terras Riho
Published: November 2008

The eigenfunctions for four types of bounded plane domains are constructed by a group-theoretic method. The group theory is then used to prove a completeness theorem and to derive a theta function transformation formula. Rapidly convergent series for the Green's functions of the Laplace operator on these domains are then constructed. Final formulas are summarized without reference to group theory.
The determination of thermal stresses in dissimilar media
Authors: Aderogba K.
Published: November 2008

It is shown that if, in an infinite homogeneous unbounded elastic heat-conducting solid, we are given the thermal stresses which arise when any arbitrarily shaped subregion of the upper half-space z > 0 is emitting any quantity of heat into the surrounding, then on introducing a different heat-conducting material into the half-space z < 0, the new thermal stresses in z >0 and in z < 0 are explicitly expressible in an invariant form in terms of the known thermal stresses in the homogeneous infinite solid. Specialization of the derived dependence shows that the physically interesting interfacial discontinuities inherent in the problem admit the representation

while the traction transmitted across the interface takes the form

where αi and βi are constants. An application is then made to the case when the region emitting heat into the surrounding is ellipsoidal, since this is a fundamental shape of practical importance. Applications can however be made to any shape of the region emitting heat, provided that the corresponding harmonic and biharmonic potentials are available.

The paper may be considered to have its origin in the half-space theorem of Lorentz in hydrodynamics.
Lipschitz classes and convolution approximation processes
Authors: Ditzian Z.
Published: November 2008

For a continuous function f(x) on the reals or on the circle T (continuous and 2π periodic) we say that f(x) belongs to the generalized Lipschitz class, denoted by f ∈ Lip* α, if

where and Δhf(x) = f(x + ½h)−f(x−½h). For a convolution approximation process given by

where

we shall investigate equivalence relations between the asymptotic behaviour of (d/dx)rAn(f, x) and f ∈ Lip* α.
An acceleration condition for b-incomplete timelike curves
Authors: Dodson C. T. J. , Sulley L. J. , Williams P. M.
Published: November 2008

The b-completion of a smooth manifold with linear connection was introduced by Schmidt (6). He pointed out that, in a spacetime, an inextensible timelike curve of finite proper length and bounded acceleration has an endpoint on the b-boundary. However, it is not clear in what sense boundedness was meant. Geroch(1) suggested that any acceptable method of completing a spacetime should have this property with boundedness interpreted through the Lorentz norm. This result for the b-completion was given by Rosso(4), based on his earlier paper (3), which, however, contains some arguments that we do not accept. We give another proof of the result and improve it by weakening the condition of boundedness of the acceleration.
A note on a problem of Baker in metrical number theory
Authors: Yu Kunrui
Published: November 2008

Let P(x) denote a polynomial with degree n and integer coefficients. By the height h of P we mean the maximum of the absolute values of the coefficients.
An independence theorem for automorphisms of torsion-free groups
Authors: Webb U. H. M.
Published: November 2008

This paper considers the relationship between the automorphism group of a torsion-free nilpotent group and the automorphism groups of its subgroups and factor groups. If G2 is the derived group of the group G let Aut (G, G2) be the group of automorphisms of G which induce the identity on G/G2, and if B is a subgroup of Aut G let B¯ be the image of B in Aut G/Aut (G, G2). A p–group or torsion-free group G is said to be special if G2 coincides with Z(G), the centre of G, and G/G2 and G2 are both elementary abelian p–groups or free abelian groups.
The factorization of simple knots
Authors: Bayer E. , Hillman J. A. , Kearton C.
Published: November 2008

For high-dimensional simple knots we give two theorems concerning unique factorization into irreducible knots, and provide examples to show that the hypotheses are necessary in each case.
Langer's method for a second order linear ordinary differential equation with a double pole
Authors: Anyanwu Donatus Uzodinma
Published: November 2008

If a second order ordinary differential equation has a simple or a double pole at a point zfl, then the standard Liouville-Green approximation could sometimes be valid near that point. In this paper we present an asymptotic series solution that is always valid near a double pole. A solution for that of a simple pole is also indicated. Asymptotic validity is proved.
On the Hopf algebra dual of an enveloping algebra
Authors: Donkin Stephen
Published: November 2008

In (1) it is claimed that the main results of that paper have applications to the representation theory of algebraic groups, of polycyclic groups and of Lie algebras. An application to algebraic groups is given in Corollary 6·4 of (1), the applications to polycyclic groups are given in (2), the purpose of this work is to deal with the outstanding case of enveloping algebras. To make use of the results of (1), in this context, we show that the Hopf algebra dual of the enveloping algebra of a finite dimensional Lie algebra over a field of characteristic zero is quasi-affine (see § 1·5). This is done by an easy field extension argument and a generalization, to the Hopf algebra dual of the smash product of Hopf algebras, of Proposition 1·6·3 of (2) on the dual of the group algebra of a semidirect product of groups. Since this paper is aimed at those readers interested in enveloping algebras, the Hopf theoretic aspects are dealt with at a fairly leisurely pace.
Boolean powers of groups
Authors: Apps A. B.
Published: November 2008

If M is any algebraic structure, and R is any Boolean ring, then a structure called the (bounded) Boolean power of M by R, denoted MR, can be defined. This construction, which is also called a bounded Boolean extension, is a sort of generalized direct power, and was introduced by Foster in the 1950's (as a refinement of his previous notion of a Boolean extension). In this paper we shall study isomorphism types and automorphisms of Boolean powers of groups, and obtain information about their characteristic subgroups: we shall be chiefly concerned with Boolean powers of finite groups.
Groups whose irreducible representations have finite degree: III
Authors: Wehrfritz B. A. F.
Published: November 2008

If F is a (commutative) field let XF denote the class of all groups G such that every irreducible FG module has finite dimension over F. In the first paper (9) of this series we classified finitely generated soluble XF-groups for each field F and in the second (10) we characterized soluble XF-groups for each field F of characteristic zero. Here we consider soluble XF-groups over fields F of positive characteristic.
A theorem about countable decomposability
Authors: Davies Roy O. , Tricot Claude
Published: November 2008

A functionf:X→ ℝ iscountably decomposable(into continuous functions) if the topological spaceXcan be partitioned into countably many setsAnwith each restrictionf│Ancontinuous. According to L. V. Keldysh(2), the question whether every Baire function is countably decomposable was first raised by N. N. Luzin, and answered by P. S. Novikov. The answer is negative even for Baire-1 functions, as is shown in (2) (see also (1). In this paper we develop a characterization of the countably decomposable functions on a separable metric spaceX(see Corollary 1). We deduce that whenXis complete they include all functions possessing the propertyPdefined by D. E. Peek in (3):each non-empty σ-perfect set H contains a point at which f│ H is continuous. The example given by Peek shows that not every countably decomposable Baire-1 function has propertyP.
Achromatic numbers of random graphs
Authors: McDiarmid Colin
Published: November 2008

The achromatic number ψ(G) of a graph G is the greatest number of colours in a proper colouring of the vertices of G such that for every pair of colours some vertex of the first colour and some vertex of the second colour are adjacent. We prove that almost all graphs Gn with n vertices satisfy n/(k+l) < ψ(Gn) < n/(k–1), where k = k(n) = (log2n)½. We show also that the achromatic number is a ‘global’ invariant.
Growth conditions on powers of Hermitian elements
Authors: Falconer K. J.
Published: November 2008

Roe (7) has recently given a striking characterization of the sine function as essentially the only function defined on the real line which has all its derivatives and successive ‘integrals’ bounded by a uniform bound, and this result has since been generalized by Burkill (5). In this note we relate this work to Banach algebra theory in a natural way by demonstrating the equivalence of Theorems 1 and 2 below, and also by giving a direct proof of Theorem 1. (Theorem 2 is Burkill's generalization of Roe's result stated in complex form.) We enunciate a Banach space version of the result (Theorem 3), and a further generalization of all these results is given in Theorem 4.
A lifting result for local cohomology of graded modules
Authors: Brodmann M.
Published: November 2008

In this paper we prove a lifting result for local cohomology. As a special case we get the following result for the Serre-cohomology over a projective variety:

Proposition (1·1). Let ℱ be a coherent sheaf over X, where X is a projective variety over an algebraically closed field k. Let i ≽ 0 and assume that there is a pencil P of hyper-plane sections which is in general position with respect to ℱ (which means that x ∉ H, ∀x ∈ Ass(ℱ), ∀H∈p), and such that for each H ∈ P Hi(X, ℱ│H(n)) = 0, ∀n ≪ 0. Then Hi + 1(X, ℱ) = 0, ∀n ≪ 0.
Isometric immersions into manifolds without conjugate points
Authors: Bolton J.
Published: November 2008

1. Introduction and statement of results. Let f: Mn-1 → ℝn be an immersion into Euclidean space ℝn. Each unit vector v to ℝn determines a height function bv: ℝn → ℝ. The corresponding half-space Lv = b-1([0, ∞) has boundary Hv = (b−1). and L is a (globally) supporting half-space for M at m є M if (m) є H and f(M) ∩ Lv = f(M) ∩ Hv.
Topological decompositions of the duals of locally convex operator spaces
Authors: Fleming D. J. , Giarrusso D. M.
Published: November 2008

If Z and E are Hausdorff locally convex spaces (LCS) then by Lb(Z, E) we mean the space of continuous linear maps from Z to E endowed with the topology of uniform convergence on the bounded subsets of Z. The dual Lb(Z, E)′ will always carry the topology of uniform convergence on the bounded subsets of Lb(Z, E). If K(Z, E) is a linear subspace of L(Z, E) then Kb(Z, E) will be used to denote K(Z, E) with the relative topology and Kb(Z, E)″ will mean the dual of Kb(Z, E)′ with the natural topology of uniform convergence on the equicontinuous subsets of Kb(Z, E)′. If Z and E are Banach spaces these provide, in each instance, the usual norm topologies.
Representing 3-manifolds by a universal branching set
Authors: Montesinos José María
Published: November 2008

In this paper all 3-manifolds will be supposed to be compact, connected, oriented and without 2-spheres in the boundary.

Given a 3-manifold M we obtain a closed pseudomanifold M^ by capping off each boundary component of M with a cone. We prove that such an M^ is a covering of S3 branched over a subcomplex G of S3 which is independent of M, and such that S3 - G has free fundamental group on two generators. Hence M^ (and also M) can be represented by a transitive pair {σ, τ} of permutations in the symmetric group Σh on the set {1,2, …, h}, for some h. We show how to obtain {σ, τ} from a given Heegaard diagram of M.
Saturation results for a class of linear operators
Authors: Kuttner B. , Mohapatra R. N. , Sahney B. N.
Published: November 2008

Let B denote the space of bounded measurable functions with period 2π. We will suppose throughout that f(x) ∈ B. All norms considered are essential sup norms. Let the Fourier series of f(x) be given by

Let D = (dnk) (n, k = 0, 1, …) be an infinite matrix.

Let Ln(f; x) be the D transform of the Fourier series of f(t) at t = x, i.e.

where Sk(x) = A0(x) + A1(x) + … + Ak(x). Let us write
Arcbodies
Authors: Lozano Maria Teresa
Published: November 2008

A Haken manifold is a compact, orientable, irreducible 3-manifold which contains a properly embedded 2-sided, incompressible surface of positive genus. These manifolds are important in connection with the work of Haken, Waldhausen and the more recent work of Thurston (8). Thus it is interesting to investigate criteria for testing incompressible surfaces on 3-manifolds.
On a symbolic algebra for Hencky-Prandtl nets
Authors: Hill R.
Published: November 2008

In the classical theory of plane deformations in isotropic plastic media, the field equations are hyperbolic and the orthogonal families of characteristics are known as Hencky-Prandtl nets. Their distinctive geometry has been given symbolic expression by Collins (1968), in an algebra of infinite matrices associated with canonical series representations of the general solution. This has become the standard technique when investigating boundary-value problems, both analytically and numerically. The basic framework of the algebra is here reorganized and developed. A systematic approach then leads to new identities which are shown to be fundamental in the algebraic hierarchy.
A continuous generalization of the transversal property
Authors: Komjáth P.
Published: November 2008

A transversal for a set-system is a one-to-one choice function. A necessary and sufficient condition for the existence of a transversal in the case of finite sets was given by P. Hall (see [4, 3]). The corresponding condition for the case when countably many countable sets are given was conjectured by Nash-Williams and later proved by Damerell and Milner [2]. B. Bollobás and N. Varopoulos stated and proved the following measure theoretic counterpart of Hall's theorem: if (X, μ) is an atomless measure space, ℋ = {Hi: i∈I} is a family of measurable sets with finite measure, λi (i∈I) are non-negative real numbers, then we can choose a subset Ti ⊆ Hi with μ(Ti) = λi and μ(Ti ∩ Ti′) = 0 (i ≠ i′) if and only if μ({U Hi: iεJ}) ≥ Σ{λi: iεJ}: for every finite subset J of I. In this note we generalize this result giving a necessary and sufficient condition for the case when I is countable and X is the union of countably many sets of finite measure.
Eigenvalues of smooth kernels
Authors: Reade J. B.
Published: November 2008

Suppose is a symmetric square integrable kernel on the unit square [0, 1]2. Then

is a compact symmetric operator on the Hilbert space L2[0, 1]. H. Weyl (see [2]) has shown that, if then the eigenvalues

of T satisfy as n → ∞. We prove a related result. Let W12[0, 1]2 denote the space of all K(x, t) ε L2[0, 1]2 which are absolutely continuous in x for each t and absolutely continuous in t for each x, and the partial derivatives ∂K/∂x(x, t), ∂K/∂t(x, t) are both in L2[0, 1]2. We slow that the eigenvalues of any satisfy .
Poisson integrals of absolutely continuous and other measures
Authors: Madan Shobha , Sjögren Peter
Published: November 2008

We characterize absolutely continuous and continuous measures by means of the g-function and distribution function, respectively, of the Poisson integral in a half space. Some other ways of measuring the Poisson integral are found to make such measures indistinguishable. A variant of the Poisson integral is also studied.
On the calculation of cross-sections for electron neutral atom collisions in the Born approximation to the reactance matrix
Authors: Whelan Colm T.
Published: November 2008

Born partial wave integrals are considered for electron-neutral atom collisions. It is shown that for relatively general atomic wave functions these may be evaluated analytically. These form the Born reactance matrix RB and can be used to calculate the collision strengths in the approximations ωI, ωII.
The core model for sequences of measures. I
Authors: Mitchell William J.
Published: November 2008

The model K() presented in this paper is a new inner model of ZFC which can contain measurable cardinals of high order. Like the model L() of [14], from which it is derived, K() is constructed from a sequence of filters such that K() satisfies for each (α, β) ε domain () that (α,β) is a measure of order β on α and the only measures in K() are the measures (α,β). Furthermore K(), like L(), has many of the basic properties of L: the GCH and ⃟ hold and there is a definable well ordering which is on the reals. The model K() is derived from L() by using techniques of Dodd and Jensen [2–5] to build in absoluteness for measurability and related properties.
Realcompact spaces and regular σ -frames
Authors: Gilmour Christopher R. A.
Published: November 2008

We show that there is an adjoint dual equivalence between realcompact Alexandroff spaces and the Alexandroff σ-frames. This gives a corresponding adjoint duality for realcompact Tychonoff spaces. Consequently we characterize lattice theoretically the cozero-sets of a topological space.
A sequence of Gamma-type approximation operators
Authors: Upreti Rita , Joshi J. M. C.
Published: November 2008

A sequence of Gamma-type approximation operators n(f) (n = 1,2,…) (which reduce to the Gamma operators, Gn (n = 1,2,…), defined by Müller in a particular case) has been defined. Uniform convergence of n(f) towards f on fixed intervals [x1, x2] (0 ≦ x1 ≦ x2 < ∞) has been proved and a simple example has been given in support of the proof.
The role of the principal part in factorizing block maps
Authors: Rhodes Frank
Published: November 2008

An n-block is a sequence b1 … bn where bi ε {0,1} for 1 ≤ i ≤ n, and an n-block map is a function from the set of n-blocks to the set {0,1}. Block maps can be used to study endomorphisms of the shift dynamical system [7] and shift register sequences [4]. Composition of endomorphisms and cascading of shift registers [6] can be studied via composition of block maps. If fog is a given block map which is linear in the first variable and if g is also given, then f is unique and can be determined. If fog and f are given then g is unique and can be determined, at least up to a constant [10]. However, little is known about the level of computational complexity of the general task of searching for factors of a given block map. In this paper I identify a substantial class of maps which are linear in the first variable but not linear, for which there are effective methods of searching for factors. The methods are based on the presentation of block maps via successive principal parts, introduced in [9]. There I define the principal vector of a block map. One of the key results gives conditions under which there is a particularly close relationship between the principal vectors of two block maps f and g and their composition fog. In the second section of this paper I show that the same relationship holds under weaker conditions.
Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder
Authors: Mandal B. N. , Goswami S. K.
Published: November 2008

The problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods.
On the supports of Gauss measures on algebraic groups
Authors: McCrudden M.
Published: November 2008

For any locally compact topological group G let M(G) denote the topological semigroup of all probability (Borel) measures on G, furnished with the weak topology and with convolution as the multiplication. A Gauss semigroup on G is a homomorphism t→ μt of the strictly positive reals (under addition) into M(G) such that

(i) no μt is a point mesaure,

(ii) for each neighbourhood V of 1 in G we have
A note on decomposition numbers for general linear groups and symmetric groups
Authors: Donkin S.
Published: November 2008

In [5] James proved theorems on the decomposition numbers, for the general linear groups and symmetric groups, involving the removal of the first row or column from partitions. In [1] we gave different proofs of these theorems based on a result valid for the decomposition numbers of any reductive group. (I am grateful to J. C. Jantzen for pointing out that the Theorem in [1] may also be derived from the universal Chevalley group case, which follows from the proof of 1 ·18 Satz of [6] – the analogue of equation (1) of the proof being obtained by means of the natural isometry (with respect to contra-variant forms) between a certain sum of weight spaces of a Weyl module V(λ) of highest weight λ and the Weyl module corresponding to λ for the Chevalley group determined by the subset of the base involved.) However, we have recently noticed that this result for reductive groups, even when specialized to the case of GLn, gives a substantial generalization of James's Theorems. This generalization, which we give here, is an expression for the decomposition number [λ: μ] for a pair of partitions λ, μ whose diagrams can be simultaneously cut by a horizontal (or vertical) line so as to leave the same number of nodes above the line (or to the left of the line for a vertical cut) in both cases. Cutting between the first and second rows gives James's principal of row removal ([5], theorem 1) and cutting between the first and second column gives his principle of column removal ([5], theorem 2). Another special case of our horizontal result, involving the removal of bottom rows of a pair of partitions, is stated in [7], Satz 8.
Uniform boundedness for non-abelian groups
Authors: Moskowitz Martin
Published: November 2008

In this note we will prove a number of facts which generalize to various non-abelian groups some results of Glicksberg[2]. In the non-abelian form they will have application to certain results of the author on the 2 dimensional continuous cohomology associated with central extensions [6].
The dimension of Euclidean subspaces of quasi-normed spaces
Authors: Dilworth S. J.
Published: November 2008

The purpose of this article is to extend certain results which are known to hold for convex bodies to a class of non-convex bodies occurring in the theory of topological vector spaces. In the first section after this introduction an analogue of F. John's Theorem on the distance of a finite dimensional space from Euclidean space is obtained, and the result is shown to be best possible. The Dvoretzky-Rogers Lemma on the points of contact of a symmetric convex body with the ellipsoid of maximum volume contained within it is discussed for certain non-convex bodies. In the next part the Dvoretzky Theorem on the existence of ellipsoidal sections is shown to hold with the best possible estimate for the dimension of the sections. It follows from estimates involving cotype constants that the finite dimensional subspaces of Lp (0 < p < 1) possess large almost Hilbertian subspaces. The final section extends the theorem of S. Szarek relating the volume of a body to the existence of ellipsoidal sections.
Projective modules over pullback rings
Authors: Wiseman A. N.
Published: November 2008

Given two homomorphisms of rings j1:R1 → R' and j2: R2 → R' we may construct a new ring R called the pullback of R1 and R2 over R', together with homomorphisms i1:R →R1 and i2:R→R2 such that j1i1= j2i2. There are many instances where special cases of pullbacks have been studied, either to construct new examples of rings or to reduce various problems to those concerning much simpler rings. A few of these instances are given in the references. Thus a general study of the properties of pullbacks in terms of those of the component rings would seem to be useful.
Abelian semigroups whose Stone-Čech compactifications have left ideal decompositions
Authors: Parsons D. J.
Published: November 2008

Stone-Čech compactifications of semigroups have aroused a good deal of interest recently. Several authors, for example Milnes [6], Marcri [5] and Baker and Butcher [1], have concentrated on problems of the existence of continuous extensions to βSof the operation in a topological semigroupS.For a discrete semigroup a separately continuous extension always exists, and others such as Pym and Vasudeva[8] have studied the compactifications of particular classes of semigroups. Further interest has centred on the algebraic structure of these compactifications; see for example Hindman[3].
Brandt semigroups of quotients
Authors: Fountain John , Petrich Mario
Published: November 2008

In an earlier paper [3], we introduced a new notion of completely 0-simple semigroup of quotients. The definition is motivated by a connection between Artinian simple rings and completely 0-simple semigroups. Given an Artinian simple ring Q, one obtains a completely 0-simple multiplicative sub-semigroup by taking the union of the subsets eiQej(i, j = l,…, n), where 1 = e1 + … + en and the ei are primitive orthogonal idempotents. If Q is the classical ring of left quotients of R, then is a semigroup of left quotients of in the sense that every element q in can be written as q = a-1b for some elements a, b in with a2 ≠ 0.
Some combinatorial results involving shifted Young diagrams
Authors: Morris A. O. , Yaseen A. K.
Published: November 2008

In [6] the first author introduced some combinatorial concepts involving Young diagrams corresponding to partitions with distinct parts and applied them to the projective representations of the symmetric group Sn. A conjecture concerning the p-block structure of the projective representations of Sn was formulated in terms of these concepts which corresponds to the well-known, but long proved, Nakayama ‘conjecture’ for the p-block structure of the linear representations of Sn. This conjecture has recently been proved by Humphreys [1].
Unitary dilations, polynomial identities and the von Neumann inequality
Authors: Dixon P. G. , Drury S. W.
Published: November 2008

Letp(X1, …,Xn) be a polynomial in the commuting indeterminatesX1, …,Xn.

Define