bluuebunny/crossref_metadata_2025 huggingface dataset:
The turnpike result for approximate solutions of nonautonomous variational problems
Authors: Zaslavski Alexander J.
Published: April 2009

In this work we study the structure of approximate solutions of variational problems with continuous integrands f: [0, ∞) × Rn × Rn → R1 which belong to a complete metric space of functions. The main result in this paper deals with the turnpike property of variational problems. To have this property means that the approximate solutions of the problems are determined mainly by the integrand, and are essentially independent of the choice of interval and endpoint conditions, except in regions close to the endpoints.
Ribbon concordance of surface-knots via quandle cocycle invariants
Authors: Carter J. Scott , Saito Masahico , Satoh Shin
Published: April 2009

We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the invariant already known. We demonstrate that twist-spins of some torus knots are not ribbon concordant to their orientation reversed images.
Minkowski's fundamental inequality for reduced positive quadratic forms
Authors: Barnes E. S.
Published: April 2009

Forms which are reduced in the sense of Minkowski satisfy the “fundamental inequality” a11a22 hellipann≤λnD; the best possible value of λn is known for n≤5. A more precise result for the minimum value of D in terms of the diagonal coefficients has been stated by Oppenheim for ternary forms. The corresponding precise result for quaternary forms is established here by considering a convex polytope D(α), defined as the intersection of the cone of reduced forms with the hyperplanes aii = αi (i = 1, hellip n).
Denominator sequences for continued fractions, III
Authors: Worley R. T.
Published: April 2009

It is shown that for every irrational α the set of α′ for which α and α′ have infinitely many convergents with the same denomintor, has the cardinality of the continuum.

Subject classification (Amer. Math. Soc. (MOS), 1970): 10 A 30.
Orders in simple Lie algebras of Chevalley type
Authors: Hurley James F.
Published: April 2009

The integral structure of a simple Lie algebra L of Chevalley type over a field F of fractions of an integral domain D is studied. Sandwich relations for sufficiently large orders are obtained, including a new general sandwich relation for orders of L in case D is an integrally closed Noetherian domain. Generalizations of the principal results of Hyman (1966) in the case when D is a ring of algebraic integers are obtained, using techniques developed by the author and Stewart (1973) which are applied to certain orders in L that arise in a natural fashion from the Chevalley basis.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 17 B 20; secondary 17 B 10, 17 B 45, 20 G 15, 20 G 05.
A note on Rado's theorem
Authors: Chong Kong-Ming
Published: April 2009

In this note, a theorem of Rado which characterizes the convex hull of the set of all rearrangements of a given real n-tuple in terms of the Hardy—Littlewood—Pólya spectral order relation < is shown to be a consequence of a result of Hardy—Littlewood—Pólya and a strong spectral inequality.

Subject classification (Amer. Math. Soc. (MOS) 1970): 52 A 40, 52 A 20.
Soluble groups in which every finitely generated subgroup is finitely presented
Authors: Groves J. R. J.
Published: April 2009

The class of finitely generated soluble coherent groups is considered. It is shown that these groups have the maximal condition on normal subgroups and can be characterized in a number of ways. In particular, they are precisely the class of finitely generated soluble groups G with the property:

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 20 E 15; secondary 20 F 05.
On when a topologically simple semigroup is simple
Authors: Sigmon Kermit
Published: April 2009

The compact semigroups in which each topologically simple subsemigroup is simple are characterized as those in which no subgroup sontains an element of infinite order. It is also shown that a locally compact toplogically simple subsemigroup of a compact semigroup must be simple. The note closes with an open problem.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 15; secondary 20 M 10.
Inner functions and the maximal ideal space of L∞(Tn)
Authors: Kon S. H.
Published: April 2009

Let Un be the unit polydisc in Cn and let Tn be its distinguished boundary. It is shown that a function f ∈ H∞(Un) is inner if and only if ∣f(Φ)∣ = 1 for all Φ in the maximal ideal space of L∞(Tn). This generalizes a result of Csordas.
Eigenvalues of matrix-valued analytic maps
Authors: Parthasarathy K. R.
Published: April 2009

An elementary and self-contained account of analytic Jordan decomposition of matrix-valued analytic functions is given. An integral representation for their eigenvalues is obtained. This leads to estimates of the differences in eigenvalues and the number of points of degeneracy.
Automorphisms of permutational wreath products
Authors: Hassanabadi A. Mohammadi
Published: April 2009

Ore (1942) studied the automorphisms of finite monomial groups and Holmes (1956, pp. 23–93) has given the form of the automorphisms of the restricted monomial groups in the infinite case. The automorphism group of a standard wreath product has been studied by Houghton (1962) and Segal (1973, Chapter 4). Monomial groups and standard wreath products are both special cases of permutational wreath product. Here we investigate the automorphisms of the permutational wreath product and consider to what extent the results holding in the special cases remain true for the general construction. Our results extend those of Bunt (1968).
Pseudocomplements in groupoids
Authors: Amma K. Nirmala Kumari
Published: April 2009

This paper is devoted to a study of pseudocomplements in groupoids. A characterization of an intraregular groupoid is obtained in terms of prime ideals. It is proved that the set of dense elements of an intraregular groupoid S with 0 is the intersection of all the maximal filters of S and that the set of normal elements of an intraregular groupoid closed for pseudocomplements forms a Boolean algebra under natural operations. It is shown that the pseudocomplement of an ideal of an intraregular groupoid with 0 is the intersection of all the minimal prime ideas not containing it.
Infinite τTproducts of distribution functions
Authors: Moynihan Richard
Published: April 2009

LetTbe a continuoust-norm (a suitable binary operation on[0, 1]) and Δ+the space of distribution functions which are concertratede on [0,∞. theτTproduct of anyF, Gin Δ+is defined at any realxby, and the pair (Δ+, τT) forms a semigroup. Thus, given a sequence {Fi} in Δ+, then-fold product τT(F1…Fn) is well-defined for eachn. Moreover, that resulting sequence {τT(F1, …,Fn)} is pointwise non-increasing and hence has a weak limit. This paper establishes a convergence theorem which yields a representation for this weak limit. In addition, we prove the Zero-One law that, for Archimedeant-norms, the weak limit is either identically zero or has supremum 1.
Pairwise concepts in bitopological spaces
Authors: Lal Sunder
Published: April 2009

Several pairwise concepts have been studied for bitopological spaces. In this note an attempt has been made to see how much ‘bitopological’ these pairwise concepts are. For example pairwise T1 is purely a topological concept whereas pairwise normality is very much ‘bitopological’. Several questions pertaining to this theme are dealt with.
On the prime factorization of binomial coefficients
Authors: Ecklund E. F. , Eggleton R. B. , Erdös P. , Selfridge J. L.
Published: April 2009

For positive integersnandk, withn≥2k, let, where each prime factor ofuis less thank, and each prime factor ofvis at least equal tok. It is shown thatu<vholds with just 12 exceptions, which are determined. If, where each prime factor ofUis at most equal tok, and each prime factor ofVis greater thank, thenU<Vholds with at most finitely many exceptions, 19 of which are determined. It is conjectured that there are no others.
Strong differentiability of the norm and rotundity of the dual
Authors: Giles J. R.
Published: April 2009

For normed linear spaces two similar characterizations of strong differentiability of the norm and rotundity of the dual space are established, but it is shown that in general there is no causal relation between these two concepts.
On reducing to zero the remainder of an asymptotic series
Authors: Drummond J. E.
Published: April 2009

If a weighted Euler transformation is applied to the asymptotic series for ezE1(z) the remainder can be expressed as an integral. Examination of this integral shows that for a transformation of given order the smallest term of the resulting series remains at approximately a constant distance from the start of the series. If, however, there is no restriction on the order of transformation the remainder may be decreased to zero by increasing the number of terms used, but if z is close to the negative real axis the rate of decrease is small. A more general theorem for alternating real series and Taylor's series is also given.
On doubly transitive permutation groups of degree prime squared plus one
Authors: Cameron Peter J.
Published: April 2009

Groups with the property of the title were considered by Chillag (1977); this paper completes his results by showing that, with known exceptions, they are triply transitive.
Semigroup endomorphisms of rings
Authors: Sullivan R. P.
Published: April 2009

We show that rings for which every non-constant multiplicative endomorphism is additive are trivial or power rings (that is, rings R such that R = R2 and x2 = 0 = x+x for all x ∈ R) and that if R is a power ring for which every multiplicative endomorphism is additive, then End (R) is a zero semigroup or a semilattice according to how the product is defined.
Oscillation of a functional differential equation arising from an industrial problem
Authors: Onose Hiroshi
Published: April 2009

In the last few years, the oscillatory behavior of functional differential equations has been investigated by many authors. But much less is known about the first-order functional differential equations. Recently, Tomaras (1975b) considered the functional differential equation and gave very interesting results on this problem, namely the sufficient conditions for its solutions to oscillate. The purpose of this paper is to extend and improve them, by examining the more general functional differential equation
Finitely projective modules over a Dedekind domain
Authors: Hiremath V. A.
Published: April 2009

As dual to the notion of “finitely injective modules” introduced and studied by Ramamurth and Rangaswamy (1973), we define a right R-module M to be finitely projective if it is projective. with respect to short exact sequences of right R-modules of the form 0 → A → B → C → 0 with C finitely generated. We have completely characterized finitely projective modules over a Dedekind domain. If R is a Dedekind domain, then an R-module M is finitely projective if and only if its reduced part is torsionless and coseparable.

For a Dedekind domain R, finite projectivity, unlike projectivity is not hereditary. But it is proved to be pure hereditary, that is, every pure submodule of a finitely projective R-module is finitely projective.
Aleph–zero categorical Stone algebras
Authors: Olin Philip
Published: April 2009

This paper is a contribution to the problem of characterizing the ℵ0-categorical Stone algebras. If the dense set is either finite or a chain, the problem is solved by reducing it to the ℵ0-categoricity of the skeleton and the dense set, solutions for these being known. If the dense set is a Boolean algebra, we show that this type of reduction works for certain subclasses but not for all such algebras. For generalized Post algebras the characterization problem is solved completely.
The relationship between fixing subgraphs and smoothly embeddable subgraphs
Authors: Chidzey Keith
Published: April 2009

Grant (1976) has attempted to establish a relationship between fixing subgraphs and smoothly embeddable subgraphs. Here we give counterexamples to his two main lemmas and two characterizing theorems. We then go on to give our own version of these lemmas and theorems.
On the fixed points of Sylow subgroups of transitive permutation groups: corrigendum
Authors: Herzog Marcel , Praeger Cheryl E.
Published: April 2009

The proof of Theorem 5 in a paper with the same title is incorrect. In this note weaker versions of that theorem are proved.
On normal closures related to elliptic curves
Authors: Lewis D. J. , Morton Patrick
Published: April 2009

LetF(z)be a polynomial with coefficients in a perfect fieldkand letKbe the normal closure ofk(z)overk(F). All polynomials for which the genus ofKoverkis one are determined; they depend in part on the characteristic ofk. Some results for higher genus are given.

Subject classification (Amer. Math. Soc. (MOS)1970): 12 F 10.
Bicyclic semirings
Authors: Bertman Martha O.
Published: April 2009

Let Bp be the bicyclic semigroup over P=G⋒[1,∞ where G is a subgroup of the multiplicative group of positive real numbers. If + is an addition which makes Bp, with its usual multiplication, into a semiring, then + is idempotent, and P is embedded as a sub-semiring in Bp and for each x in p, 1≦x+1≦x and 1≦1+x≦x. We show that any idempotent addition on P with these inequalities holding is max, min or trivial. The trivial addition on P extends trivially. If addition on P is min, then let , and . We charactertize all additions on Bp in terms of U and U′; and, in particular If U=U′ is a proper subset of R1 we demonstrate a correspondence between all such additions and certain homomorphisms of G to (0,∞)

Subject classification (Amer. math. Soc. (MOS) 1970): primary 16 A 80; secondary 22 A 15.
The range of a multimeasure
Authors: Tu Le Van
Published: April 2009

In this paper, the author generalizes the concept of thinness introduced by Kingman and Robertson (1968) to study the convexity of the range of a multimeasure. It is proved that every thin multimeasure taking values in a Fréchet space has convex range, and that, for a suitable measureable space, if a multimeasure is non-atomic, then the weak closure of its range is convex.
Extended semi-hereditary rings
Authors: Evans M. W.
Published: April 2009

A ring R for which every finitely generated right submodule of SR, the left flat epimorphic hull of R, is projective is termed an extended semi-hereditary ring. It is shown that several of the characterizing properties of Prufer domains may be generalized to give characterizations of extended semi-hereditary rings. A suitable class of PP rings is introduced which in this case serves as a generalization of commutative integral domains.
Isomorphisms in switching classes of graphs
Authors: Harries David , Liebeck Hans
Published: April 2009

We investigate conditions on a permutation group G sufficient to ensure that G fixes a graph in any switching class of graphs that it stabilizes. Our main result gives a necessary and sufficient condition for a dihedral group G to have this property.
A note on the conjugacy of Cartan subalgebras
Authors: Winter David J.
Published: April 2009

The conjugacy of Cartan subalgebras of a Lie algebra L over an algebraically closed field under the connected automorphism group G of L is inherited by those G-stable ideals B for which B/Ci is restrictable for some hypercenter Ci of B. Concequently, if L is a restrictable Lie algebra such that L/Ci restrictable for some hypercenter Ci of L, and if the Lie algebra of Aut L contains ad L, then the Cartan subalgebras of L are conjugate under G. (The techniques here apply in particular to Lie algebras of characteristic 0 and classical Lie algebras, showing how the conjugacy of Cartan subgroups of algebraic groups leads quickly in these cases to the conjugacy of Cartan subalgebras.)
Algebraic independence by a method of Mahler
Authors: Flicker Yuval Z.
Published: April 2009

We establish a general algebraic independence theorem for the solutions of a certain kind of functional equations. As a particular application, we prove that for any real irrational ζ, the numbers are algebraically independent, for multiplicatively independent algebraic αi with 0<|<| <1.
A class of polynomial permutations on groups
Authors: Kowol G.
Published: April 2009

LetGbe a finite andu(G) the group of all invertible transformations (polynomial permutations) of the form x→a1x1→ xka2⃛arxkrar+1(aiεG, x runs throughG). Continuing investigations of H. Lausch of groups satisfyingu(G)= {X→axkb} we show here that this condition implies thatGis the direct product of its {2, 3}-Hall subgroup and its {2, 3}′-Hall subgroupHwhereHis nilpoint of class ≤2. Essentially all non-nilpoint groupsGof order 2m3nare described having the property u(G)= {x→axkb}
Coproducts of Kleene algebras
Authors: Cornish William H. , Fowler Peter R.
Published: April 2009

The coproduct of a family of Kleene algebras is determined firstly by describing the maximal homomorphic image of a De Morgan algebra in the subvariety of Kleene algebras and, secondly, by characterizing the categorical product in the dual category of Kleene spaces.
Supports of Borel measures
Authors: Okada Susumu
Published: April 2009

We present a new class of topological spaces called SL-spaces, on which every Borel measure has a Lindelöf support. The class contains all metacompact spaces. However, a θ-refinable space is not necessarily an SL-space.
Local polynomial functions on factor rings of the integers
Authors: Lausch Hans , Nöbauer Wilfried
Published: April 2009

Let A be a universal algebra. A function ϕ Ak-A is called a t-local polynomial function, if ϕ can ve interpolated on any t places of Ak by a polynomial function— for the definition of a polynomial function on A, see Lausch and Nöbauer (1973), Let Pk(A) be the set of the polynomial functions, LkPk(A) the set of all t-local polynmial functions on A and LPk(A) the intersection of all LtPk(A), then . If A is an abelian group, then this chain has at most five distinct members— see Hule and Nöbauer (1977)— and if A is a lattice, then it has at most three distinct members— see Dorninger and Nöbauer (1978). In this paper we show that in the case of commutative rings with identity there does not exist such a bound on the length of the chain and that, in this case, there exist chains of even infinite length.
On coabsolute paracompact spaces
Authors: Gates Catherine L.
Published: April 2009

We are interested in determining whether two spaces are coabsolute by comparing their Boolean algebras of regular closed sets. It is known that when the spaces are compact Hausdorff they are coabsolute precisely when the Boolean algebras of regular closed sets are isomorphic; but in general this condition is not strong enough to insure that the spaces be coabsolute. In this paper we show that for paracompact Hausdorff spaces, the spaces are coabsolute when the Boolean algebra isomorphism and its inverse ‘preserve’ local finiteness, and for locally compact paracompact Hausdorff spaces, the spaces are coabsolute when the collections of compact regular closed subsets are ‘isomorphic’.
Two notes on frames
Authors: Wigner D.
Published: April 2009

The coproduct of two frames A, B (equivalently the product of two locales, see Isbell (1972a)) will be shown to be given by the lattice of Galois connections between A and B (the connection product in the sense of Isbell (1972b)). We show the inverse limit of a direct system of locales to be given by the set inverse limit of the underlying lattices under the bonding antimaps (see Dowker and Strauss (1975)). This implies the existence of infinite locale products.
Orthologic Desargues' figure
Authors: Mandan Sahib Ram
Published: April 2009

In 1894 Sondat published a theorem that the centre of perspectivity and the 2 orthologic centres of any 2 bilogic (perspective as well as orthologic) triangles lie on a line perpendicular to their axis of perspectivity. Thébault (1952) gave an elementary proof of this theorem. Here we give two new proofs, one synthetic and the other analytic, and then deduce the existence of an orthologic Desargues' figure where all the 10 pairs of perspective triangles in it are orthologic. Consequently we arrive at an orthologic Veronese configuration of 15 points and 10 pairs of perpendicular lines studied in 5 different ways.
Compact composition operators
Authors: Singh R. K. , Kumar Ashok
Published: April 2009

Let (Хζ,λ) be a σ-finite measure space, and let ϕ be a non-singular measurable transformation from X into itself. Then a composition transformation Cϕ on L2(λ) is defined by Cϕf = f ∘ ϕ. If Cϕ is a bounded operator, then it is called a composition operator. The space L2(λ) is said to admit compact composition operators if there exists a ϕ such that Cϕ is compact. This note is a report on the spaces which admit or which do not admit compact composition operators.
On the degree of an indecomposable representation of a finite group
Authors: Cliff Gerald H.
Published: April 2009

Let k be an algebraically closed field of characteristic p, and G a finite group. Let M be an indecomposable kG-module with vertex V and source X, and let P be a Sylow p-subgroup of G containing V. Theorem: If dimkX is prime to p and if NG(V) is p-solvable, then the p-part of dimkM equals [P:V]; dimkX is prime to p if V is cyclic.
Four-discordant permutations
Authors: Whitehead Earl Glen
Published: April 2009

A permutation π of the set {1, 2, …, n} is four-discordant if π(i) ≢ i, i+ 1, i + 2, i +3 (mod n) for 1 ≦i ≦ n. Generating functions for rook polynomials associated with four-discordant permutations are derived. Hit polynomials associated with four-discordant permutations are studied. Finally, it is shown that the leading coefficients of these rook polynomials form a “tribonacci” sequence which is a generalized Fibonacci sequence.
Commutative subsemigroups of the composition semigroup of formal power series over an integral domain
Authors: Kautschitsch Hermann
Published: April 2009

Let R be a commutative ring with identity. R[[x]] denotes the ring of formal power series, in which we consider the composition ○, defined by f(x)○g(x)=f(g(x)). This operation is well defined in the subring R+[[x]] of formal power series of positive order. The algebra= 〈R+[[x]], ○〉 is learly a semigroup, which is not commutative for ∣R∣>1. In this paper we consider all those commutative subsemigroups of , which consist of power series of all positive orders, which are called ‘permutable chains’.
0-Hecke algebras
Authors: Norton P. N.
Published: April 2009

The structure of a 0-Hecke algebra H of type (W, R) over a field is examined. H has 2n distinct irreducible representations, where n = ∣R∣, all of which are one-dimensional, and correspond in a natural way with subsets of R. H can be written as a direct sum of 2n indecomposable left ideals, in a similar way to Solomon's (1968) decomposition of the underlying Coxeter group W.
The Hope property and free products of semigroups
Authors: Jones P. R.
Published: April 2009

The free product of two Hopfian groups (in the category of groups) need not be Hopfian. We prove, by elementary methods, that the free product of two simple Hopfian inverse semigroups is Hopfian. In particular the free product of any two Hopfian groups, in the category of inverse semigroups, is again Hopfian. In fact the same is true in the category of all semigroups.
IFP near-rings
Authors: Ramakotaiah D. , Rao G. Koteswara
Published: April 2009

The set of all nilpotent elements in an IFP near-ring is characterized and necessary and sufficient conditions for the set of all nilpotent elements of an IFP near-ring to form an ideal are obtained.
Uniform labelled semilattices
Authors: Ash C. J.
Published: April 2009

Let P be a partially-ordered set in which every two elements have a common lower bound. It is proved that there exists a lower semilattice L whose elements are labelled with elements of P in such a way that (i) comparable elements of L are labelled with elements of P in the same strict order relation; (ii) each element of P is used as a label and every two comparable elements of P are labels of comparable elements of L; (iii) for any two elements of L with the same label, there is a label-preserving isomorphism between the corresponding principal ideals. Such a structure is called a full, uniform P-labelled semilattice.
Trace polynomials of words in special linear groups
Authors: Southcott J. B.
Published: April 2009

If w is a group word in n variables, x1,…,xn, then R. Horowitz has proved that under an arbitrary mapping of these variables into a two-dimensional special linear group, the trace of the image of w can be expressed as a polynomial with integer coefficients in traces of the images of 2n−1 products of the form xσ1xσ2…xσm 1 ≤ σ1 < σ2 <… <σm ≤ n. A refinement of this result is proved which shows that such trace polynomials fall into 2n classes corresponding to a division of n-variable words into 2n classes. There is also a discussion of conditions which two words must satisfy if their images have the same trace for any mapping of their variables into a two-dimensional special linear group over a ring of characteristic zero.
Harmonic functions for a class of Markov chains
Authors: Cohn H.
Published: April 2009

A class of Markov chains is considered for which a certain property of the tail events makes bounded harmonic functions obtainable from bounded space-time harmonic functions. Applications to almost surely convergent Markov chains are given and, in particular, a representation of Martin-Doob-Hunt type is derived for all bounded harmonic functions of a finite mean supercritical branching process.
Near-rings of continuous functions on disconnected groups
Authors: Hofer Robert D.
Published: April 2009

N(G) denotes the near-ring of all continuous selfmaps of the topological group G (under composition and the pointwise induced operation) and N0(G) is the subnear-ring of N(G) consisting of all functions having the identity element of G fixed. It is known that if G is discrete then (a) N0(G) is simple and (b) N(G) is simple if and only if G is not of order 2. We begin a study of the ideal structure of these near-rings when G is a disconnected group.
Some asymptotic methods in combinatorics
Authors: Plotkin J. M. , Rosenthal John
Published: April 2009

Let 〈fn≧0 be nonnegative real numbers with generating function f(x) = Σfnxn. Assume f(x) has the following properties: it has a finite nonzero radius of convergence x0 with its only singularity on the circle of convergence at x = x0 and f(x0) converges to y0; y = f(x) satisfies an analytic identity F(x, y) = 0 near (x0, y0); Fy(l) (x0, y0)= 0, 0 ≦ i < k and Fy(k) (x0, y0) ≠ 0. There are constants γ, a positive rational, and c such that fn~cx0−n n−(1 +ggr;). Furthermore, we show (i) in all cases how to determine γ and c from f(x) and (ii) in certain cases how to determine them from F(x, y).
Relative stability, characteristic functions and stochastic compactness
Authors: Maller R. A.
Published: April 2009

A recent result of Rogozin on the relative stability of a distribution function is extended, by giving equivalences for relative stability in terms of truncated moments of the distribution and in terms of the real and imaginary parts of the characteristic function. As an application, the known results on centering distributions in the domain of attraction of a stable law are extended to the case of stochastically compact distributions.
Errata: Mal'cev conditions spectra and Kronecker product
Authors: Neumann Walter D.
Published: April 2009

I am grateful to W. Taylor for pointing out that Lemma 2.3 of Neumann (1978), which claimed that a variety and its finitary reduct have the same finite algebras, is incorrect. This weakens several results of the paper: the lattice homomorphism of Lemma 3.1 is not complete, Theorem 4.1 is false, and the Mal'cev conditions claimed to be strong in 6.1, 6.2 and 7.1 are not strong. Taylor (1980) shows one cannot improve on this.
Weak and norm sequential convergence in M(S)
Authors: Tong A. , Wilken D.
Published: April 2009

Let S be a compact Hausdorff space; let C(S) be the algebra of all continuous complex valued functions on S; and let M(S) be the dual space of (S) (the space of all regular Borel measures on S). In [2] Grothendieck gave a description of weak sequential convergence in M(S) in terms of uniform convergence on sequences of disjoint open sets in S. In this note we give a condition on the carriers of measures to guarantee that weak zero convergent sequences are norm zero convergent. While this condition is interesting in its own right, it can also be used to obtain immediately some well-known results about compact operators from C(S) to c0.
Idempotent-generated regular semigroups
Authors: Eberhart C. , Williams W. , Kinch L.
Published: April 2009

Suppose S is a regular semigroup and E is its set of idempotents. If E is subsemigroup of S, then S has been called orthodox and studied recently by Hall [3], Meakin [6], and Yamada [8]. In this paper we assume that E is not (necessarily) a subsemigroup of S and consider the subsemigroup generated by E, denoted . If E denotes the set of all elements of S which can be written E, denoted . If E denotes the set of all elements of S which can be written as the product of n (not necessarily distinct) idempotents of S, then . We show that  is always a regular subsemigroup of S and investigate relationships between it and S. The case where  = S is of particular interest to us; such semigroups will be referred to as idempotent-generated regular semi- groups.
Two contact problems in anisotropic elasticity
Authors: Clements D. L.
Published: April 2009

In this paper we consider two contact problems for an anisotropic elastic half-space in which the stress is independent of one of the Cartesian co-ordinates. The results hold for the most general anisotropy in which no symmetry elements of the material are assumed. Problems of this type have been considered by Brilla [1], Clements [2], Galin [3], Green and Zerna [4] and Milne-Thomson [5], but the work of these authors is only applicable to a restricted class of anisotropic materials. We begin in section 1 by deriving some fundamental equations for the stress and displacement. It will be noted that at an early stage (equation (7)) the roots of a sextic polynomial are required. Since these cannot be obtained explicitly any application of the general theory must, of necessity, be numerical. However the calculation of the stress and displacement is simplified if certain symmetry elements of the material are assumed and the way in which these simplifications occur is indicated in section 2. In sections 3 and 4 we consider contact problems in which the elastic half-space is indented by a rigid body. For the problem considered in section 3, the rigid body is assumed to be able to move relative to the surface of the half-space, while for the problem considered in section 4 it is assumed to be linked to the half-space.
On a lemma of L. Lorch and D. J. Newman
Authors: Ustina Fred
Published: April 2009

In [6], Lorch and Newman proved the following lemma:Ifg(u)is continuous and of bounded variation, 0 ≦ u ≦ 1, then(1). This was extended more recently by Leviatan and Lorch ([5], Lemma 3) to functions which are of bounded variation on the positive real axis, where non the upper limit of integration on the inner integral is infinite.
Characterization of finite amenable transformation semigroups
Authors: Wilde Carroll
Published: April 2009

Abstract. In this paper we develop necessary and sufficient conditions for a finite transformation semigroup to have a mean value which is invariant under the induced shift operators. The structure of such transformation semigroups is described and an explicit description of all possible invariant means given.
Orthomodular generalizations of homogeneous Boolean algebras
Authors: Randall C. H. , Janowitz M. F. , Foulis D. J.
Published: April 2009

It is well known that the so-called reduced Borel algebra, that is, the Boolean algebra of all Borel subsets of the unit interval modulo the meager Borel sets of this interval, can be abstractly characterized as a complete, totally non-atomic Boolean algebra containing a countable join dense subset. (For an indication of the history of this result, see, for example, ([2], p. 483, footnote 12.) From this characterization, it easily follows that the reduced Borel algebra B is “homogeneous” in the sense that every non-trivial in B is isomorphic to B.
Compatible tight Riesz orders
Authors: Wirth Andrew
Published: April 2009

Loy and Miller [4] have studied tight Riesz groups (G, ≦), without pseudozeros, and with (G, ≼) an l-group. In this paper we study abelian l-groups (G, ≼) on which a tight Riesz order can the defined, such that ⋞ is precisely the associated order. Such an order we call a CTRO (compatible tight Riesz order).
Point (Countable) paracompactness
Authors: Boyte J. M.
Published: April 2009

This paper introduces two new separation axioms, point paracompactness and point countable paracompactness, both somewhat weaker than regularity, and shows that they can replace regularity in several standard theorems about paracompact or absolutely H-closed or Lindelöf spaces. Thus we obtain sharpened versions of these theorems. We also show that under certain hypotheses the new properties are equivalent to regularity.
Concavity properties for certain linear combinations of Stirling numbers
Authors: Ahuja J. C.
Published: April 2009

In the notation of Riordan ([5], p. 33), the Stirling numbers, s(n, k) and S(n, k), of the first and second kind respectively are defined by the relation where (x)n = x(x − 1) … (x − n + 1) is the factorial power function. They have been used by Jordan ([3], p. 184) to define the numbers C(m, k) and D(m, k), as linear combinations of s(n, k) and S(n, k) respectively, given by where and and where and D(m, O.
Sum functions of k-ary and semi-k-ary divisors
Authors: Suryanarayana D. , Prasad V. Siva Rama
Published: April 2009

It is known that a divisor d>0 of the positive integer n is called unitary [3;§ 1] if dδ = n and (d, δ) = 1, where (d, δ) denotes the g.c.d. of d and δ. We write d¶. Let k be a fixed positive integer. A positve integer n is called k-free if n is not divisible by the kth power of any prime.
A refinement of theorems of Kirchberger and Carathéodory
Authors: Watson Donald
Published: April 2009

I can indicate the type of refinement mentioned in the title by referring to Kirchberger's theorem [4]. Its picturesque form in the plane is: if sheep and goats are grazing in a field and for every four animals there exists a line separating the sheep from the goats then there exists such a line for all the animals. The refinement is that the words ‘every four animals’ may be replaced by ‘every four animals including an arbitraily chosen animal’; this reduces the ‘Kirchberger number’ from four to, effectively, three.
Factoring a group as an amalgamated free product
Authors: Ordman Edward T.
Published: April 2009

Even if in a decomposition of a group the Ai are completely indecomposable, there may be another decomposition with each Cj properly contained in some Ai a proper subgroup of B. The example of Bryce ([1], p. 636) may be modified, at the cost of having one Ai = B, so that I = J and Ci > Ai for all i. It is our object to study this relationship between decompositions of a group.
Hermite-Birkhoff trigonometric interpolation in the (0, 1, 2, M) case
Authors: Varma A. K.
Published: April 2009

Following four important papers on Birkhoff interpolation by Turán and his associates ([2], [3], [4], [14]), Kis ([8], [19]) proved the following theorems.
Distribution of rational points on the real line
Authors: Sheng T. K.
Published: April 2009

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.
Am-permutation polynomials
Authors: Jeong Sangtae
Published: April 2009

We introduce a class of polynomials which induce a permutation on the set of polynomials in one variable of degree less than m over a finite field. We call then Am-permutation polynomials. We also give three criteria to characterize such polynomials.
The multidirectional mean value inequalities with second order information
Authors: Bachir Mohammed
Published: April 2009

We give a multidirectional mean value inequality with second order information. This result extends the classical Clarke-Ledyaev's inequality to the second order. As application, we give the uniqueness of viscosity solution of second order Hamilton-Jacobi equations in finite dimensions.
Verma modules over Virasoro-like algebras
Authors: Wang Xian-Dong , Zhao Kaiming
Published: April 2009

Let K be a field of characteristic 0, G the direct sum of two copies of the additive group of integers. For a total order ≺ on G, which is compatible with the addition, and for any ċ1, ċ2 ∈ K, we define G-graded highest weight modules M(ċ1, ċ2, ≺) over the Virasoro-like algebra , indexed by G. It is natural to call them Verma modules. In the present paper, the irreducibility of M (ċ1, ċ2, ≺) is completely determined and the structure of reducible module M (ċ1, ċ2, ≺)is also described.
Products of idempotents in algebraic monoids
Authors: Putcha Mohan S.
Published: April 2009

Let M be a reductive algebraic monoid with zero and unit group G. We obtain a description of the submonoid generated by the idempotents of M. In particular, we find necessary and sufficient conditions for M\G to be idempotent generated.
Expansions of inverse semigroups
Authors: Lawson Mark V. , Margolis Stuart W. , Steinberg Benjamin
Published: April 2009

We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms which we termF-morphisms. These play the same role in the theory of idempotent-pure homomorphisms thatF-inverse monoids play in the theory ofE-unitary inverse semigroups.
Twisted complex geometry
Authors: Wang Shuguang
Published: April 2009

We introduce complex differential geometry twisted by a real line bundle. This provides a new approach to understand the various real objects that are associated with an anti-holomorphic involution. We also generalize a result of Greenleaf about real analytic sheaves from dimension 2 to higher dimensions.
Orthomodular posets from sesquilinear forms
Authors: Piziak Robert
Published: April 2009

In this paper, we show how to generate orthomodular posets from sesquilinear forms on a vector space.
An arithmetic sum with an application to quasi k-free integers
Authors: Harris V. C. , Subbarao M. V.
Published: April 2009

Let n be a positive integer and let T be any nonempty set of positive integers. By (n, T) = 1 we men n is relatively prime to each element of T. Hence n can be written as n = n1n2 where n1 is the largest divisor of n such that (n1, T)= 1. Let P be a property associated with positive integers. We shall say that a positive integer n is a P-number if it satisfies the property P. If in the above representation of n, the integer n1 is a P-number. then we shall say that n is a quasi P-number relative to T, or, simply, a quasi P-number. In particular, for k a positive integer >1, n is quasi k-free for given set T) if n1 is k-free.
Maximal topologies
Authors: Raha Asit Baran
Published: April 2009

This article is devoted to studying maximal π spaces where π = Lindelöf, countably compact, connected, lightly compact or pseudocompact. Necessary and sufficient conditions for Lindelöf or countably compact spaces to be maximal Lindelöf or maximal countably compact have been obtained. On the other hand only necessary conditions for maximal π spaces have been deduced where π = connected, lightly compact or pseudocompact.
On sequential estimation of a certain estimable function of the mean vector of a multivariate normal distribution
Authors: Rohatgi V. K. , Rastogi Suresh C.
Published: April 2009

Consider a k-variable normal distribution Ν (μ,Σ where mgr; = (μ1,μ2, … μk)' and Σ is diagonal matrix of unknown elements >0,i = 1,2, … k. The problem of sequential estimation of = 1 αiμi is considered. The stopping rule is shown to have some interesting limiting properties when the σi's become infinite.
A note on constructible lattices
Authors: Adams D. H.
Published: April 2009

It is our purpose to show that the constructible orthomodular lattices defined by Janowitz in [2], are embeddable into Boolean lattices. In fact they are subdirect products of Boolean lattices, where the subdirect products are taken in the class of orthomodular posets. We shall make these notions precise. Other concepts, such as disjoint sum and constructible lattice, are defined in [1] and [2].
The uniform limit of Lipschitz functions on a Banach space
Authors: Herod J. V.
Published: April 2009

With R the set of real numbers and S a Banach space, let ℒ be the class of functions A from R × S to S which have following properties: (1) if B is a bounded subset of S then the family {A(·, P): P is in B} is equicontinuous; i.e., if t is a number and ε > 0 then there is a positive number δ such that if |s – t | < δ and P is in B then | A(s, P) – A(t, P)| < ε.
Exclusive semigroups
Authors: Yamada Miyuki
Published: April 2009

First, we introduce the following condition (C1) for semigroups S. Let n, k be fixed positive integers such that n > k. (C1) For any given sequence of n elements of S, there existK elements, where 1 ≦ i1 < i2…, < ik ≦ n, such that where
Representation and extension of semiprime rings
Authors: Davis G.
Published: April 2009

In many respects the theory of semi-prime rings (i.e. rings without proper nilpotents) is similar to that for lattice-ordered groups. In this paper semi-prime rings are faithfully represented as subrings of continuous global sections of sheaves of integral domains with Boolean base spaces. This representation allows a simple description of a particular extension of a semi-prime ring as the corresponding ring of all continuous global sections. The ideals in a semi-prime ring R that give rise to the stalks in the sheaf representation are then characterized when R is projectable. Finally equivalent conditions are given for a semi-prime ring R to satisfy a condition, that in the case of lattice-groups, was termed “weak projectability” by Spirason and Strzelecki [8]. Some of the results that are common to semi-prime rings and lattice-groups (and semi-prime semigroups) have been extended to certain universal algebras by Davey [3].
On the existence of solution of the Greenspan-Carrier equation
Authors: Heinig H. P. , Tam K. Kuen
Published: April 2009

We are concerned with the flow of a viscous incompressible electrically conducting fluid of constant properties past a semi-infinite rigid plate. The governing boundary layer equations were derived by Greenspan and Carrier [2] in 1959. Numerical solutions of these equations subject to different boundary conditions have been considered by Stewartson and Wilson [5], Wilson [8], and recently by Bramley [1].
Consecutive integers with no large prime factors
Authors: Eggleton R. B. , Selfridge J. L.
Published: April 2009

For fixed integers k and m, with k ≥m ≥ 2, there are only finitely many runs of m consecutive integers with no prime factor exceeding k. We obatin lower bounds for the last such run. Let g(k, m) be its smallest member. For 2 ≤ m ≤ 5 it is shown that g(k, m) > kc logloglogk holds for all sufficiently large k, where c is a constant depending only on m. We also obtain a number of lower bounds with explict ranges of validity. A typical result of this type g(k, 3) > k3 holds just if k ≥ 41.
Hermite interpolation andp-adic exponential polynomials
Authors: van der Poorten A. J.
Published: April 2009

By employing a precise form of the Hermite interpolation formula we obtain a best possible bound for the number of zeros ofp-adic exponential polynomials. As companion to this quantitative result we give a best possible bound on the coefficients, if the exponential polynomial is small at sufficiently many points.
Sum-free sets, coloured graphs and designs
Authors: Street Anne Penfold , Wallis W. D.
Published: April 2009

Sum-free sets may be used to colour the edges of a complete graph in such a way as to avoid monochromatic triangles. We discuss the automorphism groups of such graphs. Embedding of colourings is considered. Finally we illustrate a way of constructing colourings using block designs.
On the estimates of the algebraic independence measures of the values of E-functions
Authors: Shidlovskii A. B.
Published: April 2009

The work establishes the estimates of linear independence, transcendence, and algebraic independence measures of the values at algebraic points of a set of E-functions, satisfying linear differential equations with coefficients from C(z), rather close to their natural bounds.
A note on pseudocompact spaces
Authors: Joseph James E.
Published: April 2009

In this note we give several new characterizations of arbitrary pseudocompact spaces, that is spaces characterized by the property that all continuous real-valued functions on the space are bounded.
A lower bound for the degree of polynomials satisfied by matrices
Authors: Pearson K. R.
Published: April 2009

R. Paré and W. Schelter (1978) have extended the Cayley-Hamilton theorem by showing that for each n<1 there is an integer k such that all n x n matrices over any (possibly noncommutative) ring satisfy a monic polynomial of degree k. We give a lower bound for this degree, namely π(n), which is defined as the shortest possible length of a sequence with entries from {1, 2, …, n}.
A class of regularities for rings
Authors: Roos C.
Published: April 2009

In this paper a general concept of regularity for rings is defined. It is shown that every regularity determines in a natural way a subradical and a radical for rings. A wide class of regularities is constructed: the class of polynomial regularities. All well-known regularities, such as the Perlis-Jacobson regularity, the von Neumann regularity and many others, belong to this class. Special attention is paid to regularities which are elementary in the sense that the so-called unic and nullic polynomial regularities can be thought of as intersections of the elementary ones.
Approximation by a sum of polynomials of different degrees involving primes
Authors: Liu Ming-Chit
Published: April 2009

Let λj(1 ≦j≦ 4) be any nonzero real numbers which are not all of the same sign and not all in rational ratio and let pjbe polynomials of degree one or two with integer coefficients and positive leading coefficients. The author proves that if exactly two pjare of degree two then for any real n there are infinitely many solutions in primes pjof the inequality. where 0 <β < (√(21)–1)∖5760.
The Moore–Penrose inverse of particular bordered matrices
Authors: Hall Frank J.
Published: April 2009

The Moore-Penrose inverse of a general bordered matrix is found under various conditions. The Moore-Penrose inverses obtained by Hall and Hartwig (1976) are shown to be special cases of these more general results.
Retracts of partially ordered sets
Authors: Duffus Dwight , Rival Ivan
Published: April 2009

Let P be a finite, connected partially ordered set containing no crowns and let Q be a subset of P. Then the following conditions are equivalent: (1) Q is a retract of P; (2) Q is the set of fixed points of an order-preserving mapping of P to P; (3) Q is obtained from P by dismantling by irreducibles.