bluuebunny/crossref_metadata_2025_split huggingface dataset:
Seminormal and subnormal subgroup lattices for transitive permutation groups
Authors: Praeger Cheryl E. 
Published: April 2009

AbstractVarious lattices of subgroups of a finite transitive permutation group G can be used to define a set of ‘basic’ permutation groups associated with G that are analogues of composition factors for abstract finite groups. In particular G can be embedded in an iterated wreath product of a chain of its associated basic permutation groups. The basic permutation groups corresponding to the lattice L of all subgroups of G containing a given point stabiliser are a set of primitive permutation groups. We introduce two new subgroup lattices contained in L, called the seminormal subgroup lattice and the subnormal subgroup lattice. For these lattices the basic permutation groups are quasiprimitive and innately transitive groups, respectively.
The turnpike result for approximate solutions of nonautonomous variational problems
Authors: Zaslavski Alexander J. 
Published: April 2009

AbstractIn 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

AbstractWe 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

AbstractForms 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

AbstractIt 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

AbstractThe 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

AbstractIn 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

AbstractThe 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

AbstractThe 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

AbstractLet 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.
Automorphisms of permutational wreath products
Authors: Hassanabadi A. Mohammadi 
Published: April 2009

AbstractOre (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

AbstractThis 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

AbstractLetTbe 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

AbstractSeveral 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

AbstractFor 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.
On reducing to zero the remainder of an asymptotic series
Authors: Drummond J. E. 
Published: April 2009

AbstractIf 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.
Semigroup endomorphisms of rings
Authors: Sullivan R. P. 
Published: April 2009

AbstractWe 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

AbstractIn 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

AbstractAs 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

AbstractThis 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

AbstractGrant (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 normal closures related to elliptic curves
Authors: Lewis D. J. , Morton Patrick 
Published: April 2009

AbstractLetF(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

AbstractLet 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

AbstractIn 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

AbstractA 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.
A note on the conjugacy of Cartan subalgebras
Authors: Winter David J. 
Published: April 2009

AbstractThe 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.)
A class of polynomial permutations on groups
Authors: Kowol G. 
Published: April 2009

AbstractLetGbe 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}
Local polynomial functions on factor rings of the integers
Authors: Lausch Hans , Nöbauer Wilfried 
Published: April 2009

AbstractLet 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

AbstractWe 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

AbstractThe 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

AbstractIn 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

AbstractLet (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

AbstractLet 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

AbstractA 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

AbstractLet 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

AbstractThe 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

AbstractThe 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.
Uniform labelled semilattices
Authors: Ash C. J. 
Published: April 2009

AbstractLet 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

AbstractIf 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

AbstractA 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.