bluuebunny/crossref_metadata_2025 huggingface dataset:
Local and Systemic Consequences of Large Retroperitoneal Clot Burdens
Authors: Loor Gabriel , Bassiouny Hisham , Valentin Carl , Shao Michael Y. , Funaki Brian , Desai Tina
Published: May 2009

Background

There is a paucity of data regarding the impact of retroperitoneal hematoma (RPH) volumes, as detected by computed tomography (CT) scanning, on patient morbidity and mortality. Therefore, we wanted to determine the natural history of RPHs and the effect of size on local and systemic outcomes.

Methods

We performed a volumetric analysis of CT‐documented RPHs managed at our institution between 1985 and 2006 along with a retrospective chart review.

Results

We included 81 cases of RPH in this study. The mean Acute Physiology, Age, and Chronic Health Evaluation II (APACHE II) score was 12.8 ± 0.72 (score ± SE). By univariate analysis, the size of the hematoma showed a significant correlation with the development of local mass effects, delayed mass effects, 6‐month mortality, major morbidity, pulmonary complications, fluid overload, and the requirement for operative evacuation (p < 0.05). Receiver operating characteristic analysis revealed that a size ≥1600 cm3 was >80% sensitive and specific for predicting a delayed mass effect or an increase in 6‐month mortality. Multivariate analysis controlling for factors such as APACHE II and packed red blood cells transfused showed that the volume of the RPH was an independent predictor for the development of local mass effects, pulmonary insufficiency, and fluid overload.

Conclusions

Large RPHs are clearly associated with worse patient outcomes. Surgical intervention may be warranted for the treatment of RPHs ≥1600 cm3.
Endovascular Stent‐Graft Repair of Mycotic Aneurysms of the Aorta: A Case Series with a 22‐Month Follow‐Up
Authors: Zhou Tao , Guo Daqiao , Chen Bin , Jiang Junhao , Fu Weiguo , Wang Yuqi
Published: May 2009

Background

The purpose of the present study was to present a single‐institution series of patients with mycotic aneurysms of the aorta treated with endovascular stent‐graft technology, and to report the efficacy and short‐term durability of this repair.

Methods

A retrospective review of seven consecutive patients with mycotic aneurysms of the aorta treated with stent‐graft between May 2006 and July 2007. Patients were diagnosed based on typical appearance of imaging together with a positive bacteriology culture or clinical evidence of infection. A bifurcated, aorto‐uni‐iliac (AUI) stent‐graft and cuff were used in the endovascular repair after infection control. The follow‐up protocol included regular clinical examination, hematologic tests, and computed tomography scans at 3, 6, 12, and 24 months.

Results

Endovascular aneurysm repair (EVAR) was performed successfully in the seven patients (all men, median age 56 years), with complete exclusion of the aneurysms. Five of the patients had infrarenal aortic aneurysms, and the other two had descending thoracic aortic aneurysms. The median hospital stay was 22 days, with no hospital deaths. No paraplegia or other major complications occurred. The patients remained well, with no evidence of graft infection at a mean follow‐up of 22.7 months (range: 17–26 months). A significant reduction in the diameter of the aneurysm sac was noted on computed tomography scans in all the patients at 1 year (mean: 6.5 mm; range: 3–40 mm).

Conclusions

Endovascular stent‐graft treatment represents an alternative treatment with acceptable short‐term outcomes for patients with mycotic aneurysms of the aorta.
Endogenous protease inhibitor uptake within the graft during reperfusion in human liver transplantation
Authors: Ilmakunnas Minna , Höckerstedt Krister , Mäkisalo Heikki , Siitonen Sanna , Repo Heikki , Pesonen Eero J.
Published: May 2009

Background

In experimental liver transplantation, endogenous protease inhibitors alleviate ischemia–reperfusion (I/R) injury by inhibiting proteolysis and by direct anti‐inflammatory actions. We described the kinetics of endogenous protease inhibitors and explored their anti‐inflammatory potential during reperfusion and their effects on graft function in human liver transplantation.

Methods

We measured circulating levels of protease inhibitors (secretory leukocyte proteinase inhibitor, SLPI; tissue inhibitor of metalloproteinases‐1, TIMP‐1) and proteolytic enzymes (elastase; matrix metalloproteinase‐9, MMP‐9) with ELISA, and neutrophil and monocyte CD11b andl‐selectin expression with flow cytometry during liver transplantation in ten patients. To assess changes within the graft during reperfusion, blood samples from portal and hepatic veins were obtained simultaneously.

Results

Circulating SLPI and TIMP‐1 levels decreased during surgery. During initial reperfusion, the transhepatic SLPI gradient was −27 (−35 to −22) ng/ml,P = 0.005, and TIMP‐1 −510 (−636 to −362) ng/ml,P = 0.005, indicating graft protease inhibitor uptake. Concomitantly, hepatic phagocyte activation and sequestration as well as elastase and MMP‐9 release into the circulation occurred. The transhepatic SLPI gradient correlated with postoperative liver enzymes (ALTR = −0.648,P = 0.043; ALPR = −0.661,P = 0.038; bilirubinR = −0.821,P = 0.004; GGTR = −0.648,P = 0.043).

Conclusions

The results suggest a relative shortage of protease inhibitors within the liver during reperfusion, which may contribute to the development of graft injury.
Cities in traditional Chinese fiction and their modern interpretation
Authors: Xun SUN , Fang LIU
Published: May 2009

The complex space of cities exerted a profound and far-reaching influence on traditional Chinese fiction writing. Starting from the description of city spaces, particularly urban landmarks, as the backdrop for stories and ranging through the urban political culture of political struggles, power symbols, the selection of talent, and festivals and carnivals to the daily life of city dwellers with their dreams of prosperity, legendary love stories and inner yearning for justice , the cities of traditional Chinese fiction offer us a picture that goes far beyond the merely geographic to show political and cultural indicators and the content s of daily life. Such descriptions created vivid and distinct city images that in turn became the common life experience and cultural imagination of urban dwellers and offered a common cultural identity and standpoint for those living in the same city.
Synthesis and Some Properties of Fluorinated Cationic Surfactants
Authors: Mohamed M. Z. , Mohamed A. S.
Published: May 2009

Three fluorinated cationic surfactants were prepared by condensing N‐methyl diethanol amine pentafluoro benzoate with stoichiometric amounts of octyl, dodecyl or hexadecyl bromide. The surface properties and parameters were investigated to find the relationship between the structures of the hydrophobic portion of such compounds. The properties studied include surface tension, critical micelle concentration (CMC), effectiveness (Πcmc), maximum surface excess (Γmax) and minimum surface area (Amin) were investigated with respect to different concentrations at 25 °C. Standard free energies of micellization and adsorption of the prepared surfactants in the aqueous solution were studied. The values of Γmax, standard free energies of micellization and adsorption were found to increase with the chain length, while the cmc and minimum surface area occupied by one molecule Amin were found to decrease. The biocidal activity was determined through the inhibition zone diameter of prepared compounds which were measured against five strains of a representative group of microorganisms.
Effects of a gluten-free diet on gut microbiota and immune function in healthy adult human subjects
Authors: De Palma Giada , Nadal Inmaculada , Collado Maria Carmen , Sanz Yolanda
Published: May 2009

Diet influences the composition of the gut microbiota and host's health, particularly in patients suffering from food-related diseases. Coeliac disease (CD) is a permanent intolerance to cereal gluten proteins and the only therapy for the patients is to adhere to a life-long gluten-free diet (GFD). In the present preliminary study, the effects of a GFD on the composition and immune function of the gut microbiota were analysed in ten healthy subjects (mean age 30·3 years) over 1 month. Faecal microbiota was analysed by fluorescencein situhybridisation (FISH) and quantitative PCR (qPCR). The ability of faecal bacteria to stimulate cytokine production by peripheral blood mononuclear cells (PBMC) was determined by ELISA. No significant differences in dietary intake were found before and after the GFD except for reductions (P = 0·001) in polysaccharides.Bifidobacterium,Clostridium lituseburenseandFaecalibacterium prausnitziiproportions decreased (P = 0·007,P = 0·031 andP = 0·009, respectively) as a result of the GFD analysed by FISH.Bifidobacterium,LactobacillusandBifidobacterium longumcounts decreased (P = 0·020,P = 0·001 andP = 0·017, respectively), whileEnterobacteriaceaeandEscherichia colicounts increased (P = 0·005 andP = 0·003) after the GFD assessed by qPCR. TNF-α, interferon-γ, IL-10 and IL-8 production by PBMC stimulated with faecal samples was also reduced (P = 0·021,P = 0·037,P = 0·002 andP = 0·007, respectively) after the diet. Therefore, the GFD led to reductions in beneficial gut bacteria populations and the ability of faecal samples to stimulate the host's immunity. Thus, the GFD may constitute an environmental variable to be considered in treated CD patients for its possible effects on gut health.
Enumerative proofs of certain q-identities
Authors: Andrews George E.
Published: May 2009

Many q-identities have been proved combinatorially. For example
Some integral equations involving finite parts of divergent integrals
Authors: Erdélyi A.
Published: May 2009

In recent years, a number of special integral equations of the first kind was discussed by several authors (see [l]–[4], [6], [7], [9]–[18]). The kernels of these integral equations are special functions of the hypergeometric family, and it was necessary to restrict the parameters appearing in these functions to secure convergence of the integrals. If these restrictions are removed, the integral fails to converge but it may possess a finite part (in Hadamard's sense), and the question arises whether the methods used in the restricted case will alsoapply in the new situation. Indeed, one could pose the moregeneral problem of Volterra integral equations involving finite parts of divergent integrals [19]
On maximal nilpotent subrings of right Noetherian rings
Authors: Michler Gerhard
Published: May 2009

Applying Hopkins's Theorem asserting that each unitary right Artinian ring is right Noetherian, G. Köthe and K. Shoda proved the following theorem (cf. Köthe [7], p. 360, Theorem 1 and p. 363, Theorem 5): If R is a unitary right Artinian ring, then the following statements hold:

(i) Each nilpotent subring of R is contained in a maximal nilpotent subring of R.

(ii) The intersection of all maximal nilpotent subrings of R is the maximal nilpotent twosided ideal of R.

(iii) All maximal nilpotent subrings of R are conjugate.
Some results on coherent rings II
Authors: Harris Morton E.
Published: May 2009

According to Bourbaki [1, pp. 62–63, Exercise 11], a left (resp. right) A-module M is said to be pseudo-coherent if every finitely generated submodule of M is finitely presented, and is said to be coherent if it is both pseudo-coherent and finitely generated. This Bourbaki reference contains various results on pseudo-coherent and coherent modules. Then, in [1, p. 63, Exercise 12], a ring which as a left (resp. right) module over itself is coherent is said to be a left (resp. right) coherent ring, and various results on and examples of coherent rings are presented. The result stated in [1, p. 63, Exercise 12a] is a basic theorem of [2] and first appeared there. A variety of results on and examples of coherent rings and modules are presented in [3].
Translational hull and semigroups of binary relations
Authors: Petrich Mario
Published: May 2009

Various semigroups of partial transformations (and more generally, semigroups of binary relations) on a set have been studied by a number of Soviet mathematicians; to mention only a few: Gluskin [2], Ljapin [4], Shutov [6], Zaretski [7], [8]. In their study the densely embedded ideal of a semigroup introduced by Ljapin [4] plays a central role. In fact, a concrete semigrouQis described in several instances by its abstract characteristic, namely either by a set of postulates on an abstract semigroup or by a set of postulates (which are usually much simpler) on an abstract semigroup S which is a densely embedded ideal of a semigroupTisomorphic toQ. In many cases, the densely embedded idealSis a completely 0-simple semigroup. The following theorem [3, 1.7.1] reduces the study of a semigroupQwith a weakly reductive densely embedded ideal S to the study of the translational hull ofS:

Theorem (Gluskin).If S is a weakly reductive densely embedded ideal of a semigroup Q, then Q is isomorphic to the translational hullω(S)of S.
The torsion of a semi-infinite elastic solid by an elliptical stamp
Authors: Kassir Mumtaz K.
Published: May 2009

The problem of determining, within the limits of the classical theory of elasticity, the displacements and stresses in the interior of a semi-infinite solid (z≧ 0) when a part of the boundary surface (z= 0) is forced to rotate through a given angle ω about an axis which is normal to the undeformed plane surface of the solid, has been discussed by several authors [7, 8, 9, 1, 11,and others]. All of this work is concerned with rotating a circular area of the boundary surface and the field equation to be solved is, essentially, J. H. Mitchell's equation for the torsion of bars of varying circular cross-sections.
On the prime factors of the number 2p-1 - 1
Authors: Rotkiewicz A.
Published: May 2009

From the proof of Theorem 2 of [5] it follows that for every positive integer k there exist infinitely many primes p in the arithmetical progression ax + b (x = 0, 1, 2,…), where a and b are relatively prime positive integers, such that the number 2p−1 − 1 has at least k composite factors of the form (p − 1)x + 1. The following question arises:

For any given natural number k, do there exist infinitely many primes p such that the number 2p−1 − 1 has k prime factors of the form(p − 1)x + 1 and p ≡ b (mod a), where a and b are coprime positive integers?
A characterisation and two examples of Riesz operators
Authors: Gillespie T. A. , West T. T.
Published: May 2009

A Riesz operator is a bounded linear operator on a Banach space which possesses a Riesz spectral theory. These operators have been studied in [5] and [6]. In §2 of this paper we characterise Riesz operators in terms of their resolvent operators. In [6] it was shown that every Riesz operator on a Hilbert space can be decomposed into the sum of compact and quasi-nilpotent parts. §3 contains an example to show that these parts cannot, in general, be chosen to commute. In §4 the eigenset of a Riesz operator is defined. It is a sequence of quadruples each of which consists of an eigenvalue, the corresponding spectral projection, index and nilpotent part. This sequence satisfies certain obvious conditions, and the question arises of the existence of a Riesz operator which has such a sequence as its eigenset. We give an example of an eigenset which has no corresponding Riesz operator.
Semiconvex spaces
Authors: Iyahen S. O.
Published: May 2009

Many of the techniques and notions used to study various important theorems in locally convex spaces are not effective for general linear topological spaces. In [4], a study is made of notionsin general linear topological spaces which can be used to replace barrelled, bornological, and quasi-barrelled spaces. The present paper contains a parallel study in the context of semiconvex spaces.
Elements of finite order in free product sixth-groups
Authors: McCool James
Published: May 2009

A free product sixth-group (FPS-group) is, roughly speaking, a free product of groups with a number of additional defining relators, where, if two of these relators have a subword in common, then the length of this subword is less than one sixth of the lengths of either of the two relators.

Britton [1,2] has proved a general algebraic result for FPS-groups and has used this result in a discussion of the word problem for such groups.
Certain congruence and quotient lattices related to completely 0-simple and primitive regular semigroups
Authors: Scheiblich H. E.
Published: May 2009

G. Lallement [4] has shown that the lattice of congruences, Λ(S), on a completely 0-simple semigroupSis semimodular, thus improving G. B. Preston's result [5] that such a lattice satisfies the Jordan-Dedekind chain condition. More recently, J. M. Howie [2] has given a new and more simple proof of Lallement's result using work due to Tamura [9]. The purpose of this note is to extend the semimodularity result to primitive regular semigroups, to establish a theorem relating certain congruence and quotient lattices, and to provide a theorem for congruences on any regular semigroup.
Simple proof of a theorem on permanents
Authors: Djoković D. Ž.
Published: May 2009

Let A = (aij) be an n × n complex matrix. The permanent of this matrix is

where the sum is taken over all permutations p of the set {1, …, n}.

In a recent paper [1] E. H. Lieb proved an interesting theorem (see below) which he applied to verify some conjectures of M. Marcus and M. Newman. The purpose of this note is to give a simple proof of Lieb's theorem.
The evaluation functionals associated with an algebra of bounded operators
Authors: Duncan J.
Published: May 2009

In this note we shall employ the notation of [1] without further mention. Thus X denotes a normed space and P the subset of X × X′ given by

Given a subalgebra of B(X), the set {Φ(X,f):(x,f) ∈ P} of evaluation functional on is denoted by II. We shall prove that if X is a Banach space and if contains all the bounded operators of finite rank, then Π is norm closed in ′. We give an example to show that Π need not be weak* closed in ″. We show also that FT need not be norm closed in ″ if X is not complete.
Packing of spheres in lp
Authors: Spence E.
Published: May 2009

The Banach space lp(p≥1) is the space of all infinite sequences x = (x1, x2, x3, …) of real or complex numbers such that is convergent, with the norm defined by

The unit sphere S of lp is the set of all points x ∈ lp with ∥x∥ ≤ 1 and the sphere of radius a ≥ 0 centred at y ∈ lp is denoted by Sa(y), so that
Remarks on the Asymptotic Behaviour of Perturbed Linear Systems
Authors: Wong James S. W.
Published: May 2009

Remarks 1, 3 and 5 are incorrect as stated. They should be supplemented by the following observations:

(i) In case the perturbing term is linear in y, i.e. f(t, y) = B(t)y, the conclusion of Theorem 1 will follow from Lemma 1 when applied to equation (15) if we assume, instead of (6),

The hypothesis given in Trench's theorem is sufficient to imply (*) but not (6). A similar comment applies to Remark 5.
On the dimension of Veblen-Wedderburn systems
Authors: Maxson Carlton J.
Published: May 2009

In [1, p. 97], Bruck and Bose ask the question ”Has every (right) Veblen-Wedderburn system finite dimension over its left operator skew-field?” It is the purpose of this note to show that, in general, this question has a negative answer.
On the natural ordering of -classes and of idempotents in a regular semigroup
Authors: Hall T. E.
Published: May 2009

In this paper we prove the following:

Let S be a regular semigroup anda, bany elements of S such that Jb = ≦ Ja. Then, for each idempotent e∈Ja, there exists an idempotent f∈ Jb such that f = ≦e.
On semigroups whose nontrlvial left congruence classes are left ideals
Authors: Hotzel E.
Published: May 2009

An equivalence relation δ on a semigroup S is called a left congruence of S if (u, v) Ε λ implies that (su, sv) Ε λ for every s in S. With every set ℒ of pairwise disjoint left ideals (i. e. subsets L of S such that SL⊂EL), one can associate the left congruence {(u, v)|u = v or there exists an L in ℒ such that u Ε L and v Ε L}. Thus every nonempty left ideal is a left congruence class (i. e. an equivalence class of some left congruence). A left congruence has the form just described if and only if all its nontrivial classes (i. e. its classes containing at least two elements) are left ideals. Such a left congruence is called a Rees left congruence if there is at most one nontrivial class. The identity relation on S is a Rees left congruence since the empty set is a left ideal by definition.
A stability condition for nth order difference equations
Authors: Smith Russell A.
Published: May 2009

Consider the system of difference equations

in which the unknown x(t) is a complex m-vector, t is a real variable and a1, …, an are complex m × m matrices whose elements are functions of t, x(t), x(t+1), …, x(t+n – 1). A positive definite hermitian form V(x1x2, …, xn), with constant coefficients, is called a strong autonomous quadratic Lyapunov function (written strong AQLF) of (1) if there exists a constant K > 1 such that K2v(t+1) < v(t) for all non-zero solutions x(t)of (1), where v(t) = V(x(t), x(t+ 1), …, x(t+n —1)). The existence of a strong AQLF is a sufficient condition for the trivial solution x =0 of (1) to be globally asymptotically stable. It is a necessary condition only in the special case of an equation
On smallest radical and semi-simple classes
Authors: Leavitt W. G. , Watters J. F.
Published: May 2009

In a recent paper [5] one of us has given a sufficient condition to be satisfied by a given property of radical classes within a universal classwin order that, for any subclassℳofw, there should be a smallest radical class having the given property and containingℳ. The sufficient condition is that the classof all radical classes with the given property can be characterised as the class of all radical classes fixed by an admissible function F (see Section 1 below). In this paper a necessary and sufficient condition is derived and the corresponding result for semi-simpleclasses is also presented. These results are given in Section 2.
Bounded generators in linear topological spaces
Authors: Iyahen S. O.
Published: May 2009

Ito and Seidman in [5] define a BG space as a locally convex space in whichthere exists a bounded set with a dense span. In this note we extend the idea to a class of not necessarily locally convex linear topological spaces (l.t.s.). We note the link between the idea of a BG space and Weston’s characterization in [7] of separable Banach spaces. Finally we examine σ-BG spaces; here the bounded set in the definition of a BG space is replaced by the union of a sequence of bounded sets.
Generalized semigroups of quotients
Authors: Berthiaume Pierre
Published: May 2009

In ([6]; pages 36–41), Lambek constructs the maximal ring of quotients Q(R) of a commutative ring R by denning a multiplication on Homr(D, R) where D ranges over all the dense ideals of R, and this generalizes the classical construction of ring of quotients, (cf. [6] for all the references on the subject.)

This programme is carried over, in the first section of this article, to the categoryof commutative reductive semigroups. Examples show that the maximal semigroup of quotients of a commutative monoid can be different from the classical one.
On extensions of inequalities of Kolmogoroff and others and some applications to almost periodic functions
Authors: Upton C. J. F.
Published: May 2009

Let f(x) be a complex function of a real variable, defined over the whole real line, which possesses n derivatives (the nth at least almost everywhere) and is such that . Then, if k is any integer for which 0< k < n, Kolmogoroff's inequality may be written as

,

or, by putting ,

The constant K=K (k, n) known explicitly and is the best possible, i.e., there is a (real) function for which equality holds (see Bang [1]).
Injective hulls as completions
Authors: Bacsich Paul D.
Published: May 2009

A preliminary attempt is made to place the theory of completions of boolean algebras and of partially ordered sets in a wider context. The theory and construction of injective hulls in abelian categories is generalised and it is demonstrated that any variety with enough injectives admits injective hulls. Then the methods developed are applied to a non-algebraic bicategory, that of ordered sets.
The expansion of continuous functions in series of integrals of orthonormal functions
Authors: Finlayson H. C.
Published: May 2009

This paper deals with the following problem: Can an arbitrary continuous function on [0, 1], which vanishes at the origin, be represented in some sense as a series of constant multiples of indefinite integrals of a complete orthonormal set of functions on [0,1]? Four contexts in which this problem arises naturally will be given in the introduction and the remainder of the paper will be devoted to giving a partial answer to the specific problem formulated in one of these contexts.
The extremal points of the range of a vector-valued measure
Authors: Tweddle I.
Published: May 2009

Recently, several papers have investigated conditions under which the range of a vectorvalued measure is a compact convex set (see e.g. [1], [2], [3]). It therefore seems of interest to characterise the extremal points of the range in such cases.
A note on integral equations
Authors: Williams W. E.
Published: May 2009

In a recent paper Cooke [1] obtained a solution of the integral equation

by using the identity

and the technique, first used by Copson, of interchanging the orders of integration and hence reducing the problem to that of the successive solution of two Abel integral equations. It is also shown in [1] that the above identity can also be used to solve the dual series equations

The kernel in equation (1) is a particular member of a general class of kernels which the author [6] has shown to be such that the resulting integral equation is directly soluble by using Copson's technique. The particular example of equation (1) is given in [6] and the identity of equation (2) was used by the author [7] to obtain the solution of equation (3).
On commutative V*-algebras II
Authors: Spain P. G.
Published: May 2009

We show that the commutative V*-algebras with relatively weakly compact unit spheres are those that are representable by means of hermitian spectral measures. This provides a more unified approach to the results of [15], and allows us to generalise some of them.
Character modules, dimension and purity
Authors: Fieldhouse David J.
Published: May 2009

In this paper we use the Bourbaki conventions for rings and modules: all rings are associative but not necessarily commutative and have an identity element; all modules are unital.
An inverse limit representation for complete Boolean algebras
Authors: Beazer R.
Published: May 2009

There are two well-known methods to build up algebras from given algebras, the direct and inverse limits, and a systematic account of these constructions may be found in [2]. It is known that every algebra can be represented as a direct limit of finitely generated algebras although in some cases the representation is trivial. Furthermore, Haimo [3] has established a certain inverse limit representation for the class of all infinite Boolean algebras which generalises, in actual fact, to the class of all infinite lattices with 1. The purpose of this note is to exhibit a certain nontrivial inverse limit representation which is peculiar to the class of infinite, complete Boolean algebras.
Congruences and Green's relations on regular semigroups
Authors: Hall T. E.
Published: May 2009

It is sometimes possible to reconstruct semigroups from some of their homomorphic images. Some recent examples have been the construction of bisimple inverse semigroups from fundamental bisimple inverse semigroups [9], and the construction of generalized inverse semigroups from inverse semigroups [12].
Topologies on Boolean algebras defined by ideals and dual ideals
Authors: Beazer R.
Published: May 2009

In the paper [5], Rema used the well-known fact that in a Boolean algebra the binary operation d: B × B → B defined by is a “metric“ operation to show that, if D is any dual ideal of ^, then the sets Up = {(x, y): d(x, y)
 being called an auto-topologized Boolean algebra. Recently, Kent and Atherton [1, 4] exhibited a family of topologies on an arbitrary lattice ℒ defined in terms of ideals and dual ideals. More specifically, if I and D are respectively an ideal and a dual ideal of ℒ, then the T[I:D] topology on ℒ is the topology defined by taking the sets of the form a*⋂b+, where , as sub-base for the open sets. It is these topologies that are studied in this paper.
Any group is a maximal subgroup of the semigroup of binary relations on some set
Authors: Preston G. B.
Published: May 2009

We show that the theorem stated in the title is a corollary to a result of K. A. Zaretskii [5] and a theorem of G. Birkhoff [1]. The construction we use further shows that all groups with cardinal less than or equal to the cardinal of the given group are simultaneously realised as maximal subgroups of the same semigroup of binary relations ℬx. For finite or countable groups, when Xmay be taken to be finite or countable, respectively, and for an entirely different method of proof, the paper of J. S. Montague and R. J. Plemmons [3] should be consulted. For two further proofs of the theorem of the title to this note, this time for any X, see also R. J. Plemmons and B. M. Schein [4] and A. H. Clifford [2].
On Salié's sum
Authors: Mordell L. J.
Published: May 2009

Let p be an odd prime and let f(x) be a complex-valued function such that f(x+p) = f(x) for all integers x. Write e(x) = exp(2πix/p), and define l/x by , where We consider the sum

where is the Legendre symbol. The sum is zero if as is clear on replacing x by bjax. Salié has found a result which can be written in the form

when h2 ≡ 4ab(modp).
Regular semigroups which are subdirect products of a band and a semilattice of groups
Authors: Petrich Mario
Published: May 2009

In the study of the structure of regular semigroups, it is customary to impose several conditions restricting the behaviour of ideals, idempotents or elements. In a few instances, one may represent them as subdirect products of some much more restricted types of regular semigroups, e.g., completely (0-) simple semigroups, bands, semilattices, etc. In particular, studying the structure of completely regular semigroups, one quickly distinguishes certain special cases of interest when these semigroups are represented as semilattices of completely simple semigroups. In fact, this semilattice of semigroups may be built in a particular way, idempotents may form a subsemigroup, ℋ may be a congruence, and so on.
An elementary proof of some character sum identities of Apostol
Authors: Berndt Bruce C.
Published: May 2009

Let х denote a primitive character modulo k. Using two different representations for Dirichlet L-functions, Apostol [1] recently derived a representation for

involving the sums

where m is a positive integer. Furthermore, if х(r) = (r|p)the residue class character modulo the odd prime p, he derived a representation for Mm(х) involving the sums
The translational hull of an inverse semigroup
Authors: Ault Janet E.
Published: May 2009

An ideal extension of one semigroup by another is determined by a partial homomorphism into the translational hull of the first semigroup [3, §2, Theorem 5]. In most ins tances, the development of the theory of ideal extensions has been hindered by inadequate knowledge of the translational hull; it is our purpose here to characterize certain basic structures in the translational hull of an arbitrary inverse semigroup.
Spaces of closed subgroups of a connected Lie group
Authors: Oler N.
Published: May 2009

In a sequence of two papers which appeared in 1968 and 1969 Herbert Abels [1, 2] has developed, from a method originated by Gerstenhaber [6], a means for extending the study of properly discontinuous groups of transformations to that of proper transformation groups in general. We recall that, if G is a Hausdorff locally compact group of transformations of a locally compact space X, then the action of Gis proper when, for any two compact subsets K and L, the subset G(K, L) = {g ɛ G: gL∩K # 0} of G is compact (see [3], p. 55). In what follows all groups and spaces will be Hausdorff and locally compact. If H is a closed subgroup of G, then it is clear that the property just defined is possessed by the action of H as a group of left translations of G.
Factorization and arithmetic functions for orders in composition algebras
Authors: Lamont P. J. C.
Published: May 2009

A well-known product, referred to as the Dirichlet convolution product, is generalized to arithmetic functions defined on an order in a Cayley division algebra. Factorization results for orders, multiplicative functions and analogues of the Moebius inversion formula are discussed.
A generalized inductive limit topology for linear spaces
Authors: Iyahen S. O. , Popoola J. O.
Published: May 2009

In the usual definition of an inductive limit of locally convex spaces, one is given a linear space E, a family (Eα) of locally convex spaces and a set (iα) of linear maps from Eα into E. Garling in [2] studies an extension of this, looking at absolutely convex subsets Sα of Eα and restrictions jα of iα to such sets. If, in the definition of Garling [2, p. 3], each Sα is instead a balanced semiconvex set, then the finest linear (not necessarily locally convex) topology on E for which the maps ja are continuous, will be referred to as the generalized *-inductive limit topology of the semiconvex sets. This topology is our object of study in the present paper; we find applications in the closed graph theorem.
Simplex algebras and their representation
Authors: Vijayakumar M. S.
Published: May 2009

This paper establishes a relationship (Theorem 4.1) between the approaches of A. C. Thompson [8, 9] and E. G. Effros [2] to the representation of simplex algebras, that is, real unital Banach algebras that are simplex spaces with the unit for order identity. It proves that the (nonempty) interior of the associated cone is contained in the principal component of the set of all regular elements of the algebra. It also conjectures that each maximal ideal (in the order sense—see below) of a simplex algebra contains a maximal left ideal of the algebra. This conjecture and other aspects of the relationship are illustrated by considering algebras of n × n real matrices.
Some precisions on the Fourier-Borel transform and infinite order differential equations
Authors: Gruman Lawrence
Published: May 2009

Let f(z) be an entire function (of several variables). We define the function

which is increasing. The orderof f(z) is the constant (perhaps infinite)
A note on B*-algebras
Authors: Murphy I. S.
Published: May 2009

Let A be a Banach *-algebra. We assume neither that A has an identity element, nor that the involution on A is continuous.
The lattice of congruences on a band of groups
Authors: Spitznagel C.
Published: May 2009

It is implicit in a result of Kapp and Schneider [3] that, if Sisa completely simple semigroup, then the lattice Λ(S) of congruences on S can be embedded in the product of certain sublattices. In this paper we consider the problem of embedding Λ(S) in a product of sublattices, when S is an arbitrary band of groups. The principal tool is the θ-relation of Reilly and Scheiblich [7]. The class of θ-modular bands of groups is definedby means of a type of modularity condition on Λ(S). It is shown that the θ-modular bands of groups are precisely those for which a certain function is an embedding of Λ(S) into a product of sublattices. The problem of embedding the inverse semigroup congruences into a certain product lattice is also considered.
A Fourier-Neumann series and its application to the reduction of triple cosine series
Authors: Tranter C. J. , Cooke J. C.
Published: May 2009

The Jacobi expansion

is well known and easily obtained from the generating function of the Besselcoefficients. The sum of the series on the right of equation (1) when sin (n+½)x is replaced by cos (n+½)x cannot be found in this way but it can be expressed in terms of a definite integral as shown below. The result so obtained is useful in reducing certain triple cosine series to dual series and so simplifying the solution given by one of us for such series in an earlier paper [1].
On Schoeneberg's theorem
Authors: Maclachlan C.
Published: May 2009

Let Sbe a compact Riemann surface of genus g ≥ 2 and σ an automorphism (conformal self-homeomorphism) of S of order n. Let S* = S/ « σ« have genus g*. In [5], Schoeneberg gave a sufficient condition that a fixed point P ∈ S of σ should be a Weierstrass point of S, i.e., that Sshould support a function that has a pole of order less than or equal to g at P and is elsewhere regular.
Order and norm convergence in Banach lattices
Authors: Wirth Andrew
Published: May 2009

Let(V, ≧, ‖ · ‖) be a Banach lattice, and denote V\{0} by V'. For the definition of a Banach lattice and other undefined terms used below, see Vulikh [4]. Leader [3] shows that, if norm convergence is equivalent to order convergence for sequences in V, then the norm is equivalent to an M-norm. By assuming the equivalence for nets in V we can strengthen this result.
Partitioned transversals
Authors: Mirsky L.
Published: May 2009

Let E be a finite set and let= (Al, …, A2) be a family of subsets of E. A subset T of E iscalled atransversal ofif there exists a bijection Φ: T → {l, …, n} such thatx∈Aψ(x)for allx∈ T. If I ⊆ {1, …,n}, we shall, for brevity, write

(and similarly for families denoted by other letters). The cardinal of a set S will be denoted by |S|. If λ is a non-negative integer, we define λS as S or Ø according as λ > 0 or λ = 0.
Hecke invariants of knot groups
Authors: Riley Robert
Published: May 2009

For each characteristic p, let Fp be the prime field and let Ώp be a fixed universal field which is algebraically closed and of infinite transcendence degree over Fp. When p = 0 we take Ώp = ℂ. Let F be a subfield of Ώp and let R be an integral domain whose quotient field is F. We abbreviate SL(2, R), PGL(2, R), PSL(2, R) to SL(R), PGL(R), PSL(R) respectively, and we cohsider PSL(R) as a group of projective transformations of the projective line ℘(Ώp) and of the “subline” ℘(F) ⊂ ℘(ΏP). The elements of PSL(R) are classified by the number of fixed points they have on ℘(F). If x ∈ PSL(R) has one such fixed point P, then P is the unique fixed point of x on ℘(ΏP) and x is called parabolic. All other x (except the identity E) have two distinct fixed points on ℘(Ώp) and x is called hyperbolic if these are on ℘(F), and elliptic otherwise. We put symbols for operators on the right.
A local mean-value theorem for analytic functions with smooth boundary values
Authors: Novinger W. P.
Published: May 2009

Let f be an analytic function on a connected open set Ώ in the complex plane. Then, for given a, b ∈ Ώ, the equation

need not have a solution z ∈ Ώ. As a matter of fact, this would happen with each locally one-to-one analytic function which is not one-to-one on Ώ. But if we fix a a ∈ Ώ, then, for all b sufficiently close to a, (1) is solvable for z. This is an easy consequence of the Open Mapping Theorem applied to f'. For, assuming that f' is non-constant (otherwise, (1) holds for all a, b, z ∈Ώ), the Open Mapping Theorem tells us that f'(Ώ), the image under f' of Ώ, is an open neighbourhood of f'(a); so it is a direct consequence of the definition of f'(a) that there exists δ > 0 such that 0 < |b – a| < δ implies (f(b) – f(a))/(b – a) ∈f'(Ώ). A stronger statement has been obtained by J. M. Robertson [1, p. 329], who has shown that

and, if f''(a) ≠ 0, then

.
A characterization of determinants over topological fields
Authors: Odoni R. W. K.
Published: May 2009

Let K be a topological field. On introducing the vector-space topology on the n × n matrices over K, it becomes clear that the determinant map φ enjoys the following properties:

(A) φ is a continuous surjective homomorphism from GLn(K) to K*,

(B) φ(μa) = μn φ(a) for each non-zero φ in K, and all a in GLn(K).
A direct proof of a theorem of West on sequences of Riesz operators
Authors: Ruston Anthony F.
Published: May 2009

We recall (cf. [2] Definitions 3.1 and 3.2, p. 322) that a bounded linear operator T on a Banach space ℵ into itself is said to be asymptotically quasi-compact if K(Tn)⅟n → 0 as n → ∞. where K(U) = inf ∥U–C∥ for every bounded linear operator U on ℵ into itself, the infimum being taken over all compact linear operators C on ℵ into itself. For a complex Banach space, this is equivalent (cf. [2], pp. 319, 321 and 326) to T being a Riesz operator.
Certain congruences on a completely regular semigroup
Authors: Pirnot Thomas L.
Published: May 2009

Congruences on a semigroup S such that the corresponding factor semigroups are of a special type have been considered by several authors. Frequently it has been difficult to obtain worthwhile results unless restrictions have been imposed on the type of semigroup considered. For example, Munn [6] has studied minimum group congruences on an inverse semigroup, R. R. Stoll [9] has considered the maximal group homomorphic image of a Rees matrix semigroup which immediately determines the smallest group congruence on a Rees matrix semigroup. The smallest semilattice congruence on a general or commutative semigroup has been studied by Tamura and Kimura [10], Yamada [12] and Petrich [8]. In this paper we shall study congruences ρ on a completely regular semigroup S such that S/ρ is a semilattice of groups. We shall call such a congruence an SG-congruence.
Free products of two real cyclic matrix groups
Authors: Evans R. J.
Published: May 2009

We exhibit a large class K* of real 2 × 2 matrices of determinant ±1 such that, for nearly all A and B in K*, the group generated by A and B1 (the transpose of B) is the free product of the cyclic groups It is shown that K* contains all matrices of determinant ±1 with integer entries satisfying |b| > |a|, |c|, |d|. This gives a generalization of a theorem of Goldberg and Newman [2]. We also prove related results concerning the dominance of b and the discreteness of the free products .
On relative difference sets and projective planes
Authors: Piper Fred
Published: May 2009

A permutation group is quasiregular if it acts regularly on each of its orbits (i.e. the stabiliser of an element fixes every other element in its orbit). So, in particular, any permutation representation of an abelian or hamiltonian group must be quasiregular.
A note on regular local Noether lattices
Authors: Johnson Johnny A.
Published: May 2009

If R is a local (Noetherian) ring, it is well known that R is regular if and only if its completion is regular. It is the purpose of this note to show that a similar result is true for Noether lattices.
The Convergence of Least Squares Approximations for dual Orthogonal Series
Authors: Feinerman Robert P. , Kelman Robert B.
Published: May 2009

1. Equation (4) should read

2. On p. 83 below equation (7) replace

3. On p. 83 two lines above equation (9) replace
Group structure and properties of block ideals of the group algebra
Authors: Hamernik Wolfgang
Published: May 2009

In this note relations between the structure of a finite group G and ringtheoretical properties of the group algebra FG over a field F with characteristic p > 0 are investigated. Denoting by J(R) the Jacobson radical and by Z(R) the centre of the ring R, our aim is to prove the following theorem generalizing results of Wallace [10] and Spiegel [9]:

Theorem. Let G be a finite group and let F be an arbitrary field of characteristic p > 0. Denoting by BL the principal block ideal of the group algebra FG the following statements are equivalent:

(i) J(B1) ≤ Z(B1)

(ii) J(B1)is commutative,

(iii) G is p-nilpotent with abelian Sylowp-subgroups.
Some generating-function equivalences
Authors: Srivastava H. M.
Published: May 2009

A generalization is given of a theorem of F. Brafman [1] on the equivalence of generating relations for a certain sequence of functions. The main result, contained in Theorem 2 below, may be applied to several special functions including the classical orthogonal polynomials such as Hermite, Jacobi (and, of course, Legendre and ultraspherical), and Laguerre polynomials.
Nonparabolic subgroups of the modular group
Authors: Tretkoff Carol
Published: May 2009

In this paper we shall discuss maximal nonparabolic and maximal normal nonparabolic subgroups of the modular group Г = 〈ω, φ; ω2=φ3= 1〉. The modular group may also be defined as the group of fractional linear transformationsw= (az+b)/(cz+d), wherea, b, c, dare rational integers withad − bc= 1. Here, a maximal nonparabolic subgroup of Г is a subgroup that contains no parabolic elements and any proper subgroup of Г which containsScontains parabolic elements. Similarly, a maximal normal nonparabolic subgroup is a normal nonparabolic subgroup of Г which is not contained in any larger normal nonparabolic subgroup of Г.
Some expansions of hypergeometric functions in series of hypergeometric functions
Authors: Srivastava H. M. , Panda Rekha
Published: May 2009

Throughout the present note we abbreviate the set of p parameters a1,…,ap by (ap), with similar interpretations for (bq), etc. Also, by [(ap)]m we mean the product , where [λ]m = Г(λ + m)/ Г(λ), and so on. One of the main results we give here is the expansion formula

(1)

which is valid, by analytic continuation, when, p,q,r,s,t and u are nonnegative integers such that p+r < q+s+l (or p+r = q+s+l and |zω| <1), p+t < q+u (or p + t = q + u and |z| < 1), and the various parameters including μ are so restricted that each side of equation (1) has a meaning.
The Higher homotopy groups of the p-spun trefoil knot
Authors: McCallum W. A.
Published: May 2009

In this paper we show that the (p+l)st homotopy group of the p-spun trefoil knot is nontrivial. This result was obtained for p = 1 in [1] using duality arguments. Here we take a totally different approach via the algorithm given in [3] and a module representation giving a simpler and more natural argument.
Class numbers and quadratic residues
Authors: Chowla S. , Friedlander J.
Published: May 2009

It has long been known that there is a strong connection between the class numbers of quadratic fields and the distribution of quadratic residues. This connection is exemplified, for instance, by the class number formulae of Dirichlet, which have formed the basis of much of the work on the subject of class numbers.
On non-commutative regular local rings
Authors: Smith P. F.
Published: May 2009

Let R be a ring (with identity). We shall call R a local ring if R is aright noetherian ring such that the Jacobson radical M is a maximal ideal (and so is the only maximal ideal), and R/M is a simple artinian ring. A local ring R with maximal ideal M is called regular if there exists a chain

of ideals Mi of such that Mi–1/Mi is generated by a central regular element of R/Mi (1 ≦ i ≦ n). For such a ring R, Walker [6, Theorem 2. 7] proved that R is prime and n is the right global dimension of R, the Krull dimension of R, the homological dimension of theR-module R/M and the supremum of the lengths of chains of prime ideals of R. Such regular local rings will be called n-dimensional. The aim of this note is to give examples of regular local rings. These arise as localizations of universal enveloping algebras of nilpotent Lie algebras over fields and localizations of group algebras of certain finitely generated finite-by-nilpotent groups.
On certain triple integral equations with trigonometric kernels
Authors: Stocks D. C.
Published: May 2009

In this note we formally solve the following triple integral equations,

where f1(x), f2(x) and f3(x) are integrable for 0<x<α, α<x<β and β<x<∞, respectively, and the function g(λ) is assumed to satisfy sufficient conditions for the Fourier sine transform to exist. A special case of this system arose in a problem concerned with transistors.