bluuebunny/crossref_metadata_2025 huggingface dataset:
Stress Intensity Factor Evaluation of Anisotropic Cracked Sheets under Dynamic Loads Using Energy Domain Integral
Authors: Mauler M. , Sollero P. , Albuquerque E.L.
Published: December 2010

The aim of this paper is to present a procedure to perform the evaluation of dynamic stress intensity factors of composite cracked sheets. The numerical method that is used to perform the modeling of the crack is the dual boundary element method. The inertial effects are modeled using the dual reciprocity boundary elements method. The Houbolt Method is used to integrate time, and the energy domain integral is used to evaluate stress intensity factors.
Alloantibodies Prevent the Induction of Transplantation Tolerance by Enhancing Alloreactive T Cell Priming
Authors: Burns Audrea M. , Chong Anita S.
Published: December 2010

Circulating alloantibodies in transplant recipients are often associated with increased Ab-mediated as well as cellular rejection. We tested the hypothesis that alloantibodies facilitate cellular rejection by functioning as opsonins to enhance T cell activation using a BALB/c to C57BL/6 heart or skin transplant model. Long-term heart and skin survival induced with anti-CD154 alone or in combination with donor-specific transfusion (DST), respectively, was abrogated by the presence of anti-Kd mAbs, and alloreactive T cell activation as well as acute rejection was observed. The prevention of graft acceptance in the skin model was dependent on anti-Kd binding to and converting DST from tolerigenic to immunogenic. Adoptive transfer of CFSE-labeled TCR-transgenic T cells into B6 recipients treated with anti-CD154/DST revealed the ability of anti-Kd to enhance the proliferation of anti–Kd-specific T cells via the indirect pathway as well as of non–Kd-reactive, recipient MHC-restricted CD4+ and CD8+ T cells. Thus, alloantibodies with restricted specificity are able to facilitate the indirect presentation as well as the cross-presentation of a larger repertoire of “linked” donor-derived Ags. These observations highlight the ability of alloantibodies to function not only in classical humoral rejection but also as opsonins that facilitate the CD40-CD154–independent activation of alloreactive T cells.
Inhibition of Tumor-Induced Myeloid-Derived Suppressor Cell Function by a Nanoparticulated Adjuvant
Authors: Fernández Audry , Mesa Circe , Marigo Ilaria , Dolcetti Luigi , Clavell Marilyn , Oliver Liliana , Fernández Luis E. , Bronte Vincenzo
Published: December 2010

The interaction between cancer vaccine adjuvants and myeloid-derived suppressor cells (MDSCs) is currently poorly understood. Very small size proteoliposomes (VSSP) are a nanoparticulated adjuvant under investigation in clinical trials in patients with renal carcinoma, breast cancer, prostate cancer, and cervical intraepithelial neoplasia grade III. We found that VSSP adjuvant induced a significant splenomegaly due to accumulation of CD11b+Gr-1+ cells. However, VSSP-derived MDSCs showed a reduced capacity to suppress both allogeneic and Ag-specific CTL response compared with that of tumor-induced MDSCs. Moreover, splenic MDSCs isolated from tumor-bearing mice treated with VSSP were phenotypically more similar to those isolated from VSSP-treated tumor-free mice and much less suppressive than tumor-induced MDSCs, both in vitro and in vivo. Furthermore, different from dendritic cell vaccination, inoculation of VSSP-based vaccine in EG.7-OVA tumor-bearing mice was sufficient to avoid tumor-induced tolerance and stimulate an immune response against OVA Ag, similar to that observed in tumor-free mice. This effect correlated with an accelerated differentiation of MDSCs into mature APCs that was promoted by VSSP. VSSP used as a cancer vaccine adjuvant might thus improve antitumor efficacy not only by stimulating a potent immune response against tumor Ags but also by reducing tumor-induced immunosuppression.
Hypoxia Selectively Inhibits Respiratory Burst Activity and Killing of Staphylococcus aureus in Human Neutrophils
Authors: McGovern Naomi N. , Cowburn Andrew S. , Porter Linsey , Walmsley Sarah R. , Summers Charlotte , Thompson Alfred A. R. , Anwar Sadia , Willcocks Lisa C. , Whyte Moira K. B. , Condliffe Alison M. , Chilvers Edwin R.
Published: December 2010

Neutrophils play a central role in the innate immune response and a critical role in bacterial killing. Most studies of neutrophil function have been conducted under conditions of ambient oxygen, but inflamed sites where neutrophils operate may be extremely hypoxic. Previous studies indicate that neutrophils sense and respond to hypoxia via the ubiquitous prolyl hydroxylase/hypoxia-inducible factor pathway and that this can signal for enhanced survival. In the current study, human neutrophils were shown to upregulate hypoxia-inducible factor (HIF)-1α–dependent gene expression under hypoxic incubation conditions (3 kPa), with a consequent substantial delay in the onset of apoptosis. Despite this, polarization and chemotactic responsiveness to IL-8 and fMLP were entirely unaffected by hypoxia. Similarly, hypoxia did not diminish the ability of neutrophils to phagocytose serum-opsonized heat-killed streptococci. Of the secretory functions examined, IL-8 generation was preserved and elastase release was enhanced by hypoxia. Hypoxia did, however, cause a major reduction in respiratory burst activity induced both by the soluble agonist fMLP and by ingestion of opsonized zymosan, without affecting expression of the NADPH oxidase subunits. Critically, this reduction in respiratory burst activity under hypoxia was associated with a significant defect in the killing of Staphylococcus aureus. In contrast, killing of Escherichia coli, which is predominantly oxidase independent, was fully preserved under hypoxia. In conclusion, these studies suggest that although the NADPH oxidase-dependent bacterial killing mechanism may be compromised by hypoxia, neutrophils overall appear extremely well adapted to operate successfully under severely hypoxic conditions.
Glucocorticosteroids Modify Langerhans Cells To Produce TGF-β and Expand Regulatory T Cells
Authors: Stary Georg , Klein Irene , Bauer Wolfgang , Koszik Frieder , Reininger Bärbel , Kohlhofer Sabine , Gruber Kristina , Skvara Hans , Jung Thomas , Stingl Georg
Published: December 2010

Although glucocorticosteroids (GCSs) have been used for many decades in transplantation and (auto)inflammatory diseases, the exact mechanisms responsible for their immunosuppressive properties are not fully understood. The purpose of this study was to characterize the effects of oral GCSs on the cutaneous immune response. We analyzed, by immunofluorescence staining and quantitative RT-PCR, residual skin biopsy material from a clinical study in which we had used oral GCS as positive control for determining the effects of candidate anti-inflammatory compounds on epicutaneous patch tests of Ni-allergic patients. Expectedly, oral GCS treatment led to a reduction of clinical symptoms and infiltrating leukocytes. Notably, we observed increased numbers of dermal FOXP3+CD25+ T cells and epidermal Langerhans cells (LCs) that were associated with upregulated mRNA expression of TGF-β in lesions of GCS-treated Ni-allergic patients. To investigate this phenomenon further, we exposed purified LCs to GCS. They exhibited, in contrast to GCS-nonexposed LCs, 1) a more immature phenotype, 2) higher intracellular amounts of TGF-β, and 3) increased receptor activator for NF-κB expression, conditions that reportedly favor the expansion of regulatory T cells (Tregs). Indeed, we observed an enhancement of functionally suppressive FOXP3+ T cells when CD3+ cells were incubated with GCS-pretreated LCs. The expansion of Tregs was inhibited by TGF-β blockage alone, and their suppressive activity was neutralized by a combination of anti–TGF-β and anti–IL-10 Abs. Our data show that systemically applied GCSs endow LCs with Treg-promoting properties and thus shed new light on the mechanisms of GCS-mediated immunosuppression.
Cutting Edge: Critical Role of Intracellular Osteopontin in Antifungal Innate Immune Responses
Authors: Inoue Makoto , Moriwaki Yasuhiro , Arikawa Tomohiro , Chen Yu-Hsun , Oh Young Joo , Oliver Timothy , Shinohara Mari L.
Published: December 2010

We found that absence of osteopontin (OPN) in immunocompromised Rag2−/− mice, which lack T and B cells, made the mice extremely susceptible to an opportunistic fungus Pneumocystis, although immunocompetent OPN-deficient mice could clear Pneumocystis as well as wild-type mice. OPN has been studied as an extracellular protein, and the role of an intracellular isoform of OPN (iOPN) is still largely unknown. In this study, we elucidated the mechanism by which iOPN was involved in antifungal innate immunity. First, iOPN was essential for cluster formation of fungal receptors that detect Pneumocystis, including dectin-1, TLR2, and mannose receptor. Second, iOPN played a role as an adaptor molecule in TLR2 and dectin-1 signaling pathways and mediated ERK activation and cytokine production by zymosan, which simultaneously activates TLR2 and dectin-1 pathways. Third, iOPN enhanced phagocytosis and clearance of Pneumocystis. Our study suggests the critical involvement of iOPN in antifungal innate immunity.
Kommt nur darauf an, wie man dazu kommt und was man damit macht. Die Gefahren und Chancen von Geld im Neuen Testament
Authors: Stenschke Christoph
Published: December 2010

It only matters how it is obtained and how it is employed � the dangers and chances of money in the New Testament This article examines statements about money and other forms of material wealth in the New Testament. After a general survey of the surprisingly many occurrences of money, coins, wealth or property and the contexts in which they appear, the article describes the spiritual dangers involved in the desire for and use of money as addressed by various New Testament books. A further section is devoted to an often neglected aspect, namely the positive chances of money rightly used that are also mentioned. Money, otherwise also called mammon, can be used to support those in need and to further the kingdom of God and even to express spiritual truths and bonds. This is followed by a summary of New Testament statements on obtaining money legitimately and using it properly. A final section reflects on the way how Christians today are to use the means that have been entrusted to them.
�The hastening that waits�: A critical assessment of the tangebility of unity within the Uniting Reformed Church in Southern Africa
Authors: Tshaka Rothney S. , Maruping Peter M.
Published: December 2010

The tale of the Reformed Church tradition in South Africa remains conspicuous with challenges also within the current democratic context. Whilst the political past of South Africa contributed towards a Reformed church divided along racial lines, a struggle continues for a genuinely unified Reformed church today. Conceding to the present discussions about the possibility of uniting all Reformed congregations that were divided along racial categories of Black, Coloured, Indian and White, this article aspires to delve into the intricacies pertaining to the already achieved unity between the �Coloured� and a huge portion of the �Black� Reformed congregations, that is to say, the Uniting Reformed Church in Southern Africa. This article will argue that although it is fundamental that the church of Christ must be united, it is equally imperative that the Uniting Reformed Church in Southern Africa (URCSA) waits and assesses whether it has already achieved tangible unity.
Note Upon The Generalized Cayleyan Operator
Authors: Turnbull H. W.
Published: December 2010

The following note which deals with the effect of a certain determinantal operator when it acts upon a product of determinants was suggested by the original proof which Dr. Alfred Young gave of the property

subsisting between the positive P and the negative N substitutional operators, θ being a positive integer. This result which establishes the idempotency of the expression θ−1NP within an appropriate algebra is fundamental in the Quantitative Substitutional Analysis that Young developed.
On The Critical Lattices of Arbitrary Point Sets
Authors: Mahler K.
Published: December 2010

In this note, I shall establish necessary and sufficient conditions for the existence of critical lattices of an arbitrary point set, and I shall construct a non-trivial example of a point set without any critical lattice. In a previous paper, I proved that every star body of the finite type possesses at least one critical lattice.
Boundedness Properties in Function-Lattices
Authors: Stone M. H.
Published: December 2010

The continuous real functions on a topological space X are partially ordered in a natural way by putting ƒ ≦ g if and only if ƒ(x)≦ g(x) for all x in X. With respect to this partial ordering these functions constitute a lattice, the lattice operations ∪ and ∩ being defined by the relations (ƒ ∪ g) (x) = max (ƒ(x), g(x)) ƒ ∩ g )(x) = min (ƒ(x), g(x)). The lattice character of any partially ordered system merely expresses the existence of least upper and greatest lower bounds for any finite set of elements in the system. Many partially ordered systems enjoy much stronger boundedness properties than these: for example, every subset with an upper bound may have a least upper bound, as in the case of the real number system.
Direct Theorems on Methods of Summability
Authors: Lorentz G. G.
Published: December 2010

1.1. A regular Toeplitz method of summability is given by a transformation m = 0, 1, 2 , … of the sequence sn into the sequence σm. According to the definition of regularity, every such method sums a convergent sequence sn to the value lim sn. The question naturally arises, whether there are more extensive classes of sequences summable by all regular methods 1.1(1) or at least by all such methods subject to some simple additional conditions. Questions of this kind have been treated by the author (Lorentz [2], [5]) and, from another point of view, by R. P. Agnew [2] [3] ; in this paper we wish to discuss the problem systematically.
Periodic Linear Transformations of Affine and Projective Geometries
Authors: Snapper Ernst
Published: December 2010

Introduction. In a paper called “A Theorem in Finite Projective Geometry and some Applications to Number Theory” [Trans. Amer. Math. Soc, vol. 43 (1938), 377-385], J. Singer proved that the finite projective geometry PG(s — 1,pn), that is the projective geometry of dimension s — 1 whose coordinate field is the Galois field GF(pn), admits a collineation L of period q = (psn — 1)/ (pn — 1). Since this q is the number of points of PG(s — 1, pn), Singer's result states that the points of PG(s — 1, pn) are cyclically arranged. Singer's construction of L uses the notion of a “primitive irreducible polynomial of degree 5 belonging to a field GF(pn) which defines a PG(s — 1, pn).”
The Relation Between Functions Satisfying a Certain Integral Equation and
General Watson Transforms
Authors: Goodspeed F. M.
Published: December 2010

In some work of Ramanujan certain results are given which are equivalent to the following.

If

(1)
Simultaneous Diophantine Approximation
Authors: Raisbeck Gordon
Published: December 2010

Summary of results. The principal result of this paper is as follows: given
any set of real numbers z1, z2, & , zn and an integer t we can find an integer and a set of integers p1, p2 & , pn such that

(0.11).

Also, if n = 2, we can, given t, produce numbers z1 and z2 such that

(0.12)

This supersedes the results of Nils Pipping (Acta Aboensis, vol. 13, no. 9, 1942)
that there is a q satisfying (0.11) such that , and also the
classical result of Dirichlet that there is such a q less than tn.
Note on a Paper by Robinson
Authors: Todd J. A.
Published: December 2010

In a recent paper Robinson has obtained an explicit formula for the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices. The object of the present note is to show that this formula may be deduced from known properties of Schur functions, with the aid of a result which the author has proved elsewhere.
The Iteration of Certain Arithmetic Functions
Authors: Niven Ivan
Published: December 2010

1. Introduction. For define C(n) to be the integer j such that , where denotes the j th iterate of the Euler ø-function. Define C(l) = C(2) = 0. This function has been studied by S. S. Pillai [1], with the notation R(n) for 1 + C(n) if , and R(l) = 0. H. Shapiro [2] has also investigated this function, proving the basic relations

(1)
Union Curves of a Hypersurface
Authors: Springer C. E.
Published: December 2010

1. Introduction. A curve on an ordinary surface is a union curve if its osculating plane at each point contains the line of a specified rectilinear congruence through the point. The author has obtained the differential equations of union curves on a metric surface in ordinary space and has exhibited certain generalizations for union curves of known results concerning geodesic curves on a surface. It is the purpose of the present paper to develop the differential equations of the union curves of a hypersurface Vn immersed in a Riemannian manifold Vn+1 of n + 1 dimensions. The osculating plane to a curve on a surface is generalized to a totally geodesic surface the straight lines of which are geodesies in the space Vn+1. A formula is given for the union curvature vector of a curve in Vn.
The Hamiltonian Form of Field Dynamics
Authors: Dirac P. A. M.
Published: December 2010

In classical dynamics one has usually supposed that when one has solved the
equations of motion one has done everything worth doing. However, with the further
insight into general dynamical theory which has been provided by the discovery of
quantum mechanics, one is lead to believe that this is not the case. It seems that
there is some further work to be done, namely to group the solutions into families
(each family corresponding to one principal function satisfying the
Hamilton-Jacobi equation). The family does not have any importance from the point
of view of Newtonian mechanics; but it is a family which corresponds to one state
of motion in the quantum theory, so presumably the family has some deep
significance in nature, not yet properly understood.
Short Formulations of Boolean Algebra, Using Ring Operations
Authors: Byrne Lee
Published: December 2010

Special interest has recently attached to formulations of Boolean algebra in
terms of ring operations [7], [1]. These axiomatizations have not been as brief as
those reached through other modes of approach.

The present note will show that the number of axioms when ring operations are
used may be as small as in any present version that is not metamathematical, that
is, the number of axioms finally employed will be two.
Finite Nets, I. Numerical Invariants
Authors: Bruck R. H.
Published: December 2010

A finite net N of degree
k, order n, is a
geometrical object of which the precise definition will be given in §1. The
geometrical language of the paper proves convenient, but other terminologies are
perhaps more familiar. A finite affine (or Euclidean) plane with n points on each
line is simply a net of
degree n+ 1, order n
(Marshall Hall [1]). A loop of order n is essentially a
net of degree 3, order n (Baer [1], Bates [1]). More
generally, for , a set of k —2
mutually orthogonal n ⨯ n
latin squares may be used to define a net of degree k,
order n (and conversely) by paralleling Bose's
correspondence (Bose [1]) between affine planes and complete sets of orthogonal
latin squares.
A Cyclic Involution of Period Eleven
Authors: Hutcherson W. R.
Published: December 2010

In two earlier papers * the writer discussed involutions
of periods five and seven on certain cubic surfaces in S3. In
this paper, a quartic surface containing a cyclic involution of period eleven is
considered.

The surface
Non-Normal Galois Theory for Non-Commutative and Non-semisimple Rings
Authors: Nakayama Tadasi
Published: December 2010

The purpose of the present work is to give, as a continuation of the writer's
study of Galois theory for general rings ([8], [9], [10]), a kind of Galois theory
for general, non-commutative and non-semisimple rings, which includes, at least in
its main features, the Kaloujnine-Jacobson Galois theory of non-normal fields
([3]; cf. [4], [5]). To deal with the non-commutativity we bring to the fore
certain double-moduli rather than self-composites, while the non-semisimplicity is
manipulated by the method and idea used in the writer's above mentioned study on
(normal) Galois theory and commuter systems of nonsemisimple rings. (For the
normal Galois theory of rings cf. [1], [2], [6], [7], [11], besides the above.)
Some of our arguments may even serve to make some simplification in Jacobson's
treatment of ordinary fields.
Direct Theorems on Methods of Summability II
Authors: Lorentz G. G.
Published: December 2010

1.1. This paper is a continuation of the papers of the author [14], [15]. We
begin by recapitulating the main definitions. If {n,} is an increasing sequence of
positive integers, the value of the characteristic or the counting
function ω(n) of {nv} is, for any
, the number of n
satisfying the inequality . Suppose that A is
a linear method of summation corresponding to the transformation
On Euclid's Algorithm in Cyclic Fields
Authors: Heilbronn H.
Published: December 2010

In two papers I have proved that there are only a finite number of quadratic
fields [6] and of cyclic cubic fields [7] in which Euclid's algorithm (E.A.)
holds. Davenport has shown by a different method that there are only a finite
number of quadratic fields [1, 2], of non-totally real cubic fields [3, 4] and of
totally complex quartic fields in which E.A. holds.
Two Vertex-Regular Polyhedra
Authors: Apsimon Hugh
Published: December 2010

The definition of a regular polyhedron may be enunciated as follows:

(α) A polyhedron is said to be regular if its faces are equal regular
polygons, and its vertex figures are equal regular polygons

In a recent note1 I gave three examples of uniform non-regular polyhedra,
which I called facially-regular, using the
definition:

(β) A polyhedron is said to be facially-regular if it is uniform and all its
faces are equal.
On Certain Intersection Properties of Convex Sets
Authors: Klee V. L.
Published: December 2010

A collection of n + 1 convex subsets of a Euclidean space E will be called an
n-set in E provided each n of the sets have a common interior point although the
intersection of all n + 1 interiors is empty. It is well-known that if
{C0,C1} is a 1-set, then
C0 and C1 can be separated by a
hyperplane.
On the Topological Theory of Functions
Authors: Jenkins James A.
Published: December 2010

The present paper constitutes a continuation of the ideas and methods of M.
Morse and M. Heins [1]. As in that work the subject treated is the theory of
deformation classes of meromorphic functions and interior transformations. There
the functions considered were defined over the open disc < 1 and had
only a finite number of zeros, poles and branch point antecedents. It is possible
to transfer the results obtained to the situation where the domain of definition
is any simply-connected domain of hyperbolic type or, alternatively, of parabolic
type.
A Note on Some Perfect Squared Squares
Authors: Willcocks T. H.
Published: December 2010

In a recent paper [5], general methods were described for the dissection of a
square into a finite number n of unequal non-overlapping squares. In this note,
examples of such perfect squares are given in which the sides and elements are
relatively small integers; in particular, a dissection of a square into 24
different elements, which is believed to be the squaring of least order known at
the present time.
Modular Representations of the Symmetric Group
Authors: Chung J. H.
Published: December 2010

The theory of modular representations of the symmetric group was studied
first by Nakayama (5, 6), and later by Thrall and Nesbitt (11) and Robinson (7, 8,
9). Nakayama built up his elaborate theory of hooks for the express purpose of
studying this problem, while Robinson's extensive work on the various phases of
the relationship between Young diagrams, skew diagrams and star diagrams on the
one hand, and representations of the symmetric group on the other, culminating in
a set of relations among the degrees of the representations, serves as a starting
point for this paper.
Some Theorems on Absolute Summability
Authors: Macphail M. S.
Published: December 2010

A summation method defined by the linear transformation

will be called an l-l
method if ∑|yr| < ∞ whenever
∑|xk| < ∞; if in addition we have
∑yr = ∑xk whenever
∑|xk| < ∞ we shall say the method is
absolutely regular. (It should be observed that we
are dealing with series-to-series methods, not sequence-to-sequence as
usual.)
Note on Normal Decimals
Authors: Davenport H. , Erdös P.
Published: December 2010

A real number, expressed as a decimal, is said to be normal (in the scale of 10) if every combination of digits occurs in the decimal with the proper frequency. If a1a2 … ak is any combination of k digits, and N(t) is the number of times this combination occurs among the first t digits, the condition is that

1
Some Theorems on Difference Sets
Authors: Mann Henry B.
Published: December 2010

A set a1 …, ak of different residues mod v is called a difference set (v, k, λ) (v>k > λ) if the congruence ai — aj ≡ d (mod v) has exactly λ solutions for d ≢ 0 (mod v). Singer [4] has demonstrated the existence of a difference set (v, k, 1) if k — 1 is a prime power, and difference sets for λ > 1 have been constructed by various authors; but necessary and sufficient conditions for the existence of a (v, k, λ) are not known. It has not been possible so far to find a difference set with λ = 1 if k — 1 is not a prime power and it has therefore been conjectured that no such difference set exists.
F-Equation Fourier Transforms
Authors: Duff G. F. D.
Published: December 2010

For solutions of the differential difference 'F-equation

1

there are representations as a generating series [5],

2

and as a contour integral [3],

3
The Index of an Extremal Arc
Authors: Karush William
Published: December 2010

We are concerned with extremal arcs for the problem of minimizing a function

over a class of parametric curves C in ay-space of the form

and satisfying end conditions of the type

The components ah are constants and the functions g, yis, and/are given, with the last function positively homogeneous of degree one.
Finite Projective Geometries
Authors: Berman Gerald
Published: December 2010

James Singer [12] has shown that there exists a collineation which is transitive on the (t - 1)-spaces, that is, (t - 1)-dimensional linear subspaces, of PG(t, pn). In this paper we shall generalize this result showing that there exist t - r collineations which together are transitive on the s-spaces of PG(t, pn). An explicit construction will be given for such a set of collineations with the aid of primitive elements of Galois fields. This leads to a calculus for the linear subspaces of finite projective geometries.
Groups with a Certain Condition on Conjugates
Authors: Haimo Franklin
Published: December 2010

In this paper, we shall show that if is a nilpotent [5] group and if M, a positive integer, is a uniform bound on the number of conjugates that any element of may have, then there exist “large” integers n for which x → xn is a central endomorphism of . If is not necessarily nilpotent, if the above condition on the conjugates is retained, and if we can find a member of the lower central series [1], every element of which lies in some member of the ascending central series, then we shall show that every non-unity element of the “high” derivatives has finite order.
On the Irreducible Representations
of the Symmetric Group
Authors: Osima Masaru
Published: December 2010

Let T be a Young diagram of n nodes:

(1)

ai being the length of its ith row. With respect to a prime p, we denote by T0
the p-core of T. If T0 consists of m nodes, then

(2) m=n-lp,

where l is the number of successive p-hooks [3] removable from T to yield its p-core T0. We have stated in [4] the following theorem :
On the Possible Forms of Differential Equation which Can be Factorized by the Schrödinger-Infeld Method
Authors: Stevenson A. F. , Bassali W. A.
Published: December 2010

The factorization method, initiated by Schrödinger [4] and modified and developed by Infeld [2], Duff [1], and Infeld and Hull [3], furnishes an elegant method of solving eigenvalue problems associated with certain ordinary differential equations of the second order. Not only the eigenvalues and eigenfunctions can thus be obtained, but also certain matrix elements associated with the eigenfunctions. Even if the method cannot be applied directly to eigenvalue problems, the factorization of an equation may still be of interest, since recurrence formulae may thus be established, e.g. for Bessel functions [3]. The connection of the method with Truesdell's [5] method of the “F -equation” has been discussed by Duff [1].
A Coefficient Problem for Functions Regular in an Annulus
Authors: Robertson M. S.
Published: December 2010

1. Introduction A solution will be given in this paper for the following problem.

Let

(1.1)
Partitioning an Arithmetic Interval
Authors: Gustin William
Published: December 2010

The purpose of this paper is to characterize all ways in which an initial
interval of natural numbers can be partitioned into a unique arithmetic sum
of certain of its subsets.
Generating Functions for Bessel and Related
Polynomials
Authors: Rainville E. D.
Published: December 2010

Krall and Frink [4] aroused interest in what they term Bessel polynomials.
They studied in some detail what may, in hypergeometric form, be written
as
Systems of Partial Differential Equations Which Generalize the
Heat Equation
Authors: Hirschman I. I.
Published: December 2010

The distribution of heat in an infinite rod is closely bound up with the
theory of the Weierstrass transform. This connection is exhibited most
clearly in the theory of Widder [3]. Consider the heat equation
Sur Les Applications Lineaires Faiblement Compactes D'Espaces Du
Type C(K)
Authors: Grothendieck A.
Published: December 2010

Soit K un espace compact, C(K) l'espace
des fonctions complexes continues sur K, muni de la norme
uniforme, son dual
(espace des mesures de Radon sur K). Cet article est
consacré essentiellement à l'étude des applications linéaires faiblement
compactes de C(K) dans des espaces
localement convexes F quelconques i.e. les applications linéaires qui
transforment la boule unité de C(K) en une
partie faiblement relativement compacte de F.
A Criterion for Irrationality
Authors: Churchhouse R. F.
Published: December 2010

The question of the irrationality of functions defined by power series, for
rational values of the variable, has attracted much attention for over a
hundred years. Legendre, in generalizing Lambert's proof of the
irrationality of tan x for rational x, proved an important theorem on the
irrationality of continued fractions with integer elements. Here we use
Legendre's theorem (Lemma 3) to prove that at least one of a certain pair of
power series is irrational whenever the variable is rational and satisfies a
further condition. We prove the following:
Stable Lattices
Authors: Cohn Harvey
Published: December 2010

The consideration of relative extrema to correspond to the absolute extremum
which is the critical lattice has been going on for some time. As far back
as 1873, Korkine and Zolotareff [6] worked with the ellipsoid in hyperspace
(i.e., with quadratic forms), and later Minkowski [8] worked with a general
convex body in two or three dimensions. They showed how to find critical
lattices by selection from among a finite number of relative extrema. They
were aided by the long-recognized premise that only a finite number of
lattice points can enter into consideration [1] when one deals with lattices
“admissible to convex bodies.”
Some Remarks on the Characters of the Symmetric
Group
Authors: Osima Masaru
Published: December 2010

In [2], we derived some character relations of the symmetric group
Sn. These relations were also obtained in [1] independently.
In the present paper, we shall study the properties of these character
relations in some detail. In the last section, using a result obtained in
[3], we shall further determine the number of modular irreducible
representations in a p-block of Sn.
Concerning Difference Sets
Authors: Ostrom T. G.
Published: December 2010

A set of integers {a0, a1, … , an} is said
to be a difference set modulo N if the set of differences {ai —
aj (i,j = 0, 1, … , n) contains each non-zero residue mod N
exactly once. It follows that N and n are connected by the relation N =
n2 + n + 1. If {a0, a1 … an}
is a difference set mod N, so is the set {a0 + s, a1 +
s, … , an + s} (s = 0, 1, … , N). These difference sets form a
finite projective plane of N points, with each difference set constituting a
line in the plane.
Note on the Linear Symmetric Congruence in n
Variables
Authors: Mordell L. J.
Published: December 2010

Let/ = /(x1, x2, … , xn) be a polynomial in
n > 2 variables with integer coefficients, and let p be a large prime.
Very little appears to be known about estimates for the number N of
solutions of the congruence
Focal Series in Finite Groups
Authors: Higman D. G.
Published: December 2010

If there is given a subgroup 5 of a (finite) group G, we may ask what
information is to be obtained about the structure of G from a knowledge of
the location of S in G. Thus, for example, famed theorems of Frobenius and
Burnside give criteria for the existence of a normal subgroup N of G such
that G = NS and 1 = N ⋂ S, and hence in particular for the non-simplicity of
G. To aid in locating S in G, and to facilitate exploitation of the
transfer, we single out a descending chain of normal subgroups of S. Namely,
we introduce the focal series of S in G by means of the
recursive formulae
Representation of Linear Functionals on Köthe
Spaces
Authors: Lorentz G. G. , Wertheim D. G.
Published: December 2010

Kothe spaces, in the terminology of Diendonné [2], are certain spaces X of
real valued integrable functions. In this paper we consider the problem of
representation of continuous linear functional on vector valued Kothe
spaces. The elements of a Kôthe space X(B) are functions with values in a Banach space B (see §2).
Unitary Transformations
Authors: Mitchell B. E.
Published: December 2010

We consider the problem of finding a unique canonical form for complex matrices under unitary transformation, the analogue of the Jordan form (1, p. 305, §3), and of determining the transforming unitary matrix (1, p. 298, 1. 2). The term “canonical form” appears in the literature with different meanings. It might mean merely a general pattern as a triangular form (the Jacobi canonical form (8, p. 64)). Again it might mean a certain matrix which can be obtained from a given matrix only by following a specific set of instructions (1). More generally, and this is the sense in which we take it, it might mean a form that can actually be described, which is independent of the method used to obtain it, and with the property that any two matrices in this form which are unitarily equivalent are identical.
Maps of Certain Algebraic Curves Invariant under Cyclic Involutions of Periods Three, Five, and Seven
Authors: Hutcherson W. R. , Gormsen S. T.
Published: December 2010

In earlier papers (4; 5; 6), certain space curves, invariant under cyclic involutions of periods three, five, and seven, have been mapped. Lucien Godeaux (2; 3) in 1916 mapped plane cubic curves, invariant under an involution of period three, onto a cubic surface in ordinary three-space. Mlle. J. Dessart (1) in 1931 mapped plane quintic curves, invariant under an involution of order five, onto a fifth order surface in a space of four dimensions.
Sur Certains Sous-Espaces Vectoriels De Lp
Authors: Grothendieck A.
Published: December 2010

Le théoréme qui suit résoud une question qui m'avait été posée indépendamment par M. H. Mirkil et Professeur E. Farah, dans le cas particulier de p = 2 :

Théorème 1. Soit M un espace localement compact muni d'une mesure bornée μ, et soit 1 ≤ p < + ∞. Soit H un sous-espace vectoriel de L∞(μ), fermé dans LP(μ). Alors H est de dimension finie.
The Spectral Matrix and Green's Function for Singular Self-Adjoint Boundary Value Problems
Authors: Coddington E. A.
Published: December 2010

Let L denote the formal ordinary differential operator

,

where we assume the pk are complex-valued functions with n-k continuous derivatives
on an open real interval a < x < b (a = — ∞, b = + ∞, or both may occur), p0(x) ≠ 0 on a < x < b, and L coincides with its Lagrange adjoint L+ given by

.
An Elementary Proof of a Theorem About the Representation of Primes by Quadratic Forms
Authors: Briggs W. E.
Published: December 2010

The theorem that every properly primitive binary quadratic form is capable of representing infinitely many prime numbers was first proved completely by H. Weber (5). The purpose of this paper is to give an elementary proof of the case where the form is ax2 + 2bxy + cy2, with a > 0, (a, 2b, c) = 1, and D = b2 — ac not a square. The cases where the form is ax2 + bxy + cy2 with b odd, and the case where the form is ax2+ 2bxy + cy2 with D a square, can be settled very simply once the first case is taken care of, and this is done in a page and a half in the Weber paper.
The Relaxation Method for Linear Inequalities
Authors: Agmon Shmuel
Published: December 2010

In various numerical problems one is confronted with the task of solving a system of linear inequalities:

(1.1) (i = 1, … ,m)

assuming, of course, that the above system is consistent. Sometimes one has, in addition, to minimize a given linear form l(x). Thus, in linear programming one obtains a problem of the latter type.
On Some Recent Developments in the Theory of Series
Authors: Macphail M. S.
Published: December 2010

In a number of recent papers, especially by Wilansky (4; 6), Zeller (8), and Peyerimhoff (3), the sequence-to-sequence transformation

A : (n = 0, 1, …)

has been studied under certain conditions, designated by FAK, PMI, etc. (see §3). The purpose of this note is to point out some relations among these conditions, and to show that some theorems previously obtained hold under weaker assumptions.
On Discriminants of Binary Quadratic Forms with a Single Class in Each Genus
Authors: Chowla S. , Briggs W. E.
Published: December 2010

Consider the classes of positive, primitive binary quadratic forms ax2 + bxy + cy2 of discriminant — Δ = d = b2 − 4ac < 0. Dickson (2, p. 89) lists 101 values of A such that — Δ is a discriminant having a single class in each genus. The largest value given is 7392, and Swift (7) has shown that there are no more up to 107.
On an Exceptional Phenomenon in Certain Quadratic Extensions
Authors: Mann H. B.
Published: December 2010

Let Ω be a cyclic extension of degree l over the field Σ. Correcting an error which for some time had been haunting the literature, Hasse (1, p. 272) noted that for l = 2, the field Ω may contain a unit ξ such that

.
On Lattice Embeddings for Partially Ordered Sets
Authors: Botts Truman
Published: December 2010

Let P be a set partially ordered by a (reflexive, antisymmetric, and transitive) binary relation ≺. Let be the family of all subsets K of P having the property that x ∈ P and y ∈ K and y ≺ x imply x ∈ K.
On Laves' Graph Of Girth Ten
Authors: Coxeter H. S. M.
Published: December 2010

1. Introduction. This note shows how a certain infinite graph of degree three, discovered by Laves in connection with crystal structure, can be inscribed (in sixteen ways, all alike) in an infinite regular skew polyhedron which has square faces, six at each vertex. One-eighth of the vertices of the polyhedron are vertices of the graph, and the three edges of the graph that meet at such a vertex are diagonals of alternate squares. Thus either diagonal of any face of the polyhedron can serve as an edge, and the whole graph can then be completed in a unique manner.
On The Homology Theory Of Abelian Groups
Authors: Eilenberg Samuel , Maclane Saunders
Published: December 2010

1. Introduction. In (1) we have introduced the notions of “construction” and “ generic acyclicity” in order to determine a homology theory for any class of multiplicative systems defined by identities. Among these classes the most interesting one is the class of associative and commutative systems II with a unit element (containing the class of abelian groups).
A Canonical Set For Matrices Over a Principal Ideal Ring Modulo m
Authors: Fuller L. E.
Published: December 2010

If m ∈ P where P is a p.i.r. (principal ideal ring), then P/ {m} is a commutative ring with unit element. The elements of this ring are designated by ā where a ∈ P. The set of square matrices of order n with elements in P/ {m} forms a ring with unit element. The units in this ring are the unimodular matrices, i.e., the matrices whose determinants are units of P/ {m}.
The Wedderburn Theorem
Authors: Goheen Harry
Published: December 2010

Wedderburn, in 1905, proved that there are no finite skew-fields (5). Wedderburn's result has also been proved by Dickson, Artin, Witt, and Zassenhaus (2; 1; 6; 7); however, it seems to the author that the proofs so far given introduce concepts not obviously related to the theorem. It is the purpose of this note to use a result of Cartan, which was later proved in greater generality by Hua (4), to give a simpler and more direct version of the proof of Zassenhaus.
On Solutions of xd = 1 In Symmetric Groups
Authors: Moser Leo
Published: December 2010

1. Introduction. Several recent papers have dealt with the number of solutions of xd = 1 in Sn, the symmetric group of degree n. Let us denote this number by An,d and let An,2 = Tn.
On Algebraic Surfaces Termwise Invariant Under Cyclic Collineations
Authors: Morelock J. C. , Perry N. C.
Published: December 2010

In algebraic geometry it is of interest to examine polynomial surfaces F which transform into themselves under the collineation T defined by:

where Ep = 1, and p is a prime (2). One of the most obvious ways to ensure
invariance of a surface is for each term X1ax2bX3cX4d of F to go into itself. We present initially, therefore, a theorem which will be useful in the study of such termwise invariance for polynomials of composite degree.
Conformal Maps With Least Distortion
Authors: Helfenstein H. G.
Published: December 2010

1. Introduction. Our problem is related to the construction of geographical maps as follows. The reason for using conformai geographical maps is that the scale (viz., the ratio of two corresponding line-elements) does not depend on the direction of these line-elements. In an ideal map the scale, being responsible for the preservation of shape, would also be independent of the points where the line-elements begin.
Isomorphisms Of Factors Of Infinite Type
Authors: Kadison R. V.
Published: December 2010

1. Introduction. One of the striking results of the work done by Murray and von Neumann (9) in the analysis of rings of operators on a Hilbert space is the reduction of the unitary equivalence problem for certain types of factors to the problem of algebraic equivalence. Roughly speaking, they associate with each concrete representation of a factor a number (which measures the relative size of the factor and its commutant)—the so-called “coupling constant.”
Two Remarks On The Commutativity Of Rings
Authors: Herstein I. N.
Published: December 2010

In (1) and (2) we proved that under certain conditions a given ring R must be commutative. The conditions used there were “global” in the sense that they were imposed at once on the relation of a given element to all the other elements of the ring R.
Weighted Quadratic Norms and Legendre Polynomials
Authors: Hirschman I. I.
Published: December 2010

1. Introduction. Let , n = 0, 1, … , be the normalized Legendre polynomials. If and if

then we write

.
Metamathematical Considerations On The Relative Irreducibility Of Polynomials
Authors: Gilmore P. C. , Robinson A.
Published: December 2010

1. Introduction. In this paper, infinite fields K will be discussed which
satisfy the following condition :

CONDITION C: for any polynomial p(t, x) in x, coefficients in K(t), t transcendental with respect to K, which has no zeros in K (t), there is a t* in K for which p(t*, x) has no zeros in K.
Note On a Matrix Theorem Of A. Brauer and its Extension
Authors: Goddard L. S.
Published: December 2010

1. Introduction. In one of his papers on limits for the characteristic roots of a Matrix, Brauer (1) has stated a theorem, which connects the roots of a given square matrix A, with those of a matrix A* derived from A by a certain process. The proof of this theorem involves a continuity argument and in a recent paper on the construction of stochastic matrices Hazel Perfect (5) has given a proof which avoids considerations of continuity.
Certain Diophantine Equations Linear In One Unknown
Authors: Mills W. H.
Published: December 2010

1. Introduction. A. Brauer and R. Brauer (2) and Barnes (1) (following a method of Mordell (6)) have solved the Diophantine equation x2+y2+c = xyz subject to the condition (x, y) = 1. Independently, but using the same methods, I treated (4) the equation

x2+y2+ax+ay+l = xyz,

and subsequently (5) gave a method of obtaining all integral solutions of

x2±y2+ax+by+c = xyz,

thereby generalizing (2), (1), and (4).
Differentiable Points Of Arcs In Conformal 3-Space
Authors: Lane N. D. , Sherk F. A.
Published: December 2010

Introduction. This paper is a generalization of the classification of the differentiable points in the conformai plane given in (1). The main tools are the intersection and support properties of all the spheres through a differentiable point of an arc in conformal 3-space.
Algebraic and Diagonable Rings
Authors: Drazin M. P.
Published: December 2010

1. Introduction. In a well-known paper (7) Jacobson has shown how his structure theory for arbitrary rings can be applied to give more precise information about the so-called “algebraic” algebras. This specialization of his general theory is, however, perhaps not completely satisfying in that it deals only with algebras, i.e. rings admitting a field of operators, whereas neither the general structure theory nor the definition of the property of being “algebraic”
seems to depend in any essential way on the precise nature of the operators.
A Generalized Averaging Operator
Authors: Sumner D. B.
Published: December 2010

1. Introduction. The averaging operator has an extensive literature, the most detailed account being that of Nörlund

(4). In discussing solutions of the functional relation

1.1

he defines a “principal solution” (4, p. 41) by means of a summability process, and later, working in terms of complex numbers, he obtains (4, p. 70) a principal solution of (1.1) by means of a contour integral. He distinguishes his principal solution from other solutions, by showing that it is continuous at h = 0.
On The Extension Of Measure By The Method Of Borel
Authors: LeBlanc L. , Fox G. E.
Published: December 2010

Introduction. This paper concerns the problem of extending a given measure defined on a Boolean ring to a measure on the generated σ-ring. Two general methods are familiar to the literature, that of Lebesgue (outer measure) and a method proposed by Borel using transfinite induction (4, 49-134; 2, 228-238).
Non-Desarguesian Projective Plane Geometries Which Satisfy The Harmonic Point Axiom
Authors: Mendelsohn N. S.
Published: December 2010

1. Introduction and summary. In her papers (12) and (13) R. Moufang discusses projective plane geometries which satisfy the axiom of the uniqueness of the fourth harmonic point. Her main result is that in such geometries non-homogeneous co-ordinates may be assigned to the points of the plane (except for the “line at infinity”) in such a way that straight lines have equations of the forms aαx + y + β = 0, or x + γ − 0.
A Note on the Mathieu Groups
Authors: Paige Lowell J.
Published: December 2010

The principal result of this paper is the representation of the Mathieu
group M23 as a group of 11 × 11 matrices over the Galois Field GF(2).
This is a new representation of M23 and in §5 an indication of how the techniques of this result
might be extended to the Mathieu group M11 is given.