bluuebunny/crossref_metadata_2025 huggingface dataset:
Fog Collection by Mimicking Nature
Authors: Ahmad Zaki , Ahmad Intesar , Patel Faheemuddin
Published: December 2010

Research on fog harvesting for drinking water is uncommon because it is not a continuous climatic phenomenon and concerns only arid and semi-arid regions abundant with fog. This paper proposes a new biomimetic-inspired method of harvesting fog by mimicking the skin of the Namib desert beetle. Stainless steel mesh panels are subjected to ultra shortening and annealing to create a hierarchical nano/micro hybrid surface, and an emulsion of PTFE, polyvinyl acetate and sodium benzene sulfonate is sprayed over the steel mesh. This produces hydrophilic nano/micro mounts and hydrophobic troughs. This method, although initially costly, offers a sustainable fog collecting system which can be adopted for arid and semi-arid regions of Pakistan and other similar regions.
Prospects and Pits on the Path of Biomimetics: The Case of Tooth Enamel
Authors: Uskoković Vuk
Published: December 2010

This review presents a discourse on challenges in understanding and imitating the process of amelogenesis in vitro on the molecular scale. In light of the analysis of imitation of the growth of dental enamel, it also impends on the prospects and potential drawbacks of the biomimetic approach in general. As the formation of enamel proceeds with the protein matrix guiding the crystal growth, while at the same time conducting its own degradation and removal, it is argued that three aspects of amelogenesis need to be induced in parallel: a) crystal growth; b) protein assembly; c) proteolytic degradation. A particular emphasis is therefore placed on ensuring conditions for proteolysis-coupled protein-guided crystallization to occur. Discussed are structural and functional properties of the protein species involved in amelogenesis, mainly amelogenin and enamelysin, the main protein and the protease of the developing enamel matrix, respectively. A model of enamel growth based on controlled delivery of constituent ions or crystalline or amorphous building blocks by means of amelogenin is proposed. The importance of high viscosity of the enamel matrix and a more intricate role that water may play in such a gelatinous medium are also touched upon. The tendency of amelogenin to self-assemble into fibrous and rod-shaped morphologies is considered as potentially important in explaining the formation of elongated apatite crystals. The idea that a pre-assembling protein matrix serves as a template for the uniaxial growth of apatite crystals in enamel is finally challenged with the one based on co-assembly of the protein and the mineral phases.
Study on Influence of Implant Thickness and Fixation Position on Implant Stability Using Finite Element Analysis
Authors: Devika D. , Arumaikkannu G.
Published: December 2010

Patient anatomy specific orthopaedic implant design, fabrication and identification of the most suitable position to fix implants onto bone fractures are challenging problems for surgeons to overcome of the existing shortcomings of commercially available implants. In this work, a 3D finite element model of the left tibial bone of an adult male is developed from Computed Tomography scan images. Proximal tibial fracture type B1 (as per Association for the Study of Internal Fixation) is simulated on the bone model. A geometry specific implant is obtained in order to promote better bone ingrowths and uniform stress distribution, by extracting the surface features of the bone. Finite Element Analysis is performed to evaluate and compare the mechanical properties such as stress, strain and displacement of the bone and implant of four various thicknesses which are fixed at two different positions. The design objectives such as low stress and displacement combination is obtained through the antero-lateral position with 1.8 mm implant thickness. Various material properties are assigned to cortical, cancellous, trabecular regions of the bone and to implants made up of titanium alloy. The results obtained from the Finite Element Analysis are used to evaluate the stability and suitability of the implant for that particular fracture.
Development of a Bioabsorbable Glass-Reinforced-Glass Intra-Osseous Scaffold for Fracture Healing
Authors: Boughton Philip , Chen Y. , Thompson C. , Roger G. , Hyvarinen Jari , Ruys Andrew John
Published: December 2010

Intramedullary (IM) nails are routinely used to stabilize long bone fractures. They can however lead to stress shielding, pain, migration, obstruct hematopoietic tissue, become a loci for infection, and require subsequent surgical retrieval. Novel intra-osseous scaffold (IOS™) prototypes for fracture healing have been developed to function as a regenerative scaffold to enhance callous formation under mechanically stabilized conditions then resorb. Prototype fixation pins and rod systems were formed from glass-reinforced-glass. Flexion, torsion and shear tests were performed to evaluate the composite pins and rods. A modular rod design was successfully deployed and dilated while in a deformable state. When fitted and gripping the intramedullary canal then set in a rigid state. An obliquely sectioned ovine femur was used as a long bone fracture model for deployment and mechanical verification. Flexural support provided by the intramedullary scaffold was superior to multiple k-wire fixation, while the k-wire approach was more stabilizing under torsional loads. Glass reinforced glass samples were mechanically tested after soaking for up to 4 weeks in saline. Strength and modulus of the composite was reduced to approximately 25% of initial values after 2 weeks.
Carbon Nanomaterials, Relevance to Solving the Hydrogen Storage Problem
Authors: Nechaev Yuriy S.
Published: December 2010

Empiric evaluations of fundamental characteristics of interactions of gaseous hydrogen with different kinds of graphite and novel carbonaceous nanomaterials and revealing the micromechanisms have been carried out. The approaches used were those of the thermodynamics of reversible and irreversible processes for analysis of the adsorption, absorption, diffusion, TPD and other experimental data and comparing the analytical results with first-principle calculations. Such analysis of a number of the known experimental and theoretical data has shown a real possibility of the multilayer specific adsorption (intercalation) of hydrogen between graphene layers in novel carbonaceous nanomaterials, relevance for solving the bottle-neck problem of the hydrogen on-board storage in fuel-cell-powered vehicles, and other technical applications.
Small Scale Reforming Separation Systems with Nanomembrane Reactors for Direct Fuel Cell Applications
Authors: Vasileiadis Savvas , Ziaka Zoe
Published: December 2010

Our recent communication focuses on small scale and nanoscale type engineering applications of alumina inorganic membrane reactors and reactor-permeator systems for the conversion of renewable and non-renewable hydrocarbons and methane rich streams into hydrogen rich gas for direct inner application and operation of fuel cell systems. This study elaborates on new nanomembrane reactors for the steam-methane/hydrocarbon reforming and water gas shift reactions, including work in the synthesis, manufacturing, modeling and operation of such microreaction systems. The projected small scale reactors, separators and overall reaction systems are of current significance in the area of multifunctional microreactor and nanoreactor design and operation in connection with the operation of fuel cells for transportation, stationary, and portable power generation applications. An added advantage of such systems is the reactive and separative operations of the fuel cell membrane-processor which are combined to convert the hydrocarbon with steam to valuable fuel gas for continuous fuel cell operation. Moreover, the nanomembrane systems under development have the unique characteristics to perform multiple operations per unit volume, such as to utilize beneficial equilibrium shift principles in reactant conversion and product yield through the removal of permselective species (i.e., hydrogen) via the inorganic membrane out of the conversion/reaction zone. In this way, improved hydrogen and product yields can be achieved which exceed the equilibrium calculated yields. Simultaneously, the reaction products, such as synthesis gas (i.e., H2, CO and CO2) at the reactor exit can be used as fuel in mostly solid oxide and molten carbonate fuel cells. The role of the alumina nanomembrane is also in the main conversion and upgrading sections of these feedstocks in order to overcome existing heat and mass transfer limitations and increase the overall efficiency of the microreactor-fuel cell system.
Carrier-Phonon Scattering Rate and Charge Transport in Spherical and TMV Nanometric Viruses
Authors: Gupta Sanjeev K. , Jha Prafulla K.
Published: December 2010

The present paper presents the carrier-acoustic phonon scattering rate and charge transport in spherical and TMV viruses. We demonstrate theoretically that the absorption rate changes according to the phonon energy while emission of phonon is limited by the both electron and hole energy. The obtained conductivity for spherical and TMV viruses suggest that the TMV virus is more conducting and therefore may be a good candidate for the connector or wire to be used in the nano- and molecular- electronics . The value of resistance obtained for TMV virus is lower than the resistance of DNA.
Novel, Simple, Versatile and General Synthesis of Nanoparticles Made from Proteins, Nucleic Acids and other Materials
Authors: Kumar Challa V. , Deshapriya Inoka K. , Duff Michael R. , Blakeley Brett , Lee Haye Denise
Published: December 2010

A new, simple, and versatile method was developed to prepare protein nanoparticles, for the first time, and the approach was extended to prepare organic, inorganic, and biological nanomaterials. For example, nanoparticles of met-hemoglobin and glucose oxidase are readily prepared by contacting a fine spray of aqueous solutions of the proteins to an organic solvent such as methanol or acetonitrile. The protein nanoparticles suspended in organic solvents retained their secondary structure and biological activities to a significant extent. Using this approach, we also successfully prepared nanoparticles of transition metal complexes, organic molecules, nucleic acids, inorganic polymers, and organic polymers. Particle size depended on reagent concentrations, pH and the solvent used, and particle sizes have been controlled from 20 to 200 nm by adjusting these parameters. In each case, particle sizes and size distributions were determined by dynamic light scattering and the data have been confirmed by electron microscopy. Addition of appropriate electrolytes to the nanoparticle supensions stabilized them against aggregation or crystallization, and particles were stable over months of storage at 4°C. Nanoparticles of met-hemoglobin, glucose oxidase, and calf thymus DNA indicated retention of their native-like structures, as evidenced from their respective circular dichroism spectra. Enzyme nanoparticles retained their catalytic activities to a significant extent. For example, peroxidase-like activity of met-hemoglobin nanoparticles suspended in methanol was 0.3 M-1 s-1, which is comparable to the activity of met-hmoglobin in aqueous buffer (1.0 M-1 s-1) even though the former has been measured in methanol. This activity is far greater than the activity of free heme in methanol. Thus, the nanobiocatalysts retained substantial activity in organic solvents. Nanoparticles of anthracene indicated extensive excitonic coupling due to inter-chromophore interactions. The current method of nanoparticle synthesis is rapid, simple, versatile, reproducible and resulted in the formation of nanoparticles from a variety of materials, many of them for the first time.
Inactivation of Salmonella typhi Using Fe3+ Doped TiO2/3SnO2 Photocatalytic Powders and Films
Authors: Sikong Lek , Kongreong Budsabakorn , Kantachote Duangporn , Sutthisripok Weerawan
Published: December 2010

The aim of the present study is to synthesize Fe3+-doped TiO2/3SnO2 powder and evaluate its antibacterial performance coated on polyvinylchloride films for fresh food packaging. Fe3+-doped TiO2/3SnO2 nanoparticles were prepared as a photocatalyst through the sol-gel method with concentrations of 0.3-1.2 mol% and a calcination temperature of 400°C. It was found that calcination temperatures strongly affect the phases and phase transformation of TiO2. According to XRD analysis, the anatase crystalline was formed at the calcination temperature of 400°C. In the present work, the photocatalytic performance was determined through methylene blue degradation. The antibacterial activity against Salmonella typhi was investigated with a vitro test, from which the mixture of conidial suspension and Fe3+-doped TiO2/3SnO2 powder was added to Nutrient agar (NA) plates under UV and visible light irradiation, respectively. It was found that Fe3+-doped TiO2/3SnO2 nanoparticles enhance photocatalytic activity and bacterial inactivation efficiency. In addition, Fe3+-doped TiO2/3SnO2 thin films can destroy the cell walls of bacteria within 240 min. Furthermore, the disinfection efficiency of TiO2/3SnO2/0.5 Fe3+ is greater under UV irradiation than it is under visible light.
Boundary Element Analysis of Three-Dimensional Interface Cracks in Transversely Isotropic Bimaterials Using the Energy Domain Integral
Authors: Larrosa N.O. , Ortiz J.E. , Cisilino A.P.
Published: December 2010

It is presented in this paper a three-dimensional Boundary Element Method (BEM) implementation of the Energy Domain Integral for the fracture mechanical analysis of three-dimensional interface cracks in transversely isotropic bimaterials. The J-integral is evaluated using a domain representation naturally compatible with the BEM, in which the stresses, strains and derivatives of displacements at internal points are evaluated using their appropriate boundary integral equations. Several examples are solved and the results compared with those available in the literature to demonstrate the efficiency and accuracy of the implementation to solve straight and curved crack-front problems.
Sequential Binding of αvβ3 and ICAM-1 Determines Fibrin-Mediated Melanoma Capture and Stable Adhesion to CD11b/CD18 on Neutrophils
Authors: Zhang Pu , Ozdemir Tugba , Chung Chin-Ying , Robertson Gavin P. , Dong Cheng
Published: December 2010

Fibrin (Fn) deposition defines several type 1 immune responses, including delayed-type hypersensitivity and autoimmunity in which polymorphonuclear leukocytes (PMNs) are involved. Fn monomer and fibrinogen are multivalent ligands for a variety of cell receptors during cell adhesion. These cell receptors provide critical linkage among thrombosis, inflammation, and cancer metastasis under venous flow conditions. However, the mechanisms of Fn-mediated interactions among immune cells and circulating tumor cells remain elusive. By using a cone-plate viscometer shear assay and dual-color flow cytometry, we demonstrated that soluble fibrinogen and Fn had different abilities to enhance heterotypic aggregation between PMNs and Lu1205 melanoma cells in a shear flow, regulated by thrombin levels. In addition, the involvement of integrin αvβ3, ICAM-1, and CD11b/CD18 (Mac-1) in fibrin(ogen)-mediated melanoma–PMN aggregations was explored. Kinetic studies provided evidence that ICAM-1 mediated initial capture of melanoma cells by PMNs, whereas αvβ3 played a role in sustained adhesion of the two cell types at a shear rate of 62.5 s−1. Quantitative analysis of the melanoma–PMN interactions conducted by a parallel-plate flow chamber assay further revealed that at a shear rate of 20 s−1, αvβ3 had enough contact time to form bonds with Mac-1 via Fn, which could not otherwise occur at a shear rate higher than 62.5 s−1. Our studies have captured a novel finding that leukocytes could be recruited to tumor cells via thrombin-mediated Fn formation within a tumor microenvironment, and αvβ3 and ICAM-1 may participate in multistep fibrin(ogen)-mediated melanoma cell adhesion within the circulation.
Persistent Survival of Prevalent Clonotypes within an Immunodominant HIV Gag-Specific CD8+ T Cell Response
Authors: van Bockel David J. , Price David A. , Munier Mee Ling , Venturi Vanessa , Asher Tedi E. , Ladell Kristin , Greenaway Hui Yee , Zaunders John , Douek Daniel C. , Cooper David A. , Davenport Miles P. , Kelleher Anthony D.
Published: December 2010

CD8+ T cells play a significant role in the control of HIV replication, yet the associated qualitative and quantitative factors that determine the outcome of infection remain obscure. In this study, we examined Ag-specific CD8+ TCR repertoires longitudinally in a cohort of HLA-B*2705+ long-term nonprogressors with chronic HIV-1 infection using a combination of molecular clonotype analysis and polychromatic flow cytometry. In each case, CD8+ T cell populations specific for the immunodominant p24 Gag epitope KRWIILGLNK (KK10; residues 263–272) and naturally occurring variants thereof, restricted by HLA-B*2705, were studied at multiple time points; in addition, comparative data were collected for CD8+ T cell populations specific for the CMV pp65 epitope NLVPMVATV (NV9; residues 495–503), restricted by HLA-A*0201. Dominant KK10-specific clonotypes persisted for several years and exhibited greater stability than their contemporaneous NV9-specific counterparts. Furthermore, these dominant KK10-specific clonotypes exhibited cross-reactivity with antigenic variants and expressed significantly higher levels of CD127 (IL-7Rα) and Bcl-2. Of note, we also found evidence that promiscuous TCR α-chain pairing associated with alterations in fine specificity for KK10 variants could contribute to TCR β-chain prevalence. Taken together, these data suggest that an antiapoptotic phenotype and the ability to cross-recognize variant epitopes contribute to clonotype longevity and selection within the peripheral memory T cell pool in the presence of persistent infection with a genetically unstable virus.
H2 Control of Natural T Regulatory Cell Frequency in the Lymph Node Correlates with Susceptibility to Day 3 Thymectomy-Induced Autoimmune Disease
Authors: del Rio Roxana , Sun Yuefang , Alard Pascale , Tung Kenneth S. K. , Teuscher Cory
Published: December 2010

Day 3 thymectomy (D3Tx) results in a loss of peripheral tolerance mediated by natural regulatory T cells (nTregs) and development of autoimmune ovarian dysgenesis (AOD) and autoimmune dacryoadenitis (ADA) in A/J and (C57BL/6J × A/J) F1 hybrids (B6A), but not in C57BL/6J (B6) mice. Previously, using quantitative trait locus (QTL) linkage analysis, we showed that D3Tx-AOD is controlled by five unlinked QTL (Aod1-Aod5) and H2. In this study, using D3Tx B6-ChrA/J/NaJ chromosome (Chr) substitution strains, we confirm that QTL on Chr16 (Aod1a/Aod1b), Chr3 (Aod2), Chr1 (Aod3), Chr2 (Aod4), Chr7 (Aod5), and Chr17 (H2) control D3Tx-AOD susceptibility. In addition, we also present data mapping QTL controlling D3Tx-ADA to Chr17 (Ada1/H2), Chr1 (Ada2), and Chr3 (Ada3). Importantly, B6-ChrXA/J mice were as resistant to D3Tx-AOD and D3Tx-ADA as B6 mice, thereby excluding Foxp3 as a susceptibility gene in these models. Moreover, we report quantitative differences in the frequency of nTregs in the lymph nodes (LNs), but not spleen or thymus, of AOD/ADA-resistant B6 and AOD/ADA-susceptible A/J, B6A, and B6-Chr17A/J mice. Similar results correlating with experimental allergic encephalomyelitis and orchitis susceptibility were seen with B10.S and SJL/J mice. Using H2-congenic mice, we show that the observed difference in frequency of LN nTregs is controlled by Ada1/H2. These data support the existence of an LN-specific, H2-controlled mechanism regulating the prevalence of nTregs in autoimmune disease susceptibility.
Elementary Algebraic Treatment of the Quantum Mechanical Symmetry Problem
Authors: Weyl Hermann
Published: December 2010

A function η(i1, …, if) of ƒ quantities i, varying over the finite range i = 1,2, …, n, is usually called an n-dimensional tensor of rank ƒ. Any permutation p: 1 → 1, … , ƒ → ƒ… changes this tensor into a tensor pη according to the equation pη(i1, ...,if) = η(i1', ...,if')Thus the permutation p appears as a linear operator p in the n-dimensional space Σ = Σn,ƒ of all n-dimensional tensors of rank ƒ, η is symmetric if pη = η for all permutations p, it is antisymmetric if pη δp.η where δp = + 1 for the even and — 1 for the odd permutations.
The Nonexistence of Certain Finite Projective Planes
Authors: Bruck R. H. , Ryser H. J.
Published: December 2010

A projective plane geometry π is a mathematical system composed of undefined elements called points and undefined sets of points (at least two in number) called lines, subject to the following three postulates:

(P1) Two distinct points are contained in a unique line.

(P2) Two distinct lines contain a unique common point.

(P3) Each line contains at least three points.
Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
Authors: Minakshisundaram S. , Pleijel Å.
Published: December 2010

Let V be a connected, compact, differentiable Riemannian manifold. If V is not closed we denote its boundary by S. In terms of local coordinates (xi), i = 1, 2, … Ν, the line-element dr is given by where gik (x1, x2, … xN) are the components of the metric tensor on V We denote by Δ the Beltrami-Laplace-Operator and we consider on V the differential equation (1) Δu + λu = 0.
On Surface Waves
Authors: Weinstein Alexander
Published: December 2010

The linearized theory of surface waves leads to several mixed boundary value problems which have been investigated by various methods. As the physical background of the theory has been repeatedly discussed, it will suffice to deal here mainly with the mathematical aspect of the question.
The Density of Redugible Integers
Authors: Chowla S. D. , Todd John
Published: December 2010

Introduction. The concept of a reducible integer was introduced recently [3] : if P(m) denotes the greatest prime factor of m then n is said to be reducible if P ( 1 + n2) < 2n. The reason for the term is that reducibility is a condition necessary and sufficient for the existence of a relation of the form where the ƒi are integers and the ni positive integers less than n. J. C. P. Miller pointed out to us the regularity of the distribution of the reducible integers (less than 600).
Un Thoérème De Transfert D'un Anneau Abstrait á L'Anneau Des Polynomes
Authors: Lesieur Léonce
Published: December 2010

Certains théorèmes démontrent pour l'anneau des polynomes A [x1, …, xn] une propriété supposée valable dans l'anneau A, par exemple le théorème de la base finie de Hilbert pour tout idéal d'un anneau commutatif qui possède un élément unité. (Voir P. Dubreil [2] p. 210, ou B. L. Van der Waerden [7] §80, ou le mémoire original de Hilbert [3], p. 473.) E. Lasker [5] a montré que tout idéal de l'lanneau K[x1, x2 … , xn] des polynomes à n variables à coefficients dans un corps K commutatif est l'intersection d'un nombre fini d'idéaux primaires.
Combinatorial Problems
Authors: Chowla S. , Ryser H. J.
Published: December 2010

Let it be required to arrange v elements into v sets such that every set contains exactly k distinct elements and such that every pair of sets has exactly elements in common . This combinatorial problem is studied in conjunction with several similar problems, and these problems are proved impossible for an infinitude of v and k. An incidence matrix is associated with each of the combinatorial problems, and the problems are then studied almost entirely in terms of their incidence matrices. The techniques used are similar to those developed by Bruck and Ryser for finite projective planes [3]. The results obtained are of significance in the study of Hadamard matrices [6;8], finite projective planes [9], symmetrical balanced incomplete block designs [2; 5], and difference sets [7].
Generalized Hamiltonian Dynamics
Authors: Dirac P. A. M.
Published: December 2010

1. Introduction. The equations of dynamics were put into a general form
by Lagrange, who expressed them in terms of a set of generalized coordinates
and velocities. An alternative general form was later given by Hamilton, in
terms of coordinates and momenta. Let us consider the relative merits of the
two forms.
Water Waves Over a Channel of Finite Depth With a Submerged Plane Barrier
Authors: Heins Albert E.
Published: December 2010

This is the third in a series of problems in the study of surface waves which have been disturbed by the presence of a plane barrier and to which a solution may be provided. We assume as in part I, that the fluid is incompressible and non-viscous, and that motion is irrotational.
Helly's Theorems on Convex Domains and Tchebycheff's Approximation Problem
Authors: Rademacher Hans , Schoenberg I. J.
Published: December 2010

Professor Dresden called to our attention the following theorem :

If S1, S2, … , Sm are m line segments parallel to the y-axis, all of equal lengths, whose projections on the x-axis are equally spaced, and if we assume that a straight line can be made to intersect every set of three among these segments, then there exists a straight line intersecting all the segments.
A Generalized Integral II
Authors: James R. D.
Published: December 2010

The definition and some of the properties of what may be called a Perron second integral (P2-integral) were given in a previous paper [4]. This integral starts with a function f(x) defined in an interval (a, c) and goes directly to a second primitive F(x) with the property that the generalized second derivative D2F is equal to f(x) for almost all x in (a, c). In the present paper the definition is changed slightly and further properties are deduced.
Three Facially-Regular Polyhedra
Authors: Apsimon Hugh
Published: December 2010

H. S. M. Coxeter has shown the existence of three infinite regular polyhedra, and has proved that there are no infinite regular polyhedra other than these. In his paper he gives the definition of regularity of a polyhedron :

A polyhedron is said to be regular if it possesses two particular symmetries: one which cyclically permutes the vertices ox any face c, and one which cyclically permutes the faces that meet at a vertex C, C being a vertex of c.
Iterates of Fractional Order
Authors: Isaacs Rufus
Published: December 2010

The body of this paper is a complete answer to the following question:

Let E be any space whatever. g(x) is a function mapping E into E. When does there exist a function f(x), of the same type, such that

(1)
A Generalization of a Theorem of Jacobi on Systems of Linear Differential Equations
Authors: Cramlet Clyde M.
Published: December 2010

Jacobi proved a curious theorem regarding the solutions of the system of
equations

for functions λ=(x1, … , xn) satisfying
Postulates For Distributive Lattices
Authors: Sholander Marlow
Published: December 2010

Many sets of postulates have been given for distributive lattices and for
Boolean algebra. For a description of some of the most interesting and for
references to others the reader is referred to Birkhoff's “Lattice Theory”[1]. In
this paper we give sets of postulates which have some intrinsic interest because
of their simplicity. In the first two sections binary operations are used to
describe a distributive lattice by 2 identities in 3 variables and a Boolean
algebra by 3 identities in 3 variables. In the third section a ternary operation
is used to describe distributive lattices with 0 and J by 2 identities in 5
variables.
The Immersibility of a Semigroup into a Group
Authors: Lambek J.
Published: December 2010

A semigroup is a set of elements which is closed under an associative
operation, usually called multiplication. When can a semigroup be embedded in a
group, i.e., under what condition is it isomorphic to a subset of a group? A
necessary condition for immersibility is clearly the so-called
cancellation law:
A Property of Farey Sequences, With Applications to qTH Power Residues
Authors: Porcelli Pasquale , Pall Gordon
Published: December 2010

The Farey sequence of order h — 1 consists of the reduced rational fractions
from 0 to 1 inclusive, with denominators less than h, and arranged in order of
magnitude. Thus, if h = 6, the sequence is

(1) 0/1,1/5, 1/4,1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1.
Certain Fourier Transforms of Distributions
Authors: Lukacs Eugene , Szasz Otto
Published: December 2010

Fourier transforms of distribution functions are frequently studied in the
theory of probability. In this connection they are called characteristic functions
of probability distributions. It is often of interest to decide whether a given
function φ(t) can be the characteristic function of a probability distribution,
that is, whether it admits the representation
The Mathieu Groups
Authors: Stanton R. G.
Published: December 2010

An enumeration of known simple groups has been given by Dickson [17]; to this
list, he made certain additions in later papers [15], [16]. However, with but five
exceptions, all known simple groups fall into infinite families; these five
unusual simple groups were discovered by Mathieu [21], [22] and, after occasioning
some discussion [20], [23], [27], were relegated to the position, which they still
hold, of freakish groups without known relatives. Further interest is attached to
these Mathieu groups in virtue of their providing the only known examples (other
than the trivial examples of the symmetric and alternating groups) of quadruply
and quintuply transitive permutation groups.
Distance Sets
Authors: Kelly L. M.
Published: December 2010

With each set of points S of a distance space there is associated a set of
non-negative real munbers D(S) called the distance set of 5. The number x is an
element of D(S) if and only if x is a distance between some pair of points of 5.
The number zero is always an element of any distance set and no two distinct
elements are equal.
The Representations of GL(3,q), GL(4,q), PGL(3,q), and PGL(4,q)
Authors: Steinberg Robert
Published: December 2010

This paper is a result of an investigation into general methods of
determining the irreducible characters of GL(n, q), the
group of all non-singular linear substitutions with marks in
GF(q), and of the related groups, SL(n,
q), PGL(n, q), PSL(n,
q), the corresponding group of determinant unity, projective
group, projective group of determinant unity, respectively.
A Generalization of the Pappus Configuration
Authors: Berman Gerald
Published: December 2010

A configuration is a system of m points and
n lines such that each point lies on
μ of the lines and each line contains
v of the points. It is usually denoted by the symbol
(mμ,nμ
) with mμ =
nv. Two configurations corresponding to the same symbol
are said to be equivalent if there exist 1-1 mappings of the points and lines of
one onto the points and lines of the other which preserve the incidence
relations.
A New Viewpoint in Differential Geometry
Authors: Bochner S.
Published: December 2010

The law of transformation for a general mixed tensor

(1)

is somewhat complicated at first sight, but algebraically it can be stated
succinctly in the following manner. If, without regard to the original position of
various indices, we denote the components of the tensor in some fixed simple
ordering by

(2)
Contributions to Noncommutative
Ideal Theory
Authors: Murdoch D. C.
Published: December 2010

The well-known results of Krull concerning the minimal prime divisors and the radical of an ideal in a commutative ring have been extended to the noncommutative case in a recent paper [5] by N. H. McCoy. In that paper systematic use was made of the concept of an m-system, a set M of elements of the ring such that if a ∈ M and b ∈ M then axb ∈ M for some element x of the ring.
Axioms for Elliptic Geometry
Authors: Gans David
Published: December 2010

Until recently the literature contained little on the axiomatic foundations of elliptic geometry that was non-analytical and independent of projective geometry. During the past decade this subject has come in for further study, notably by Busemann [2] and Blumenthal [1], who supplied such foundations. This paper presents another and, it is believed, simpler effort in the same general direction, proceeding by the familiar synthetic methods of elementary geometry and using only elementary topological notions and ideas concerning metric spaces. Specifically, elliptic 2-space is obtained on the basis of six axioms, most notable of which is one assuming the existence of translations. The writer wishes to express his deep appreciation to Herbert Busemann for his invaluable help.
An Extension of Meyer's Theorem on Indefinite Ternary Quadratic Forms
Authors: Jones Burton W.
Published: December 2010

Let f be a ternary quadratic form whose matrix F has integral elements with g.c.d. 1, that is, an improperly or properly primitive form according as all diagonal elements are even or not. Let d be the determinant of f (denoted by ) Ω, the g.c.d. of the 2-rowed minors of F. Then d = Ω2 Δ determines an integer Δ. Two forms f in the same genus have the same invariants Ω, Δ, d. The form whose matrix is adj F/Ω, is called the reciprocal form of f.
Iterated Transforms
Authors: Fox Charles
Published: December 2010

In his work on Laplace and Stieltjes transforms Widder
[6, ch. 8] has investigated relationships of the type

1

2

3
A Theory of Normal Chains
Authors: Ayoub Christine Williams
Published: December 2010

In this paper we deal with a group-theoretic configuration of the following type: G is an additive group (not necessarily abelian) for which an operator system M and a complete lattice ø of M admissible subgroups are defined; we call G and M-ø group. In §1 we make various definitions and note that analogues of some of the classical theorems of group theory hold.
Analytic Functions with an Irregular
Linearly Measurable Set of Singular Points
Authors: Glover I. E.
Published: December 2010

V. V. Golubev, in his study [6], has constructed, by using definite integrals, various examples of analytic functions having a perfect nowhere-dense set of singular points. These functions were shown to be single-valued with a bounded imaginary part. In attempting to extend his work to the problem of constructing analytic functions having perfect, nowhere-dense singular sets under quite general conditions, he posed the following question: Given an arbitrary, perfect, nowhere-dense point-set E of positive measure in the complex plane, is it possible to construct, by passing a Jordan curve through E and by using definite integrals, an example of a single-valued analytic function, which has E as its singular set, with its imaginary part bounded.
The Supremum of a Family of
Additive Functions
Authors: Halperin Israel
Published: December 2010

Any system S in which an addition is defined for some, but not necessarily all, pairs of elements can be imbedded in a natural way in a commutative semi-group G, although different elements in S need not always determine different elements in G (see §2). Theorem 2.1 gives necessary and sufficient conditions in order that a functional p(x) on S can be represented as the su prémuni of some family of additive functionals on S, and one such set of conditions is in terms of possible extensions of p(x) to G. This generalizes the case with 5 a Boolean ring treated by Lorentz [4], Lorentz imbeds the Boolean ring in a vector space and this could be done for the general S; but we prefer to imbed S in a commutative semi-group and to give a proof (see § 1) generalizing the classical Hahn-Banach theorem to the case of an arbitrary commutative semigroup.
On D. E. Littlewood's Algebra of S-Functions
Authors: Duncan D. G.
Published: December 2010

Several papers have been written on the “new” multiplication of S-functions since Littlewood [3, p. 206] first suggested the problem. M. Zia-ud-Din [13] calculated the case {m} ⊗ {n} for mn ≤ 12, making use of the tables of the characters of the symmetric group of degree mn. Later Thrall [10,pp. 378-382] developed explicit formulae for the cases {m} ⊗ {2},{m} ⊗ {3}, {2} ⊗ {m} (where m is any integer).
Multiple Quantization
Authors: Scheidegger A. E.
Published: December 2010

The efforts of most theoretical physicists of this century have been
directed towards that branch of the physical science which is commonly
called “Quantum Theory.” Physically, Quantum Theory was postulated because
of a vast amount of physical evidence which led to the postulates of states,
observables, superposition, and commutation relations. From these four
postulates, all quantum mechanics follows.
Corresponding Polyhedra in the Three Spaces of Constant
Curvature
Authors: Roeser Ernst
Published: December 2010

The five Platonic solids can be drawn in elliptic or hyperbolic space just
as well as in Euclidean space. Their numerical properties are, of course,
the same in all three. So are the various angles subtended at the centre.
But the face-angles and dihedral angles are greater in elliptic space,
smaller in hyperbolic. It is a special feature of the non-Euclidean spaces
that we cannot change the size of a solid without changing its shape.
On Two-Dimensional Bernstein Polynomials
Authors: Butzer P. L.
Published: December 2010

Let the function of two real variablesf(x, y) be given over the square
A Convolution Transform Admitting an Inversion Formula of
Integro-Differential Type
Authors: Sumner D. B.
Published: December 2010

Following Wiener's fundamental work on the Operational Calculus [9, pp.
557-584], Widder suggested [5, p. 219] that the inversion operator for the
convolution transform
Some Multiplicative Functionals
Authors: Bourgin D. G.
Published: December 2010

This note concerns itself primarily with the representation of continuous
multiplicative functionals on L2 types of rings or Banach algebras to the real or complex fields
where convolution is taken as the ring multiplication. In a recent
publication [1] such functionals were studied for the continuous function
ring C(S) over a compact space
S.
A Remark Concerning Graves' Closure Criterion
Authors: Rudin Walter
Published: December 2010

In a paper recently published in this journal [1], R. E. Graves proved a
closure criterion for orthonormal sets of functions. A refined form of it
may be stated as follows :
Boundary Value Problems Associated With the Tensor Laplace
Equation
Authors: Duff G. F. D.
Published: December 2010

The boundary value problems considered in this paper relate to harmonic
p-tensors on Riemannian manifolds with boundary. We study the equation of
Beltrami-Laplace
On Some Matrix Theorems of Frobenius and McCoy
Authors: Goldhaber J. K. , Whaples G.
Published: December 2010

McCoy, following Frobenius, studied a problem which can be described as
follows. Let k be an arbitrary field, kc its algebraic closure,
and any algebra
of n ⨯ n matrices over k which contains the identity I . Define a
canonical ordering to be a set of n mappings λ of
, or of a
subset of
, into
kc such that the sequence λ1(A),λ2(A),
…, λn(A), for each A ∈ , consists
of the characteristic values (roots of det(A — xI) = 0) of A, each with the
right multiplicity. Define a canonical ordering to be a Frobenius
ordering if, for all non-commutative polynomials
f(x1, x2, … , xm) and all finite subsets
A1, A2, …, Am of ,
A Characterization of Implicative Boolean Rings
Authors: Copeland A. H. , Harary Frank
Published: December 2010

In the theory of probability, the conditional can be treated by an operation
analogous to division. Many properties of the conditional can best be
studied by means of the corresponding multiplication (called the
cross-product). An implicative Boolean ring is defined [2] in terms of a
cross-product and the usual Boolean operations. The cross-product is the
only device yet known in which the events corresponding to conditional
probabilities are themselves elements of the Boolean ring. The fact that
such advice was not introduced by Boole is probably the reason why Boolean
algebra has been very little used in the theory of probability, although
probability was one of the principal applications which Boole had in
mind.
Extensions of Lie Algebras and the Third Cohomology
Group
Authors: Goldberg S. I.
Published: December 2010

Cohomology theories of various algebraic structures have been investigated
by several authors. The most noteworthy are due to Hochschild, MacLane and
Eckmann, Chevalley and Eilenberg, who developed the theory of cohomology
groups of associative algebras, abstract groups, and Lie algebras
respectively. In this paper we are concerned primarily with a
characterization of the third cohomology group of a Lie algebra by its
extension properties.
Differentiable Points in the Conformal Plane
Authors: Lane N. D. , Scherk Peter
Published: December 2010

The purpose of this note is the classification of thedifferentiable points on curves in the conformai plane. We introduce tangent and osculating circles at such points and study the intersection and support properties of these circles.
Null Trigonometric Series in Differential
Equations
Authors: Walmsley Charles
Published: December 2010

In this paper it is shown how trigonometric series which are Cesàro-summable
to zero may be used to solve differential equations. The explicit solution
of the general ordinary linear equation with constant coefficients is found
in terms of trigonometric series and special cases are dealt with.
The First Factor of the Class Number of a Cyclic Field
Authors: Carlitz Leonard
Published: December 2010

Let p be a fixed prime > 3. The first factor of the field R(ζ), where R is the rational field and , is determined by means of

1.1,

where

r is a primitive root (mod p), and ri is the least positive residue of ri (mod p).
A Construction for Wythoffian Polytopes
Authors: Shephard G. C.
Published: December 2010

This paper contains an account of a simple method of deriving the coordinates of the vertices of any uniform polytope or honeycomb (degenerate polytope) whose symmetry group is generated by reflections.
Certain Fourier Transforms of Distributions: II
Authors: Lukacs Eugene , Szász Otto
Published: December 2010

In an earlier paper (1), published in this journal, a necessary condition was given which the reciprocal of a polynomial without multiple roots must satisfy in order to be a characteristic function. This condition is, however, valid for a wider class of functions since it can be shown (2, theorem 2 and corollary to theorem 3) that it holds for all analytic characteristic functions. The proof given in (1) is elementary and has some methodological interest since it avoids the use of theorems on singularities of Laplace transforms. Moreover the method used in (1) yields some additional necessary conditions which were not given in (1) and which do not seem to follow easily from the properties of analytic characteristic functions.
Stable Lattices
Authors: Cohn Harvey
Published: December 2010

The most interesting cases of stable lattices, introduced in an earlier volume of this journal (12), were the (algebraic) modules of stable norm, or modules whose ratio of minimum absolute non-zero norm to lattice determinant (i.e., to the square root of module-discriminant) is a local maximum for small variations of the basis. We soon found that these modules were perhaps more numerous than we should have desired if we were interested only in finding an absolute maximum.
Finite Unitary Reflection Groups
Authors: Shephard G. C. , Todd J. A.
Published: December 2010

Any finite group of linear transformations onnvariables leaves invariant a positive definite Hermitian form, and can therefore be expressed, after a suitable change of variables, as a group of unitary transformations (5, p. 257). Such a group may be thought of as a group of congruent transformations, keeping the origin fixed, in a unitary space Unofndimensions, in which the points are specified by complex vectors withncomponents, and the distance between two points is the norm of the difference between their corresponding vectors.
The Hook Graphs of the Symmetric Group
Authors: Frame J. S. , Robinson G. de B. , Thrall R. M.
Published: December 2010

Each irreducible representation [λ] of the symmetric group Sn may be identified by a partition [λ] of n into non-negative integral parts λ1 ≥ λ2 ≥ … λn ≥ 0, of which the first λ'j parts are ≥j, or by a right (Young) diagram also called [λ], that contains λi nodes in its ith row and λ'j
nodes in its jth column.
Substitution Groups of Formal Power Series
Authors: Jennings S. A.
Published: December 2010

In this paper we are concerned with the group of formal power series of the form

,

the coefficients being elements of a commutative ring R and the group operation being substitution. Little seems to be known of the properties of groups of this type, except in special cases, although groups of formal power series in several variables with complex coefficients have been investigated from a different point of view by Bochner and Martin (1, chap. I) and Gotô (2).
A Short Proof of the Factor Theorem for Finite Graphs
Authors: Tutte W. T.
Published: December 2010

We define a graph as a set V of objects called vertices together with a set E of objects called edges, the two sets having no common element. With each edge there are associated just two vertices, called its ends. We say that an edge joins its ends. Two vertices may be joined by more than one edge.
Ring Isomorphisms of Banach Algebras
Authors: Kaplansky Irving
Published: December 2010

In discussing an isomorphism between two Banach algebras, one will ordinarily tacitly assume that the mapping is linear (i.e., preserves the complex scalars as well as the ring operations). In general this cannot be avoided; for instance if the two Banach algebras are just the field
of complex numbers, then the isomorphism is unrestricted, and could be given by any one of the myriads of discontinuous automorphisms of the complex numbers.
A Tensor Boundary Value Problem of Mixed Type
Authors: Duff G. F. D.
Published: December 2010

The boundary value problems of generalized potential theory on finite Riemannian manifolds may be regarded as extensions of the Dirichlet and Neumann problems for harmonic functions. In the tensor theory there is, in fact, a greater variety of such problems; that is to say, these generalizations
from classical potential theory can be made in various ways. We here introduce yet another pair of boundary value problems for the tensor equation of Laplace.
The Maximal Prime Divisors of Linear Recurrences
Authors: Ward Morgan
Published: December 2010

Let

(W): W0, W1,…, Wn,…

be a linear integral recurring sequence of order r ≥ 2; that is, a particular solution of the recurrence

(1.1) ,

where P1, P2,… , Pr ≠ 0 are integers, and the initial values W0, W1, … , Wr−1 are integers.
Some Relations Between Various Types of Normality of Numbers
Authors: Hanson H. A.
Published: December 2010

In this paper certain relations will be proved between ∊-normality of integers, (k, ∊)-normality of integers, and normality of real numbers. Also a new type of normality of numbers will be introduced, namely, quasi-normality, as defined below.

A simply normal number is a real number, expressed in some scale B, in which each digit of the scale B occurs with the asymptotic frequency 1/B.
On the Modular Representations of the Symmetric Group
Authors: Robinson G. de B.
Published: December 2010

The study of the modular representation theory of the symmetric group has been greatly facilitated lately by the introduction of the graph (9, III ), the q-graph (5) and the hook-graph (4) of a Young diagram [λ]. In the present paper we seek to coordinate these ideas and relate them to the r-inducing and restricting processes (9, II ).
Differential Equations of Non-Integer Order
Authors: Barrett J. H.
Published: December 2010

In §1, we define a differential-integral operator, which for positive real indices is commonly known as the Liouville-Riemann generalized integral. For positive integer indices, we obtain an iterated integral. For negative real indices we obtain the Riemann-Holmgren (5; 9) generalized derivative, which for negative integer indices gives the ordinary derivative of order corresponding to the negative of such an integer. Following M. Riesz (10) we extend these ideas to include complex indices.