bluuebunny/crossref_metadata_2025 huggingface dataset:
Study on Preparation and Properties of Fluorescent Offset Printing Ink
Authors: Xu Wen Cai , Yang Yin , Sun Jia Yue
Published: December 2010

The ultraviolet (UV) fluorescent anti-counterfeiting offset printing ink, which can emit visible light (400-800 nm) under the excitation of ultraviolet light (200-400 nm), has been extensively adopted in the modern printing technology. In this paper, we used the red-emitting phosphor BaCaBO3F: Eu3+, Li+ as the fluorescent pigment for printing ink and investigated the influence on additive amount of the luminescence properties of fluorescent ink in order to determine a more ideal ratio of fluorescent ink .Besides, the shear viscosity, thixotropy, visco-elasticity and the temperature dependence of viscosity according to the rheology theory and rheological technique were also studied, and finally the valuable parameters and patterns were successfully obtained.
Study on the Curing Kinetics of UV-Curable Inkjet Ink
Authors: Ni Ping Xiu , Wei Xian Fu , Huang Pei Qing , Wei Wei
Published: December 2010

In order to make different UV curing inkjet ink system and test the relationship between the dynamic elastic modulus and UV curing time, the same monomer and pre-polymer were mixed in different proportions, and different functional monomers and pre-polymer were mixed. The results show that the larger the proportion of the pre-polymer and the greater the number of monomer functional groups, the shorter the induction period of the UV curing of UV inkjet ink system and the faster the UV curing rate. Then, the UV curing kinetics of UV inkjet inks was analyzed preliminarily.
Study on Photopolymerization Performance of Waterborne UV Cured Ink
Authors: Xu Rui Xin , Chen Guang Xue
Published: December 2010

The anion UV-curing water soluble prepolymer was synthesized with toluene diisocyanate, dihydroxy compound, dihydroxyalkyl carboxylic acid and polyurethane acrylate. The structure of the prepolymer was characterized by infrared spectroscopy. The effect of different photoinitiators, pigment content, drying technology on the curing speed of ink was also researched. The results shown that the photoinitiator system 819DW and MBF was best matched with the yellow pigment, cyan pigment and black pigment, the optimum content of the pigment was about 10 percent, 10 percent and 11 percent. The photoinitiator system 819DW and 500 was best matched with the magenta pigment, the optimum content of the pigment was about 10 percent．Under the conditions of this experiment, the best pigment content of the yellow, magenta, cyan, black was about 6 percent, 7 percent, 6 percent and 7 percent. The curing rate without pre-drying increased.
Influence of Monomer on the Performance of UV Waterless Offset Ink
Authors: Jia Xiao Xue , Huang Pei Qing , Wei Xian Fu , Yang Lei
Published: December 2010

Waterless offset doesn't use dampening solution, so it has the advantage of color saturation that the water offset can not reach. Monomer is an important component of the UV waterless offset ink; it has great influence on the performances of ink. Ink samples were made separately by using different monomers. The flow curve, thixotropy crack index, surface tension, gloss, curing speed and other performance parameters of the ink samples were tested, and the influence of different kinds of monomer on the performance of ink was analysised. The results show that the viscosity of monomer affects the viscosity of ink sample directly; six monomers we used have good curing speed; the lowest surface tension can be got when using monomer with single functionality; and six ink samples have large thixotropy. The result of the compound EOEOEA, TPGDA and TMPTA is 0∶3∶7 by using the functionality design principle.
The Effect of Photoinitiator on UV Screen Printing Photochromic Ink’S Curing Performance
Authors: Zhang Wan , Wei Xian Fu , Huang Pei Qing , Lu Chao
Published: December 2010

UV screen printing Photochromic ink mainly includes pre-polymer, monomer, Photochromic materials, Photoinitiator, etc, and the curing process of ink is that under the irradiation of UV light source, the liquid substances with chemical reactivity are rapidly changed to the solid state, in this reaction process, Photoinitiator can promote the advancement of reaction, therefore, Photoinitiator directly affect the curing performance of inks. The inks are respectively prepared by changing the quantity and type of Photoinitiator, and the curing speeds are tested. The result shows when the quantity of Photoinitiator is 10%, the curing performance of ink is the best. In addition, the formulation experiment is made by selecting three Photoinitiators with best curing performance. The result indicates that compared to other formulations, the ink can obtain the biggest curing speed only by Photoinitiator 907, and the optimal curing speed is 68m/min under curing power 100w/cm.
Green Plate Making Technology Based on Nano-Materials
Authors: Zhou Hai Hua , Song Yan Lin
Published: December 2010

Laser phototypesetting and computer to plate (CTP) technologies are widely used in print industry. These technologies are based on the complex photosensitive image process. The exposing and development processes result in waste of photosensitive materials and environment pollution. Green plate making technology is not based on photosensitive materials but nano-materials. The image process of the technology is to jet the nano-composite transfer printing material on super hydrophilic print plate with special nano and micro-structure. Then the oleophilic image area and hydrophilic non image area are formed by adjusting interface characters between the nano-composite transfer printing material and super hydrophilic print plate. The plate is used for printing without exposing and development. Without photosensitive image process, the technology has many advantages such as no operation in darkroom, simple process, environmental friendly and low cost. The key problems of print resolution and press life have been solved effectively by preparation of nano composite transfer printing material and super hydrophilic print plate. In this paper, the research process of the nano composite material and the print plate are presented.
Preparation and Characterization of Nanomaterials for Intelligent Temperature Control Package
Authors: Liu Xing Hai , Wang Yan , Li Hou Bin , Huang Chi , Chen Song Zhou
Published: December 2010

The low-dimensional VO2 (B) namomaterials were prepared by solvothermal or hydrothermal method. And then the powders were calcined in 623K under high purity N2 (99.999%) atmosphere. The as-obtained samples were characterized by X-ray powder diffraction (XRD), X-ray photoelecton spectroscopy (XPS), Fourier transform infrared spectroscopy (FT-IR), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM). The VO2 (M) nanobelts, with several micrometers long, typically 100-150 nm wide, and 20-30 nm thick, were obtained from hydrothermal method. The VO2 (M) petaloid clusters, which were composed of ultrathin flakes with several nanometers in diameter, were prepared by solvothermal reduction of self-synthesized nano-V2O5 and absolute EtOH. The Intelligent temperature control package (ITCP) was prepared by mixing of the modified VO2 (M) nanomaterials, dispersant agent and silicone. It was found that the phase transition of ITCP (Tc) occurred at 341K through FTIR. It was laid the foundation for the application of VO2 (M) in the region of intelligent controlling temperature package.
Research on the Characterization and the Properties of SiOx Coating on Plastic Film
Authors: Zhang Gai Mei , Chen Qiang , He Cun Fu , Zhu Hui Qin , Li Yu Ling
Published: December 2010

The nano-thickness SiOx deposited on polyethylene terephthalate (PET) film and biaxially oriented polypropylene (BOPP) were fabricated by plasma enhanced chemical vapor deposition (PECVD) in a radio frequency (13.56 MHz) glow discharge. The nano-coatings were characterized by using Fourier transform infrared spectroscopy (FTIR), atomic force microscopy (AFM) and ultrasonic atomic force microscopy (UAFM). With AFM and UAFM, the topography and ultrasonic amplitude images were obtained. In particular, the UAFM images reveal the subsurface defects in the coating. The tensile property, contact angle and OTR of the PET present and absent of the SiOx coating were investigated experimentally respectively. The results can show that the SiOx coating can improved the barrier and the tensile strength.
Study on Method of Simulating Dynamic Cushioning Performance of Molded Pulp Packaging Pad
Authors: Geng Dong Wei , Xu Wen Cai
Published: December 2010

This paper mainly introduce the ANSYS LS - DYNA software and the detailed simulation of dynamic compression process on molded pulp product, and simulate the acceleration - time curves with the hammer massing 2Kg, and different drop height. when the results were compared to the physical experimentalism , simulation results and physical are consistent. A new method was given to research on the cushioning performance of molded pulp products.
A Set of Constitutive Models for a Kind of Corn Straw Fiber Based Composite Cushioning Packaging Material
Authors: Gao De , Wang Yu , Liu Zhuang
Published: December 2010

A static compressive model and a dynamic compressive model have been constructed based on Sherwood-Frost’s constitutive model for a corn straw fiber reinforced composite cushioning packaging material. In deriving the models, material density, shape function, strain and strain ratio are considered. The validity of models has been verified by static compressive and dynamic impact testing. The proposed models will provide important theoretic guideline for designing this kind of cushioning material.
Research on Preparation and Characterization of Easy-to-Open Tear Tape for Corrugated Carton
Authors: Huang Li Qiang , Liu Mo
Published: December 2010

This paper presented a novel tape, which was used to open the corrugated cartons more easily and quickly. Structure of the tear tape consisted of backing materials (acrylic fibers), adhesive (acrylic pressure-sensitive adhesive) and release paper. Prepared tear tapes with different thickness, analyzed the influence of tear tape thickness on performance of open system and added them to the corrugated board, then tested the opening properties of the corrugated board above. The results indicate that the tape, with 0.18mm in thickness and about 25mm in width, can split high quantitative corrugated board smoothly, the tensile strength for opening is 105N at maximum, which means these tape can satisfy the needs of easy-to-open technique.
A Research on Early Spread of Traditional Hand-Made Paper in East Asia Countries
Authors: Gao Zhi Yong
Published: December 2010

Lots of unearthed objects and historical documents indicate the paper-making technology which had been invented in Western Han Dynasty moved to Japan through the Korean peninsula. This paper took the development of paper-making technology and how it spread to the major countries of East Asia as a clue to find out evidence of the early transmission of traditional handmade paper from the ancient literature, archaeological materials, research papers, and museum collections. Literature studies, field inspections and the traditional ways of recovery process were the main methods we used. After collecting and studying the materials, we drew the outline of the general picture of traditional handmade paper transmitting in the major countries of East Asia, and made a discussion about the relevant issues on the condition that the traditional handmade paper how to adapt to the geographical variation and the printing technology.
Research on the Spot Color Matching System Based on Ink Volume
Authors: Bai Wei Guo , Hu Xing Yue , Yan Yan
Published: December 2010

The admixture of Spot-color ink is generally determined by experience to make sure the type of primary color and the use of each ink, and then change the proportion of each primary color by the chromaticity control or visual experience. While this approach is difficult to admixture a qualified spot color ink, it also easily leads to the waste of ink. This paper did many researches and experiments on how to establish a spot color matching system based on the calculation of ink. Through the calculation of the largest ink thickness on paper, the model of the total estimated amount of printing based on image is established. Then this paper adopts the method of three stimulate value matching to establish the spot-color matching model based on Kubelka-Munk law. Through the combination of these two models above, spot color matching system based on ink calculation is finally established, and verified through the actual printing.
Evaluation and Controlling Influence of Papers Containing Optical Brightening Agents (OBA) for Color Management
Authors: Tian Quan Hui , Liu Zhen
Published: December 2010

Color management has been applied in the printing industry since 1993. Press papers as one of traditional substrates, its properties impact the quality of color reproductions. At present, almost all kinds of papers contain OBA. OBA works by absorbing ultraviolet wavelengths of the illuminant, emitting fluorescence at blue wavelengths, increasing the amount of light, and making the paper brighter. This effect of OBA is difficult to measure with common spectrophotometers accurately, which creates a mismatch between color proofing and printing. Furthermore, both the printing standards, as ISO 12647-2 defined substrate without fluorescence. It results in some problems in printing conformance using paper with OBA. This research discovered influence of OBA to color samples, derived colorimetric conversion method to correct and compensate the effects of OBA in papers, and demonstrated the efficient of the colorimetric conversion method in color management workflow with soft proofing.
The Impact of Different Viewing Light Illuminance on Cross-Media Color Reproduction
Authors: Huang Min , Liu Hao Xue , Cui Gui Hua , Luo Ming Ronnier
Published: December 2010

In order to reveal the impact of different D65 illuminance value on observer metamerism of cross-media color reproduction (CMCR) between display and printed samples. An EIZO display and viewing cabinet were placed simultaneously in front of the observers. 19 observers were asked to match 17 test colors for each configuration. Observers adjusted a color displayed on the monitor to match a printed patch inside the viewing cabinet under different light illuminance value, i.e.252lx，850lx and 1900lx respectively. The matched color patches were measured by Monitor- Optimizer in this experiment, observers had similar observation variability in the three configurations. Both sets of results had smaller observer variability and a closer agreement to the CIE standard colorimetric observer and with the increasing of the illuminance of the light, the higher saturation of the matched colors on the monitor. With the accuracy of the 19 observers, the higher the light illuminance the smaller the matching color difference.
Comparative Study of Metrics for Spectral Color Grouping
Authors: Liu Qiang , Teng Chong , Liu Zhen
Published: December 2010

A new combined metric for color grouping was proposed after comparing to the grouping performance of several color metrics, including dominant wavelength, color purity and some metrics in color appearance model. The performance of this method was compared to four existing methods and the experiment result proved that our proposed method not only gained excellent colorimetric and spectral accuracy but also saved the calculating time obviously.
Research on Selecting Region of Interest in the Application of Spectral Imaging in Forensic Science
Authors: Huang Wei , Wang Gui Qiang , Xu Xiao Jing , Yu Tao , Yang Zhi Cheng
Published: December 2010

Objectives Spectral imaging as the latest undestroyed identification method is being paid more and more attention by forensic science researchers ever since its introduction into the field. The general law of the selection of region of interest in spectral imaging technique makes the main purpose this paper tries to solve via experiments. In this study, spectral images were classified and analyzed under different regions of interest by specialist spectral imaging software. Tt was found that there are much more spectrum differences among various concentration regions even if the specimen is uniform. It’s clearly that selecting different regions of interest is quite important for forensic analysis and classification. It is summarized that imaging quality is affected by the selection of regions of interest and the concentration in visible scope.
Study on Key Issues of Multi-Spectral Color Reproduction Technique
Authors: Wang Hai Wen , Li Jie , Chen Guang Xue
Published: December 2010

Based on four fundamental deficiencies of the current color reproduction theory and technique, it proposed a new theoretical and technical approach of multi-spectral color reproduction technique. And it investigated five key issues of multi-spectral color reproduction technique systematically, namely the establishment and optimization of multi-spectral acquisition system, the fusion of multi-spectral image, the reconstruction of spectral color information, the multi-spectral display and print, the establishment of spectral color management standard. Finally it pointed out the main research directions and application prospects of multi-spectral color reproduction technique.
Nonlinear Viscoelastic Fracture Mechanics Using Boundary Elements
Authors: Syngellakis Stavros , Wu Jiang Wei
Published: December 2010

The boundary element methodology is applied to the fracture mechanics of non-linear viscoelastic solids. The adopted non-linear model is based on the ‘free volume’ concept, which is introduced into the relaxation moduli entering the linear viscoelastic relations through a time shift depending on the volumetric strain. Nonlinearity generates an irreducible domain integral into the original boundary integral equation governing the behaviour of linear viscoelastic solids. This necessitates the evaluation of domain strains, which relies on a non-standard differentiation of an integral with a strong kernel singularity. A time domain formulation based on constant shape functions over boundary elements and domain cells is computer-implemented through a numerical integration algorithm. The effectiveness of the developed numerical tool is demonstrated through the analysis of a plate with a central crack. The predicted stress field around the crack tip is compared with respective results obtained by the finite element method.
Symmetric-Galerkin Boundary Element Transient Analysis of the DSIFs for the Interaction of a Crack with a Circular Inclusion
Authors: Phan A.V. , Gray L.J. , Salvadori A.
Published: December 2010

A dynamic analysis of crack-inclusion interaction is described in this paper. The analysis employs a two-dimensional symmetric-Galerkin boundary integral formulation for multi-domain elastodynamic fracture analysis in the frequency domain. The multi-domain technique is based on the assumption of perfectly bonded inclusions. The numerical implementation of this boundary integral formulation is carried out with standard quadratic elements, allowing the use of an improved quarter-point element for accurately determining frequency responses of the dynamic stress intensity factors (DSIFs). To deal with singular and hypersingular integrals, the formulation is decomposed into two parts: the rst part is identical to that for elastostatics while the second part contains at most logarithmic singularities. The treatment of the elastostatic singular and hypersingular singular integrals employs an exterior limit to the boundary, while the weakly singular integrals in the second part are handled by Gauss quadrature. Time histories (transient responses) of the DSIFs are obtained in a post-processing step by applying the fast Fourier transform (FFT) and inverse FFT to the frequency responses of these DSIFs. Two numerical examples are presented for the computation of the DSIFs due to crack-inclusion interaction under two types of impact loading: Heaviside step loading and blast loading. The numerical results are consistent and conrm the well known crack tip shielding mechanism observed during the interaction between a crack and a much stier inclusion.
Autoimmune Kidney Disease and Impaired Engulfment of Apoptotic Cells in Mice with Macrophage Peroxisome Proliferator-Activated Receptor γ or Retinoid X Receptor α Deficiency
Authors: Rőszer Tamás , Menéndez-Gutiérrez María P. , Lefterova Martina I. , Alameda Daniel , Núñez Vanessa , Lazar Mitchell A. , Fischer Thierry , Ricote Mercedes
Published: December 2010

Autoimmune glomerulonephritis is a common manifestation of systemic lupus erythematosus (SLE). In this study, we show that mice lacking macrophage expression of the heterodimeric nuclear receptors PPARγ or RXRα develop glomerulonephritis and autoantibodies to nuclear Ags, resembling the nephritis seen in SLE. These mice show deficiencies in phagocytosis and clearance of apoptotic cells, and they are unable to acquire an anti-inflammatory phenotype upon feeding of apoptotic cells, which is critical for the maintenance of self-tolerance. These results demonstrate that stimulation of PPARγ and RXRα in macrophages facilitates apoptotic cell engulfment, and they provide a potential strategy to avoid autoimmunity against dying cells and to attenuate SLE.
Orthogonal Matrices in Four-Space
Authors: MacDuffee C. C.
Published: December 2010

Every proper orthogonal matrix A can be written

where Q is a skew matrix [6], and conversely every such matrix A is orthogonal. It is also known that every proper orthogonal transformation in real Euclidean four-space may be characterized in term of quaternions [1, 3] by the equation

determines with the origin a vector having the coordinates (XQ, XI, x2, x3). The relationship between these two representations was clearly shown by Murnaghan [5].
Generalized Vector Spaces. I.
Authors: Menger Karl
Published: December 2010

During the last fifty years, the concept of the Euclidean space (an ndimensional coordinate space with a Pythagorean distance) has undergone various profound generalizations.

Hilbert introduced the infinitely-dimensional Euclidean space whose points are infinite sequences of coordinates having from the origin, and thus from each other, finite Pythagorean distances.
Groups with Representations of Bounded Degree
Authors: Kaplansky Irving
Published: December 2010

Let G be a compact group. According to the celebrated theorem of Peter-Weyl there exists a complete set of finite-dimensional irreducible unitary representations of G, the completeness meaning that for any group element other than the identity there is a representation sending it into a matrix other than the unit matrix. If G is commutative, the representations are necessarily one-dimensional. It is an immediate consequence of the Peter-Weyl theorem that the converse also holds: if every representation is one-dimensional, G is commutative. The main theorem in the present paper is a generalization of this result to the case where the representations have bounded degree.
Note on Newtonian Force-Fields
Authors: Birkhoff Garrett , Burton Lindley
Published: December 2010

Although the behaviour of Newtonian potentials inside n-dimensional distributions of mass or charge has been discussed in the sense of Lebesgue-Stieltjes integrals by various authors, the discussion of various important theorems seems to have been made only in the sense of Riemann integration, and assuming the Hälder conditions (or at least piecewise continuity) for the volume density p. We shall generalize these theorems below.
On The Motion of Particles in General Relativity Theory
Authors: Einstein A. , Infeld L.
Published: December 2010

The gravitational field manifests itself in the motion of bodies. Therefore the problem of determining the motion of such bodies from the field equations alone is of fundamental importance. This problem was solved for the first time some ten years ago and the equations of motion for two particles were then deduced [1]. A more general and simplified version of this problem was given shortly thereafter [2].

Mr. Lewison pointed out to us, that from our approximation procedure, it does not follow that the field equations can be solved up to an arbitrarily high approximation. This is indeed true.
Old and New Results on Knots
Authors: Seifert Herbert , Threlfall William
Published: December 2010

The theory of knots undertakes the task of giving a complete survey of all
existing knots. A solid mathematical foundation was not laid to this theory
until our century. A mathematician of the rank of Felix Klein thought it to
be nearly hopeless to treat knot problems with the same exactness as we are accustomed to from classical mathematics. We want to give here a short summary of the modern topological methods enabling us to approach the knot problem in a mathematical way.

In order to exclude pathological knots, as for instance knots being entangled an infinite number of times, we will define a knot as a polygon lying in the space. In other words: a knot is a closed sequence of segments without double points. In Figure 1 some examples of knots are given in plane projection.
On Frequencies and Semicontinuous Functions
Authors: Levi F. W.
Published: December 2010

This paper deals with a particular class of distributive properties which appear to be important for Analysis and which I call frequencies. They can be defined for any kind of sets but it essential for proper application that a condition L (the statement of Lindelöf's lemma) is satisfied. From this condition follows Theorem 1, which is characteristic for frequencies but does not hold for other distributive properties. For every frequency F of a space Σ, one can build up an Analysis mod F of Σ the classical case is the Analysis mod F0. It is convenient to introduce the words “nearly every” with such a meaning that “every” and “almost every” are the special cases which, when we use the notation of this paper, correspond to F = F0 and F = FC.
The Factorization of Locally Finite Graphs
Authors: Tutte W. T.
Published: December 2010

1. Introduction. A graph G consists of a set V(G) of objects called nodes and a set M (G) of objects called links, V(G) and M (G) having no members in common. With each link A there is associated just two nodes said to be the ends of A, or to be incident with A, or to be joined by A. The sets V(G) and M(G) may be finite or infinite. There may be nodes with which no link is incident. Such nodes are said to be isolated.
An Elementary Proof of the Prime-Number Theorem for Arithmetic Progressions
Authors: Selberg Atle
Published: December 2010

In this paper we shall give an elementary proof of the theorem

(1.1)

where φ(k) denotes Euler's function, and

(1.2)

where p denotes the prime, and and are integers with (,) = 1, positive.
Spherical Geometries and Multigroups
Authors: Prenowitz Walter
Published: December 2010

1. Introduction. The notion spherical geometry is suggested by the familiar geometry of the Euclidean 2-sphere in which the role of path is played by “arc of great circle”. The first postulational treatment of the subject seems to be that of Halsted [10] for the two-dimensional case. Kline [11] under the name double elliptic geometry, gave a greatly simplified foundation for the three-dimensional case based on the primitive notions point and order. Halsted and Kline study not merely descriptive (that is positional, non-metrical) properties of figures but also introduce metrical notions by postulating or defining congruence. Kline includes a continuity postulate designed to yield real spherical geometry.
Identities and Congruences of the
Ramanujan Type
Authors: Ramanathan K. G.
Published: December 2010

Let P(n) denote the number of unrestricted partitions of the positive
integer n. Ramanujan conjectured that

(1.1)

if . He also indicated that such congruences could be
deduced from identities of the type
A Class of Self-Dual Maps
Authors: Smith C. A. B. , Tutte W. T.
Published: December 2010

1. Introduction. A dissection of a rectangle R into a finite number n of non-overlapping squares is called a squaring of R of order n. The n squares are called the elements of the dissection. If there is more than one element and the elements are all unequal the squaring is called perfect and R is a perfect rectangle. (We use R to denote both a rectangle and a particular squaring of it). If a squared (perfect) rectangle is a square we call it a squared (perfect) square.
Enveloping Algebras of Semi-Simple Lie Algebras
Authors: Jacobson N.
Published: December 2010

In a recent paper we studied systems of equations of the form

(1)

(2)

where as usual [a,b] =ab—baandϕ(λ) is a polynomial. Equations of this type have arisen in quantum mechanics. In our paper we gave a method of determining the matrix solutions of such equations. The starting point of our discussion was the observation that if the elementsxisatisfy (1) then the elementsxi, [xj,xk] satisfy the multiplication table of a certain basis of the Lie algebraof skew symmetric (n+ 1) ⨯ (n+ 1) matrices. We proved that if (2) is imposed as an added condition, then the algebra generated by thehas a finite basis, and we obtained the structure of the most general associative algebra that is generated in this way.
Euclid's Algorithm in real Quadratic Fields
Authors: Chatland H. , Davenport H.
Published: December 2010

1. Let m be a positive square-free integer. Euclid's Algorithm is said to hold
in the field if, given any non-integral element a in the field, an integer
a can be found so that
Note on the Uniqueness of the Green'S Functions Associated With Certain Differential Equations
Authors: Sears D. B.
Published: December 2010

Conditions to be imposed on q(x) which ensure the uniqueness of the Green's function associated with the linear second-order differential equation
Induced Representations and Invariants
Authors: Robinson G. DE B.
Published: December 2010

1. Introduction. The problem of the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices is intimately associated with the representation theory of the full linear group on the one hand and with the representation theory of the symmetric group on the other. In a previous paper the author gave an explicit formula for this reduction in terms of characters of the symmetric group. Later J. A. Todd derived the same formula using Schur functions, i.e. characters of representations of the full linear group.
Unified Field Theory
Authors: Wyman Max
Published: December 2010

Introduction. In a recent unified theory originated by Einstein and Straus [l], the gravitational and electromagnetic fields are represented by a single nonsymmetric tensor gy which is a function of four coordinates xr(r = 1, 2, 3, 4). In addition a non-symmetric linear connection Γjki is assumed for the space and a Hamiltonian function is defined in terms of gij and Γjki. By means of a variational principle in which the gij and Γjki are allowed to vary independently the field equations are obtained and can be written

(0.1)

(0.2)

(0.3)

(0.4)
Some Properties of C-Convex Sets
Authors: Valentine F. A.
Published: December 2010

The notion of convexity in (m-dimensional Euclidean spaces) can be generalized to apply to non-connected sets as follows.

A set is said to be C-convex if each of its components is convex. If the number of components of such a set is n, it is called a Cn-convex set.
On the Vector Sum of Continua
Authors: Green J. W. , Gustin W.
Published: December 2010

In this note we investigate certain properties of a set formed as t he vector sum of continua. Our interest in this subject arose in connection with the preceding paper Quasiconvex sets where we use, but do not prove, item 3 below.
Axiomatique Des Lattices Distributives
Authors: Croisot R.
Published: December 2010

Cette note a pour principal objet de répondre à deux questions posées par G.
Birkhoff.

Théorème 1. Les lattices distributives avec O et I sont exactement les
systèmes algébriques avec une opération ternaire (a, b, c) et des éléments O et I
tels que:

(1.1) (O, a, I) =
a,

(1.2) (a, b, a) =
a,

(1.3) (d, (a, b, c),
e) = (b, (c,
d, e), (a, d, e)).
A Compactness Theorem For Affine Equivalence-Classes of Convex Regions
Authors: Macbeath A. M.
Published: December 2010

In some parts of the Geometry of Numbers it is convenient to know that
certain affine invariants associated with convex regions attain their upper and
lower bounds. A classical example is the quotient of the critical determinant by
the content (if the region is symmetrical) for which Minkowski determined the
exact lower bound 2–n. The object of this paper is to prove
that for continuous functions of bounded regions the bounds are attained. The
result is, of course, deduced from the selection theorem of Blaschke, and itself
is a compactness theorem about the space of affine equivalence-classes.
The Bessel Polynomials
Authors: Burchnall J. L.
Published: December 2010

1. Krall and Frink [2] have recently considered in connection with certain
solutions of the wave equation a system of polynomials yn(x),
{n = 0, 1, 2, …), where yn is defined as that polynomial
solution of the differential equation
Autometrized Boolean Algebras I: Fundamental Distance-Theoretic Properties of
B
Authors: Ellis David
Published: December 2010

There have been several brief studies made [3, 4, 7, 8, 9, 11] of systems in
which a “distance function” is defined on the set of pairs of elements of some
abstract set to another abstract set. Frequently both of the sets involved are
given algebraic structures. One of the more novel of these systems is the
naturally metrized group [3, 7] originated by Karl Menger in 1931. This system is
analogous to the Euclidean line in that it assigns to each pair, a, b of elements
of an additively written Abelian group the “absolute value”, (a-b, b-a) = (b-a,
a-b), of the "difference" of the elements as ”distance“.
Autometrized Boolean Algebras II
Authors: Ellis David
Published: December 2010

The writer [1] has previously examined the fundamental concepts of distance
geometry in a Boolean algebra, B, with distance defined by . Any technical terms
from distance geometry which are not defined in this paper may be found in [1]. A
Boolean algebra bearing the given distance function is called an
autometrized Boolean algebra. It is clear that the
set of motions B (congruences of B with itself) form a group under substitution.
This group we denote by M(B).
Discrete Semi-Ordered Linear Spaces
Authors: Halperin Israel , Nakano Hidegoro
Published: December 2010

Let R be a semi-ordered linear space, that is, a
vector lattice in Birkhoff's terminology [2]. An
element a ∈ R is said to be discrete, if for every
element x ∈ R such that there exists a real number a for which x = aa. For every
pair of discrete elements a, b ∈ R we have or there exists a real number a for which b = aa or a =
ab.
On the Nature of the Spectrum of Singular Second Order Linear Differential
Equations
Authors: Coddington E. A. , Levinson N.
Published: December 2010

Let p(x) > 0, q(x) be two real-valued continuous functions on
. Suppose that the
differential equation with the real parameter λ
Sur Les Solutions Périodiques De Certains Systémes Differentiels
Perturbés
Authors: Reeb Georges
Published: December 2010

Les systémes différentiels dont il est question dans ce travail, sont du type
suivant:
Spinor Space and Line Geometry
Authors: Hlavatý Václav
Published: December 2010

Synopsis. This is the first of two papers dealing with the projective theory
of spinors. It contains the algebraic introduction to the projective spinor
analysis which will be dealt with in the second paper.
Sur Un Problème De Configurations Et Sur Les Fractions Continues
Authors: Touchard Jacques
Published: December 2010

Dans un précédent article [6, §4] j'ai essayé de traiter le problème suivant, qui fait l'objet du présent travail: on donne 2n abscisses, marquées 1 , 2 , … , 2n, de gauche à droite, sur un axe horizontal. On les joint deux à deux par n arcs convexes, tracés au-dessus de l'axe, de manière que chaque abscisse soit l'origine ou l'extrémité d'un seul arc, l'origine étant à gauche et l'extrémité à droite. On obtient ainsi p2n = 1.3.5. … (2n — 1) configurations et on demande le nombre de celles qui ont p points doubles.
Zeta Functions on the Unitary Sphere
Authors: Minakshisundaram S.
Published: December 2010

In an earlier paper [5], the author defined a zeta function on the real sphere , whereas in the present paper it is proposed to define one on the unitary sphere where xi's are complex numbers and their complex conjugates. Following E. Cartan, harmonics on the unitary sphere are defined and then a zeta function formed just as in the case of a real sphere. The unitary sphere is seen to behave like an even-dimensional closed manifold, since results similar to the ones proved by the author and A. Pleijel [6] for closed manifolds (of even dimensions) are observed here also.
The Fourier Coefficients of the Modular Function λ(τ)
Authors: Simons William H.
Published: December 2010

In [3], H. Rademacher obtained a convergent series for the Fourier coefficients of the modular invariant J(τ). He found that in the expansion
A Remark on the Existence of a Denumerable Base for a Family of Functions
Authors: Rothberger Fritz
Published: December 2010

A family F of functions is said to have a denumerable base if there exists a sequence of functions {fn(x)} (not necessarily ∈ F) such that any function f ∈ F is the limit of a subsequence of {fn (x)}. The domain X of a function f(x) is the set of x´s for which f(x) is defined ; we say f(x) is a function on X. A dyadic function is a function taking only the values 0 and 1.
On Surfaces Whose Canonical System is Hyperelliptic
Authors: Du Val Patrick
Published: December 2010

On a surface F of genus pg = pa = p and linear genus p(1) = n + 1 whose canonical system is irreducible, and which we shall ordinarily think of as simple and free from exceptional curves, the characteristic series of the canonical system is a semicanonical since the adjoint system of the canonical system is its double, so that the canonical series on a curve of the canonical system is its characteristic series doubled.
On a Galois Connection Between Algebras of Linear Transformations and Lattices of Subspaces of a Vector Space
Authors: Thrall R. M.
Published: December 2010

Representation theory has contributed much to the study of linear associative algebras. The central problem of representation theory per se is the determination for each algebra of all its indecomposable representations. This turns out to be a much deeper problem than the classification of algebras, in the sense that there are algebras for which any “internal question” can be answered but for which the number and nature of representations is almost completely unknown, or if known is much more complicated than the internal theory. This can be illustrated by the example of a commutative algebra of order three for which the representation theory can be shown to be essentially the same as the problem of classifying pairs of rectangular matrices under equivalence. (This algebra has indecomposable representations of every integral degree.)
Some Characterizations of Generalized
Manifolds With Boundaries
Authors: White Paul A.
Published: December 2010

In R. L. Wilder's book [2] the open and closed generalized manifolds are extensively studied. However, no study is made of the generalized manifold with boundary nor is a definition of such a space given except in the case of the generalized closed n-cell. A definition of a generalized manifold with boundary was given by the author in his paper [1]. Before undertaking the study of further properties of these manifolds it seems appropriate to characterize the manifolds with boundary in terms of the open and closed manifolds of Wilder. It is to that purpose that this paper is directed and in particular the generalized closed n-cell of Wilder is characterized as a special manifold with boundary.
On a Conjecture by J. H. Chung
Authors: Robinson G. de B.
Published: December 2010

The present paper is a sequel to that of J. H. Chung (2) and contains a proof of a conjecture made by him, namely, that the number of ordinary (modular) irreducible representations contained in a given p-block of Sn is independent of the p-core. A summary of the results contained herein appeared in the Proceedings of the National Academy of Sciences (9).
Measure in Semigroups
Authors: Gelbaum B. R. , Kalisch G. K.
Published: December 2010

The major portion of this paper is devoted to an investigation of the conditions which imply that a semigroup (no identity or commutativity assumed) with a bounded invariant measure is a group. We find in §3 that a weakened form of “shearing” is sufficient and a counter-example (§5) shows that “shearing” may not be dispensed with entirely. In §4 we discuss topological measures in locally compact semigroups and find that shearing may be dropped without affecting the results of the earlier sections (Theorem 2). The next two theorems show that under certain circumstances (shearing or commutativity) the topology of the semigroup (already known to be a group by virtue of earlier results) can be weakened so that the structure becomes a separated compact topological group. The last section treats the problem of extending an invariant measure on a commutative semigroup to an invariant measure on its quotient structure.
On the Subalgebras of Finite Division Algebras
Authors: Zemmer Joseph L.
Published: December 2010

In 1893 it was shown by Moore that the only commutative, associative division algebras with a finite number of elements are the well-known Galois fields [10, p. 220]. Twelve years later it was shown by Wedderburn that every associative division algebra with a finite number of elements is commutative [11], and hence a Galois field. It is conceivable that these results, particularly the theorem of Moore, motivated some of the work done by Dickson and published in two papers in 1906 [4;5]. The work referred to is an attempt to determine all commutative, non-associative1 division algebras with a finite number of elements.
A Simple Bounding Formula for Integrals
Authors: Synge J. L.
Published: December 2010

In this paper I establish the following bounding formula for the integral of
a function of n variables:

(1.1)
Constant Holomorphic Curvature
Authors: Hawley N. S.
Published: December 2010

We shall present in this paper a certain theorem concerning complex
manifolds provided with an Hermitian metric satisfying the Kaehler
restriction. The variables z1, z2, …, zn
denote local complex coordinates in the manifold and their conjugates. The subscripts a, b, c, … run
from 1 to n and by .
Harmonic p-Tensors on Normal Hyperbolic Riemannian
Spaces
Authors: Duff G. F. D.
Published: December 2010

The subject of this paper is the study of boundary value theorems for
harmonic p-tensors on a Riemannian space with an indefinite metric of the
normal hyperbolic signature.
Extension of Coverings, of Pseudometrics, and of
Linear-Space-Valued Mappings
Authors: Arens Richard
Published: December 2010

Let A be a closed subset of a topological space. We show that the following
three conditions are equivalent.

1.1 Any countable neighbourhood-finite open covering of A
(the topological terms referring to the relative topology of A) has
a refinement which can be extended to be a countable neighbourhood-finite
open covering of X.
A Theorem on Rings
Authors: Herstein I. N.
Published: December 2010

In a recent paper, Kaplansky [2] proved the following theorem: Let R be a
ring with centre Z, and such that xn(x) ∈ Z for every x∈ R. If R,
in addition, is semi-simple then it is also commutative

The existence of non-commutative rings in which every element is nilpotent
rules out the possibility of extending this result to all rings. One might
hope, however, that if R is such that xn(x) ∈ Z for all x ∈ R and
the nilpotent elements of R are reasonably “well-behaved,” then Kaplansky's
theorem should be true without the restriction of semi-simplicity.
Function Spaces
Authors: Halperin Israel
Published: December 2010

This paper is the first in a series dealing with Banach spaces
L whose elements are functions on a measure space S. If
W is a family of non-negative weight functions
wα we sometimes write LWp when the norm is given as
Autometrization and the Symmetric Difference
Authors: Elliott J. G.
Published: December 2010

The fact that the symmetric difference is a group
operation in a Boolean algebra is, of course, well known. Not so well known
is the fact observed by Ellis [3] that it possesses some of the desirable
properties of a metric distance function. Specifically, if * denotes this
operation, it is easy to verify that
Note on the Modular Representations of Symmetric
Groups
Authors: Nagao Hirosi
Published: December 2010

1. Let p be a fixed prime number. We denote by k(n) the number of partitions
of n and set
The FC-Chain of a Group
Authors: Haimo Franklin
Published: December 2010

Baer [2] and Neumann [5] have discussed groups in which there is a
limitation on the number of conjugates which an element may have. For a
given group G, let H1 be the set of all elements of G which have
only a finite number of conjugates in G, let H2 be the set of
those elements of G, the conjugates of each of which lie in only a finite
number of cosets of H1 in G; and in this fashion define
H3, H4, …. We shall show that the Hi are
strictly characteristic subgroups of G.
Variation of Congruences of Curves of an Orthogonal Ennuple in a
Riemannian Space
Authors: Pan T. K.
Published: December 2010

Consider any three congruences of an orthogonal ennuple at a point of a
Riemannian space. When one congruence is moved by local and a second
congruence is moved by parallel displacement in the direction of the third
congruence, the rate of change of cosine of the angle between the first two
congruences is well known as Ricci's coefficient of rotation and has been
extensively studied. It is the purpose of this note to investigate the
corresponding rate of change, when the third congruence is replaced by an
arbitrary one, in connection with parallelism and equidistance of
congruences as studied by Miss Peters [2; 3].
Fourier Transforms of Distribution Functions
Authors: Dyson F. J.
Published: December 2010

A distribution function ø(x) is assumed to have the following properties

(1) ø(x) is non-decreasing
Points and Spaces
Authors: Brouwer L. E. J.
Published: December 2010

The gradual disengagement of mathematics from logic. Beginning with a historical review of the development of mathematical thought, we have to consider successively (cf. 10, pp. 139-140):

(1) The observational period. For some familiar regularities of (outer or inner) experience of time and space, which, to any attainable degree of approximation, seemed invariable, absolute and sure invariability was postulated. These regularities were called axioms and were put into language. Thereupon extensive systems of properties were developed from the linguistic substratum of the axioms by means of reasoning, guided by experience but linguistically following and using the principles of classical logic. This logic was considered autonomous, and mathematics was considered more or less dependent on logic.
Note on the Gamma Function
Authors: van der Pol B.
Published: December 2010

The gamma function Γ(z + 1) = П(z) has been defined in different ways:

(1)(Weierstrass)

(2)(Kuler)

(3)(Gauss)

(4)(Euler)

(5)(Lerch)
Parallel Curves
Authors: Henderson G. P.
Published: December 2010

In the Euclidean plane a curve C has a one-parameter family of parallel involutes and a unique evolute C* which coincides with the locus of the centres of the osculating circles of C. If is parallel to C, C* is also the evolute of . We will study parallel curves in n-dimensional Euclidean space and obtain generalizations of the properties given above.

We will study parallel curves in n-dimensional Euclidean space and obtain generalizations of the properties given above.