bluuebunny/crossref_metadata_2025 huggingface dataset:
A characterization of minimal prime ideals
Authors: Birkenmeier Gary F. , Kim Jin Yong , Park Jae Keol
Published: May 2009

Let P be a prime ideal of a ring R, O(P) = {a ∊ R | aRs = 0, for some s ∊ R/P} | and Ō(P) = {x ∊ R | xn ∊ O(P), for some positive integer n}. Several authors have obtained sheaf representations of rings whose stalks are of the form R/O(P). Also in a commutative ring a minimal prime ideal has been characterized as a prime ideal P such that P= Ō(P). In this paper we derive various conditions which ensure that a prime ideal P = Ō(P). The property that P = Ō(P) is then used to obtain conditions which determine when R/O(P) has a unique minimal prime ideal. Various generalizations of O(P) and Ō(P) are considered. Examples are provided to illustrate and delimit our results.
Free elasticae and Willmore tori in warped product spaces
Authors: Barros Manuel
Published: May 2009

We use the principle of symmetric criticality to connect the Willmore variational problem for surfaces in a warped product space with base a circle, and the free elastica variational problem for curves on its fiber. In addition we obtain a rational oneparameter family of closed helices in the anti De Sitter 3-space which are critical points of the total squared curvature functional. This means they are free elasticae. Also they are spacelike; this allows us to construct a corresponding family of spacelike Willmore tori in a certain kind of spacetime close to the Robertson-Walker spaces.
On the fourth-powerfree part of x2 + 2
Authors: de Weger Benjamin M. M.
Published: May 2009

We show that x = 59 is the largest positive integer for which the fourth-powerfree part of x2 + 2 is at most 100. This implies the solution of the problem, posed recently by J. H. E. Cohn, to prove that (x, y) = (1, 1) is the only solution in nonnegative integers to the diophantine equation x2 – 3y4 = –2, as well as a new solution to the problem, posed a long time ago by the same J. H. E. Cohn and solved before by R. Bumby and N. Tzanakis, to prove that (x, y) = (1, 1), (11, 3) are the only solutions in nonnegative integers to the diophantine equation 2x2 – 3y4 = – 1.
Rings which are nearly principal ideal domains
Authors: Chatters A. W.
Published: May 2009

We study a class of rings which are closely related to principal ideal domains, and prove in particular that finitely-generated projective modules over such rings are free. Examples include the ring of Lipschitz quaternions; Z[a½] with d = —3 or d = —7; and any subring R of M2(Z) such that R ⊇ M2(pZ) for some prime number/? and R/M2(pZ) is a field with p2 elements.
Electronic Nose analysis of milk from cows grazing on two different Alpine vegetation types
Authors: Falchero Luca , Sala Giacomo , Gorlier Alessandra , Lombardi Giampiero , Lonati Michele , Masoero Giorgio
Published: May 2009

The nutritional distinctiveness of pasture-fed dairy products is mainly influenced by the transfer of specific chemical compounds from the grass to the milk and by their effect on rumen microflora and animal metabolism. Thus, the pasture-fed origin has to be objectively proven, using fast and reproducible analytical methods applied to finished products, in order to protect consumers against potential frauds. In this work, Electronic Nose patterns of Alpine milks produced by cows grazingTrifolium alpinumandFestuca nigrescenspasture types have been examined, in order to test the potential use of this device for routine control analyses of the botanical origin of milk and dairy products. The data have been treated with different multivariate analyses (MANOVA, LDA) and chemometrics (MPLS). The results allow a very good classification of the milks, according to the two treatments. Such results demonstrate that this device could be successfully applied to PDO dairy products food chain as a tool for the determination of their dietary origin.
Cell population, viability, and some key immunomodulatory molecules in different milk somatic cell samples in dairy cows
Authors: Baumert Amandine , Bruckmaier Rupert M. , Wellnitz Olga
Published: May 2009

Immune cells in the milk are most important in combating pathogens that invade the mammary gland. This study investigated the immune competence and viability of somatic milk cells that are already resident in milk and udders free of infection. Cells were studied in freshly removed milk to simulate conditions in the udder. Effects of incubation, cell preparation, and immunological stimulation with 0·5 μg/ml lipopolysaccharide (LPS) fromEscherichia coliwere analysed. Viability and differential counts of milk cells between high and low somatic cell count (SCC) quarters, and cisternal and alveolar milk with and without LPS stimulation were compared. Incubation and preparation of cells caused a cell loss which further increased with time independently of SCC and milk fraction. The viability of these cells was stable until 3 h post incubation and decreased until 6 h. Cell populations differed between both investigations, but did not change during the course of the experiment. mRNA expression of immune and apoptosis factors of the cells, measured by qPCR, did not change substantially: mRNA expression of caspase 3, Toll like receptor 4, and GM-CSF did not change, whereas the expression of the death receptor Fas/APO-1 (CD95), lactoferrin and lysozyme was decreased at 6 h. Cyclooxygenase-2 and TNF-α mRNA expression were decreased after 6 h of LPS treatment. In comparison with other studies in vivo or in vitro (in cell culture), in this study where cells are studied ex vivo (removed from the udder but kept in their natural environment, the milk) resident milk cells seem to be more vulnerable, less viable, less able to respond to stimulation, and thus less immune competent compared with cells that have freshly migrated from blood into milk after pathogen stimulation. The cell viability and differential cell count differed between high- and low-SCC milk and between cisternal and alveolar milk depending on the individual cow. In conclusion, the results support the view that for a most effective defence against invading pathogens the mammary gland is reliant on the recruitment of fresh immune cells from the blood.
Supplementing dairy steers and organically managed dairy cows with synthetic vitamin D3is unnecessary at pasture during exposure to summer sunlight
Authors: Hymøller Lone , Jensen Søren K , Lindqvist Hanna , Johansson Birgitta , Nielsen Mette O , Nadeau Elisabet
Published: May 2009

Use of synthetic feed additives, including synthetic vitamin D3(D3) in the feed for cows and other ruminants, is not consistent with the international principles of organic farming. If dairy farmers wish to produce in accordance with the organic principles, production animals would be left with only their endogenous production of D3from summer sunlight as a source of D3. To examine the impact of supplemental synthetic D3from the feed on the D3status of dairy cattle in organic production in Nordic countries, 20 high-yielding dairy cows and 30 dairy steers were divided into two groups: one supplemented with synthetic D3in the feed and one not supplemented with synthetic D3. Vitamin D3status of the animals was assessed by measuring the concentration of the liver-derived 25-hydroxyvitamin D3(25OHD3) in plasma. Results showed that 25OHD3concentration in plasma from dairy cattle as well as from steers decreased during winter for both supplemented and unsupplemented groups. Unsupplemented cows and steers had approximately 2 ng 25OHD3per ml plasma during winter, whereas supplemented animals had between 10 (cows) and 30 (steers) ng/ml. During summer and autumn there was no additive effect of supplementing with synthetic D3since unsupplemented and supplemented animals had the same D3status at this time of year. In all cows summer concentrations of 25OHD3were 20–25 ng/ml and in all steers 40–50 ng/ml plasma. The decrease in vitamin D3status during winter indicates that cows and steers are able to store D3only to a limited extent. The results also show that cows or steers fed supplemental D3according to Swedish recommendation throughout the year are not able to maintain their summer value of 25OHD3during winter.
Administration of a live culture ofLactococcus lactisDPC 3147 into the bovine mammary gland stimulates the local host immune response, particularlyIL-1β andIL-8gene expression
Authors: Beecher Christine , Daly Mairéad , Berry Donagh P , Klostermann Katja , Flynn James , Meaney William , Hill Colin , McCarthy Tommie V , Ross R Paul , Giblin Linda
Published: May 2009

Mastitis is one of the most costly diseases to the dairy farming industry. Conventional antibiotic therapy is often unsatisfactory for successful treatment of mastitis and alternative treatments are continually under investigation. We have previously demonstrated, in two separate field trials, that a probiotic culture,Lactococcus lactisDPC 3147, was comparable to antibiotic therapy to treat bovine mastitis. To understand the mode of action of this therapeutic, we looked at the detailed immune response of the host to delivery of this live strain directly into the mammary gland of six healthy dairy cows. All animals elicited signs of udder inflammation 7 h post infusion. At this time, clots were visible in the milk of all animals in the investigation. The most pronounced increase in immune gene expression was observed inInterleukin(IL)-1β andIL-8, with highest expression corresponding to peaks in somatic cell count. Infusion with a live culture of aLc. lactisleads to a rapid and considerable innate immune response.
A semi-lumped microstrip UWB bandpass filter
Authors: Kaddour Darine , Arnould Jean-Daniel , Ferrari Philippe
Published: May 2009

In this paper, a miniaturized bandpass filter for ultra-wide-band applications is proposed. It is based on the embedding of high-pass structures in a low-pass filter. A semi-lumped technology combining surface-mounted capacitors and transmission lines has been used. The filter design rules have been carried out. Furthermore, two filters having a 3-dB fractional bandwidth of 142 and 150%, centered at 0.77 and 1 GHz, respectively, have been realized for a proof of concept. Measured characteristics, in good agreement with simulations, show attractive properties of return loss (|S11| <−18 dB), insertion loss (<0.3 dB), and a maximum group delay and group delay variation of 2 and 1.3 ns, respectively. A distributed filter based on the same low-pass/high-pass approach has been also realized and measured for comparison. The size reduction reaches 85% for the semi-lumped filter, and its selectivity is improved with a shape factor of 1.3:1 instead of 1.5:1. The semi-lumped filter's drawback is related to a smaller rejection bandwidth compared to the distributed one. To improve the high-frequency stopband, an original technique for spurious responses suppression based on capacitively loaded stubs has been proposed. Even if the performances do not reach that obtained for the distributed approach, with this technique spurious responses are pushed until eight times the center frequency. A sensitivity study vs. critical parameters has also been carried out, showing the robustness of the design.
On Neumann's Formula for the Legendre Functions
Authors: Macrobert T. M.
Published: May 2009

§1. Introductory. The formula

where w is zero or a positive integer and | ζ | > 1, was given by F. E. Neumann “Crelle's Journal, XXXVII (1848), p. 24”. In § 2 of this paper some related formulae are given; the extension to the case when n is not integral is dealt with in § 3; while in § 4 the corresponding formulae for the Associated Legendre Functions when the sum of the degree and the order is a positive integer are established.
Integrals of Lommel's Type for Confluent Hypergeometric Functions
Authors: Martin D.
Published: May 2009

In this note we derive some integrals involving confluent hypergeometric functions and analogous to Lommel's integrals for Bessel functions. Although the method of derivation is straightforward, the integrals do not seem to be mentioned in the literature.
Inequalities for a Class of Terminating Generalised Hypergeometric Functions
Authors: MacRobert T. M.
Published: May 2009

By applying Gauss's Theorem it can be seen that, if n is a positive integer and α is not integral,

so that

In section 2 it will be proved that, if

Where α and β are not integers

Where μ and M are constants independent of n.
Propagation of a Boundary of Fusion
Authors: Paterson Stewart
Published: May 2009

We consider a volume of material, divided into two regions 1 and 2. each of density ρ, by a moving surface S. On S a change of phase occurs, at a definite temperature (which we may take to be zero) and with absorption or liberation of a latent heat L per unit mass. If θl, kl, K1 are the temperature, thermal conductivity and diffusivity of phase 1, and θ2, k2, K2 corresponding quantities for phase 2, the surface S is the isothermal

and the boundary condition on this surface is

Subscript letters denote partial differentiation.
Contiguous Hypergeometric Functions of the Type 3F2(1)
Authors: Bailey W. N.
Published: May 2009

In a paper published recently in this Journal, Watson obtained a reduction formul for the integral

He showed that this reduction formula could be written in the form:

If

then

where

and 2σ = α + β + γ + δ, 2θ3 = α − β − γ + δ.
The Closest Packing of Spherical Caps in n Dimensions
Authors: Rankin R. A.
Published: May 2009

Let Sn denote the “surface” of an n-dimensional unit sphere in Euclidean space of n dimensions. We may suppose that the sphere is centred at the origin of coordinates O, so that the points P(x1, x2, …, xn) of Sn satisfy

We suppose that n≥2.
Solution of the Word Problem for Certain Types of Groups I
Authors: Britton J. L.
Published: May 2009

The main result of this series of papers is a theorem on the free product of groups (Theorem 1) which formed part of a doctoral thesis. This theorem has an immediate application to the word problem (Theorem 2). Usually the word problem refers to a finite system of generators and a finite number of defining relations, but in this context it is more natural to allow an infinite number of generators and defining relations. This (infinite) word problem is not solvable in general (Example 2).
Solution of the word problem for certain types of groups II
Authors: Britton J. L.
Published: May 2009

The purpose of this paper is to prove a theorem which concerns the normal subgroup of a free product Π generated by a given subset Ω. This theorem was stated in the first paper of this series (Britton [1]) and an application was made to the word problem. The present work is, however, independent.
Completely continuous movements in topological vector spaces
Authors: Michael J. H.
Published: May 2009

Let A be a closed subset of a topological space X and f a continuous mapping of A into X with the following two properties:

1.1. f {Fr (A)} & f {Int (A)} are disjoint.

1.2. The mapping f* = f | Fr (A) is 1–1.

It is proved in [5], that if X is the euclidean n–sphere Sn = {x; x e Rn+1 and ― x ― = 1}, then

1.3. f {Fr(A)} = Fr {f(A)}.

[ Hence f{Int (A)} = Int {f(A)}].
A note on positive definite matrices
Authors: Everitt W. N.
Published: May 2009

This note is concerned with an inequality for even order positive definite hermitian matrices together with an application to vector spaces.

The abbreviations p.d. and p.s-d. are used for positive definite and positive semi-definite respectively. An asterisk denotes the conjugate transpose of a matrix.
On a problem of Rankin about the Epstein zeta-function
Authors: Cassels J. W. S.
Published: May 2009

Let

be a positive definite quadratic form with determinant αβ−X2= 1. A special form of this kind is

We consider the Epstein zeta-function

the series converging fors> 1. Fors≥ 1·035 Rankin [1] proved the following

STatementR.

The sign of equality is needed only when h is equivalent to Q.
Further Duals of a verbal Subgroup
Authors: Moran S.
Published: May 2009

In a previous paper [3] we gave two methods for constructing subgroups which in certain senses may be considered to be dual to a verbal subgroupVf(G) of an arbitrary groupG.Associated with a wordh(u, v) in the two symbolsuandv, we have (i) the first dual subgroupwhich is defined as the minimal subgroup of G containing all elements ξ of G for which

for all values ofx1,x2, …, inxninG, and (ii), the second dual subgroupwhich is defined as the minimal subgroup ofGcontaining all elementszofGfor which

for all values of x1, x2, …, xninG.Below we introduce slight variations to these definitions, which give rise to the concepts of the third and the fourth dual subgroups respectively. For certain values ofh(u, v) we obtain concepts which also arise fromand, namely, the marginal subgroup, the invariable subgroup and the centralizer of a verbal subgroup. We also obtain the new concepts of elemental subgroups and commutal subgroups and briefly sketch some of their properties. Finally we conclude by showing that MacLane's dual for the centralizer of a verbal subgroup is a closely related verbal subgroup.
On Differences of Unitarily Equivalent Self-Adjoint Operators
Authors: Putnam C. R.
Published: May 2009

1. All operators considered in this paper are bounded operators on a Hilbert space. In case A and B are self-adjoint, certain conditions on A, B and their difference

assuring the unitary equivalence of Aand B,

have recently been obtained by Rosenblum [6] and Kato [2]. The present paper will consider the problem of investigating consequences of an assumed relation of type (2) for some unitary U together with an additional hypothesis that the difference H of (1) be non-negative, so that

First, it is easy to see that if only (2) and (3) are assumed, thereby allowing H = 0, relation (2) can hold for A arbitrary with U = I (identity) and B = A. If H = 0 in (3) is not allowed, however (an impossible assumption in the finite dimensional case, incidentally, since then the trace of H is zero and hence H = 0), it will be shown, among other things, that any unitary operator U for which (2) and (3) hold must have a spectrum with a positive measure (as a consequence of (i) of Theorem 2 below). Moreover A (hence B) cannot differ from a completely continuous operator by a constant multiple of the identity (Theorem 1). In case 0 is not in the point spectrum of H, then U is even absolutely continuous (see (iv) of Theorem 2). In § 4, applications to semi-normal operators will be given.
The elementary solution of dual integral equations
Authors: Sneddon Ian N.
Published: May 2009

When the theory of Hankel transforms is applied to the solution of certain mixed boundary value problems in mathematical physics, the problems are reduced to the solution of dual integral equations of the type

where α and ν are prescribed constants and f(ρ) is a prescribed function of ρ [1]. The formal solution of these equations was first derived by Titchmarsh [2]. The method employed by Titchmarsh in deriving the solution in the general case is difficult, involving the theory of Mellin transforms and what is essentially a Wiener-Hopf procedure. In lecturing to students on this subject one often feels the need for an elementary solution of these equations, especially in the cases α = ± 1, ν = 0. That such an elementary solution exists is suggested by Copson's solution [3] of the problem of the electrified disc which corresponds to the case α = –l, ν = 0. A systematic use of a procedure similar to Copson's has in fact been made by Noble [4] to find the solution of a pair of general dual integral equations, but again the analysis is involved and long. The object of the present note is to give a simple solution of the pairs of equations which arise most frequently in physical applications. The method of solution was suggested by a procedure used by Lebedev and Uflyand [5] in the solution of a much more general problem.
Some order properties of coverings of finite-dimensional spaces
Authors: Parnaby T. W.
Published: May 2009

Definitions and introduction. Let Ц = {Ui|i ∈ I} be a system of subsets of a normal topological space R; i.e. a mapping from the index set I into the set of all subsets of R. The order of a point x is the number of distinct member sets of Ц which contain x, and is denoted by x: Ц; the sets Ui are here considered distinct if they have distinct indices. Thus x: Ц is the number of indices i for which x ∈ Ui; ν(Ц) = max {x: Ц | x ∈ R} is called the order of the system Ц. If every point has an (open) neighbourhood meeting only finitely many members of Ц, then Ц is said to be locally finite.
The Divisors of a Quadratic Polynomial
Authors: Scourfield E. J.
Published: May 2009

Let f(n) = an2+ bn + c be an irreducible quadratic polynomial with integer coefficients, and let D denote the discriminant b2 – 4ac of f(n).We shall assume that (D, k) = 1, and that for all positive integer n, f(n) is positive and coprime with k, where k is a fixed integer greater than 1.
Note on a conjecture of Coxeter
Authors: Leech John , Mennicke Jens
Published: May 2009

Coxeter [1] has studied groups defined by the relations

and gives lists of finite groups known to be completely defined by such sets of relations. In a later paper [2] he shows that G3, n, p is finite if n, p are both even and satisfy

and expresses the conjecture that the restriction to even values may be removed. The only case satisfying this inequality and not already known to be finite is G3, 7, 16. In this note we show that G3, 7, 16 is indeed finite, being of order 21504 = 210.3.7, by showing that its subgroup

of index 2 is finite and of order 10752. Thus we add one entry to each of the lists of finite groups in Coxeter [1].
Upon A Second Confluent Form of the Ɛ-Algorithm
Authors: Wynn P.
Published: May 2009

In two previous papers [1], [2] the confluent form

of the δ-algorithm [3]

was established, and various properties which the confluent form of the algorithm possesses were discussed. It was shown, among other things, that if in (1)

and the notation

is used, then (1) is satisfied by

and further that under certain conditions, and for a certainn,

identically. It is the purpose of this note to derive another confluent form of the Ɛ-algorithm and to discuss its properties.
Some definitions of Klein's simple group of order 168 and other groups
Authors: Leech John
Published: May 2009

In a previous note [3], Mennicke and I showed that the relations

(8, 7|2, 3): A8=B7=(AB)2=(AB)2=(A-1B)2=(A-1B)3=E

define a group of order 10752. As we remarked, the results of §§ 2, 3 of that note are not restricted in their application to this group; they apply to the group

[3, 7]+: B7=(AB)2=(A-1B)3=E

and to any factor group of this group which in turn has Klein's simple group of order 168, defined by

(4,7|2, 3): A4=B7=(AB)2=(A-1B)3=E,

as a factor group. In this note I use these results to establish alternative “weaker” definitions for Klein's group and for two groups discussed by Sinkov [4], namely (8, 7|2, 3) defined above and a factor group of this group of order 1344. These latter groups are eloquently discussed by Coxeter [1].
Sur une inégalité
Authors: Djoković D. Ž.
Published: May 2009

Dans cet article nous considerons l'inégalité

où lesxidésignent les nombres réels qui remplissent les conditions suivantes

Cette inégalité est proposée par H. S. Shapiro [1].
Integrals involving E-functions
Authors: Macrobert T. M.
Published: May 2009

1. Introductory. The following two integrals will be established in § 2.

If m is a positive integer, if p ≧ q + 1 and if R(ar+kt) > 0 (r = 1, 2,…, p, t = 1, 2,…, m),

where co is 1 or e±in according as m is even or odd, the dash denotes that the factor sin (k,–k,)π does not appear and the asterisk that the parameter kt–kt + 1 is omitted. If pp ≧ qthe result holds if the integral is convergent.
Inverses of Boolean matrices
Authors: Rutherford D. E.
Published: May 2009

This note is concerned with square matrices, denoted by capital letters, whose elements belong to aBoolean algebra with null element 0 and all element 1. Such matrices, which have important applicationsin the theory of electric circuits, can be compounded in the three following ways.
On harmonic continuation
Authors: Eastham M. S. P.
Published: May 2009

Let D be a bounded, closed, simply-connected domain whose boundary C consists of a finite number of analytic Jordan curves. Let γ be any analytic arc of C. Then we shall prove the following theorem.

Theorem 1. Let u(x, y) be harmonic in the interior of D and continuous on γ, and let ϱu(x, y)/ϱn=g(s) when (x, y) is on γ, where g(s) is an analytic function of arc-length s along γ. Then u(x, y) can be harmonically continued across γ.
Integrals involving products of modified Bessel functions of the second kind
Authors: Ragab F. M.
Published: May 2009

It is proposed to establish the two following integrals.

where n is a positive integer, x is real and positive, μi and ν are complex, and Δ (n; a) represents the set of parameters

where n is a positive integer and x is real and positive.
A generalisation of Divinsky's radical
Authors: Bostock F. A. , Patterson E. M.
Published: May 2009

Let A be an associative ring. Given a ∊ A, an element b ∊ A is called a left identity for a if

Given a subset S of A, an element b ∊ A is, called a left identity for S if (1) is satisfied for all a ∊ S. An element of A need not have a left identity; for example, if A is nilpotent then no non-zero element of A has a left identity. If a does have a left identity, the latter need not be unique; if every element of a subset S of A has a left identity, then it is not necessarily true that S has a left identity.
The solution of dual series and dual integral equations
Authors: Williams W. E.
Published: May 2009

There exist several different approaches to the problem of solving dual integral equations involving Bessel Functions [1, 2, 3, 4, 5, 6,7], and Erdelyi and Sneddon in a recent paper [8] have shown that the introduction of certain operators occurring in the theory of fractional integration enables the relationships between the various methods to be clearly demonstrated. For dual integral equations other than those involving Bessel Functions the operators introduced by Erdélyi and Sneddon are not always the appropriate ones to use and it seems to be of interest to consider this more general type of situation.
A note on principal sequences
Authors: Rotman B.
Published: May 2009

A fundamental problem in the theory of ordinals is the assignation of principal sequences to limit numbers of the second number class.

It is our main object here to show that a certain class of methods, which are a natural generalisation of those used in the solution of the corresponding problem for the real numbers (the description of which we omit), must fail to solve the problem. The methods are those which rest on the following assumption: the principal sequence assigned to any limit number of the second number class is determined once the first i terms of that sequence are known.
On polylogarithms
Authors: Eastham M. S. P.
Published: May 2009

The nth order polylogarithm Lin(z) is defined for |z| ≦ 1 by

([4, p. 169], cf. [2, §1. 11 (14) and § 1. 11. 1]). The definition can be extended to all values of zin the z-plane cut along the real axis from 1 to ∝ by the formula

[2, §1. 11(3)]. Then Lin(z) is regular in the cut plane, and there is a differential recurrence relation [4, p. 169]

It is convenient to extend the sequence Lin(z) backwards in the manner suggested by (2) and define

Then Li1(z)= – log(l–z), and Lin(z) is a rational function of z for n= 0, – 1, – 2,…. Formula (2) now holds for all integers n.
Continuous sums of measures and continuous spectra
Authors: Sankaran S.
Published: May 2009

Von Neumann's definition of the continuous sum of Hilbert spaces led Segal [3] to define the continuous sum of measures on a measurable space. In this note we employ Segal's definition to investigate the measure structures associated with a self-adjoint transformation of pure point spectrum and a self-adjoint transformation of pure continuous spectrum. While these transformations, as operators on separable Hilbert spaces, are the antithesis of each other we show that in their measure structure one is a particular case of the other.
Inequalities involving the genus of a graph and its thicknesses
Authors: Beineke Lowell W. , Harary Frank
Published: May 2009

Let G be a graph with p points and q lines, and genus γ. The thicknesst(G) has been introduced as the minimum number of planar subgraphs whose union is G. This topological invariant of a graph has been studied by Battle, Harary and Kodama [1], Tutte [7], Beineke, Harary and Moon [3], and Beineke and Harary [2].

It is natural to generalise this concept of the thickness of a graph to the union of graphs with a specified genus. We say that the n-thickness of G is the minimum number of subgraphs of genus at most n whose union is G. Denoting the n-thickness of G by tn, we write in particular t0 the 0-thickness, i.e., the thickness.
Lucas and fibonacci numbers and some diophantine Equations
Authors: Cohn J. H. E.
Published: May 2009

The Lucas numbers υn and the Fibonacci numbers υn are defined by υ1 = 1, υ2= 3, υn+2 = υn+1 + υn and u1 = u2 = 1, un+2 = un+1 + un for all integers n. The elementary properties of these numbers are easily established; see for example [2].However, despite the ease with which many such properties are proved, there are a number of more difficult questions connected with these numbers, of which some are as yet unanswered. Among these there is the well-known conjecture that un is a perfect square only if n = 0, ± 1, 2 or 12. This conjecture was proved correct in [1]. The object of this paper is to prove similar results for υn, ½un and ½υn, and incidentally to simplify considerably the proof for un. Secondly, we shall use these results to solve certain Diophantine equations.
On minimal n-universal graphs
Authors: Moon J. W.
Published: May 2009

A graph Gn consists of n distinct vertices x1x2, …, xn some pairs of which are joined by an edge. We stipulate that at most one edge joins any two vertices and that no edge joins a vertex to itself. If xi, and xj are joined by an edge, we denote this by writing xi ∘ xj.

Consider a second graph HN, where n ≦ N. Following Rado [1], we say that a one-to-one mapping/of the vertices of Gn into the vertices of HN defines an embedding if xi ∘ xj implies f(xi) ∘ f(xj), and conversely, for all i, j = 1, 2,…, n. If there exists an embedding of Gn into HN, we denote this by writing Gn <HN. The particular graph HN is said to be n-universal if Gn < HN for every graph Gn with n vertices.
Two integral transform pairs involving hypergeometric functions
Authors: Wimp Jet
Published: May 2009

In this note, we first establish an integral transform pair where the kernel of each integral involves the Gaussian hypergeometric function. Special cases of Theorem 1 have been studied by several authors [1, 2, 5, 6]. In Theorem 2 a similar integral transform pair involving a confluent hypergeometric function is given.
Adjunction of roots to nilpotent groups
Authors: Allenby R. B. J. T.
Published: May 2009

For any nilpotent groupBof class c and any given elementhofBgenerating the subgroupH, Wiegold [1] has shown that if, in addition, [B, H] has exponentprfor some primepand integerr, thenBcan be embedded in a nilpotent groupGsuch thatGalso containspsth root forh(s ≧ 1). In fact, Wiegold has gone further and calculated an upper bound for the class ofGin terms of the variablesc, p, r, s.
The Reissner-Sagoci problem
Authors: Sneddon Ian N.
Published: May 2009

The statical Reissner-Sagoci problem [1, 2, 3] is that of determining the components of stress and displacement in the interior of the semi-infinite homogeneous isotropic elastic solid z ≧ 0 when a circular area (0 ≦ p ≦ a, z = 0) of the boundary surface is forced to rotate through an angle a about an axis which is normal to the undeformed plane surface of the medium. It is easily shown that, if we use cylindrical coordinates (p, φ, z), the displacement vector has only one non-vanishing component uφ (p, z), and the stress tensor has only two non-vanishing components, σρπ(p, z) and σπz(p, z). The stress-strain relations reduce to the two simple equations

where μ is the shear modulus of the material. From these equations, it follows immediately that the equilibrium equation

is satisfied provided that the function uπ(ρ, z) is a solution of the partial differential equation

The boundary conditions can be written in the form

where, in the case in which we are most interested, f(p) = αρ. We also assume that, as r → ∞, uπ, σρπ and σπz all tend to zero.
The semigroup of doubly-stochastic matrices
Authors: Farahat H. K.
Published: May 2009

The set Dn of all n × n doubly-stochastic matrices is a semigroup with respect to ordinary matrix multiplication. This note is concerned with the determination of the maximal subgroups of Dn. It is shown that the number of subgroups is finite, that each subgroup is finite and is in fact isomorphic to a direct product of symmetric groups. These results are applied in § 3 to yield information about the least number of permutation matrices whose convex hull contains a given doubly-stochastic matrix.
A Group-Theoretic Proof of a Theorem of MacLagan-Wedderburn
Authors: Zassenhaus Hans J.
Published: May 2009

The purpose of this paper is to present a proof of the following theorem of Maclagan-Wedderburn.*

Every finite skew-field† is a field.

The proof depends on group theory and on the properties of Galois fields. As an introduction, §§1–4 are devoted to a systematic and self-contained account of the theory of Galois fields.
Integral of an E-function expressed as a Sum of two E-functions
Authors: Macrobert T. M.
Published: May 2009

§ 1. Introductory. The formula to be proved is

where ρq+1 – αp+1 > 0, αr – ρq+1 > 0, r = 1,2, …, p, and p≧q + 1.
Integrals involving E-functions
Authors: Ragab Fouad M.
Published: May 2009

§ 1. Introductory. The formula to be proved is

where b>0.
Comparison of AIRS and AMSU‐B monthly mean estimates of upper tropospheric humidity
Authors: Milz M. , Buehler S. A. , John V. O.
Published: May 2009

Satellite‐borne measurements provide valuable information on the global distribution of upper tropospheric humidity (UTH), which represents the mean relative humidity in a layer approximately enclosed by the atmospheric pressure levels 500 and 200 hPa. Monthly mean distributions of microwave observations of UTH obtained from the Advanced Microwave Sounding Unit‐B (AMSU‐B) and the Humidity Sounder for Brazil (HSB) are compared to infrared observations of UTH from the Atmospheric Infrared Sounder (AIRS). All data sets for January 2003 show distributions as expected from climatologies. Data of AIRS and AMSU‐B averaged on 1.5° × 1.5° lat‐lon bins for January 2003 show good overall agreement. However, with 2.7%RH AIRS shows an unexpected wet mean bias, especially for regions where the influence of clouds is small or cloud affected measurements are excluded for both sensors. In regions where AIRS is sensitive to cloud affected measurements but not AMSU‐B, the bias is reduced and partly negative.
The role of magnetic field fluctuations in nonadiabatic acceleration of ions during dipolarization
Authors: Ono Y. , Nosé M. , Christon S. P. , Lui A. T. Y.
Published: May 2009

We statistically examine changes in the composition of two different ion species, proton and oxygen ions, in the near‐Earth plasma sheet (X = −16 RE ∼ −6 RE) during substorm‐associated dipolarization. We use 10 years of energetic (9–212 keV/e) ion data obtained by the suprathermal ion composition spectrometer (STICS) sensor of the energetic particles and ion composition (EPIC) instrument on board the Geotail spacecraft. The results are as follows: (1) Although the percentage increase in the energy density of O+ ions before and after a dipolarization exceeds that of H+ ions in the low‐energy range (9–36 keV/e), this property is not evident in the high‐energy range (56–212 keV/e); (2) the energy spectrum of H+ and that of O+ become harder after dipolarization in almost all events; and (3) in some events the energy spectrum of O+ becomes harder than that of H+ as reported by previous studies, and, importantly, in other events, the spectrum of H+ becomes harder than that of O+. In order to investigate what mechanism causes these observational results, we focus on magnetic field fluctuations during dipolarization. It is found that the increase of the spectrum slope is positively correlated with the power of waves whose frequencies are close to the gyrofrequency of H+ or O+, respectively (the correlation coefficient is 0.48 for H+ and 0.68 for O+). In conclusion, ions are nonadiabatically accelerated by the electric field induced by the magnetic field fluctuations whose frequencies are close to their gyrofrequencies.
Reanalyses of the radiation belt electron phase space density using nearly equatorial CRRES and polar‐orbiting Akebono satellite observations
Authors: Ni Binbin , Shprits Yuri , Nagai Tsugunobu , Thorne Richard , Chen Yue , Kondrashov Dmitri , Kim Hee‐jeong
Published: May 2009

Data assimilation techniques provide algorithms that allow for blending of incomplete and inaccurate data with physics‐based dynamic models to reconstruct the electron phase space density (PSD) in the radiation belts. In this study, we perform reanalyses of the radial PSD profile using two independent data sources from the nearly equatorial CRRES Medium Electron A (MEA) observations and the polar‐orbiting Akebono Radiation Monitor (RDM) measurements for a 50‐day period from 18 August to 6 October 1990. We utilize the University of California, Los Angeles, One‐Dimensional Versatile Electron Radiation Belt (UCLA 1‐D VERB) code and a Kalman filtering approach. Comparison of the reanalyses obtained independently using the CRRES MEA and Akebono RDM measurements shows that the dynamics of the PSD can be accurately reconstructed using Kalman filtering even when available data are sparse, inaccurate, and contaminated by random errors. The reanalyses exhibit similarities in the locations and magnitudes of peaks in radial profiles of PSD and the rate and radial extent of the dropouts during storms. This study shows that when unidirectional data are not available, pitch angle averaged flux measurements can be used to infer the long‐term behavior (climatology) of the radiation belts. The methodology of obtaining PSD from pitch angle averaged and unidirectional fluxes using the Tsyganenko and Stern (1996) magnetic field model is described in detail.
Evidence of dynamic recrystallization in polar firn
Authors: Kipfstuhl Sepp , Faria Sérgio H. , Azuma Nobuhiko , Freitag Johannes , Hamann Ilka , Kaufmann Patrik , Miller Heinrich , Weiler Karin , Wilhelms Frank
Published: May 2009

Microstructural analyses have been performed on polar firn from the European Project for Ice Coring in Antarctica drilling site in Dronning Maud Land, Antarctica. The results derived from images of the firn structure in microscopic resolution indicate that dynamic recrystallization is active in firn at all depths, and it dominates the evolution of the microstructure when the firn density exceeds a critical value of 730 kg/m3(overburden snow load ∼0.2 MPa). At the firn‐ice transition (density ∼820 kg/m3) the microstructure is characterized by many small grains and bulged or irregularly shaped grain boundaries. More than half of all grains show subgrain boundaries. Thus, strain‐induced boundary migration is an essential feature to describe the irregular grain structure. In agreement with previous studies, significant grain growth has been observed with depth for the largest grains in the samples. However, our microscopic analysis reveals that the grain growth with depth in fact vanishes if all grains larger than 65μm in diameter are taken into account. This result reflects the fact that the growth of the largest grains is counteracted by grain size reduction by shrinking and subdivision of old grains, as well as production of new grains. Consequently, previous conclusions that grain growth in polar firn is essentially analogous to normal grain growth in metallic and ceramic sinters and that the stored strain energy is small in comparison with grain boundary energy can no longer be supported. Additionally, our observations show that the incipience of dynamic recrystallization in polar ice sheets is not as sensitive to temperature as supposed so far. A discussion of the change of the mean grain size due to the measuring technique is imperative.
Direct measures of lateral velocity variation in the deep Earth
Authors: Sun Daoyuan , Helmberger Don , Ni Sidao , Bower Dan
Published: May 2009

Current tomographic models of the Earth display perturbations to a radial stratified reference model. However, structures in the deep mantle that are chemically dense with low Rayleigh numbers can develop enormous relief, perhaps with boundaries closer to vertical than to radial. Such features are hard to detect with present tomographic modeling techniques because the timing anomalies are based on long‐period filtered waveforms with complexity removed. Here we develop a new tool for processing array data on the basis of a decomposition referred to as a multipath detector, which can be used to distinguish between horizontal structure (in‐plane multipathing) and vertical (out‐of‐plane multipathing) directly from processing array waveforms. A lateral gradient coefficient based on this detector provides a direct constraint on the sharpness of the boundaries and material properties. We demonstrate the usefulness of this approach by processing samples of both P and S data from the Kaapvaal array in southern Africa, which are compared with synthetic predictions from a metastable dynamic model containing sharp edges. Both data and simulations produce timing gradients larger than 2 s/deg in azimuthal changes for S waves, where only minor effects are obtained for P waves. These results further validate the case for distinct chemistry inside the African Low Shear Velocity Province.
Frictional and hydrologic properties of clay‐rich fault gouge
Authors: Ikari Matt J. , Saffer Demian M. , Marone Chris
Published: May 2009

The slip behavior of major faults depends largely on the frictional and hydrologic properties of fault gouge. We report on laboratory experiments designed to measure the strength, friction constitutive properties, and permeability of a suite of saturated clay‐rich fault gouges, including: a 50:50% mixture of montmorillonite‐quartz, powdered illite shale, and powdered chlorite schist. Friction measurements indicate that clay‐rich gouges are consistently weak, with steady state coefficient of sliding friction of <0.35. The montmorillonite gouge (μ = 0.19–0.23) is consistently weaker than the illite and chlorite gouges (μ = 0.27–0.32). At effective normal stresses from 12 to 59 MPa, all gouges show velocity‐strengthening frictional behavior in the sliding velocity range 0.5–300 μm/s. We suggest that the velocity‐strengthening behavior we observe is related to saturation of real contact area, as documented by the friction parameter b, and is an inherent characteristic of noncohesive, unlithified clay‐rich gouge. Permeability normal to the gouge layer measured before, during, and after shear ranges from 8.3 × 10−21 m2 to 3.6 × 10−16 m2; permeability decreases dramatically with shearing, and to a lesser extent with increasing effective normal stress. The chlorite gouge is consistently more permeable than the montmorillonite and illite gouge and maintains a higher permeability after shearing. Permeability reduction via shear is pronounced at shear strains ≲5 and is smaller at higher strain, suggesting that shear‐induced permeability reduction is linked to fabric development early in the deformation history. Our results imply that the potential for development of excess pore pressure in low‐permeability fault gouge depends on both clay mineralogy and shear strain.
Effect of wind on continental shelf carbon fluxes off southeast Australia: A numerical model
Authors: Macdonald Helen S. , Baird Mark E. , Middleton Jason H.
Published: May 2009

A coupled physical‐biological‐chemical model is used to study the effect of upwelling‐favorable and downwelling‐favorable winds on carbon biogeochemistry on the continental shelf off the southeast Australian mainland. Along the continental shelf, from 30°S to 34°S, upwelling‐favorable winds, with the aid of bottom Ekman transport, bring dissolved‐inorganic‐carbon (DIC)‐rich slope waters onto the shelf, increasing the carbon held in shelf waters. For downwelling‐favorable winds, bottom Ekman transport still lifts slope waters onto the shelf, but the slope water transport, and therefore carbon held, is reduced compared with the upwelling scenario. Under upwelling‐favorable winds, filaments of DIC and dissolved‐inorganic‐nitrogen (DIN)‐rich water reaching the surface produce an outgassing near the site of upwelling and absorption downstream due to primary productivity. In a region of the ocean that is generally absorbing, the net effect of upwelling is a reduced absorption of atmospheric CO2 as a result of the ratio of deep DIC and DIN (12.2:1 mol C:mol N) being greater than the Redfield ratio (6.625). Carbon fluxes in the waters off the southeast Australian mainland are variable in space, with the transport of continental shelf waters to deep waters occurring mainly where alongshore currents separate from the coast and flow over the 200‐m isobath.
Localization of shear along a lithospheric strength discontinuity: Application of a continuous deformation model to the boundary between Tibet and the Tarim Basin
Authors: Dayem Katherine E. , Houseman Gregory A. , Molnar Peter
Published: May 2009

A marked contrast in strength (or viscosity) within a continuously deforming zone can lead to concentration of shear strain in the weaker material adjacent to the boundary between them, but localization comparable to the width of the Altyn Tagh shear zone requires an additional weakening process. During numerical experiments on a thin viscous sheet indented by a rigid object, a shear zone develops adjacent to a strong region mimicking the Tarim Basin, when the boundary between the weak and strong regions is oblique to the orientation of convergence. The width of this shear zone narrows with increased strain, and for comparable penetration by the indenter, the strain is more concentrated for larger values of n, the exponent that relates strain rate to a power of stress, and for smaller values of the Argand number Ar, a measure of buoyancy‐induced stress relative to viscous stress. Increasing concentration of shear occurs as the indentation develops without weakening because of a change in material properties. Additional localization develops with the inclusion of strain‐dependent weakening associated with, for instance, a temperature increase due to shear heating. For such localization to scale to the width of the Altyn Tagh fault zone of Tibet, the initial temperature near the Moho must be relatively low (∼600°C), and a large value of n (∼10) is required. This suggests that deformation there is described by a high‐strength flow law, such as that proposed by Evans and Goetze (1979), in which the lithosphere would deform approximately plastically.
Aerosol effects in the UV‐B spectral region over Pune, an urban site in India
Authors: Panicker A. S. , Pandithurai G. , Takamura T. , Pinker R. T.
Published: May 2009

Collocated measurements of UV‐B irradiance and aerosol optical characteristics have been carried out over Pune, western India from April 2004 to March 2005 to estimate the role of aerosols in UV‐B radiation at the surface. It is found that a unit increases in aerosol optical depth reduces by about 40–56% of the harmful UV‐B radiation that reaches the site. Ultraviolet‐impact on human health is usually characterized by the UV‐index (UV‐I), and is estimated with the aid of a radiative transfer model using aerosol and ozone measurements over the site. The index is found to be in the extreme range (10.1 to 13.5) during pre‐monsoon, high to extreme (8.5 to 11) during post‐ monsoon and high (7 to 10) during the winter seasons, vulnerable to sensitive skin. The estimated UV‐I values are found to be compared well with SCIAMACHY satellite observed UV‐I values with mean ratio of 0.95 ± 0.05.