bluuebunny/crossref_metadata_2025_split huggingface dataset:
The effects of a low-sodium base-producing diet including red meat compared with a high-carbohydrate, low-fat diet on bone turnover markers in women aged 45–75 years
Authors: Nowson Caryl A. , Patchett Annabelle , Wattanapenpaiboon Naiyana 
Published: May 2009

A randomised, parallel-design dietary intervention study was conducted in women (aged 45–75 years) with prehypertension or stage 1 hypertension. The aim was to compare the effects on bone turnover of a low-Na base-producing (LNAB) Dietary Approaches to Stop Hypertension (DASH)-type diet (including six serves lean red meat/week) with a high-carbohydrate low-fat (HCLF) diet with a higher acid load (both >800 mg dietary Ca/d). Fasting serum bone markers (baseline and week 14) and 24 h urinary electrolyte excretion (baseline, weeks 4, 8, 12 and 14) were measured. After the intervention period, the LNAB group (n46) had a fall of 26 (sem6) % (P < 0·0001) in urinary Na, an increase in K excretion (6·8 (sem3·6) mmol/d;P = 0·07) and, compared with the HCLF group (n49), a greater reduction in urinary Ca excretion by 0·7 (sem0·3) mmol/d. Serum 25-hydroxyvitamin D, intact parathyroid hormone and osteocalcin did not change, and both groups had a similar increase of 23 (sem5) % (P < 0·0001) in C-terminal telopeptide of type I collagen. The HCLF group had an 11 (sem4) % increase (P = 0·003) in N-terminal propeptide, type I procollagen, which could indicate an increased rate of bone turnover. The fall in urinary Ca with the lower-Na lower-acid load diet is likely to have long-term beneficial effects on bone. As bone resorption was not different between the two dietary patterns with relatively high Ca intake, the effect on bone health of a dietary pattern with a lower acid load warrants further study on a lower Ca intake.
Growth and nutrient intake among very-low-birth-weight infants fed fortified human milk during hospitalisation
Authors: Henriksen Christine , Westerberg Ane C. , Rønnestad Arild , Nakstad Britt , Veierød Marit B. , Drevon Christian A. , Iversen Per O. 
Published: May 2009

Postnatal growth failure in preterm infants is due to interactions between genetic and environmental factors, which are not fully understood. We assessed dietary supply of nutrients in very-low-birth-weight (VLBW, < 1500 g) infants fed fortified human milk, and examined the association between nutrient intake, medical factors and growth during hospitalisation lasting on average 70 d. We studied 127 VLBW infants during the early neonatal period. Data were obtained from medical records on nutrient intake, growth and growth-related factors. Extra-uterine growth restriction was defined as body weight < 10th percentile of the predicted value at discharge. Using logistic regression, we evaluated nutrient intake and other relevant factors associated with extra-uterine growth restriction in the subgroup of VLBW infants with adequate weight for gestational age at birth. The proportion of growth restriction was 33 % at birth and increased to 58 % at discharge from hospital. Recommended values for energy intake (>500 kJ/kg per d) and intra-uterine growth rate (15 g/kg per d) were not met, neither in the period from birth to 28 weeks post-conceptional age (PCA), nor from 37 weeks PCA to discharge. Factors negatively associated with growth restriction were energy intake (Ptrend = 0·002), non-Caucasian ethnicity (P = 0·04) and weight/predicted birth weight at birth (Ptrend = 0·004). Extra-uterine growth restriction is common in VLBW infants fed primarily fortified human milk. Currently recommended energy and nutrient intake for growing preterm infants was not achieved. Reduced energy supply and non-Caucasian ethnicity were risk factors for growth restriction at discharge from hospital.
Late Cretaceous–Early Eocene tectonic development of the Tethyan suture zone in the Erzincan area, Eastern Pontides, Turkey
Authors: RICE SAMUEL P. , ROBERTSON ALASTAIR H. F. , USTAÖMER TIMUR , İNAN NURDAN , TASLI KEMAL 
Published: May 2009

AbstractSix individual tectonostratigraphic units are identified within the İzmir–Ankara–Erzincan Suture Zone in the critical Erzincan area of the Eastern Pontides. The Ayıkayası Formation of Campanian–Maastrichtian age is composed of bedded pelagic limestones intercalated with polymict, massive conglomerates. The Ayıkayası Formation conformably overlies the Tauride passive margin sequence in the Munzur Mountains to the south and is interpreted as an underfilled foredeep basin. The Refahiye Complex, of possible Late Cretaceous age, is a partial ophiolite composed of ~75% (by volume) serpentinized peridotite (mainly harzburgite), ~20% diabase and minor amounts of gabbro and plagiogranite. The complex is interpreted as oceanic lithosphere that formed by spreading above a subduction zone. Unusual screens of metamorphic rocks (e.g. marble and schist) locally occur between sheeted diabase dykes. The Upper Cretaceous Karayaprak Mélange exhibits two lithological associations: (1) the basalt + radiolarite + serpentinite association, including depleted arc-type basalts; (2) the massive neritic limestone + lava + volcaniclastic association that includes fractionated, intermediate-composition lavas, and is interpreted as accreted Neotethyan seamount(s). The several-kilometre-thick Karadağ Formation, of Campanian–Maastrichtian age, is composed of greenschist-facies volcanogenic rocks of mainly basaltic to andesitic composition, and is interpreted as an emplaced Upper Cretaceous volcanic arc. The Campanian–Early Eocene Sütpınar Formation (~1500 m thick) is a coarsening-upward succession of turbiditic calcarenite, sandstone, laminated mudrock, volcaniclastic sedimentary rocks that includes rare andesitic lava, and is interpreted as a regressive forearc basin. The Late Paleocene–Eocene Sipikör Formation is a laterally varied succession of shallow-marine carbonate and siliciclastic lithofacies that overlies deformed Upper Cretaceous units with an angular unconformity. Structural study indicates that the assembled accretionary prism, supra-subduction zone-type oceanic lithosphere and volcanic arc units were emplaced northwards onto the Eurasian margin and also southwards onto the Tauride (Gondwana-related) margin during Campanian–Maastrichtian time. Further, mainly southward thrusting took place during the Eocene in this area, related to final closure of Tethys. Our preferred tectonic model involves northward subduction, supra-subduction zone ophiolite genesis and arc magmatism near the northerly, Eurasian margin of the Mesozoic Tethys.
Proof of a conjecture of Ramanujan
Authors: Atkin A. O. L. 
Published: May 2009

We writeandso thatp(n) is the number of unrestricted partitions ofn. Ramanujan [1] conjectured in 1919 that ifq= 5, 7, or 11, and 24m≡ 1 (modqn), then p(m) ≡ 0 (modqn). He proved his conecture forn= 1 and 2†, but it was not until 1938 that Watson [4] proved the conjecture forq= 5 and alln, and a suitably modified form forq= 7 and alln. (Chowla [5] had previously observed that the conjecture failed forq= 7 andn= 3.) Watson's method of modular equations, while theoretically available for the caseq= 11, does not seem to be so in practice even with the help of present-day computers. Lehner [6, 7] has developed an essentially different method, which, while not as powerful as Watson's in the cases where Γ0(q) has genus zero, is applicable in principle to all primesqwithout prohibitive calculation. In particular he proved the conjecture forq= 11 andn= 3 in [7]. Here I shall prove the conjecture forq= 11 and alln, following Lehner's approach rather than Watson's. I also prove the analogous and essentially simpler result forc(m), the Fourier coefficient‡ of Klein's modular invariantj(τ) as
A new class of Hadamard matrices
Authors: Spence E. 
Published: May 2009

A Hadamard matrixHis an orthogonal square matrix of ordermall the entries of which are either + 1 or - 1; i. e.whereH′denotes the transpose ofHandImis the identity matrix of orderm. For such a matrix to exist it is necessary [1] thatIt has been conjectured, but not yet proved, that this condition is also sufficient. However, many values ofmhave been found for which a Hadamard matrix of ordermcan be constructed. The following is a list of suchm(pdenotes an odd prime).
On Riemann surfaces with maximal automorphism groups
Authors: Lehner Joseph , Newman Morris 
Published: May 2009

Let S be a closed Riemann surface of genusg > 1,so that Ŝ, the universal covering surface of S, is hyperbolic. We can then uniformize S by a discrete, nonabelian group Γ1 of Möbius transformations of the upper half-plane ℋ. It follows that N1 = NΩ(Γ1) is discrete; here N1is the normalizer of Γ in Ω, the group of (conformal) automorphisms of ℋ. An automorphism of S can be lifted to a coset of Nl/Γl. Hence C(S), the group of automorphisms of S, is isomorphic to Nl/Γ1. The order of C = C(S) equals the index of Γ1 in N1, which in turn equals ⃒Γ1⃒ / ⃒Nl⃒, where ⃒Nl⃒ is the hyperbolic area of a fundamental region of Nl. Since Γ1 uniformizes a surface, we have ⃒Γ1⃒ = 4π(g – 1), while, by Siegel's results [7], ⃒N1 ⃒ ≧ π/21 and N1 can only be the triangle group (2, 3, 7). Hence in all cases the order of C(S) is at most 84(g–1), an old result of Hurwitz [1]. The surfaces that permit a maximal automorphism group (= automorphism group of maximum order) can therefore be obtained by studying the finite factor groups of (2, 3, 7). Such a treatment, purely algebraic in nature, has been promised by Macbeath [5].
Remarks on the asymptotic behaviour of perturbed linear systems
Authors: Wong James S. W. 
Published: May 2009

We are here concerned with following result of Trench:Theorem. (Trench [5]). Let v1 and v2 be two linearly independent solutions of the differential equationwhere a(t) is continuous on [0, ∞), and let b(t) be a continuous function of t for t ≧ 0 satisfyingwhere m(t) = max {|v1(t)|2, |v2(t)|2}. Then, if α1and α2are two arbitrary constants, there exists a solution u ofwhich can be written in the form,withfori = 1, 2.
A variance method in combinatorial number theory
Authors: Anderson Ian 
Published: May 2009

Let s = s(a1, a2,...., ar) denote the number of integer solutions of the equationsubject to the conditionsthe ai being given positive integers, and square brackets denoting the integral part. Clearly s (a1,..., ar) is also the number s = s(m) of divisors of which contain exactly λ prime factors counted according to multiplicity, and is therefore, as is proved in [1], the cardinality of the largest possible set of divisors of m, no one of which divides another.
The wave, Laplace, and heat equations and related transforms
Authors: Dettman J. W. 
Published: May 2009

This paper is concerned with three basic transformsThe first of these has been studied by Widder [1], who points out that f(t) can be interpreted as the temperature u(0, t) on the time axis, where u(x, t) is the solution of the heat equation withsymmetric initial temperature u(x, 0) = g(|x|). The second has also been studied by Widder [2], where it is pointed out that f(t) can be interpreted as the value of the harmonic function u(x, t) on the t-axis arising from the boundary data u(x, 0) = g(|x|).
A note on Köthe spaces
Authors: Các Nguyen Phuong 
Published: May 2009

LetEbe a locally compact space which can be expressed as the union of an increasing sequence of compact subsetsKn(n=1, 2, …) and let μ be a positive Radon measure onE. Ω is the space of equivalence classes of locally integrable functions onE. We denote the equivalence class of a function f byand ifis an equivalence class then f denotes any function belonging to f. Provided with the topology defined by the sequence of seminormsΩ is a Fréchet space. The dual of Ω is the space φ of equivalence classes of measurable, p.p. bounded functions vanishing outside a compact subset ofE. For a subset Γ of Ω, the collection Λ of all∊Ω, such that for eachg∊Γ the productfgis integrable, is called a Köthe space and Γ is said to be the denning set of Λ. The Köthe space Λxwhich has Λ as a denning set is called the associated Kothe space of Λ. Λ and Λxare put into duality by the bilinear form
Kleinian groups with unbounded limit sets
Authors: Beardon A. F. 
Published: May 2009

The easiest way to construct automorphic functions is by means of the Poincaré series. If G is a Kleinian group with ∞ an ordinary point of G and if k ≧ 4, thenwhere Vz=(az+b)/(cz+d) and ad-bc=1. The convergence of this series is the crucial step in showing that the Poincaré series converges and is an automorphic form on G If ∞ is a limit point of ∞ the series in (1) may diverge and one can derive automorphic forms on ∞ from the Poincaré series of some conjugate group. These constructions are described in greater detail in /3, pp. 155–165].
Boundary value problems of singular elliptic partial differential equations
Authors: Lo Chi Yeung 
Published: May 2009

In a recent paper [6], this author has extended the method of the kernel function [1] to the boundary value problems of the generalized axially symmetric potentialsThis method can also be applied to a more general class of singular differential equations, namelyor, equivalently,We shall derive in the sequel explicit formulas for the Dirichlet problems of (1.1) in the first quadrant of the x-y plane in terms of sufficiently smooth boundary data, and obtain an error-bound for their approximate solutions. We shall also indicate how the Neumann problem can be solved.
Compactness and ordinals
Authors: Knight C. J. 
Published: May 2009

If p and q are cardinal numbers and E is a topological space, then the following property may or may not hold:Every cover of Eby fewer than q open sets has a subcover by fewer than pof them. (1)Clearly these properties, for various numbers p and q, are far from being independent; in this paper, we investigate some of the interrelationships between them.
On two-sided artinian quotient rings
Authors: Smith P. F. 
Published: May 2009

Djabali [1] has proved that, if R is a right and left noetherian ring with an identity and if the proper prime ideals of R are maximal, then R has a right and left artinian two-sided quotient ring. Robson [5, Theorem 2.11] and Small [6, Theorem 2.13] have proved independently that, if Ris a commutative noetherian ring, then Rhas an artinian quotient ring if and only if the prime ideals of Rthat belong to the zero ideal are all minimal. We shall generalise these results by proving theTheorem. Let R be a right and left noetherian ring with a regular element. Then R has a right and left artinian two-sided quotient ring if and only if each prime ideal of R consisting of zero–divisors is minimal.
Commutative rings whose quotients are Goldie
Authors: Camillo Victor P. 
Published: May 2009

All rings considered here have units. A (non-commutative) ring is right Goldieif it has no infinite direct sums of right ideals and has the ascending chain condition on annihilator right ideals. A right ideal A is an annihilator if it is of the form {a ∈ R/xa = 0 for all x ∈ X}, where X is some subset of R. Naturally, any noetherian ring is Goldie, but so is any commutative domain, so that the converse is not true. On the other hand, since any quotient ring of a noetherian ring is noetherian, it is true that every quotient is Goldie. A reasonable question therefore is the following: must a ring, such that every quotient ring is Goldie, be noetherian? We prove the following theorem:Theorem. A commutative ring is noetherian if and only if every quotient is Goldie.
On ranges of Lyapunov transformations IV
Authors: Loewy Raphael 
Published: May 2009

Let ℂn,n denote the space of n × n matrices with complex entries and let ℋn denote the set of n × n hermitian matrices. Given any matrix A∊ℂn,n, the Lyapunov transformation corresponding to A is defined by ℐA(H) = AH+HA*, where H∊ℋn. Let PSD(n) be the set of all n × n hermitian positive semidefinite matrices. Taussky [8, 9] raised the problems of determiningandBoth of these problems seem to be difficult.
The diophantine equation (X[X − 1])2 = 3Y[Y − 1]
Authors: Veluppillai Manoranjitham 
Published: May 2009

The object of this paper is to prove that the only non-trivial solution in positive integers of the equation of the title is X = 3, Y = 4.Substituting x = 2X – 1, y = 2Y – 1 gives with a little manipulation
On topological spaces with a unique compatible quasi-uniformity
Authors: Brown Lawrence M. 
Published: May 2009

It is shown in [2] that a uqu space satisfies the following conditions.(DC) There is no infinite, strictly decreasing sequence of open sets with open intersection.(IC) There is no infinite, strictly increasing sequence of open sets.In this note we show that for a transitive space these conditions are sufficient for the space to be uqu. This will follow as a consequence of the following result.
A bipartite Ramsey problem and the Zarankiewicz numbers
Authors: Irving Robert W. 
Published: May 2009

Beineke and Schwenk [1] have defined the bipartite Ramsey number R(m,n), for integers m, n (1≤m≤n ), to be the smallest integer p such that any 2-colouring of the edges of the complete bipartite graph Kp, v forces the appearance of a monochromatic Km, n. In [1] the following results are established:with equality if there is a Hadamard matrix of order 2(n−1), n odd,if there is a Hadamard matrix of order 4(n−1),
On images and inverse images of Weierstrass points
Authors: Lax R. F. 
Published: May 2009

The classical theory of Weierstrass points on a compact Riemann surface is well-known (see, for example, [3]). Ogawa [6] has defined generalized Weierstrass points. Let Y denote a compact complex manifold of (complex) dimension n. Let E denote a holomorphic vector bundle on Y of rank q. Let Jk(E) (k = 0, 1, …) denote the holomorphic vector bundle of k-jets of E [2, p. 112]. Put rk(E) = rank Jk(E) = q.(n + k)!/n!k!. Suppose that Γ(E), the vector space of global holomorphic sections of E, is of dimension γ(E)>0. Consider the trivial bundle Y × Γ(E) and the mapwhich at a point Q∈Y takes a section of E to its k-jet at Q. Put μ = min(γ(E),rk(E)).
Lower central depth in finitely generated soluble-by-finite groups
Authors: Lennox John C. 
Published: May 2009

We say that a group G has finite lower central depth (or simply, finite depth) if the lower central series of G stabilises after a finite number of steps.In [1], we proved that if G is a finitely generated soluble group in which each two generator subgroup has finite depth then G is a finite-by-nilpotent group. Here, in answer to a question of R. Baer, we prove the following stronger version of this result.
Discrete free products of two complex cyclic matrix groups
Authors: Evans Ronald J. 
Published: May 2009

All 2-by-2 matrices in this paper are to be viewed as linear fractional transformations on the extended complex plane ℂ*. Let L+ and L− be the open half-planes to the right and left, respectively, of the extended imaginary axis L. Let Λ be the set of complex 2-by-2 matrices A with real trace and determinant ±1 such that A(L+) ⊂L−. Let Ω = Ω1 ∪ Ω2 ∪ Ω3 ∪ Ω4, Whereand
On well-bounded operators of class Г
Authors: Jibril Adnan A. S. 
Published: May 2009

Let T be a linear operator acting in a Banach space X. It has been shown by Smart [5] and Ringrose [3] that, if X is reflexive, then T is well-bounded if and only if it may be expressed in the formwhere {E(λ)} is a suitable family of projections in X and the integral exists as the strong limit of Riemann sums.
Fonction de Hilbert-Samuel dans les anneaux locaux réguliers non-commutatifs
Authors: Alev J. 
Published: May 2009

En algèbre non-commutative, on dit qu'un anneau noethérien A est local si:(i) le radical de Jacobson M de A est un idéal maximal,(ii) ∩ Mn = (0),(iii) A/M est artinien simple.Dans [9], Walker definit un anneau local régulier comme un anneau local A dont le radical de Jacobson M est engendré par une A-suite centralisante x1; x2, …, xt, [4], et demontre alors que:t = cldim A = Kdim A = rgldim A = pdAA/M.
The number of sparsely edged labelled Hamiltonian graphs
Authors: Wright E. M. 
Published: May 2009

An (n, q) graph is a graph on n labelled points and q lines, no loops and no multiple lines. We write N = ½n(n – 1), B(a, b) = a!/{b!(a – b)!} and B(a, 0) = 1, so that there are just B(N, q)different (n, q) graphs. Again h(n, q) is the number of Hamiltonian (n, q) graphs. Much attention has been devoted to the problem of determining for which q = q(n) “almost all” (n, q) graphs are Hamiltonian, i.e. for which q we haveas n → ∞. I proved [8, Theorem 4] that qn–3/2; → ∞ is a sufficient condition by showing that, for such q, almost all (n, q) graphs have about the average number of Hamiltonian circuits (H.c.s).
Subalgebras of C*-algebras and von Neumann algebras
Authors: Akemann Charles A. 
Published: May 2009

Recent work [2, 6] on subalgebras of matrix algebras leads naturally to the following situation. Let A be a C*-subalgebra of the C*-algebra B andM be a weakly closed *-subalgebra of the von Neumann algebra N. Consider the following Conditions.Condition 1. For every b≠ 0 in B there exists a ∈ A such that O≠ab ∈ A.Condition 2. For every b∈B there exists a ≠ 0 in A such that ab ∈ A.If we replace A by M and B by N in Conditions 1 and 2 we get von Neumann algebra versions which we shall call Condition 1'and Condition 2'. Clearly Condition 1 implies Condition 2, and both conditions suggest that A is some kind of weak ideal of B. This paper explores the extent to which this is true. The paper grew out of the author's attempts [1, 3] to generalize the Stone-Weierstrass theorem to C*-algebras.
On Dirichlet series attached to cusp forms and the Siegel-zero
Authors: Grupp F. 
Published: May 2009

Let k be an even integer greater than or equal to 12 and f an nonzero cusp form of weight k on SL(2, Z). We assume, further, that f is an eigenfunction for all Hecke-Operators and has the Fourier expansionFor every Dirichlet character xmod Q we define
A spectral approach to an integral equation
Authors: Lamb W. 
Published: May 2009

In a recent paper [7], Rooney used a technique involving the Mellin transform to obtain solutions in certain spaces ℒμ, ρ of an integral equation which had been studied previously by Šub-Sizonenko [9]. The integral equation in question can be written aswhere I denotes the identity operator and G0.1/2 is given bywith the inversion formula obtained by Rooney taking the formRooney verified that (1.1) and (1.2) formed an inversion pair in ℒμ, ρ for 1 ≤ p < ∞ and μ > 0.
On the cohomology of loop spaces of compact Lie groups
Authors: Hiller Howard 
Published: May 2009

Let G be a compact, simply-connected Lie group. The cohomology of the loop space ΏG has been described by Bott, both in terms of a cell decomposition [1] and certain homogeneous spaces called generating varieties [2]. It is possible to view ΏG as an infinite dimensional “Grassmannian” associated to an appropriate infinite dimensional group, cf. [3], [7]. From this point of view the above cell-decomposition of Bott arises from a Bruhat decomposition of the associated group. We choose a generator H ∈ H2(ΏG, ℤ) and call it the hyperplane class. For a finite-dimensional Grassmannian the highest power of H carries geometric information about the variety, namely, its degree. An analogous question for ΏG is: What is the largest integer Nk = Nk(G) which divides Hk ∈ H2k(ΏG, ℤ)?Of course, if G = SU(2) = S3, one knows Nk = h!. In general, the deviation of Nk from k! measures the failure of H to generate a divided polynomial algebra in H*(ΏG, ℤ).
Biduals of Banach spaces with bases
Authors: Bellenot Steven F. 
Published: May 2009

R. C. James [2] (or see p. 7ff of [3]) gave a useful representation of the bidual of any space with a shrinking basis. This note gives a representation of the bidual of any space with a basis.Our notation follows that of [3], where undefined terms can be found. Let {en} be a basic sequence with coefficient functionals {fn}. We will assume {en} is bimonotone; that is. The space {en}LIM is the set of scalar sequences {an} so that ∥{an}∥ = . We will abuse notation and squate such {an} with the formal sum Σ anen.