bluuebunny/crossref_metadata_2025_split huggingface dataset:
Uniqueness of Compatible Quasi-Uniformities
Authors: Votaw Charles I. 
Published: December 2010

AbstractIt is shown that a topological space has a unique compatible quasi-uniformity if its topology is finite. Examples are given to show the converse is false for T1 and for normal second countable spaces. Two sufficient conditions are given for a topological space to have a compatible quasi-uniformity strictly finer than the associated Császár-Pervin quasi-uniformity. These conditions are used to show that a Hausdorff, semi-regular or first countable T1 space has a unique compatible quasi-uniformity if and only if its topology is finite. Császár and Pervin described, in quite different ways, quasi-uniformities which induce a given topology. It is shown that, for a given topological space, Császár and Pervin described the same quasi-uniformity.
On Nagumo's Condition
Authors: Rogers Thomas 
Published: December 2010

The classical uniqueness theorem of Nagumo [1] for ordinary differential equations is as follows.Theorem. If f(t, y) is continuous on 0≤t≤1, -∞<y<∞ and ifthen there is at most one solution to the initial value problem y'=f(t, y), y(0)=0.
Oscillation Criteria for Matrix Differential Inequalities(1)
Authors: Allegretto W. , Erbe L. 
Published: December 2010

Several authors have recently considered the problem of obtaining sufficient conditions for the oscillation of the quasilinear matrix differential equation(1)and the associated inequality VTLV ≤ 0 (as a form). Here A, B, and V are m x m matrix functions, A(x) is symmetric, positive semidefinite and continuous in an interval [a, ∞) and B(x,V, V') is symmetric and continuous in a≤ x < ∞ for all V and V'.
A Divergence-Free Antisymmetric Tensor
Authors: Tupper B. O. J. 
Published: December 2010

Consider a Vn with metric tensor gαβ. It is well known that the only tensor containing derivatives of gαβno higher than the second order, linear in the second order derivatives, and having vanishing covariant divergence is the Einstein tensor(1)Suppose that a system of ennuple vectors hiαand their inverses hαi is set up at each point of the Vn.
On Characterizations of Conditional Expectation
Authors: Al-Hussaini A. N. 
Published: December 2010

In the following (Ω, α, μ) is a totally σ-finite measure space except where noted. For a sub-σ-algebra β ⊂ α, the conditional expectation E{f|β} off given β is a function measurable relative to β, such thatIn [5] R.G.Douglas proved, among other things the following, in the finite case:Suppose μ(Ω)=l. Then a linear operator T on L1(Ω, α,μ) is a conditional expect ion if and only if1.11.21.3The point of this note is to characterize conditional expectation in the σ-finite case (Theorems 2, 3).
Theoreme de Müntz Pour les Fonctions de Plusieurs Variables
Authors: Aupetit Bernard H. 
Published: December 2010

Le théorème de Weierstrass affirme que toute fonction réelle continue sur l'intervalle [0, 1] est limite uniforme d'une suite de polynômes (voir [5]). Dans [4], Ch. Müntz généralise ce résultat de la façon suivante.Soit α1, α2, α3,… une suite strictement croissante et non bornée de nombres réels.
A New Method in Arithmetical Functions and Contour Integration
Authors: Berndt Bruce C. 
Published: December 2010

If f is a suitable meromorphic function, then by a classical technique in the calculus of residues, one can evaluate in closed form series of the form,Suppose that a(n) is an arithmetical function. It is natural to ask whether or not one can evaluate by contour integration(1.1)where f belongs to a suitable class of meromorphic functions. We shall give here only a partial answer for a very limited class of arithmetical functions.
Note on "Paracompactness in Small Products"
Authors: Chew James 
Published: December 2010

In [1], Willard proves the followingIf a regular paracompact space X has a dense Lindelöfsubspace, then X is Lindelöf.Willard notes that the above is a generalization of the standard theorem: A separable paracompact space is Lindelöf. Actually, it is a standard fact ([2, p. 24]) that a separable metacompact space is Lindelöf. Moreover, one discovers that if a separable space X is such that each open cover of X has a point-countable open refinement, then X is Lindelöf.
Inclusion Relations for General Riesz Typical Means
Authors: Jakimovski A. , Tzimbalario J. 
Published: December 2010

Let α be a non-negative real number, λ≡{λ,n}(n≥0) a strictly increasing unbounded sequence with λ0≥0 and let be an arbitrary series with partial sums s≡{sn}. Writewhere s(t)=sn for λn<t≤λn+1, s(t)=0 for 0≤t≤λ0. The series ∑ an or the sequence of partial sums s={sn} is summable to ṡ by the Riesz method (R, λ, α) ifas ω→∞.
A Singular Perturbation Problem and A Neutral Differential-Difference Equation
Authors: Moore Edward 
Published: December 2010

Vasil’eva, [2], demonstrates a close connection between the explicit formulae for solutions to the linear difference equation with constant coefficients(1.1)where z is an n-vector, A an n×n constant matrix, τ>0, and a corresponding differential equation with constant coefficients(1.2)(1.2) is obtained from (1.1) by replacing the difference z(t—τ) by the first two terms of its Taylor Series expansion, combined with a suitable rearrangement of the terms.
On A Problem of Purdy Related to Sperner Systems
Authors: Schonheim J. 
Published: December 2010

Purdy asked whether the following conjecture is trueConjecture. Let E be a set of 2n elements. If S={Sl, S2, …, St} is a Sperner system of E, i.e. for i≠j, i, j, =1, 2, …, t; and if(1)thenThe proof of the conjecture will be obtained using the following theorem of Katona (Acta Math. 15 (1964), 329-337):
The Influence on a Finite Group of its Permutable Subgroups
Authors: Agrawal Ram K. 
Published: December 2010

Huppert, Janko and Mann have proved the following theorems for a finite group G.(Huppert [4]). If each second maximal subgroup of G is normal in G, then G is supersolvable. If the order of G is divisible by at least three different primes, then G is nilpotent.(Huppert [4]). Let each third maximal subgroup of G be normal in G. Then: (i) G′ is nilpotent; (ii) the rank of G=r(G)≤2; (iii) if |G| is divisible by at least three different primes, then G is supersolvable.
Modules Et Anneaux Quasi-Continus
Authors: Jeremy Louis 
Published: December 2010

Le but de ce travail est de prolonger les travaux de Y. Utumi sur les anneaux continus.Nous appelons module quasi-continu un module stable par tout projecteur de son enveloppe injective. Un anneau unitaire A est dit quasi-continu à gauche (resp. à droite) si le A-module à gauche (resp. à droite ) est quasi-continu. Cette définition est plus générale que celle d'anneau continu à gauche donnée par Yuzo Utumi, et quand l'anneau est régulier, elles coïncident (§111).
A Note on the Rate of Convergence of Hermite-Fejér Interpolation Polynomials*
Authors: Saxena R. B. 
Published: December 2010

The Hermite-Fejér interpolation polynomial Hn[f] of degree ≤2n—1 is defined by(1)Where(2)are the zeroes of Chebyshev polynomial of first kind Tn(x)=cos n(arc cos x).
A General and Sharpened form of Opial's Inequality
Authors: Shum D. T. 
Published: December 2010

Z. Opial [11] proved in 1960 the following theorem:Theorem 1. If u is a continuously differentiable function on [0, b], and if u(0)= u(b)=0 and u(x) > 0 for x ∊ (0, b), then1where the constant b/4 is the best possible.
A Note on Klein’s Oscillation Theorem for Periodic Boundary Conditions
Authors: Faierman M. 
Published: December 2010

Recently Howe [4] has considered the oscillation theory for the two-parameter eigenvalue problem1a1bsubjected to the boundary conditions2a2bwhere for i = 1, 2, — ∞<ai<bi<∞, and qi are real-valued, continuous functions in [ai, bi], pi is positive in [ai, biz], and pi(ai)=pi(bi). Furthermore, it is also assumed that (A1B2—A2B1)≠0 for all values of x1 and x2 in their respective intervals.
Hamiltonian Circuits on the N-Cube
Authors: Smith D. H. 
Published: December 2010

The problem of finding bounds for the number h(n) of Hamiltonian circuits on the n-cube has been studied by several authors, (1), (2), (3). The best upper bound known is due to Larman (5) who proved that .In this paper we use a result of Nijenhuis and Wilf (4) on permanents of (0, 1)- matrices to show that for n≥5where τ, a and c are constants.
Conditions for a Zero Sum Modulo n
Authors: Bovey J. D. , Erdös Paul , Niven Ivan 
Published: December 2010

In this paper the following result is proved.Let n > 0 and k ≥ 0 be integers with n — 2k ≥ 1. Given any n — k integersthere is a non-empty subset of indices I ⊂ {1, 2,…, n — k} such that the sum Σi∊I ≡ 0(mod n) if at most n — 2k of the integers (1) lie in the same residue class modulo n.The result is best possible if n ≥ 3k — 2 in the sense that if "at most n — 2k" is replaced by "at most n — 2k + 1" the result becomes false. This can be seen by taking aj = 1 for 1 ≤ j ≤ n — 2k + 1 and aj = 2 for n —2k + 2 ≤ j ≤ n — k, noting that the number of 2's here is n — k — (n — 2k + 1)= k — 1 ≤ n — 2k + 1.
Most Power Series have Radius of Convergence 0 or 1*
Authors: Fournier J. J. F. , Gauthier P. M. 
Published: December 2010

Consider a random power series Σ0∞ cn zn, that is, with coefficients {cn}0∞ chosen independently at random from the complex plane. What is the radius of convergence of such a series likely to be?One approach to this question is to let the {cn}0∞ be independent random variables on some probability space. It turns out that, with probability one, the radius of convergence is constant. Moreover, if the cn are symmetric and have the same distribution, then the circle of convergence is almost surely a natural boundary for the analytic function given by the power series (See [1, Ch. IV, Section 3]). Our treatment of the question will be elementary and will not use these facts.
The Maximal Ideal Space of Subalgebras of the Disk Algebra
Authors: Lund Bruce 
Published: December 2010

Let X be a compact Hausdorff space and C(X) the complexvalued continuous functions on X. We say A is a function algebra on X if A is a point separating, uniformly closed subalgebra of C(X) containing the constant functions. Equipped with the sup-norm ‖f‖ = sup{|f(x)|: x ∊ X} for f ∊ A, A is a Banach algebra. Let MA denote the maximal ideal space.Let D be the closed unit disk in C and let U be the open unit disk. We call A(D)={f ∊ C(D):f is analytic on U} the disk algebra. Let T be the unit circle and set C1(T) = {f ∊ C(T): f'(t) ∊ C(T)}.
Note on Integers Representable by Binary Quadratic Forms
Authors: Williams Kenneth S. 
Published: December 2010

Let B be the set of positive integers prime to d which are representable by some primitive, positive, integral binary quadratic form of discriminant d. It is the purpose of this note to show that the following asymptotic estimate for the number of integers in B less than or equal to x can be proved using only elementary arguments:(1)where c1 is the positive constant given in (17) below. (Using the deeper methods of complex analysis James [2] has proved this result with the error term ((log x)-1/2) replacing ((log log x)-1). Heupel [1] using a transcendental method as in James [2] improved this to ((log x)-1).)
Absolutely Continuous Measures on Locally Compact Semigroups(1)
Authors: Wong James C. S. 
Published: December 2010

AbstractLet S be a locally compact Borel subsemigroup of a locally compact semigroup G. It is shown that the algebra of all "absolutely continuous' measures on S is isometrically order isomorphic to the algebra of all measures in M(G) which are "concentrated" and "absolutely continuous" on S.
On a Theorem of Rav Concerning Egyptian Fractions
Authors: Webb William A. 
Published: December 2010

Problems involving Egyptian fractions (rationals whose numerator is 1 and whose denominator is a positive integer) have been extensively studied. (See [1] for a more complete bibliography). Some of the most interesting questions, many still unsolved, concern the solvability ofwhere k is fixed.In [2] Rav proved necessary and sufficient conditions for the solvabilty of the above equation, as a consequence of some other theorems which are rather complicated in their proofs. In this note we give a short, elementary proof of this theorem, and at the same time generalize it slightly.
Semi-Simple Artinian Rings of Fixed Points
Authors: Cohen Miriam , Montgomery Susan 
Published: December 2010

Let G be a finite group of automorphisms of the ring R, and let RG denote the ring of fixed points of G in R; that is, RG={x∊R|Xg = x,∀∊ G}. Let |G| denote the order of G. In this note, we prove the following:Theorem.Assume that R has no nilpotent ideals and no |G|-torsion. Then if RG is semi-simple Artinian, R is semi-simple Artinian.
On Ring Properties of Injective Hulls
Authors: Lang N. C. 
Published: December 2010

Let R be an associative ring and denote by the injective hull of the right module RR. If can be endowed with a ring multiplication which extends the existing module multiplication, we say that is a ring and the statement that R is a ring will always mean in this sense.It is known that is a regular ring (in the sense of von Neumann) if and only if the singular ideal of R is zero.
A Note on Upper Bounds for the Eigenvalues ofy″ + λpy=0
Authors: Gentry Rodney D. 
Published: December 2010

The natural modes of a small planar transversal vibration of a fixed string of unit length and tension are determined by the eigenvalues and associated eigenfunctions of the differential equation(1)subject to the boundary condition(2)where the non-negative functionpdescribes the mass distribution of the string. That the distribution of mass on the string influences the modes of vibration, may be reflected by observing that the eigenvalues determined by the system (1–2) may be considered functions of the densityp, λn(p), where λ1(p)<λ2(p)<….
Degrees of Vertices in a Friendship Graph
Authors: Kotzig Anton 
Published: December 2010

AbstractA friendship graph is a graph in which every two distinct vertices have exactly one common adjacent vertex (called a neighbour). Finite friendship graphs have been characterized by Erdós, Rényi and Sós [2]: Each finite friendship graph Fn which consists of n edge disjoint triangles such that all n>1 triangles have one vertex in common (F1 is a triangle i.e. the complete graph with three vertices). Thus Fn has 2n+1 vertices, 2n of them being of degree two and the remaining one (the common vertex of n triangles if n>1) being of degree 2n.
The Range of a Gap Series
Authors: Hwang J. S. 
Published: December 2010

Theorem. Letbe a function holomorphic in the disk, wherep is a natural number andIfthen then f(z) assumes every complex value infinitely often in every sector.The purpose of this note is to prove the above result. To do this, we first observe that from the condition a<∞, we can easily show that the derivative f′(z) satisfying
Modules Whose Cyclic Submodules Have Finite Dimension
Authors: Berry David 
Published: December 2010

R denotes an associative ring with identity. Module means unitary right R-module. A module has finite Goldie dimension over R if it does not contain an infinite direct sum of nonzero submodules [6]. We say R has finite (right) dimension if it has finite dimension as a right R-module. We denote the fact that M has finite dimension by dim (M)<∞.A nonzero submodule N of a module M is large in M if N has nontrivial intersection with nonzero submodules of M [7]. In this case M is called an essential extension of N. N⊆′M will denote N is essential (large) in M. If N has no proper essential extension in M, then N is closed in M. An injective essential extension of M, denoted I(M), is called the injective hull of M.
On the Property (PU) for *-Regular Rank Rings
Authors: Burke John L. 
Published: December 2010

In this paper we consider an irreducible *-regular ring with order k for some k≥4. If is also a Baer ring it is a rank ring. Our first result is:Theorem 1.3. Let be an irreducible *-regular Baer ring with order k for some k≥4. The following are equivalent.
Alternating Chebyshev Approximation with A Non-Continuous Weight Function
Authors: Dunham Charles B. 
Published: December 2010

Let [α, β] be a closed interval and C[α, β] be the space of continuous functions on [α, β], For g a function on [α, β] defineLet s be a non-negative function on [α, β]. Let F be an approximating function with parameter space P such that F(A, .)∊ C[α, β] for all A∊P. The Chebyshev problem with weight s is given f ∊ C[α, β], to find a parameter A* ∊ P to minimize e(A) = ||s * (f - F(A, .))|| over A∊P. Such a parameter A* is called best and F(A*,.) is called a best approximation to f.
Local Compactness in Set Valued Function Spaces
Authors: Kaul Saroop K. 
Published: December 2010

Recently Hunsaker and Naimpally [2] have proved: The pointwise closure of an equicontinuous family of point compact relations from a compact T2-space to a locally compact uniform space is locally compact in the topology of uniform convergence. This is a generalization of the same result of Fuller [1] for single valued continuous functions.For a range space which is locally compact normal and uniform theorem B below is an improvement on the result of Hunsaker and Naimpally quoted above [see Remark 3 at the end of this paper].
Closure Theorem for Analytic Subgroups of Real Lie Groups
Authors: Djoković D. Ž. 
Published: December 2010

Let G be a real Lie group, A a closed subgroup of G and B an analytic subgroup of G. Assume that B normalizes A and that AB is closed in G. Then our main result (Theorem 1) asserts that .This result generalizes Lemma 2 in the paper [4], G. Hochschild has pointed out to me that the proof of that lemma given in [4] is not complete but that it can be easily completed.
About the # Function
Authors: Klincsek G. T. 
Published: December 2010

AbstractThe use of decreasing rearrangement formulas, and particularly that of the weak N inequality, is illustrated by deriving from Eτ |f-f(τ -)|≤Eτu (where ft is some stochastic process and τ arbitrary stopping time) the estimate ||f||≤Const||u|| in the class of structureless norms with finite dual Hardy bound.The basic estimate is
Beatty Sequences, Continued Fractions, and Certain Shift Operators
Authors: Stolarsky Kenneth B. 
Published: December 2010

AbstractLetθ=θ(k) be the positive root ofθ2+ (k-2)θ-k= 0. Letf(n) = [(n+ l)θ]-[nθ] for positive integersn, where [x] denotes the greatest integer inx. Then the elements of the infinite sequence (f(l),f(2),f(3),…) can be rapidly generated from the finite sequence (f(l),f(2),…,f(k)) by means of certain shift operators. For k = 1 we can generate (the characteristic function of) the sequence [nθ] itself in this manner.
A Note on the Hopficity of Finitely Generated Free-by-Nilpotent Groups
Authors: Boler James 
Published: December 2010

Our purpose is to deduce from a theorem of P. Hall the following observation.Let G be a finitely generated group and F a free normal subgroup of G with G/F nilpotent. Then G is hopfian.Here a group G is hopfian if every epiendomorphism G→G is an automorphism.
Numerical-Valued Fourier Transforms
Authors: Struble Raimond A. 
Published: December 2010

AbstractIt is shown that the classical Fourier transform can be extended as an algebra isomorphism onto the algebra of all complex-valued functions, which are measurable and finite a.e., under pointwise addition and multiplication. The extended Fourier transform agrees with the distributional Fourier transform on the space of all distributions which have regular transforms. It is defined on an algebra of Mikusiński-type operators in which multiplication is convolution in the subspace of integrable distributions.
Boundary-Value Problems of a Degenerate Sobolev-Type Differential Equation
Authors: Pao C. V. 
Published: December 2010

AbstractThe purpose of this paper is to study a degenerate Sobolev type partial differential equation in the form of Mut + Lu = f, where M and L are second order partial differential operators defined in a domain (0, T]×Ω in Rn+1. The degenerate property of the equation is in the sense that both M and L are not necessarily strongly elliptic and their coefficients may vanish or be negative in some part of the domain (0, T]×Ω. Two types of boundary conditions are investigated.
A Note on Convergence of Fourier Series of a Function on Wiener's Class Vp
Authors: Siddiqi Rafat N. 
Published: December 2010

Let f be a 2π-periodic function defined on [0, 2π]. We setwhere suprema have been taken with respect to all partitions P:a = t0<t1<t2<…<tn<=b of any segment [a, b] contained in [0, 2π]. We call the pth total variation of f on [a, b]. If we denote pth total variaiton of f on [0, 2π] by Vp(f), then we can define Wiener's class simply by
A Note on Injective Modules Over a d.g. Near-Ring
Authors: Oswald A. 
Published: December 2010

In [3] an attempt was made at proving the following result:(A) An N-module M over a d.g. near-ring is injective if and only if for each right ideal u of N and each N-homomorphism f:u→M there exists an element mϵM with f(a) = ma for all aϵu.In this note we present two examples. The first is a counterexample to (A) and the second illustrates one point at which the attempt made in [3] fails.
A Characterization of the Lebesgue Integral
Authors: Thomson B. S. 
Published: December 2010

The first general integrability criterion is due to Riemann. He observed that a necessary and sufficient condition for a function f(x) on [a, b] to be integrable in his sense is that for each ε > 0 there exists a δ > 0 so thatwhere {x0, x1, …, xn} is a partition of [a, b] with diameter less than δ (and ω(f, I) denotes the oscillation of f on the interval I).
On the Order of the Error Function of the (k, r)-Integers—II
Authors: Subbarao M. V. , Suryanarayana D. 
Published: December 2010

AbstractIn the first part of this note we give a very simple and elegant proof of the theorem on the order of the error function of the (k, r)-integers, which the authors proved earlier using elaborate calculations. We also obtain an improvement of an earlier result on the order of the same error function on the basis of the Riemann hypothesis.
Isomorphisms of Function Algebras and Algebras of Analytic Functions
Authors: Lund Bruce 
Published: December 2010

AbstractLet R be a finite open Riemann surface with analytic boundary Γ. Set and define is analytic on R}. Conditions are given on a function algebra A on a compact Hausdorff space X which imply that A is isomorphic to a subalgebra of A(R) of finite codimension.
Uniform Contractification
Authors: Tan Kok-Keong 
Published: December 2010

AbstractLet (X, τ) be a metrizable space and {fn: n = 1,2,…} be a commuting family of continuous mappings on X with a common fixed point ξ ∈ X such that (I) for each k = l, 2, … and (II) Then for each c ∈ (0,1), there exists a metric d on X inducing the topology τ such that , for all x, y∈X and n = l, 2, …. The above result is also generalized to Tychonoff spaces.
A Characterization of Biregular Group Rings
Authors: Burgess W. D. 
Published: December 2010

In this note biregular group rings are characterized and an example is given to show that Renault′s conjecture is false.A ring A with 1 is biregular if for all a∈A, AaA is generated by a central idempotent Equivalently, A is biregular iff all the stalks of its Pierce sheaf are simple.In [1] Bovdi and Mihovski showed that for a ring A, if the group ring AG is biregular then: (*) A is biregular and G is locally normal with the order of each finite normal sub-group of G invertible in A. A proof is found in Renault [7]. In [6] Renault showed that (*) is necessary and sufficient in case A is a finitely generated module over its centre or if A is right self-injective. He conjectured that (*) is necessary and sufficient in general. In fact (*) is not sufficient as the example below shows. Some familiarity with Pierce sheaf techniques is assumed (see [5] or [2]).