bluuebunny/crossref_metadata_2025_split huggingface dataset:
‘On projective planes of type (6, m)’
Authors: Lorimer P. 
Published: November 2008

Alan Rahilly has pointed out to me that the proof of the Theorem in my paper (2) is incomplete. This correction will now complete it. I would also like to acknowledge here that the results which are actually established in (2) can also be found in the paper (5) by Praeger and Rahilly.The trouble was in the proof of Proposition 2. Although the group G has a subgroup H1 which intersects each of its conjugates trivially, the same is not necessarily true of the image H1N/N of H1 in the 2-transitive representation G/N of G referred to in the paper. A theorem of M. E. O'Nan from (4) was used along with Proposition 2 to establish my theorem. What should have been done was to look at O'Nan's results more deeply and combine them with other results. Here is the way that it is done.There is nothing actually wrong with the argument in my paper; it is just that it is not complete. The proof here will continue the argument of (2) using the notations established there.
A note on the strong regularity of Nrlund means
Authors: Nurcombe J. R. 
Published: November 2008

Let (pn), (qn) and (un) be sequences of real or complex numbers withThe sequence (sn) is strongly generalized Nrlund summable with index 0, to s, or s or snsN, p, Q ifand pnv=pnvpnv1, with p10. Strong Nrlund summability N, p was first studied by Borweing and Cass (1), and its generalization N, p, Q by Thorp (6). We shall say that (sn) is strongly generalized convergent of index 0, to s, and write snsC, 0, Q if sns and where sn=a0+a1++an. When qn all n, this definition reduces to strong convergence of index , introduced by Hyslop (4). If as n, the sequence (sn) is summable (, q) to s sns(, q).
The norm of a Möbius transformation
Authors: Beardon A. F. , Wilker J. B. 
Published: November 2008

A Möbius transformation z → (az + b)/(cz + d), ad — bc = 1, acts as a conformal transformation of the Riemann sphere , and its Poincaré extension acts as an isometry of hyperbolic 3-space modelled in the ball < 1. The size of this transformation can be measured by the matrix normor by the hyperbolic distance ρ through which its extension moves the point (0, 0, 0).
A generation theorem for operators commuting with group actions
Authors: Davies E. B. 
Published: November 2008

AbstractWe prove that an unbounded operator Z on a Banach space , which commutes with a representation of a Lie group G, is the generator of a contraction semigroup, under conditions on Z and G which have not previously been investigated. The case of an unbounded derivation Z on a C*-algebra is considered in particular detail.
3-transpositions in infinite groups
Authors: Weiss Richard 
Published: November 2008

Let G be a group. A subset D will be called a set of 3-transpositions if |x| = 2 for xεD and |xy| = 3 whenever x, yεD do not commute. We will call the set D closed if xDx−1 = D for each xεD. For each xεD, letFor each subset X of D, we denote by [X] the graph with vertex set X where two elements x, yεX are joined by an edge whenever they commute. We denote by (X) the complement graph; thus two elements x, yεX are joined by an edge of (X) whenever they do not commute.
Mean values and classes of harmonic functions
Authors: Ramsey Thomas , Weit Yitzhak 
Published: November 2008

Let μ be a finite complex Borel measure supported on the unit circle.In this paper, we are concerned with the characterization of the sets of functions satisfying the generalized mean value equation of the form.and for all ξ ∈ , | ξ | = R for some fixed R > 0.
On ( h(n)) summability methods
Authors: Kuttner B. , Sukla I. L. 
Published: November 2008

AbstractIn 1967 Segal introduced the Dirichlet convolution (, h(n)), generalizing a method of Ingham developed in studies on the Prime Number Theorem. In this paper we establish necessary and sufficient conditions on the sequence h(n) in order that the convolution method (, h(n)) be conservative. Further conditions are established for the method to be absolutely conservative.
Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups
Authors: Lau Anthony To-Ming 
Published: November 2008

Let G be a topological semigroup, i.e. G is a semigroup with a Hausdorff topology such that the map (a, b) → a.b from G × G into G is continuous when G × G has the product topology. Let C(G) denote the space of complex-valued bounded continuous functions on G with the supremum norm. Let LUC (G) denote the space of bounded left uniformly continuous complex-valued functions on G i.e. all f ε C(G) such that the map a → laf of G into C(G) is continuous when C(G) has a norm topology, where (laf )(x) = f (ax) (a, x ε G). Then LUC (G) is a closed subalgebra of C(G) invariant under translations. Furthermore, if m ε LUC (G)*, f ε LUC (G), then the functionis also in LUC (G). Hence we may define a productfor n, m ε LUC(G)*. LUC (G)* with this product is a Banach algebra. Furthermore, ʘ is precisely the restriction of the Arens product defined on the second conjugate algebra l∞(G)* = l1(G)** to LUC (G)*. We refer the reader to [1] and [10] for more details.
On Bohr almost periodicity
Authors: Milnes Paul 
Published: November 2008

AbstractThe first examples of Bohr almost periodic functions that are not almost periodic were given by T. -S. Wu. Later, the present author showed that Bohr almost periodic functions could be distal (and not almost periodic) and even merely minimal. Here it is proved that all Bohr almost periodic functions are minimal. The proof yields an unusual feature about the orbit of a Bohr almost periodic function, one which does not characterize Bohr almost periodic functions, but can be used to show that a Bohr almost periodic function f that is point distal must be distal or, if f is almost automorphic, it must be almost periodic. Some pathologies of Bohr almost periodic functions are discussed.
Improving certain simple eigenvalue bounds
Authors: Hyydö Seppo , Merikoski Jorma Kaarlo , Virtanen Ari 
Published: November 2008

Throughout this paper we let A = (aij) be a non-zero n × n matrix-we study real matrices only–with row sums R1,…Rn and eigenvalues λ1,…,λn, ordered λ1≥…≥λn if they are real. We denote E = (1,…,1)T and su A = ΣiΣjaij = ETAE. If A is symmetric, a simple property of the Rayleigh quotient is thatsatisfiesand
An almost everywhere central limit theorem
Authors: Brosamler Gunnar A. 
Published: November 2008

The purpose of this paper is the proof of an almost everywhere version of the classical central limit theorem (CLT). As is well known, the latter states that for IID random variables Y1, Y2, … on a probability space (Ω, , P) with we have weak convergence of the distributions of to the standard normal distribution on ℝ. We recall that weak convergence of finite measures μn on a metric space S to a finite measure μ on S is defined to mean thatfor all bounded, continuous real functions on S. Equivalently, one may require the validity of (1·1) only for bounded, uniformly continuous real functions, or even for all bounded measurable real functions which are μ-a.e. continuous.
The spectrum of a one-dimensional pseudo-differential operator
Authors: Wong M. W. 
Published: November 2008

AbstractWe describe the spectrum of a self-adjoint pseudo-differential operator on L2 (– ∞, ∞). We show that the essential spectrum coincides with the interval ([1, ∞) and give a lower bound for the lowest eigenvalue in (– ∞, 1). A sufficient condition for the existence of an eigenvalue in (– ∞, 1) is also given.
Locally compact topologies on abelian groups
Authors: Morris Sidney A. 
Published: November 2008

AbstractIt is shown that an abelian group admits a non-discrete locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group ofp-adic integers or to an infinite product of non-trivial finite cyclic groups. It is also proved that an abelian group admits a non-totally-disconnected locally compact group topology if and only if it has a subgroup algebraically isomorphic to the group of real numbers. Further, if an abelian group admits one non-totally-disconnected locally compact group topology then it admits a continuum of such topologies, no two of which yield topologically isomorphic topological groups.
Symmetries of generalized Klein-Gordon (including sine-Gordon) equations in three or more dimensions
Authors: Gordon T. J. 
Published: November 2008

Much recent attention has been devoted to those nonlinear partial differential equations admitting higher-order conservation laws (e.g. [2] and references therein) or equivalently admitting higher-order symmetries. In particular the sine-Gordon equation possesses such symmetries [5, 7] where is the two-dimensional d'Alembertian operator. The question posed and solved here is whether such behaviour is possible in higher dimensions. We therefore consider the ‘Generalized Klein–Gordon’ (GKG) equationin N dimensions where and N ≥ 3.
The growth of the number of prime knots
Authors: Ernst C. , Sumners D. W. 
Published: November 2008

A fundamental and interesting question in knot theory is:Question 1. How many prime knots of n crossings are there ?Over time, knot theorists have answered this question for n ≤ 13 by the method of exhaustion: one writes down a list of all possible knots of n crossings, and then works hard to eliminate duplications from the list [12]. A perhaps easier question is the following:
Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients
Authors: Borwein David 
Published: November 2008

AbstractThe paper is concerned with properties of the Dirichlet series where {λn} is a strictly increasing unbounded sequence of real numbers with λ1 > 0. One of the main Tauberian results proved is that if a1 ≥ 0, an > 0 for n = 2, 3, …, a(x) ≤ ∞ for all x ≥ 0, An:= a1 + a2 + … + an → ∞, an λn = o((λn+1-λn)An), an λn sn > − H(λn+1 − λn) An and then A new summability method Dλ, a based on the Dirichlet series a(x) is defined and its relationship to the weighted mean method Ma investigated.
The Hilbert transform of Schwartz distributions. II
Authors: Chaudhry M. Aslam , Pandey J. N. 
Published: November 2008

AbstractLet D(R) be the Schwartz space of C∞ functions with compact support on R and let H(D) be the space of all C∞ functions defined on R for which every element is the Hilbert transform of an element in D(R), i.e.where the integral is defined in the Cauchy principal-value sense. Introducing an appropriate topology in H(D), Pandey [3] defined the Hilbert transform Hf of f ∈ (D(R))′ as an element of (H(D))′ by the relationand then with an appropriate interpretation he proved that.In this paper we give an intrinsic description of the space H(D) and its topology, thereby providing a solution to an open problem posed by Pandey ([4], p. 90).
Residually finite groups of finite rank
Authors: Lubotzky Alexander , Mann Avinoam 
Published: November 2008

The recent constructions, by Rips and Olshanskii, of infinite groups with all proper subgroups of prime order, and similar ‘monsters’, show that even under the imposition of apparently very strong finiteness conditions, the structure of infinite groups can be rather weird. Thus it seems reasonable to impose the type of condition that enables us to apply the theory of finite groups. Two such conditions are local finiteness and residual finiteness, and here we are interested in the latter. Specifically, we consider residually finite groups of finite rank, where a group is said to have rank r, if all finitely generated subgroups of it can be generated by r elements. Recall that a group is said to be virtually of some property, if it has a subgroup of finite index with this property. We prove the following result:Theorem 1. A residually finite group of finite rank is virtually locally soluble.
The asymptotic behaviour of bounded semigroups in a Banach algebra
Authors: Bercovici Hari 
Published: November 2008

Let T be an operator on a complex Banach space such that sup {‖Tn‖: n ≥ 0} < ∞; such operators are said to be power-bounded. For such an operator one defines the peripheral spectrum to be the setwhere σ(T) denotes the spectrum of T, and T is the unit circle in ℂ. Esterle proved in [3] that limnn→∞ ‖Tn−Tn+1‖ = 0 provided that ‖T‖ ≤ 1 and σ{T} = {1}. Later Katznelson and Tzafriri [6] proved the same result for power-bounded operators such that σΓ(T) = {1}, and in fact they proved a more general result. More precisely, let be an absolutely convergent Taylor series, i.e. , and assume that f is of spectral synthesis for σΓ(T) (in particular f|σΓ(T) ≡ 0). Then limn→∞ ‖f(T) Tn‖ = 0. Katznelson and Tzafriri prove an analogous result, in which T is replaced by a commuting k-tuple (T1, T2, …, Tk) of contractions. In this case they consider functions of the form f(T1, T2, …, Tk), where f is either an absolutely convergent Taylor series if k is odd, or an element of a smaller algebra if k is even. The result of Katznelson and Tzafriri was further extended in the case of a single contraction T by Esterle, Strouse and Zouakia[4], who consider functions f(T) where f is allowed to be in a more general function algebra. For instance, if T acts on a Hilbert space, they allow f to be an element of the disk algebra.
The number of infinite substructures
Authors: Macpherson Dugald , Mekler Alan H. , Shelah Saharon 
Published: November 2008

AbstractGiven a relational structure M and a cardinal λ < |M|, let øλ denote the number of isomorphism types of substructures of M of size λ. It is shown that if μ < λ are cardinals, and |M| is sufficiently larger than λ, then øμ ≤ øλ. A description is also given for structures with few substructures of given infinite cardinality.
Points of egress in problems of Hamiltonian dynamics
Authors: Amick C. J. , Toland J. F. 
Published: November 2008

First we consider an elementary though delicate question about the trajectory in ℝn of a particle in a conservative field of force whose dynamics are governed by the equationHere the potential function V is supposed to have Lipschitz continuous first derivative at every point of ℝn. This is a natural assumption which ensures that the initial-value problem is well-posed. We suppose also that there is a closed convex set C with non-empty interior C° such that V ≥ 0 in C and V = 0 on the boundary ∂C of C. It is noteworthy that we make no assumptions about the degeneracy (or otherwise) of V on ∂C (i.e. whether ∇V = 0 on ∂C, or not); thus ∂C is a Lipschitz boundary because of its convexity but not necessarily any smoother in general. We remark also that there are no convexity assumptions about V and nothing is known about the behaviour of V outside C.
The Lindelöf Tychonoff Theorem and choice principles
Authors: Schlitt G. 
Published: November 2008

AbstractIt is an important result in frame theory that the coproduct of a family of regular Lindelöf frames is Lindelöf [3]. We show that this ‘Lindelöf Tychonoff Theorem’ or ‘LTT’ is independent of ZF and indeed lies close in logical strength to the Axiom of Countable Choice, quite unlike the case with the usual (frame) Tychonoff Theorem. Along the way we construct the regular Lindelöf coreflection and obtain a simple proof of the LTT as a corollary.
Cofiniteness and vanishing of local cohomology modules
Authors: Huneke Craig , Koh Jee 
Published: November 2008

Let R be a noetherian local ring with maximal ideal m and residue field k. If M is a finitely generated R-module then the local cohomology modules are known to be Artinian. Grothendieck [3], exposé 13, 1·2 made the following conjecture:If I is an ideal of R and M is a finitely generated R-module, then HomR (R/I, ) is finitely generated.
Pointwise bounded approximation by polynomials
Authors: O'Farrell Anthony G. , Perez-Gonzalez Fernando 
Published: November 2008

For a bounded open set U ⊂ ℂ, we denote by H∞(U) the collection of all bounded analytic functions on U. We let X denote bdy (U), the boundary of U, Y denote the polynomial hull of U (the complement of the unbounded component of ℂ / X), and U* denote mt (Y), the interior of Y. We denote the sup norm of a function f: A → ℂ by ∥f∥A:We denote the space of all analytic polynomials by ℂ[z], and we denote the open unit disc by D and the unit circle by S1.
Invariance principles for logarithmic averages
Authors: Csörgő Miklós , Horváth Lajos 
Published: November 2008

AbstractWe obtain weak and strong Gaussian approximations for logarithmic averages of indicators of normalized partial sums. The proofs are based on invariance principles for integrals of an Ornstein–Uhlenbeck process and on strong approximations of normalized partial sums by Orstein–Uhlenbeck processes.
Odd perfect numbers
Authors: Heath-Brown D. R. 
Published: November 2008

It is not known whether or not odd perfect numbers can exist. However it is known that there is no such number below 10300 (see Brent[1]). Moreover it has been proved by Hagis[4]and Chein[2] independently that an odd perfect number must have at least 8 prime factors. In fact results of this latter type can in priniciple be obtained solely by calculation, in view of the result of Pomerance[6] who showed that if N is an odd perfect number with at most k prime factors, thenPomerance's work was preceded by a theorem of Dickson[3]showing that there can be only a finite number of such N. Clearly however the above bound is vastly too large to be of any practical use. The principal object of the present paper is to sharpen the estimate (1). Indeed we shall handle odd ‘multiply perfect’ numbers in general, as did Kanold[5], who extended Dickson's work, and Pomerance. Our result is the following.
Diophantine approximation in Kleinian groups
Authors: Stratmann Bernd 
Published: November 2008

AbstractThe δ-homogeneity of the Patterson measure is used for a closer study of the limit sets of Kleinian groups. A combination of the properties of this measure with concepts of diophantine approximations is shown to lead to a more detailed understanding of these limit sets. In particular, it is seen to how great an extent the studies of these sets, in terms of Hausdorff measure or Hausdorff dimension, are limited in a natural way.
A family of 2(p − 1)-sparse cohomology theories and some actions on
Authors: Brunetti Maurizio 
Published: November 2008

AbstractLet p be an odd prime, and h*( − ) a multiplicative mod p cohomology theory with a complex orientation satisfying the 2(p − 1)-sparseness condition. A formula concerning the formal group law for such h*( − ) is used to investigate the structure of h*(BG), G being a finite group whose p-Sylow subgroups are cyclic.
Non-simple geodesics in hyperbolic 3-manifolds
Authors: Jones Kerry N. , Reid Alan W. 
Published: November 2008

AbstractChinburg and Reid have recently constructed examples of hyperbolic 3-manifolds in which every closed geodesic is simple. These examples are constructed in a highly non-generic way and it is of interest to understand in the general case the geometry of and structure of the set of closed geodesics in hyperbolic 3-manifolds. For hyperbolic 3-manifolds which contain immersed totally geodesic surfaces there are always non-simple closed geodesics. Here we construct examples of manifolds with non-simple closed geodesics and no totally geodesic surfaces.
H1 boundedness of oscillatory singular integrals with degenerate phase functions
Authors: Pan Yibiao 
Published: November 2008

AbstractIn this paper we study the uniform boundedness of oscillatory singular integral operators with degenerate phase functions on the Hardy space H1. The H1 boundedness was previously known when the phase function is nondegenerate. Here we obtain a sufficient condition for H1 boundedness which allows the phase function vanishing to infinite order.
Rigidity of superconformal minimal surfaces lying fully in odd-dimensional unit spheres
Authors: Sakaki Makoto 
Published: November 2008

AbstractLetSndenote then-dimensional unit sphere. Recently, Bolton, Pedit and Woodward [1,3] have begun to study a class of minimal surfaces inSn, which are called superconformal. In this paper we will discuss the rigidity of superconformal minimal surfaces lying fully inS2m−1among all superconformal minimal surfaces lying fully in odd-dimensional unit spheres.
Numbers badly approximate by fractions with prime denominator
Authors: Harman Glyn 
Published: November 2008

We write ‖x‖ to denote the least distance from x to an integer, and write p for a prime variable. Duffin and Schaeffer [l] showed that for almost all real α the inequalityhas infinitely many solutions if and only ifdiverges. Thus f(x) = (x log log (10x))−1 is a suitable choice to obtain infinitely many solutions for almost all α. It has been shown [2] that for all real irrational α there are infinitely many solutions to (1) with f(p) = p−/13. We will show elsewhere that the exponent can be increased to 7/22. A very strong result on primes in arithmetic progressions (far stronger than anything within reach at the present time) would lead to an improvement on this result. On the other hand, it is very easy to find irrational a such that no convergent to its continued fraction expansion has prime denominator (for example (45– √10)/186 does not even have a square-free denominator in its continued fraction expansion, since the denominators are alternately divisible by 4 and 9).
Continuity of functions operating on characteristic functions
Authors: Norvidas Saulius 
Published: November 2008

AbstractFor a locally compact abelian group G let P0(G) denote the set of all characteristic functions on G (i.e., continuous positive definite functions φ with φ(0) = 1). A complex-valued function f is said to operate on P0(G) if f(φ(·)) ∈ P0(G) whenever φ ∈ P0(G). The natural domain for functions operating on P0(G) is the set D(G) = {z ∈ C: z = φ(g), g ∈ G, φ ∈ P0(G)}. It is known that every function operating on P0(G) is continuous on the interior of D(G) for each infinite group G. On the other hand, functions discontinuous on D(G) operate on P0(G) for any discrete G. We show that, for any non-discrete group G, every function operating on P0(G) is continuous on D(G). Together with some earlier results, this statement allows us to obtain a constructive description of operating functions on the whole set D(G).
On positive harmonic functions
Authors: Allen A. C. 
Published: November 2008

Any harmonic function which is defined and positive in the half-plane η > 0 may be expressed bywhere C is a non-negative number, and G(x) is a bounded non-decreasing function. For a simple proof see Loomis and Widder (2). Let us writewhere w(z) is a regular function of z in η > 0, and satisfies the following conditions: (i) w(z) is real and continuous at all points of the open interval (a, b) of the real axis [the interval may be unbounded]; (ii) there exists a simply connected domain Δ, lying in the half-plane η > 0, whose frontier contains the interval (a, b) of the real axis and which is mapped ‘simply’ on the half-plane υ > 0 by the conformal transformation w = w(z).
The relativistically rigid rod
Authors: Hogarth J. E. , McCrea W. H. 
Published: November 2008

AbstractA relativistically rigid rod is defined as one along which any disturbance travels with the fundamental speed c without dissipation of energy. A necessary consequence of this definition is that the rod should satisfy a certain ‘equation of elasticity’. If this equation is satisfied, it is shown in accordance with relativistic mechanics that a disturbance of any amplitude is propagated along the (unstressed or stressed) rod with speed c and without dissipation. Consequently, the equation provides also a sufficient condition for rigidity in the sense defined.
On some theorems of Hurwitz and Sheil-Small
Authors: Hall R. R. 
Published: November 2008

We recall a theorem of Hurwitz [5]: let f(θ) be real-valued and periodic, f(θ) ≢ 0, andwhere an = bn = 0, 0 ≤ n < N. Then f(θ) has at least 2N sign changes in each period. A similar result with a trigonometric polynomial on the right-hand side of (1) had been obtained earlier by Sturm [7].