bluuebunny/crossref_metadata_2025_split huggingface dataset:
Generalisations of Turán's main theorems on lower bounds for sums of powers
Authors: van der Poorten A.J. 
Published: April 2009

In his book,Eine neue Methode in der Analysis und deren Andwendungen, P. Turán proved a number of new theorems given lower bounds for sums of powers. Since it was only his intention to demonstrate a new type of result, his bounds are by no means best possible nor are his proofs easily susceptible of improvement.We generalise Turán's so-called Main Theorems to exponential sums with polynomial coefficients by a simple method involving only the evaluation and estimation of certain determinants. This approach gives in each case a result known to be asymptotically correct in the various exponents, and when specialised to the case of constant coefficients it provides in each case best-known results.Our method moreover applies in more general circumstances and provided only that the determinants which arise can be conveniently estimated serves to provide lower bounds for other than exponential sums.
On commutativity in certain rings
Authors: Moore H.G. 
Published: April 2009

I.N. Herstein has shown that an associative ring in which the nilpotent elements are “well-behaved”, and such that every element satisfies a certain polynomial identity, is commutative. This result is generalized here. Specifically, it is shown that an alternative ring R which satisfies the following three properties is commutative:(i) for x ∈ R, there exists an integer n(x) and a polynomial px (t) with integer coefficients such that xn+1p(x) = xn;(ii) for a fixed positive integer m, a a nilpotent and b an arbitrary element of R, a - am commutes with b - bm;(iii) for the same m, a and b, (ab+b)m = (ba+b)m and (ab)m = ambm.Examples are given to show that all three properties are essential, and it is shown that for associative rings certain modified versions of these properties are individually enough to assure that the commutator ideal of the ring is nil.
Averaging and integral manifolds (II)
Authors: Palmer K. J. 
Published: April 2009

In the first part of this paper (written jointly with W.A. Coppel) the existence and properties of an integral manifold were established for the systemx′ =f(t, x, y)y′ =A(t)y + g(t, x, y)where f and g are “integrally small”. In this second part of the paper the stability properties of the integral manifold are investigated. Solutions are found which are bounded on the positive half of the real line and it is shown that these solutions approach the manifold exponentially and, moreover, that they are asymptotic to particular solutions on the manifold.
The conjugate of a smooth Banach space
Authors: Tacon D. G. 
Published: April 2009

A Banach space X is smooth if at every point of the unit sphere there is only one supporting hyperplane of the unit ball; and strictly convex, or rotund, if the unit sphere contains no line segment.Although there is a strong duality between these notions, Klee has produced a smooth space whose conjugate is not rotund. However there is no known example of a smooth space with conjugate not isomorphic to a rotund space.The main purpose of this note is to show that if X is a smooth space with a certain property, X* is isomorphic to a rotund space. This will follow from a mapping theorem which implies the existence of a set Γ and a continuous one-to-one linear map T of X* into co(Γ).
Divergence of Fourier series
Authors: Izuml Masako , Izumi Shin-Ichi 
Published: April 2009

Carleson has proved that the Fourier series of functions belonging to the class L2 converge almost everywhere.Improving his method, Hunt proved that the Fourier series of functions belonging to the class Lp (p > 1) converge almost everywhere. On the other hand, Kolmogoroff proved that there is an integrable function whose Fourier series diverges almost everywhere. We shall generalise Kolmogoroff's Theorem as follows: There is a function belonging to the class L(logL)p (p > 0) whose Fourier series diverges almost everywhere. The following problem is still open: whether “almost everywhere” in the last theorem can be replaced by “everywhere” or not. This problem is affirmatively answered for the class L by Kolmogoroff and for the class L(log logL)p (0 < p < 1) by Tandori.
Corrigendum: On the relation of a distributive lattice to its lattice of ideals
Authors: Gaskill Herbert S. 
Published: April 2009

There are errors in my paper [1], Lemma 1 and from the end of Lemma 4 to the end of the paper.LEMMA 1. If L is any finite lattice and L has a point which is both join and meet reducible then L is not weakly transferable.We replace Lemma 5 by the following sequence.
A note on quasi-uniform continuity
Authors: Lambrinos Panayotis Th. 
Published: April 2009

It is shown that:(i) a continuous function from a compact quasi-uniform space into a quasi-uniform space is not necessarily quasiuniformly continuous;(ii) if the range of the function is a uniform space, the function will be necessarily quasi-uniformly continuous.(This contradicts an example in the literature and generalizes a classical result.) Finally, a generalization of (ii) is given by means of a suitable boundedness notion.
Differential equations in Banach spaces
Authors: Noussair E.S. 
Published: April 2009

Let H be a fixed Hilbert space and B(H, H) be the Banach space of bounded linear operators from H to H with the uniform operator topology. Oscillation criteria are obtained for the operator differential equationwhere the coefficients A, C are linear operators from B(H, H) to B(H, H), for each t ≤ 0. A solution Y: R+ → B(H, H) is said to be oscillatory if there exists a sequence of points ti ∈ R+, so that ti → ∞ as i → ∞, and Y(ti) fails to have a bounded inverse. The main theorem states that a solution Y is oscillatory if an associated scalar differential equation is oscillatory.
On a random solution of a nonlinear perturbed stochastic integral equation of the Volterra type
Authors: Milton J. Susan , Tsokos Chris P. 
Published: April 2009

The object of this present paper is to study a nonlinear perturbed stochastic integral equation of the formwhere ω ∈ Ω, the supporting set of the complete probability measure space (Ω A, μ). We are concerned with the existence and uniqueness of a random solution to the above equation. A random solution, x(t; ω), of the above equation is defined to be a vector random variable which satisfies the equation μ almost everywhere.
On the complex complementarity problem
Authors: Mond Bertram 
Published: April 2009

The complex linear complementarity problem considered here is the following: Find z such thatwhere S is a polyhedral convex cone in Cp, S* the polar cone, M ∈ Cp×p and q ∈ Cp.Generalizing earlier results in real and complex space, it is shown that if M satisfies RezHMz ≥ 0 for all z ∈ Cp and if the set satisfying Mz + q ∈ S*, z ∈ S is not empty, then a solution to the complex linear complementarity problem exists. If RezHMz > 0 unless z = 0, then a solution to this problem always exists.
A converse of Bernstein's inequality for locally compact groups
Authors: Bloom Walter R. 
Published: April 2009

Let G be a Hausdorff locally compact abelian group, Γ its character group. We shall prove that, if S is a translation-invariant subspace of Lp (G) (p ∈ [1, ∞]),for each a ∈ G and , then is relatively compact (where Σ(f) denotes the spectrum of f). We also obtain a similar result when G is a Hausdorff compact (not necessarily abelian) group. These results can be considered as a converse of Bernstein's inequality for locally compact groups.
A note on simultaneous polynomial approximation of exponential functions
Authors: Loxton J.H. , van der Poorten A.J. 
Published: April 2009

Let α1, …, αmbe distinct complex numbers and τ(1), …, τ(m) be non-negative integers. We obtain conditions under which the functionsform a perfect system, that is, for every set ρ(1), …, ρ(m) of non-negative integers, there are polynomialsa1(z), …,am(z) with respective degrees exactly ρ(1)−1, …, ρ(m)−1, such that the functionhas a zero of order at least ρ(1) + … + ρ(m)−1 at the origin. Moreover, subject to the evaluation of certain determinants, we give explicit formulae for the approximating polynomialsa1(z), …,am(z).
Sequences defined as minima of two Fibonacci-type relations
Authors: Booth R.S. 
Published: April 2009

If {Ln} is a sequence defined by
Ln = min {Ln-a +Ln-b, Ln-c +Ln-d},
with a, b, c, d positive integers, then one can ask if necessarily Ln = Ln-b + Ln-b, for all sufficiently large n.The answer is yes if a and b are relatively prime, Ln > 0 initially, and λ < μ, where λ-a + λ-b = 1, μ-c + μ-d = 1. The answer is no if instead a and b have greatest common divisor k ≥2, with c ≡ 0 (mod k), d ≢ 0 (mod k).
Asymptotic analysis of a linearized trailing edge flow
Authors: Capell K. 
Published: April 2009

An Oseén type linearization of the Navier-Stokes equations is made with respect to a uniform shear flow at the trailing edge of a flat plate. Asymptotic expansions are obtained to describe a symmetrical merging flow for distances from the trailing edge that are, in a certain sense, large. Expansions for three regions are found:(i) a wake region,(ii) an inviscid region, and(iii) an upstream lower order boundary layer.The results are compared with those of Hakkinen and O'Neil (Douglas Aircraft Co. Report, 1967) and Stewartson (Proc. Roy. Soc. Ser. A 306 (1968)). They are further related to the results of Stewartson (Mathematika 16 (1969)) and Messiter (SIAM J. Appl. Math. 18 (1970)).
An algebraic characterization of symmetric graphs with a prime number of vertices
Authors: Berggren J.L. 
Published: April 2009

A graph Γ is called symmetric if its automorphism group is transitive on its vertices and edges. Let p be an odd prime, Z(p) the field of integers modulo p, and Z*(p) = (a ∈ Z(p) | a ≠ 0}, the multiplicative subgroup of Z(p). This paper gives a simple proof of the equivalence of two statements:(1) Γ is a symmetric graph with p vertices, each having degree n ≥ 1;(2) the integer n is an even divisor of p − 1 and Γ is isomorphic to the graph whose vertices are the elements of Z(p) and whose edges are the pairs {a, a+h} where a ∈ Z(p) and h ∈ H, the unique subgroup of Z*(p) of order n.In addition, the automorphism group of Γ is determined.
Classical groups over division rings of characteristic two: Corrigenda and an acknowledgement
Authors: Pender William M. 
Published: April 2009

In my paper [1], part (b) of Lemma 3.4 and the remark following it are incorrect and should be omitted.The isometry P in page 215, line 2, need not be a generator of T(E, q) as asserted, but can be shown to lie in T(E, q).I am indebted to Professor Tits for pointing out that extended ideas of quadratic forms have already appeared in his paper [2] and in Wall's paper [3]. Professor Tits also discusses the corresponding groups and Clifford algebras in detail.
Mean-square stability of a class of stochastic integral equations
Authors: Padgett W.J. 
Published: April 2009

The object of this paper is to investigate under very general conditions the existence and mean-square stability of a random solution of a class of stochastic integral equations in the formfor t ≥ 0, where a random solution is a second order stochastic process {x(t; w) t ≥ 0} which satisfies the equation almost certainly. A random solution x(t; w) is defined to be stable in mean-square if E[|x(t; w)|2] ≤ p for all t ≥ 0 and some p > 0 or exponentially stable in mean-square if E[|x(t; w)|2] ≤ pe-at, t ≥ 0, for some constants ρ > 0 and α > 0.
The computability of group constructions II
Authors: Gatterdam R.W. 
Published: April 2009

Finitely presented groups having word, problem solvable by functions in the relativized Grzegorczyk hierarchy, {En(A)| n ε N, A ⊂ N (N the natural numbers)} are studied. Basically the class E3 consists of the elementary functions of Kalmar and En+1 is obtained from En by unbounded recursion. The relativization En(A) is obtained by adjoining the characteristic function of A to the class En.It is shown that the Higman construction embedding, a finitely generated group with a recursively enumerable set of relations into a finitely presented group, preserves the computational level of the word problem with respect to the relativized Grzegorczyk hierarchy. As a corollary it is shown that for every n ≥ 4 and A ⊂ N recursively enumerable there exists a finitely presented group with word problem solvable at level En(A) but not En-1(A). In particular, there exist finitely presented groups with word problem solvable at level En but not En-1 for n ≥ 4, answering a question of Cannonito.
Free algebra structure: categorical algebras
Authors: Moore H. G. 
Published: April 2009

One of the more important concepts in the study of universal algebras is that of a free algebra. It is our purpose in this communication to describe the structure of the free algebra Kk() of k generators (k a positive integer) determined by a categorical algebra, and to indicate how this information encompasses results in such diverse areas as the study of Post algebras, boolean rings, p-rings, pk-rings, finite commutative rings with unity, etc.A finite algebra is called categorical if every algebra in its equational class is isomorphic to a sub-direct power of A. If has n elements, permutable identities, no non-identical automorphism and exactly m distinct one-element subalgebras, then .
A note on order topologies on ordered tensor products
Authors: Davis G. 
Published: April 2009

If E, F are regularly ordered vector spaces the tensor product E ⊗ F can be ordered by the conic hull Kπ of tensors, x ⊗ y with x ≥ 0 in E and y ≥ 0 in F, or by the cone K⊗ of tensors Φ ∈ E ⊗ F such that Φ(x′, y′) ≥ 0 for positive linear functionals x′, y′ on E, F.If E, F are locally convex spaces the tensor product can te given the π-topology which is defined by seminorms pα ⊕ qβ where {pα}, {qβ} are classes of seminorms defining the topologies on E, F. The tensor product can also be given the ε-topology which is the topology of uniform convergence on equicontinuous subsets J x H of E′ x F′. The main result of this note is that if the regularly ordered vector spaces E, F carry their order topologies then the order topology on E ⊕ F is the π-topology when E ⊕ F is ordered by kπ, and the ε-topology when E ⊕ F is ordered by K⊕.
Fundamental singularities in the theory of water waves with surface tension: Corrigenda
Authors: Rhodes-Robinson P. F. 
Published: April 2009

The Editor regrets that two errors have appeared in [1], through no fault of the author's. On page 325 the result (3.5) and the two lines following it should read:whereOn page 328 the result (4.3) and the two lines following it should read:where
Two structure theorems for homeomorphism groups
Authors: Vobach A. R. 
Published: April 2009

Let H(C) be the group of homeomorphisms of the cantor set, C onto itself. Let p: C → M be a (continuous) map of C onto a compact metric space M, and let G(p, M) be {h ∈ H(C) | ∀x ∈ C, p(x) = ph(x)}. G(p, M) is a group. The map p: C → M is standard, if for each (x, y) ∈ C × C such that p(x) = p(y), there is a sequence and a sequence such that xn → x and hn(xn) → y. Standard maps and their associated groups characterize compact metric spaces in the sense that: Two such spaces, M and N, are homeomorphic if and only if, given p standard from C onto M, there is a standard q from C onto N for which G(p, M) = h−1G(q, N)h, for some h ∈ H(C). That is, two compact metric spaces are homeomorphic if and only if they determine, via standard maps, the same classes of conjugate subgroups of H(C).The present note exhibits two natural structure theorems relating algebraic and topological properties: First, if M = H ∪ K (H, K ≠ π) , compact metric, and p : C → M are given, then G(p, M) is isomorphic to a subdirect product of G(p, M)/S(p, H\K) and G(p, M)/S(p, K\H) where, generally, S(p, N) is the normal subgroup of homeomorphisms supported on p−1M . Second, given M and N compact metric and p : M → N continuous and onto, let M ≠ M − CID*α ≠ 0 , where {Dα}α ∈ A is the collection of non-degenerate preimages of points in N Then there is a standard p : C → M such that fp : C → N is standard and there is a homomorphism.
A universal semigroup
Authors: Morris Sidney A. 
Published: April 2009

J.H. Michael recently proved that there exists a metric semigroup U such that every compact metric semigroup with property P is topologically isomorphic to a subsemigroup of U; where a semigroup S has property P if and only if for each x, y in S, x ≠ y, there is a z in S such that xs ≠ yz or zx ≠ zyA stronger result is proved here more simply. It is shown that for any set A of metric semigroups there exists a metric semigroup U such that each S in A is topologically isomorphic to a subsemigroup of U. In particular this is the case when A is the class of all separable metric semigroups, or more particularly the class of all compact metric semigroups.
Locally finite varieties of groups arising from Cross varieties: Corrigendum
Authors: Macdonald Sheila Oates 
Published: April 2009

One condition on D was omitted from the statement of Theorem B in the paper [1], namely that (and the corresponding condition in Theorem A). The proof of the theorem clearly requires that this be so and it is not difficult to see that such a D can always be chosen. However, Dr R.M. Bryant has pointed out that not only is the theorem true as it stands, but indeed the conditions can be relaxed slightly to allow D to be any group such that.
Torsion topological groups with minimal open sets
Authors: Thornton M.C. 
Published: April 2009

Torsion topological groups with the additional property that the intersection of open sets is open are considered and their topological structure is determined:1) the topology is uniquely determined by a normal subgroup;2) each group is uniquely an extension of an indiscrete group by a discrete group;3) the topology may be changed within limits without changing the dual group.
On product varieties of groups
Authors: Vaughan-Lee M.R. 
Published: April 2009

An example is given of a finitely based variety of groups such that is not finitely based.Let be the variety of groups determined by the laws
(1) [[x1, x2], [x3, x4, [x5, x6]],
(2) [[x1, x2, x3], [x4, x5]] [[x1x2], [x4, x5, x3]]−1,
[[x1, x2, x3], [x1, x2]]. Then is not finitely based.
Brand Perceptions and the Market for Common Stock
Authors: Frieder Laura , Subrahmanyam Avanidhar 
Published: April 2009

AbstractThis paper investigates the effect of company brand perceptions on investor propensities to hold stocks. We find that, after controlling for other determinants of stockholdings, there is a negative and significant cross-sectional relation between institutional holdings and brand visibility, which is consistent with the notion that individual investors prefer to invest in stocks with easily recognized products. Furthermore, we find that institutional holdings are positively related to firm size and beta. Our analysis supports the notion that institutional portfolios eschew relatively neglected small firms, whereas individuals prefer holding stocks with high recognition and, consequently, greater information precision.
Firm Performance, Capital Structure, and the Tax Benefits of Employee Stock Options
Authors: Kahle Kathleen M. , Shastri Kuldeep 
Published: April 2009

AbstractThis paper analyzes the relation between the capital structure of a firm and the tax benefits realized from the exercise of stock options. Theory suggests that firms with tax benefits from the exercise of stock options should carry less debt since tax benefits are a non-debt tax shield. We find that both long- and short-term debt ratios are negatively related to the size of tax benefits from option exercise. Moreover, one-year changes in long-term leverage are negatively related to changes in the number of options exercised. Such a relation does not exist for changes in short-term leverage. Finally, firms with option-related tax benefits tend to issue equity, with the net amount of equity issued an increasing function of these tax benefits.
Packaging Liquidity: Blind Auctions and Transaction Efficiencies
Authors: Kavajecz Kenneth A. , Keim Donald B. 
Published: April 2009

AbstractThe costs of implementing investment strategies represent a significant drag on the performance of mutual funds and other institutional investors. It is the responsibility of institutional investors, and in the interests of the individual investors they represent, to seek market mechanisms that mitigate trading costs. We investigate an example of one such liquidity provision mechanism whereby liquidity demanders auction a set of trades as a package directly to potential liquidity providers. A critical feature of the auction is that the identities of the securities in the package are not revealed to the bidder. We demonstrate that this mechanism provides a transactions cost savings relative to more traditional trading mechanisms for the liquidity demander as well as an efficient way for liquidity suppliers to obtain order flow. We argue that the cost savings afforded this new mechanism are due to the potential for low cost crosses with the bidder's existing inventory positions and through the longer trading horizon, and superior trading ability, of the bidders. This research suggests that the ability to innovate via new liquidity provision mechanisms can provide market participants with transaction cost savings that cannot be easily duplicated on more traditional exchanges.
Information vs. Entry Costs: What Explains U.S. Stock Market Evolution?
Authors: Peress Joel 
Published: April 2009

AbstractI investigate whether changes in stock market participation costs can explain the long-term increase in the number of U.S. stockholders. I separate these costs into two components: an information cost (the cost of collecting market information), and an entry cost (all other costs, including commissions and fees), and disentangle their general equilibrium implications in a noisy rational expectations economy. While a falling information cost cannot explain the observed increase in stock market participation, a falling entry cost can account for this plus several other features of the U.S. economy, including the falling equity premium, rising return variances, and the boom in passive relative to active investing.
Information Quality, Learning, and Stock Market Returns
Authors: Li George 
Published: April 2009

AbstractThis paper studies how the precision of noisy public information that investors receive about the expected aggregate dividend growth rate affects stock market returns. I show that less precise information can increase the risk premium and stock return volatility. The numerical results from my calibrated model also show that noisy information can significantly increase the risk premium and stock return volatility. My finding implies that the presence of noisy information may help explain the large average risk premium and return volatility in the U.S. financial market. In addition, my finding suggests it is optimal for firms to disclose to investors more precise information to reduce the cost of equity capital.
Bayesian Analysis of Stochastic Betas
Authors: Jostova Gergana , Philipov Alexander 
Published: April 2009

AbstractWe propose a mean-reverting stochastic process for the market beta. In a simulation study, the proposed model generates significantly more precise beta estimates than GARCH betas, betas conditioned on aggregate or firm-level variables, and rolling regression betas, even when the true betas are generated based on these competing specifications. Our model significantly improves out-of-sample hedging effectiveness. In asset pricing tests, our model provides substantially stronger support for the conditional CAPM relative to competing beta models and helps resolve asset pricing anomalies such as the size, book-to-market, and idiosyncratic volatility effects in the cross section of stock returns.