bluuebunny/crossref_metadata_2025_split huggingface dataset:
Discrete quadratic estimates and holomorphic functional calculi in Banach spaces
Authors: Franks Edwin , McIntosh Alan 
Published: April 2009

We develop a discrete version of the weak quadratic estimates for operators of type w explained by Cowling, Doust, McIntosh and Yagi, and show that analogous theorems hold. The method is direct and can be generalised to the case of finding necessary and sufficient conditions for an operator T to have a bounded functional calculus on a domain which touches σ(T) nontangentially at several points. For operators on Lp, 1 < p < ∞, it follows that T has a bounded functional calculus if and only if T satisfies discrete quadratic estimates. Using this, one easily obtains Albrecht's extension to a joint functional calculus for several commuting operators. In Hilbert space the methods show that an operator with a bounded functional calculus has a uniformly bounded matricial functional calculus.The basic idea is to take a dyadic decomposition of the boundary of a sector Sv. Then on the kth ingerval consider an orthonormal sequence of polynomials . For h ∈ H∞(Sν), estimates for the uniform norm of h on a smaller sector Sμ are obtained from the coefficients akj = (h, ek, j). These estimates are then used to prove the theorems.
Properties of the Berezin transform of bounded functions
Authors: Lee Jaesung 
Published: April 2009

We find the spectrum of the Berezin operator T on L∞(Bn), then we show that if f ∈ L∞(Bn) satisfies Sf = rf for some r in the unit circle, where S is any convex combination of the iterations of T, then f is M-harmonic.Finally we decompose the subspace of L∞(Bn) where lim Tkf exists into the direct sum of two subspaces of L∞(Bn).
Oscillation criteria for certain second order nonlinear difference equations
Authors: Grace S.R. , El-Morshedy H.A. 
Published: April 2009

This paper is concerned with nonlinear difference equations of the formwhere δ is the forward difference operator defined by δun−1 =un−un−1 δ2un−1= δ(δun-1) and {an} is a real sequence which is not assumed to be nonnegative. The functionfis such thatuf(u) < 0 for allu≠ 0 andf(u) −f(v) =g(u, v)(u − v), for allu, v≠ 0, and for some nonnegative functiong. Our results are not only new but also improve and generalise some recent oscillation criteria. Examples illustrating the importance of our main results are also given.
G-fonctions et cohomologie des hypersurfaces singulières
Authors: Bertolin Cristiana 
Published: April 2009

Our object of study is the arithmetic of the differential modules (l)(l∈ ℕ – {0}), associated by Dwork's theory to a homogeneous polynomialf(λ,X) with coefficients in a number field. Our main result is that (1)is a differential module of typeG, c'est-à-dire, a module those solutions areG-functions. For the proof we distinguish two cases: the regular one and the non regular one.Our method gives usan effective upper bound for the global radius of(l),which doesn't depend on “l”but only on the polynomialf(λ,X). This upper bound is interesting because it gives an explicit estimate for the coefficients of the solutions of (l).In the regular case we know there is an isomorphism of differential modules between (1)and a certain De Rham cohomology group, endowed with the Gauss-Manin connection, c'est-à-dire, our module “comes from geometry”. Therefore our main result is a particular case of André's theorem which assert thatat least in the regular case, all modules coming from geometry are of type G.
Rendezvous numbers in normed spaces
Authors: Farkas Bálint , Révész Szilárd György 
Published: April 2009

In previous papers, we used abstract potential theory, as developed by Fuglede and Ohtsuka, to a systematic treatment of rendezvous numbers. We considered Chebyshev constants and energies as two variable set functions, and introduced a modified notion of rendezvous intervals which proved to be rather nicely behaved even for only lower semicontinuous kernels or for not necessarily compact metric spaces.Here we study the rendezvous and average numbers of possibly infinite dimensional normed spaces. It turns out that very general existence and uniqueness results hold for the modified rendezvous numbers in all Banach spaces. We also observe the connections of these magical numbers to Chebyshev constants, Chebyshev radius and entropy. Applying the developed notions with the available methods we calculate the rendezvous numbers or rendezvous intervals of certain concrete Banach spaces. In particular, a satisfactory description of the case of Lp spaces is obtained for all p > 0.
A functional inequality for the polygamma functions
Authors: Alzer Horst 
Published: April 2009

Let
where ψ denotes the logarithmic derivative of Euler's gamma function. We prove that the functional inequalityholds if and only if 0 < r ≤ 1. And, we show that the converse is valid if and only if r < 0 or r ≥ n + 1.
Finite dimensional characteristics related to superreflexivity of Banach spaces
Authors: Ostrovskii M. I. 
Published: April 2009

One of the important problems of the local theory of Banach Spaces can be stated in the following way. We consider a condition on finite sets in normed spaces that makes sense for a finite set any cardinality. Suppose that the condition is such that to each set satisfying it there corresponds a constant describing “how well” the set satisfies the condition.The problem is:Suppose that a normed space X has a set of large cardinality satisfying the condition with “poor” constant. Does there exist in X a set of smaller cardinality satisfying the condition with a better constant?In the paper this problem is studied for conditions associated with one of R.C. James's characterisations of superreflexivity.
On the n-parameter abstract Cauchy problem
Authors: Janfada M. , Niknam A. 
Published: April 2009

Let Hi(i = 1, 2, …, n), be closed operators in a Banach space X. The generalised initialvalue problem
of the abstract Cauchy problem is studied. We show that the uniqueness of solution u: [0, T1] × [0, T2] × … × [0, Tn] → X of this n-abstract Cauchy problem is closely related to C0-n-parameter semigroups of bounded linear operators on X. Also as another application of C0-n-parameter semigroups, we prove that many n-parameter initial value problems cannot have a unique solution for some initial values.
Periodic solutions of some differential delay equations created by Hamiltonian systems
Authors: Li Jibin , Liu Zhengrong , He Xuezhong 
Published: April 2009

This paper is concerned with finding periodic solutions of differential delay systemsandwhereri(i= 1, 2,…,n− 1) are positive constants. By using the theory of Hamiltonian systems, we obtain some sufficient conditions under which these systems have many periodic solutions with known periods.
On the fitting core of a formation
Authors: Beidleman J. C. , Heineken H. 
Published: April 2009

Dedicated to the memory of Bernhard H. NeumannNot often is a formation also a Fitting class. In this article groups are exhibited that are contained in a given saturated formation and that do not lead out of this formation by forming normal products with other groups of it. This generalises a result of Cossey on T-groups and supersolvable groups.
Hyperconvex spaces revisited
Authors: Borkowski Marcin , Bugajewski Dariusz , Przybycień Hubert 
Published: April 2009

In this paper we describe a construction of a large class of hyperconvex metric spaces. In particular, this construction contains well-known examples of hyperconvex spaces such as ℝ2with the “river” metric or with the radial one.Further, we investigate linear hyperconvex spaces with extremal points of their unit balls. We prove that only in the case of a plane (and obviously a line) is there a strict connection between the number of extremal points of the unit ball and the hyperconvexity of the space.Some additional properties concerning the notion of hyperconvexity are also investigated.
Equicontinuity of a graph map
Authors: Sun Taixiang , Zhang Yongping , Zhang Xiaoyan 
Published: April 2009

LetGbe a graph, andf:G→Gbe a continuous map with periodic points. In this paper we show that the following five statements are equivalent.(1)fis equicontinuous.(2) There exists some positive integerNsuch thatfNis uniformly convergent.(3)fisS-equicontinuous for some positive integer sequenceS= {n1<n2< …}.(4) Ω(x, f) =ω(x, f)for everyx∈G.(5)is a periodic map.
A deformation of the Alexander polynomials of knots yielding lens spaces
Authors: Kadokami Teruhisa , Yamada Yuichi 
Published: April 2009

For a knotKin a homology 3-sphere Σ, by Σ(K;p/q), we denote the resulting 3-manifold ofp/q-surgery alongK. We say that the manifold or the surgery isof lens typeif Σ(K;p/q) has the same Reidemeister torsion as a lens space.We prove that, for Σ(K;p/q) to be of lens type, it is a necessary and sufficient condition that the Alexander polynomialΔK(t)ofKis equal to that of an (i, j)-torus knotT(i, j)modulo (tp– 1).We also deduce two results: If Σ(K;p/q) has the same Reidemeister torsion asL(p, q')then (1)(2) The multiple of ΣK(tk) overk∈ (i) is ±tmmodulo (tp– 1), where (i) is the subgroup in (Z/pZ)×/{±1} generated byi. Conversely, if a subgroupHof (Z/pZ)×/{±l} satisfying that the product of ΣK(tk) (k∈H) is ±tmmodulo (tp– 1), thenHincludesiorj.Here,i, jare the parameters of the torus knot above.
Some remarks on the number of points on elliptic curves over finite prime field
Authors: He Saiying , McLaughlin J. 
Published: April 2009

Let p ≥ 5 be a prime and for a, b ε p, let Ea, b denote the elliptic curve over p with equation y2 = x3 + ax + b. As usual define the trace of Frobenius ap, a, b by
We use elementary facts about exponential sums and known results about binary quadratic forms over finite fields to evaluate the sums and for primes p in various congruence classes.As an example of our results, we prove the following: Let p ≡ 5 (mod 6) be prime and let b ε *p. Then
Exponential attractors for abstract parabolic systems with bounded delay
Authors: Pražák Dalibor 
Published: April 2009

We show that a suitable adaptation of the so-called method of trajectories can be used to construct an exponential attractor for a very general class of nonlinear reaction-diffusion systems with a bounded delay.In particular, we assume that the dependence on the past history is controlled via convolution with a possibly singular measure. Assuming a priori that the solutions are bounded, a simple proof of the existence of an exponential attractor is given under very little regularity requirements.
Macmahon's partition analysis IX:K-gon partitions
Authors: Andrews George E. , Paule Peter , Riese Axel 
Published: April 2009

Dedicated to George Szekeres on the occasion of his 90th birthdayMacMahon devoted a significant portion of Volume II of his famous bookCombinatory Analysisto the introduction of Partition Analysis as a computational method for solving combinatorial problems in connection with systems of linear diophantine inequalities and equations. In a series of papers we have shown that MacMahon's method turns into an extremely powerful tool when implemented in computer algebra. In this note we explain how the use of the package Omega developed by the authors has led to a generalisation of a classical counting problem related to triangles with sides of integer length.
Nonoscillation of third order retarded equations
Authors: Singh Bhagat , Dahiya R.S. 
Published: April 2009

The third order delay equationy‴(t) + a(t)yτ(t) = 0is studied for its nonoscillatory nature under the general condition in which a(t) has been allowed to oscillate. It is shown by way of a differential inequality that if g(t) is a thrice differentiable and eventually positive function theng‴(t) + t2|a(t)|g(t) ≤ 0is sufficient for this equation to have bounded nonoscillatory solutions.
Jackson's Theorem for locally compact abelian groups
Authors: Bloom Walter R. 
Published: April 2009

If f is a p–th integrable function on the circle group and ω(p; f; δ) is its mean modulus of continuity with exponent p then an extended version of the classical theorem of Jackson states the for each positive integer n, there exists a trigonometric polynomial tn of degree at most n for which‖f-tn‖p ≤(p; f; 1/n).In this paper it will be shewn that for G a Hausdorff locally compact abelian group, the algebra L1(G) admits a certain bounded positive approximate unit which, in turn, will be used to prove an analogue of the above result for Lp(G).
On rational approximations of the exponential function at rational points
Authors: Mahler Kurt 
Published: April 2009

Letp, q, u, andvbe any four positive integers, and let further δ be a number in the interval 0 < δ ≤ 2. In this note an effective lower bound forqwill be obtained which insures thatIn the special case whenu=v= 1, it was shown by J. Popken,Math. Z. 29 (1929), 525–541, thatHerecandCare two positive absolute constants which, however, were not determined explicity. A similarly non-effective result was given in my paper,J. reine angew. Math. 166 (1932), 118–150.The method of this note depends again on the classical formulae by Hermite which I applied alsoop. cit.
The hyper-archimedean kernel sequence of a lattice-ordered group
Authors: Martinez Jorge 
Published: April 2009

Thehyper-archimedean kernel Ar(G)of a lattice-ordered group (hence forthl–group) is the largest hyper-archimedean convexl–subgroup of thel–groupG. One definesArσ(G), for an ordinal σ asif a is a limit ordinal, and as the uniquel–ideal with the property thatArσ(G)/Ar.σ–1(G)=Ar(G/Arσ–1(G)), otherwise. The resulting "Loewy"-like sequence of characteristicl–ideals,Ar(G)⊆Ar2(G) ⊆ … ⊆Arσ(G)⊆ …, is called thehyper-archimedean kernel sequence. The first result of this note says that eachArσ(G)⊆Ar(G)”.Most of the paper concentrates on archimedeanl–groups; in particular, the hyper-archimedean kernels are identified for:D(X), whereXis a Stone space, a large class of free products of abelianl–groups, and certainl–subrings of a product of real groups.It is shown that even for archimedeanl–groups the hyper-archimedean kernel sequence may proceed pastAr(G).
On a new finite non–abelian simple group of Janko
Authors: Wong S. K. 
Published: April 2009

Two new simple groups have recently been discovered by Z. Janko. One of these groups has order 50,232,960. As a first step in showing that there is precisely one (up to isomorphism) simple group of order 50,232,960, the author proves in this paper the following result: If G is a non-abelian simple group of order 50,232,960, then the structure of the centralizer of an element of order two in G is uniquely determined.In a note added on 21 April 1969 to this paper, the author announces that he has proved the uniqueness of the simple group of order 50,232,960.
Varieties of topological groups II
Authors: Morris Sidney A. 
Published: April 2009

This paper is a sequel to one entitled “Varieties of topological groups”. The variety V of topological groups is said to be full if it contains every group which is algebraically isomorphic to a group in V For any Tychonoff space X, the free group F of V on X exists, is Hausdorff and disconnected, and has X as a closed subset. Any subgroup of F which is algebraically fully invariant is a closed subset of F. If X is a compact Hausdorff space, then F is normal. Let V be a full Schreier variety and X a Tychonoff space, then all finitely generated subgroups of F are free in V.A β-variety V is one for which the free group of V on each compact Hausdorff space exists and is Hausdorff. For any β-variety V and Tychonoff space X, the free group of V exists, is Hausdorff and has X as a closed subset. A necessary and sufficient condition for V to be a β-variety is given.The concept of a projective (topological) group of a variety V is introduced. The projective groups of V are shown to be precisely the summands of the free groups of V. A finitely generated Hausdorff projective group of a Schreier variety V is free in V.
High Reynolds number flow between torsionally oscillating disks
Authors: Smith K.G. , Pillow A.F. 
Published: April 2009

In this paper the problem solved is that of unsteady flow of a viscous incompressible fluid between two parallel infinite disks, which are performing torsional oscillations about a common axis. The solution is restricted to high Reynolds numbers, and thus extends an earlier solution by Rosenblat for low Reynolds numbers.The solution is obtained by the method of matched asymptotic expansions. In the main body of the fluid the flow is inviscid, but may be rotational, and in the boundary layers adjacent to the disks the non-linear convection terms are small. These two regions do not overlap, and it is found that in order to match the solutions a third region is required in which viscous diffusion is balanced by steady convection. The angular velocity is found to be non-zero only in the boundary layers adjacent to the disks.
Quantum logic as an implication algebra
Authors: Finch P.D. 
Published: April 2009

For the purpose of this paper a logic is defined to be a non-empty set of propositions which is partially ordered by a relation of logical implication, denoted by “≤”, and which, as a poset, is orthocomplemented by a unary operation of negation. The negation of the proposition x is denoted by NX and the least element in the logic is denoted by 0, we write NO = 1.A binary operation “→” is introduced into a logic, the operation is interpreted as material implication so that “x → y” is a proposition of the logic and is read as “x materially implies y”. If material implication has the properties11. (x → 0) = NX,
12. if x ≤ y then (z → x) ≤ (z → y),
13. if x ≤ y then x ≤ (y ≤ z)= x → z,
14. x ≤ {y → N(y → Nx)},
then the logic is an orthomodular lattice. The lattice operations of join and meet are given by
x ∨ y = Nx → N(Nx → Ny)
x ∧ y = N(X → N(x → y))
and, in terms of the lattice operations, the material implication is given by
(x → y) = (y ∧ x) ∨ NX.Moreover the logic is a Boolean algebra if, and only if, in addition to the properties above, material implication satifies
15. (x → y) = (Ny → Nx).
One variable equations over semigroups
Authors: Levin Frank 
Published: April 2009

An analogue of the theorem on the existence of a primitive element for separable extensions of fields is presented for semigroups. This has two immediate consequences.(i) A semigroup is algebraically closed with respect to equations in several variables if and only if it is closed with respect to equations in a single variable.(ii) Any countable semigroup C is embedded in a two-generator semigroup, one of whose generators is in C.Further, a proof is given that any free product of a semigroup of order one with one of order two is SQ–universal, that is, its factor semigroups embed all countable semigroups. The proofs are adaptations of one used by Trevor Evans, Proc. Amer. Math. Soc. 3 (1952), 614–620. to show that a free product of two infinite cyclic semigroups is SQ–universal.
An application of a theorem of Gaschütz
Authors: Lausch H. 
Published: April 2009

A theorem of Gaschütz is used to prove: Let τ be a homomorphism of the distributively generated near-ring R with identity element and descending chain condition for left modules, τ have finite kernel, and U(R) be the group of units of R; then U(Rτ) = U(R)τ.Furthermore it is shown that the finiteness condition for ker τ can be dropped in the case of R being a ring.
A Fritz John theorem in complex space
Authors: Craven B.D. , Mond B. 
Published: April 2009

Necessary conditions of the Fritz John type are given for a class of nonlinear programming problems over polyhedral cones in finite dimensional complex space.Consider the problem towhereSis a polyhedral cone in, andCmandf:C2n→C,g:C2n→Cmare differentiable functions. A necessary condition for a feasible pointz0to be optimal is that there exist τ≥0, ν ∈S*, (τ, ν) ≠ 0, such thatand
On a class of diophantine inequalities
Authors: Mahler Kurt 
Published: April 2009

As a special case of more general results, it is proved in this note that, if α is any real number and δ any positive number, then there exists a positive integer X such that the inequalityhas infinitely many solutions in positive integers h and Yh.The method depends on the study of infinite sequences of real linear forms in a fixed number of variables. It has relations to that used by Kronecker in the proof of his classical theorem and can be generalised.
A remark on a mean value theorem of Alexander Weinstein in Generalized Axially Symmetric Potential Theory
Authors: Diaz J.B. , Leschen John G. 
Published: April 2009

Cordially dedicated to Professor Alexander Weinstein, on the occasion of his Seventyseventh birthday, January 21, 1974.This note contains the proof of an extension of Alexander Weinstein's mean value theorem for Generalized Axially Symmetric Potential Theory.
Polar analogues of two theorems by Minkowski
Authors: Mahler Kurt 
Published: April 2009

Since Minkowski's time, much progress has been made in the geometry of numbers, even as far as the geometry of numbers of convex bodies is concerned. But, surprisingly, one rather obvious interpretation of classical theorems in this theory has so far escaped notice.Minkowski's basic theorem establishes an upper estimate for the smallest positive value of a convex distance function F(x) on the lattice of all points x with integral coordinates. By contrast, we shall establish a lower estimate for F(x) at all the real points X on a suitable hyperplanewith integral coefficients u1, …, un not all zero. We arrive at this estimate by means of applying to Minkowski's Theorem the classical concept of polarity relative to the unit hypersphereThis concept of polarity allows generally to associate with known theorems on point lattices analogous theorems on what we call hyperplane lattices. These new theorems, although implicit in the old ones, seem to have some interest and perhaps further work on hyperplane lattices may lead to useful results.In the first sections of this note a number of notations and results from the classical theory will be collected. The later sections deal then with the consequences of polarity.
Preregular maps between Banach lattices
Authors: Birnbaum David A. 
Published: April 2009

A continuous linear map from a Banach lattice E into a Banach lattice F is preregular if it is the difference of positive continuous linear maps from E into the bidual F″ of F. This paper characterizes Banach lattices B with either of the following properties:(1) for any Banach lattice E, each map in L(E, B) is preregular;(2) for any Banach lattice F, each map in L(B, F) is preregular.It is shown that B satisfies (1) (repectively (2)) if and only if B′ satisfies (2) (respectively (1)). Several order properties of a Banach lattice satisfying (2) are discussed and it is shown that if B satisfies (2) and if B is also an atomic vector lattice then B is isomorphic as a Banach lattice to 11(Γ) for some index set Γ.
On a problem of K. A. Bush concerning Hadamard matrices
Authors: Wallis W.D. 
Published: April 2009

K.A. Bush has asked whether there is a symmetric Hadamard matrix of order m2, m even, which can be partitioned into an m × m array of m × m blocks, such that:(i) each diagonal block has every entry 1;(ii) each non-diagonal block has every row-sum zero?We give two ways of constructing such matrices.
A note on the countable chain condition and sigma-finiteness of measures
Authors: Bhaskara Rao K.P.S. , Rao M. Bhaskara 
Published: April 2009

The objectives of this paper are the following:(1) to show that a theorem of Ficker is incorrect;(2) to show that a stronger version of Ficker's Theorem is valid for a certain class of measures;(3) characterize all σ-algebras on which every measure is a countable sum of finite measures.