bluuebunny/crossref_metadata_2025_split huggingface dataset:
Two-dimensional flow past a flat plate in the presence of boundary walls
Authors: Todd L. 
Published: November 2008

1. Introduction. Flow of viscous fluid at low Reynolds number has attracted a great deal of attention over the last hundred years or so and is still an area of active research at the present time. For a general background on this field, we refer the reader to Langois(4). The present paper is concerned with steady flow past a finite flat plate which spans a long rectangular channel, of large aspect-ratio, at the centre ‘line’ (see Fig. 1). The flow is motivated by a constant pressure difference which is appliedbetween the ends of the channel. We examine such flows when the Reynolds number based on the semi-channel height, a, is much less than 1. Our main task is to show that Stokes approximation, i.e. neglection of the inertia terms, is uniformly valid † over the whole flow field. (†Such a result contrasts with the non-uniformity of the approximation when the channel walls are removed and the external flow is a uniform stream.) Harper & Chang (1) who treat the corresponding problem for a circular cylinder, give a full account of recent theoretical and experimental work on this class of fluid flows. We shall therefore defer comments on related papers until the appropriate part of the text.
Some cyclic and other inequalities. III
Authors: Diananda P. H. 
Published: November 2008

1. Introduction. In a recent paper (2) Daykin has made the Conjecture. If t is real, thenwhereHe has proved (1, 2) that (i) Φ(t) is a convex function of t, (ii) Φ(t)≥ n if t ≥ 0 or 2, and (iii) Φ(t) takes values arbitrarily close to ½n if n is even, x2 = x4 = … = xn = 1, and xl = x3 = … = xn-1 and t have suitable small positive values. It is known (3) that (1) is true if t = 1.
The generation of surface waves over a sloping beach by an oscillating line-source. I. The general solution
Authors: Morris Clare A. N. 
Published: November 2008

AbstractThe problem of wave generation by a line source of sinusoidally varying strength situated in water above a beach of arbitrary angle α(0 < α ≤ π) is solved by the use of a Laplace-integral representation of the solution. It is shown that a solution can be constructed which is regular at the shoreline and gives an outgoing wave-train at infinity.
Almost-conservative second-order differential equations
Authors: Swinnerton-Dyer H. P. F. 
Published: November 2008

During the last thirty years an immense amount of research has been done on differential equations of the formwhere ε > 0 is small. It is usually assumed that the perturbing term on the right-hand side is a ‘good’ function of its arguments and that its dependence on t is purely trigonometric; this means that there is an expansion of the formwhere the ωn are constants, and that one may impose any conditions on the rate of convergence of the series which turn out to be convenient. Without loss of generality we can assumeand for convenience we shall sometimes write ω0 = 0. Often f is assumed to be periodic in t, in which case it is implicit that the period is independent of x and ẋ (We can also allow f to depend on ε, provided it does so in a sensible manner.)
On a summation method of S. Verblunsky
Authors: Kwee B. 
Published: November 2008

Let 0 ≤ λ0 < λ1 < … < λn → ∞, and letIf as ω → ∞, we write Suppose thatconverges for σ > 0,where τp(h) is finite for |h| < δ. Ifwe write
Anticritical graphs
Authors: Harary Frank , Thomassen Carsten 
Published: November 2008

AbstractThe term ‘critical graph’ has been used most frequently to mean a graph such that the removal of any line decreases the chromatic number. This can be generalized to define a graph G to be ‘critical (μ)’ for an arbitrary invariant, μ if, for each line e, μ(G – e) ≠ μ(G). Analogously we may consider any line e which joins two points not already adjacent in G and define G as ‘anticritical (μ)’ if μ(G + e) ≠ μ(G). Anticritical graphs are investigated here with respect to the following invariants: chromatic number, line-chromatic number, point-connectivity, line-connectivity, point-independence number, line-independence number, diameter, radius, and cyclability number.
Automorphism sequences of free nilpotent groups of class two
Authors: Dyer Joan L. , Formanek Edward 
Published: November 2008

In this paper we prove that the automorphism group A(N) of a free nilpotent group N of class 2 and finite rank n is complete, except when n is 1 or 3. Equivalently, the centre of A(N) is trivial and every automorphism of A(N) is inner, provided n ≠ 1 or 3. When n = 3, A(N) has an our automorphism of order 2, so A(A(N)) is a split extension of A(N) by . In this case, A(A(N)) is complete. These results provide some evidence supporting a conjecture of Gilbert Baumslag that the sequencebecomes periodic if N is a finitely generated nilpotent group.
Prototurbulent motions in dissipative model systems
Authors: Thyagaraja A. 
Published: November 2008

AbstractTwo different models of open, dissipative systems are considered. The stability and the asymptotic manifold of solutions are studied with respect to the variation of a model viscosity ν. Bifurcation theorems result from the analysis which shows the existence of a class of ‘prototurbulent’ motions. These are generalisations of the quasi-periodic asymptotic motions characteristic of Hopf's well-known mathematical model of turbulence. Given the statistics of the driving external field, it is shown how to calculate the correlation functions of the asymptotic motions (as t → ∞) for arbitrary values of the model viscosity. The systems treated are non-linear and except in special cases, cannot be solved in closed form. The relation to real systems is discussed. The effects of dimensionality on the qualitative nature of the motion is explored. It is found that for the models treated, perturbations of the external field do not affect the qualitative properties. Certain ‘mean’ quantities vary smoothly with the variation of the external field, but the details of the motion may be sensitive to the external perturbations. It is also found that even if the motion is strictly not quasiperiodic in the sense of Hopf and Landau, almost all asymptotic motions have a recurrent character under certain conditions. Some of the models also show the reverse of this behaviour, i.e. a non-dissipative, quasi-recurrent approach to ‘equilibrium’. This phenomenon can occur if the number of active degrees of freedom at a non-zero model viscosity is infinite.
On Baker's inequality for linear forms in logarithms
Authors: van der Poorten Alfred J. 
Published: November 2008

AbstractLet α1, …, αn an be non-zero algebraic numbers with degrees at most d and heights respectively Al, …, An (all Aj ≥ 4) and let b1, …, bn be rational integers with absolute values at most B (≥ 4). Denote by p a prime ideal of the field and suppose that p divides the rational prime p. WriteThen it is shown thatfor some effectively computable constant C > 0 depending only on n, d and p. The argument suffices to prove similarly that in the complex case, iffor any fixed determination of the logarithms, thenfor some effectively computable constant C′ > 0 depending only on n and d (and he determination of the logarithms).
The positive-definiteness of the complete symmetric functions of even order
Authors: Hunter D. B. 
Published: November 2008

An important role in the classical theory of symmetric functions of a real n-tuple x = (x1, x2, …, xn) is played by the complete symmetric functions or homogeneous product sums hr defined by the generating function(see Littlewood (5), p. 82). In an earlier paper (4) I conjectured that h2r is positive definite. The main object of the present paper is to prove this conjecture in a rather sharper form.
On the null spaces of linear Fredholm operators depending on several parameters
Authors: Shearer M. 
Published: November 2008

AbstractLet X, Y be real Banach spaces, and let = {f(λ):λ ∈ m} be an m-parameter family of bounded linear operators from X to Y, with f(λ) depending continuously on λ. The cases m = 1 and m = 2 are considered, and conditions on are found which determine the null space of f(λ) for all λ near a given λ0 such that f(λ0): X → Y is a Fredholm operator. The results obtained are shown to be of particular interest in perturbed bifurcation theory.
On the norm of an inner derivation of a C*-algebra
Authors: Archbold R. J. 
Published: November 2008

Let A be a C*-algebra with centre Z. If a ∈ A, the bounded linear mapping x → + ax – xa (x ∈ A) is called the inner derivation of A induced by a, and we denote it by D(a, A). A simple application of the triangle inequality shows thatwhere d (a; Z) denotes the distance from a to Z in the normed space A.
Normal bundles in flag bundles
Authors: Ilori Samuel A. 
Published: November 2008

AbstractLet i: Y ↪ X be an inclusion map of non-singular irreducible algebraic quasi-projective varieties defined over an algebraically closed field. Let E be an algebraic vector bundle over X and H be a sub-bundle of the induced bundle, i*E. If j:F(H) ↪ F(E) is the corresponding inclusion map of (incomplete) flag bundles, then we derive the normal bundle N(F(H), F(E)) in terms of the bundles H and E, the tangent bundles of Y and X as well as the tautological bundles over F(H).
The structure of type I JBW-algebras
Authors: Stagey P. J. 
Published: November 2008

A complete normed real Jordan algebra A with 1 is said to be a JB-algebra if and only if, for all a, b ∈ A,where o denotes the Jordan product on A. If A is a Banach dual space then A is known as a JBW-algebra. In this case, by Theorem 3·9 of (7),where Aex is an exceptional Jordan algebra and Asp is Jordan isomorphic to a JW-algebra (i.e. a weakly closed Jordan algebra of self-adjoint operators on a complex Hilbert space). Theorem 3–9 of (7) gives a description of Aex and so in this paper attention will be restricted to JW-algebras. Such an algebra A is said to be of type I if there exists an idempotent e in A with central cover equal to 1 such that e is abelian i.e. such that eAe is commutative as a set of operators. (See § 7 of (11) for further details.) A type I algebra A is said to be of type In, where n is some cardinal number, if there exists an orthogonal family {eα: α ∈ Λ} of n abelian projections in A such that Σαeα = 1 and such that, for each α ≠ β, there exists a symmetry sαβ in A with eβ = sαβeαsαβ. (A symmetry is an element sαβ of A such that ). By theorems 15 and 16 of (11) any type I JW-algebra A can be uniquely decomposed into a direct sum of type In(α) JW-algebras for suitable cardinal numbers n(α). Thus in order to investigate the structure of type I JW-algebras it is sufficient to consider type In JW-algebras.
Holomorphic sectional curvatures of indefinite complex Grassmann manifolds
Authors: Montiel Sebastian , Romero Alfonso 
Published: November 2008

In (2), indefinite Kählerian manifolds have been examined from the point of view of holomorphic sectional curvature. Examples in (2) show that the analogue of Kulkarni's theorem (see (4), p. 173) for the holomorphic sectional curvature is false and the best possible result in the direction is:Theorem 1 (known, (2)). Let M be a connected indefinite Kählerian manifold with complex dimension n ≥ 2. If the holomorphic sectional curvature of M is bounded above and bounded below, then M is an indefinite complex space form.
On intrinsic eigenstates in plasticity with generalized variables
Authors: Hill R. 
Published: November 2008

AbstractThe classical specification of elastic/plastic or rigid/plastic response in metals is reformulated in generalized variables. The allowed measures of strain are sets of any geometric magnitudes that jointly determine the shape of a material element; the allowed measures of stress are generated by work-conjugacy. The choice of variables affects the parameters and qualitative features of the constitutive framework; these dependences are made explicit by concise formulae of transformation.Eigenstates intrinsic to the material are considered wherein the strain can change while the conjugate stress is either stationary or coupled differentially with the strain. Such configurations are associated with incipient branching of the strain response to a prescribed variation of the conjugate stress. Sensitivity to the loading environment is evaluated for both elastic/plastic and rigid/plastic materials. This synoptic approach to eigenproblems is illustrated in the context of materials testing.
Two limit theorems for ergodically regenerated stochastic processes
Authors: Kupka Joseph 
Published: November 2008

AbstractThere is a subtle difference between the recurrent event of Feller and the regenerative phenomenon of Kingman: The former regenerates an entire ambient process, whereas the latter regenerates only itself. This paper generalizes Feller's definition to a discrete regenerative phenomenon E in association with an arbitrary discrete-time stochastic process X. Two limit theorems of a general character are proved for the process X when it is regenerated by an ergodic phenomenon E. The first implies that X becomes strictly stationary at a uniform rate which is determined solely by the asymptotic behaviour of E. The second is essentially a mixing convergence theorem which implies the asymptotic independence of regenerating and regenerated events. Applications include (1) the outright independence of the regenerating events and the regenerated events which occur ‘at the end of time’, and (2) the identification of the transient features of X with the null sets of the stationary limiting probability. Numerous open questions are posed.
Countable lattice-ordered groups
Authors: Glass A. M. W. 
Published: November 2008

A lattice-ordered group is a group and a lattice such that the group operation distributes through the lattice operations (i.e. f(g ∨ h)k = fgk ∨ fhk and dually). Lattice-ordered groups are torsion-free groups and distributive lattices. They further satisfy f ∧ g = (f−1 ∨ g−1)−1 and f ∨ g = (f−1 ∧ g−1)−1. Since the lattice is distributive, each lattice-ordered group word can be written in the form ∨A ∧B ωαβ where A and B are finite and each ωαβ is a group word in {xi: i ∈ I}. Unfortunately, even for free lattice-ordered groups, this form is not unique. We will use the prefix l- for maps between lattice-ordered groups that preserve both the group and lattice operations, and e for the identity element. A presentation (xi;rj(x) = e)i∈I, j∈J is the quotient of the free lattice-ordered group F on {xi: i∈I} by the l-ideal (convex normal sublattice subgroup) generated by its subset {rj(x): j ∈ J}. {xi: i ∈ I} is called a generating set and {ri(x):j∈J} a defining set of relations. If I and J are finite we have a finitely presented lattice-ordered group. If we can effectively enumerate all lattice-ordered group words r1(x), r2(x),… in xi; i∈I}. If I is finite and J (for this enumeration) is a recursively enumerable set, we say that we have a recursively presented lattice-ordered group. Throughout Z denotes the group of integers and ℝ the real line.Our purpose in this paper is to prove the natural analogues of three theorems from combinatorial group theory (5), chapter IV, theorems 4·9, 3·1 and 3·5-in particular, theorem C is a natural analogue of an unpublished theorem of Philip Hall (4).
On conjectures of Moore and Serre in the case of torsion-free suspensions
Authors: Selick Paul 
Published: November 2008

Let p be a prime. A space X is said to have a homotopy exponent at p if multiplication by pr annihilates the p-torsion of πn(X) for some non-negative integer r independent of n. X is said to have totally finite rational homotopy if ⊕n πn (X) ⊗ ℚ is a finite vector space. Moore has conjectured that these properties are related for finite simply connected CW complexes.Moore's Conjecture. A space having the homotopy type of a finite simply connected CW complex has a homotopy exponent at p if and only if it has totally finite rational homotopy.For convenience I will divide the conjecture into its two implications so that I can refer to each separately.
The number of small-amplitude limit cycles of Liénard equations
Authors: Blows T. R. , Lloyd N. G. 
Published: November 2008

We consider second order differential equations of Liénard type:Such equations have been very widely studied and arise frequently in applications. There is an extensive literature relating to the existence and uniqueness of periodic solutions: the paper of Staude[6] is a comprehensive survey. Our interest is in the number of periodic solutions of such equations.
Holomorphic and abstract inducing
Authors: Hannabuss K. C. 
Published: November 2008

AbstractA method of constructing projective representations of separable locally compact groups in reproducing kernel Hilbert spaces is presented, based on the generalized inducing process of Rieffel and Fell. Examples show that the method can be used to construct some well-known holomorphically induced representations. Some representations on cohomology spaces are also described.
a-convexity
Authors: Pinch R. G. E. 
Published: November 2008

For a ε R, we define a subset V of Rn to be a-convex if x, y ε V impliesClearly V is (1 — a)-convex iff it is a-convex: V is convex iff it is a-convex for all a ε [0, 1], and any set is 1-convex. We define the a-convex hull of V to be the intersection of all a-convex subsets of Rn containing V. Put D = 0,1} and D(a) the a-convex hull of D in R1. If V is a-convex and x, y ε V, then V must contain the points of the line through x, y given by {tx + (1 — t) y: t ε D(a)} and so in this paper we concentrate on the study of D(a).
Holomorphic maps of discs into balls of lp-spaces
Authors: Globevnik Josip 
Published: November 2008

AbstractLet 1 ≤ p < ∞, let be the open unit ball of lp and let Δ be the open unit disc in ℂ. We prove that there is a holomorphic map such that F(Δ) is dense in and such that whenever .
Inequivalent, bordant group actions on a surface
Authors: Livingston Charles 
Published: November 2008

An action of a group, G, on a surface, F, consists of a homomorphismø: G → Homeo (F).We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with ø(g) orientation-preserving for all g ε G. In addition we will consider only effective (ø is injective) free actions. Free means that ø(g) is fixed-point-free for all g ε G, g ≠ 1. This paper addresses the classification of such actions.
A lower bound for the spectrum of a one-dimensional pseudo-differential operator
Authors: Wong M. W. 
Published: November 2008

In a 1928 paper [1], Hardy and Littlewood published the following inequality which is valid for all non-negative measurable functions ƒ and g on ( − ∞, ∞):where 1 < p, q < ∞, 0 < λ < 1, l/p + 1/q + λ = 2 and Cλp, q depends only on λ, p, q; ‖ƒ‖p and ‖g‖q are the Lp and Lq norms of ƒ and g respectively. See also p. 288 of the monograph [2] by Hardy, Littlewood and Pólya for a discussion of this inequality and related matters.
The Markov branching process with density-independent catastrophes I. Behaviour of extinction probabilities
Authors: Pakes Anthony G. 
Published: November 2008

Let (Xt: t ≥ 0) be the Markov branching process (MBP) with a density independent catastrophe component. It is denned to be the Feller process on the non-negative integers having the generatorHere {pj} is the offspring distribution which satisfies p1 = 0 and p0 < 1, ρ is the per capita birth rate, κ is the rate of occurrence of catastrophe events, {δj: j ≥ 0} is the decrement distribution and . Thus Xt can be interpreted as the size of a population in which individuals reproduce according to the rules of a MBP – see Athreya and Ney[1], chap, III – and where there is an external and independent Poisson process of catastrophe events, κ per unit time, and if j < i each such event reduces the population size by j with probability δj. Usually we assume that δ0 = 0 on the basis that a catastrophe always reduces the population size. Let f(s) = Σpjsj and assume that . This ensures that the MBP obtained by setting κ = 0 is regular ([1], p. 105) and hence (Xt) is the unique Markov process corresponding to the above generator when κ > 0.
Some groups which classify knots
Authors: Zimmermann B. 
Published: November 2008

Groups associated to a knot in S3 which classify the knot have been constructed by Conway and Gordon [4], Simon [12] and Whitten[16]; see also [1] and [19] for certain special classes of knots. In this note we show that for a knot K in S3 of the groups π1(S3/K)/〈malb〉 classify the knot; here m resp. l denote a meridian resp. longitude of the knot and 〈〉 denotes normal closure. This is based on Thurston's orbifold geometrization theorem [13–15] and the following result (see also [8, 19]):Theorem 1. Let O1 and O2 be good closed irreducible 3-orbifolds which possess a decomposition into geometric pieces (along Euclidean 2-suborbifolds, see [2, 15]) and have infinite (orbifold-) fundamental group. Then O1 and O2 are diffeomorphic (as orbifolds) if and only if π1 O1 and π1 02 are isomorphic.
The reduction of a pair of singular integral equations
Authors: Porter D. 
Published: November 2008

AbstractA method is derived for converting a pair of coupled singular integral equations of a certain form into a single equation of the same (Cauchy-separable) type. Reduction methods for systems of singular integral equations are generally directed towards the construction of equivalent Fredholm equations. Preservation of the singular nature of the kernel in the reduction process permits the powerful techniques associated with Cauchy kernels to be used in seeking closed solutions of the original pair.The example given, derived previously from a problem in wave diffraction theory, illustrates many aspects of the method.
Existentially closed central extensions of locally finite p-groups
Authors: Leinen Felix , Phillips Richard E. 
Published: November 2008

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.
Two notes on ideal-transforms
Authors: Katz Daniel , Ratliff Louis J. 
Published: November 2008

AbstractThe first note gives two new characterization of the ideal-transform T(I) of a finitely generated regular ideal I in a large class of rings. Specifically, if b is a regular element in I, then there exists a regular element c ∈ I and a multiplicatively closed set S of regular elements in R such that T(I) = T((b, c)R) = Rb ∩ Rc = Rb ∩ Rs, so T(I) is the ideal-transform of an ideal generated by two elements, and every ring of the form Rb ∩ Rs is an ideal-transform. The second theorem shows that if T(I) is integrally closed, then it is a Krull ring. As an application of these results we strengthen some known results concerning when certain ideal-transforms of the Rees ring R(R, I) are finite or integral extension rings of R(R, I).
Torsion classes in the cohomology of congruence subgroups
Authors: Arlettaz Dominique 
Published: November 2008

For any prime number p, let Γn, p denote the congruence subgroup of SLn(ℤ) of level p, i.e. the kernel of the surjective homomorphism fp: SLn(ℤ) → SLn(p) induced by the reduction mod p (Fp is the field with p elements). We defineusing upper left inclusions Γn, p ↪ Γn+1, p. Recall that the groups Γn, p are homology stable with M-coefficients, for instance if M = ℚ, ℤ[1/p], or ℤ/q with q prime and q ╪ p: Hi(Γn, p; M) ≅ Hi(Γp; M) for n ≥ 2i + 5 from [7] (but the homology stability fails if M = ℤ or ℤ/p).
Perturbation of functions by the paths of a Lévy process
Authors: Evans Steven N. 
Published: November 2008

In a recent paper Mountford [4] showed, using an ingenious probabilistic argument, that if X is a real-valued stable process with index α < 1 and f: [0, ∞) → ℝ is a non-constant continuous function, thenwhere we use the notation |A| for the Lebesgue measure of a Lebesgue measurable set A ⊂ ℝ. The argument in [4] appears to make strong use of the strict scaling properties of X and the ‘intermediate value’ property of f.