On K‐Theory of Simplicial Rings and Degreewise Constructions

We give a measure of the difference between Waldhausen's definition of the Ktheory of a simplicial ring and the definition we obtain by extending Quillen's definition degreewise. This has computational advantages as the degreewise Ktheory sometimes is simpler to work with.     

Hardy and Bellman Transformations in Spaces Close to L ∞ and L 1

The replacement of coefficients of a trigonometric series by their arithmetic averages gives rise to the Hardy operator. The Bellman operator is its adjoint. The spaces _Lp with p[1,) are invariant under the Hardy transformation. This result was proved by Hardy. On the other hand, the space L is not invariant under the Hardy transformation, and the space _L1 is not invariant under the Bellman transformation. Golubov proved that the space BMO is not invariant under the Hardy transformation and is not invariant under the Bellman operator. In the present paper, the exact ``shift' of the domain under the action of these operators is described for certain Orlicz, Lorenz, and Marcinkiewicz spaces and the spaces BMO and . For the Hardy operator, this shift occurs if the domain is close to L , and for the Bellman operator the same happens if the domain is close to L ₁. Bibliography: 15 titles.     

Distinguishing Between Symmetric Spaces and L ∞ by a Differential Basis

One of the fundamental problems in the theory of differentiation of integrals is the following. Let X and Y be two spaces which are different in some sense. Does there exist a differential basis that differentiates the space X, i.e., all integrals of functions from X, but not integrals of functions from Y, i.e., there exists a function from Y whose integral cannot be differentiated by this basis. In this paper we construct a basis which differentiates the space L but does not differentiate any other symmetric space X L.     

Inhomogeneous Lévy Processes in Lie Groups and Homogeneous Spaces

We obtain a representation of an inhomogeneous Lévy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Since the stochastic continuity is not assumed, our result generalizes the well-known Lévy–Itô representation for stochastic continuous processes with independent increments in ? ^d and its extension to Lie groups.     

Functionals of a Lévy Process on Canonical and Generic Probability Spaces

We develop an approach to Malliavin calculus for Lévy processes from the perspective of expressing a random variable \(Y\) by a functional \(F\) mapping from the Skorohod space of càdlàg functions to \(\mathbb {R}\), such that \(Y=F(X)\) where \(X\) denotes the Lévy process. We also present a chain-rule-type application for random variables of the form \(f(\omega ,Y(\omega ))\). An important tool for these results is a technique which allows us to transfer identities proved on the canonical probability space (in the sense of Solé et al.) associated to a Lévy process with triplet \((\gamma ,\sigma ,\nu )\) to an arbitrary probability space \((\varOmega ,\mathcal {F},\mathbb {P})\) which carries a Lévy process with the same triplet.     

A comparison of the alpha‐ and beta‐characteristic functions in cooperative non‐sidepayment n‐person games 1

This article reports a test of theories of payoff allocation in n‐person game‐theoretic systems. An experimental study was conducted to test the relative predictive accuracy of three solution concepts (imputation set, stable set, core) in the context of 4‐person, 2‐strategy non‐sidepayment games. Predictions from each of the three solution concepts were computed on the basis of both α‐effectiveness (von Neumann‐Morgenstern) and β‐effectiveness (Aumann), making a total of six predictive theories under test. Two important results emerged. First, the data show that the g‐imputation set was more accurate than the a‐imputation set, the β‐stable set was more accurate than the α‐stable set, and the (3‐core was more accurate than the α‐core; in other words, for each of the solutions tested, the prediction from any solution concept based on (β‐effectiveness was more accurate than the prediction from the same solution based on a‐effectiveness. Second, the β‐core was the most accurate of the six theories tested. Results are interpreted as showing that β‐effectiveness is superior to a‐effectiveness as a basis for payoff predictions in cooperative non‐sidepayment games.     

Pólya-Type Polynomial Inequalities in L P Spaces and Best Local Approximation

In this paper, we obtain an extension of the Pólya inequality for univariate real polynomials in L ^p spaces and new estimates for certain class of measurable sets. Inequalities for complex polynomials are also considered. We give an application to a multipoint best local approximation problem for real and complex polynomials.     

On a Hardy Type General Weighted Inequality in Spaces L p(·)

A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L ^p(·). Equivalent necessary and sufficient conditions are found for the ${L^{p(\cdot)} \longrightarrow L^{q(\cdot)}}A Hardy type two-weighted inequality is investigated for the multidimensional Hardy operator in the norms of generalized Lebesgue spaces L ^p(·). Equivalent necessary and sufficient conditions are found for the L^p(·) ? L^q(·){L^{p(\cdot)} \longrightarrow L^{q(\cdot)}} boundedness of the Hardy operator when exponents q(0) < p(0), q(∞) < p(∞). It is proved that the condition for such an inequality to hold coincides with the condition for the validity of two-weighted Hardy inequalities with constant exponents if we require of the exponents to be regular near zero and at infinity.     

Theory and practice in OR and town planning: a continuing creative synergy?

The paper looks at the parallel experiences of OR and town (land use) planning since the Second World War. The existence of three ‘waves of enthusiasm’ for planning in the UK is noted: from 1947; from mid-1960s to 1979; and currently from 1990 to date. The significant mutually beneficial synergy between OR and town planning theory and practice during the second of these periods is recounted. Subsequent, current, and potential future developments are reviewed, and the implications for OR and (especially) town planning of a lack of awareness of this history are discussed.     

Schauder Decompositions and the Grothendieck and Dunford-Pettis Properties in Köthe Echelon Spaces of Infinite Order

It is shown that every echelon space λ_∞(A), with A an arbitrary Köthe matrix, is a Grothendieck space with the Dunford-Pettis property. Since λ_∞(A) is Montel if and only if it coincides with λ₀(A), this identifies an extensive class of non-normable, non-Montel Fréchet spaces having these two properties. Even though the canonical unit vectors in λ_∞(A) fail to form an unconditional basis whenever λ_∞(A) ≠ λ₀(A), it is shown, nevertheless, that in this case λ_∞(A) still admits unconditional Schauder decompositions (provided it satisfies the density condition). This is in complete contrast to the Banach space setting, where Schauder decompositions never exist. Consequences for spectral measures are also given.     

Heavy tails of a Lévy process and its maximum over a random time interval

Let {Xt,t0} be a Lévy process with Lévy measure ν on(∞,∞),and let τ be a nonnegative random variable independent of {Xt,t0}.We are interested in the tail probabilities of X τ and X(τ) = sup0≤t≤τXt.For various cases,under the assumption that either the Lévy measure ν or the random variable τ has a heavy right tail we prove that both Pr(X τ > x) and Pr(X(τ) > x) are asymptotic to Eτν((x,∞)) + Pr(τ > x/(0 ∨ EX 1)) as x →∞,where Pr(τ > x/0) = 0 by convention.     

Torsion in K‐Theory for Boundary Actions on Affine Buildings of Type ?n

Let be a torsionfree lattice in G=PGL(n+1, , where n 1 and is a nonArchimedean local field. Then acts on the Furstenberg boundary G/P, where P is a minimal parabolic subgroup of G. The identity element I in the crossedproduct C ^*algebra C(G/P) generates a class [I] in the K ₀ group of C(G/P) . It is shown that [I] is a torsion element of K ₀ and there is an explicit bound for the order of [I]. The result is proved more generally for groups acting on affine buildings of type à _n. For n=1, 2 the Euler–Poincaré characteristic () annihilates the class [I].     

Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

In this paper we establish the general solution of the functional equation

Approximation by Classical Orthogonal Polynomials with Weight in Spaces L2,γ(a,b) and Widths of Some Functional Classes

Russian Mathematics - We investigate approximations of functions of classes W2(Dγ;(a,b)), r = 2, 3, …, by classical orthogonal polynomials with a weight γ in the spaces...     

L1-Norm Estimation and Random Weighting Method in a Semiparametric Model

In this paper, the L_1-norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L_1-norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method.     

Divisibility in the K0‐Group of the Algebra of Operators on a Banach Space

Let Figiel's reflexive Banach space which is not isomorphic to its Cartesian square. We show that the K ₀group of the algebra of continuous, linear operators on contain a subgroup isomorphic to the group c ₀₀( ) of sequences rational numbers with z _n=0 eventually.     

An Extension of a Simply Inequality Between von Neumann–Jordan and James Constants in Banach Spaces

For a non-trivial Banach space X, let J(X), CNJ(X), C_(NJ)~(p)(X) respectively stand for the James constant, the von Neumann–Jordan constant and the generalized von Neumann–Jordan constant recently inroduced by Cui et al. In this paper, we discuss the relation between the James and the generalized von Neumann–Jordan constants, and establish an inequality between them: C_(NJ)~(p)(X) ≤J(X) with p ≥ 2, which covers the well-known inequality CNJ(X) ≤ J(X). We also introduce a new constant, from which we establish another inequality that extends a result of Alonso et al.