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Sample records for weighted sobolev spaces

  1. POINCAR(E) INEQUALITIES IN WEIGHTED SOBOLEV SPACES

    Institute of Scientific and Technical Information of China (English)

    WANG Wan-yi; SUN Jiong; ZHENG Zhi-ming

    2006-01-01

    The weighted Poincaré inequalities in weighted Sobolev spaces are discussed,and the necessary and sufficient conditions for them to hold are given. That is, the natural embedding of weighted Sobolev spaces is less than 1.

  2. Traces of weighted Sobolev spaces. Old and new

    OpenAIRE

    2015-01-01

    International audience; We give short simple proofs of Uspenskii's results characterizing Besov spaces as trace spaces of weighted Sobolev spaces. We generalize Uspenskii's results and prove the optimality of these generalizations. We next show how classical results on the functional calculus in the Besov spaces can be obtained as straightforward consequences of the theory of weighted Sobolev spaces.

  3. Sobolev spaces

    CERN Document Server

    Adams, Robert A

    2003-01-01

    Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces. This theory is widely used in pure and Applied Mathematics and in the Physical Sciences.This second edition of Adam''s ''classic'' reference text contains many additions and much modernizing and refining of material. The basic premise of the book remains unchanged: Sobolev Spaces is intended to provide a solid foundation in these spaces for graduate students and researchers alike.* Self-contained and accessible for readers in other disciplines.* Written at elementary level making it accessible to graduate students.

  4. Trace theorems for Sobolev-Slobodeckij spaces with or without weights

    Directory of Open Access Journals (Sweden)

    Doyoon Kim

    2007-01-01

    Full Text Available We prove that the well-known trace theorem for weighted Sobolev spaces holds true under minimal regularity assumptions on the domain. Using this result, we prove the existence of a bounded linear right inverse of the trace operator for Sobolev-Slobodeckij spaces Wps(Ω when s-1/p is an integer.

  5. Basicity of Systems of Sines with Linear Phase in Weighted Sobolev Spaces

    Directory of Open Access Journals (Sweden)

    V. F. Salmanov

    2013-01-01

    Full Text Available The perturbed systems of sines, which appear when solving some partial differential equations by the Fourier method, are considered in this paper. Basis properties of these systems in weighted Sobolev spaces of functions are studied.

  6. Persistence of solutions to nonlinear evolution equations in weighted Sobolev spaces

    Directory of Open Access Journals (Sweden)

    Xavier Carvajal Paredes

    2010-11-01

    Full Text Available In this article, we prove that the initial value problem associated with the Korteweg-de Vries equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq 2heta ge 2$ and the initial value problem associated with the nonlinear Schrodinger equation is well-posed in weighted Sobolev spaces $mathcal{X}^{s,heta}$, for $s geq heta geq 1$. Persistence property has been proved by approximation of the solutions and using a priori estimates.

  7. Ground states for a modified capillary surface equation in weighted Orlicz-Sobolev space

    Directory of Open Access Journals (Sweden)

    Guoqing Zhang

    2015-03-01

    Full Text Available In this article, we prove a compact embedding theorem for the weighted Orlicz-Sobolev space of radially symmetric functions. Using the embedding theorem and critical points theory, we prove the existence of multiple radial solutions and radial ground states for the following modified capillary surface equation $$\\displaylines{ -\\operatorname{div}\\Big(\\frac{|\

  8. Solvability of the Dirichlet Problem for Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

    Directory of Open Access Journals (Sweden)

    Maria Transirico

    2008-10-01

    Full Text Available This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of ℝn, n≥3. We state a regularity result and we can deduce an existence and uniqueness theorem.

  9. Solvability of the Dirichlet Problem for Elliptic Equations in Weighted Sobolev Spaces on Unbounded Domains

    Directory of Open Access Journals (Sweden)

    Boccia Serena

    2008-01-01

    Full Text Available This paper is concerned with the study of the Dirichlet problem for a class of second-order linear elliptic equations in weighted Sobolev spaces on unbounded domains of , . We state a regularity result and we can deduce an existence and uniqueness theorem.

  10. Electromagnetic transmission problems with a large parameter in weighted Sobolev spaces

    Directory of Open Access Journals (Sweden)

    Jorge Eliecer Ospino

    2013-11-01

    Full Text Available We present an a priori estimate for an electromagnetic transmission problem in unbounded exterior domains in R^3. We consider Maxwell's equations in two sub-domains, the bounded interior representing a conducting material (metal and the unbounded exterior representing an insulating material (air. The behavior of the solution at infinity is described by means of families of weighted Sobolev spaces, so-called Beppo-Levi spaces [11]. We prove the existence and uniqueness of the solution.

  11. Some embeddings of weighted sobolev spaces on finite measure and quasibounded domains

    Directory of Open Access Journals (Sweden)

    Brown RC

    1998-01-01

    Full Text Available We show that several of the classical Sobolev embedding theorems extend in the case of weighted Sobolev spaces to a class of quasibounded domains which properly include all bounded or finite measure domains when the weights have an arbitrarily weak singularity or degeneracy at the boundary. Sharper results are also shown to hold when the domain satisfies an integrability condition which is equivalent to the Minkowski dimension of the boundary being less than . We apply these results to derive a class of weighted Poincaré inequalities which are similar to those recently discovered by Edmunds and Hurri. We also point out a formal analogy between one of our results and an interpolation theorem of Cwikel.

  12. Cauchy problems for fifth-order KdV equations in weighted Sobolev spaces

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    Eddye Bustamante

    2015-05-01

    Full Text Available In this work we study the initial-value problem for the fifth-order Korteweg-de Vries equation $$ \\partial_{t}u+\\partial_{x}^{5}u+u^k\\partial_{x}u=0, \\quad x,t\\in \\mathbb{R}, \\; k=1,2, $$ in weighted Sobolev spaces $H^s(\\mathbb{R}\\cap L^2(\\langle x \\rangle^{2r}dx$. We prove local and global results. For the case $k=2$ we point out the relationship between decay and regularity of solutions of the initial-value problem.

  13. HEISENBERG'S INEQUALITY IN SOBOLEV SPACES

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitative representation of uncertainty principle.

  14. On $L^1$-Matrices with Degenerate Spectrum and Weak Convergence in Associated Weighted Sobolev Spaces

    Directory of Open Access Journals (Sweden)

    P.I. Kogut

    2012-08-01

    Full Text Available We study the compactness property of the weak convergence in variable Sobolev spaces of the following sequences $\\left\\{ (A_n,u_n \\in L^1(\\Omega; {\\mathbb{R}}^{N\\times N} \\times W_{A_n}(\\Omega; {\\Gamma}_D \\right\\}$, where the squared symmetric matrices $A\\colon \\Omega \\rightarrow {\\mathbb{R}}^{N\\times N}$ belong to the Lebesgue space $L^1(\\Omega; {\\mathbb{R}}^{N\\times N}$ and their eigenvalues may vanish on subdomains of $\\Omega$ with zero Lebesgue measure.

  15. New characterizations of Hajlasz-Sobolev spaces on metric spaces

    Institute of Scientific and Technical Information of China (English)

    YANG; Dachun(杨大春)

    2003-01-01

    This paper introduces the fractional Sobolev spaces on spaces of homogeneous type, includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels. The author establishes various characterizations of (sharp) maximal functions for these spaces. Asapplications, the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces. Moreover,some embedding theorems are also given.

  16. A convergence result for discreet steepest decent in weighted sobolev spaces

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    W. T. Mahavier

    1997-01-01

    Full Text Available A convergence result is given for discrete descent based on Sobolev gradients arising from differential equations which may be expressed as quadratic forms. The argument is an extension of the result of David G. Luenberger on Euclidean descent and compliments the work of John W. Neuberger on Sobolev descent.

  17. Sobolev Spaces Associated to the Harmonic Oscillator

    Indian Academy of Sciences (India)

    B Bongioanni; J L Torrea

    2006-08-01

    We define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator $H= - + |x|^2$. Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrödinger equation are also considered.

  18. Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups

    Institute of Scientific and Technical Information of China (English)

    CUI Xiao-yue; LAM Nguyen; LU Guo-zhen

    2013-01-01

    Recently, many new features of Sobolev spaces W k,p ?RN ? were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].

  19. Polynomial approximation of functions in Sobolev spaces

    Science.gov (United States)

    Dupont, T.; Scott, R.

    1980-01-01

    Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.

  20. Multiwavelet sampling theorem in Sobolev spaces

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    This paper is to establish the multiwavelet sampling theorem in Sobolev spaces. Sampling theorem plays a very important role in digital signal communication. The most classical sampling theorem is Shannon sampling theorem, which works for bandlimited signals. Recently, sampling theorems in wavelets or multiwavelets subspaces are extensively studied in the literature. In this paper, we firstly propose the concept of dual multiwavelet frames in dual Sobolev spaces (H s (R) , H-s (R)). Then we construct a special class of dual multiwavelet frames, from which the multiwavelet sampling theorem in Sobolev spaces is obtained. That is, for any f ∈ H s (R) with s > 1/2, it can be exactly recovered by its samples. Especially, the sampling theorem works for continuous signals in L 2 (R), whose Sobolev exponents are greater than 1 /2.

  1. HARDY-SOBOLEV INEQUALITIES WITH GENERAL WEIGHTS AND REMAINDER TERMS

    Institute of Scientific and Technical Information of China (English)

    Chen Zhihui; Shen Yaotian

    2008-01-01

    The Hardy-Sobolev inequality with general weights is established, and it is shown that the constant is optimal. The two weights in this inequality are determined by a Bernoulli equation. In addition, the authors obtain the Hardy-Sobolev inequality with general weights and remainder terms. By choosing special weights, it turns to be many versions of the Hardy-Sobolev inequality and the Caffarelli-Kohn-Nirenberg inequality with remainder terms in the literature.

  2. Parabolic Equations in Musielak-Orlicz-Sobolev Spaces

    Directory of Open Access Journals (Sweden)

    M.L. Ahmed Oubeid

    2013-11-01

    Full Text Available We prove in this paper the existence of solutions of nonlinear parabolic problems in Musielak-Orlicz-Sobolev spaces. An approximation and a trace results in inhomogeneous Musielak-Orlicz-Sobolev spaces have also been provided.

  3. Differential operators on Hermite Sobolev spaces

    Indian Academy of Sciences (India)

    Suprio Bhar; B Rajeev

    2015-02-01

    In this paper, we compute the Hilbert space adjoint * of the derivative operator on the Hermite Sobolev spaces $\\mathcal{S}_{q}$. We use this calculation to give a different proof of the ‘monotonicity inequality’ for a class of differential operators (, ) for which the inequality was proved in Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2(4) (2009) 515–591. We also prove the monotonicity inequality for (, ), when these correspond to the Ornstein–Uhlenbeck diffusion.

  4. Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure

    Science.gov (United States)

    Cappa, G.; Ferrari, S.

    2016-12-01

    Let X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron-Martin space is denoted by H. Let ν =e-U μ, where U : X → R is a sufficiently regular convex and continuous function. In this paper we are interested in the W 2 , 2 regularity of the weak solutions of elliptic equations of the type

  5. Hitchhiker's guide to the fractional Sobolev spaces

    CERN Document Server

    Di Nezza, Eleonora; Valdinoci, Enrico

    2011-01-01

    These pages are for students and young researchers of all ages who may like to hitchhike their way from 1 to $s\\in(0,1)$. To wit, for anybody who, only endowed with some basic undergraduate analysis course (and knowing {\\tt where his towel is}), would like to pick up some quick, crash and essentially self-contained information on the fractional Sobolev spaces $W^{s,p}$. The reasons for such a hitchhiker to start this adventurous trip might be of different kind: (s)he could be driven by mathematical curiosity, or could be tempted by the many applications that fractional calculus seems to have recently experienced. [...] different from other Guides, this one is not {\\tt definitive}, and we know that we cannot {\\tt solve any major problems just with potatoes} -- it's fun to try and see how far one can get though. In this sense, while most of the results we present here are probably well known to the experts, we believe that the exposition is somewhat original.

  6. Herz-type Sobolev and Bessel potential spaces and their applications

    Institute of Scientific and Technical Information of China (English)

    陆善镇; 杨大春

    1997-01-01

    The Herz-type Sobolev spaces are introduced and the Sobolev theorem is established. The Herz-type Bessel potential spaces and the relation between the Herz-type Sobolev spaces and Bessel potential spaces are discussed. As applications of these theories, some regularity results of nonlinear quantities appearing in the compensated compactness theory on Herz-type Hardy spaces are given.

  7. Sobolev type spaces associated with the q-Rubin's operator

    Directory of Open Access Journals (Sweden)

    Neji Bettaibi

    2014-05-01

    Full Text Available In this paper we introduce and   study   some $q$-Sobolev type spaces by using the harmonic analysis associated with the q-Rubin operator. In particular, embedding theorems for these spaces are established.  Next, we introduce the q-Rubin potential spaces and study some of its properties.

  8. Weinstein-Sobolev Spaces of Exponential Type and Applications

    Institute of Scientific and Technical Information of China (English)

    Hassen BEN MOHAMED; Belgacem GHRIBI

    2013-01-01

    In this paper,we introduce and study the Sobolev spaces of exponential type associated with the Weinstein operator,via some elements of harmonic analysis related to this operator.In particular,some properties,including completeness and imbedding theorem,are proved.Finally,using the theory of reproducing kernels,some applications are given for these spaces.

  9. N-Widths and Average Widths of Besov Classes in Sobolev Spaces

    Institute of Scientific and Technical Information of China (English)

    Gui Qiao XU; Yong Sheng SUN; Yong Ping LIU

    2006-01-01

    In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths,the Gel'fand n-widths, in the Sobolev spaces on Td, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Rd are obtained, respectively.

  10. An atomic decomposition of the Haj{\\l}asz Sobolev space $\\Mone$ on manifolds

    CERN Document Server

    Badr, Nadine

    2009-01-01

    Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincar\\'e inequality, the space $\\Mone$, defined by Haj{\\l}asz, is identified with a Hardy-Sobolev space defined in terms of atoms. Decomposition results are proved for both the homogeneous and the nonhomogeneous spaces.

  11. Boundary trace embedding theorems for variable exponent Sobolev spaces

    Science.gov (United States)

    Fan, Xianling

    2008-03-01

    We study boundary trace embedding theorems for variable exponent Sobolev space W1,p([dot operator])([Omega]). Let [Omega] be an open (bounded or unbounded)[thin space]domain in satisfying strong local Lipschitz condition. Under the hypotheses that p[set membership, variant]L[infinity]([Omega]), 1[less-than-or-equals, slant]infp(x)[less-than-or-equals, slant]supp(x)N, we prove that there is a continuous boundary trace embedding W1,p([dot operator])([Omega])-->Lq([dot operator])([not partial differential][Omega]) provided q([dot operator]), a measurable function on [not partial differential][Omega], satisfies condition for x[set membership, variant][not partial differential][Omega].

  12. Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces

    Directory of Open Access Journals (Sweden)

    Przemysław Górka

    2014-01-01

    Full Text Available We continue our research on Sobolev spaces on locally compact abelian (LCA groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lp-spaces.

  13. An algebra of noncommutative differential operators and Sobolev spaces

    CERN Document Server

    Beggs, E J

    2011-01-01

    We consider differential operators over a noncommutative algebra $A$ generated by vector fields. This is shown to form an associative algebra of differential operators, and acts on $A$-modules $E$ with covariant derivative. For bimodule covariant derivatives on $E$, we consider a module map $U_E$ which classifies how similar to the classical case the bimodule covariant derivative is. If this module map vanishes, we give an action of differential operators on tensor products. This turns out to be quite simple, and is related to the braided shuffle product. However technical issues with tensor products mean that we are not yet able to give a form of Hopf algebroid structure to the algebra of differential operators. We end by using the repeated differentials given in the paper to give a definition of noncommutative Sobolev space.

  14. Optimal limiting embeddings for $\\Delta$-reduced Sobolev spaces in $L^1$

    CERN Document Server

    Fontana, Luigi

    2012-01-01

    We prove sharp embeddings for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with $L^1$ data. In particular, we improve and extend some recent results by Cassani-Ruf-Tarsi, regarding sharp embedding inequalities. We also find the optimal target spaces for such embeddings, which in dimension 2 could be considered as limiting cases of the Hansson-Brezis-Wainger spaces, for the optimal embeddings of borderline Sobolev spaces $W_0^{k,n/k}$.

  15. Atlas of products for wave-Sobolev spaces on $\\mathbf R^{1+3}$

    CERN Document Server

    D'Ancona, Piero; Selberg, Sigmund

    2010-01-01

    The wave-Sobolev spaces $H^{s,b}$ are $L^2$-based Sobolev spaces on the Minkowski space-time $\\R^{1+n}$, with Fourier weights are adapted to the symbol of the d'Alembertian. They are a standard tool in the study of regularity properties of nonlinear wave equations, and in such applications the need arises for product estimates in these spaces. Unfortunately, it seems that with every new application some estimates come up which have not yet appeared in the literature, and then one has to resort to a set of well-established procedures for proving the missing estimates. To relieve the tedium of having to constantly fill in such gaps "by hand", we make here a systematic effort to determine the complete set of estimates in the bilinear case. We determine a set of necessary conditions for a product estimate $H^{s_1,b_1} \\cdot H^{s_2,b_2} \\hookrightarrow H^{-s_0,-b_0}$ to hold. These conditions define a polyhedron $\\Omega$ in the space $\\R^6$ of exponents $(s_0,s_1,s_2,b_0,b_1,b_2)$. We then show, in space dimension...

  16. Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights

    Science.gov (United States)

    Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

    2009-12-01

    We obtain the (contracted) weak zero asymptotics for orthogonal polynomials with respect to Sobolev inner products with exponential weights in the real semiaxis, of the form , with [gamma]>0, which include as particular cases the counterparts of the so-called Freud (i.e., when [phi] has a polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) weights. In addition, the boundness of the distance of the zeros of these Sobolev orthogonal polynomials to the convex hull of the support and, as a consequence, a result on logarithmic asymptotics are derived.

  17. On the gradient of Schwarz symmetrization of functions in Sobolev spaces

    CERN Document Server

    Bramanti, Marco

    2010-01-01

    Let S be a Sobolev or Orlicz-Sobolev space of functions not necessarily vanishing at the boundary of the domain. We give sufficient conditions on a nonnegative function in S in order that its spherical rearrangement ("Schwartz symmetrization") still belongs to S. These results are obtained via relative isoperimetric inequalities and somewhat generalize a well-known Polya-Szego's theorem. We also prove that the rearrangement of any function in S is locally in S.

  18. Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality

    Science.gov (United States)

    Díaz Mendoza, C.; Orive, R.; Pijeira Cabrera, H.

    2008-10-01

    We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same nth root asymptotic behavior as the weighted norms of certain extremal polynomials. This result is applied to obtain the (contracted) weak zero distribution for orthogonal polynomials with respect to a Sobolev inner product with exponential weights of the form e-[phi](x), giving a unified treatment for the so-called Freud (i.e., when [phi] has polynomial growth at infinity) and Erdös (when [phi] grows faster than any polynomial at infinity) cases. In addition, we provide a new proof for the bound of the distance of the zeros to the convex hull of the support for these Sobolev orthogonal polynomials.

  19. Characterization of subdifferentials of a singular convex functional in Sobolev spaces of order minus one

    CERN Document Server

    Kashima, Yohei

    2011-01-01

    Subdifferentials of a singular convex functional representing the surface free energy of a crystal under the roughening temperature are characterized. The energy functional is defined on Sobolev spaces of order -1, so the subdifferential mathematically formulates the energy's gradient which formally involves 4th order spacial derivatives of the surface's height. The subdifferentials are analyzed in the negative Sobolev spaces of arbitrary spacial dimension on which both a periodic boundary condition and a Dirichlet boundary condition are separately imposed. Based on the characterization theorem of subdifferentials, the smallest element contained in the subdifferential of the energy for a spherically symmetric surface is calculated under the Dirichlet boundary condition.

  20. Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces

    Directory of Open Access Journals (Sweden)

    K. Balachandran

    2006-09-01

    Full Text Available In this paper we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed point theorem.

  1. Problem with Critical Sobolev Exponent and with Weight

    Institute of Scientific and Technical Information of China (English)

    Rejeb HADIJI; Habib YAZIDI

    2007-01-01

    The authors consider the problem:-div(p▽u)=uq-1+λu,u>0 in Ω,u=0 on aΩ.where Ω is a bounded domain in Rn,n≥3,P:Ω-→R is a given positive weight such that p ∈H1(Ω)∩C(Ω-),λis a real constant and q=2n/n-2,and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem.

  2. Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov-Sobolev-type spaces

    Science.gov (United States)

    Ma, Haitao; Zhai, Xiaoping; Yan, Wei; Li, Yongsheng

    2017-02-01

    In this paper, we study the global well posedness of the 3D incompressible magnetohydrodynamic system with horizontal dissipation and horizontal magnetic diffusion in the scaling invariant Besov-Sobolev-type spaces. We first get a unique global solution to this system with small initial data by the classical Friedrich's regularization method. Then using a weighted Chemin-Lerner-type norm, we prove the system also can generate a global solution if the horizontal components of the initial data are small enough compared to the vertical components. In particular, our results imply the global large solutions with highly oscillating initial data.

  3. The approximation property of some vector valued Sobolev-Slobodeckij spaces

    Directory of Open Access Journals (Sweden)

    Carlos Bosch

    1992-01-01

    Full Text Available In this paper we consider the Sobolev-Slobodeckij spaces Wm,p(ℜn,E where E is a strict (LF-space, m∈(0,∞\\ℕ and p∈[1,∞. We prove that Wm,p(ℜn,E has the approximation property provided E has it, furthermore if E is a Banach space with the strict approximation property then Wm,p(ℜn,E has this property.

  4. Generalized Lions-Peetre interpolation construction and optimal embedding theorems for Sobolev spaces

    Energy Technology Data Exchange (ETDEWEB)

    Ovchinnikov, V I [Voronezh State University (Russian Federation)

    2014-01-31

    In the paper, a new description of the generalized Lions-Peetre method of means is found, which enables one to evaluate the interpolation orbits of spaces constructed by this method. The list of these spaces includes all Lorentz spaces with functional parameters, Orlicz spaces, and spaces close to them. This leads in turn to new optimal embedding theorems for Sobolev spaces produced using the Lions-Peetre construction in rearrangement invariant spaces. It turns out that the optimal space of the embedding is also a generalized Lions-Peetre space whose parameters are explicitly evaluated. Bibliography: 18 titles.

  5. Characterization for the Kuratowski Limits of a Sequence of Sobolev Spaces

    Science.gov (United States)

    Bucur, Dorin

    1999-01-01

    The purpose of this paper is to study the strong lower and the weak upper limits in the sense of Kuratowski of a sequence of Sobolev spaces {W1, p0(Ωn)}n∈Nand compare them to a fixed spaceW1, p0(Ω). The results are expressed in terms of the behavior of the local capacity in balls of the complementary sets. If these two limits coeı̈ncide, we obtain necessary and sufficient conditions for the convergence in the sense of Mosco of the Sobolev spaces, hence for the continuity of the solution of a Dirichlet problem associated to thep-Laplacian in terms of the geometric domain variation.

  6. Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of “Noises”

    Directory of Open Access Journals (Sweden)

    A. Favini

    2015-01-01

    Full Text Available The concept of “white noise,” initially established in finite-dimensional spaces, is transferred to infinite-dimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of “noises” are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable “noises.” The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application.

  7. On the Sobolev embedding theorem for variable exponent spaces in the critical range

    CERN Document Server

    Bonder, Julian Fernandez; Silva, Analia

    2011-01-01

    In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration--Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico.

  8. A Poincaré Inequality in a Sobolev Space with a Variable Exponent

    Institute of Scientific and Technical Information of China (English)

    Philippe G.CIARLET; George DINCA

    2011-01-01

    Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space W1,p(·)(Ω), where p(·) :(-Ω)→ [1,∞[ is a variable exponent. This inequality is itself a corollary to a more general result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising from the possible lack of density of the space D(Ω) in the space {v ∈ W1,p(·)(Ω);tr v= 0 on aΩ}. Two applications are also discussed.

  9. Embedding and Maximal Regular Differential Operators in Sobolev-Lions Spaces

    Institute of Scientific and Technical Information of China (English)

    Veli B. SHAKHMUROV

    2006-01-01

    This study focuses on vector-valued anisotropic Sobolev-Lions spaces associated with Banach spaces E0, E. Several conditions are found that ensure the continuity and compactness of embedding operators that are optimal regular in these spaces in terms of interpolations of spaces E0 and E. In particular, the most regular class of interpolation spaces Eα between E0, E depending on α and the order of space are found and the boundedness of differential operators Dα from this space to Eα -valued Lp,γ spaces is proved. These results are applied to partial differential-operator equationswith parameters to obtain conditions that guarantee the maximal Lp,γ regularity and R-positivity uniformly with respect to these parameters.

  10. A direct proof of Sobolev embeddings for Triebel-Lizorkin spaces, including mixed norms and quasi-homogeneity

    DEFF Research Database (Denmark)

    Johnsen, Jon

    The article deals with a simplified proof of the Sobolev embedding theorem for Triebel-Lizorkin spaces (that contain the $L_p$-Sobolev spaces $H^s_p$ as special cases). The method extends to a proof of the corresponding fact for general Triebel–Lizorkin spaces based on mixed $L_p$-norms. In this ......_p$-norms. In this context a Nikol’skij– Plancherel-Polya inequality for sequences of functions satisfying a geometric rectangle condition is proved. The results extend also to anisotropic spaces of the quasi-homogeneous type....

  11. A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin–Triebel spaces with mixed norms

    Directory of Open Access Journals (Sweden)

    Jon Johnsen

    2007-01-01

    Full Text Available The article deals with a simplified proof of the Sobolev embedding theorem for Lizorkin–Triebel spaces (that contain the Lp-Sobolev spaces Hps as special cases. The method extends to a proof of the corresponding fact for general Lizorkin–Triebel spaces based on mixed Lp-norms. In this context a Nikol' skij–Plancherel–Polya inequality for sequences of functions satisfying a geometric rectangle condition is proved. The results extend also to anisotropic spaces of the quasi-homogeneous type.

  12. Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

    Directory of Open Access Journals (Sweden)

    Mourad Kerboua

    2014-12-01

    Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

  13. Sobolev spaces of maps and the Dirichlet problem for harmonic maps

    OpenAIRE

    Pigola, Stefano; Veronelli, Giona

    2014-01-01

    In this paper we prove the existence of a solution to the Dirichlet problem for harmonic maps into a geodesic ball on which the squared distance function from the origin is strictly convex. This improves a celebrated theorem obtained by S. Hildebrandt, H. Kaul and K. Widman in 1977. In particular no curvature assumptions on the target are required. Our proof relies on a careful analysis of the Sobolev spaces of maps involved in the variational process, and on a deformation result which permit...

  14. Space-Dependent Sobolev Gradients as a Regularization for Inverse Radiative Transfer Problems

    Directory of Open Access Journals (Sweden)

    Y. Favennec

    2016-01-01

    Full Text Available Diffuse optical tomography problems rely on the solution of an optimization problem for which the dimension of the parameter space is usually large. Thus, gradient-type optimizers are likely to be used, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS algorithm, along with the adjoint-state method to compute the cost function gradient. Usually, the L2-inner product is chosen within the extraction procedure (i.e., in the definition of the relationship between the cost function gradient and the directional derivative of the cost function while alternative inner products that act as regularization can be used. This paper presents some results based on space-dependent Sobolev inner products and shows that this method acts as an efficient low-pass filter on the cost function gradient. Numerical results indicate that the use of Sobolev gradients can be particularly attractive in the context of inverse problems, particularly because of the simplicity of this regularization, since a single additional diffusion equation is to be solved, and also because the quality of the solution is smoothly varying with respect to the regularization parameter.

  15. Effective Numerical Methods for Solving Elliptical Problems in Strengthened Sobolev Spaces

    Science.gov (United States)

    D'yakonov, Eugene G.

    1996-01-01

    Fourth-order elliptic boundary value problems in the plane can be reduced to operator equations in Hilbert spaces G that are certain subspaces of the Sobolev space W(sub 2)(exp 2)(Omega) is identical with G(sup (2)). Appearance of asymptotically optimal algorithms for Stokes type problems made it natural to focus on an approach that considers rot w is identical with (D(sub 2)w - D(sub 1)w) is identical with vector of u as a new unknown vector-function, which automatically satisfies the condition div vector of u = 0. In this work, we show that this approach can also be developed for an important class of problems from the theory of plates and shells with stiffeners. The main mathematical problem was to show that the well-known inf-sup condition (normal solvability of the divergence operator) holds for special Hilbert spaces. This result is also essential for certain hydrodynamics problems.

  16. Approximation of functions on the Sobolev space with a Gaussian measure

    Institute of Scientific and Technical Information of China (English)

    2010-01-01

    We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

  17. Strong Ill-posedness of the incompressible Euler equation in borderline Sobolev spaces

    CERN Document Server

    Bourgain, Jean

    2013-01-01

    For the $d$-dimensional incompressible Euler equation, the standard energy method gives local wellposedness for initial velocity in Sobolev space $H^s(\\mathbb R^d)$, $s>s_c:=d/2+1$. The borderline case $s=s_c$ was a folklore open problem. In this paper we consider the physical dimensions $d=2,3$ and show that if we perturb any given smooth initial data in $H^{s_c}$ norm, then the corresponding solution can have infinite $H^{s_c}$ norm instantaneously at $t>0$. The constructed solutions are unique and even $C^{\\infty}$-smooth in some cases. To prove these results we introduce a new strategy: large Lagrangian deformation induces critical norm inflation. As an application we also settle several closely related open problems.

  18. Existence of Solutions of Nonlinear Integrodifferential Equations of Sobolev Type with Nonlocal Condition in Banach Spaces

    Indian Academy of Sciences (India)

    K Balachandran; K Uchiyama

    2000-05-01

    In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.

  19. WELL-POSEDNESS FOR THE CAUCHY PROBLEM TO THE HIROTA EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

    Institute of Scientific and Technical Information of China (English)

    HUOZHAOHUI; JIA YUELING

    2005-01-01

    The local well-posedness of the Cauchy problem for the Hirota equation is established for low regularity data in Sobolev spaces Hs(s ≥ -1-4). Moreover, the global well-posedness for L2 data follows from the local well-posedness and the conserved quantity. For data in Hs(s > 0), the global well-posedness is also proved. The main idea is to use the generalized trilinear estimates, associated with the Fourier restriction norm method.

  20. Sobolev spaces, their generalizations and elliptic problems in smooth and Lipschitz domains

    CERN Document Server

    Agranovich, Mikhail S

    2015-01-01

    This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems.   The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory, and pseudodifferential operators, has included his own very recent findings in the present book.   The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems, and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date.   Graduate and post-graduate student...

  1. Salt-body Inversion with Minimum Gradient Support and Sobolev Space Norm Regularizations

    KAUST Repository

    Kazei, V.V.

    2017-05-26

    Full-waveform inversion (FWI) is a technique which solves the ill-posed seismic inversion problem of fitting our model data to the measured ones from the field. FWI is capable of providing high-resolution estimates of the model, and of handling wave propagation of arbitrary complexity (visco-elastic, anisotropic); yet, it often fails to retrieve high-contrast geological structures, such as salt. One of the reasons for the FWI failure is that the updates at earlier iterations are too smooth to capture the sharp edges of the salt boundary. We compare several regularization approaches, which promote sharpness of the edges. Minimum gradient support (MGS) regularization focuses the inversion on blocky models, even more than the total variation (TV) does. However, both approaches try to invert undesirable high wavenumbers in the model too early for a model of complex structure. Therefore, we apply the Sobolev space norm as a regularizing term in order to maintain a balance between sharp and smooth updates in FWI. We demonstrate the application of these regularizations on a Marmousi model, enriched by a chunk of salt. The model turns out to be too complex in some parts to retrieve its full velocity distribution, yet the salt shape and contrast are retrieved.

  2. Mixed Norm Estimate for Radon Transform on Weighted $L^p$ Spaces

    Indian Academy of Sciences (India)

    Ashisha Kumar; Swagato K Ray

    2010-09-01

    We will discuss about the mapping property of Radon transform on $L^p$ spaces with power weight. It will be shown that the Pitt’s inequality together with the weighted version of Hardy–Littlewood–Sobolev lemma imply weighted inequality for the Radon transform.

  3. Minors of mappings in anisotropic Sobolev spaces%各向异性Sobolev空间中映射的子式

    Institute of Scientific and Technical Information of China (English)

    高红亚; 乔金静; 郭静

    2012-01-01

    The Jacobian Determinants of space mappings are effective tools in the study of geometric funcion theory in high - dimensional spaces and nonlinear analysis. The study of integrability of mappings in high - dimensional spaces is often attributed to the study of the integrability of Jacobian determinants. The minors of the Jacobian determinants of mappings in anisotropic Sobolev spaces is studied. An estimate related to the minors of space maps is established by using Stokes' formula and the analytic technique of Sobolev spaces, which generalizes a known result due to Iwaniec and Martin. This estimate is useful to the study of the integrability of space mappings.%空间映射的Jacobi行列式是研究高维空间几何函数论与非线性分析的有力工具.高维空间映射的可积性研究往往归结于Jacobi行列式可积性的研究.研究各向异性条件下的空间映射Jacobi行列式的子式,利用Stokes公式和Sobolev空间的分析技巧,建立了一个与空间映射的子式有关的估计式,推广了Iwaniec,Martin等人的结果.这个估计式对高维空间映射可积性的研究具有一定的意义.

  4. Optimal Recovery of Functions on the Sphere on a Sobolev Spaces with a Gaussian Measure in the Average Case Setting

    Institute of Scientific and Technical Information of China (English)

    Zexia Huang; Heping Wang

    2015-01-01

    In this paper, we study optimal recovery (reconstruction) of functions on the sphere in the average case setting.We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq(Sd−1) metric for 1≤q≤∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq(Sd−1) metric for 1≤q≤∞.

  5. On the Boundary Limits of Monotone Sobolev Functions in Variable Exponent Orlicz Spaces

    Institute of Scientific and Technical Information of China (English)

    Toshihide FUTAMURA; Tetsu SHIMOMURA

    2013-01-01

    Our aim in this note is to deal with boundary limits of monotone Sobolev functions with ▽u ∈ Lp(·) logLq(·)(B) for the unit ball B (C) Rn.Here p(·) and q(·) are variable exponents satisfying the log-H(o)lder and the log log-H(o)lder conditions,respectively.

  6. Sobolev regularity of the $\\bar{\\partial}$-equation on the Hartogs triangle

    CERN Document Server

    Chakrabarti, Debraj

    2011-01-01

    The regularity of the $\\bar{\\partial}$-problem on the domain $\\{|{z_1}|<|{z_2}|<1\\}$ in $\\mathbb{C}^2$ is studied using $L^2$ methods. Estimates are obtained for the canonical solution in weighted $L^2$-Sobolev spaces with a weight that is singular at the point $(0,0)$. The canonical solution for $\\dbar$ with weights is exact regular in the weighted Sobolev spaces away from the singularity $(0,0)$. In particular, the singularity of the Bergman projection for the Hartogs triangle is contained at the singular point and it does not propagate.

  7. Sobolev gradients and differential equations

    CERN Document Server

    Neuberger, John William

    1997-01-01

    A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.

  8. QUANTUM COMPLEXITY OF SOBOLEV IMBEDDINGS

    Institute of Scientific and Technical Information of China (English)

    Ye Peixin

    2012-01-01

    Using a new reduction approach,we derive a lower bound of quantum complexity for the approximation of imbeddings from anisotropic Sobolev classes B(Wrp([0,1]d)) to anisotropic Sobolev space Wrq([0,1]d) for all 1 ≤ p,q ≤ ∞.When p ≥ q,we show this bound is optimal by deriving the matching upper bound.In this case,the quantum algorithms are not significantly better than the classical deterministic or randomized ones.We conjecture that the bound is also optimal for the case p < q.This conjecture was confirmed in the situation s =0.

  9. Sobolev gradients and differential equations

    CERN Document Server

    Neuberger, J W

    2010-01-01

    A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients. Aside from the first edition of this work, this is the only known account of Sobolev gradients in book form. Most of the applications in this book have emerged since the first edition was published some twelve years ago. What remains of the first edition has been extensively revised. There are a number of plots of results from calculations and a sample MatLab code is included for a simple problem. Those working through a fair p...

  10. A DISTRIBUTION-THEORETICAL APPROACH TO CERTAIN LEBESGUE AND SOBOLEV SPACES.

    Science.gov (United States)

    FUNCTIONAL ANALYSIS, * DISTRIBUTION THEORY ), PARTIAL DIFFERENTIAL EQUATIONS, OPERATORS(MATHEMATICS), FOURIER ANALYSIS, HILBERT SPACE, INTEGRAL TRANSFORMS, NUMERICAL INTEGRATION, TOPOLOGY, SERIES(MATHEMATICS), THEOREMS

  11. WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES

    Institute of Scientific and Technical Information of China (English)

    刘永平; 许贵桥

    2003-01-01

    This paper concerns the problem of the Kolmogorov n-width, the linear n-width, the Gel'fand n-width and the Bernstein n-width of Sobolev classes of the periodicmultivariate functions in the space Lp(Td) and the average Bernstein σ-width, averageKolmogorov σ-widths, the average linear σ-widths of Sobolev classes of the multivariatequantities.

  12. Multiplication operators on Sobolev disk algebra

    Institute of Scientific and Technical Information of China (English)

    WANG; Zongyao

    2005-01-01

    In this paper, we study the algebra consisting of analytic functions in the Sobolev space W2,2(D) (D is the unit disk), called the Sobolev disk algebra, explore the properties of the multiplication operators Mf on it and give the characterization of the commutant algebra A'(Mf) of Mf. We show that A'(Mf) is commutative if and only if Mf* is a Cowen-Douglas operator of index 1.

  13. Approximation of functions in variable-exponent Lebesgue and Sobolev spaces by de la Vallée-Poussin means

    Science.gov (United States)

    Sharapudinov, I. I.

    2016-07-01

    We consider the space Lp(\\cdot)2π formed by 2π-periodic real measurable functions f for which the integral \\displaystyle\\int-ππ\\vert f(x)\\vertp(x) dx exists and is finite, where p(x), 1≤ p(x), is a 2π-periodic measurable function (a variable exponent). If p(x)≤ \\overline p0:\\int-ππ\\biggl\\vert\\frac{f(x)}{α\\biggr\\vertp(x) dx≤1\\biggr\\}. In the space Lp(\\cdot)2π we distinguish a subspace Wr,p(\\cdot)2π of Sobolev type. We investigate the approximation properties of the de la Vallée-Poussin means for trigonometric Fourier sums for functions in the space Wr,p(\\cdot)2π. In particular, we prove that if the variable exponent p=p(x) satisfies the Dini-Lipschitz condition \\vert p(x)-p(y)\\vert\\ln\\frac{2π}{\\vert x-y\\vert}≤ c and if f\\in Wr,p(\\cdot)2π, then the de la Vallée-Poussin means V_m^n(f)=V_m^n(f,x) with n≤ am satisfy \\displaystyle \\Vert f-V_m^n(f)\\Vert p(\\cdot)≤ \\frac{c_r(p,a)}{n^r}Ω\\biggl(f(r), \\frac1n\\biggr)p(\\cdot), where Ω(g,δ)p(\\cdot) is a modulus of continuity of the function g\\in Lp(\\cdot)2π defined in terms of the Steklov functions. It is proved that if 1, r≥1, f\\in Wr,p(\\cdot)2π and the Dini-Lipschitz condition holds, then \\displaystyle \\vert f(x)-V_m^n(f,x)\\vert≤\\frac{c_r(p)}{m+1}\\sumk=nn+m\\frac{E_k(f(r))p(\\cdot)}{(k+1)r-{{1/{p(x)}}}}, where E_k(g)p(\\cdot) stands for the best approximation to g\\in Lp(\\cdot)2π by trigonometric polynomials of order k. Bibliography: 19 titles.

  14. An Eulerian-Lagrangian Form for the Euler Equations in Sobolev Spaces

    Science.gov (United States)

    Pooley, Benjamin C.; Robinson, James C.

    2016-12-01

    In 2000 Constantin showed that the incompressible Euler equations can be written in an "Eulerian-Lagrangian" form which involves the back-to-labels map (the inverse of the trajectory map for each fixed time). In the same paper a local existence result is proved in certain Hölder spaces {C^{1,μ}}. We review the Eulerian-Lagrangian formulation of the equations and prove that given initial data in H s for {n ≥ 2} and {s > n/2+1}, a unique local-in-time solution exists on the n-torus that is continuous into H s and C 1 into H s-1. These solutions automatically have C 1 trajectories. The proof here is direct and does not appeal to results already known about the classical formulation. Moreover, these solutions are regular enough that the classical and Eulerian-Lagrangian formulations are equivalent, therefore what we present amounts to an alternative approach to some of the standard theory.

  15. Avangardistid Moskvas / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2000-01-01

    Valdek Alberi ja Taave Tuutma videoinstallatsioonist "Think different" näitusel "Salon 2000" Moskva Kunstnike Keskmajas 16.-26. III. Kuraator Mari Sobolev. Eesti väljapaneku vastukajast ja Jüri Arrakust, kelle maalid olid näitusel "Balti meistrid", ajalehes "Kommersant". Moskva kunstinäitustest.

  16. Avangardistid Moskvas / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2000-01-01

    Valdek Alberi ja Taave Tuutma videoinstallatsioonist "Think different" näitusel "Salon 2000" Moskva Kunstnike Keskmajas 16.-26. III. Kuraator Mari Sobolev. Eesti väljapaneku vastukajast ja Jüri Arrakust, kelle maalid olid näitusel "Balti meistrid", ajalehes "Kommersant". Moskva kunstinäitustest.

  17. An Extension of Sobolev's Theorem

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    Sobolev's Theorem is the most fundamental theorem in the theory of Invariant Cubature Formulas (ICFs). In this paper, a quantitative structure is established for the classical ICFs. Enlightened by this structure, the author generalizes the concept of ICFs and extends the Sobolev's Theorem to the case of generalized ICFs. Several illustrative examples are given.

  18. Quantum logarithmic Sobolev inequalities and rapid mixing

    Energy Technology Data Exchange (ETDEWEB)

    Kastoryano, Michael J. [Dahlem Center for Complex Quantum Systems, Freie Universitaet Berlin, 14195 Berlin (Germany); Temme, Kristan [Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

    2013-05-15

    A family of logarithmic Sobolev inequalities on finite dimensional quantum state spaces is introduced. The framework of non-commutative L{sub p}-spaces is reviewed and the relationship between quantum logarithmic Sobolev inequalities and the hypercontractivity of quantum semigroups is discussed. This relationship is central for the derivation of lower bounds for the logarithmic Sobolev (LS) constants. Essential results for the family of inequalities are proved, and we show an upper bound to the generalized LS constant in terms of the spectral gap of the generator of the semigroup. These inequalities provide a framework for the derivation of improved bounds on the convergence time of quantum dynamical semigroups, when the LS constant and the spectral gap are of the same order. Convergence bounds on finite dimensional state spaces are particularly relevant for the field of quantum information theory. We provide a number of examples, where improved bounds on the mixing time of several semigroups are obtained, including the depolarizing semigroup and quantum expanders.

  19. On the constants for some Sobolev imbeddings

    Directory of Open Access Journals (Sweden)

    Pizzocchero Livio

    2001-01-01

    Full Text Available We consider the imbedding inequality is the Sobolev space (or Bessel potential space of type and (integer or fractional order . We write down upper bounds for the constants , using an argument previously applied in the literature in particular cases. We prove that the upper bounds computed in this way are in fact the sharp constants if , , and exhibit the maximising functions. Furthermore, using convenient trial functions, we derive lower bounds on for in many cases these are close to the previous upper bounds, as illustrated by a number of examples, thus characterizing the sharp constants with little uncertainty.

  20. Sobolev index: A classification of L\\'evy processes

    CERN Document Server

    Glau, Kathrin

    2012-01-01

    We classify L\\'evy processes according to the solution spaces of the associated parabolic PIDEs. This classification reveals structural characteristics of the processes and is relevant for applications such as for solving PIDEs numerically for pricing options in L\\'evy models. The classification is done via the Fourier transform i.e. via the symbol of the process. We define the Sobolev index of a L\\'evy process by a certain growth condition on the symbol. It follows that for L\\'evy processes with Sobolev index $\\alpha$ the corresponding evolution problem has a unique weak solution in the Sobolev-Slobodeckii space $H^{\\alpha/2}$. We show that this classification applies to a wide range of processes. Examples are the Brownian motion with or without drift, generalised hyperbolic (GH), CGMY and (semi) stable L\\'evy processes. A comparison of the Sobolev index with the Blumenthal-Getoor index sheds light on the structural implication of the classification. More precisely, we discuss the Sobolev index as an indicat...

  1. On the second eigenvalue of a Hardy-Sobolev operator

    Directory of Open Access Journals (Sweden)

    Konijeti Sreenadh

    2004-01-01

    Full Text Available In this note, we study the variational characterization and some properties of the second smallest eigenvalue of the Hardy-Sobolev operator $L_{mu}:=-Delta_{p}-frac{mu}{|x|^p}$ with respect to an indefinite weight $V(x$.

  2. Weighted BMO Estimates for Toeplitz Operators on Weighted Lebesgue Spaces

    Directory of Open Access Journals (Sweden)

    Yan Lin

    2015-01-01

    Full Text Available The authors establish the weighted BMO estimates for a class of Toeplitz operators related to strongly singular Calderón-Zygmund operators on weighted Lebesgue spaces. Moreover, the corresponding result for the Toeplitz operators related to classical Calderón-Zygmund operators can be deduced.

  3. Interpolation theorems on weighted Lorentz martingale spaces

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    In this paper several interpolation theorems on martingale Lorentz spaces are given.The proofs are based on the atomic decompositions of martingale Hardy spaces over weighted measure spaces.Applying the interpolation theorems,we obtain some inequalities on martingale transform operator.

  4. WEIGHTED COMPOSITION OPERATORS BETWEEN DIRICHLET SPACES

    Institute of Scientific and Technical Information of China (English)

    Wang Maofa

    2011-01-01

    In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.

  5. Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Shuanglin Shao

    2009-01-01

    Full Text Available In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrodinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schroindger equation with initial data in the homogeneous Sobolev space; as a consequence, there exists a maximizer for the Sobolev-Strichartz inequality.

  6. Sobolev orthogonal polynomials on a simplex

    CERN Document Server

    Aktas, Rabia

    2011-01-01

    The Jacobi polynomials on the simplex are orthogonal polynomials with respect to the weight function $W_\\bg(x) = x_1^{\\g_1} ... x_d^{\\g_d} (1- |x|)^{\\g_{d+1}}$ when all $\\g_i > -1$ and they are eigenfunctions of a second order partial differential operator $L_\\bg$. The singular cases that some, or all, $\\g_1,...,\\g_{d+1}$ are -1 are studied in this paper. Firstly a complete basis of polynomials that are eigenfunctions of $L_\\bg$ in each singular case is found. Secondly, these polynomials are shown to be orthogonal with respect to an inner product which is explicitly determined. This inner product involves derivatives of the functions, hence the name Sobolev orthogonal polynomials.

  7. FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon

    2002-01-01

    A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.

  8. Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space

    CERN Document Server

    Ihnatsyeva, Lizaveta

    2011-01-01

    We study Sobolev type spaces defined in terms of sharp maximal functions on Ahlfors regular subsets of the Euclidean space and the relation between these spaces and traces of classical Sobolev spaces.

  9. Optimal query error of quantum approximation on some Sobolev classes

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    We study the approximation of the imbedding of functions from anisotropic and general-ized Sobolev classes into Lq([0,1]d) space in the quantum model of computation. Based on the quantum algorithms for approximation of finite imbedding from LpN to LNq , we develop quantum algorithms for approximating the imbedding from anisotropic Sobolev classes B(Wpr ([0,1]d)) to Lq([0,1]d) space for all 1 q,p ∞ and prove their optimality. Our results show that for p < q the quantum model of computation can bring a speedup roughly up to a squaring of the rate in the classical deterministic and randomized settings.

  10. Randomized Error of Scrambled Net Quadrature for Tensor Product Sobolev and Korobov Spaces%攀登伪蒙特卡罗积分法在Sobolev和Korobov空间中的随机化误差

    Institute of Scientific and Technical Information of China (English)

    岳荣先

    2003-01-01

    Scrambled quasi-Monte Carlo quadrature is a hybrid of Monte carlo and quasi-Monte Carlo methods, which combines the best of these two methods for integration. This article studies the performance of the scrambled quadrature rules in randomized settings for the tensor product Sobolev and Korobov spaces of integrands. It is shown that the randomized error of the scrambled (λ,t,m,s)-nets is of order n-3/2[logn](s-1)/2 for these two spaces.%攀登伪蒙特卡罗积分法是由伪蒙特卡罗与蒙特卡罗方法混合而成的一种新方法,它体现了两者的优点.本文研究这种积分法在Sobolev空间和Korobov空间中的随机化误差.我们证明攀登(λ,t,m,s)-网积分法在这两个空间中的随机化误差的渐近阶为n-3/2[logn](s-1)/2.

  11. ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED Lp SPACES

    Institute of Scientific and Technical Information of China (English)

    Baohuai SHENG

    2007-01-01

    In this paper, we investigate the order of approximation by reproducing kernel spaces on (-1, 1) in weighted Lp spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate.Finally, The results are used to discuss an approximation problem arising from learning theory.

  12. Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

    Directory of Open Access Journals (Sweden)

    Flavia Colonna

    2012-01-01

    Full Text Available The logarithmic Bloch space Blog⁡ is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=sup⁡z∈𝔻(1-|z|2log⁡  (2/(1-|z|2|f'(z|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy space Hp (with 1≤p≤∞ into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mapping Hp into the little logarithmic Bloch space defined as the subspace of Blog⁡ consisting of the functions f such that lim⁡|z|→1(1-|z|2log⁡  (2/(1-|z|2|f'(z|=0.

  13. A note on the zeros of Freud-Sobolev orthogonal polynomials

    Science.gov (United States)

    Moreno-Balcazar, Juan J.

    2007-10-01

    We prove that the zeros of a certain family of Sobolev orthogonal polynomials involving the Freud weight function e-x4 on are real, simple, and interlace with the zeros of the Freud polynomials, i.e., those polynomials orthogonal with respect to the weight function e-x4. Some numerical examples are shown.

  14. Best approximation with wavelets in weighted Orlicz spaces

    CERN Document Server

    de Natividade, Maria

    2009-01-01

    Democracy functions of wavelet admissible bases are computed for weighted Orlicz Spaces in terms of its fundamental function. In particular, we prove that these bases are greedy if and only if the Orlicz space is a Lebesgue space. Also, sharp embeddings for the approximation spaces are given in terms of weighted discrete Lorentz spaces. For Lebesgue spaces the approximation spaces are identified with weighted Besov spaces.

  15. Time-Parallel Solutions to Ordinary Differential Equations on GPUs with a New Functional Optimization Approach Related to the Sobolev Gradient Method

    Science.gov (United States)

    2012-10-01

    534– 552, 1998. ISSN 1064-8275. [11] Fox, C. An introduction to the calculus of variations. Courier Dover Publications. (1987). [12] Neuberger ...in Sobolev spaces.” Missouri J. of Math. Sci. 11(1):19-32. [20] Mujeeb, D., Neuberger , J.W., and Sial, S. “Recursive Form of Sobolev Gradient

  16. A counterexample for Improved Sobolev Inequalities over the 2-adic group

    CERN Document Server

    Chamorro, Diego

    2010-01-01

    On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\\infty,\\infty) norm. We first show, using the special topological properties of the p-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space B(1,\\infty,1). This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

  17. Viktor V. Sobolev and radiative transfer theory

    Science.gov (United States)

    Nagirner, Dmitrij I.

    2016-11-01

    Invited review A detailed review of V.V. Sobolev's contributions to the theory of radiative transfer is presented. First, the basic problems of the theory of monochromatic scattering are formulated, which were introduced and solved approximately by the founders of the theory (E. Milne, A. Eddington, and others). Then the fundamental contribution by academician V.A. Ambartsumian, Sobolev's scientific adviser, to the analytical radiative transfer theory is summarized. Academician V.V. Sobolev continued and profoundly developed this theory. He pioneered new areas of the theory of multiple light scattering: the scattering of polarized radiation; the theory of a time-dependent radiation field; and the scattering in inhomogeneous media, in plane-parallel media with reflecting boundaries, and in media expanding with a velocity gradient. He proposed new approximate methods for solving the problems of anisotropic monochromatic scattering as well as scattering in spectral lines in stationary and expanding media which are still in use today. The most important Sobolev's contribution was to the exact analytical theory of radiative transfer. He proposed the probability method to solve radiative transfer problems and the probabilistic treatment of scattering processes; he introduced and justified the approximation of CFR in spectral lines; he developed the resolvent method for the exact solution to the basic integral equation describing monochromatic scattering and scattering in spectral lines; and he developed the theory of anisotropic scattering to analytic perfection. V.V. Sobolev applied these solutions to the interpretation of observation data for many astrophysical objects: photometric, polarimetric, and spectral characteristics of planetary atmospheres; spectra of stationary and non-stationary stars; and polarization of X-ray sources and quasars. V.V. Sobolev coauthored several papers with his students. The publications by Sobolev's disciples that continued his research

  18. WEIGHTED COMPOSITION OPERATORS BETWEEN BERS-TYPE SPACES AND BERGMAN SPACES

    Institute of Scientific and Technical Information of China (English)

    Tang Xiaomin

    2007-01-01

    This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space (or little Bers-type space) and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.

  19. Linearization stability of coupled gravitational and scalar fields in asymptotically flat space-times

    Energy Technology Data Exchange (ETDEWEB)

    Sarayakar, R.V. (Nagpur Univ. (India). Dept. of Mathematics)

    1982-07-01

    Using the methods of Choquet-Bruhat, Fischer and Marsden and using weighted Sobolev spaces developed recently by Christodoulou and Choquet-Bruhat, it is proved that the Einstein field equations coupled with self-gravitating scalar fields are linearization stable in asymptotically flat space-times.

  20. Remarks on a Sobolev-Hardy inequality

    OpenAIRE

    Secchi, S.; Smets, D.; Willem, M

    2002-01-01

    We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a nonlinear elliptic equation arising in astrophysics.

  1. Estimates of Oseen kernels in weighted $L^{p}$ spaces

    OpenAIRE

    KRAČMAR, Stanislav; Novotný, Antonín; Pokorný, Milan

    2001-01-01

    We study convolutions with Oseen kernels (weakly singular and singular) in both two- and three-dimensional space. We give a detailed weighted $L^{p}$ theory for $ p\\in(1;\\infty$ ] for anisotropic weights.

  2. Exponential convergence rates for weighted sums in noncommutative probability space

    Science.gov (United States)

    Choi, Byoung Jin; Ji, Un Cig

    2016-11-01

    We study exponential convergence rates for weighted sums of successive independent random variables in a noncommutative probability space of which the weights are in a von Neumann algebra. Then we prove a noncommutative extension of the result for the exponential convergence rate by Baum, Katz and Read. As applications, we first study a large deviation type inequality for weighted sums in a noncommutative probability space, and secondly we study exponential convergence rates for weighted free additive convolution sums of probability measures.

  3. Weighted Composition Operators on Weighted Bergman Spaces of Bounded Symmetric Domains

    Indian Academy of Sciences (India)

    Sanjay Kumar; Kanwar Jatinder Singh

    2007-05-01

    In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator $W_{\\varphi,\\psi}$ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, we study the Schatten -class weighted composition operators.

  4. Non Linear Travel Time Tomography With The Use of Sobolev Norms

    Science.gov (United States)

    Tondi, R.; de Franco, R.

    We present a method for the determination of 3-D velocity crustal structure and in- terface geometry, by inversion of seismic refraction and wide-angle reflection trav- eltimes. To minimize the deviation between the synthetic and exact wavefields we consider the minimization of a nonlinear objective function which considers: 1. the Euclidean norm of the misfit between observed and calculated data; 2. the L_2 norm of the misfit between the value of the parameter in the model been sought and the value of the parameter in the "a priori" mean model; 3. the minimization of the inaccuracies and costs of ray tracing in complex models, expressed in terms of the Sobolev norms of the relative parameters. In particular two Sobolev norms are relevant to ray tracing: as the complicated behaviour of rays depends on the second velocity derivatives, it may be restricted by minimizing the Sobolev norm of the velocity function in the H^2 space; as the second order travel-time perturbations depend on the perturbation of the first velocity derivatives, it may be useful to limit the velocity model updates, within individual iterations of the linearized inversion, by means of the minimization of the Sobolev norm in the H^1 space (Klimes, "PAGEOPH", 2002). Through the use of 3-D synthetic tests recovered from real models, we show that including the minimization of Sobolev norm is necessary, when modelling with ray methods. The initial model to be inverted is chosen in order to satisfy mathematical stability and, in analysing final solution reliability, estimate of the misfit or chi squared and "a posteriori" model covariance is given. Calculations were performed with the use of programs developed by the Consortium for Seismic Waves in Complex 3-D Structures (CW3D) at Charles University in Prague. Application of the method to field data collected in the framework of TOMOVES (TOMOgraphy of Mt.VESuvius) experiment is a check on the validity of the inversion scheme.

  5. WeightLifter: Visual Weight Space Exploration for Multi-Criteria Decision Making.

    Science.gov (United States)

    Pajer, Stephan; Streit, Marc; Torsney-Weir, Thomas; Spechtenhauser, Florian; Muller, Torsten; Piringer, Harald

    2017-01-01

    A common strategy in Multi-Criteria Decision Making (MCDM) is to rank alternative solutions by weighted summary scores. Weights, however, are often abstract to the decision maker and can only be set by vague intuition. While previous work supports a point-wise exploration of weight spaces, we argue that MCDM can benefit from a regional and global visual analysis of weight spaces. Our main contribution is WeightLifter, a novel interactive visualization technique for weight-based MCDM that facilitates the exploration of weight spaces with up to ten criteria. Our technique enables users to better understand the sensitivity of a decision to changes of weights, to efficiently localize weight regions where a given solution ranks high, and to filter out solutions which do not rank high enough for any plausible combination of weights. We provide a comprehensive requirement analysis for weight-based MCDM and describe an interactive workflow that meets these requirements. For evaluation, we describe a usage scenario of WeightLifter in automotive engineering and report qualitative feedback from users of a deployed version as well as preliminary feedback from decision makers in multiple domains. This feedback confirms that WeightLifter increases both the efficiency of weight-based MCDM and the awareness of uncertainty in the ultimate decisions.

  6. Light Weight Silicon Mirrors for Space Instrumentation

    Science.gov (United States)

    Bly, Vincent T.; Hill, Peter C.; Hagopian, John G.; Strojay, Carl R.; Miller, Timothy

    2012-01-01

    Each mirror is a monolithic structure from a single crystal of silicon. The mirrors are light weighted after the optical surface is ground and polished. Mirrors made during the initial phase of this work were typically 1/50 lambda or better (RMS at 633 n m)

  7. A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem

    Directory of Open Access Journals (Sweden)

    Dou Jingbo

    2007-01-01

    Full Text Available Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the -sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.

  8. A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem

    Directory of Open Access Journals (Sweden)

    Zixia Yuan

    2007-12-01

    Full Text Available Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the p-sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.

  9. APPROXIMATION BY GENERALIZED MKZ-OPERATORS IN POLYNOMIAL WEIGHTED SPACES

    Institute of Scientific and Technical Information of China (English)

    Lucyna Rempulska; Mariola Skorupka

    2007-01-01

    We prove some approximation properties of generalized Meyer-K(o)nig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [ 1-3,7-16].

  10. -Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Lee HyunYoung

    2010-01-01

    Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

  11. Finite Blaschke product and the multiplication operators on Sobolev disk algebra

    Institute of Scientific and Technical Information of China (English)

    2009-01-01

    Let R(D) be the algebra generated in Sobolev space W22(D) by the rational functions with poles outside the unit disk D. In this paper the multiplication operators Mg on R(D) is studied and it is proved that Mg ~ Mzn if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then Mg has uncountably many Banach reducing subspaces if and only if n > 1.

  12. WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES

    Institute of Scientific and Technical Information of China (English)

    V. S. Guliyev; Zhijian Wu

    2005-01-01

    We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.

  13. A Mehler-Heine-type formula for Hermite-Sobolev orthogonal polynomials

    Science.gov (United States)

    Castaño-García, Laura; Moreno-Balcázar, Juan J.

    2003-01-01

    We consider a Sobolev inner product such as (f,g)S=[integral operator]f(x)g(x) d[mu]0(x)+[lambda][integral operator]f'(x)g'(x) d[mu]1(x), [lambda]>0,with ([mu]0,[mu]1) being a symmetrically coherent pair of measures with unbounded support. Denote by Qn the orthogonal polynomials with respect to (1) and they are so-called Hermite-Sobolev orthogonal polynomials. We give a Mehler-Heine-type formula for Qn when [mu]1 is the measure corresponding to Hermite weight on , that is, d[mu]1=e-x2 dx and as a consequence an asymptotic property of both the zeros and critical points of Qn is obtained, illustrated by numerical examples. Some remarks and numerical experiments are carried out for d[mu]0=e-x2 dx. An upper bound for Qn on is also provided in both cases.

  14. The weighted Herz-type Hardy space and its applications

    Institute of Scientific and Technical Information of China (English)

    陆善镇; 杨大春

    1995-01-01

    A certain weighted Herz-type Hardy space is introduced and its atom-decomposition theory is established. As applications of this theory, a boundedness theorem of sublinear operators and an interpolation theorem of linear operators on these spaces are given.

  15. SINGULAR INTEGRAL OPERATORS IN L2 SPACE WITH CHEBYSHEV WEIGHTS

    Institute of Scientific and Technical Information of China (English)

    2000-01-01

    This paper defines a class of singular integral operators Iwj on L2wj space,where wights wj(j=1-4) are four kinds of Chebyshev weights.The authors prove that Iwj is an unique linear extension of classic singular integral operator Iwj on Holder space,some important properties of Iwj and some results of singular integral equation in L2wj space.

  16. Bundles over Quantum RealWeighted Projective Spaces

    Directory of Open Access Journals (Sweden)

    Tomasz Brzeziński

    2012-09-01

    Full Text Available The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1-bundles over quantum real weighted projective spaces are constructed. As the spaces in question fall into two separate classes, the negative or odd class that generalises quantum real projective planes and the positive or even class that generalises the quantum disc, so do the constructed principal bundles. In the negative case the principal bundle is proven to be non-trivial and associated projective modules are described. In the positive case the principal bundles turn out to be trivial, and so all the associated modules are free. It is also shown that the circle (coactions on the quantum Seifert manifold that define quantum real weighted projective spaces are almost free.

  17. The molecular characterization of weighted Hardy spaces

    Institute of Scientific and Technical Information of China (English)

    LI; Xingmin

    2001-01-01

    Surveys, 1993, 7: 305.[16]Shephand, N., Statistical aspects of ARCH and stochastic volatility, in Time Series Models in Econometrics, Finance and Other Fields (eds. Cox, D. R., Hinkley, D. V., Barndorff-Nielsen, O. E.), London: Chapman & Hall, 1996, 1.[17]Pantula, S. G., Estimation of autoregressive models with ARCH errors, Sankhya, Ser. B, 1988, 50: 119.[18]Campbell, J. Y., Lo, A. W., Mackinlay, A. C., The Econometrics of Financial Markets, Princeton: Princeton University Press, 1997, 488.[19]Fan, J., Gijbels, I., Local Polynomial Modeling and Its Applications, London: Chapman & Hall, 1996.[20]Lu, Z. D., A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model, Statistics and Probability Letters, 1996, 30: 305.[21]Robinson, P. M., Nonparametric estimators for time series, Journal of Time Series Analysis, 1983, 4: 185.[22]Stone, C. J., Optimal rates of convergence for nonparametric estimators, Annals of Statistics, 1980, 8: 1348.[23]Stone, C. J., Optimal global rates of convergence for nonparametric kernel regression, Annals of Statistics, 1982, 10: 1040.[24]Truong, Y. M., Stone, C. J., Nonparametric function estimation involving time series, Annals of Statistics, 1992, 20: 77.[25]Masry, E., Multivariate polynomial regression for time series; uniform strong consistency and rates, Journal of Time Series Analysis, 1996, 17: 571.[26]Ruppert, D., Wand, M. P., Multivariate locally weighted least squares regression, Annals of Statistics, 1994, 22: 1346.[27]Bollerslev, T., Generalized autoregressive conditional heteroscedasticity, Journal of Econometrics, 1986, 31: 307.[28]Engle, R. F., Granger, C. W. J., Co-integration and error-correction: representation, estimation and testing, Econometrica, 1987, 55: 251.

  18. Integral type operators from normal weighted Bloch spaces to QT,S spaces

    Directory of Open Access Journals (Sweden)

    Yongyi GU

    2016-08-01

    Full Text Available Operator theory is an important research content of the analytic function space theory. The discussion of simultaneous operator and function space is an effective way to study operator and function space. Assuming that  is an analytic self map on the unit disk Δ, and the normal weighted bloch space μ-B is a Banach space on the unit disk Δ, defining a composition operator C∶C(f=f on μ-B for all f∈μ-B, integral type operator JhC and CJh are generalized by integral operator and composition operator. The boundeness and compactness of the integral type operator JhC acting from normal weighted Bloch spaces to QT,S spaces are discussed, as well as the boundeness of the integral type operators CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.

  19. On improved fractional Sobolev-Poincaré inequalities

    Science.gov (United States)

    Dyda, Bartłomiej; Ihnatsyeva, Lizaveta; Vähäkangas, Antti V.

    2016-10-01

    We study a certain improved fractional Sobolev-Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev-Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev-Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a `separation property', is a John domain.

  20. BOUNDEDNESS OF VECTOR-VALUED OPERATORS ON WEIGHTED HERZ SPACES

    Institute of Scientific and Technical Information of China (English)

    Tang Lin; Yang Dachun

    2000-01-01

    In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator;and using this ,the authors obtain the weightd inequalies for a wide class of sublinear singular operators definedon Rn which include the Calderón-Zygmund operators as special cases. The fractional versions of these resultsare also given.

  1. Weighted Composition Operators from Bergman-Type Spaces into Bloch Spaces

    Indian Academy of Sciences (India)

    Songxiao Li; Stevo Stević

    2007-08-01

    Let be an analytic self-map and be a fixed analytic function on the open unit disk in the complex plane $\\mathbb{C}$. The weighted composition operator is defined by $$u C_\\varphi f=u\\cdot p (f\\circ\\varphi), f\\in H(D).$$ Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.

  2. Understanding redshift space distortions in density-weighted peculiar velocity

    CERN Document Server

    Sugiyama, Naonori S; Spergel, David N

    2015-01-01

    Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of the density-weighted velocity is the change of the sign of infall velocity at small scales due to the nonlinear redshift space distortion. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to $\\sim10\\ h^{-1} {\\rm Mpc}$...

  3. Intrinsic square functions on the weighted Morrey spaces

    OpenAIRE

    Wang, Hua

    2011-01-01

    In this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley $g$-function and $g^*_\\lambda$-function on the weighted Morrey spaces $L^{p,\\kappa}(w)$ for $1

  4. A Note on Noneffective Weights in Variable Lebesgue Spaces

    Directory of Open Access Journals (Sweden)

    Alberto Fiorenza

    2012-01-01

    Full Text Available We study noneffective weights in the framework of variable exponent Lebesgue spaces, and we show that Lp(⋅(Ω=Lωp(⋅(Ω if and only if ω(x1/p(x~constant in the set where p(⋅<∞, and ω(x~constant in the set where p(⋅=∞.

  5. Cubature Methods For Stochastic (Partial) Differential Equations In Weighted Spaces

    CERN Document Server

    Doersek, Philipp; Veluscek, Dejan

    2012-01-01

    The cubature on Wiener space method, a high-order weak approximation scheme, is established for SPDEs in the case of unbounded characteristics and unbounded payoffs. We first introduce a recently described flexible functional analytic framework, so called weighted spaces, where Feller-like properties hold. A refined analysis of vector fields on weighted spaces then yields optimal convergence rates of cubature methods for stochastic partial differential equations of Da Prato-Zabczyk type. The ubiquitous stability for the local approximation operator within the functional analytic setting is proved for SPDEs, however, in the infinite dimensional case we need a newly introduced assumption on weak symmetry of the cubature formula. In finite dimensions, we use the UFG condition to obtain optimal rates of convergence on non-uniform meshes for nonsmooth payoffs with exponential growth.

  6. Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra

    Institute of Scientific and Technical Information of China (English)

    Ran SHEN; Yu Cai SU

    2007-01-01

    We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenberg-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module (and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series).

  7. On the Morse-Sard property and level sets of $W^{n,1}$ Sobolev functions on ${\\mathbb R}^n$

    CERN Document Server

    Bourgain, Jean; Kristensen, Jan

    2012-01-01

    We establish Luzin N and Morse--Sard properties for functions from the Sobolev space $W^{n,1}({\\mathbb R}^{n})$. Using these results we prove that almost all level sets are finite disjoint unions of $C^1$--smooth compact manifolds of dimension $n-1$. These results remain valid also within the larger space of functions of bounded variation $BV_{n}({\\mathbb R}^{n})$. For the proofs we establish and use some new results on Luzin--type approximation of Sobolev and BV--functions by $C^k$--functions, where the exceptional sets have small Hausdorff content.

  8. MULTIPLIERS AND TENSOR PRODUCTS OF WEIGHTED LP-SPACES

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Let G be a locally compact uninmodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space APωq,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Furthermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in L1ω. (G). It is also proved that the space Lpωp (G) L1ω lPω(G) is isometrically isomorphic to the space Apω.q (G) and the space of multipliers from Lωp (G) to Lqωq-1 (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from L1ω (G) to Aωp,q (G) is the space Aωp,q (G).

  9. Weighted Inequalities for the Generalized Maximal Operator in Martingale Spaces

    Institute of Scientific and Technical Information of China (English)

    Wei CHEN; Peide LIU

    2011-01-01

    The generalized maximal operator M in martingale spaces is considered.For 1 < p ≤ q < ∞,the authors give a necessary and sufficient condition on the pair ((μ),v)for M to be a bounded operator from martingale space LP(v) into Lq((μ)) or weak-Lq((μ)),where (μ) is a measure on Ω× N and v a weight on Ω.Moreover,the similar inequalities for usual maximal operator are discussed.

  10. Strongly Singular Integral Operators on Weighted Hardy Space

    Institute of Scientific and Technical Information of China (English)

    Jun Feng LI; Shan Zhen LU

    2006-01-01

    In this paper, we obtain that a strongly singular integral operator is bounded on Lpw space for 1<p<∞.We also obtain that a strongly singular integral operator is a bounded operator from Hpw to Lpw for some weight w and 0<p≤1. And by an atomic decomposition, we obtain that a strongly singular integral operator is a bounded operator on Hpw, for some w and 0<p<1.

  11. Spectral analysis of difference and differential operators in weighted spaces

    Energy Technology Data Exchange (ETDEWEB)

    Bichegkuev, M S [North-Ossetia State University, Vladikavkaz (Russian Federation)

    2013-11-30

    This paper is concerned with describing the spectrum of the difference operator K:l{sub α}{sup p}(Z,X)→l{sub α}{sup p}(Z......athscrKx)(n)=Bx(n−1),  n∈Z,  x∈l{sub α}{sup p}(Z,X), with a constant operator coefficient B, which is a bounded linear operator in a Banach space X. It is assumed that K acts in the weighted space l{sub α}{sup p}(Z,X), 1≤p≤∞, of two-sided sequences of vectors from X. The main results are obtained in terms of the spectrum σ(B) of the operator coefficient B and properties of the weight function. Applications to the study of the spectrum of a differential operator with an unbounded operator coefficient (the generator of a strongly continuous semigroup of operators) in weighted function spaces are given. Bibliography: 23 titles.

  12. The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Hong Yu

    2015-01-01

    Full Text Available We combine the H1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at most q-1 with the time variable. The existence and uniqueness of the solutions are proved, and the optimal H1-norm error estimates are derived. We get high accuracy for both the space and time variables.

  13. Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

    Science.gov (United States)

    Krylov, N. V.; Priola, E.

    2017-09-01

    We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

  14. L2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations

    Directory of Open Access Journals (Sweden)

    Hyun Young Lee

    2010-01-01

    Full Text Available We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ℓ∞(L2 error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

  15. Weighted composition operators from F(p, q, s) spaces to Bers-type spaces in the unit ball

    Institute of Scientific and Technical Information of China (English)

    L(U) Xiao-fen

    2009-01-01

    This paper deals with the boundedness and compactness of the weighted compo-sition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Q~p space,BMOA space, Besov space and α-Bloch space, to Bers-type spaces H_ν~∞( or little Bets-type spaces H_(ν,0)~∞ ), where ν is normal.

  16. Geometric-type Sobolev inequalities and applications to the regularity of minimizers

    CERN Document Server

    Cabre, Xavier

    2011-01-01

    The purpose of this paper is twofold. We first prove a weighted Sobolev inequality and part of a weighted Morrey's inequality, where the weights are a power of the mean curvature of the level sets of the function appearing in the inequalities. Then, as main application of our inequalities, we establish new $L^q$ and $W^{1,q}$ estimates for semi-stable solutions of $-\\Delta u=g(u)$ in a bounded domain $\\Omega$ of $\\mathbb{R}^n$. These estimates lead to an $L^{2n/(n-4)}(\\Omega)$ bound for the extremal solution of $-\\Delta u=\\lambda f(u)$ when $n\\geq 5$ and the domain is convex. We recall that extremal solutions are known to be bounded in convex domains if $n\\leq 4$, and that their boundedness is expected ---but still unkwown--- for $n\\leq 9$.

  17. A Characterization for the Gevrey-Sobolev Wave Front Set

    Institute of Scientific and Technical Information of China (English)

    Hua CHEN

    2001-01-01

    In this note, we use the so-called microlocal energy method to give a characterization of theGevrey-Sobolev wave front set W FHστσ (u), which will be useful in the study of non-linear microlocalanalysis in Gevrey classes.

  18. On Hirschman and log-Sobolev inequalities in {mu}-deformed Segal-Bargmann analysis

    Energy Technology Data Exchange (ETDEWEB)

    Velasco, Claudio de Jesus Pita Ruiz [Universidad Panamericana, Mexico City (Mexico); Sontz, Stephen Bruce [Centro de Investigacion en Matematicas, A C (CIMAT), Guanajuato (Mexico)

    2006-07-07

    We consider a {mu}-deformation of the Segal-Bargmann transform, which is a unitary map from a {mu}-deformed ground state representation onto a {mu}-deformed Segal-Bargmann space. We study the {mu}-deformed Segal-Bargmann transform as an operator between L{sup p} spaces and then we obtain sufficient conditions on the Lebesgue indices for this operator to be bounded. A family of Hirschman inequalities involving the Shannon entropies of a function and of its {mu}-deformed Segal-Bargmann transform are proved. We also prove a parametrized family of log-Sobolev inequalities, in which a new quantity that we call 'dilation energy' appears. This quantity generalizes the 'energy term' that has appeared in a previous work.

  19. A new expanded mixed element method for convection-dominated Sobolev equation.

    Science.gov (United States)

    Wang, Jinfeng; Liu, Yang; Li, Hong; Fang, Zhichao

    2014-01-01

    We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in L (2)-norm for the scalar unknown u and a priori error estimates in (L (2))(2)-norm for its gradient λ and its flux σ . Moreover, we obtain the optimal a priori error estimates in H (1)-norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method.

  20. Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-Class Domains

    Science.gov (United States)

    Cheng, C. H. Arthur; Shkoller, Steve

    2017-09-01

    We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field u are prescribed in an open, bounded, Sobolev-class domain {Ω \\subseteq R^n}, and either the normal component {{u} \\cdot {N}} or the tangential components of the vector field {{u} × {N}} are prescribed on the boundary {partial Ω}. For {k > n/2}, we prove that u is in the Sobolev space {H^k+1(Ω)} if {Ω} is an {H^k+1}-domain, and the divergence, curl, and either the normal or tangential trace of u has sufficient regularity. The proof is based on a regularity theory for vector elliptic equations set on Sobolev-class domains and with Sobolev-class coefficients, and with a rather general set of Dirichlet and Neumann boundary conditions. The resulting regularity theory for the vector u is fundamental in the analysis of free-boundary and moving interface problems in fluid dynamics.

  1. Spectral Gap and Logarithmic Sobolev Constant for Continuous Spin Systems

    Institute of Scientific and Technical Information of China (English)

    Mu Fa CHEN

    2008-01-01

    The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap of finite dimensional systems is given by Theorem 1.1, in terms of the spectral gap for one-dimensional marginals. The study of this topic provides us a chance, and it is indeed another aim of the paper, to justify the power of the results obtained previously. The exact order in dimension one (Proposition 1.4), and then the precise leading order and the explicit positive regions of the spectral gap and the logarithmic Sobolev constant for two typical infinite-dimensional models are presented (Theorems 6.2 and 6.3). Since we are interested in explicit estimates, the computations become quite involved. A long section (Section 4) is devoted to the study of the spectral gap in dimension one.

  2. Jacobi-Sobolev Orthogonal Polynomials: Asymptotics for N-Coherence of Measures

    Directory of Open Access Journals (Sweden)

    Marcellán Francisco

    2011-01-01

    Full Text Available Let us introduce the Sobolev-type inner product , where and , , with and for all A Mehler-Heine-type formula and the inner strong asymptotics on as well as some estimates for the polynomials orthogonal with respect to the above Sobolev inner product are obtained. Necessary conditions for the norm convergence of Fourier expansions in terms of such Sobolev orthogonal polynomials are given.

  3. Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals

    Science.gov (United States)

    Raza, Nauman; Sial, Sultan; Siddiqi, Shahid S.

    2009-04-01

    The Sobolev gradient technique has been discussed previously in this journal as an efficient method for finding energy minima of certain Ginzburg-Landau type functionals [S. Sial, J. Neuberger, T. Lookman, A. Saxena, Energy minimization using Sobolev gradients: application to phase separation and ordering, J. Comput. Phys. 189 (2003) 88-97]. In this article a Sobolev gradient method for the related time evolution is discussed.

  4. Anisotropic rectangular nonconforming finite element analysis for Sobolev equations

    Institute of Scientific and Technical Information of China (English)

    SHI Dong-yang; WANG Hai-hong; GUO Cheng

    2008-01-01

    An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes.The corresponding optimal convergence error estimates and superclose property are derived,which are the same as the traditional conforming finite elements.Furthermore,the global superconvergence is obtained using a post-processing technique.The numerical results show the validity of the theoretical analysis.

  5. Weighted Composition Operators between Different Bergman Spaces of Bounded Symmetric Domains

    Indian Academy of Sciences (India)

    Xiaofen Lv; Xiaomin Tang

    2009-09-01

    In this paper, we consider the boundedness and compactness of the weighted composition operators between different Bergman spaces of bounded symmetric domains in terms of the Carleson measure. As an application, we study the multipliers between different Bergman spaces.

  6. An Advanced Light Weight Recuperator for Space Power Systems Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Nuclear Electric Propulsion (NEP) technology holds great promise for power and propulsion demands of NASA current and future deep space explorations. Closed Brayton...

  7. An Advanced Light Weight Recuperator for Space Power Systems Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Closed Brayton Cycle (CBC) space power system is one of the most efficient energy conversion technologies for nuclear and solar electric propulsion. The recuperator...

  8. Irreducible quantum group modules with finite dimensional weight spaces

    DEFF Research Database (Denmark)

    Pedersen, Dennis Hasselstrøm

    We classify all irreducible weight modules for a quantized enveloping algebra U q (g) at most q ∈ C ∗ when the simple Lie algebra g is not of type G 2 . More precisely, our classificiation is carried out when q is either an odd root of unity or transcendental over Q. By a weight module we mean...

  9. On the characterization of the compact embedding of Sobolev spaces

    CERN Document Server

    Bucur, D

    2009-01-01

    For every positive regular Borel measure, possibly infinite valued, vanishing on all sets of $p$-capacity zero, we characterize the compactness of the embedding $W^{1,p}({\\bf R}^N)\\cap L^p ({\\bf R}^N,\\mu)\\hr L^q({\\bf R}^N)$ in terms of the qualitative behavior of some characteristic PDE. This question is related to the well posedness of a class of geometric inequalities involving the torsional rigidity and the spectrum of the Dirichlet Laplacian introduced by Polya and Szeg\\"o in 1951. In particular, we prove that finite torsional rigidity of an arbitrary domain (possibly with infinite measure), implies the compactness of the resolvent of the Laplacian.

  10. Uniform Concentration-Compactness for Sobolev Spaces on Variable Domains

    Science.gov (United States)

    Bucur, Dorin

    2000-04-01

    We present a new method for proving existence results in shape optimization problems involving the eigenvalues of the Dirichlet-Laplace operator. This method brings together the γ-convergence theory and the concentration-compactness principle. Given a sequence of open sets (An)n∈N in RN, not necessarily bounded, but of uniformly bounded measure, we prove a concentration-compactness result in L(L2(RN)) for the sequence of resolvent operators (RAn)n∈N, where RAn: L2(RN)→H10(An), RAn=(-Δ)-1.

  11. Leslie ja Naomi juhtum / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2004-01-01

    Readingi Ülikoolis (Inglismaa) toimunud feminismikonverentsiga kaasnenud näitusest "Virtue and Vulgarity" ja selle silmapaistvamatest töödest. Analüüsitakse naiste ja meeste kunstile omaseid erinevusi ning võimalust aktsepteerida feminiinsusena ka malbust, alalhoidlikkust. Esitati Mare Tralla CD-ROM "her.space"

  12. Leslie ja Naomi juhtum / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2004-01-01

    Readingi Ülikoolis (Inglismaa) toimunud feminismikonverentsiga kaasnenud näitusest "Virtue and Vulgarity" ja selle silmapaistvamatest töödest. Analüüsitakse naiste ja meeste kunstile omaseid erinevusi ning võimalust aktsepteerida feminiinsusena ka malbust, alalhoidlikkust. Esitati Mare Tralla CD-ROM "her.space"

  13. Weak type estimates of intrinsic square functions on the weighted Hardy spaces

    CERN Document Server

    Wang, Hua

    2010-01-01

    In this paper, by using the atomic decomposition theory of weighted Hardy spaces, we will give some weighted weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $g$-function and $g^*_\\lambda$-function on these spaces.

  14. Weak type estimates of intrinsic square functions on the weighted Herz-type Hardy spaces

    CERN Document Server

    Wang, Hua

    2010-01-01

    In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we will obtain some weighted weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley $g$-function and $g^*_\\lambda$-function on these spaces.

  15. Weighted Multi-Parameter Non-Isotropic Flag Triebel-Lizorkin and Besov Spaces

    OpenAIRE

    Liao, F; Liu, Z.

    2014-01-01

    In this paper, the authors use the discrete Littlewood-Paley-Stein theory to introduce weighted multi-parameter Triebel-Lizorkin and Besov spaces associated with non-isotropic flag singular integrals under a rather weak weight condition $(w\\in A_\\infty)$. They also obtain the boundedness of flag singular integrals on these spaces.

  16. WEIGHTED INEQUALITIES FOR THE GEOMETRIC MAXIMAL OPERATOR ON MARTINGALE SPACES

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this article, the authors introduce two operators-geometrical maximal operator Mo and the closely related limiting operator M*O, then they give sufficient conditions under which the equality MO = M*O holds, and characterize the equivalent relations between the weak or strong type weighted inequality and the property of W∞-weight or W*∞-weight for the geometrical maximal operator in the case of two-weight condition. What should be mentioned is that the new operator-the geometrical minimal operator is equal to the limitation of the minimal operator sequence, and the results for the minimal operator proved in [12] makes the proof elegant and evident.

  17. Interior Lp-estimates for elliptic and parabolic Schr\\"odinger type operators and local Ap-weights

    OpenAIRE

    Cardoso, Isolda; Viola, Pablo; Viviani, Beatriz

    2015-01-01

    Let Omega be a non-empty open proper and connected subset of R^n. Consider p elliptic Schr\\"odinger type operator L_{E}u=A_{E}u+V in Omega, and the linear parabolic operator L_{P}u=A_{P}u+Vu in Omega x (0,T), where the coefficients of A_{E} and A_{P} are in VMO and the potential V satisfies a reverse-H\\"older condition. The aim of this paper is to obtain a priori estimates for the operators L_{E} and L_{P} in weighted Sobolev spaces involving the distance to the boundary and weights in a loca...

  18. Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

    Directory of Open Access Journals (Sweden)

    Hua Wang

    2017-01-01

    Full Text Available Abstract In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators I α $I_{\\alpha}$ in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [ b , I α ] $[b,I_{\\alpha}]$ formed by b and I α $I_{\\alpha}$ are established. Also we study related problems about two-weight, weak type inequalities for I α $I_{\\alpha}$ and [ b , I α ] $[b,I_{\\alpha}]$ in the Morrey-type spaces and give partial results.

  19. On the Projective Description of Weighted (LF-Spaces of Continuous Functions

    Directory of Open Access Journals (Sweden)

    Catherine V. Komarchuk

    2014-01-01

    Full Text Available We solve the problem of the topological or algebraic description of countable inductive limits of weighted Fréchet spaces of continuous functions on a cone. This problem is investigated for two families of weights defined by positively homogeneous functions. Weights of this form play the important role in Fourier analysis.

  20. ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY

    Institute of Scientific and Technical Information of China (English)

    姜惠强; 林芳华

    2004-01-01

    Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation.After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model.

  1. Lower Profile, Lighter Weight Space Suit Bearings Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Air-Lock will deliver a final report based on the follwoing: 1. Historical summary of bearing design evolution throughout the life of the EMU Program 2. Material...

  2. Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups

    Energy Technology Data Exchange (ETDEWEB)

    Avdeev, Roman S [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)

    2010-12-22

    The extended weight semigroup of a homogeneous space G/H of a connected semisimple algebraic group G characterizes the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over G/H, including the space of regular functions on G/H. We compute the extended weight semigroups for all strictly irreducible affine spherical homogeneous spaces G/H, where G is a simply connected non-simple semisimple complex algebraic group and H is a connected closed subgroup of G. In all cases we also find the highest-weight functions corresponding to the indecomposable elements of this semigroup. Among other things, our results complete the computation of the weight semigroups for all strictly irreducible simply connected affine spherical homogeneous spaces of semisimple complex algebraic groups.

  3. Weight, muscle and bone loss during space flight: another perspective.

    Science.gov (United States)

    Stein, T P

    2013-09-01

    Space flight is a new experience for humans. Humans adapt if not perfectly, rather well to life without gravity. There is a reductive remodeling of the musculo-skeletal system. Protein is lost from muscles and calcium from bones with anti-gravity functions. The observed biochemical and physiological changes reflect this accommodative process. The two major direct effects of the muscle loss are weakness post-flight and the increased incidence of low back ache pre- and post-flight. The muscle protein losses are compromised by the inability to maintain energy balance inflight. Voluntary dietary intake is reduced during space flight by ~20 %. These adaptations to weightlessness leave astronauts ill-equipped for life with gravity. Exercise, the obvious counter-measure has been repeatedly tried and since the muscle and bone losses persist it is not unreasonable to assume that success has been limited at best. Nevertheless, more than 500 people have now flown in space for up to 1 year and have done remarkably well. This review addresses the question of whether enough is now known about these three problems (negative energy balance, muscle loss and bone loss) for to the risks to be considered either acceptable or correctible enough to meet the requirements for a Mars mission.

  4. Weighted E-Spaces and Epistemic Information Operators

    Directory of Open Access Journals (Sweden)

    Mark Burgin

    2014-06-01

    Full Text Available Information is usually related to knowledge. Here, we present a broader picture in which information is associated with epistemic structures, which form cognitive infological systems as basic recipients and creators of cognitive information. Infological systems are modeled by epistemic spaces, while operators in these spaces are mathematical models of information. Information that acts on epistemic structures is called cognitive information, while information that acts on knowledge structures is called epistemic information. The latter brings new and updates existing knowledge, being of primary importance to people. In this paper, both types of information are studied as operators in epistemic spaces based on the general theory of information. As a synthetic approach, which reveals the essence of information, organizing and encompassing all main directions in information theory, the general theory of information provides efficient means for such a study. Different types of information dynamics representation use tools from various mathematical disciplines, such as the theory of categories, functional analysis, mathematical logic and algebra. In this paper, we base our exploration of information and knowledge dynamics on functional analysis further developing the mathematical stratum of the general theory of information.

  5. Time and space, weight and inertia a chronogeometrical introduction to Einstein's theory

    CERN Document Server

    Fokker, Adriaan Daniel

    1965-01-01

    Time and Space Weight and Inertia covers the relationship between time, space weight, and inertia using the principles of theory of relativity and chronogeometry. This book is composed of 12 chapters, and begins with a brief overview of the fundamental aspects of space and time within events. The subsequent chapters deal with the chronogeometry of time and space, and the concept of the Lorentz transformations and pseudo-revolutions. These topics are followed by discussions on the dynamical relationships of metric and other tensors and a presentation of the equations of the theory of electrons

  6. Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160

    Institute of Scientific and Technical Information of China (English)

    WANG Gong-bao

    2001-01-01

    In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160are presented at the end of the paper.

  7. WEIGHTED ESTIMATES FOR COMMUTATORS OF POTENTIAL OPERATORS ON SPACES OF HOMOGENEOUS TYPE

    Institute of Scientific and Technical Information of China (English)

    Wenming Li; Xiaowu Yu; Xuefang Yan

    2009-01-01

    We derive some strong type and weak type weighted norm estimates which relate the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.

  8. The boundedness of intrinsic square functions on the weighted Herz-type Hardy spaces

    CERN Document Server

    Wang, Hua

    2010-01-01

    In this paper, the boundedness properties are obtained for intrinsic square functions including the Lusin area function, Littlewood-Paley $g$-function and $g^*_\\lambda$-function on the weighted Herz-type Hardy spaces.

  9. Weighting of Auditory Feedback Across the English Vowel Space

    OpenAIRE

    Purcell, David; Munhall, Kevin

    2008-01-01

    Auditory feedback in the headphones of talkers was manipulated in the F1 dimension using a real-time vowel formant filtering system. Minimum formant shifts required to elicit a response and the amount of compensation were measured for vowels across the English vowel space. The largest response in production of F1 was observed for the vowel /ε/ and smaller or non-significant changes were found for point vowels. In general, changes in production were of a compensatory nature that reduced the er...

  10. Weighted Projective Spaces from the toric point of view with computational applications

    CERN Document Server

    Rossi, Michele

    2011-01-01

    The purpose of the present paper is threefold. First: giving a survey on weighted projective spaces by the toric point of view, which seems to be missing in the literature. Second: providing characterizations of fans and polytopes giving (polarized, in case) weighted projective spaces, so inaugurating a kind of \\emph{recognition process} of toric data like fans and polytopes. Third: building a mathematical framework for an algorithmic and computational approach to wps's, actually realized in [19,20].

  11. Weighted Weak-type Estimates for Multilinear Commutators of Fractional Integrals on Spaces of Homogeneous Type

    Institute of Scientific and Technical Information of China (English)

    Osvaldo GOROSITO; Gladis PRADOLINI; Oscar SALINAS

    2007-01-01

    We obtain weighted distributional inequalities for multilinear commutators of the fractional integral on spaces of homogeneous type. The techniques developed in this work involve the behavior of some fractional maximal functions. In relation to these operators, as a main tool, we prove a weighted weak type boundedness result, which is interesting in itself.

  12. On nowhere first-countable compact spaces with countable pi-weight

    NARCIS (Netherlands)

    van Mill, J.

    2015-01-01

    The minimum weight of a nowhere first-countable compact space of countable $\\pi$-weight is shown to be $\\kappa_B$, the least cardinal $\\kappa$ for which the real line $\\mathbb R$ can be covered by $\\kappa$ many nowhere dense sets.

  13. Trigonometric bases for matrix weighted Lp-spaces

    DEFF Research Database (Denmark)

    Nielsen, Morten

    2010-01-01

    We give a complete characterization of 2π-periodic matrix weights W for which the vector-valued trigonometric system forms a Schauder basis for the matrix weighted space Lp(T;W). Then trigonometric quasi-greedy bases for Lp(T;W) are considered. Quasi-greedy bases are systems for which the simple ...

  14. The Sobolev-P method - A generalization of the Sobolev method for the treatment of the polarization state of radiation and the polarizing effect of resonance line scattering

    Energy Technology Data Exchange (ETDEWEB)

    Jeffrey, D.J. (Oklahoma Univ., Norman (USA))

    1989-12-01

    The Sobolev-P method, a generalization of the Sobolev method, is developed for the treatment of the polarization state of radiation and the polarizing effect of resonance line scattering. The polarization state of the radiation is described by the Stokes parameters. The photon angular redistribution is described by a linear combination of the Rayleigh and isotropic phase matrices. Using this form of photon redistribution the Sobolev-P method formulas are derived for the case of axisymmetric systems. For continuum radiative transfer it is shown that quantitatively accurate calculations can be done using the Sobolev-P method and a discretized continuous opacity approximation. Sample synthetic flux and polarization spectra for model axisymmetric supernova systems calculated using Sobolev-P method are reported. A comparison of these sample results with spectropolarimetric data for SN 1987A shows some qualitative agreement of the features and indicates that it is pausible that SN 1987A has a length-width asymmetry of order 20 percent. 68 refs.

  15. A NOTE ON SOBOLEV ORTHOGONALITY FOR LAGUERRE MATRIX POLYNOMIALS

    Institute of Scientific and Technical Information of China (English)

    Zhihui Zhu; Zhongkai Li

    2007-01-01

    Let {Ln(A,λ)(x)}n≥0 be the sequence of monic Laguerre matrix polynomials defined on [0, ∞) by Ln(A,λ)(x)=n!/(-λ)n∑nk=0(-λ)κ/k!(n-1)! (A+I)n[(A+I)k]-1 xk,where A ∈ Cr×r. It is known that {Ln(A,λ)(x)}n≥0 is orthogonal with respect to a matrix moment functional when A satisfies the spectral condition that Re(z) > - 1 for every z ∈σ(A).In this note we show that forA such that σ(A) does not contain negative integers, the Laguerre matrix polynomials Ln(A,λ) (x) are orthogonal with respect to a non-diagonal SobolevLaguerre matrix moment functional, which extends two cases: the above matrix case and the known scalar case.

  16. Estimates for Vector-valued Commutators on Weighted Morrey Space and Applications

    Institute of Scientific and Technical Information of China (English)

    Shao Guang SHI

    2013-01-01

    In this paper,we introduce weighted vector-valued Morrey spaces and obtain some estimates for vector-valued commutators on these spaces.Applications to Calderón-Zygmund singular integral operators,oscillatory singular integral operators and parabolic difference equations are considered.

  17. Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases

    Directory of Open Access Journals (Sweden)

    Dorothee D. Haroske

    2011-01-01

    Full Text Available We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt Ap class. This extends our previous results [25] to more general weights of logarithmically disturbed polynomial growth, both near some singular point and at infinity. We obtain sharp asymptotic estimates for the entropy numbers of this embedding. Essential tools are a discretisation in terms of wavelet bases, as well as a refined study of associated embeddings in sequence spaces and interpolation arguments in endpoint situations.

  18. Variational Formulas of Poincaré-Type Inequalities in Banach Spaces of Functions on the Line

    Institute of Scientific and Technical Information of China (English)

    Mu Fa CHEN

    2002-01-01

    Motivated from the study on logarithmic Sobolev, Nash and other functional inequalities,spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimatesfor the optimal constants in the inequalities are presented. As a typical application, the logarithmicSobolev constant is carefully examined.

  19. EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

    Institute of Scientific and Technical Information of China (English)

    康东升

    2004-01-01

    This paper is concerned with the quasi-linear equation with critical SobolevHardy exponent where Ω RN(N ≥ 3) is a smooth bounded domain, 0 ∈Ω, 0 ≤ s < p, 1 < p < N,p* (s) :=p(N- s)/N-p is the critical Sobolev-Hardy exponent, λ> 0,p ≤ r < p* ,p* := Np/N-p is the critical Sobolev exponent, μ> 0, 0 ≤ t < p, p ≤ q < p* (t) = P(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.

  20. Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.

    Science.gov (United States)

    Beckner, W

    1992-06-01

    Hypercontractive estimates are obtained for the Poisson semigroup on Lp(Sn). Such estimates are determined by a sharp logarithmic Sobolev inequality that relates the entropy of a function on Sn to its smoothness.

  1. PERTURBATION METHODS IN SEMILINEAR ELLIPTIC PROBLEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENT

    Institute of Scientific and Technical Information of China (English)

    蓝永艺; 唐春雷

    2014-01-01

    In this article, we deal with a class of semilinear elliptic equations which are perturbations of the problems with the critical Hardy-Sobolev exponent. Some existence results are given via an abstract perturbation method in critical point theory.

  2. Associations between multiple green space measures and birth weight across two US cities.

    Science.gov (United States)

    Cusack, Leanne; Larkin, Andrew; Carozza, Susan E; Hystad, Perry

    2017-09-01

    Several measures of green space exposure have been used in epidemiological research, but their relevance to health, and representation of exposure pathways, remains unclear. Here we examine the relationships between multiple urban green space metrics and associations with term birth weight across two diverse US cities. We used Vital Statistics data to create a birth cohort from 2005 to 2009 in the cities of Portland, Oregon (n = 90,265) and Austin, Texas (n = 88,807). These cities have similar green space levels but very different population and contextual characteristics. Green space metrics derived from mother's full residential address using multiple buffer distances (50-1000m) included: Landsat Normalized Difference Vegetation Index (NDVI), % tree cover, % green space, % street tree buffering, and access to parks (using US EPA EnviroAtlas Data). Correlation between green space metrics were assessed and mixed models were used to determine associations with term birth weight, controlling for a comprehensive set of individual and neighborhood factors. City-specific models were run to determine how contextual and population differences affected green space associations with birth weight. We observed moderate to high degrees of correlation between different green space metrics (except park access), with similar patterns between cities. Unadjusted associations demonstrated consistent protective effects of NDVI, % green space, % tree cover, and % street tree buffering for most buffer sizes on birth weight; however, in fully adjusted models most metrics were no longer statistically significant and no clear patterns remained. For example, in Austin the difference in birth weight for the highest versus lowest quartile of % green space within 50m was 38.3g (95% CI: 30.4, 46.1) in unadjusted and -1.5g (98% CI: -8.8, 6.3) in adjusted models compared to 55.7g (95%CI: 47.9, -63.6) and 12.9g (95% CI: 4.4, 21.4) in Portland. Maternal race, ethnicity and education had the

  3. ON THE WEIGHTED VARIABLE EXPONENT AMALGAM SPACE W (Lp(x), Lqm)

    Institute of Scientific and Technical Information of China (English)

    A.Turan GURKANLI; Ismail AYDIN

    2014-01-01

    In [4] , a new family W (Lp(x), Lqm) of Wiener amalgam spaces was defined and investigated some properties of these spaces, where local component is a variable exponent Lebesgue space Lp(x) (R) and the global component is a weighted Lebesgue space Lqm (R). This present paper is a sequel to our work [4]. In Section 2, we discuss necessary and sufficient conditions for the equality W Lp(x), Lqm=Lq (R) . Later we give some characterization of Wiener amalgam space WLp(x), Lqm. In Section 3 we define the Wiener amalgam space W FLp(x),Lq m and investigate some properties of this space, where F Lp(x) is the image of Lp(x) under the Fourier transform. In Section 4, we discuss boundedness of the Hardy-Littlewood maximal operator between some Wiener amalgam spaces.

  4. MRI Brain Tumor Segmentation and Necrosis Detection Using Adaptive Sobolev Snakes

    Science.gov (United States)

    Nakhmani, Arie; Kikinis, Ron; Tannenbaum, Allen

    2014-01-01

    Brain tumor segmentation in brain MRI volumes is used in neurosurgical planning and illness staging. It is important to explore the tumor shape and necrosis regions at different points of time to evaluate the disease progression. We propose an algorithm for semi-automatic tumor segmentation and necrosis detection. Our algorithm consists of three parts: conversion of MRI volume to a probability space based on the on-line learned model, tumor probability density estimation, and adaptive segmentation in the probability space. We use manually selected acceptance and rejection classes on a single MRI slice to learn the background and foreground statistical models. Then, we propagate this model to all MRI slices to compute the most probable regions of the tumor. Anisotropic 3D diffusion is used to estimate the probability density. Finally, the estimated density is segmented by the Sobolev active contour (snake) algorithm to select smoothed regions of the maximum tumor probability. The segmentation approach is robust to noise and not very sensitive to the manual initialization in the volumes tested. Also, it is appropriate for low contrast imagery. The irregular necrosis regions are detected by using the outliers of the probability distribution inside the segmented region. The necrosis regions of small width are removed due to a high probability of noisy measurements. The MRI volume segmentation results obtained by our algorithm are very similar to expert manual segmentation. PMID:25302005

  5. Toeplitz Type Operators Associated with Generalized Calderón-Zygmund Operator on Weighted Morrey Spaces

    Directory of Open Access Journals (Sweden)

    Bijun Ren

    2016-01-01

    Full Text Available Let T1 be a generalized Calderón-Zygmund operator or ±I (the identity operator, let T2 and T4 be the linear operators, and let T3=±I. Denote the Toeplitz type operator by Tb=T1MbIαT2+T3IαMbT4, where Mbf=bf and Iα is the fractional integral operator. In this paper, we investigate the boundedness of the operator Tb on weighted Morrey space when b belongs to the weighted BMO spaces.

  6. ON THE mth ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS

    Institute of Scientific and Technical Information of China (English)

    Metin BA(S)ARIR; Emrah Evren KARA

    2013-01-01

    In this article,using generalized weighted mean and difference matrix of order m,we introduce the paranormed sequence space l(u,v,p; △(m)),which consist of the sequences whose generalized weighted △(m)-difference means are in the linear space l(p) defined by I.J.Maddox.Also,we determine the basis of this space and compute its α-,β-and γ-duals.Further,we give the characterization of the classes of matrix mappings from l(u,v,p,△(m))to l∞,c,and c0.Finally,we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp(u,v,△(m)) (1 ≤ p < ∞).

  7. SOLUTIONS FOR A NONHOMOGENEOUS ELLIPTIC PROBLEM INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT IN RN

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    For the following elliptic problem{-△u -μu/|x|2=|u|2*(s)-2u/|x|s+h(x),on RNu∈D1,2(RN), N≥3, 0≤μ<(μ)=(N-2)2/4, 0≤s<2,where 2*(s)= 2(N-s)/N-2 is the critical Sobolev-Hardy exponent, h(x) ∈ (D1,2(RN))*, the dual space of (D1,2(RN)), with h(x) ≥ ((≠))0. By Ekeland's variational principle, subsuper solutions and a Mountain Pass theorem, the authors prove that the above problem has at least two distinct solutions if‖h‖* < CN,sASN-s/4-2s (1 -μ/μ)1/2, CN,s =4-2s/N-2(N-2/N+2-2s)N+2-2s/4-2s and As =infu∈D1,2(RN)\\{0}∫RN(|▽u|2-μu2/|x|2)dx/(∫RN|u|2*(s)/|x|sdx)2/2*(s).

  8. Identification of LPV Models with Non-uniformly Spaced Operating Points by Using Asymmetric Gaussian Weights

    Institute of Scientific and Technical Information of China (English)

    Jie You; Qinmin Yang; Jiangang Lu; Youxian Sun

    2014-01-01

    In this paper, asymmetric Gaussian weighting functions are introduced for the identification of linear parameter varying systems by utilizing an input-output multi-model structure. It is not required to select operating points with uniform spacing and more flexibility is achieved. To verify the effectiveness of the proposed approach, sev-eral weighting functions, including linear, Gaussian and asymmetric Gaussian weighting functions, are evaluated and compared. It is demonstrated through simulations with a continuous stirred tank reactor model that the proposed approach provides more satisfactory approximation.

  9. Boundedness of Composition of Operators Associated with Different Homogeneities on Weighted Besov and Triebel-Lizorkin Spaces

    Indian Academy of Sciences (India)

    Xinfeng Wu

    2014-02-01

    In this paper, we introduce weighted Besov spaces and weighted Triebel–Lizorkin spaces associated with different homogeneities and prove that the composition of two Calderón–Zygmund operators is bounded on these spaces. This extends a recent result in Han et al, Revista Mat. Iber.

  10. How Weight Affects the Perceived Spacing between the Thumb and Fingers during Grasping.

    Directory of Open Access Journals (Sweden)

    Annie A Butler

    Full Text Available We know much about mechanisms determining the perceived size and weight of lifted objects, but little about how these properties of size and weight affect the body representation (e.g. grasp aperture of the hand. Without vision, subjects (n = 16 estimated spacing between fingers and thumb (perceived grasp aperture while lifting canisters of the same width (6.6cm but varied weights (300, 600, 900, and 1200 g. Lifts were performed by movement of either the wrist, elbow or shoulder to examine whether lifting with different muscle groups affects the judgement of grasp aperture. Results for perceived grasp aperture were compared with changes in perceived weight of objects of different sizes (5.2, 6.6, and 10 cm but the same weight (600 g. When canisters of the same width but different weights were lifted, perceived grasp aperture decreased 4.8% [2.2 ‒ 7.4] (mean [95% CI]; P < 0.001 from the lightest to the heaviest canister, no matter how they were lifted. For objects of the same weight but different widths, perceived weight decreased 42.3% [38.2 ‒ 46.4] from narrowest to widest (P < 0.001, as expected from the size-weight illusion. Thus, despite a highly distorted perception of the weight of objects based on their size, we conclude that proprioceptive afferents maintain a reasonably stable perception of the aperture of the grasping hand over a wide range of object weights. Given the small magnitude of this 'weight-grasp aperture' illusion, we propose the brain has access to a relatively stable 'perceptual ruler' to aid the manipulation of different objects.

  11. Efficient Love wave modelling via Sobolev gradient steepest descent

    Science.gov (United States)

    Browning, Matt; Ferguson, John; McMechan, George

    2016-05-01

    A new method for finding solutions to ordinary differential equation boundary value problems is introduced, in which Sobolev gradient steepest descent is used to determine eigenfunctions and eigenvalues simultaneously in an iterative scheme. The technique is then applied to the 1-D Love wave problem. The algorithm has several advantages when computing dispersion curves. It avoids the problem of mode skipping, and can handle arbitrary Earth structure profiles in depth. For a given frequency range, computation times scale approximately as the square root of the number of frequencies, and the computation of dispersion curves can be implemented in a fully parallel manner over the modes involved. The steepest descent solutions are within a fraction of a per cent of the analytic solutions for the first 25 modes for a two-layer model. Since all corresponding eigenfunctions are computed along with the dispersion curves, the impact on group and phase velocity of the displacement behaviour with depth is thoroughly examined. The dispersion curves are used to compute synthetic Love wave seismograms that include many higher order modes. An example includes addition of attenuation to a model with a low-velocity zone, with values as low as Q = 20. Finally, a confirming comparison is made with a layer matrix method on the upper 700 km of a whole Earth model.

  12. Unique Concept for a Low Cost, Light Weight Space Deployable Antenna Structure

    Science.gov (United States)

    Freeland, Robert E.; Bilyeu, Gayle D.; Veal, Gordon R.

    1993-01-01

    Large space deployable antennas are needed for a variety of applications that include Mobile Communications, Radiometry, Active Microwave Sensing, Very Long Baseline Interferometry and DoD Space Based Radar. These user requirements identify the need for structures up to tens of meters in size for operation from 1 to 90 GHz, based on different aperture configurations. However, the one thing the users have in common is a concept selection criteria for low cost, light weight and highly reliable deployable structures. Fortunately, a unique class of space structures has recently emerged that have tremendous potential for satisfying these criteria. They are referred to as inflatable deployable structures.

  13. (m,λ-Berezin Transform on the Weighted Bergman Spaces over the Polydisk

    Directory of Open Access Journals (Sweden)

    Ran Li

    2016-01-01

    Full Text Available We prove that every bounded linear operator on weighted Bergman space over the polydisk can be approximated by Toeplitz operators under some conditions. The main tool here is the so-called (m,λ-Berezin transform. In particular, our results generalized the results of K. Nam and D. C. Zheng to the case of operators acting on Aλ2(Dn.

  14. Weighted composition operators between growth spaces on circular and strictly convex domain

    Directory of Open Access Journals (Sweden)

    Shayesteh Rezaei

    2015-06-01

    Full Text Available Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X$ is the space of all $finmathcal{H}(Omega_X$ for which $$|f(x|leqslant C omega(r_{Omega_X}(x,quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the Minkowski functional on $Omega_X$ and $omega :[0,1rightarrow(0,infty$ is a nondecreasing, continuous and unbounded function. Boundedness and compactness of weighted composition operators between growth spaces on circular and strictly convex domains were investigated.

  15. A Novel Transfer Learning Method Based on Common Space Mapping and Weighted Domain Matching

    KAUST Repository

    Liang, Ru-Ze

    2017-01-17

    In this paper, we propose a novel learning framework for the problem of domain transfer learning. We map the data of two domains to one single common space, and learn a classifier in this common space. Then we adapt the common classifier to the two domains by adding two adaptive functions to it respectively. In the common space, the target domain data points are weighted and matched to the target domain in term of distributions. The weighting terms of source domain data points and the target domain classification responses are also regularized by the local reconstruction coefficients. The novel transfer learning framework is evaluated over some benchmark cross-domain data sets, and it outperforms the existing state-of-the-art transfer learning methods.

  16. Elliptic Equations in Weighted Besov Spaces on Asymptotically Flat Riemannian Manifolds

    CERN Document Server

    Brauer, Uwe

    2012-01-01

    This paper deals with the applications of weighted Besov spaces to elliptic equations on asymptotically flat Riemannian manifolds, and in particular to the solutions of Einstein's constraints equations. We establish existence theorems for the Hamiltonian an momentum constraints with constant mean curvature and with a background metric which satisfies very low regularity assumptions. These results extend the regularity results of Holst, Nagy and Tsogtgerel about the constraint equations on compact manifolds in the Besov space $B_{p,p}^s$, to asymptotically flat manifolds. We also consider the Brill--Cantor criterion in the weighted Besov spaces. Our results improve the regularity assumptions on asymptotically flat manifolds Choquet--Bruhat, Isenberg and Pollack, and Maxwell, as well as they enable us to construct the initial data for the Einstein--Euler system.

  17. Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces

    Institute of Scientific and Technical Information of China (English)

    Hua Wang∗

    2015-01-01

    Let L=−∆+V be a Schrödinger operator acting on L2(Rn), n≥1, where V 6≡0 is a nonnegative locally integrable function on Rn.In this article, we will intro-duce weighted Hardy spaces HpL (w) associated with L by means of the square function and then study their atomic decomposition theory.We will also show that the Riesz transform ∇L−1/2 associated with L is bounded from our new space HpL (w) to the classical weighted Hardy space Hp(w) when n/(n+1)

  18. Weighted statistics for unevenly spaced SEM-grids on Linac4 line.

    CERN Document Server

    Granemann Souza, E; Lombardi, A; Comblin, J-F

    2013-01-01

    A beam profile may be measured in several ways [1]. Independent of the method chosen, the agreement between the simulation and measurements need to be accurate enough to minimize errors. In order to improve this comparison, we introduce new beam size estimators based in weighted statistics. We show that, for the situations in which the SEM-grid wires are unevenly spaced, the weighted standard deviation reveal us as an efficient alternative for determine the beam rms size. These theoretical predictions, implemented in the java application Linac4 SEM-grids 1.0, are than compared with measurements of the Linac4 line showing the pros and cons together with Gaussian fittings.

  19. Around a Sobolev-Orlicz inequality for operators of given spectral density

    CERN Document Server

    Rumin, Michel

    2009-01-01

    We prove some general Sobolev-Orlicz, Nash and Faber-Krahn inequalities for positive operators of given ultracontractive norms of the spectral projectors on ]0, lambda]. For invariant operators on coverings of finite simplicial complexes this "ultracontractive spectral decay" is equivalent to von-Neumann's spectral density function. This allows in the polynomial decay case to relate the Novikov-Shubin numbers of such coverings to Sobolev inequalities on exact $\\ell^2$-cochains, and to the vanishing of the torsion of the $\\ell^{p,2}$-cohomology for some $p \\geq 2$.

  20. Green Space and Child Weight Status: Does Outcome Measurement Matter? Evidence from an Australian Longitudinal Study

    Directory of Open Access Journals (Sweden)

    Taren Sanders

    2015-01-01

    Full Text Available Objective. To examine whether neighbourhood green space is beneficially associated with (i waist circumference (WC and (ii waist-to-height ratio (WtHR across childhood. Methods. Gender-stratified multilevel linear regressions were used to examine associations between green space and objective measures of weight status in the Longitudinal Study of Australian Children, a nationally representative source of data on 4,423 children aged 6 y to 13 y. WC and WtHR were measured objectively. Percentage green space within the local area of residence was calculated. Effect modification by age was explored, adjusting for socioeconomic confounding. Results. Compared to peers with 0–5% green space locally, boys and girls with >40% green space tended to have lower WC (βboys  −1.15, 95% CI −2.44, 0.14; βgirls  −0.21, 95% CI −1.47, 1.05 and WtHR (βboys  −0.82, 95% CI −1.65, 0.01; βgirls  −0.32, 95% CI −1.13, 0.49. Associations among boys were contingent upon age (p  valuesage∗green  space40% green space at 73.85 cm and 45.75% compared to those with 0–5% green space at 75.18 cm and 46.62%, respectively. Conclusions. Greener neighbourhoods appear beneficial to alternative child weight status measures, particularly among boys.

  1. Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions

    CERN Document Server

    Popov, A D; Popov, Alexander D.; Wolf, Martin

    2004-01-01

    It was recently shown by Witten on the basis of several examples that the topological B-model whose target space is a Calabi-Yau (CY) supermanifold is equivalent to holomorphic Chern-Simons (hCS) theory on the same supermanifold. Moreover, for the supertwistor space CP^{3|4} as target space, it has been demonstrated that hCS theory on CP^{3|4} is equivalent to self-dual N=4 super Yang-Mills (SYM) theory in four dimensions. We consider as target spaces for the B-model the weighted projective spaces WCP^{3|2}(1,1,1,1|p,q) with two fermionic coordinates of weight p and q, respectively - which are CY supermanifolds for p+q=4 - and discuss hCS theory on them. By using twistor techniques, we obtain certain field theories in four dimensions which are equivalent to hCS theory. These theories turn out to be self-dual truncations of N=4 SYM theory or of its twisted (topological) version.

  2. Fixed point theorems for generalized Lipschitzian semigroups in Banach spaces

    Directory of Open Access Journals (Sweden)

    Balwant Singh Thakur

    1999-01-01

    Full Text Available Fixed point theorems for generalized Lipschitzian semigroups are proved in p-uniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp, and in Sobolev spaces Hk,p, for 1

  3. Blow-up of Solution for the Nonlinear Sobolev-Galpern Equation%非线性Sobolev-Galpern型方程解的Blow-up性质

    Institute of Scientific and Technical Information of China (English)

    张恩彪; 江成顺

    2009-01-01

    In this paper,the initial boundary value problems of the nonlinear Sobolev Galpern equation are studied.The existence,uniqueness of local solution for the problem are obtained by means of a special Green's function and the contraction mapping principle.Finally,the blow-up of solution in finite time under some assumed conditions is proved with the aid of Jensen's inequality.

  4. BLOW-UP CRITERION OF SMOOTH SOLUTIONS TO THE MHD EQUATIONS IN BESOV SPACES

    Institute of Scientific and Technical Information of China (English)

    YUAN Baoquan

    2005-01-01

    In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces,and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.

  5. Fokker-Planck Type Equations with Sobolev Diffusion Coefficients and BV Drift Coefficients

    Institute of Scientific and Technical Information of China (English)

    De Jun LUO

    2013-01-01

    Combining Le Bris and Lions' arguments with Ambrosio's commutator estimate for BV vector fields,we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients.

  6. Energy minimization using Sobolev gradients application to phase separation and ordering

    CERN Document Server

    Sial, S; Lookman, T; Saxena, A

    2003-01-01

    A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg-Landau models commonly used in pattern formation and ordering processes.

  7. A Sobolev gradient algorithm for minimum energy states of s-wave superconductors - finite element setting

    Energy Technology Data Exchange (ETDEWEB)

    Sial, S. [Lahore Univ. of Management Sciences (Pakistan). Dept. of Mathematics

    2005-07-01

    The application of a Sobolev gradient method for finding vortices in s-wave superconductors via minimization of their Landau-Ginzburg energies is demonstrated in a finite element setting. It is seen that the method is highly efficient while at the same time retaining the simplicity of the steepest descent algorithm. (Author)

  8. GLOBAL SUPERCONVERGENCE ANALYSIS OF WILSON ELEMENT FOR SOBOLEV AND VISCOELASTICITY TYPE EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    JIN Dayong; LIU Tang; ZHANG Shuhua

    2004-01-01

    In this paper the Wilson nonconforming finite element is employed to solve Sobolev and viscoelasticity type equations. By means of post-processing technique, global superconvergence estimates are obtained for quasi-uniform rectangular meshes. Finally, an error correction scheme is presented.

  9. Average Widths of Sobolev-Wiener Classes with Mixed Smoothness in Lq(rd)

    Institute of Scientific and Technical Information of China (English)

    He Ping WANG

    2001-01-01

    In this paper, the average σ-K width of Sobolev-Wiener classes Srpq W with mixed smooth ness in Lq(Rd) is studied for 1 < q ≤ p <∞ and the weak asymptotical behavior of these quantities is obtained.

  10. On conditions for invertibility of difference and differential operators in weight spaces

    Energy Technology Data Exchange (ETDEWEB)

    Bichegkuev, Mairbek S [North-Ossetia State University, Vladikavkaz (Russian Federation)

    2011-08-31

    We obtain necessary and sufficient conditions for the invertibility of the difference operator D{sub E}:D(D{sub E}) subset of l{sup p}{sub {alpha}}{yields}l{sup p}{sub {alpha}}, (D{sub E} x)(n)=x(n+1)-Bx(n), n element of Z{sub +}, whose domain D(D{sub E}) is given by the condition x(0) element of E, where l{sup p}{sub {alpha}}=l{sup p}{sub {alpha}}(Z{sub +},X), p element of [1,{infinity}], is the Banach space of sequences (of vectors in a Banach space X) summable with weight {alpha}:Z{sub +}{yields}(0,{infinity}) for p element of [1,{infinity}) and bounded with respect to {alpha} for p={infinity}, B:X{yields}X is a bounded linear operator, and E is a closed B-invariant subspace of X. We give applications to the invertibility of differential operators with an unbounded operator coefficient (the generator of a strongly continuous operator semigroup) in weight spaces of functions.

  11. Absorption and scattering 2-D volcano images from numerically calculated space-weighting functions

    Science.gov (United States)

    Del Pezzo, Edoardo; Ibañez, Jesus; Prudencio, Janire; Bianco, Francesca; De Siena, Luca

    2016-08-01

    Short-period small magnitude seismograms mainly comprise scattered waves in the form of coda waves (the tail part of the seismogram, starting after S waves and ending when the noise prevails), spanning more than 70 per cent of the whole seismogram duration. Corresponding coda envelopes provide important information about the earth inhomogeneity, which can be stochastically modeled in terms of distribution of scatterers in a random medium. In suitable experimental conditions (i.e. high earth heterogeneity), either the two parameters describing heterogeneity (scattering coefficient), intrinsic energy dissipation (coefficient of intrinsic attenuation) or a combination of them (extinction length and seismic albedo) can be used to image Earth structures. Once a set of such parameter couples has been measured in a given area and for a number of sources and receivers, imaging their space distribution with standard methods is straightforward. However, as for finite-frequency and full-waveform tomography, the essential problem for a correct imaging is the determination of the weighting function describing the spatial sensitivity of observable data to scattering and absorption anomalies. Due to the nature of coda waves, the measured parameter couple can be seen as a weighted space average of the real parameters characterizing the rock volumes illuminated by the scattered waves. This paper uses the Monte Carlo numerical solution of the Energy Transport Equation to find approximate but realistic 2-D space-weighting functions for coda waves. Separate images for scattering and absorption based on these sensitivity functions are then compared with those obtained with commonly used sensitivity functions in an application to data from an active seismic experiment carried out at Deception Island (Antarctica). Results show that these novel functions are based on a reliable and physically grounded method to image magnitude and shape of scattering and absorption anomalies. Their

  12. On the Multilinear Singular Integrals and Commutators in the Weighted Amalgam Spaces

    Directory of Open Access Journals (Sweden)

    Feng Liu

    2014-01-01

    Full Text Available This paper is concerned with the norm estimates for the multilinear singular integral operators and their commutators formed by BMO functions on the weighted amalgam spaces Lvw→q,Lpαℝn. Some criterions of boundedness for such operators in Lvw→q,Lpαℝn are given. As applications, the norm inequalities for the multilinear Calderón-Zygmund operators and multilinear singular integrals with nonsmooth kernels as well as the corresponding commutators on Lvw→q,Lpαℝn are obtained.

  13. Computation of Yukawa couplings for Calabi-Yau hypersurfaces in weighted projective spaces

    CERN Document Server

    Kanter, Yu

    1994-01-01

    Greene, Morrison and Plesser \\cite{GMP} have recently suggested a general method for constructing a mirror map between a d-dimensional Calabi-Yau hypersurface and its mirror partner for d > 3. We apply their method to smooth hypersurfaces in weighted projective spaces and compute the Chern numbers of holomorphic curves on these hypersurfaces. As anticipated, the results satisfy nontrivial integrality constraints. These examples differ from those studied previously in that standard methods of algebraic geometry which work in the ordinary projective space case for low degree curves are not generally applicable. In the limited special cases in which they do work we can get independent predictions, and we find agreement with our results.

  14. Quasi-uniformity of Minimal Weighted Energy Points on Compact Metric Spaces

    CERN Document Server

    Hardin, D P; Whitehouse, J T

    2011-01-01

    For a closed subset $K$ of a compact metric space $A$ possessing an $\\alpha$-regular measure $\\mu$ with $\\mu(K)>0$, we prove that whenever $s>\\alpha$, any sequence of weighted minimal Riesz $s$-energy configurations $\\omega_N=\\{x_{i,N}^{(s)}\\}_{i=1}^N$ on $K$ (for `nice' weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as $N$ grows large. Furthermore, if $K$ is an $\\alpha$-rectifiable compact subset of Euclidean space with positive and finite $\\alpha$-dimensional Hausdorff measure, it is possible to generate such a quasi-uniform sequence of configurations that also has (as $N\\to \\infty$) a prescribed positive continuous limit distribution with respect to $\\alpha$-dimensional Hausdorff measure. As a consequence of our energy related results for the unweighted case, we deduce that if $A$ is a compact $C^1$ manifold, then there exists a sequence of $N$-point best-packing configurations on $A$ whose mesh-separation ratios have limit superior (as $N\\to \\...

  15. Second order elastic metrics on the shape space of curves

    DEFF Research Database (Denmark)

    Bauer, Martin; Bruveris, Martins; Harms, Philipp

    2015-01-01

    problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover......Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value......, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects....

  16. Vector Cascade Algorithms with Infinitely Supported Masks in Weighted L2-Spaces

    Institute of Scientific and Technical Information of China (English)

    Jian Bin YANG

    2013-01-01

    In this paper,we shall study the solutions of functional equations of the form φ =Σ a(α) φ(M.-α),α∈Zswhere φ =(Φ1,...,Φr)T is an r × 1 column vector of functions on the s-dimensional Euclidean space,a:=(a(α))α∈zs is an exponentially decaying sequence of r × r complex matrices called refinement mask and M is an s × s integer matrix such that limn→∞ M-n =0.We are interested in the question,for a mask a with exponential decay,if there exists a solution Φ to the functional equation with each function Φj,j =1,...,r,belonging to L2(IRs) and having exponential decay in some sense? Our approach will be to consider the convergence of vector cascade algorithms in weighted L2 spaces.The vector cascade operator Qa,M associated with mask a and matrix M is defined by Qa,Mf:=Σ a(α)f(M.-α),f =(f1,...,fr)T ∈ (L2,μ(IRs))r.αα∈ZsThe iterative scheme (Qna,Mf)n=1,2 is called a vector cascade algorithm or a vector subdivision scheme.The purpose of this paper is to provide some conditions for the vector cascade algorithm to converge in (L2,μ(IRs))r,the weighted L2 space.Inspired by some ideas in [Jia,R.Q.,Li,S.:Refinable functions with exponential decay:An approach via cascade algorithms.J.Fourier Anal.Appl.,17,1008-1034 (2011)],we prove that if the vector cascade algorithm associated with a and M converges in (L2(IRs))r,then its limit function belongs to (L2,μ(IRs))r for some μ > 0.

  17. Right-invariant Sobolev metrics ${H}^{s}$ on the diffeomorphisms group of the circle

    CERN Document Server

    Escher, Joachim

    2012-01-01

    We study the geodesic flow on the diffeomorphisms group of the circle with respect to the right-invariant metric induced by the fractional Sobolev norm $H^s$ for $s\\ge1/2$. We show that the corresponding initial value problem possesses a maximal solution in the smooth category and that the Riemannian exponential mapping is a smooth diffeomorphism from a neighbourhood of 0 in $C^{\\infty}(S)$ onto a neighbourhood of the identity in $Diff^{\\infty}(S)$.

  18. AN ANISOTROPIC NONCONFORMING FINITE ELEMENT METHOD FOR APPROXIMATING A CLASS OF NONLINEAR SOBOLEV EQUATIONS

    Institute of Scientific and Technical Information of China (English)

    Dongyang Shi; Haihong Wang; Yuepeng Du

    2009-01-01

    An anisotropic nonconforming finite element method is presented for a class of nonlinear Sobolev equations. The optimal error estimates and supercloseness are obtained for both semi-discrete and fully-discrete approximate schemes, which are the same as the traditional finite element methods. In addition, the global superconvergence is derived through the postprocessing technique. Numerical experiments are included to illustrate the feasibility of the proposed method.

  19. EXISTENCE AND MULTIPLICITY RESULTS FOR ELLIPTIC EQUATIONS WITH CRITICAL SOBOLEV EXPONENT AND HARDY TERM

    Institute of Scientific and Technical Information of China (English)

    Shang Yanying; Tang Chunlei

    2007-01-01

    This paper concerns the existence and multiplicity of solutions for some semilinear elliptic equations with critical Sobolev exponent,Hardy term and the sublinear nonlinearity at origin.By using Ekeland's variational principle,we conclude the existence of nontrivial solution for this problem,the Clark's critical point theorem is used to prove the existence of infinitely many solutions for this problem with odd nonlinearity.

  20. SOLUTION OF A CLASS OF NONHOMOGENEOUS ELLIPTIC SYSTEM INVOLVING CRITICAL SOBOLEV EXPONENT

    Institute of Scientific and Technical Information of China (English)

    ZhangGuoqing; LiuSanyang

    2005-01-01

    In this paper, we discuss the problem of solving a class of nonhomogeneous semilinear elliptic system with critical Sobolev exponent changing into one of critical points of some given functional. Using Nehari technique, the given functional attain its minimum by adding suitable constraints, and the minimal point becomes a critical point of the original functional after eliminating the added constraints, thus the solution of the nonhomogeneous elliptic system is obtained.

  1. Convergence of Symmetric Diffusions on Wiener Spaces

    Institute of Scientific and Technical Information of China (English)

    A.Posilicano; T.S.Zhang

    2004-01-01

    In this paper,we study the distorted Ornstein-Uhlenbeck processes associated with given densities on an abstract Wiener space.We prove that the laws of distorted Ornstein-Uhlenbeck processes converge in total variation norm if the densities converge in Sobolev space D 1/2.

  2. Development of a fluid bed granulation design space using critical quality attribute weighted tolerance intervals.

    Science.gov (United States)

    Zacour, Brian M; Drennen, James K; Anderson, Carl A

    2012-08-01

    The fluid bed granulation and drying unit operation were used as a case study for control systems implementation. This single processor was used to blend, granulate, dry, and cool the materials. The current study demonstrated control of each of the phases using a fully automated, hybrid control system that incorporated first-principle modeling, empirical design of experiments (DOE), and process analytical technology to assure the production of constant product quality. The system allowed data to be collected efficiently for the development of a rigorous design space that combined formulation factors, process factors, and their interactions to define a tolerance surface where risk of future product failure was significantly reduced. The DOE incorporated microcrystalline cellulose and lactose monohydrate, excipients with substantially different wetting properties, to elucidate the relationship between the critical process parameters of the unit operation and the material properties of the formulation components. The extended analysis of covariance model enabled these factors and their interaction terms to be described in a single model. The results indicate that the development of a tolerance interval-based weighted design space can enhance product understanding and thereby help to assure future product quality.

  3. Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups

    Directory of Open Access Journals (Sweden)

    Han Yazhou

    2010-01-01

    Full Text Available We prove a sharp weighted Rellich inequality associated with a class of Greiner-type vector fields on H-type groups. We also obtain some weighted Hardy- and Rellich-type inequalities on nonisotropic Heisenberg groups. As an application, we get a Rellich-Sobolev-type inequality on Heisenberg groups.

  4. About One Approach to Determine the Weights of the State Space Method

    Directory of Open Access Journals (Sweden)

    I. K. Romanova

    2015-01-01

    Full Text Available The article studies methods of determining weight coefficients, also called coefficients of criteria importance in multiobjective optimization (MOO. It is assumed that these coefficients indicate a degree of individual criteria influence on the final selection (final or summary assessment: the more is coefficient, the greater is contribution of its corresponding criterion.Today in the framework of modern information systems to support decision making for various purposes a number of methods for determining relative importance of criteria has been developed. Among those methods we can distinguish a utility method, method of weighted power average; weighted median; method of matching clustered rankings, method of paired comparison of importance, etc.However, it should be noted that different techniques available for calculating weights does not eliminate the main problem of multicriteria optimization namely, the inconsistency of individual criteria. The basis for solving multicriteria problems is a fundamental principle of multi-criteria selection i.e. Edgeworth - Pareto principle.Despite a large number of methods to determine the weights, the task remains relevant not only for reasons of evaluations subjectivity, but also because of the mathematical aspects. Today, recognized is the fact that, for example, such a popular method as linear convolution of private criteria, essentially, represents one of the heuristic approaches and, applying it, you can have got not the best final choice. Carlin lemma reflects the limits of the method application.The aim of this work is to offer one of the methods to calculate the weights applied to the problem of dynamic system optimization, the quality of which is determined by the criterion of a special type, namely integral quadratic quality criterion. The main challenge relates to the method of state space, which in the literature also is called the method of analytical design of optimal controllers.Despite the

  5. ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

    Institute of Scientific and Technical Information of China (English)

    曾六川

    2003-01-01

    The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in Lp spaces, in Hardy spaces Hp , and in Sobolev spaces Hr,p, for 1 < p < + ∞ and r ≥ 0.

  6. Error Estimates for Mixed Finite Element Methods for Sobolev Equation%Sobolev方程混合有限元方法的误差估计

    Institute of Scientific and Technical Information of China (English)

    姜子文; 陈焕祯

    2001-01-01

    The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation based on the Raviart-Thomas space Vh × Wh H(div; Ω) × L2(Ω). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L∞(0, T; L2(Ω)), L∞(0, T; L2(Ω)), L∞(0, T; L2(Ω)2), and L∞ (0, T; L2 (Ω)). Quasi-optimal order estimates are obtained for the approximations of u, ut in L∞(0,T;L∞(Ω)) and p in L∞(0,T;L∞(Ω)2).

  7. Regularity of the inverse of a planar Sobolev homeomorphism

    Science.gov (United States)

    Hencl, Stanislav; Koskela, Pekka; Onninen, Jani

    2007-12-01

    We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that f -1 is of bounded variation provided that f γ W 1,1(Ω; R n ) is a homeomorphism with | Df| in the Lorentz space L n-1,1(Ω).

  8. Ulexite-galena intermediate-weight concrete as a novel design for overcoming space and weight limitations in the construction of efficient shields against neutrons and photons.

    Science.gov (United States)

    Aghamiri, S M R; Mortazavi, S M J; Razi, Z; Mosleh-Shirazi, M A; Baradaran-Ghahfarokhi, M; Rahmani, F; Faeghi, F

    2013-01-01

    Recently, due to space and weight limitations, scientists have tried to design and produce concrete shields with increased attenuation of radiation but not increased mass density. Over the past years, the authors' had focused on the production of heavy concrete for radiation shielding, but this is the first experience of producing intermediate-weight concrete. In this study, ulexite (hydrated sodium calcium borate hydroxide) and galena (lead ore) have been used for the production of a special intermediate-weight concrete. Shielding properties of this intermediate-weight concrete against photons have been investigated by exposing the samples to narrow and broad beams of gamma rays emitted from a ⁶⁰Co radiotherapy unit. Densities of the intermediate-weight concrete samples ranged 3.64-3.90 g cm⁻³, based on the proportion of the ulexite in the mix design. The narrow-beam half-value layer (HVL) of the ulexite-galena concrete samples for 1.25 MeV ⁶⁰Co gamma rays was 2.84 cm, much less than that of ordinary concrete (6.0 cm). The Monte Carlo (MC) code MCNP4C was also used to model the attenuation of ⁶⁰Co gamma-ray photons and Am-Be neutrons of the ulexite-galena concrete with different thicknesses. The ⁶⁰Co HVL calculated by MCNP simulation was 2.87 cm, indicating a good agreement between experimental measurements and MC simulation. Furthermore, MC-calculated results showed that thick ulexite-galena concrete shields (60-cm thickness) had a 7.22 times (722 %) greater neutron attenuation compared with ordinary concrete. The intermediate-weight ulexite-galena concrete manufactured in this study may have many important applications in the construction of radiation shields with weight limitations such as the swing or sliding doors that are currently used for radiotherapy treatment rooms.

  9. Associations among q-space MRI, diffusion-weighted MRI and histopathological parameters in meningiomas

    Energy Technology Data Exchange (ETDEWEB)

    Fatima, Zareen; Motosugi, Utaroh; Ishigame, Keiichi; Araki, Tsutomu [University of Yamanashi, Department of Radiology, Chuo-shi, Yamanashi (Japan); Waqar, Ahmed Bilal [University of Yamanashi, Department of Molecular Pathology, Interdisciplinary Graduate School of Medicine and Engineering, Chuo-shi, Yamanashi (Japan); Hori, Masaaki [Juntendo University, Department of Radiology, School of Medicine, Tokyo (Japan); Oishi, Naoki; Katoh, Ryohei [University of Yamanashi, Department of Pathology, Chuo-shi, Yamanashi (Japan); Onodera, Toshiyuki; Yagi, Kazuo [Tokyo Metropolitan University, Department of Radiological Sciences, Graduate School of Human Health Sciences, Tokyo (Japan)

    2013-08-15

    The purposes of this MR-based study were to calculate q-space imaging (QSI)-derived mean displacement (MDP) in meningiomas, to evaluate the correlation of MDP values with apparent diffusion coefficient (ADC) and to investigate the relationships among these diffusion parameters, tumour cell count (TCC) and MIB-1 labelling index (LI). MRI, including QSI and conventional diffusion-weighted imaging (DWI), was performed in 44 meningioma patients (52 lesions). ADC and MDP maps were acquired from post-processing of the data. Quantitative analyses of these maps were performed by applying regions of interest. Pearson correlation coefficients were calculated for ADC and MDP in all lesions and for ADC and TCC, MDP and TCC, ADC and MIB-1 LI, and MDP and MIB-1 LI in 17 patients who underwent subsequent surgery. ADC and MDP values were found to have a strong correlation: r = 0.78 (P = <0.0001). Both ADC and MDP values had a significant negative association with TCC: r = -0.53 (p = 0.02) and -0.48 (P = 0.04), respectively. MIB-1 LI was not, however, found to have a significant association with these diffusion parameters. In meningiomas, both ADC and MDP may be representative of cell density. (orig.)

  10. Study of weighted space deconvolution algorithm in computer controlled optical surfacing formation

    Institute of Scientific and Technical Information of China (English)

    Hongyu Li; Wei Zhang; Guoyu Yu

    2009-01-01

    Theoretical and experimental research on the deconvolution algorithm of dwell time in the technology of computer controlled optical surfacing (CCOS) formation is made to get an ultra-smooth surface of space optical element. Based on the Preston equation, the convolution model of CCOS is deduced. Considering the morbidity problem of deconvolution algorithm and the actual situation of CCOS technology, the weighting spatial deconvolution algorithm is presented based on the non-periodic matrix model, which avoids solving morbidity resulting from the noise induced by measurement error. The discrete convolution equation is solved using conjugate gradient iterative method and the workload of iterative calculation in spatial domain is reduced effectively. Considering the edge effect of convolution algorithm, the method adopts a marginal factor to control the edge precision and attains a good effect. The simulated processing test shows that the convergence ratio of processed surface shape error reaches 80%. This algorithm is further verified through an experiment on a numerical control bonnet polishing machine, and an ultra-smooth glass surface with the root-mean-square (RMS) error of 0.0088 μm is achieved. The simulation and experimental results indicate that this algorithm is steady, convergent, and precise, and it can satisfy the solving requirement of actual dwell time.

  11. Existence, uniqueness, and stability of stochastic neutral functional differential equations of Sobolev-type

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Xuetao; Zhu, Quanxin, E-mail: zqx22@126.com [School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, Jiangsu (China)

    2015-12-15

    In this paper, we are mainly concerned with a class of stochastic neutral functional differential equations of Sobolev-type with Poisson jumps. Under two different sets of conditions, we establish the existence of the mild solution by applying the Leray-Schauder alternative theory and the Sadakovskii’s fixed point theorem, respectively. Furthermore, we use the Bihari’s inequality to prove the Osgood type uniqueness. Also, the mean square exponential stability is investigated by applying the Gronwall inequality. Finally, two examples are given to illustrate the theory results.

  12. Sobolev, Poincare and isoperimetric inequalities for subelliptic diffusion operators satisfying a generalized curvature dimension inequality

    CERN Document Server

    Baudoin, Fabrice

    2012-01-01

    By adapting some ideas of M. Ledoux \\cite{ledoux2}, \\cite{ledoux-stflour} and \\cite{Led} to a sub-Riemannian framework we study Sobolev, Poincar\\'e and isoperimetric inequalities associated to subelliptic diffusion operators that satisfy the generalized curvature dimension inequality that was introduced by F. Baudoin and N. Garofalo in \\cite{Bau2}. Our results apply in particular on all CR Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature is non negative, all Carnot groups with step two, and wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is non negative.

  13. Modelling CH$_3$OH masers: Sobolev approximation and accelerated lambda iteration method

    CERN Document Server

    Nesterenok, Aleksandr

    2015-01-01

    A simple one-dimensional model of CH$_3$OH maser is considered. Two techniques are used for the calculation of molecule level populations: the accelerated lambda iteration (ALI) method and the large velocity gradient (LVG), or Sobolev, approximation. The LVG approximation gives accurate results provided that the characteristic dimensions of the medium are larger than 5-10 lengths of the resonance region. We presume that this condition can be satisfied only for the largest observed maser spot distributions. Factors controlling the pumping of class I and class II methanol masers are considered.

  14. The Average Widths of Sobolev-Wiener Classes and Besov-Wiener Classes

    Institute of Scientific and Technical Information of China (English)

    Gui Qiao XU; Yong Ping LIU

    2004-01-01

    This paper concerns the problem of average σ-width of Sobolev Wiener classes Wrpq(Rd),Wrpq(M, Rd), and Besov-Wiener classes Srpqθb(Rd), SrpqθB( Rd), Srpqθb(M, Rd), SrpqθB( Rd) in the metric Lq(Rd) for 1 ≤ q ≤ p ≤∞. The weak asymptotic results concerning the average linear widths, the average Bernstein widths and the infinite-dimensional Gel'fand widths are obtained, respectively.

  15. Boundedness for multilinear fractional integral operators on Herz type spaces

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    In this paper the boundedness for the multilinear fractional integral operator I(m)a on the product of Herz spaces and Herz-Morrey spaces are founded,which improves the Hardy-Littlewood-Sobolev inequality for classical fractional integral Ia.The method given in the note is useful for more general multilinear integral operators.

  16. Effects of Variety and Spacing on Percentage (% Emergence and Grain Weight of Maize in Asaba Area of Delta State

    Directory of Open Access Journals (Sweden)

    Enujeke E. C.

    2013-07-01

    Full Text Available This study was carried out in the Teaching and Research Farm of Delta State University, Asaba Campus from March 2008 to December 2009 to evaluate the response of maize varieties to three different plant spacings. It was a factorial experiment carried out in a Randomized Complete Block Design (RCBD replicated three times. Ten maize varieties were evaluated under three different plant spacings for their percentage emergence and grain weight. The results of percentage emergence showed that open-pollinated variety BR9922-DMRSF2 which had 93.2% in 2008 and 93.8% in 2009 had highest percentage emergence. The results obtained from the grain weights indicated that hybrid variety 9022-13 that was sown at 75cm x 15cm which yielded 6.3 tha-1 in 2008 and 6.4 tha-1 in 2009 was superior, followed by open-pollinated variety BR9922-DMRSF2 which yielded 4.7tha-1 in 2008 and 4.9tha-1 in 2009. The effects of interaction showed that variety and space were significantly (p<0.05 different and positively affected maize grain weight. Based on the study, it is recommended that (i Hybrid maize variety 9022-13 which was outstanding in grain weight be grown in the study area. Alternatively, farmers who prefer open-pollinated varieties could grow BR9922-DMRSF2. (ii Spacing of 75cm x 15cm which resulted in better percentage emergence and highest grain weight be adopted in maize production.

  17. Preliminary studies on growth and fresh weight of lettuce (Lactuca sativa) as affected by clay pot irrigation and spacing.

    Science.gov (United States)

    Abubakari, Abdul-Halim; Nyarko, George; Maalinyuur, Sheila

    2011-07-15

    An experiment (Completely Randomized Design) was set up to determine the effects of Clay Pot Sub-surface Irrigation (CPSI) and spacing on the growth and fresh weight of lettuce (Lactuca sativa). The treatments were: CPSI with spacing; 15 x 15 cm, 20 x 20 cm and 30 x 30 cm. Control treatments were Watering Can Irrigation (WCI) with the same spacing as above. Treatments were replicated three times given a total of 18 experimental units. Eighteen large enamel basins of 50/20 cm (diameter/height) were filled with good topsoil and a clay pot buried neck deep in each of the basins. Seedlings were planted in all the eighteen basins. Five Hundred mL of wastewater was applied daily to plants in each container having either clay pot or watering can treatment. Plant height increased from 2.50 to 4.25 cm within 6 Weeks after Transplanting (WAT) under CPSI and only increased from 2.14 to 2.99 cm under WCI. The CPSI also supported better leave growth and fresh weight. The fresh weight of lettuce increased almost two fold under 15 x 15 cm spacing compared to 20 x 20 and 30 x 30 cm.

  18. Looijenga's weighted projective space, Tate's algorithm and Mordell-Weil Lattice in F-theory and heterotic string theory

    CERN Document Server

    Mizoguchi, Shun'ya

    2016-01-01

    It is now well known that the moduli space of a vector bundle for heterotic string compactifications to four dimensions is parameterized by a set of sections of a weighted projective space bundle of a particular kind, known as Looijenga's weighted projective space bundle. We show that the requisite weighted projective spaces and the Weierstrass equations describing the spectral covers for gauge groups E_N (N=4,...,8) and SU(n+1) (n=1,2,3) can be obtained systematically by a series of blowing-up procedures according to Tate's algorithm, thereby the sections of correct line bundles claimed to arise by Looijenga's theorem can be automatically obtained. They are nothing but the four-dimensional analogue of the set of independent polynomials in the six-dimensional F-theory parameterizing the complex structure, which is further confirmed in the constructions of D_4, A_5, D_6 and E_3 bundles. We also explain why we can obtain them in this way by using the structure theorem of the Mordell-Weil lattice, which is also ...

  19. Optimal weights for measuring redshift space distortions in multitracer galaxy catalogues

    Science.gov (United States)

    Pearson, David W.; Samushia, Lado; Gagrani, Praful

    2016-12-01

    Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of emission line galaxies and luminous red galaxies from the Dark Energy Spectroscopic Instrument survey, the variance in the measured growth rate parameter can be reduced by as much as 36 per cent.

  20. Optimal Weights For Measuring Redshift Space Distortions in Multi-tracer Galaxy Catalogues

    CERN Document Server

    Pearson, David W; Gagrani, Praful

    2016-01-01

    Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from the Dark Energy ...

  1. Travelling Wave Solutions to the Benney-Luke and the Higher-Order Improved Boussinesq Equations of Sobolev Type

    Directory of Open Access Journals (Sweden)

    Ömer Faruk Gözükızıl

    2012-01-01

    Full Text Available By using the tanh-coth method, we obtained some travelling wave solutions of two well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation and the higher-order improved Boussinesq equation. We show that the tanh-coth method is a useful, reliable, and concise method to solve these types of equations.

  2. A Sobolev gradient algorithm for minimum energy states of s-wave superconductors-finite element setting

    Energy Technology Data Exchange (ETDEWEB)

    Sial, S [Department of Mathematics, Lahore University of Management Sciences, Opposite Sector U, DHA, Lahore Cantt. 54792 (Pakistan)

    2005-05-01

    The application of a Sobolev gradient method for finding vortices in s-wave superconductors via minimization of their Landau-Ginzburg energies is demonstrated in a finite element setting. It is seen that the method is highly efficient while at the same time retaining the simplicity of the steepest descent algorithm.

  3. Talagrand's T2-Transportation Inequality and Log-Sobolev Inequality for Dissipative SPDEs and Applications to Reaction-Diffusion Equations

    Institute of Scientific and Technical Information of China (English)

    Liming WU; Zhengliang ZHANG

    2006-01-01

    We establish Talagrand's T2-transportation inequalities for infinite dimensional dissipative diffusions with sharp constants, through Galerkin type's approximations and the known results in the finite dimensional case. Furthermore in the additive noise case we prove also logarithmic Sobolev inequalities with sharp constants. Applications to ReactionDiffusion equations are provided.

  4. Function spaces on local fields

    Institute of Scientific and Technical Information of China (English)

    SU; Weiyi; XU; Qiang

    2006-01-01

    We study the function spaces on local fields in this paper, such as Triebel Btype and F-type spaces, Holder type spaces, Sobolev type spaces, and so on, moreover,study the relationship between the p-type derivatives and the Holder type spaces. Our obtained results show that there exists quite difference between the functions defined on Euclidean spaces and local fields, respectively. Furthermore, many properties of functions defined on local fields motivate the new idea of solving some important topics on fractal analysis.

  5. Local Existence for the Non-Resistive MHD Equations in Nearly Optimal Sobolev Spaces

    Science.gov (United States)

    Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L.

    2017-02-01

    This paper establishes the local-in-time existence and uniqueness of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in {R^d}, where d = 2, 3, with initial data {B_0in H^s(R^d)} and {u_0in H^{s-1+ɛ}(R^d)} for {s > d/2} and any {0 < ɛ < 1}. The proof relies on maximal regularity estimates for the Stokes equation. The obstruction to taking {ɛ=0} is explained by the failure of solutions of the heat equation with initial data {u_0in H^{s-1}} to satisfy {uin L^1(0,T; H^{s+1})}; we provide an explicit example of this phenomenon.

  6. Global solutions for the generalized Boussinesq equation in low-order Sobolev spaces

    CERN Document Server

    Farah, Luiz Gustavo

    2010-01-01

    We show that the Cauchy problem for the defocusing generalized Boussinesq equation $u_{tt}-u_{xx}+u_{xxxx}-(|u|^{2k}u)_{xx}=0$, $k\\geq1$, on the real line is globally well-posed in $H^{s}(\\R)$ for $s>1-({1}/{3k})$. We use the "$I$-method" to define a modification of the energy functional that is "almost conserved" in time. Our result extends the previous one obtained by Farah and Linares (2010 \\textit{J. London Math. Soc.} \\textbf{81} 241-254) when $k=1$.

  7. Variational and topological methods for operator equations involving duality mappings on Orlicz-Sobolev spaces

    Directory of Open Access Journals (Sweden)

    Pavel Matei

    2007-06-01

    Full Text Available Let $a:mathbb{R}o mathbb{R}$ be a strictly increasing odd continuous function with $lim_{to +infty }a(t=+infty $ and $A(t=int_{0}^{t}a(s,ds$, $tin mathbb{R}$, the $N$-function generated by $a$. Let $Omega $ be a bounded open subset of $mathbb{R}^{N}$, $Ngeq 2$, $T[u,u]$ a nonnegative quadratic form involving the only generalized derivatives of order $m$ of the function $uin W_{0}^{m}E_{A}(Omega $ and $g_{alpha }:Omegaimesmathbb{R}omathbb{R}$, $| alpha |

  8. The influence of the free space environment on the superlight-weight thermal protection system: conception, methods, and risk analysis

    Science.gov (United States)

    Yatsenko, Vitaliy; Falchenko, Iurii; Fedorchuk, Viktor; Petrushynets, Lidiia

    2016-07-01

    This report focuses on the results of the EU project "Superlight-weight thermal protection system for space application (LIGHT-TPS)". The bottom line is an analysis of influence of the free space environment on the superlight-weight thermal protection system (TPS). This report focuses on new methods that based on the following models: synergetic, physical, and computational. This report concentrates on four approaches. The first concerns the synergetic approach. The synergetic approach to the solution of problems of self-controlled synthesis of structures and creation of self-organizing technologies is considered in connection with the super-problem of creation of materials with new functional properties. Synergetics methods and mathematical design are considered according to actual problems of material science. The second approach describes how the optimization methods can be used to determine material microstructures with optimized or targeted properties. This technique enables one to find unexpected microstructures with exotic behavior (e.g., negative thermal expansion coefficients). The third approach concerns the dynamic probabilistic risk analysis of TPS l elements with complex characterizations for damages using a physical model of TPS system and a predictable level of ionizing radiation and space weather. Focusing is given mainly on the TPS model, mathematical models for dynamic probabilistic risk assessment and software for the modeling and prediction of the influence of the free space environment. The probabilistic risk assessment method for TPS is presented considering some deterministic and stochastic factors. The last approach concerns results of experimental research of the temperature distribution on the surface of the honeycomb sandwich panel size 150 x 150 x 20 mm at the diffusion welding in vacuum are considered. An equipment, which provides alignment of temperature fields in a product for the formation of equal strength of welded joints is

  9. Nonexistence of Weyl-Heisenberg Frame on Sobolev Space Hs(Rd)%Sobolev 空间Hs(Rd)上的Weyl-Heisenberg框架的不存在性

    Institute of Scientific and Technical Information of China (English)

    李锐; 郝祥晖; 李登峰

    2002-01-01

    研究在窗函数的Fourier变换具有紧支集条件下,Sobolev空间Hs(Rd)上不存在Weyl-Heisenberg框架.这个结果表明:对Sobolev空间Hs(Rd)上的Weyl-Heisenberg框架的研究意义不大.

  10. Aluminum-Lithium Alloy 2050 for Reduced-Weight, Increased-Stiffness Space Structures Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Touchstone Research Laboratory, along with Alcan Rolled Products ? Ravenswood WV, has identified the Aluminum-Lithium Alloy 2050 as a potentially game-changing...

  11. Light-Weight Self-Correcting Inflatable/Rigidizable Space Antennas Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The NASA/L'Garde Inflatable Antenna Experiment (IAE)flown in STS-77 has showed the potential of this class of structures in significantly reducing the costs for...

  12. A Compact, Light-weight, Reliable and Highly Efficient Heat Pump for Space Applications Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Extra-vehicular activities (EVA) on the Moon and Mars will require suits with sophisticated thermal control systems allowing astronauts to work for extended periods...

  13. Fock space resolutions of the Virasoro highest weight modules with c<=1

    CERN Document Server

    Bouwknegt, P; Pilch, K; Bouwknegt, Peter; Carthy, Jim Mc; Pilch, Krzysztof

    1991-01-01

    We extend Felder's construction of Fock space resolutions for the Virasoro minimal models to all irreducible modules with $c\\leq 1$. In particular, we provide resolutions for the representations corresponding to the boundary and exterior of the Kac table.

  14. Extremal functions in Poincare-Sobolev inequalities for functions of bounded variation

    CERN Document Server

    Bouchez, Vincent

    2010-01-01

    If $\\Omega \\subset \\R^n$ is a smooth bounded domain and $q \\in (0, \\frac{n}{n-1})$ we consider the Poincare-Sobolev inequality \\[ c \\Bigl(\\int_{\\Omega} \\abs{u}^\\frac{n}{n-1}\\Bigr)^{1-\\frac{1}{n}} \\le \\int_{\\Omega} \\abs{Du}, \\] for every $u \\in \\mathrm{BV}(\\Omega)$ such that $\\int_{\\Omega} \\abs{u}^{q-1} u = 0$. We show that the sharp constant is achieved. We also consider the same inequality on an $n$--dimensional compact Riemannian manifold $M$. When $n \\ge 3$ and the scalar curvature is positive at some point, then the sharp constant is achieved. In the case $n \\ge 2$, we need the maximal scalar curvature to satisfy some strict inequality.

  15. Energy balance and the composition of weight loss during prolonged space flight

    Science.gov (United States)

    Leonard, J. I.

    1982-01-01

    Integrated metabolic balance analysis, Skylab integrated metabolic balance analysis and computer simulation of fluid-electrolyte responses to zero-g, overall mission weight and tissue losses, energy balance, diet and exercise, continuous changes, electrolyte losses, caloric and exercise requirements, and body composition are discussed.

  16. Weighted asymptotic behavior of solutions to semilinear integro-differential equations in Banach spaces

    Directory of Open Access Journals (Sweden)

    Yan-Tao Bian

    2014-04-01

    Full Text Available In this article, we study weighted asymptotic behavior of solutions to the semilinear integro-differential equation $$ u'(t=Au(t+\\alpha\\int_{-\\infty}^{t}e^{-\\beta(t-s}Au(sds+f(t,u(t, \\quad t\\in \\mathbb{R}, $$ where $\\alpha, \\beta \\in \\mathbb{R}$, with $\\beta > 0, \\alpha \

  17. Weighted Robust Adaptive Filtering in Krein Space and Its Application in Active Noise Control

    NARCIS (Netherlands)

    Jayawardhana, Bayu; Yuan, Shuqing; Xie, Lihua

    2002-01-01

    Robust adaptive filtering ensures the minimization of the transfer function from the disturbance to the estimation error and thus, guarantees the robustness against the worst-case disturbance in the system. However, a more general approach will be given in this paper hy employing frequency weighting

  18. A weighted isoperimetric inequality and applications to symmetrization

    Directory of Open Access Journals (Sweden)

    Brock F

    1999-01-01

    Full Text Available We prove an inequality of the form , where is a bounded domain in with smooth boundary, is a ball centered in the origin having the same measure as . From this we derive inequalities comparing a weighted Sobolev norm of a given function with the norm of its symmetric decreasing rearrangement. Furthermore, we use the inequality to obtain comparison results for elliptic boundary value problems.

  19. 加权Bergman空间上的紧算子%Compact Toeplitz Operators on the Weighted Bergman Spaces

    Institute of Scientific and Technical Information of China (English)

    于涛; 孙善利

    2001-01-01

    In this paper, we investigate the Toeplitz operators on the weighted Bergman spaces. It is shown that if S is the finite sum of finite product of Toeplitz operators,then S is compact iff the Berezin transform of S vanishes at the boundary of the unit disk.%本文讨论了加权Bergnan空间上的Toeplitz算子,证明了Toeplitz算子的有限乘积的有限和是紧的当且仅当它的Berezin变换在边界上趋向于零.

  20. Necessary and Sufficient Conditions for Boundedness of Commutators of the General Fractional Integral Operators on Weighted Morrey Spaces

    Directory of Open Access Journals (Sweden)

    Zengyan Si

    2012-01-01

    Full Text Available We prove that b is in Lipβ(ω if and only if the commutator [b,L-α/2] of the multiplication operator by b and the general fractional integral operator L-α/2 is bounded from the weighted Morrey space Lp,k(ω to Lq,kq/p(ω1-(1-α/nq,ω, where 0(1-k/(p/(q-k, and here rω denotes the critical index of ω for the reverse Hölder condition.

  1. Um estudo sobre a boa colocação local da equação não linear de Schrödinger cúbica unidimensional em espaços de Sobolev periódicos

    OpenAIRE

    2009-01-01

    In this work we study, in details, the Cauchy problem of the nonlinear Schrödinger equation, with initial datas in periodic Sobolev spaces. Specifically, we prove that this problem is locally well posed for datas in Hsper, with s ≥ 0. Particularly, for initial datas in L2 the problem is globally well posed, due to the conservation law of the equation in this space. Moreover, we prove the this result is the best one, seeing we expose examples that show that the equation flow is not local...

  2. Commuting Dual Toeplitz Operators on the Orthogonal Complement of the Dirichlet Space

    Institute of Scientific and Technical Information of China (English)

    Tao YU; Shi Yue WU

    2009-01-01

    In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.

  3. Development of Light Weight High Strength Carbon Dioxide Monitor for Sub Orbital Space Craft

    Science.gov (United States)

    Karavolos, A. P.

    2011-12-01

    Introduction No commercially material is currently available that can satisfy the performance requirements for Suborbital Sampling of Carbon Dioxide in air .Satellite interrogation is not feasible because of the low altitude, and the altitude is too high for satisfactory performance from balloons. A hybrid material in a light weight canister may be the solution to satisfying the above requirements. An example fiber with carbon dioxide capture agent is wound in an equilateral triangle pattern 3 mm in diameter, and heat bonded to a carbon fiber panel. A layer of polypropylene-methyl cellulose 1 mm thick underlies the carbon fiber. The interior contains a metallized organic polymer heat bonded to this surface. Methodology All component materials were purchased through 3M and Sigma Aldrich Chemical Company. The carbon prepreg panel was first placed in a stainless steel mold for non reactivity with container. Polypropylene powder was homogenized with various percentages of methyl cellulose powder and tantalum nano particles. This mixture was then placed in a mold to make panel parts; epoxy bonded to a carbon fiber resin prepreg, and allowed to outgas for 24 hours before materials and chemical testing. Preliminary Results Preliminary finding of the newly tested material are shown in the table below are that the tensile strength is about 74.5 kPa, has maximum CO2 capture efficiency, and regeneration of O2 by weight of total CO2 captured. Conclusions Based on the initial experimentation accomplished, it appears that the proposed hybrid construction of carbon pre preg backing material, coupled with an inner lining of polypropylene-methyl cellulose, satisfies the strength requirements of the habitat building material. In addition, carbon dioxide adsorption and oxygen replenishment requirements also have been met.

  4. High Conductivity Carbon-Carbon Heat Pipes for Light Weight Space Power System Radiators

    Science.gov (United States)

    Juhasz, Albert J.

    2008-01-01

    Based on prior successful fabrication and demonstration testing of a carbon-carbon heat pipe radiator element with integral fins this paper examines the hypothetical extension of the technology via substitution of high thermal conductivity composites which would permit increasing fin length while still maintaining high fin effectiveness. As a result the specific radiator mass could approach an ultimate asymptotic minimum value near 1.0 kg/m2, which is less than one fourth the value of present day satellite radiators. The implied mass savings would be even greater for high capacity space and planetary surface power systems, which may require radiator areas ranging from hundreds to thousands of square meters, depending on system power level.

  5. Space Station Control Requirements and Flywheel System Weights for Combined Momentum and Energy Storage

    Science.gov (United States)

    Elam, F. M.

    1983-01-01

    The specifications of the flywheel system for momentum storage and vehicle torquing are somewhat dependent upon the attitude control requirements of the space station in orbit. As a ground rule, the flywheel system will be sized large enough to provide all attitude maneuvers, if practical, to avoid or minimize turning on the reaction control system (RCS). The RCS, whenever used, expels expensive mass and tends to contaminate optical surfaces of the vehicle. The vehicle rate and acceleration specifications of 0.10 deg/sec and 0.01 deg/square sec are tentative, and may be reduced if lesser values are more practical for flywheel design. For local vertical attitude hold, the average attitude error should be zero, and not the classical 1 degree, since control moment gyro (CMG) gimbal angles provide an exact reference feedback for gravity gradient momentum. Docking presents a problem for docking transients and attitude alignment which will require use of the RCS.

  6. Primary Dendrite Arm Spacing and Trunk Diameter in Al-7-Weight-Percentage Si Alloy Directionally Solidified Aboard the International Space Station

    Science.gov (United States)

    Ghods, M.; Tewari, S. N.; Lauer, M.; Poirier, D. R.; Grugel, R. N.

    2016-01-01

    Under a NASA-ESA collaborative research project, three Al-7-weight-percentage Si samples (MICAST-6, MICAST-7 and MICAST 2-12) were directionally solidified aboard the International Space Station to determine the effect of mitigating convection on the primary dendrite array. The samples were approximately 25 centimeters in length with a diameter of 7.8 millimeter-diameter cylinders that were machined from [100] oriented terrestrially grown dendritic Al-7Si samples and inserted into alumina ampoules within the Sample Cartridge Assembly (SCA) inserts of the Low Gradient Furnace (LGF). The feed rods were partially remelted in space and directionally solidified to effect the [100] dendrite-orientation. MICAST-6 was grown at 5 microns per second for 3.75 centimeters and then at 50 microns per second for its remaining 11.2 centimeters of its length. MICAST-7 was grown at 20 microns per second for 8.5 centimeters and then at 10 microns per second for 9 centimeters of its remaining length. MICAST2-12 was grown at 40 microns per second for 11 centimeters. The thermal gradient at the liquidus temperature varied from 22 to 14 degrees Kelvin per centimeter during growth of MICAST-6, from 26 to 24 degrees Kelvin per centimeter for MICAST-7 and from 33 to 31 degrees Kelvin per centimeter for MICAST2-12. Microstructures on the transverse sections along the sample length were analyzed to determine nearest-neighbor spacing of the primary dendrite arms and trunk diameters of the primary dendrite-arrays. This was done along the lengths where steady-state growth prevailed and also during the transients associated with the speed-changes. The observed nearest-neighbor spacings during steady-state growth of the MICAST samples show a very good agreement with predictions from the Hunt-Lu primary spacing model for diffusion controlled growth. The observed primary dendrite trunk diameters during steady-state growth of these samples also agree with predictions from a coarsening-based model

  7. The best quadrature based on given Hermite information for the Sobolev class KWr[a,b

    Institute of Scientific and Technical Information of China (English)

    WANG; Xinghua; YANG; Shijun

    2006-01-01

    As usual, denote by KWr[a,b] the Sobolev class consisting of every function whose (r-1)th derivative is absolutely continuous on the interval [a,b] and rth derivative is bounded by K a.e. In [a,b]. For a function f ∈ KWr[a,b], its values and derivatives up to r-1 order at a set of nodes x are known. These values are said to be the given Hermite information.This work reports the results on the best quadrature based on the given Hermite information for the class KWr[a,b]. Existence and concrete construction issue of the best quadrature are settled down by a perfect spline interpolation. It turns out that the best quadrature depends on a system of algebraic equations satisfied by a set of free nodes of the interpolation perfect spline. From our another new result, it is shown that the system can be converted in a closed form to two single-variable polynomial equations, each being of degree approximately r/2. As a by-product,the best interpolation formula for the class KWr[a,b] is also obtained.

  8. Asymptotics of polynomials orthogonal with respect to a discrete-complex Sobolev inner product

    Science.gov (United States)

    Rocha, I. Alvarez; Salto, L.

    2005-06-01

    Let [mu] be a finite positive Borel measure supported on a compact set of the real line and introduce the discrete Sobolev-type inner productwhere the mass points ck belong to supp([mu]) and Mk,i are complex numbers such that Mk,Nk[not equal to]0. In this paper we investigate the asymptotics of the polynomials orthogonal with this product. When the mass points ck belong to , the problem was solved in a paper by G. Lopez, et al. (Constr. Approx. 11 (1995) 107-137) and, for mass points in supp([mu])=[-1,1], the solution was given by I.A. Rocha et al. (J. Approx. Theory, 121 (2003) 336-356) provided that [mu]'(x)>0 a.e. x[set membership, variant][-1,1] and Mk,i are nonnegative constants. If [mu][set membership, variant]M(0,1), the possibility ck[set membership, variant]supp([mu])[-45 degree rule][-1,1] must be considered. Here we solve this last case with complex constants Mk,i.

  9. Shape tracking with occlusions via coarse-to-fine region-based sobolev descent

    KAUST Repository

    Yang, Yanchao

    2015-05-01

    We present a method to track the shape of an object from video. The method uses a joint shape and appearance model of the object, which is propagated to match shape and radiance in subsequent frames, determining object shape. Self-occlusions and dis-occlusions of the object from camera and object motion pose difficulties to joint shape and appearance models in tracking. They are unable to adapt to new shape and appearance information, leading to inaccurate shape detection. In this work, we model self-occlusions and dis-occlusions in a joint shape and appearance tracking framework. Self-occlusions and the warp to propagate the model are coupled, thus we formulate a joint optimization problem. We derive a coarse-to-fine optimization method, advantageous in tracking, that initially perturbs the model by coarse perturbations before transitioning to finer-scale perturbations seamlessly. This coarse-to-fine behavior is automatically induced by gradient descent on a novel infinite-dimensional Riemannian manifold that we introduce. The manifold consists of planar parameterized regions, and the metric that we introduce is a novel Sobolev metric. Experiments on video exhibiting occlusions/dis-occlusions, complex radiance and background show that occlusion/dis-occlusion modeling leads to superior shape accuracy. © 2014 IEEE.

  10. Sobolev Duals for Random Frames and Sigma-Delta Quantization of Compressed Sensing Measurements

    CERN Document Server

    Güntürk, S; Saab, R; Y\\ilmaz, Ö

    2010-01-01

    Quantization of compressed sensing measurements is typically justified by the robust recovery results of Cand\\`es, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size $\\delta$ is used to quantize $m$ measurements $y = \\Phi x$ of a $k$-sparse signal $x \\in \\R^N$, where $\\Phi$ satisfies the restricted isometry property, then the approximate recovery $x^#$ via $\\ell_1$-minimization is within $O(\\delta)$ of $x$. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an $r$th order $\\Sigma\\Delta$ quantization scheme with the same output alphabet is used to quantize $y$, then there is an alternative recovery method via Sobolev dual frames which guarantees a reduction of the approximation error by a factor of $(m/k)^{(r-1/2)\\alpha}$ for any $0 < \\alpha < 1$, if $m \\gtrsim_r k (\\log N)^{1/(1-\\alpha)}$. The result holds with high probability on the initial draw of the measurement matrix $\\Phi$ f...

  11. 加权Bergman空间上的Toeplitz算子的数值域%The Numerical Range of a Toeplitz Operator on the Weighted Bergman Space

    Institute of Scientific and Technical Information of China (English)

    孔德尧; 张波

    2012-01-01

    The Bergman space is a Hilbert space,we can define a Toeplitz operator on this space and study the numerical range of this operator.On the weighted Bergman space,we can also define a Toeplitz operator.In this paper,we discuss the properties of the numerical range of a Toeplitz operator on the weighted Bergman space,and get some useful results.%Bergman空间是一类特殊的Hilbert空间,其上可以定义Toeplitz算子,进而可以讨论此类算子的数值域.若将Bergman空间推广到加权Bergman空间,也可以讨论其上的Toeplitz算子的数值域.本文主要讨论加权Bergman空间上Toeplitz算子的数值域的性质,并得到了一些非常有意义的结论.

  12. On the Nemytskii Operator in the Space of Functions of Bounded (p, 2, α-Variation with Respect to the Weight Function

    Directory of Open Access Journals (Sweden)

    Aziz Wadie

    2014-12-01

    Full Text Available In this paper, we consider the Nemytskii operator (Hf(t = h(t, f(t, generated by a given function h. It is shown that if H is globally Lipschitzian and maps the space of functions of bounded (p,2,α-variation (with respect to a weight function α into the space of functions of bounded (q,2,α-variation (with respect to α 1space of bounded variation with weight function in the sense of Merentes into another space of the same type, its generator function is an affine function.

  13. Comparative empirical analysis of flow-weighted transit route networks in R-space and evolution modeling

    Science.gov (United States)

    Huang, Ailing; Zang, Guangzhi; He, Zhengbing; Guan, Wei

    2017-05-01

    Urban public transit system is a typical mixed complex network with dynamic flow, and its evolution should be a process coupling topological structure with flow dynamics, which has received little attention. This paper presents the R-space to make a comparative empirical analysis on Beijing’s flow-weighted transit route network (TRN) and we found that both the Beijing’s TRNs in the year of 2011 and 2015 exhibit the scale-free properties. As such, we propose an evolution model driven by flow to simulate the development of TRNs with consideration of the passengers’ dynamical behaviors triggered by topological change. The model simulates that the evolution of TRN is an iterative process. At each time step, a certain number of new routes are generated driven by travel demands, which leads to dynamical evolution of new routes’ flow and triggers perturbation in nearby routes that will further impact the next round of opening new routes. We present the theoretical analysis based on the mean-field theory, as well as the numerical simulation for this model. The results obtained agree well with our empirical analysis results, which indicate that our model can simulate the TRN evolution with scale-free properties for distributions of node’s strength and degree. The purpose of this paper is to illustrate the global evolutional mechanism of transit network that will be used to exploit planning and design strategies for real TRNs.

  14. Weighted augmented Jacobian matrix with a variable coefficient method for kinematics mapping of space teleoperation based on human-robot motion similarity

    Science.gov (United States)

    Shi, Zhong; Huang, Xuexiang; Hu, Tianjian; Tan, Qian; Hou, Yuzhuo

    2016-10-01

    Space teleoperation is an important space technology, and human-robot motion similarity can improve the flexibility and intuition of space teleoperation. This paper aims to obtain an appropriate kinematics mapping method of coupled Cartesian-joint space for space teleoperation. First, the coupled Cartesian-joint similarity principles concerning kinematics differences are defined. Then, a novel weighted augmented Jacobian matrix with a variable coefficient (WAJM-VC) method for kinematics mapping is proposed. The Jacobian matrix is augmented to achieve a global similarity of human-robot motion. A clamping weighted least norm scheme is introduced to achieve local optimizations, and the operating ratio coefficient is variable to pursue similarity in the elbow joint. Similarity in Cartesian space and the property of joint constraint satisfaction is analysed to determine the damping factor and clamping velocity. Finally, a teleoperation system based on human motion capture is established, and the experimental results indicate that the proposed WAJM-VC method can improve the flexibility and intuition of space teleoperation to complete complex space tasks.

  15. On First Order Interpolation Inequalities with Weights on the Heisenberg Group

    Institute of Scientific and Technical Information of China (English)

    Ya Zhou HAN; Peng Cheng NIU; Shu Tao ZHANG

    2011-01-01

    In this paper,sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg group are given.The necessity is discussed by polar coordinates changes of the Heisenberg group.Establishing a class of Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,we derive the sufficiency.Finally,sharp constants for Hardy type inequalities are determined.

  16. A boundary-value problem in weighted Hölder spaces for elliptic equations which degenerate at the boundary of the domain

    Energy Technology Data Exchange (ETDEWEB)

    Bazalii, B V; Degtyarev, S P [Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Donetsk (Ukraine)

    2013-07-31

    An elliptic boundary-value problem for second-order equations with nonnegative characteristic form is investigated in the situation when there is a weak degeneracy on the boundary of the domain. A priori estimates are obtained for solutions and the problem is proved to be solvable in some weighted Hölder spaces. Bibliography: 18 titles.

  17. Solution to the Volterra integral equations of the first kind with piecewise continuous kernels in class of Sobolev-Schwartz distributions

    CERN Document Server

    Sidorov, Denis

    2012-01-01

    Sufficient conditions for existence and uniqueness of the solution of the Volterra integral equations of the first kind with piecewise continuous kernels are derived in framework of Sobolev-Schwartz distribution theory. The asymptotic approximation of the parametric family of generalized solutions is constructed. The method for the solution's regular part refinement is proposed using the successive approximations method.

  18. On Some Geometrical Properties of Generalized Modular Spaces of Cesáro Type Defined by Weighted Means

    Directory of Open Access Journals (Sweden)

    Necip Şimşek

    2009-01-01

    Full Text Available The main purpose of this paper is to introduce modular structure of the sequence space defined by Altay and Başar (2007, and to study Kadec-Klee (H and uniform Opial properties of this sequence space on Köthe sequence spaces.

  19. On Some Geometrical Properties of Generalized Modular Spaces of Cesáro Type Defined by Weighted Means

    Directory of Open Access Journals (Sweden)

    Karakaya Vatan

    2009-01-01

    Full Text Available Abstract The main purpose of this paper is to introduce modular structure of the sequence space defined by Altay and Başar (2007, and to study Kadec-Klee ( and uniform Opial properties of this sequence space on Köthe sequence spaces.

  20. EXISTENCE OF SOLUTIONS TO THE PARABOLIC EQUATION WITH A SINGULAR POTENTIAL OF THE SOBOLEV-HARDY TYPE

    Institute of Scientific and Technical Information of China (English)

    Han Junqiang; Wang Yongda; Niu Pengcheng

    2012-01-01

    We study the existence of solutions to the following parabolic equation {ut-△pu =λ/|x|s|u|q-2 u,(x,t) ∈ Ω × (0,∞),u(x,0) =f(x),x ∈ Ω,(P)u(x,t) =0,(x,t) ∈ δΩ × (0,∞),where-△pu ≡-div(|▽u|p-2 ▽u),1 < p < N,0 < s ≤ p,p≤s≤ q ≤ p*(s) =N-s/N-pp,Ω is a bounded domain in RN such that 0 ∈ Ω with a C1 boundary δΩ,f ≥ 0 satisfying some convenient regularity assumptions.The analysis reveals that the existence of solutions for (P) depends on p,q,s in general,and on the relation between λ and the best constant in the Sobolev-Hardy inequality.

  1. Composition proceeded by differential operator from Bloch space to weighted-type space%空间到加权型空间的复合微分前置算子

    Institute of Scientific and Technical Information of China (English)

    余建; 伍鹏程

    2016-01-01

    In this paper,the boundedness and compactness of the composite differential prior operator were studied,which was used to support the mapping,from Bloch space to the weighted space. And we obtained the necessary and sufficient conditions for the boundedness and compactness of this opera-tor.%从算子的性质出发,研究Bloch空间到加权型空间的复合微分前置算子的有界性和紧性,得到了算子有界性和紧性的充分必要条件。

  2. EFFECTS OF PLANTING SPACE AND HARVEST TIME ON THE NUMBER, WEIGHT AND DIAMETER OF MARIGOLD (CALENDULA OFFICINALIS L. FLOWERS

    Directory of Open Access Journals (Sweden)

    Nada Parađiković

    2013-06-01

    Full Text Available The study was conducted during 2010 in marigold (Calendula officinalis L. to determine the effects of three plant densities (plant density A - 65 cm x 35 cm; plant density B - 65 cm x 25 cm; plant density C – 55 cm x 25 cm and harvest time on the number, weight and diameter of marigold flowers. The results showed that the plant density significantly influenced the number of flowers per plant and flower weight. The largest number of flowers per plant was recorded in the plant density B (13.2 and the lowest (9.87 in the plant density C. The lowest flower weight was recorded in the plant density C (1.31 g and was statistically lower than the flower weight in the plant densities A (1.42 g and B (1.38 g. The plant density significantly influenced the number of flowers on side branches, being the highest in the plant density B. The diameter of the marigold flower was not significantly influenced by the plant density. During the experiment, a total of 13 harvests were achieved. The greatest number of flowers per plant was harvested in the eighth, ninth and tenth harvest, while the largest flower weight was measured in the fifth and twelfth harvest. On the average, the number of flowers per plant / harvest was 11.63 and the weight of flowers was 1.38 g. Diameter of marigold flowers ranged from 2.89 cm to 3.59 cm in the thirteenth and the third harvest, respectively. The number of flowers on side branches per plant / harvest was 11.61.

  3. Self-Biased Radiation Hardened Ka-Band Circulators for Size, Weight and Power Restricted Long Range Space Applications Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Ferrite control components including circulators and isolators are fundamental building blocks of Transmit/Receive modules (TRM) utilized in high data rate active...

  4. Self-Biased Radiation Hardened Ka-Band Circulators for Size, Weight and Power Restricted Long Range Space Applications Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Ferrite control components including circulators and isolators are fundamental building blocks of Transmit/Receive modules (TRM) utilized in high data rate active...

  5. 赋权控制分配策略的空间优化设计%The Design of Space Optimization for Weighted Control Allocation Scheme

    Institute of Scientific and Technical Information of China (English)

    陈勇; 董新民; 王发威; 赵丽

    2012-01-01

    To increase the using rate of attainable virtual instruction set in static weighted control allocation, a design scheme of space optimization for determining the best weights of instructions offline is proposed based on the improved particle swarm optimization. The mathematical models of weighted pseudo-inverse and mixed optimization methods are built respectively whose uniform control law is deducted and attainable set constructing algorithm is presented. By introducing the quantum and genetic factors, the diversity of particle swarm is enhanced through cross operation to obtain the global optimal weights of control instructions quickly. The simulation results show that the designed scheme can achieve the maximal attainable set space of weighted control allocation.%为提高静态赋权控制分配策略虚拟指令可达集的使用率,基于改进粒子群算法提出了一种离线确定控制指令最优化权值的空间优化设计方案.分别建立了加权伪逆法和混合优化法的数学模型,推导出统一的控制律形式,并给出了构造可达集空间的算法:引入量子和遗传因了,通过粒子的交叉操作增强粒子群的多样性,以快速求解控制指令权值的全局最优点.仿真结果表明,设计的方案可以实现赋权控制分配策略可达集空间的最大化.

  6. Twistor quantization of the space of half-differentiable vector functions on the circle revisited

    Institute of Scientific and Technical Information of China (English)

    SERGEEV; Armen

    2009-01-01

    We discuss the twistor quantization problem for the classical system(Vd,Ad),represented by the phase space Vd,identified with the Sobolev space H 1/2 0 (S1,Rd)of half-differentiable vector functions on the circle,and the algebra of observables Ad,identified with the semi-direct product of the Heisenberg algebra of Vd and the algebra Vect(S1)of tangent vector fields on the circle.

  7. Algebraic Properties of Dual Toeplitz Operators on the Orthogonal Complement of the Dirichlet Space

    Institute of Scientific and Technical Information of China (English)

    Tao YU; Shi Yue WU

    2008-01-01

    In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space.We completely characterize commuting dual Toeplitz operators with harmonic symbols,and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic.We also obtain the sufficient and necessary conditions on the harmonic symbols for SψSψ=Sψψ.

  8. Local well-posedness for a higher order nonlinear Schrodinger equation in Sobolev spaces of negative indices

    Directory of Open Access Journals (Sweden)

    Xavier Carvajal

    2004-01-01

    Full Text Available We prove that the initial value problem associated with $$ partial_tu+ialpha partial^2_x u+Beta partial^3_x u +igamma|u|^2u = 0, quad x,t in mathbb{R}, $$ is locally well-posed in $H^s$ for $s>-1/4$.

  9. A Weighted Inner Product Estimator in the Geometric Algebra of Euclidean 3-Space for Source Localization Using an EM Vector-sensor

    Institute of Scientific and Technical Information of China (English)

    JIANG Jingfei; ZHANG Jianqiu

    2012-01-01

    In this paper,the source localization by utilizing the measurements of a single electromagnetic (EM) vector-sensor is investigated in the framework of the geometric algebra of Euclidean 3-space.In order to describe the orthogonality among the electric and magnetic measurements,two multivectors of the geometric algebra of Euclidean 3-space (G3) are used to model the outputs of a spatially collocated EM vector-sensor.Two estimators for the wave propagation vector estimation are then formulated by the inner product between a vector and a bivector in the G3.Since the information used by the two estimators is different,a weighted inner product estimator is then proposed to fuse the two estimators together in the sense of the minimum mean square error (MMSE).Analytical results show that the statistical performances of the weighted inner product estimator are always better than its traditional cross product counterpart.The efficacy of the weighted inner product estimator and the correctness of the analytical predictions are demonstrated by simulation results.

  10. T2-weighted MR imaging of the liver: qualitative and quantitative comparison of SPACE MR imaging with turbo spin-echo MR imaging.

    Science.gov (United States)

    Dohan, Anthony; Gavini, Jean-Philippe; Placé, Vinciane; Sebbag, Delphine; Vignaud, Alexandre; Herbin, Christine; Hamzi, Lounis; Boudiaf, Mourad; Soyer, Philippe

    2013-11-01

    To qualitatively and quantitatively compare T2-weighted MR imaging of the liver using volumetric spin-echo with sampling perfection with application-optimized contrast using different flip angle evolutions (SPACE) with conventional turbo spin-echo (TSE) sequence for fat-suppressed T2-weighted MR imaging of the liver. Thirty-three patients with suspected focal liver lesions had SPACE MR imaging and conventional fat-suppressed TSE MR imaging. Images were analyzed quantitatively by measuring the lesion-to-liver contrast-to-noise ratio (CNR), and the signal-to-noise ratio (SNR) of main focal hepatic lesions, hepatic and splenic parenchyma and qualitatively by evaluating the presence of vascular, respiratory motion and cardiac artifacts. Wilcoxon signed rank test was used to search for differences between the two sequences. SPACE MR imaging showed significantly greater CNR for focal liver lesions (median=22.82) than TSE MR imaging (median=14.15) (Pcomparison with the conventional TSE sequence. These results should stimulate further clinical studies with a surgical standard of reference to compare the two techniques in terms of sensitivity for malignant lesions. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

  11. Antioxidant effect of hyaluronan on polymorphonuclear leukocyte-derived reactive oxygen species is dependent on its molecular weight and concentration and mainly involves the extracellular space

    Directory of Open Access Journals (Sweden)

    Rafał Krasiński

    2009-05-01

    Full Text Available Introduction: Hyaluronan (HA, a component of the extracellular matrix, may regulate immune cell functions through its interactions with cellular receptors. Besides its effect on cytokine and chemokine production, its antioxidant properties have been described. However, the mechanisms of this are not fully elucidated. The aim of this study was to evaluate the relationship between HA concentration and molecular weight and its antioxidant properties towards human neutrophils. Also assessed was whether the antioxidant effect of HA is connected with a reduction in intracellular oxygen potential, which could indicate its direct effect on neutrophil respiratory burst.Materials/Methods: The relationship between HA’s antioxidant properties and its concentration and molecular weight was assessed by the luminol-enhanced chemiluminescence method (CL. To evaluate the effect of HA on intracellular oxygen potential selectively, the dihydrorhodamine 123 (DHR123 flow cytometric method was used.Results: Reduction of both HA molecular weight and its concentration decreased its antioxidant properties in the CL method. A selective effect of HA on intracellular oxygen potential measured by the DHR123 method was not shown.Conclusions: The antioxidant properties of HA are related to both its molecular weight and its concentration. The lack of an antioxidant effect of HA in the DHR123 test compared with a significant reduction in CL values at the same HA concentration suggests that HA acts mainly as a chemical ROI scavenger in the extracellular space.

  12. Integral-type Operators Between Two Types of Weighted Spaces%两类加权空间之间的积分型算子

    Institute of Scientific and Technical Information of China (English)

    李海英; 范利萍

    2012-01-01

    设0<p<∞,-2<q<∞,0<s<∞,a>0.利用符号函数(φ)和映射φ的函数论性质,主要给出广义加权Bloch空间与Flog(p,q,s)空间之间的积分型算子C(φ)φ的有界性和紧性的充分必要条件.%Let 00. In this paper, using the function theory properties of symbol function φ and map φ, sufficient and necessary condition of integral-type operators Cψφ between generally weighted Bloch space Blog and Floe ( p,q,s) space to be bounded and compaci are mainiy given.

  13. Theory of function spaces II

    CERN Document Server

    Triebel, Hans

    1992-01-01

    Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is s...

  14. Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces

    CERN Document Server

    Si, Zengyan

    2012-01-01

    We prove that $b$ is in $Lip_{\\bz}(\\bz)$ if and only if the commutator $[b,L^{-\\alpha/2}]$ of the multiplication operator by $b$ and the general fractional integral operator $L^{-\\alpha/2}$ is bounded from the weighed Morrey space $L^{p,k}(\\omega)$ to $L^{q,kq/p}(\\omega^{1-(1-\\alpha/n)q},\\omega)$, where $0 \\frac{1-k}{p/q-k},$ and here $r_\\omega$ denotes the critical index of $\\omega$ for the reverse H\\"{o}lder condition.

  15. Cortical and Trabecular Bone Microstructure Did Not Recover at Weight-Bearing Skeletal Sites and Progressively Deteriorated at Non-Weight-Bearing Sites During the Year Following International Space Station Missions.

    Science.gov (United States)

    Vico, Laurence; van Rietbergen, Bert; Vilayphiou, Nicolas; Linossier, Marie-Thérèse; Locrelle, Hervé; Normand, Myriam; Zouch, Mohamed; Gerbaix, Maude; Bonnet, Nicolas; Novikov, Valery; Thomas, Thierry; Vassilieva, Galina

    2017-06-02

    Risk for premature osteoporosis is a major health concern in astronauts and cosmonauts; the reversibility of the bone lost at the weight-bearing bone sites is not established, although it is suspected to take longer than the mission length. The bone three-dimensional structure and strength that could be uniquely affected by weightlessness is currently unknown. Our objective is to evaluate bone mass, microarchitecture, and strength of weight-bearing and non-weight-bearing bone in 13 cosmonauts before and for 12 months after a 4-month to 6-month sojourn in the International Space Station (ISS). Standard and advanced evaluations of trabecular and cortical parameters were performed using high-resolution peripheral quantitative computed tomography. In particular, cortical analyses involved determination of the largest common volume of each successive individual scan to improve the precision of cortical porosity and density measurements. Bone resorption and formation serum markers, and markers reflecting osteocyte activity or periosteal metabolism (sclerostin, periostin) were evaluated. At the tibia, in addition to decreased bone mineral densities at cortical and trabecular compartments, a 4% decrease in cortical thickness and a 15% increase in cortical porosity were observed at landing. Cortical size and density subsequently recovered and serum periostin changes were associated with cortical recovery during the year after landing. However, tibial cortical porosity or trabecular bone failed to recover, resulting in compromised strength. The radius, preserved at landing, unexpectedly developed postflight fragility, from 3 months post-landing onward, particularly in its cortical structure. Remodeling markers, uncoupled in favor of bone resorption at landing, returned to preflight values within 6 months, then declined farther to lower than preflight values. Our findings highlight the need for specific protective measures not only during, but also after spaceflight, because

  16. High-efficiency space-based software radio architectures & algorithms (a minimum size, weight, and power TeraOps processor)

    Energy Technology Data Exchange (ETDEWEB)

    Dunham, Mark Edward [Los Alamos National Laboratory; Baker, Zachary K [Los Alamos National Laboratory; Stettler, Matthew W [Los Alamos National Laboratory; Pigue, Michael J [Los Alamos National Laboratory; Schmierer, Eric N [Los Alamos National Laboratory; Power, John F [Los Alamos National Laboratory; Graham, Paul S [Los Alamos National Laboratory

    2009-01-01

    Los Alamos has recently completed the latest in a series of Reconfigurable Software Radios, which incorporates several key innovations in both hardware design and algorithms. Due to our focus on satellite applications, each design must extract the best size, weight, and power performance possible from the ensemble of Commodity Off-the-Shelf (COTS) parts available at the time of design. In this case we have achieved 1 TeraOps/second signal processing on a 1920 Megabit/second datastream, while using only 53 Watts mains power, 5.5 kg, and 3 liters. This processing capability enables very advanced algorithms such as our wideband RF compression scheme to operate remotely, allowing network bandwidth constrained applications to deliver previously unattainable performance.

  17. Partial Differential Equations A unified Hilbert Space Approach

    CERN Document Server

    Picard, Rainer

    2011-01-01

    This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. Thefocus on a Hilbert space setting is a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations.This global point of view is takenby focussing on the issues involved in determining the appropriate func

  18. Hörmander spaces, interpolation, and elliptic problems

    CERN Document Server

    Mikhailets, Vladimir A; Malyshev, Peter V

    2014-01-01

    The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a

  19. Cellular Multi-User Two-Way MIMO AF Relaying via Signal Space Alignment: Minimum Weighted SINR Maximization

    CERN Document Server

    Chiu, Eddy

    2012-01-01

    In this paper, we consider linear MIMO transceiver design for a cellular two-way amplify-and-forward relaying system consisting of a single multi-antenna base station, a single multi-antenna relay station, and multiple multi-antenna mobile stations (MSs). Due to the two-way transmission, the MSs could suffer from tremendous multi-user interference. We apply an interference management model exploiting signal space alignment and propose a transceiver design algorithm, which allows for alleviating the loss in spectral efficiency due to half-duplex operation and providing flexible performance optimization accounting for each user's quality of service priorities. Numerical comparisons to conventional two-way relaying schemes based on bidirectional channel inversion and spatial division multiple access-only processing show that the proposed scheme achieves superior error rate and average data rate performance.

  20. Spaces

    Directory of Open Access Journals (Sweden)

    Maziar Nekovee

    2010-01-01

    Full Text Available Cognitive radio is being intensively researched as the enabling technology for license-exempt access to the so-called TV White Spaces (TVWS, large portions of spectrum in the UHF/VHF bands which become available on a geographical basis after digital switchover. Both in the US, and more recently, in the UK the regulators have given conditional endorsement to this new mode of access. This paper reviews the state-of-the-art in technology, regulation, and standardisation of cognitive access to TVWS. It examines the spectrum opportunity and commercial use cases associated with this form of secondary access.

  1. Evaluating the removal of pigs from a group and subsequent floor space allowance on the growth performance of heavy-weight finishing pigs.

    Science.gov (United States)

    Flohr, J R; Tokach, M D; DeRouchey, J M; Woodworth, J C; Goodband, R D; Dritz, S S

    2016-10-01

    A total of 1,092 finishing pigs (initially 36.3 kg) were used in a 117-d study to evaluate the impact of initial floor space allowance and removal strategy on the growth of pigs up to 140 kg BW. There were 4 experimental treatments with 14 pens per treatment. The first treatment provided 0.91 m per pig (15 pigs/pen). The other 3 treatments initially provided 0.65 m per pig (21 pigs/pen) with 3 different removal strategies. The second treatment (2:2:2) removed the 2 heaviest pigs from pens on d 64, 76, and 95 when floor space allowance was predicted to be limiting. Treatment 3 (2:4) removed the 2 heaviest pigs on d 76 and the 4 heaviest pigs on d 105. Treatment 4 (6) removed the heaviest 6 pigs on d 105. All pigs remaining in pens after removals were fed to d 117. Overall (d 0 to 117), pigs initially provided 0.91 m of floor space had increased ( strategy, but ADG was not different compared with pigs on the 2:2:2 removal strategy. Total BW gain per pen was greater ( strategies; however, feed usage per pig was greater ( strategies. Feed usage, on a pig or pen basis, was less ( strategy compared to pigs on the 2:4 or the 6 removal strategy. Income over feed and facility cost (IOFFC) was less ( strategies. Also, IOFFC was less ( strategies. In conclusion, increasing the floor space allowance or the time points at which pigs are removed from the pen improved the growth of pigs remaining in the pen; however, IOFFC may be reduced because fewer pigs are marketed from each pen (pigs stocked at 0.91 m throughout the study) or from reducing total weight produced (2:2:2 removal strategy).

  2. Infinitesimally Lipschitz functions on metric spaces

    CERN Document Server

    Durand, E

    2009-01-01

    For a metric space $X$, we study the space $D^{\\infty}(X)$ of bounded functions on $X$ whose infinitesimal Lipschitz constant is uniformly bounded. $D^{\\infty}(X)$ is compared with the space $\\LIP^{\\infty}(X)$ of bounded Lipschitz functions on $X$, in terms of different properties regarding the geometry of $X$. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare $D^{\\infty}(X)$ with the Newtonian-Sobolev space $N^{1, \\infty}(X)$. In particular, if $X$ supports a doubling measure and satisfies a local Poincar{\\'e} inequality, we obtain that $D^{\\infty}(X)=N^{1, \\infty}(X)$.

  3. On the Singular Biharmonic Problems Involving Critical Sobolev Exponents%带有临界Sobolev指数的奇异双调和问题

    Institute of Scientific and Technical Information of China (English)

    胡丽平; 周世国

    2007-01-01

    LetΩ(∪)RN be a smooth bounded domain such that 0 ∈Ω, N ≥ 5, 2* := 2N/N-4 is the critical Sobolev exponent, and f(x) is a given function. By using the variational methods,the paper proves the existence of solutions for the singular critical in the homogeneous problem △-μu/|x|4 = |u|2* -2u + f(x) with Dirichlet boundary condition on (e)Ω under some assumptions on f(x) and μ.

  4. Free-breathing contrast-enhanced T1-weighted gradient-echo imaging with radial k-space sampling for paediatric abdominopelvic MRI

    Energy Technology Data Exchange (ETDEWEB)

    Chandarana, Hersh; Block, Kai T.; Winfeld, Matthew J.; Lala, Shailee V.; Mazori, Daniel; Giuffrida, Emalyn; Babb, James S.; Milla, Sarah S. [New York University Langone Medical Center, Department of Radiology, New York, NY (United States)

    2014-02-15

    To compare the image quality of contrast-enhanced abdominopelvic 3D fat-suppressed T1-weighted gradient-echo imaging with radial and conventional Cartesian k-space acquisition schemes in paediatric patients. Seventy-three consecutive paediatric patients were imaged at 1.5 T with sequential contrast-enhanced T1-weighted Cartesian (VIBE) and radial gradient echo (GRE) acquisition schemes with matching parameters when possible. Cartesian VIBE was acquired as a breath-hold or as free breathing in patients who could not suspend respiration, followed by free-breathing radial GRE in all patients. Two paediatric radiologists blinded to the acquisition schemes evaluated multiple parameters of image quality on a five-point scale, with higher score indicating a more optimal examination. Lesion presence or absence, conspicuity and edge sharpness were also evaluated. Mixed-model analysis of variance was performed to compare radial GRE and Cartesian VIBE. Radial GRE had significantly (all P < 0.001) higher scores for overall image quality, hepatic edge sharpness, hepatic vessel clarity and respiratory motion robustness than Cartesian VIBE. More lesions were detected on radial GRE by both readers than on Cartesian VIBE, with significantly higher scores for lesion conspicuity and edge sharpness (all P < 0.001). Radial GRE has better image quality and lesion conspicuity than conventional Cartesian VIBE in paediatric patients undergoing contrast-enhanced abdominopelvic MRI. (orig.)

  5. On the differential structure of metric measure spaces and applications

    CERN Document Server

    Gigli, Nicola

    2015-01-01

    The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like \\Delta g=\\mu, where g is a functi

  6. Weight Management

    Science.gov (United States)

    ... Anger Weight Management Weight Management Smoking and Weight Healthy Weight Loss Being Comfortable in Your Own Skin Your Weight Loss Expectations & Goals Healthier Lifestyle Healthier Lifestyle Physical Fitness Food & Nutrition Sleep, Stress & Relaxation Emotions & Relationships HealthyYouTXT ...

  7. Geometric Sobolev-like embedding using high-dimensional Menger-like curvature

    CERN Document Server

    Kolasiński, Sławomir

    2012-01-01

    We study a modified version of Lerman-Whitehouse Menger-like curvature defined for m+2 points in an n-dimensional Euclidean space. For 1 <= l <= m+2 and an m-dimensional subset S of R^n we also introduce global versions of this discrete curvature, by taking supremum with respect to m+2-l points on S. We then define geometric curvature energies by integrating one of the global Menger-like curvatures, raised to a certain power p, over all l-tuples of points on S. Next, we prove that if S is compact and m-Ahlfors regular and if p is greater than ml, then the P. Jones' \\beta-numbers of S must decay as r^t with r \\to 0 for some t in (0,1). If S is an immersed C^1 manifold or a bilipschitz image of such set then it follows that it is Reifenberg flat with vanishing constant, hence (by a theorem of David, Kenig and Toro) an embedded C^{1,t} manifold. We also define a wide class of other sets for which this assertion is true. After that, we bootstrap the exponent t to the optimal one a = 1 - ml/p showing an anal...

  8. Sobolev型方程高次Wilson元逼近及超收敛分析%Approximation and Superconvergence Analysis for a New Higher Order Wilson Element to Sobolev Type Equations

    Institute of Scientific and Technical Information of China (English)

    石东洋; 郝晓斌

    2008-01-01

    In this paper,a new higher order Wilson element is presented,and the convergence is proved.Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.

  9. Simulation of seismic wave propagation in 2-D poroelastic media using weighted-averaging finite difference stencils in the frequency-space domain

    Science.gov (United States)

    Yang, Qingjie; Mao, Weijian

    2017-01-01

    The poroelastodynamic equations are used to describe the dynamic solid-fluid interaction in the reservoir. To obtain the intrinsic properties of reservoir rocks from geophysical data measured in both laboratory and field, we need an accurate solution of the wave propagation in porous media. At present, the poroelastic wave equations are mostly solved in the time domain, which involves a difficult and complicated time convolution. In order to avoid the issues caused by the time convolution, we propose a frequency-space domain method. The poroelastic wave equations are composed of a linear system in the frequency domain, which easily takes into account the effects of all frequencies on the dispersion and attenuation of seismic wave. A 25-point weighted-averaging finite different scheme is proposed to discretize the equations. For the finite model, the perfectly matched layer technique is applied at the model boundaries. We validated the proposed algorithm by testing three numerical examples of poroelastic models, which are homogenous, two-layered and heterogeneous with different fluids, respectively. The testing results are encouraging in the aspects of both computational accuracy and efficiency.

  10. Integral potential method for a transmission problem with Lipschitz interface in R3 for the Stokes and Darcy-Forchheimer-Brinkman PDE systems

    Science.gov (United States)

    Kohr, Mirela; Lanza de Cristoforis, Massimo; Mikhailov, Sergey E.; Wendland, Wolfgang L.

    2016-10-01

    The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the nonlinear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain {Ω} with connected boundary, and the other one is the exterior Lipschitz domain R3 setminus overline{Ω}. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces.

  11. Contrast-enhanced MR Imaging of Metastatic Brain Tumor at 3 Tesla: Utility of T1-weighted SPACE Compared with 2D Spin Echo and 3D Gradient Echo Sequence

    National Research Council Canada - National Science Library

    KOMADA, Tomohiro; NAGANAWA, Shinji; OGAWA, Hiroshi; MATSUSHIMA, Masaya; KUBOTA, Seiji; KAWAI, Hisashi; FUKATSU, Hiroshi; IKEDA, Mitsuru; KAWAMURA, Minako; SAKURAI, Yasuo; MARUYAMA, Katsuya

    2008-01-01

    ...), and 2-dimensional T1-weighted spin echo (2D-SE) imaging at 3T. We quantitatively compared SPACE, MP-RAGE, and 2D-SE images by using signal-to-noise ratios (SNRs) for gray matter (GM) and white matter (WM...

  12. 非线性Sobolev-Galpern型湿气迁移方程的非协调类Carey元超收敛分析%Superconvergence Analysis of the Nonconforming Quasi-Carey Finite Element for Nonlinear Sobolev-Galpern Type Moisture Migration Equation

    Institute of Scientific and Technical Information of China (English)

    陈宝凤; 石玉

    2014-01-01

    主要目的是将非协调类Carey元应用于非线性Sobolev-Galpern型湿气迁移方程.借助于单元的特殊性质(即在能量模意义下相容误差比插值误差高一阶)、线性三角元的高精度分析以及平均值技巧,得到了解的超逼近性质.进一步地利用插值后处理技术导出了整体超收敛结果.

  13. Klassika & ekskremendid / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2002-01-01

    20.-21. aprillil toimus Pärnus 8. Fideo- ja Vilmifestival alapealkirjaga "Eksperimendid ja klassika". Peakorraldaja Rael Artel. Rami Raski filmist "Legowitz 1999" (soome rühmitus Vivid), läti filmist "Love, death & television", Concordia ülikooli ("Ülemus") ja Academia Grata (portreefilmid Asta Isakist, Andrus Joonasest jm.) programmist, Kadriann Kibuse ja Liina Paakspuu filmist "Urban Obsessions", Mirja-Mari Smidti ja Allan Tõnissoo videost, Marianne Männi koomiksitest kataloogis

  14. Hoolimine kohvris / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1999-01-01

    Rahvusvaheline rändnäitus 'Suitcases' ('Kohvrid') Tallinna Kunstihoones. Tallinna näituse alateema on 'Who Cares?' ('Kelle asi?'). Näituse kuraator on soomlane Timo Mähonen. Eestit esindab näitusel kunstnik Helena Palm.

  15. Klassika & ekskremendid / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2002-01-01

    20.-21. aprillil toimus Pärnus 8. Fideo- ja Vilmifestival alapealkirjaga "Eksperimendid ja klassika". Peakorraldaja Rael Artel. Rami Raski filmist "Legowitz 1999" (soome rühmitus Vivid), läti filmist "Love, death & television", Concordia ülikooli ("Ülemus") ja Academia Grata (portreefilmid Asta Isakist, Andrus Joonasest jm.) programmist, Kadriann Kibuse ja Liina Paakspuu filmist "Urban Obsessions", Mirja-Mari Smidti ja Allan Tõnissoo videost, Marianne Männi koomiksitest kataloogis

  16. Desperaado Viljandis / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2002-01-01

    Taave Tuutma korraldatud Öeksanda Märtsi tegevuskunstifestivalist. Näitusest "Taave Tuutma ja/kui märk" ja Academia Grata performance'ist Kilpkonna galeriis. Kiwa audioperformance'ist "Venus on Soma" Ugala keldrisaalis

  17. Galeriid, galeriid... / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2000-01-01

    Märt Väljataga, Lennart Männi ja Rauno Remme näitus "Sada tuhat miljardit millenniumisonetti" Linnagaleriis Tallinnas. Asko Künnapi graafika galeriis "Vaal". Tiia Külvi maalid galeriis "Sammas". Ülevaade Vladimir Anshoni loomingust Kunstihoone galeriis. "In Graafika" festival Pärnus

  18. Weight Management

    Science.gov (United States)

    ... Health Information Weight Management English English Español Weight Management Obesity is a chronic condition that affects more ... Liver (NASH) Heart Disease & Stroke Sleep Apnea Weight Management Topics About Food Portions Bariatric Surgery for Severe ...

  19. Weighted Clustering

    CERN Document Server

    Ackerman, Margareta; Branzei, Simina; Loker, David

    2011-01-01

    In this paper we investigate clustering in the weighted setting, in which every data point is assigned a real valued weight. We conduct a theoretical analysis on the influence of weighted data on standard clustering algorithms in each of the partitional and hierarchical settings, characterising the precise conditions under which such algorithms react to weights, and classifying clustering methods into three broad categories: weight-responsive, weight-considering, and weight-robust. Our analysis raises several interesting questions and can be directly mapped to the classical unweighted setting.

  20. Weight Calculation for Computational Geometry Combining Classifier Using Regularity of Class Space%类空间规整度的计算几何组合分类器权重分配

    Institute of Scientific and Technical Information of China (English)

    张涛; 洪文学

    2012-01-01

    在计算几何组合分类器中,子分类器的权重分配一直未能充分利用空间视觉信息,使得分类器的可视化特性无法完全得到发挥.本文从类空间类别分布特性出发,提出基于类空间规整度的权重分配方法.该方法首先将子分类器由空间的类别表示转变为类别的空间表示,进而利用共生原则分析不同类别在空间中的分布规整度.由于分布规整度为类别分布信息的整体体现,可以用于刻画类空间中不同类别样本的离散程度,因此可以利用当前类空间的规整度信息作为该子分类器的权重.实验表明,利用规整度信息进行加权后的分类器不但与可视化特性更好的吻合,增强了分类过程的可理解性,而且在分类精度上得到了进一步的提升,扩展了应用领域.%In all the tissues about computational geometry combining classifier, the weight calculation for sub classifiers has not taken the advantage of visual information in the spaces, which retains the visual performance about classifier. According to the category distribution in class space, a weight calculation method based on space regulation is proposed. In this method, the space is turned from category information in space to space information in category. And the space regularity is obtained from the later based on co occur rules. As the regularity reflects the distribution of categories and describes the separation of the samples, which makes it as the weight for the sub classifier. The experiments show that the classifier weighted by the regularity not only enhance the visual performance, but also the classify performance of the classifier. It means that the comprehensibility of the classifier is enhanced and the application of the classifier is extended.

  1. Nonclassical Problem for Ultraparabolic Equation in Abstract Spaces

    Directory of Open Access Journals (Sweden)

    Gia Avalishvili

    2016-01-01

    Full Text Available Nonclassical problem for ultraparabolic equation with nonlocal initial condition with respect to one time variable is studied in abstract Hilbert spaces. We define the space of square integrable vector-functions with values in Hilbert spaces corresponding to the variational formulation of the nonlocal problem for ultraparabolic equation and prove trace theorem, which allows one to interpret initial conditions of the nonlocal problem. We obtain suitable a priori estimates and prove the existence and uniqueness of solution of the nonclassical problem and continuous dependence upon the data of the solution to the nonlocal problem. We consider an application of the obtained abstract results to nonlocal problem for ultraparabolic partial differential equation with second-order elliptic operator and obtain well-posedness result in Sobolev spaces.

  2. Space space space

    CERN Document Server

    Trembach, Vera

    2014-01-01

    Space is an introduction to the mysteries of the Universe. Included are Task Cards for independent learning, Journal Word Cards for creative writing, and Hands-On Activities for reinforcing skills in Math and Language Arts. Space is a perfect introduction to further research of the Solar System.

  3. Weight Control

    Science.gov (United States)

    ... obese. Achieving a healthy weight can help you control your cholesterol, blood pressure and blood sugar. It ... use more calories than you eat. A weight-control strategy might include Choosing low-fat, low-calorie ...

  4. Weighted Clustering

    DEFF Research Database (Denmark)

    Ackerman, Margareta; Ben-David, Shai; Branzei, Simina

    2012-01-01

    We investigate a natural generalization of the classical clustering problem, considering clustering tasks in which different instances may have different weights.We conduct the first extensive theoretical analysis on the influence of weighted data on standard clustering algorithms in both...... the partitional and hierarchical settings, characterizing the conditions under which algorithms react to weights. Extending a recent framework for clustering algorithm selection, we propose intuitive properties that would allow users to choose between clustering algorithms in the weighted setting and classify...

  5. T2‐Weighted intracranial vessel wall imaging at 7 Tesla using a DANTE‐prepared variable flip angle turbo spin echo readout (DANTE‐SPACE)

    Science.gov (United States)

    Viessmann, Olivia; Li, Linqing; Benjamin, Philip

    2016-01-01

    Purpose To optimize intracranial vessel wall imaging (VWI) at 7T for sharp wall depiction and high boundary contrast. Methods A variable flip angle turbo spin echo scheme (SPACE) was optimized for VWI. SPACE provides black‐blood contrast, but has less crushing effect on cerebrospinal fluid (CSF). However, a delay alternating with nutation for tailored excitation (DANTE) preparation suppresses the signal from slowly moving spins of a few mm per second. Therefore, we optimized a DANTE‐preparation module for 7T. Signal‐to‐noise ratio (SNR), contrast‐to‐noise ratio (CNR), and signal ratio for vessel wall, CSF, and lumen were calculated for SPACE and DANTE‐SPACE in 11 volunteers at the middle cerebral artery (MCA). An exemplar MCA stenosis patient was scanned with DANTE‐SPACE. Results The 7T‐optimized SPACE sequence improved the vessel wall point‐spread function by 17%. The CNR between the wall and CSF was doubled (12.2 versus 5.6) for the DANTE‐SPACE scans compared with the unprepared SPACE. This increase was significant in the right hemisphere (P = 0.016), but not in the left (P = 0.090). The CNR between wall and lumen was halved, but remained at a high value (24.9 versus 56.5). Conclusion The optimized SPACE sequence improves VWI at 7T. Additional DANTE preparation increases the contrast between the wall and CSF. Increased outer boundary contrast comes at the cost of reduced inner boundary contrast. Magn Reson Med 77:655–663, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. PMID:26890988

  6. Birth Weight

    Science.gov (United States)

    ... baby, taken just after he or she is born. A low birth weight is less than 5.5 pounds. A high ... weight is more than 8.8 pounds. A low birth weight baby can be born too small, too early (premature), or both. This ...

  7. 14 CFR 25.1519 - Weight, center of gravity, and weight distribution.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight, center of gravity, and weight... Information Operating Limitations § 25.1519 Weight, center of gravity, and weight distribution. The airplane weight, center of gravity, and weight distribution limitations determined under §§ 25.23 through 25.27...

  8. Is the current pertussis incidence only the results of testing? A spatial and space-time analysis of pertussis surveillance data using cluster detection methods and geographically weighted regression modelling

    Science.gov (United States)

    Kauhl, Boris; Heil, Jeanne; Hoebe, Christian J. P. A.; Schweikart, Jürgen; Krafft, Thomas; Dukers-Muijrers, Nicole H. T. M.

    2017-01-01

    Background Despite high vaccination coverage, pertussis incidence in the Netherlands is amongst the highest in Europe with a shifting tendency towards adults and elderly. Early detection of outbreaks and preventive actions are necessary to prevent severe complications in infants. Efficient pertussis control requires additional background knowledge about the determinants of testing and possible determinants of the current pertussis incidence. Therefore, the aim of our study is to examine the possibility of locating possible pertussis outbreaks using space-time cluster detection and to examine the determinants of pertussis testing and incidence using geographically weighted regression models. Methods We analysed laboratory registry data including all geocoded pertussis tests in the southern area of the Netherlands between 2007 and 2013. Socio-demographic and infrastructure-related population data were matched to the geo-coded laboratory data. The spatial scan statistic was applied to detect spatial and space-time clusters of testing, incidence and test-positivity. Geographically weighted Poisson regression (GWPR) models were then constructed to model the associations between the age-specific rates of testing and incidence and possible population-based determinants. Results Space-time clusters for pertussis incidence overlapped with space-time clusters for testing, reflecting a strong relationship between testing and incidence, irrespective of the examined age group. Testing for pertussis itself was overall associated with lower socio-economic status, multi-person-households, proximity to primary school and availability of healthcare. The current incidence in contradiction is mainly determined by testing and is not associated with a lower socioeconomic status. Discussion Testing for pertussis follows to an extent the general healthcare seeking behaviour for common respiratory infections, whereas the current pertussis incidence is largely the result of testing. More

  9. Interpolation functors and interpolation spaces

    CERN Document Server

    Brudnyi, Yu A

    1991-01-01

    The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...

  10. Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces

    Directory of Open Access Journals (Sweden)

    Toka Diagana

    2012-03-01

    Full Text Available In this article, first we introduce and study the concept of $mathbb{S}_{gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy, which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in $mathbb{S}_{gamma}^p$-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient.

  11. Heat flow and calculus on metric measure spaces with Ricci curvature bounded below - the compact case

    CERN Document Server

    Ambrosio, Luigi; Savaré, Giuseppe

    2012-01-01

    We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.

  12. 加权空间L2W(Rd)上的向量Weyl-Heisenberg标架%Vector Weyl-Heisenberg Frames on Weighted Lebesgue Space L2W(Rd)

    Institute of Scientific and Technical Information of China (English)

    李登峰; 郭运瑞

    2001-01-01

    In this paper, we obtain that there does not exist weyl-heisenberg frames in weighted lebesgue space L2W(Rd) unless weigth function W(x) is essential bounded, I.e. There exists constants A and B such that 0<A< W(x)B<+∞, a.e. X∈Rd.%得到了加权空间L2W(Rd)上不存在Weyl-Heisenberg标架,除非权函数W(t)满足0<AW(x)B<+∞,a.e.,其中A,B为常数。

  13. Atmospheric-Pressure-Spray, Chemical- Vapor-Deposited Thin-Film Materials Being Developed for High Power-to- Weight-Ratio Space Photovoltaic Applications

    Science.gov (United States)

    Hepp, Aloysius F.; Harris, Jerry D.; Raffaelle, Ryne P.; Banger, Kulbinder K.; Smith, Mark A.; Cowen, Jonathan E.

    2001-01-01

    The key to achieving high specific power (watts per kilogram) space photovoltaic arrays is the development of high-efficiency thin-film solar cells that are fabricated on lightweight, space-qualified substrates such as Kapton (DuPont) or another polymer film. Cell efficiencies of 20 percent air mass zero (AM0) are required. One of the major obstacles to developing lightweight, flexible, thin-film solar cells is the unavailability of lightweight substrate or superstrate materials that are compatible with current deposition techniques. There are two solutions for working around this problem: (1) develop new substrate or superstrate materials that are compatible with current deposition techniques, or (2) develop new deposition techniques that are compatible with existing materials. The NASA Glenn Research Center has been focusing on the latter approach and has been developing a deposition technique for depositing thin-film absorbers at temperatures below 400 C.

  14. 14 CFR 25.25 - Weight limits.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight limits. 25.25 Section 25.25 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY AIRPLANES Flight General § 25.25 Weight limits. (a) Maximum weights....

  15. 14 CFR 27.25 - Weight limits.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight limits. 27.25 Section 27.25 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: NORMAL CATEGORY ROTORCRAFT Flight General § 27.25 Weight limits. (a) Maximum weight. The...

  16. 14 CFR 29.25 - Weight limits.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight limits. 29.25 Section 29.25 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: TRANSPORT CATEGORY ROTORCRAFT Flight General § 29.25 Weight limits. (a) Maximum weight....

  17. 14 CFR 31.14 - Weight limits.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight limits. 31.14 Section 31.14 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: MANNED FREE BALLOONS Flight Requirements § 31.14 Weight limits. (a) The range of weights...

  18. Cryogenic Optical Performance of a Light-weight Mirror Assembly for Future Space Astronomical Telescopes: Optical Test Results and Thermal Optical Model

    Science.gov (United States)

    Eng, Ron; Arnold, William; Baker, Markus A.; Bevan, Ryan M.; Carpenter, James R.; Effinger, Michael R.; Gaddy, Darrell E.; Goode, Brian K.; Kegley, Jeffrey R.; Hogue, William D.; Siler, Richard D.; Smith, W. Scott; Stahl. H. Philip; Tucker, John M.; Wright, Ernest R.; Kirk, Charles S.; Hanson, Craig; Burdick, Gregory; Maffett, Steven

    2013-01-01

    A 40 cm diameter mirror assembly was interferometrically tested at room temperature down to 250 degrees Kelvin for thermal deformation. The 2.5 m radius of curvature spherical mirror assembly was constructed by low temperature fusing three abrasive waterjet core sections between two face sheets. The 93% lightweighted Corning ULE mirror assembly represents the current state of the art for future UV, optical, near IR space telescopes. During the multiple thermal test cycles, test results of interferometric test, thermal IR images of the front face were recorded in order to validate thermal optical model.

  19. On Weighted Support Vector Regression

    DEFF Research Database (Denmark)

    Han, Xixuan; Clemmensen, Line Katrine Harder

    2014-01-01

    We propose a new type of weighted support vector regression (SVR), motivated by modeling local dependencies in time and space in prediction of house prices. The classic weights of the weighted SVR are added to the slack variables in the objective function (OF‐weights). This procedure directly...... the differences and similarities of the two types of weights by demonstrating the connection between the Least Absolute Shrinkage and Selection Operator (LASSO) and the SVR. We show that an SVR problem can be transformed to a LASSO problem plus a linear constraint and a box constraint. We demonstrate...

  20. On the unboundedness of higher regularity Sobolev norms of solutions for the critical Schrödinger-Debye system with vanishing relaxation delay

    Science.gov (United States)

    Corcho, Adán J.; Drumond Silva, Jorge

    2017-01-01

    We consider the Schrödinger-Debye system in {{{R}}n} , for n  =  3,4. Developing on previously known local well-posedness results, we start by establishing global well-posedness in {{H}1}≤ft({{{R}}3}\\right)× {{L}2}≤ft({{{R}}3}\\right) for a broad class of initial data. We then concentrate on the initial value problem in n  =  4, which is the energy-critical dimension for the corresponding cubic nonlinear Schrödinger equation. We start by proving local well-posedness in {{H}1}≤ft({{{R}}4}\\right)× {{H}1}≤ft({{{R}}4}\\right) . Then, for the focusing case of the system, we derive a virial type identity and use it to prove that for radially symmetric smooth initial data with negative energy, there is a positive time T 0, depending only on the data, for which, either the {{H}1}≤ft({{{R}}4}\\right)× {{H}1}≤ft({{{R}}4}\\right) solutions blow-up in [0, T 0], or the higher regularity Sobolev norms are unbounded on the intervals [0, T ], for T  >  T 0, as the delay parameter vanishes. We finish by presenting a global well-posedness result for regular initial data which is small in the {{H}1}≤ft({{{R}}4}\\right)× {{H}1}≤ft({{{R}}4}\\right) norm.

  1. Assessment of 3D T2-weighted high-sampling-efficiency technique (SPACE) for detection of cerebellar tonsillar motion: new useful sign for Chiari I malformation.

    Science.gov (United States)

    Ucar, Murat; Tokgoz, Nil; Koc, Ali Murat; Kilic, Koray; Borcek, Alp Ozgun; Oner, Ali Yusuf; Kalkan, Gokalp; Akkan, Koray

    2015-01-01

    To describe tonsillar blackout sign (TBS) on three-dimensional (3D)-SPACE, evaluate its performance in identifying Chiari malformation (CM1) as diagnostic marker, and investigate its role in differentiation of symptomatic and asymptomatic CM1. One-hundred fifty-six patients were divided into two groups based on caudal displacement of cerebellar tonsils: CM1 (Group I) and non-CM1 (Group II). Group I was subclassified as symptomatic and asymptomatic by a neurosurgeon. Two radiologists evaluated TBS and cerebrospinal fluid flow abnormality. All subjects presenting TBS had CM1. Difference in presence of TBS between Group I and Group II was highly significant (P<.001).Grading of TBS in symptomatic patients was significantly higher than that in asymptomatic patients (P<.001). TBS is highly suggestive of CM1 and potentially useful in differentiation of symptomatic and asymptomatic CM1. Copyright © 2015 Elsevier Inc. All rights reserved.

  2. BERGMAN TYPE PROJECTIONS ON Lp SPACES

    Institute of Scientific and Technical Information of China (English)

    Kehe Zhu

    2005-01-01

    The paper is a survey on the action of Bergman type projections on various Lp spaces. The focus is on three types of holomorphic function spaces: weighted Bergman spaces, the Bloch space, and diagonal Besov spaces.

  3. Hertz potentials and asymptotic properties of massless fields

    CERN Document Server

    Andersson, Lars; Joudioux, Jérémie

    2013-01-01

    In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.

  4. Biphasic drug absorption from the epidural space of the dog may limit the utility of a slow release medium molecular weight hyaluronic acid-lidocaine ionic complex formulation.

    Science.gov (United States)

    Doherty, M M; Hughes, P J; Charman, S A; Brock, K V; Korszniak, N V; Charman, W N

    1996-12-01

    Previous epidural studies conducted in rabbits have described a viscous lidocaine-hyaluronate formulation (L-HA) that prolonged the duration of sensory blockade twofold and decreased the rate of drug absorption fourfold relative to a solution formulation. As further evaluation of the L-HA formulation required studies in a larger animal that more closely reflected the characteristic absorption kinetics observed in humans, a conscious dog model was used to functionally and kinetically evaluate the viscous formulation relative to lidocaine solution. In terms of the measured pharmacodynamic end point (loss of weight-bearing ability in hind legs), epidural administration of the L-HA formulation did not prolong the duration of action relative to lidocaine solution in spite of a markedly altered pharmacokinetic profile. For example, administration of L-HA reduced the mean plasma lidocaine Cmax value approximately 50% and increased the Tmax value approximately fivefold relative to lidocaine solution. However, the viscous L-HA formulation did cause a significant prolongation in the latency of onset (P lidocaine solution. The dog exhibited "flip-flop" pharmacokinetics and absorption was biphasic after epidural administration of lidocaine solution (apparent t1/2 of the fast and slow absorption phases were 4 min and 131 min, respectively). The L-HA formulation markedly altered the absorption kinetics such that a single, slow absorption phase was evident (apparent t1/2 of 56 min), although this rate was more rapid than the slow phase observed after lidocaine solution. It is possible that the inability of the hyaluronate-based formulation to further reduce the magnitude of the slow absorption phase resulted in the failure to prolong the duration of action. These data highlight the need to carefully consider the absorption kinetics and pharmacokinetic characteristics of the animal models chosen to evaluate new formulation of epidurally administered local anesthetics.

  5. High Chamber Pressure, Light Weight Thrusters Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The performance liquid propellant engines can be significantly improved by increasing both combustion temperature and pressure and reducing engine weight. State of...

  6. Pointwise multipliers for reverse Hölder Spaces

    OpenAIRE

    Buckley, Stephen M.

    1994-01-01

    We classify weights which map reverse Hölder weight spaces to other reverse Hölder weight spaces under pointwise multiplication. We also give some fairly general examples of weights satisfying weak reverse Hölder conditions.

  7. Weighted approximation with varying weight

    CERN Document Server

    Totik, Vilmos

    1994-01-01

    A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.

  8. Toeplitz Operators with L1 Symbols on Weighted Bergman Spaces of the Unit Ball%单位球的加权Bergman空间上具有L1符号的Toeplitz算子

    Institute of Scientific and Technical Information of China (English)

    何莉; 曹广福; 何忠华

    2013-01-01

    讨论了单位球的加权Bergman空间Aρ(Bn,dVα)(1<p<∞)上具有L1(Bn)符号的Toeplitz算子,利用单位球上Toeplitz算子的Berezin变换,等价刻画了Apα(Bn,dVα)上具有L1(Bn)符号的Toeplitz算子的有界性和紧性,推广了Agbor对L2a(D,dA)上具有L1(D)符号的Toeplitz算子的有界性和紧性等价刻画的结论.%We investigate the boundedness and compactness of Toeplitz operators with L1 symbols on weighted Bergman spaces of the unit ball Apα(Bn,dVα) (1 < p < ∞). We describe the boundedness and compactness of Toeplitz operators with L1 symbols on Apα(Bn,dVα) equivalently by using the Berezin transform of the Toeplitz operators, and promote the conclusion given by Agbor about the boundedness and compactness of Toeplitz operators with L1 symbols on Bergman space of the unit disk L2a(D).

  9. 基于判别空间条件熵加权的土地覆盖分类方法研究%A Weighted Method Using Conditional Entropy for Land Cover Mapping Based on Discriminant Space Model

    Institute of Scientific and Technical Information of China (English)

    游炯; 张景雄

    2012-01-01

    针对遥感专题类别信息的机理问题,从土地覆盖参考数据的偏差程度对分类精度的影响角度,提出了一种基于判别空间条件熵加权的土地覆盖分类方法.引入判别空间模型概念,基于此模型生成土地覆盖数据类别,并分析了土地覆盖信息类别与数据类别的语义偏差出现的深层次原因;计算信息类别与数据类别的对应关系矩阵,据此得到二者的条件熵,实现对土地覆盖信息类别与数据类别的语义偏差的量化;根据信息类别与数据类别的条件熵计算修正判别变量的权重因子,实现基于判别空间条件熵加权的土地覆盖分类.采用一景SPOT-5影像进行分类实验,并利用同一地区的Landsat 5 TM影像进行方法验证.实验表明,条件熵加权修正方法使土地覆盖分类精度有了显著提高,并对不同分辨率的遥感影像具有适用性.%In allusion to problems on the mechanism of thematic category information of remote sensing,and on the consideration of the semantic bias existed in different land cover reference data which has large influence on the classification accuracy, a weighted method using conditional entropy for land cover mapping based on discriminant space model is suggested in this paper. Discriminant space models,according to which land cover with respect to data classes can be generated,are introduced. Based on these models in discriminant space, the deep seated reasons of the semantic bias existed between land cover with respect to information classes and data classes are analyzed. Correspondence matrix between land cover with respect to information classes and data classes is generated,and the conditional entropies of land cover types with respect to information classes and data classes are also obtained, which realize the quantification of the semantic bias existed between land cover with respect to information classes and data classes. Then,weight factors to realize discriminant

  10. 14 CFR 23.25 - Weight limits.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight limits. 23.25 Section 23.25 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS STANDARDS: NORMAL, UTILITY, ACROBATIC, AND COMMUTER CATEGORY AIRPLANES Flight General § 23.25 Weight...

  11. Derived autoequivalences and a weighted Beilinson resolution

    Science.gov (United States)

    Canonaco, Alberto; Karp, Robert L.

    2008-06-01

    Given a smooth stacky Calabi-Yau hypersurface X in a weighted projective space, we consider the functor G which is the composition of the following two autoequivalences of D(X): the first one is induced by the spherical object OX, while the second one is tensoring with OX(1). The main result of the paper is that the composition of G with itself w times, where w is the sum of the weights of the weighted projective space, is isomorphic to the autoequivalence "shift by 2". The proof also involves the construction of a Beilinson type resolution of the diagonal for weighted projective spaces, viewed as smooth stacks.

  12. Adaptive Weighting in Radio Interferometric Imaging

    CERN Document Server

    Yatawatta, Sarod

    2014-01-01

    Radio interferometers observe the Fourier space of the sky, at locations determined by the array geometry. Before a real space image is constructed by a Fourier transform, the data is weighted to improve the quality of reconstruction. Two criteria for calculation of weights are maximizing sensitivity and minimizing point spread function (PSF) sidelobe levels. In this paper, we propose a novel weighting scheme suitable for ultra deep imaging experiments. The proposed weighting scheme is used to maximize sensitivity while minimizing PSF sidelobe variation across frequency and multiple epochs. We give simulation results that show the superiority of the proposed scheme compared with commonly used weighting schemes in achieving these objectives.

  13. Bessel Weighted Asymmetries

    Energy Technology Data Exchange (ETDEWEB)

    Avakian, Harut [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Gamberg, Leonard [Pennsylvania State Univ., University Park, PA (United States); Rossi, Patrizia [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Prokudin, Alexei [Pennsylvania State Univ., University Park, PA (United States)

    2016-05-01

    We review the concept of Bessel weighted asymmetries for semi-inclusive deep inelastic scattering and focus on the cross section in Fourier space, conjugate to the outgoing hadron’s transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. The procedure is applied to studies of the double longitudinal spin asymmetry in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator which includes quark intrinsic transverse momentum within the generalized parton model. We observe a few percent systematic offset of the Bessel-weighted asymmetry obtained from Monte Carlo extraction compared to input model calculations, which is due to the limitations imposed by the energy and momentum conservation at the given energy and hard scale Q2. We find that the Bessel weighting technique provides a powerful and reliable tool to study the Fourier transform of TMDs with controlled systematics due to experimental acceptances and resolutions with different TMD model inputs.

  14. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni Soolaladu: "Cweesti" (maastikuarhitektuur- ruum mere ja maa piiril); Tarbekunstimuuseum: "Pro Arte" (soome nüüdisaegse käsitöö näitus); Linnagalerii Tallinnas: Eve Kask "29 1Ü2"; Sammas-galerii: Rene Kari maalid; Kunstihoone galerii: Anne Türn "Hundid" (keraamika); Tammsaare muuseum. Karl Manbergi maalid ja pisiplastika (1914 Tallinn - 1993 Sidney); Eesti Loodusmuuseum: Marielle Liiveti maalid ja kompositsioonid; Raatus-galerii. "Euroopa koolis".

  15. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni soolaladu: 'Private Views. Taas/ avastatud ruum eesti ja briti kaasaegses kunstis'; Tarbekunstimuuseum: 'Lilled, liblikad ja...' (1970. a.-te tarbekunst); Adamson-Ericu muuseum: Mare Saare "...algus on lõpp on algus..." (klaasikunst); Raatuse galerii: Andrus Koort. Maalid; Pärnu Rannasalong:' Pärnu kuurort 160'; Nõmme galerii Marquise: Arnold Laugus (s. 1917) 'Eestimaa maastikud' (maalikunst); Tallinna Ärikeskus: Raivo V. Raam 'India-Nepaal aastal 199 999'; Rahvusraamatukogu: Fotonäitus Lübeckist.

  16. Sovhoos sinus eneses / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2001-01-01

    9.-11. VIII Moostes toimunud Evelyn Müürsepa ja Maia Mölleri korraldatud kultuurisündmusest "Postsovkhoz City & Postsovkhoz Person", mis püüdis praeguses eesti külas toimuvat lahti mõtestada. Esinejatest, ettekannetest, kunstinäitustest

  17. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni soolaladu. "Elektrokardiogramm" (tegevuskunsti üritus); Vaal-galerii. Antoni T̉pies "Litograafiaid aastatest 1973-1995"; Mari Kadanik, Eero Barndõk, Rain Ader "Pildid" (maalid); Paldiski Põhikool. "Niemenlautta ja Hugo Simbergi fotod" (soome kunstniku fotode koopiad, pildistatud enne 1915. a.; Kullo lastegalerii. Neli uut näitust.(lastekunst); Arhitektuurimuuseum. Arnold Matteus - Tartu linna arhitekt (juubelinäitus), Alvar Aalto "Kolm objekti Eestis"; Linnagalerii Tallinnas. "Valge" (ruumi- ja moekunsti näitus); Sammas-galerii. Jüri Jegorow "Insect" (arvutigraafika); Endla Teatri palmisaal. "Muzik in der Kunst" (Tallinna kunstitudengite näitus); Eesti Rahvusraamatukogu. Õie Kütt "Uued ja vanad ehted"

  18. Sovhoos sinus eneses / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2001-01-01

    9.-11. VIII Moostes toimunud Evelyn Müürsepa ja Maia Mölleri korraldatud kultuurisündmusest "Postsovkhoz City & Postsovkhoz Person", mis püüdis praeguses eesti külas toimuvat lahti mõtestada. Esinejatest, ettekannetest, kunstinäitustest

  19. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Linnagalerii Tallinnas: Urmas Viik 'Uudistoodang' (graafika); Rahvusraamatukogu: Maurits C. Escheri repoduktsioonid (graafika reprod); La Galerie Passage: Kamille Saabre 'The Whole Story' (maalid); Eesti Kunstimuuseum: 'Akantus norra rahvakunstis'; EKA galerii: Üldmaali õppetooli üliõpilaste maalinäitus; PRO Kapitali ärikeskus: Benjamin Vassermani graafika

  20. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Vaal-galerii: Peeter Laurits "Taeva Atlas" (gigitaaltehnoloogias kollaazhid); Sammas-galerii: "Maailma nägu"; Tartu Kunstimaja: "Viljandi kunstipäevad Tartus"; Estonia Talveaed: Mall Mets&Erika Pedak "Due Canzoni" (vaibakunst).

  1. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Kunstihoone ja Rotermanni soolaladu: "Kujundid, objektid, stseenid - vaatenurki prantsuse kunstile alates 1978. aastast"; Sammas-galerii: Tiiu Rebane ja Karl Nagel "Tänapäeva müüt"; Raatuse galerii: Elo Järv "Saavad uuteks liblikateks" (nahakunst); Tammsaare muuseum: "Mis jääb mällu" (sissevaade Saksamaa ajalukku ajavahemikul 1933-1949); Hotell "Olümpia" Forte saal: Gabor Dienesi personaalnäitus (maalid)

  2. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Tallinna XI graafikatriennaal. Rotermanni soolaladu: "Puudutus"; Kunstihoone: "Puutujad"; Rahvusraamatukogu: Laste ja noorte graafikanäitus; Kastellaanimaja galerii: Wim Lamboo (s. 1949) "Eesti kunstnike portreed 1997" (fotograafia); Tallinna Botaanikaaed: "Maised rõõmud"; Rahvusraamatukogu: Antanas Sutkus (s. 1939) "Pro memoria" (fotograafia); Tammsaare majamuuseum: Eve Pärnaste "Ülelend" (maalid); Haapsalu Linnagalerii: Paul Allik "Seisundid" (aktimaalid).

  3. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Stockholmi Kultuurikeskus: "ArtGenda 98". Eestist E.-L. Semper, M. Laimre, A. Kõresaar, M. Pedanik; Deco galerii: Jüri Kask "Pinsliga ja pinslita"; Kastellaanimaja &Tammsaare muuseum: "(Meta)dialoog" (R. Varblase ideenäitus); Viru tänav: "Territoorium"; Eesti Kunstiakadeemia galerii: "Tervitus Iisrealile"; Raatuse galerii: M. Helm "Talv kevades"; Linnagalerii Tallinnas: K. Puustak "Lained"; Sammas-galerii: Elna Kaasik&Ingrid Allik "Maa vee tee".

  4. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni soolaladu: 'Private Views. Taas/ avastatud ruum eesti ja briti kaasaegses kunstis'; Tarbekunstimuuseum: 'Lilled, liblikad ja...' (1970. a.-te tarbekunst); Adamson-Ericu muuseum: Mare Saare "...algus on lõpp on algus..." (klaasikunst); Raatuse galerii: Andrus Koort. Maalid; Pärnu Rannasalong:' Pärnu kuurort 160'; Nõmme galerii Marquise: Arnold Laugus (s. 1917) 'Eestimaa maastikud' (maalikunst); Tallinna Ärikeskus: Raivo V. Raam 'India-Nepaal aastal 199 999'; Rahvusraamatukogu: Fotonäitus Lübeckist.

  5. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Raatuse galerii: Kiwa. "Muzik at Vremja of my Võhod"; Tarbekunstimuuseum: Malle Agabush "Valgusega ajast aega"; EKM Jõhvi filiaal: Eduard Ole 100. sünniaastapäeva näitus; Rahvusraamatukogu: Eesti Akvarellistide Ühenduse aastanäitus; Eesti Rahva Muuseum: "Tulest jäänu" ja "Post textile"; Sammas-galerii: Helmet Raja&Karl Martin Sinijärv

  6. "OUT" elab edasi / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    "OUT'98". Kuraatorid Eve Kiiler, Piret Räni. Otsingutest videovallas (I. Helander, A. Nali, K. Sukmit, M. Laanemets, J. Zoova). Näidati ka Tokio vodeofestivalil hõbepreemia saanud R. Kelomehe videot "House". [þmobil]-galerii saatusest.

  7. Vaimne dotatsioon meediaikaldusele / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Seoses Eesti Kunstimuuseumis toimunud näitusega "Medialization" 22.-23. nov. Eesti Kunstiakadeemias korraldatud meediakonverentsist 'Action ئ Reflection'. Korraldaja Ando Keskküla. Eric Kluitenbergi (Holland), Tapio Mäkela (Soome) ja Hanno Soansi ettekannetest. Avatud kanalist.

  8. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni soolaladu. "Elektrokardiogramm" (tegevuskunsti üritus); Vaal-galerii. Antoni T̉pies "Litograafiaid aastatest 1973-1995"; Mari Kadanik, Eero Barndõk, Rain Ader "Pildid" (maalid); Paldiski Põhikool. "Niemenlautta ja Hugo Simbergi fotod" (soome kunstniku fotode koopiad, pildistatud enne 1915. a.; Kullo lastegalerii. Neli uut näitust.(lastekunst); Arhitektuurimuuseum. Arnold Matteus - Tartu linna arhitekt (juubelinäitus), Alvar Aalto "Kolm objekti Eestis"; Linnagalerii Tallinnas. "Valge" (ruumi- ja moekunsti näitus); Sammas-galerii. Jüri Jegorow "Insect" (arvutigraafika); Endla Teatri palmisaal. "Muzik in der Kunst" (Tallinna kunstitudengite näitus); Eesti Rahvusraamatukogu. Õie Kütt "Uued ja vanad ehted"

  9. Kurvitz ehitab katedraali / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1999-01-01

    Raoul Kurvitza näitus 'Sümfoonia si-bemoll minoor' alapealkirjaga 'Postapokalüptika'. Näitus on eksponeeritud Kunstihoone galeriis, Kunstihoone suures saalis ja Vabaduse väljakul. Ekspositsioon sisaldab 16 projekti, nende seas 2 videoinstallatsiooni, arvutiinstallatsioon, 3 maalisarja, mitmesuguseid objekte.

  10. Vaimne dotatsioon meediaikaldusele / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Seoses Eesti Kunstimuuseumis toimunud näitusega "Medialization" 22.-23. nov. Eesti Kunstiakadeemias korraldatud meediakonverentsist 'Action ئ Reflection'. Korraldaja Ando Keskküla. Eric Kluitenbergi (Holland), Tapio Mäkela (Soome) ja Hanno Soansi ettekannetest. Avatud kanalist.

  11. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Tallinna XI graafikatriennaal. Rotermanni soolaladu: "Puudutus"; Kunstihoone: "Puutujad"; Rahvusraamatukogu: Laste ja noorte graafikanäitus; Kastellaanimaja galerii: Wim Lamboo (s. 1949) "Eesti kunstnike portreed 1997" (fotograafia); Tallinna Botaanikaaed: "Maised rõõmud"; Rahvusraamatukogu: Antanas Sutkus (s. 1939) "Pro memoria" (fotograafia); Tammsaare majamuuseum: Eve Pärnaste "Ülelend" (maalid); Haapsalu Linnagalerii: Paul Allik "Seisundid" (aktimaalid).

  12. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni Soolaladu: "Cweesti" (maastikuarhitektuur- ruum mere ja maa piiril); Tarbekunstimuuseum: "Pro Arte" (soome nüüdisaegse käsitöö näitus); Linnagalerii Tallinnas: Eve Kask "29 1Ü2"; Sammas-galerii: Rene Kari maalid; Kunstihoone galerii: Anne Türn "Hundid" (keraamika); Tammsaare muuseum. Karl Manbergi maalid ja pisiplastika (1914 Tallinn - 1993 Sidney); Eesti Loodusmuuseum: Marielle Liiveti maalid ja kompositsioonid; Raatus-galerii. "Euroopa koolis".

  13. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni soolaladu: Mark Raidpere ja Ene-Liis Semper "Mäng 4. käel"; Kunstihoone: Tony Craggi skulptuurid; Adamson-Ericu muuseum: Eduard Ole 100. sünniaastapäevale pühendatud näitus; Kastellaanimaja galerii: "Tee Raamat": Anu Purre kirjutus-kunstistuudio EKSTEKST GRUPP ja stuudio sõprade näitus (T-särkidest raamat-installatsioonid); Tervishoiumuuseum: "In vino..."; Tammsaare muuseum:"Tiibeti muistne kultuur. Hiina maastikud"; Kullo galerii: Huvikeskuse Kullo aastanäitus.

  14. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Rotermanni soolaladu: Mark Raidpere ja Ene-Liis Semper "Mäng 4. käel"; Kunstihoone: Tony Craggi skulptuurid; Adamson-Ericu muuseum: Eduard Ole 100. sünniaastapäevale pühendatud näitus; Kastellaanimaja galerii: "Tee Raamat": Anu Purre kirjutus-kunstistuudio EKSTEKST GRUPP ja stuudio sõprade näitus (T-särkidest raamat-installatsioonid); Tervishoiumuuseum: "In vino..."; Tammsaare muuseum:"Tiibeti muistne kultuur. Hiina maastikud"; Kullo galerii: Huvikeskuse Kullo aastanäitus.

  15. Näitused / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Linnagalerii Tallinnas: Urmas Viik 'Uudistoodang' (graafika); Rahvusraamatukogu: Maurits C. Escheri repoduktsioonid (graafika reprod); La Galerie Passage: Kamille Saabre 'The Whole Story' (maalid); Eesti Kunstimuuseum: 'Akantus norra rahvakunstis'; EKA galerii: Üldmaali õppetooli üliõpilaste maalinäitus; PRO Kapitali ärikeskus: Benjamin Vassermani graafika

  16. Improved Multi-antenna Weighting and Space-hopping Secure Communication Technology%一种改进型的多天线加权跳空保密通信技术

    Institute of Scientific and Technical Information of China (English)

    朱磊; 徐家品

    2016-01-01

    The physical layer security of multi⁃antenna communication system has become an important research content of com⁃munication security in recent years.The artificial noise method and antenna array random weighting method of multi⁃antenna secure com⁃munications can realize secure information in a wireless communication system,which guarantees the security at the physical layer of wireless communications.But when the number of eavesdropper antennas are more than or equal to those of the senders,the eavesdropper can intercept signals through Music⁃like.To address this issue,an improved multi⁃antenna array weighting method is proposed.The meth⁃od combines the array weighting method and the space⁃hopping technique, in which the receiver selects the appropriate channel to receive and demodulate according to the generated pattern,but the eavesdropper cannot demodulate the signal since he doesn’ t have the pattern.Even if the eavesdropper knows the space⁃hopping pattern,he cannot obtain the correct message since the artificial noise in zero space cannot be eliminated.%多天线阵列随机加权方法和人工噪声方法可以在物理层保障无线通信的安全。但是,当窃听者天线数大于等于发送者时,窃听者就有可能通过Music⁃like窃取信号。针对此问题,提出了一种改进的多天线阵列加权方法。该方法是通过阵列加权方法和跳空技术相结合,接收者根据生成的跳空图案选择相应信道接收解调,而窃听者没有跳空图案所以不能解调出信号,即使窃听者知道跳空图案,但他不能消除零空间内的人工噪声,窃听者仍然没有办法得到正确的发送信息。仿真结果显示,该方法是一种有效的物理层保密通信方法。

  17. Vassiliev Invariants from Symmetric Spaces

    DEFF Research Database (Denmark)

    Biswas, Indranil; Gammelgaard, Niels Leth

    We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a tangent space. Among the Lie algebra weight systems, they are ......, they are exactly characterized by having the symmetries of the Riemann curvature tensor....

  18. The Existence of Positive Solution to an Elliptic System Involving Sobolev Critical Exponent%一类临界指数增长的椭圆型方程组正解的存在性

    Institute of Scientific and Technical Information of China (English)

    万优艳

    2012-01-01

    研究了一类临界指数增长的椭圆型方程组。通过变分法,得到方程组的能量泛函在零点附近的局部极小值点的存在性,且该极小值点为方程组的正解。证明了当方程组的扰动项趋于零时,方程组的正解也趋于零。%This paper studies an elliptic system involving Sobolev critical exponent. By the variational methods, we can obtain the existence of local minimum point of the energy functional related to the system which is near zero, and the local minimum point is the positive solution to this system. Moreover, It is also proved that this positive solution tends to zero when the perturbed term goes to zero.

  19. Diagnosis of nerve root compromise of the lumbar spine: Evaluation of the performance of three-dimensional isotropic T2-weighted turbo spin-echo SPACE sequence at 3T

    Energy Technology Data Exchange (ETDEWEB)

    Sung, Jin Kyeong; Jee, Won Hee; Jung, Joon Yong; Jang, Jin Hee; Kim, Jin Sung; Kim, Young Hoon; Ha, Kee Yong [Seoul St. Mary' s Hospital, College of Medicine, The Catholic University of Korea, Seoul (Korea, Republic of)

    2017-01-15

    To explore the performance of three-dimensional (3D) isotropic T2-weighted turbo spin-echo (TSE) sampling perfection with application optimized contrasts using different flip angle evolution (SPACE) sequence on a 3T system, for the evaluation of nerve root compromise by disc herniation or stenosis from central to extraforaminal location of the lumbar spine, when used alone or in combination with conventional two-dimensional (2D) TSE sequence. Thirty-seven patients who had undergone 3T spine MRI including 2D and 3D sequences, and had subsequent spine surgery for nerve root compromise at a total of 39 nerve levels, were analyzed. A total of 78 nerve roots (48 symptomatic and 30 asymptomatic sites) were graded (0 to 3) using different MRI sets of 2D, 3D (axial plus sagittal), 3D (all planes), and combination of 2D and 3D sequences, with respect to the nerve root compromise caused by posterior disc herniations, lateral recess stenoses, neural foraminal stenoses, or extraforaminal disc herniations; grading was done independently by two readers. Diagnostic performance was compared between different imaging sets using the receiver operating characteristics (ROC) curve analysis. There were no statistically significant differences (p = 0.203 to > 0.999) in the ROC curve area between the imaging sets for both readers 1 and 2, except for combined 2D and 3D (0.843) vs. 2D (0.802) for reader 1 (p = 0.035), and combined 2D and 3D (0.820) vs. 3D including all planes (0.765) for reader 2 (p = 0.049). The performance of 3D isotropic T2-weighted TSE sequence of the lumbar spine, whether axial plus sagittal images, or all planes of images, was not significantly different from that of 2D TSE sequences, for the evaluation of nerve root compromise of the lumbar spine. Combining 2D and 3D might possibly improve the diagnostic accuracy compared with either one.

  20. Diagnosis of Nerve Root Compromise of the Lumbar Spine: Evaluation of the Performance of Three-dimensional Isotropic T2-weighted Turbo Spin-Echo SPACE Sequence at 3T

    Science.gov (United States)

    Sung, Jinkyeong; Jung, Joon-Yong; Jang, Jinhee; Kim, Jin-Sung; Kim, Young-Hoon; Ha, Kee-Yong

    2017-01-01

    Objective To explore the performance of three-dimensional (3D) isotropic T2-weighted turbo spin-echo (TSE) sampling perfection with application optimized contrasts using different flip angle evolution (SPACE) sequence on a 3T system, for the evaluation of nerve root compromise by disc herniation or stenosis from central to extraforaminal location of the lumbar spine, when used alone or in combination with conventional two-dimensional (2D) TSE sequence. Materials and Methods Thirty-seven patients who had undergone 3T spine MRI including 2D and 3D sequences, and had subsequent spine surgery for nerve root compromise at a total of 39 nerve levels, were analyzed. A total of 78 nerve roots (48 symptomatic and 30 asymptomatic sites) were graded (0 to 3) using different MRI sets of 2D, 3D (axial plus sagittal), 3D (all planes), and combination of 2D and 3D sequences, with respect to the nerve root compromise caused by posterior disc herniations, lateral recess stenoses, neural foraminal stenoses, or extraforaminal disc herniations; grading was done independently by two readers. Diagnostic performance was compared between different imaging sets using the receiver operating characteristics (ROC) curve analysis. Results There were no statistically significant differences (p = 0.203 to > 0.999) in the ROC curve area between the imaging sets for both readers 1 and 2, except for combined 2D and 3D (0.843) vs. 2D (0.802) for reader 1 (p = 0.035), and combined 2D and 3D (0.820) vs. 3D including all planes (0.765) for reader 2 (p = 0.049). Conclusion The performance of 3D isotropic T2-weighted TSE sequence of the lumbar spine, whether axial plus sagittal images, or all planes of images, was not significantly different from that of 2D TSE sequences, for the evaluation of nerve root compromise of the lumbar spine. Combining 2D and 3D might possibly improve the diagnostic accuracy compared with either one. PMID:28096733

  1. Moduli of weighted hyperplane arrangements

    CERN Document Server

    Lahoz, Martí; Macrí, Emanuele; Stellari, Paolo

    2015-01-01

    This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements.

  2. Weighted norm inequalities and indices

    Directory of Open Access Journals (Sweden)

    Joaquim Martín

    2006-01-01

    Full Text Available We extend and simplify several classical results on weighted norm inequalities for classical operators acting on rearrangement invariant spaces using the theory of indices. As an application we obtain necessary and sufficient conditions for generalized Hardy type operators to be bounded on ?p(w, ?p,8(w, Gp(w and Gp,8(w.

  3. Quantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces

    Directory of Open Access Journals (Sweden)

    Sergey Ajiev

    2013-05-01

    Full Text Available We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of Hölder-Lipschitz mappings. Abstract results are further applied to the spaces and pairs from the wide classes IG and IG+ and non-commutative Lp-spaces. The intimate relation between the subspaces and quotients of the IG-spaces on one side and various types of anisotropic Besov, Lizorkin-Triebel and Sobolev spaces of functions on open subsets of an Euclidean space defined in terms of differences, local polynomial approximations, wavelet decompositions and other means (as well as the duals and the lp-sums of all these spaces on the other side, allows us to present the algorithm of extending the main results of the article to the latter spaces and pairs. Special attention is paid to the matter of sharpness. Our approach is quasi-Euclidean in its nature because it relies on the extrapolation of properties of Hilbert spaces and the study of 1-complemented subspaces of the spaces under consideration.

  4. Radial volumetric imaging breath-hold examination (VIBE) with k-space weighted image contrast (KWIC) for dynamic gadoxetic acid (Gd-EOB-DTPA)-enhanced MRI of the liver: advantages over Cartesian VIBE in the arterial phase

    Energy Technology Data Exchange (ETDEWEB)

    Fujinaga, Yasunari; Ohya, Ayumi; Tokoro, Hirokazu; Yamada, Akira; Ueda, Kazuhiko; Kadoya, Masumi [Shinshu University School of Medicine, Department of Radiology, Matsumoto (Japan); Ueda, Hitoshi; Kitou, Yoshihiro; Adachi, Yasuo; Shiobara, Aya; Tamaru, Naomichi [Radiology Division of Shinshu University Hospital, Matsumoto (Japan); Nickel, Marcel D. [Siemens AG Healthcare Sector, H IM MR PI TIO Oncology, Erlangen (Germany); Maruyama, Katsuya [Siemens Japan. K. K., Imaging and Therapy Systems Division, Shinagawa, Tokyo (Japan)

    2014-06-15

    To compare radial volumetric imaging breath-hold examination with k-space weighted image contrast reconstruction (r-VIBE-KWIC) to Cartesian VIBE (c-VIBE) in arterial phase dynamic gadoxetic acid (Gd-EOB-DTPA)-enhanced magnetic resonance imaging (DCE-MRI) of the liver. We reviewed 53 consecutive DCE-MRI studies performed on a 3-T unit using c-VIBE and 53 consecutive cases performed using r-VIBE-KWIC with full-frame image subset (r-VIBE{sub full}) and sub-frame image subsets (r-VIBE{sub sub}; temporal resolution, 2.5-3 s). All arterial phase images were scored by two readers on: (1) contrast-enhancement ratio (CER) in the abdominal aorta; (2) scan timing; (3) artefacts; (4) visualisation of the common, right, and left hepatic arteries. Mean abdominal aortic CERs for c-VIBE, r-VIBE{sub full}, and r-VIBE{sub sub} were 3.2, 4.3 and 6.5, respectively. There were significant differences between each group (P < 0.0001). The mean score for c-VIBE was significantly lower than that for r-VIBE{sub full} and r-VIBE{sub sub} in all factors except for visualisation of the common hepatic artery (P < 0.05). The mean score of all factors except for scan timing for r-VIBE{sub sub} was not significantly different from that for r-VIBE{sub full}. Radial VIBE-KWIC provides higher image quality than c-VIBE, and r-VIBE{sub sub} features high temporal resolution without image degradation in arterial phase DCE-MRI. circle Radial VIBE-KWIC minimised artefact and produced high-quality and high-temporal-resolution images. circle Maximum abdominal aortic enhancement was observed on sub-frame images of r-VIBE-KWIC. (orig.)

  5. Some Properties of Weighted Pseudo almost Periodic Functions

    Directory of Open Access Journals (Sweden)

    Zhe-Ming Zheng

    2013-01-01

    Full Text Available Several interesting and new properties of weighted pseudo almost periodic functions are established. Firstly, we obtain an equivalent definition for weighted pseudo almost periodic functions, which shows a close relationship between asymptotically almost periodic functions and weighted pseudo almost periodic functions; secondly, we prove that the space of asymptotically almost periodic functions is always a proper subspace of the space of weighted pseudo almost periodic functions; thirdly, we show that under some cases, the space of weighted pseudo almost periodic functions equals the classical space of pseudo almost periodic functions.

  6. 14 CFR 27.1519 - Weight and center of gravity.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight and center of gravity. 27.1519 Section 27.1519 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION... Operating Limitations § 27.1519 Weight and center of gravity. The weight and center of gravity limitations...

  7. 14 CFR 23.1519 - Weight and center of gravity.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight and center of gravity. 23.1519 Section 23.1519 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION... Limitations and Information § 23.1519 Weight and center of gravity. The weight and center of gravity...

  8. 14 CFR 29.1519 - Weight and center of gravity.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Weight and center of gravity. 29.1519 Section 29.1519 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION... Operating Limitations § 29.1519 Weight and center of gravity. The weight and center of gravity limitations...

  9. The Dirichlet problem with L2-boundary data for elliptic linear equations

    CERN Document Server

    Chabrowski, Jan

    1991-01-01

    The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known. In the last decade the Dirichlet problem with L2-boundary data has attracted the attention of several mathematicians. The significant features of this recent research are the use of weighted Sobolev spaces, existence results for elliptic equations under very weak regularity assumptions on coefficients, energy estimates involving L2-norm of a boundary data and the construction of a space larger than the usual Sobolev space W1,2 such that every L2-function on the boundary of a given set is the trace of a suitable element of this space. The book gives a concise account of main aspects of these recent developments and is intended for researchers and graduate students. Some basic knowledge of Sobolev spaces and measure theory is required.

  10. High Toughness Light Weight Pressure Vessel Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Proposed is a pressure vessel with 25% better Fracture Strength over equal strength designed Fiberglass to help reduce 10 to 25% weight for aerospace use. Phase I is...

  11. Cauchy problem of semi-linear parabolic equations with weak data in homogeneous space and application to the Navier-Stokes equations

    Institute of Scientific and Technical Information of China (English)

    苗长兴

    2003-01-01

    In this paper we study the Cauchy problem for a class of semi-linear parabolic type equations withweak data in the homogeneous spaces. We give a method which can be used to construct local mild solutionsof the abstract Cauchy problem in Cσ,s,p and Lq([O, T);Hs,p) by introducing the concept of both admissiblequintuplet and compatible space and establishing time-space estimates for solutions to the linear parabolic typeequations. For the small data, we prove that these results can be extended globally in time. We also study theregularity of the solution to the abstract Cauchy problem for nonlinear parabolic type equations in Cσ,s,p. Asan application, we obtain the same result for Navier-Stokes equations with weak initial data in homogeneousSobolev spaces.

  12. Dynamical Systems On Weighted Lattices: General Theory

    OpenAIRE

    Maragos, Petros

    2016-01-01

    In this work a theory is developed for unifying large classes of nonlinear discrete-time dy- namical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces which we call complete weighted lat- tices and include as special cases the nonlinear vector spaces of minimax algebra. Their algebraic structure has a polygonal geometry. Some of the special cases unified include max-plus, max- product, and probabilistic...

  13. Space Food

    Science.gov (United States)

    1994-01-01

    In planning for the long duration Apollo missions, NASA conducted extensive research into space food. One of the techniques developed was freeze drying. Action Products commercialized this technique, concentrating on snack food including the first freeze-dried ice cream. The foods are cooked, quickly frozen and then slowly heated in a vacuum chamber to remove the ice crystals formed by the freezing process. The final product retains 98 percent of its nutrition and weighs only 20 percent of its original weight. Action snacks are sold at museums, NASA facilities and are exported to a number of foreign countries. Sales run to several million dollars annually.

  14. THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES

    Institute of Scientific and Technical Information of China (English)

    2006-01-01

    In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.

  15. Small Valdivia compact spaces

    CERN Document Server

    Kubi's, W; Kubi\\'s, Wieslaw; Michalewski, Henryk

    2005-01-01

    We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\\loe\\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.

  16. Thyroid and Weight

    Science.gov (United States)

    ... weight) weight loss. As in the treatment with hyperthyroidism, treatment of the abnormal state of hypothyroidism with thyroid ... Goiter Graves’ Disease Graves’ Eye Disease Hashimoto’s Thyroiditis Hyperthyroidism ... & Weight Thyroiditis Thyroid ...

  17. Weight Loss Surgery

    Science.gov (United States)

    Weight loss surgery helps people with extreme obesity to lose weight. It may be an option if you ... caused by obesity. There are different types of weight loss surgery. They often limit the amount of food ...

  18. Functional analysis and applied optimization in Banach spaces applications to non-convex variational models

    CERN Document Server

    Botelho, Fabio

    2014-01-01

    This book introduces the basic concepts of real and functional analysis. It presents the fundamentals of the calculus of variations, convex analysis, duality, and optimization that are necessary to develop applications to physics and engineering problems. The book includes introductory and advanced concepts in measure and integration, as well as an introduction to Sobolev spaces. The problems presented are nonlinear, with non-convex variational formulation. Notably, the primal global minima may not be attained in some situations, in which cases the solution of the dual problem corresponds to an appropriate weak cluster point of minimizing sequences for the primal one. Indeed, the dual approach more readily facilitates numerical computations for some of the selected models. While intended primarily for applied mathematicians, the text will also be of interest to engineers, physicists, and other researchers in related fields.

  19. 14 CFR 31.16 - Empty weight.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Empty weight. 31.16 Section 31.16 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRWORTHINESS... determined by weighing the balloon with installed equipment but without lifting gas or heater fuel. ...

  20. 非线性Sobolev型方程一个新的非协调混合有限元格式%A New Nonconforming Mixed Finite Element Scheme for Nonlinear Sobolev Equations

    Institute of Scientific and Technical Information of China (English)

    石东洋; 王乐乐

    2012-01-01

    A new mixed finite element scheme was established, by applying a Crouzeix-Raviart type non-conforming linear triangular finite element to the nonlinear Sobolev equations, which had the advantages of simple structure, BB condition to be satisfied automatically and so on. At the same time, the optimal error estimates of related variables were obtained directly by utilizing the special properties of the interpolation on the element, instead of the general Ritz projection which was the essential tool in the traditional finite element analysis.%将Crouzeix-Raviart型非协调线性三角形元应用于非线性Sobolev方程,建立了一种新的混合元格式,它具有构造简单且BB条件自动满足等优势.同时,在摆脱传统有限元分析中广义Ritz投影这一必不可少工具的情形下,直接利用单元上插值的特殊性质,得到了相关变量的最优误差估计.

  1. Higher Accuracy Analysis for the Anisotropic Carey Element Solution to Sobolev Type Equation%Sobolev型方程各向异性Carey元解的高精度分析

    Institute of Scientific and Technical Information of China (English)

    石东洋; 郝晓斌

    2009-01-01

    By using the integral identities and the interpolation postprocessing technique, the higher accuracy approximation of the anisotropic nonconforming Carey element for solving the Sobolev type equations is investigated. Firstly, the interpolation operator is constructed, the superclose, global superconvergence and posteriori error estimate are obtained with the help of the distinct property of Carey elements, i.e., the linear interpolation of the solution for Carey elements is equal to the solution for linear triangular element. Secondly, by virtue of the extrapolation method, the accuracy of the related approximate solution with fourth order is derived through the asymptotic error expansion.%利用积分恒等式和插值后处理技术,本文在各向异性网格上对Sobolev型方程的Carey非协调有限元解进行高精度算法分析.首先,根据Carey元的特性,即其有限元解的线性插值和线性元解相同,我们构造插值后处理算子,得到了有限元解的超逼近性质和整体超收敛及后验误差估计.接着,根据误差渐近展开式,运用外推方法,进一步得到了具有四阶精度的近似解.

  2. Boundedness and regularity of solutions of degenerate elliptic partial differential equations

    Science.gov (United States)

    Chua, Seng-Kee

    2017-10-01

    We study quasilinear degenerate equations with their associated operators satisfying Sobolev and Poincaré inequalities. Our problems are similar to those in Sawyer and Wheeden (2006) [20], but we consider more general integral equations on abstract Sobolev spaces. Indeed, we provide a unified approach via abstract setting. Our main tool is Moser iteration. We obtain boundedness (assuming a weighted Sobolev embedding) of weak solutions and also Harnack inequalities for nonnegative solutions (assuming further that a weighted Poincaré inequality holds for their logarithm and existence of a sequence of cutoff functions) and hence Hölder's continuity of solutions. Our assumption is weaker than the above mentioned paper and other existing papers even in the case where the setting is on Rn; for example, we do not assume any doubling condition and we are able to deal with weighted estimates. Our results are new even when the leading term in the equations are vector fields that satisfy Hörmander's conditions.

  3. The wave equation on static singular space-times

    CERN Document Server

    Mayerhofer, Eberhard

    2006-01-01

    The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis evolved from the main topic, the wave equation on singular space-times. The second and main part of my thesis is devoted to establishing a local existence and uniqueness theorem for the wave equation on singular space-times. The singular Lorentz metric subject to our discussion is modeled within the special algebra on manifolds in the sense of Colombeau. Inspired by an approach to generalized hyperbolicity of conical-space times due to Vickers and Wilson, we succeed in establishing certain energy estimates, which by a further elaborated equivalence of energy integrals and Sobolev norms allow us to prove existence and uniqueness of local generalized solutions of the wave equation with respect to a wide class of generalized metrics. The third part of my thesis treats three diff...

  4. Association between Greenness, Urbanicity, and Birth Weight

    Science.gov (United States)

    Ebisu, Keita; Holford, Theodore R.; Bell, Michelle L.

    2015-01-01

    Background More than half of the world's population lives in urban environments. Due to urban related factors (e.g. higher air pollution), urban residents may face higher risk of adverse health outcomes, while access to green space could benefit health. Purpose We explored associations between urban and green land-use and birth weight. Methods Connecticut, U.S., birth certificate data (2000-2006) were acquired (n=239,811), and land-use data were obtained from the National Land Cover Database. We focused on three land-uses; urban space, urban open space, and green space (i.e. forest, shrub, herbaceous, and cultivated land). We estimated fractions of greenness and urbanicity within 250 m from residence. A linear mixed effects model was conducted for birth weight and a logistic mixed effects model for low birth weight (LBW) and small for gestational age (SGA). Results An interquartile range (IQR) increment in the fraction of green space within 250 m of residence was associated with 3.2g (95% Confidence Interval [0.4, 6.0]) higher birth weight. Similarly, an IQR increase in green space was associated with 7.6% [2.6, 12.4] decreased risk of LBW. Exposure to urban space was negatively correlated with green space (Pearson correlation = −0.88), and it showed negative association with birth outcomes. Results were generally robust with different buffer sizes and controlling for fine particles (PM2.5) and traffic. Conclusions We found protective associations by green space on birth outcomes. Increasing green space and/or reducing urban space (e.g. the greening of city environments) may reduce the risk of adverse birth outcomes such as LBW and SGA. Populations living in urban environments will grow in the next half century, and allocation of green space among urban areas may play a critical role for public health in urban planning. PMID:26546769

  5. Weight loss, weight regain and bone health.

    Science.gov (United States)

    Pines, Amos

    2012-08-01

    The ideal body image for women these days is being slim but, in the real world, obesity becomes a major health problem even in the developing countries. Overweight, but also underweight, may have associated adverse outcomes in many bodily systems, including the bone. Only a few studies have investigated the consequences of intentional weight loss, then weight regain, on bone metabolism and bone density. It seems that the negative impact of bone loss is not reversed when weight partially rebounds following the end of active intervention programs. Thus the benefits and risks of any weight loss program should be addressed individually, and monitoring of bone parameters is recommended.

  6. Unbounded subnormal weighted shifts on directed trees

    CERN Document Server

    Budzynski, Piotr; Jung, Il Bong; Stochel, Jan

    2011-01-01

    A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established. An approach to this issue via consistent systems of probability measures is invented. The role played by determinate Stieltjes moment sequences is elucidated. Lambert's characterization of subnormality of bounded operators is shown to be valid for unbounded weighted shifts on directed trees that have sufficiently many quasi-analytic vectors, which is a new phenomenon in this area. The cases of classical weighted shifts and weighted shifts on leafless directed trees with one branching vertex are studied.

  7. Proven Weight Loss Methods

    Science.gov (United States)

    Fact Sheet Proven Weight Loss Methods What can weight loss do for you? Losing weight can improve your health in a number of ways. ... limiting calories) usually isn’t enough to cause weight loss. But exercise plays an important part in helping ...

  8. Space of Spaces

    CERN Document Server

    Anderson, Edward

    2014-01-01

    Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I consider furthmore generalized configuration spaces to all levels within the conventional `equipped sets' paradigm of mathematical structure used in fundamental Theoretical Physics. This covers A) the more familiar issue of topology change in the sense of topological manifolds (tied to cobordisms), including via pinched manifolds. B) The less familiar issue of not regarding as fixed the yet deeper levels of structure: topological spaces themselves (and their metric space subcase), collections of subsets and sets. Isham has previously presented quantization schemes for a number of these. I consider some classical preliminaries for this program, aside from the most obvious (classical dynamics for each). Rather, I provide I) to all levels Relational and Background Independence ...

  9. Multimegawatt space power reactors

    Energy Technology Data Exchange (ETDEWEB)

    Dearien, J.A.; Whitbeck, J.F.

    1989-01-01

    In response to the need of the Strategic Defense Initiative (SDI) and long range space exploration and extra-terrestrial basing by the National Air and Space Administration (NASA), concepts for nuclear power systems in the multi-megawatt levels are being designed and evaluated. The requirements for these power systems are being driven primarily by the need to minimize weight and maximize safety and reliability. This paper will discuss the present requirements for space based advanced power systems, technological issues associated with the development of these advanced nuclear power systems, and some of the concepts proposed for generating large amounts of power in space. 31 figs.

  10. Weight loss, weight maintenance, and adaptive thermogenesis.

    Science.gov (United States)

    Camps, Stefan G J A; Verhoef, Sanne P M; Westerterp, Klaas R

    2013-05-01

    Diet-induced weight loss is accompanied by adaptive thermogenesis, ie, a disproportional or greater than expected reduction of resting metabolic rate (RMR). The aim of this study was to investigate whether adaptive thermogenesis is sustained during weight maintenance after weight loss. Subjects were 22 men and 69 women [mean ± SD age: 40 ± 9 y; body mass index (BMI; in kg/m(2)): 31.9 ± 3.0]. They followed a very-low-energy diet for 8 wk, followed by a 44-wk period of weight maintenance. Body composition was assessed with a 3-compartment model based on body weight, total body water (deuterium dilution), and body volume. RMR was measured (RMRm) with a ventilated hood. In addition, RMR was predicted (RMRp) on the basis of the measured body composition: RMRp (MJ/d) = 0.024 × fat mass (kg) + 0.102 × fat-free mass (kg) + 0.85. Measurements took place before the diet and 8, 20, and 52 wk after the start of the diet. The ratio of RMRm to RMRp decreased from 1.004 ± 0.077 before the diet to 0.963 ± 0.073 after the diet (P after 20 wk (0.983 ± 0.063; P weight loss after 8 wk (P Weight loss results in adaptive thermogenesis, and there is no indication for a change in adaptive thermogenesis up to 1 y, when weight loss is maintained. This trial was registered at clinicaltrials.gov as NCT01015508.

  11. Dietary protein, weight loss, and weight maintenance.

    Science.gov (United States)

    Westerterp-Plantenga, M S; Nieuwenhuizen, A; Tomé, D; Soenen, S; Westerterp, K R

    2009-01-01

    The role of dietary protein in weight loss and weight maintenance encompasses influences on crucial targets for body weight regulation, namely satiety, thermogenesis, energy efficiency, and body composition. Protein-induced satiety may be mainly due to oxidation of amino acids fed in excess, especially in diets with "incomplete" proteins. Protein-induced energy expenditure may be due to protein and urea synthesis and to gluconeogenesis; "complete" proteins having all essential amino acids show larger increases in energy expenditure than do lower-quality proteins. With respect to adverse effects, no protein-induced effects are observed on net bone balance or on calcium balance in young adults and elderly persons. Dietary protein even increases bone mineral mass and reduces incidence of osteoporotic fracture. During weight loss, nitrogen intake positively affects calcium balance and consequent preservation of bone mineral content. Sulphur-containing amino acids cause a blood pressure-raising effect by loss of nephron mass. Subjects with obesity, metabolic syndrome, and type 2 diabetes are particularly susceptible groups. This review provides an overview of how sustaining absolute protein intake affects metabolic targets for weight loss and weight maintenance during negative energy balance, i.e., sustaining satiety and energy expenditure and sparing fat-free mass, resulting in energy inefficiency. However, the long-term relationship between net protein synthesis and sparing fat-free mass remains to be elucidated.

  12. LP-REGULARITY FOR A CLASS OF PSEUDODIFFERENTIAL OPERATORS IN Rn

    Institute of Scientific and Technical Information of China (English)

    A Morando

    2005-01-01

    We study here a class of pseudodifferential operators with weighted symbols of Shubin type. First, we develop the basic elements of the pseudodifferential calculus for these operators, proving in particular a result of LP-boundedness. Then we derive regularity results in the frame of suitably defined functional spaces of Sobolev type.

  13. Axisymmetric nonconforming element method and its convergence analysis

    Institute of Scientific and Technical Information of China (English)

    陈万吉; 高岩

    1997-01-01

    By virtue of the weighted Sobolev space theory, three convergence tests of the axisymmetric non-conforming element method are established. They consist of the generalized patch test, the F-E-M test and a test which could be used conveniently, called the strong patch test (SPT). In the light of SPT, a class of axisymmetric nonconforming elements is established.

  14. Weight gain - unintentional

    Science.gov (United States)

    ... be due to menstruation, heart or kidney failure, preeclampsia, or medicines you take. A rapid weight gain ... al. Position of the American Dietetic Association: weight management. J Am Diet Assoc . 2009;109:330-46. ...

  15. Weight-loss medications

    Science.gov (United States)

    ... this page: //medlineplus.gov/ency/patientinstructions/000346.htm Weight-loss medicines To use the sharing features on this page, please enable JavaScript. Several weight-loss medicines are available. Ask your health care provider ...

  16. Weight management in pregnancy

    OpenAIRE

    Olander, E. K.

    2015-01-01

    Key learning points: - Women who start pregnancy in an overweight or obese weight category have increased health risks - Irrespective of pre-pregnancy weight category, there are health risks associated with gaining too much weight in pregnancy for both mother and baby - There are currently no official weight gain guidelines for pregnancy in the UK, thus focus needs to be on supporting pregnant women to eat healthily and keep active

  17. Commuting Dual Toeplitz Operators on Orthogonal Complement of Dirichlet Space%Dirichlet空间直交补上对偶Toeplitz算子的交换性

    Institute of Scientific and Technical Information of China (English)

    王芳; 邓燕

    2011-01-01

    We characterized commuting dual Toeplitz operators with pluriharmonic symbols on the orthogonal complement of Dirichlet space in Sobolev space on the unit ball. We also obtained the sufficient and necessary condition, that is, the product of two dual Toeplitz operators with pluriharmonic symbols for a dual Toeplitz operator.%在单位球Sobolev空间中,研究Dirichlet空间直交补上多重调和符号的对偶Toeplitz算子,刻画了它的交换性,并且给出了两个多重调和符号对偶Toeplitz算子乘积为对偶Toeplitz算子的充分必要条件.

  18. Geometric Spanners for Weighted Point Sets

    DEFF Research Database (Denmark)

    Abam, Mohammad; de Berg, Mark; Farshi, Mohammad

    2009-01-01

    Let (S,d) be a finite metric space, where each element p ∈ S has a non-negative weight w(p). We study spanners for the set S with respect to weighted distance function d w , where d w (p,q) is w(p) + d(p,q) + wq if p ≠ q and 0 otherwise. We present a general method for turning spanners with respe...

  19. Blogging for weight loss: personal accountability, writing selves, and the weight-loss blogosphere.

    Science.gov (United States)

    Leggatt-Cook, Chez; Chamberlain, Kerry

    2012-09-01

    Body weight is a key concern in contemporary society, with large proportions of the population attempting to control their weight. However, losing weight and maintaining weight loss is notoriously difficult, and new strategies for weight loss attract significant interest. Writing about experiences of weight loss in online journals, or blogging, has recently expanded rapidly. Weight-loss bloggers typically write about daily successes and failures, report calorie consumption and exercise output, and post photographs of their changing bodies. Many bloggers openly court the surveillance of blog readers as a motivation for accountability to their weight-loss goals. Drawing from a sample of weight-loss blogs authored by women, we explore three issues arising from this practice of disclosing a conventionally private activity within an online public domain. First, we examine motivations for blogging, focusing on accountability. Secondly, we consider the online construction of self, exploring how weight-loss bloggers negotiate discourses around fatness, and rework selves as their bodies transform. Finally, we consider the communities of interest that form around weight-loss blogs. This 'blogosphere' provides mutual support for weight loss. However, participating in online social spaces is complicated and bloggers must carefully manage issues of privacy and disclosure.

  20. Yogurt and weight management.

    Science.gov (United States)

    Jacques, Paul F; Wang, Huifen

    2014-05-01

    A large body of observational studies and randomized controlled trials (RCTs) has examined the role of dairy products in weight loss and maintenance of healthy weight. Yogurt is a dairy product that is generally very similar to milk, but it also has some unique properties that may enhance its possible role in weight maintenance. This review summarizes the human RCT and prospective observational evidence on the relation of yogurt consumption to the management and maintenance of body weight and composition. The RCT evidence is limited to 2 small, short-term, energy-restricted trials. They both showed greater weight losses with yogurt interventions, but the difference between the yogurt intervention and the control diet was only significant in one of these trials. There are 5 prospective observational studies that have examined the association between yogurt and weight gain. The results of these studies are equivocal. Two of these studies reported that individuals with higher yogurt consumption gained less weight over time. One of these same studies also considered changes in waist circumference (WC) and showed that higher yogurt consumption was associated with smaller increases in WC. A third study was inconclusive because of low statistical power. A fourth study observed no association between changes in yogurt intake and weight gain, but the results suggested that those with the largest increases in yogurt intake during the study also had the highest increase in WC. The final study examined weight and WC change separately by sex and baseline weight status and showed benefits for both weight and WC changes for higher yogurt consumption in overweight men, but it also found that higher yogurt consumption in normal-weight women was associated with a greater increase in weight over follow-up. Potential underlying mechanisms for the action of yogurt on weight are briefly discussed.

  1. Microwave Materials Processing for Space Applications Project

    Data.gov (United States)

    National Aeronautics and Space Administration — For a space-based fabrication effort to be effective, the weight, power requirements and footprint must be minimized. Because of the unique beam forming properties...

  2. Shielded ADR Magnets For Space Applications Project

    Data.gov (United States)

    National Aeronautics and Space Administration — The Phase II program will concentrate on manufacturing of qualified low-current, light-weight, 10K ADR magnets for space application. Shielded ADR solenoidal magnets...

  3. SWaP Optimized Space Transceivers Project

    Data.gov (United States)

    National Aeronautics and Space Administration — Size and weight of payloads on space platforms is limited by the launch vehicle capacity, and NASA platform designers must use every square inch and pound...

  4. Healthy weight game!: Lose weight together

    NARCIS (Netherlands)

    Lentelink, S.J.; Spil, Antonius A.M.; Broens, T.; Broens, T.H.F.; Hermens, Hermanus J.; Jones, Valerie M.

    2013-01-01

    Overweight and obesity pose a serious and increasing problem worldwide. Current treatment methods can result in weight loss in the short term but often fail in the longer term. Increasing motivation and thereby improving adherence can be a key factor in achieving the needed behavioral change. One

  5. Predictors of weight maintenance

    NARCIS (Netherlands)

    Pasman, W.J.; Saris, W.H.M.; Westerterp-Plantenga, M.S.

    1999-01-01

    Objective: To obtain predictors of weight maintenance after a weight-loss intervention. Research Methods and Procedures: An overall analysis of data from two-long intervention studies [n = 67 women; age: 37.9±1.0 years; body weight (BW): 87.0±1.2 kg; body mass index: 32.1±0.5 kg·m-2; % body fat: 42.

  6. Predictors of weight maintenance

    NARCIS (Netherlands)

    Pasman, W.J.; Saris, W.H.M.; Westerterp-Plantenga, M.S.

    1999-01-01

    Objective: To obtain predictors of weight maintenance after a weight-loss intervention. Research Methods and Procedures: An overall analysis of data from two-long intervention studies [n = 67 women; age: 37.9±1.0 years; body weight (BW): 87.0±1.2 kg; body mass index: 32.1±0.5 kg·m-2; % body fat: 42.

  7. Predictors of weight maintenance

    NARCIS (Netherlands)

    Pasman, W.J.; Saris, W.H.M.; Westerterp-Plantenga, M.S.

    1999-01-01

    Objective: To obtain predictors of weight maintenance after a weight-loss intervention. Research Methods and Procedures: An overall analysis of data from two-long intervention studies [n = 67 women; age: 37.9±1.0 years; body weight (BW): 87.0±1.2 kg; body mass index: 32.1±0.5 kg·m-2; % body fat:

  8. Walks on Weighted Networks

    Institute of Scientific and Technical Information of China (English)

    WU An-Cai; XU Xin-Jian; WU Zhi-Xi; WANG Ying-Hai

    2007-01-01

    We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.

  9. Adaptive Context Tree Weighting

    CERN Document Server

    O'Neill, Alexander; Shao, Wen; Sunehag, Peter

    2012-01-01

    We describe an adaptive context tree weighting (ACTW) algorithm, as an extension to the standard context tree weighting (CTW) algorithm. Unlike the standard CTW algorithm, which weights all observations equally regardless of the depth, ACTW gives increasing weight to more recent observations, aiming to improve performance in cases where the input sequence is from a non-stationary distribution. Data compression results show ACTW variants improving over CTW on merged files from standard compression benchmark tests while never being significantly worse on any individual file.

  10. Analytic continuation of Toeplitz operators

    OpenAIRE

    Bommier-Hato, H.; Engliš, M. (Miroslav); Youssfi, E.-H.

    2015-01-01

    Generalizing results of Rossi and Vergne for the holomorphic discrete series on symmetric domains, on the one hand, and of Chailuek and Hall for Toeplitz operators on the ball, on the other hand, we establish existence of analytic continuation of weighted Bergman spaces, in the weight (Wallach) parameter, as well as of the associated Toeplitz operators (with sufficiently nice symbols), on any smoothly bounded strictly pseudoconvex domain. Still further extension to Sobolev spaces of holomorph...

  11. Best Simultaneous Approximation to Totally Bounded Sequences in Banach Spaces

    Institute of Scientific and Technical Information of China (English)

    Xian Fa LUO; Chong LI; Genaro LOPEZ

    2008-01-01

    This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.

  12. Marijuana and body weight.

    Science.gov (United States)

    Sansone, Randy A; Sansone, Lori A

    2014-07-01

    Acute marijuana use is classically associated with snacking behavior (colloquially referred to as "the munchies"). In support of these acute appetite-enhancing effects, several authorities report that marijuana may increase body mass index in patients suffering from human immunodeficiency virus and cancer. However, for these medical conditions, while appetite may be stimulated, some studies indicate that weight gain is not always clinically meaningful. In addition, in a study of cancer patients in which weight gain did occur, it was less than the comparator drug (megestrol). However, data generally suggest that acute marijuana use stimulates appetite, and that marijuana use may stimulate appetite in low-weight individuals. As for large epidemiological studies in the general population, findings consistently indicate that users of marijuana tend to have lower body mass indices than nonusers. While paradoxical and somewhat perplexing, these findings may be explained by various study confounds, such as potential differences between acute versus chronic marijuana use; the tendency for marijuana use to be associated with other types of drug use; and/or the possible competition between food and drugs for the same reward sites in the brain. Likewise, perhaps the effects of marijuana are a function of initial weight status-i.e., maybe marijuana is a metabolic regulatory substance that increases body weight in low-weight individuals but not in normal-weight or overweight individuals. Only further research will clarify the complex relationships between marijuana and body weight.

  13. Concurrent weighted logic

    DEFF Research Database (Denmark)

    Xue, Bingtian; Larsen, Kim Guldstrand; Mardare, Radu Iulian

    2015-01-01

    We introduce Concurrent Weighted Logic (CWL), a multimodal logic for concurrent labeled weighted transition systems (LWSs). The synchronization of LWSs is described using dedicated functions that, in various concurrency paradigms, allow us to encode the compositionality of LWSs. To reflect these......-completeness results for this logic. To complete these proofs we involve advanced topological techniques from Model Theory....

  14. Adolescent Weight Status

    DEFF Research Database (Denmark)

    Holstein, Bjørn Evald; Due, Pernille; Brixval, Carina Sjöberg;

    2017-01-01

    day) communication with friends through cellphones, SMS messages, or Internet (1.66, 1.03-2.67). In the full population, overweight/obese weight status was associated with not perceiving best friend as a confidant (1.59, 1.11-2.28). No associations were found between weight status and number of close...

  15. Assessing Your Weight

    Science.gov (United States)

    ... only. To assess the weight of children or teenagers, see the Child and Teen BMI Calculator . Top of Page Want to learn more? Preventing Weight Gain Choosing a lifestyle that includes good eating habits and daily physical activity can help you maintain ...

  16. Weight loss - unintentional

    Science.gov (United States)

    ... of your weight loss. When to Contact a Medical Professional Call your health care provider if: You or a family member loses more ... to Expect at Your Office Visit The ... be asked questions about your medical history and symptoms, including: How much weight have ...

  17. Weight discrimination and bullying.

    Science.gov (United States)

    Puhl, Rebecca M; King, Kelly M

    2013-04-01

    Despite significant attention to the medical impacts of obesity, often ignored are the negative outcomes that obese children and adults experience as a result of stigma, bias, and discrimination. Obese individuals are frequently stigmatized because of their weight in many domains of daily life. Research spanning several decades has documented consistent weight bias and stigmatization in employment, health care, schools, the media, and interpersonal relationships. For overweight and obese youth, weight stigmatization translates into pervasive victimization, teasing, and bullying. Multiple adverse outcomes are associated with exposure to weight stigmatization, including depression, anxiety, low self-esteem, body dissatisfaction, suicidal ideation, poor academic performance, lower physical activity, maladaptive eating behaviors, and avoidance of health care. This review summarizes the nature and extent of weight stigmatization against overweight and obese individuals, as well as the resulting consequences that these experiences create for social, psychological, and physical health for children and adults who are targeted. Copyright © 2013 Elsevier Ltd. All rights reserved.

  18. Thermal management of space stations

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    Thermal management aims at making full use of energy resources available in the space station to reduce energy consumption, waste heat rejection and the weight of the station. It is an extension of the thermal control. This discussion introduces the concept and development of thermal management, presents the aspects of thermal management and further extends its application to subsystems of the space station.

  19. Space Station

    Science.gov (United States)

    Anderton, D. A.

    1985-01-01

    The official start of a bold new space program, essential to maintain the United States' leadership in space was signaled by a Presidential directive to move aggressively again into space by proceeding with the development of a space station. Development concepts for a permanently manned space station are discussed. Reasons for establishing an inhabited space station are given. Cost estimates and timetables are also cited.

  20. 14 CFR 29.29 - Empty weight and corresponding center of gravity.

    Science.gov (United States)

    2010-01-01

    ... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Empty weight and corresponding center of gravity. 29.29 Section 29.29 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF... weight and corresponding center of gravity. (a) The empty weight and corresponding center of gravity must...

  1. ORDERED WEIGHTED DISTANCE MEASURE

    Institute of Scientific and Technical Information of China (English)

    Zeshui XU; Jian CHEN

    2008-01-01

    The aim of this paper is to develop an ordered weighted distance (OWD) measure, which is thegeneralization of some widely used distance measures, including the normalized Hamming distance, the normalized Euclidean distance, the normalized geometric distance, the max distance, the median distance and the min distance, etc. Moreover, the ordered weighted averaging operator, the generalized ordered weighted aggregation operator, the ordered weighted geometric operator, the averaging operator, the geometric mean operator, the ordered weighted square root operator, the square root operator, the max operator, the median operator and the min operator axe also the special cases of the OWD measure. Some methods depending on the input arguments are given to determine the weights associated with the OWD measure. The prominent characteristic of the OWD measure is that it can relieve (or intensify) the influence of unduly large or unduly small deviations on the aggregation results by assigning them low (or high) weights. This desirable characteristic makes the OWD measure very suitable to be used in many actual fields, including group decision making, medical diagnosis, data mining, and pattern recognition, etc. Finally, based on the OWD measure, we develop a group decision making approach, and illustrate it with a numerical example.

  2. Future space suit design considerations.

    Science.gov (United States)

    1991-07-01

    Future space travel to the moon and Mars will present new challenges in space suit design. This paper examines the impact that working on the surface environment of the moon and Mars will have on the requirements of space suits. In particular, habitat pressures will impact suit weight and design. Potential structural materials are explored, as are the difficulties in designing a suit to withstand the severe dust conditions expected.

  3. Prizes for weight loss.

    Science.gov (United States)

    Englberger, L.

    1999-01-01

    A programme of weight loss competitions and associated activities in Tonga, intended to combat obesity and the noncommunicable diseases linked to it, has popular support and the potential to effect significant improvements in health. PMID:10063662

  4. Your Child's Weight

    Science.gov (United States)

    ... Some kids and teens are underweight because of eating disorders , like anorexia or bulimia, which ... weight. People from different races, ethnic groups, and nationalities tend to have different body fat ...

  5. Weight Gain during Pregnancy

    Science.gov (United States)

    ... Global Map Premature birth report card Careers Archives Pregnancy Before or between pregnancies Nutrition, weight & fitness Prenatal ... virus and pregnancy Folic acid Medicine safety and pregnancy Birth defects prevention Learn how to help reduce ...

  6. Preventing Weight Gain

    Science.gov (United States)

    ... this page, enter your email address: Enter Email Address What's this? Submit What's this? Submit Button About Us Division Information Nutrition Physical Activity Overweight & Obesity Healthy Weight Breastfeeding Micronutrient Malnutrition ...

  7. Weighted Multiplex Networks

    CERN Document Server

    Menichetti, Giulia; Panzarasa, Pietro; Mondragón, Raúl J; Bianconi, Ginestra

    2013-01-01

    One of the most important challenges in network science is to quantify the information encoded in complex network structures. Disentangling randomness from organizational principles is even more demanding when networks have a multiplex nature. Multiplex networks are multilayer systems of $N$ nodes that can be linked in multiple interacting and co-evolving layers. In these networks, relevant information might not be captured if the single layers were analyzed separately. Here we demonstrate that such partial analysis of layers fails to capture significant correlations between weights and topology of complex multiplex networks. To this end, we study two weighted multiplex co-authorship and citation networks involving the authors included in the American Physical Society. We show that in these networks weights are strongly correlated with multiplex structure, and provide empirical evidence in favor of the advantage of studying weighted measures of multiplex networks, such as multistrength and the inverse multipa...

  8. Homotopy weighted colimits

    CERN Document Server

    Vokřínek, Lukáš

    2012-01-01

    Let V be a cofibrantly generated closed symmetric monoidal model category and M a model V-category. We say that a weighted colimit W*D of a diagram D weighted by W is a homotopy weighted colimit if the diagram D is pointwise cofibrant and the weight W is cofibrant in the projective model structure on [C^op,V]. We then proceed to describe such homotopy weighted colimits through homotopy tensors and ordinary (conical) homotopy colimits. This is a homotopy version of the well known isomorphism W*D=\\int^C(W\\tensor D). After proving this homotopy decomposition in general we study in some detail a few special cases. For simplicial sets tensors may be replaced up to weak equivalence by conical homotopy colimits and thus the weighted homotopy colimits have no added value. The situation is completely different for model dg-categories where the desuspension cannot be constructed from conical homotopy colimits. In the last section we characterize those V-functors inducing a Quillen equivalence on the enriched presheaf c...

  9. Visually weighted reconstruction of compressive sensing MRI.

    Science.gov (United States)

    Oh, Heeseok; Lee, Sanghoon

    2014-04-01

    Compressive sensing (CS) enables the reconstruction of a magnetic resonance (MR) image from undersampled data in k-space with relatively low-quality distortion when compared to the original image. In addition, CS allows the scan time to be significantly reduced. Along with a reduction in the computational overhead, we investigate an effective way to improve visual quality through the use of a weighted optimization algorithm for reconstruction after variable density random undersampling in the phase encoding direction over k-space. In contrast to conventional magnetic resonance imaging (MRI) reconstruction methods, the visual weight, in particular, the region of interest (ROI), is investigated here for quality improvement. In addition, we employ a wavelet transform to analyze the reconstructed image in the space domain and fully utilize data sparsity over the spatial and frequency domains. The visual weight is constructed by reflecting the perceptual characteristics of the human visual system (HVS), and then applied to ℓ1 norm minimization, which gives priority to each coefficient during the reconstruction process. Using objective quality assessment metrics, it was found that an image reconstructed using the visual weight has higher local and global quality than those processed by conventional methods.

  10. Mobius invariant QK spaces

    CERN Document Server

    Wulan, Hasi

    2017-01-01

    This monograph summarizes the recent major achievements in Möbius invariant QK spaces. First introduced by Hasi Wulan and his collaborators, the theory of QK spaces has developed immensely in the last two decades, and the topics covered in this book will be helpful to graduate students and new researchers interested in the field. Featuring a wide range of subjects, including an overview of QK spaces, QK-Teichmüller spaces, K-Carleson measures and analysis of weight functions, this book serves as an important resource for analysts interested in this area of complex analysis. Notes, numerous exercises, and a comprehensive up-to-date bibliography provide an accessible entry to anyone with a standard graduate background in real and complex analysis.

  11. Innovative Product Design Based on Customer Requirement Weight Calculation Model

    Institute of Scientific and Technical Information of China (English)

    Chen-Guang Guo; Yong-Xian Liu; Shou-Ming Hou; Wei Wang

    2010-01-01

    In the processes of product innovation and design, it is important for the designers to find and capture customer's focus through customer requirement weight calculation and ranking. Based on the fuzzy set theory and Euclidean space distance, this paper puts forward a method for customer requirement weight calculation called Euclidean space distances weighting ranking method. This method is used in the fuzzy analytic hierarchy process that satisfies the additive consistent fuzzy matrix. A model for the weight calculation steps is constructed;meanwhile, a product innovation design module on the basis of the customer requirement weight calculation model is developed. Finally, combined with the instance of titanium sponge production, the customer requirement weight calculation model is validated. By the innovation design module, the structure of the titanium sponge reactor has been improved and made innovative.

  12. Weight Loss Nutritional Supplements

    Science.gov (United States)

    Eckerson, Joan M.

    Obesity has reached what may be considered epidemic proportions in the United States, not only for adults but for children. Because of the medical implications and health care costs associated with obesity, as well as the negative social and psychological impacts, many individuals turn to nonprescription nutritional weight loss supplements hoping for a quick fix, and the weight loss industry has responded by offering a variety of products that generates billions of dollars each year in sales. Most nutritional weight loss supplements are purported to work by increasing energy expenditure, modulating carbohydrate or fat metabolism, increasing satiety, inducing diuresis, or blocking fat absorption. To review the literally hundreds of nutritional weight loss supplements available on the market today is well beyond the scope of this chapter. Therefore, several of the most commonly used supplements were selected for critical review, and practical recommendations are provided based on the findings of well controlled, randomized clinical trials that examined their efficacy. In most cases, the nutritional supplements reviewed either elicited no meaningful effect or resulted in changes in body weight and composition that are similar to what occurs through a restricted diet and exercise program. Although there is some evidence to suggest that herbal forms of ephedrine, such as ma huang, combined with caffeine or caffeine and aspirin (i.e., ECA stack) is effective for inducing moderate weight loss in overweight adults, because of the recent ban on ephedra manufacturers must now use ephedra-free ingredients, such as bitter orange, which do not appear to be as effective. The dietary fiber, glucomannan, also appears to hold some promise as a possible treatment for weight loss, but other related forms of dietary fiber, including guar gum and psyllium, are ineffective.

  13. Pateetiline kukkumine XXI sajandisse / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2000-01-01

    Tartu Kunstimajas ja monumentaalgaleriis avatud Reet Varblase kureeritud näitusest "Eneseksjäämine. Väikesed rollimängud XXI sajandiks". Pikemalt Terje Ojaveri performance'ist, Kai Kaljo videost "Pateetika"

  14. Tuutma ja Alber Moskvas / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2000-01-01

    16.-26. III Moskva Kunstnike Keskmajas näitusel "Salong 2000" osalesid Eestist Valdek Alber ja Taave Tuutma videoinstallatsiooniga "Think different", mis koosnes videost "17 kevadist hetke" ning seriaalist tuntud Mülleri ja Stirlitzi portreedega posteritest.

  15. Backdoor Media : fassaadid kodututele / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1999-01-01

    6. linnakultuuri festival Tallinnas, mis koosneb neljast üritusest: "Backdoor Media", "Mutant Disco", "Operatsion B" ja ERKI moe-show. Lähemalt tutvustatekse kunsti- ja meediasündmust "Backdoor Media".

  16. Kõik ei ole action / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Noorte videoprojektidest. Marko Laimre ja Andrus Kõresaare "Egoistically Correct", ainus actionil rajanev video. Jasper Zoova "Sheeps Are Everywhere". J. Zoova ja Tarrvi Laamannni "Fuck". Karol Kallase kureeritud näitusel "Kunstnik tapab koletise" "Kullo" galeriis olnud Jan Bergi, Meelis Salujärve, Al Paldroki videod, Andrus Joonase töö põhjal tehtud Kiwa video "Kunstnik tapab koletise". Publiku soov vaatemängu järele.

  17. Kõik ei ole action / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1998-01-01

    Noorte videoprojektidest. Marko Laimre ja Andrus Kõresaare "Egoistically Correct", ainus actionil rajanev video. Jasper Zoova "Sheeps Are Everywhere". J. Zoova ja Tarrvi Laamannni "Fuck". Karol Kallase kureeritud näitusel "Kunstnik tapab koletise" "Kullo" galeriis olnud Jan Bergi, Meelis Salujärve, Al Paldroki videod, Andrus Joonase töö põhjal tehtud Kiwa video "Kunstnik tapab koletise". Publiku soov vaatemängu järele.

  18. M.O.O.D. / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1999-01-01

    Rotermanni soolalaos ja Viru tänava vaateakendel sajandi lõpu suurprojekt M.O.O.D., mis käsitleb Eesti moefenomeni aja ja kunsti mõjusfääris 1920. aastatest tänapäevani. Kuraator Liivia Leshkin.

  19. Backdoor Media : fassaadid kodututele / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1999-01-01

    6. linnakultuuri festival Tallinnas, mis koosneb neljast üritusest: "Backdoor Media", "Mutant Disco", "Operatsion B" ja ERKI moe-show. Lähemalt tutvustatekse kunsti- ja meediasündmust "Backdoor Media".

  20. M.O.O.D. / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    1999-01-01

    Rotermanni soolalaos ja Viru tänava vaateakendel sajandi lõpu suurprojekt M.O.O.D., mis käsitleb Eesti moefenomeni aja ja kunsti mõjusfääris 1920. aastatest tänapäevani. Kuraator Liivia Leshkin.

  1. Pateetiline kukkumine XXI sajandisse / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2000-01-01

    Tartu Kunstimajas ja monumentaalgaleriis avatud Reet Varblase kureeritud näitusest "Eneseksjäämine. Väikesed rollimängud XXI sajandiks". Pikemalt Terje Ojaveri performance'ist, Kai Kaljo videost "Pateetika"

  2. Radikaalsus muuseumi kaitsva teki all / Mari Sobolev

    Index Scriptorium Estoniae

    Sobolev, Mari, 1968-

    2004-01-01

    Rotermanni soolalaos avatud Marco (Marko) Laimre isiknäituse "Küsimused ja vastused" puhul 13. IV toimunud konverentsist. Johannes Saare, Eha Komissarovi, Hanno Soansi, Anders Härmi ja Mari Sobolevi ettekannetest

  3. DYNAMIC SOUNDING WITHIN THE FRAMEWORK OF CLASSICAL MECHANICS AND THEORY OF HIGH-INTENSITY STRIKES

    Directory of Open Access Journals (Sweden)

    Kashirskiy Vladimir Ivanovich

    2012-10-01

    Some results of convergence and -summability (uniformly and almost everywhere of Fourier-Sobolev series for polynomials orthogonal in continual-discrete Sobolev spaces are provided in the paper. These results expand and generalize the corresponding statements made by Fourier, Gegenbauer and Sobolev.

  4. Light weight phosphate cements

    Science.gov (United States)

    Wagh, Arun S.; Natarajan, Ramkumar,; Kahn, David

    2010-03-09

    A sealant having a specific gravity in the range of from about 0.7 to about 1.6 for heavy oil and/or coal bed methane fields is disclosed. The sealant has a binder including an oxide or hydroxide of Al or of Fe and a phosphoric acid solution. The binder may have MgO or an oxide of Fe and/or an acid phosphate. The binder is present from about 20 to about 50% by weight of the sealant with a lightweight additive present in the range of from about 1 to about 10% by weight of said sealant, a filler, and water sufficient to provide chemically bound water present in the range of from about 9 to about 36% by weight of the sealant when set. A porous ceramic is also disclosed.

  5. Family Weight School treatment

    DEFF Research Database (Denmark)

    Nowicka, Paulina; Höglund, Peter; Pietrobelli, Angelo

    2008-01-01

    OBJECTIVE: The aim was to evaluate the efficacy of a Family Weight School treatment based on family therapy in group meetings with adolescents with a high degree of obesity. METHODS: Seventy-two obese adolescents aged 12-19 years old were referred to a childhood obesity center by pediatricians...... and school nurses and offered a Family Weight School therapy program in group meetings given by a multidisciplinary team. Intervention was compared with an untreated waiting list control group. Body mass index (BMI) and BMI z-scores were calculated before and after intervention. RESULTS: Ninety percent...... group with initial BMI z-score 3.5. CONCLUSIONS: Family Weight School treatment model might be suitable for adolescents with BMI z...

  6. Weight Management in Phenylketonuria

    DEFF Research Database (Denmark)

    Rocha, Julio César; van Rijn, Margreet; van Dam, Esther

    2016-01-01

    specialized clinic, the second objective is important in establishing an understanding of the breadth of overweight and obesity in PKU in Europe. KEY MESSAGES: In PKU, the importance of adopting a European nutritional management strategy on weight management is highlighted in order to optimize long-term....... It is becoming evident that in addition to acceptable blood phenylalanine control, metabolic dieticians should regard weight management as part of routine clinical practice. SUMMARY: It is important for practitioners to differentiate the 3 levels for overweight interpretation: anthropometry, body composition...... and frequency and severity of associated metabolic comorbidities. The main objectives of this review are to suggest proposals for the minimal standard and gold standard for the assessment of weight management in PKU. While the former aims to underline the importance of nutritional status evaluation in every...

  7. Software-Defined Radio for Space-to-Space Communications

    Science.gov (United States)

    Fisher, Ken; Jih, Cindy; Moore, Michael S.; Price, Jeremy C.; Abbott, Ben A.; Fritz, Justin A.

    2011-01-01

    A paper describes the Space- to-Space Communications System (SSCS) Software- Defined Radio (SDR) research project to determine the most appropriate method for creating flexible and reconfigurable radios to implement wireless communications channels for space vehicles so that fewer radios are required, and commonality in hardware and software architecture can be leveraged for future missions. The ability to reconfigure the SDR through software enables one radio platform to be reconfigured to interoperate with many different waveforms. This means a reduction in the number of physical radio platforms necessary to support a space mission s communication requirements, thus decreasing the total size, weight, and power needed for a mission.

  8. Dairy cow disability weights.

    Science.gov (United States)

    McConnel, Craig S; McNeil, Ashleigh A; Hadrich, Joleen C; Lombard, Jason E; Garry, Franklyn B; Heller, Jane

    2017-08-01

    Over the past 175 years, data related to human disease and death have progressed to a summary measure of population health, the Disability-Adjusted Life Year (DALY). As dairies have intensified there has been no equivalent measure of the impact of disease on the productive life and well-being of animals. The development of a disease-adjusted metric requires a consistent set of disability weights that reflect the relative severity of important diseases. The objective of this study was to use an international survey of dairy authorities to derive disability weights for primary disease categories recorded on dairies. National and international dairy health and management authorities were contacted through professional organizations, dairy industry publications and conferences, and industry contacts. Estimates of minimum, most likely, and maximum disability weights were derived for 12 common dairy cow diseases. Survey participants were asked to estimate the impact of each disease on overall health and milk production. Diseases were classified from 1 (minimal adverse effects) to 10 (death). The data was modelled using BetaPERT distributions to demonstrate the variation in these dynamic disease processes, and to identify the most likely aggregated disability weights for each disease classification. A single disability weight was assigned to each disease using the average of the combined medians for the minimum, most likely, and maximum severity scores. A total of 96 respondents provided estimates of disability weights. The final disability weight values resulted in the following order from least to most severe: retained placenta, diarrhea, ketosis, metritis, mastitis, milk fever, lame (hoof only), calving trauma, left displaced abomasum, pneumonia, musculoskeletal injury (leg, hip, back), and right displaced abomasum. The peaks of the probability density functions indicated that for certain disease states such as retained placenta there was a relatively narrow range of

  9. Exercise in weight management.

    Science.gov (United States)

    Pinto, B M; Szymanski, L

    1997-11-01

    Exercise is integral to successful weight loss and maintenance. When talking to patients about exercise, consider their readiness, and address the barriers that prevent exercise. Physicians can help those patients who already exercise by encouraging them to continue and helping them anticipate, and recover from, lapses. Providing resource material to patients on behavioral strategies for exercise adoption and weight management can supplement the physician's efforts. Overall, patients need to hear that any regular exercise, be it step-aerobics, walking, or taking the stairs, will benefit them.

  10. Newton in Space

    Science.gov (United States)

    Herbert, Dexter (Editor)

    1992-01-01

    In this 'Liftoff to Learning' series video, astronauts (Charles Veach, Gregory Harbaugh, Donald McMonagle, Michael Coats, L. Blaine Hammond, Guion Bluford, Richard Hieb) from the STS-39 Mission use physical experiments and computer animation to explain how weightlessness and gravity affects everything and everyone onboard the Space Shuttle. The physics behind the differences between weight and mass, and the concepts of 'free fall', are demonstrated along with explanations and experiments of Sir Issac Newton's three laws of motion.

  11. Weight and Diabetes (For Parents)

    Science.gov (United States)

    ... help all kids maintain a healthy weight. For kids with diabetes, diet and exercise are even more important because ... weight is good for the entire family! When kids with diabetes reach and maintain a healthy weight, they feel ...

  12. Overweight, Obesity, and Weight Loss

    Science.gov (United States)

    ... Overweight, obesity, and weight loss fact sheet ePublications Overweight, obesity, and weight loss fact sheet Print this fact sheet Overweight, obesity, and weight loss fact sheet (full version) ( ...

  13. Small Sensors for Space Weather

    Science.gov (United States)

    Nicholas, A. C.

    2015-12-01

    The Naval Research Laboratory is actively pursuing enhancing the nation's space weather sensing capability. One aspect of this plan is the concept of flying Space Weather sensor suites on host spacecraft as secondary payloads. The emergence and advancement of the CubeSat spacecraft architecture has produced a viable platform for scientifically and operationally relevant Space Weather sensing. This talk will provide an overview of NRL's low size weight and power sensor technologies targeting Space Weather measurements. A summary of on-orbit results of past and current missions will be presented, as well as an overview of future flights that are manifested and potential constellation missions.

  14. Weighted exponential polynomial approximation

    Institute of Scientific and Technical Information of China (English)

    邓冠铁

    2003-01-01

    A necessary and sufficient condition for completeness of systems of exponentials with a weightin Lp is established and a quantitative relation between the weight and the system of exponential in Lp isobtained by using a generalization of Malliavin's uniqueness theorem about Watson's problem.

  15. Barrel Weight Reduction

    Science.gov (United States)

    2005-05-01

    Process 16 Prototype Hardware Testing and Results 17 Barrel Weight 17 Functional Testing 17 Barrel Deflection 18 Drop Test 19 Thermal Test 20 References 23...measurements were compliant. 19 Thermal Test As discussed in the Transient Analysis Model Verification section of this report, the analytical results from the

  16. Season and Weight

    African Journals Online (AJOL)

    hayati

    Efficiency of growth is a function of metabolisable energy retained relative to that which is .... distribution of other sexes in certain housing, initial weight or season categories ..... Fox, D.G., Johnson, R.R., Preston, R.L. & Dockerty, T.R., 1972.

  17. Swimming and birth weight.

    Science.gov (United States)

    Nieuwenhuijsen, Mark J; Northstone, Kate; Golding, Jean

    2002-11-01

    Swimmers can be exposed to high levels of trihalomethanes, byproducts of chlorination disinfection. There are no published studies on the relation between swimming and birth weight. We explored this relation in a large birth cohort, the Avon (England) Longitudinal Study of Parents and Children (ALSPAC), in 1991-1992. Information on the amount of swimming per week during the first 18-20 weeks of pregnancy was available for 11,462 pregnant women. Fifty-nine percent never swam, 31% swam up to 1 hour per week, and 10% swam for longer. We used linear regression to explore the relation between birth weight and the amount of swimming, with adjustment for gestational age, maternal age, parity, maternal education level, ethnicity, housing tenure, drug use, smoking and alcohol consumption. We found little effect of the amount of swimming on birth weight. More highly educated women were more likely to swim compared with less educated women, whereas smokers were less likely to swim compared with nonsmokers. There appears to be no relation between the duration of swimming and birth weight.

  18. Weight control (image)

    Science.gov (United States)

    Weight lifting builds muscle, which increases overall body strength, tone, and balance. Muscles also burn calories more efficiently than fat and other body tissues. So even at rest the more muscle tissue a person has the more calories a person is ...

  19. Losing Baby Weight

    Science.gov (United States)

    ... Exercise is a key component of a healthy lifestyle before, during and after pregnancy. After pregnancy, most women can start exercising as ... the skinny jeans. Focus on living a healthy lifestyle, and the rest will fall into place. More tips ... or between pregnancies Nutrition, weight & fitness Prenatal ...

  20. Multipurpose Spaces

    Science.gov (United States)

    Gordon, Douglas

    2010-01-01

    The concept of multipurpose spaces in schools is certainly not new. Especially in elementary schools, the combination of cafeteria and auditorium (and sometimes indoor physical activity space as well) is a well-established approach to maximizing the use of school space and a school district's budget. Nonetheless, there continue to be refinements…

  1. Weight Representations of Admissible Affine Vertex Algebras

    Science.gov (United States)

    Arakawa, Tomoyuki; Futorny, Vyacheslav; Ramirez, Luis Enrique

    2017-08-01

    For an admissible affine vertex algebra {V_k{(\\mathfrak{g})}} of type A, we describe a new family of relaxed highest weight representations of {V_k{(\\mathfrak{g})}}. They are simple quotients of representations of the affine Kac-Moody algebra {\\widehat{\\mathfrak{g}}} induced from the following {\\mathfrak{g}}-modules: (1) generic Gelfand-Tsetlin modules in the principal nilpotent orbit, in particular all such modules induced from {\\mathfrak{sl}_2}; (2) all Gelfand-Tsetlin modules in the principal nilpotent orbit that are induced from {\\mathfrak{sl}_3}; (3) all simple Gelfand-Tsetlin modules over {\\mathfrak{sl}_3}. This in particular gives the classification of all simple positive energy weight representations of {V_k{(\\mathfrak{g})}} with finite dimensional weight spaces for {\\mathfrak{g}=\\mathfrak{sl}_3}.

  2. Weight and weight gain during early infancy predict childhood obesity

    DEFF Research Database (Denmark)

    Andersen, Lise Geisler; Holst, Claus; Michaelsen, Kim F.

    2012-01-01

    Infant weight and weight gain are positively associated with later obesity, but whether there is a particular critical time during infancy remains uncertain.......Infant weight and weight gain are positively associated with later obesity, but whether there is a particular critical time during infancy remains uncertain....

  3. A Gauss-Newton method for the integration of spatial normal fields in shape Space

    KAUST Repository

    Balzer, Jonathan

    2011-08-09

    We address the task of adjusting a surface to a vector field of desired surface normals in space. The described method is entirely geometric in the sense, that it does not depend on a particular parametrization of the surface in question. It amounts to solving a nonlinear least-squares problem in shape space. Previously, the corresponding minimization has been performed by gradient descent, which suffers from slow convergence and susceptibility to local minima. Newton-type methods, although significantly more robust and efficient, have not been attempted as they require second-order Hadamard differentials. These are difficult to compute for the problem of interest and in general fail to be positive-definite symmetric. We propose a novel approximation of the shape Hessian, which is not only rigorously justified but also leads to excellent numerical performance of the actual optimization. Moreover, a remarkable connection to Sobolev flows is exposed. Three other established algorithms from image and geometry processing turn out to be special cases of ours. Our numerical implementation founds on a fast finite-elements formulation on the minimizing sequence of triangulated shapes. A series of examples from a wide range of different applications is discussed to underline flexibility and efficiency of the approach. © 2011 Springer Science+Business Media, LLC.

  4. Heterogeneous edge weights promote epidemic diffusion in weighted evolving networks

    Science.gov (United States)

    Duan, Wei; Song, Zhichao; Qiu, Xiaogang

    2016-08-01

    The impact that the heterogeneities of links’ weights have on epidemic diffusion in weighted networks has received much attention. Investigating how heterogeneous edge weights affect epidemic spread is helpful for disease control. In this paper, we study a Reed-Frost epidemic model in weighted evolving networks. Our results indicate that a higher heterogeneity of edge weights leads to higher epidemic prevalence and epidemic incidence at earlier stage of epidemic diffusion in weighted evolving networks. In addition, weighted evolving scale-free networks come with a higher epidemic prevalence and epidemic incidence than unweighted scale-free networks.

  5. Structural Weight Estimation for Launch Vehicles

    Science.gov (United States)

    Cerro, Jeff; Martinovic, Zoran; Su, Philip; Eldred, Lloyd

    2002-01-01

    This paper describes some of the work in progress to develop automated structural weight estimation procedures within the Vehicle Analysis Branch (VAB) of the NASA Langley Research Center. One task of the VAB is to perform system studies at the conceptual and early preliminary design stages on launch vehicles and in-space transportation systems. Some examples of these studies for Earth to Orbit (ETO) systems are the Future Space Transportation System [1], Orbit On Demand Vehicle [2], Venture Star [3], and the Personnel Rescue Vehicle[4]. Structural weight calculation for launch vehicle studies can exist on several levels of fidelity. Typically historically based weight equations are used in a vehicle sizing program. Many of the studies in the vehicle analysis branch have been enhanced in terms of structural weight fraction prediction by utilizing some level of off-line structural analysis to incorporate material property, load intensity, and configuration effects which may not be captured by the historical weight equations. Modification of Mass Estimating Relationships (MER's) to assess design and technology impacts on vehicle performance are necessary to prioritize design and technology development decisions. Modern CAD/CAE software, ever increasing computational power and platform independent computer programming languages such as JAVA provide new means to create greater depth of analysis tools which can be included into the conceptual design phase of launch vehicle development. Commercial framework computing environments provide easy to program techniques which coordinate and implement the flow of data in a distributed heterogeneous computing environment. It is the intent of this paper to present a process in development at NASA LaRC for enhanced structural weight estimation using this state of the art computational power.

  6. Design spaces

    DEFF Research Database (Denmark)

    2005-01-01

    Digital technologies and media are becoming increasingly embodied and entangled in the spaces and places at work and at home. However, our material environment is more than a geometric abstractions of space: it contains familiar places, social arenas for human action. For designers, the integration...... alternatives for integrating digital technology with space. Connecting practical design work with conceptual development and theorizing, art with technology, and usesr-centered methods with social sciences, Design Spaces provides a useful research paradigm for designing ubiquitous computing. This book...... of digital technology with space poses new challenges that call for new approaches. Creative alternatives to traditional systems methodologies are called for when designers use digital media to create new possibilities for action in space. Design Spaces explores how design and media art can provide creative...

  7. Some Dimensions of Spaces of Finite Type Invariants of Virtual Knots

    CERN Document Server

    Bar-Natan, Dror; Leung, Louis; Roukema, Fionntan

    2009-01-01

    We compute many dimensions of spaces of finite type invariants of virtual knots (of several kinds) and the dimensions of the corresponding spaces of "weight systems", finding everything to be in agreement with the conjecture that "every weight system integrates".

  8. Light weight space power reactors for nuclear electric propulsion

    Energy Technology Data Exchange (ETDEWEB)

    Ludewig, H.; Mughabghab, S.; Lazareth, O.; Perkins, K.; Schmidt, E.; Powell, J.R.

    1991-01-01

    A Nuclear Electric Propulsion (NEP) unit capable of propelling a manned vehicle to MARS will be required to have a value of {alpha} (kg/kWe) which is less than five. In order to meet this goal the reactor mass, and thus its contribution to the value of {alpha} will have to be minimized. In this paper a candidate for such a reactor is described. It consists of a gas cooled Particle Bed Reactor (PBR), with specially chosen materials which allow it to operate at an exit temperature of approximately 2000 K. One of the unique features of a PBR is the direct cooling of particulate fuel by the working fluid. This feature allows for high power densities, highest possible gas exit temperatures, for a given fuel temperature and because of the thin particle bed a low pressure drop. The PBR's described in this paper will have a ceramic moderator (Be{sub 2}C), ZrC coated fuel particles and a carbon/carbon hot frit. All the reactors will be designed with sufficient fissile loading to operate at full power for seven years. The burn up possible with particulate fuel is approximately 30%--50%. These rector designs achieve a value of {alpha} less than unity in the power range of interest (5 MWe). 5 refs., 3 figs.

  9. Weighted guided image filtering.

    Science.gov (United States)

    Li, Zhengguo; Zheng, Jinghong; Zhu, Zijian; Yao, Wei; Wu, Shiqian

    2015-01-01

    It is known that local filtering-based edge preserving smoothing techniques suffer from halo artifacts. In this paper, a weighted guided image filter (WGIF) is introduced by incorporating an edge-aware weighting into an existing guided image filter (GIF) to address the problem. The WGIF inherits advantages of both global and local smoothing filters in the sense that: 1) the complexity of the WGIF is O(N) for an image with N pixels, which is same as the GIF and 2) the WGIF can avoid halo artifacts like the existing global smoothing filters. The WGIF is applied for single image detail enhancement, single image haze removal, and fusion of differently exposed images. Experimental results show that the resultant algorithms produce images with better visual quality and at the same time halo artifacts can be reduced/avoided from appearing in the final images with negligible increment on running times.

  10. Calculating Quenching Weights

    CERN Document Server

    Salgado, C A; Salgado, Carlos A.; Wiedemann, Urs Achim

    2003-01-01

    We calculate the probability (``quenching weight'') that a hard parton radiates an additional energy fraction due to scattering in spatially extended QCD matter. This study is based on an exact treatment of finite in-medium path length, it includes the case of a dynamically expanding medium, and it extends to the angular dependence of the medium-induced gluon radiation pattern. All calculations are done in the multiple soft scattering approximation (Baier-Dokshitzer-Mueller-Peign\\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and in the single hard scattering approximation (N=1 opacity approximation). By comparison, we establish a simple relation between transport coefficient, Debye screening mass and opacity, for which both approximations lead to comparable results. Together with this paper, a CPU-inexpensive numerical subroutine for calculating quenching weights is provided electronically. To illustrate its applications, we discuss the suppression of hadronic transverse momentum spectra in nucleus-nucleus colli...

  11. Reducing rotor weight

    Energy Technology Data Exchange (ETDEWEB)

    Cheney, M.C. [PS Enterprises, Inc., Glastonbury, CT (United States)

    1997-12-31

    The cost of energy for renewables has gained greater significance in recent years due to the drop in price in some competing energy sources, particularly natural gas. In pursuit of lower manufacturing costs for wind turbine systems, work was conducted to explore an innovative rotor designed to reduce weight and cost over conventional rotor systems. Trade-off studies were conducted to measure the influence of number of blades, stiffness, and manufacturing method on COE. The study showed that increasing number of blades at constant solidity significantly reduced rotor weight and that manufacturing the blades using pultrusion technology produced the lowest cost per pound. Under contracts with the National Renewable Energy Laboratory and the California Energy Commission, a 400 kW (33m diameter) turbine was designed employing this technology. The project included tests of an 80 kW (15.5m diameter) dynamically scaled rotor which demonstrated the viability of the design.

  12. 3D Weight Matrices in Modeling Real Estate Prices

    Science.gov (United States)

    Mimis, A.

    2016-10-01

    Central role in spatial econometric models of real estate data has the definition of the weight matrix by which we capture the spatial dependence between the observations. The weight matrices presented in literature so far, treats space in a two dimensional manner leaving out the effect of the third dimension or in our case the difference in height where the property resides. To overcome this, we propose a new definition of the weight matrix including the third dimensional effect by using the Hadamard product. The results illustrated that the level effect can be absorbed into the new weight matrix.

  13. Dynamic Weighted Data Structures.

    Science.gov (United States)

    1982-06-01

    and Bonnie Hampton, who taught me much more than how to play the cello . Finally, for hours of artistic satisfaction, I thank Johannes Brahms, Ludwig...van "j Beethoven, Igor Stravinsky, Glan-Carlo Menotti, and Johann Sebastian Bach . Dynamic Weighted Data Structures Samuel W. Bent This thesis discusses...34I find It a matter of some difficulty to arrange these cards In a manner suited to my needs.’ I glanced at the cards and noticed each was labelled

  14. Space Commercialization

    Science.gov (United States)

    Martin, Gary L.

    2011-01-01

    A robust and competitive commercial space sector is vital to continued progress in space. The United States is committed to encouraging and facilitating the growth of a U.S. commercial space sector that supports U.S. needs, is globally competitive, and advances U.S. leadership in the generation of new markets and innovation-driven entrepreneurship. Energize competitive domestic industries to participate in global markets and advance the development of: satellite manufacturing; satellite-based services; space launch; terrestrial applications; and increased entrepreneurship. Purchase and use commercial space capabilities and services to the maximum practical extent Actively explore the use of inventive, nontraditional arrangements for acquiring commercial space goods and services to meet United States Government requirements, including measures such as public-private partnerships, . Refrain from conducting United States Government space activities that preclude, discourage, or compete with U.S. commercial space activities. Pursue potential opportunities for transferring routine, operational space functions to the commercial space sector where beneficial and cost-effective.

  15. Axiomatizations of symmetrically weighted solutions

    NARCIS (Netherlands)

    Kleppe, John; Reijnierse, Hans; Sudhölter, P.

    2013-01-01

    If the excesses of the coalitions in a transferable utility game are weighted, then we show that the arising weighted modifications of the well-known (pre)nucleolus and (pre)kernel satisfy the equal treatment property if and only if the weight system is symmetric in the sense that the weight of a su

  16. Online weight training.

    Science.gov (United States)

    McNamara, John M; Swalm, Ricky L; Stearne, David J; Covassin, Tracey M

    2008-07-01

    The purpose of this study was to determine how a traditional weight training class compared to nontraditional classes that were heavily laden with technology. Could students learn resistance exercises by watching video demonstrations over the Internet? Three university weight training classes, each lasting 16 weeks, were compared. Each class had the same curriculum and workout requirements but different attendance requirements. The online group made extensive use of the Internet and was allowed to complete the workouts on their own at any gym that was convenient for them. Seventy-nine college-aged students were randomized into 3 groups: traditional (n = 27), hybrid (n = 25), and online (n = 27). They completed pretest and posttest measures on upper-body strength (i.e., bench press), lower-body strength (i.e., back squat), and knowledge (i.e., written exam). The results indicated that all 3 groups showed significant improvement in knowledge (p students to attend class and may have resulted in significantly lower scores on the bench press (p motivation, low accountability, and the possibility that the self-reported workouts were not accurate. These results suggest that there is a limit to how much technology can be used in a weight training class. If this limit is exceeded, some type of monitoring system appears necessary to ensure that students are actually completing their workouts.

  17. Weighted Feature Distance

    DEFF Research Database (Denmark)

    Ortiz-Arroyo, Daniel; Yazdani, Hossein

    2017-01-01

    The accuracy of machine learning methods for clustering depends on the optimal selection of similarity functions. Conventional distance functions for the vector space might cause an algorithm to being affected by some dominant features that may skew its final results. This paper introduces a flexib...

  18. Weight Management | Smokefree.gov

    Science.gov (United States)

    Fear of gaining weight is a common reason people give for not quitting smoking. Learn healthy ways to avoid weight gain and shed unwanted pounds. These weight management strategies can help you feel better while quitting smoking and let you take control of your health for the rest of your life. Remember that losing weight can be challenging and takes time, but being a healthy weight reduces the risk of many diseases and helps you look and feel better.

  19. Learning Spaces

    CERN Document Server

    Falmagne, Jean-Claude

    2011-01-01

    Learning spaces offer a rigorous mathematical foundation for practical systems of educational technology. Learning spaces generalize partially ordered sets and are special cases of knowledge spaces. The various structures are investigated from the standpoints of combinatorial properties and stochastic processes. Leaning spaces have become the essential structures to be used in assessing students' competence of various topics. A practical example is offered by ALEKS, a Web-based, artificially intelligent assessment and learning system in mathematics and other scholarly fields. At the heart of A

  20. Morrey spaces

    CERN Document Server

    Adams, David R

    2015-01-01

    In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory. .