Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperle...
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Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be given by finitely generated submodules of Feigin-Fuchs modules. Additional evidence for this identification is obtained by comparing the formalism of lattice fusion with the fusion rules of the Virasoro Kac modules. These are obtained, at the character level, in complete generality by applying a Verlinde-like formula and, at the module level, in many explicit examples by applying the Nahm-Gaberdiel-Kausch fusion algorithm. (C) 2015 The Authors. Published by Elsevier B.V.
We give combinatorial principles GI(k), based on k-turn games, which are complete for the class of NP search problems provably total at the kth level T(2)(k) of the bounded arithmetic hierarchy and hence characterize ...
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We give combinatorial principles GI(k), based on k-turn games, which are complete for the class of NP search problems provably total at the kth level T(2)(k) of the bounded arithmetic hierarchy and hence characterize the for all Sigma(b)(1) consequences of T(2)(k). Our argument uses a translation of first-order proofs into large, uniform propositional proofs in a system in which the soundness of the rules can be witnessed by polynomial time reductions between games. We show that for all(Sigma) over cap (b)(1)(alpha) conservativity of T(2)(i+1) (alpha) over T(2)(i)(alpha) already implies. for all(Sigma) over cap (b)(1)(a) conservativity of T(2)(alpha) over T(2)(i)(alpha). We translate this into propositional form and give a polylogarithmic width CNF (GI(3)) over bar such that if (GI(3)) over bar has small R(log) refutations then so does any polylogarithmic width CNF which has small constant depth refutations. We prove a resolution lower bound for (GI(3)) over bar. We use our characterization to give a sufficient condition for the totality of a relativized NP search problem to be unprovable in T(2)(i)(alpha) in terms of a non-logical question about multiparty communication protocols.
We consider the inequality which has a "dual" relation with Beckner's logarithmic Sobolev inequality. By using the relative entropy, we identify the sharp constant and the extremal of this inequality. Mo...
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We consider the inequality which has a "dual" relation with Beckner's logarithmic Sobolev inequality. By using the relative entropy, we identify the sharp constant and the extremal of this inequality. Moreover, we derive the logarithmic uncertainty principle like Beckner's one.
We study the asymptotic behaviour of nonnegative solutions to: u(t) = Delta(p)u(m) using an entropy estimate based on a sub-family of the Gagliardo-Nirenberg inequalities - or, in the limit case m = (p - 1)(-1), on a ...
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We study the asymptotic behaviour of nonnegative solutions to: u(t) = Delta(p)u(m) using an entropy estimate based on a sub-family of the Gagliardo-Nirenberg inequalities - or, in the limit case m = (p - 1)(-1), on a logarithmic Sobolev inequality in W-1,W-p - for which optimal functions are known. (C) 2002 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
We prove a conjecture of N. Suita which says that for any bounded domain D in a", one has , where c (D) (z) is the logarithmic capacity of a",a-D with respect to zaD and K (D) the Bergman kernel on the diago...
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We prove a conjecture of N. Suita which says that for any bounded domain D in a", one has , where c (D) (z) is the logarithmic capacity of a",a-D with respect to zaD and K (D) the Bergman kernel on the diagonal. We also obtain optimal constant in the Ohsawa-Takegoshi extension theorem.
Metabolic theory proposes that individual growth is governed through the mass- and temperature-dependence of metabolism, and ecological stoichiometry posits that growth is maximized at consumer-specific optima of reso...
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Metabolic theory proposes that individual growth is governed through the mass- and temperature-dependence of metabolism, and ecological stoichiometry posits that growth is maximized at consumer-specific optima of resource elemental composition. A given consumer's optimum, the threshold elemental ratio (TER), is proportional to the ratio of its maximum elemental gross growth efficiencies (GGEs). GGE is defined by the ratio of metabolism-dependent processes such that GGEs should be independent of body mass and temperature. Understanding the metabolic-dependencies of GGEs and TERs may open the path towards a theoretical framework integrating the flow of energy and chemical elements through ecosystems. However, the mass and temperature scaling of GGEs and TERs have not been broadly evaluated. Here, we use data from 95 published studies to evaluate these metabolic-dependencies for C, N and P from unicells to vertebrates. We show that maximum GGEs commonly decline as power functions of asymptotic body mass and exponential functions of temperature. The rates of change in maximum GGEs with mass and temperature are relatively slow, however, suggesting that metabolism may not causally influence maximum GGEs. We additionally derived the theoretical expectation that the TER for C:P should not vary with body mass and this was supported empirically. A strong linear relationship between carbon and nitrogen GGEs further suggests that variation in the TER for C:N should be due to variation in consumer C:N. In general we show that GGEs may scale with metabolic rate, but it is unclear if there is a causal link between metabolism and GGEs. Further integrating stoichiometry and metabolism will provide better understanding of the processes governing the flow of energy and elements from organisms to ecosystems.
In three dimensions there is a logarithmically divergent contribution to the entanglement entropy which is due to the vertices located at the boundary of the region considered. In this work we find the corresponding u...
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In three dimensions there is a logarithmically divergent contribution to the entanglement entropy which is due to the vertices located at the boundary of the region considered. In this work we find the corresponding universal coefficient for a free Dirac field, and extend a previous work in which the scalar case was treated. The problem is equivalent to find the conformal anomaly in three-dimensional space where multiplicative boundary conditions for the field are imposed on a plane angular sector. As an intermediate step of the calculation we compute the trace of the Green function of a massive Dirac field in a two-dimensional sphere with boundary conditions imposed on a segment of a great circle. (C) 2009 Elsevier B.V. All rights reserved.
We study properties of the logarithmic matrix norm. We obtain new estimates for matrix norms as well as for the spectral radius and the spectral abscissa. We give a new proof of the Fiedler theorem and a block test fo...
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We study properties of the logarithmic matrix norm. We obtain new estimates for matrix norms as well as for the spectral radius and the spectral abscissa. We give a new proof of the Fiedler theorem and a block test for the Hurwitz property of a matrix based on the theory of nonnegative and off-diagonal-nonnegative matrices.
A theorem of Lukacs [J. Reine Angew. Math., 150, 107-112 (1920)] states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function f diverge with a logarithmic rate at the points of d...
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A theorem of Lukacs [J. Reine Angew. Math., 150, 107-112 (1920)] states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function f diverge with a logarithmic rate at the points of discontinuity of f of the first kind. Mricz [Acta Math. Hung., 98, 259-262 (2003)] proved a similar theorem for the rectangular partial sums of double conjugate trigonometric Fourier series. We consider analogs of the Mricz theorem for the generalized CesA ro means and positive linear means. In the present paper we prove a similar theorem in terms of linear operators satisfying certain conditions.
Pulsed thermography is gaining wide acceptance in the aerospace, automotive and power generation industries, owing to its quickness of inspection, repeatability and sensitivity. Recently, advancement in pulsed thermog...
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Pulsed thermography is gaining wide acceptance in the aerospace, automotive and power generation industries, owing to its quickness of inspection, repeatability and sensitivity. Recently, advancement in pulsed thermographic data processing has been made by Thermal Wave Imaging Inc (TWI) in USA. A technique called thermographic signal reconstruction (TSR) has been devised. By approximating the raw data sequence with logarithmic polynomial function, this technique produces three types of images, namely: the synthetic image and first and second time derivative images. These images facilitate detection of smaller and/or deeper defects, which are undetectable on the raw data sequence. In this work, qualitative and quantitative assessments of the TSR images have been conducted using aluminium, CFRP and GFRP composites and mild steel samples. Results have validated the significant enhancement of the TSR process. A quantitative study performed using CFRP composite has shown that an improvement of 60% in detection depth has achieved for defects greater than 4 mm diameter. Defects have been imaged at depths greater than 5 mm in composites.
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