haag theorem: Topics by WorldWideScience.org

Elementary submodels in infinite combinatorics

Fermat's last theorem

1997-01-01

Integrating Testing and Interactive Theorem Proving

We show that usage of elementary submodels is a simple but powerful method to prove theorems, or to simplify proofs in infinite combinatorics. First we introduce all the necessary concepts of logic, then we prove classical theorems using elementary submodels. We also present a new proof of Nash-Williams's theorem on cycle-decomposition of graphs, and finally we obtain some new decomposition theorems by eliminating GCH from some proofs concerning bond-faithful decompositions of graphs.

2010-01-01

Local central limit theorems in stochastic geometry

Using an interactive theorem prover to reason about programs involves a sequence of interactions where the user challenges the theorem prover with conjectures. Invariably, many of the conjectures posed are in fact false, and users often spend considerable effort examining the theorem prover's output before realizing this. We present a synergistic integration of testing with theorem proving, implemented in the ACL2 Sedan (ACL2s), for automatically generating concrete counterexamples. Our method uses the full power of the theorem prover and associated libraries to simplify conjectures; this simplification can transform conjectures for which finding counterexamples is hard into conjectures where finding counterexamples is trivial. In fact, our approach even leads to better theorem proving, e.g., if testing shows that a generalization step leads to a false ...

2011-01-01

On an assertion about Nash--Moser applications

We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply this result to various quantities arising in stochastic geometry, including: size of the largest component for percolation on a box; number of components, number of edges, or number of isolated points, for random geometric graphs; covered volume for germ-grain coverage models; number of accepted points for finite-input random sequential adsorption; sum of nearest-neighbour distances for a random sample from a continuous multidimensional distribution.

2010-01-01

Infinitely many nontrivial solutions for a class of biharmonic equations via variant fountain theorems

By an example we show that Olaf Mueller's assertion about his new theorems being able to give anew some classical results previously obtained via applications of Nash--Moser type theorems is unfounded. We also give another example indicating that the premises in related new inverse function theorems may be too restrictive.

2007-01-01

British Library Electronic Table of Contents (United Kingdom)

By a variant version of Fountain Theorem due to Zou [W. Zou, Variant fountain theorems and their applications, Manuscripta Math. 104 (2001) 343-358], the existence of infinitely many solutions is obtained for a class of biharmonic equations where the nonlinearity involves a combination of superlinear and asymptotically linear terms.

2011-01-01

Normal product states for fermisions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa/sub 2/ quantum field model

K S Krishnan and the early experimental evidences for the Jahn-Teller Theorem

We present sufficient conditions that imply duality for the algebras of local observables in all Abelian sectors of all locally normal, irreducible representations of a field algebra if twisted duality obtains in one of these representations. It is verified that the Yukawa/sub 2/ model satisfies these conditions, yielding the first proof of duality for the observable algebra in all coherent charge sectors in this model. This paper also constitutes the first verification of the assumptions of the axiomatic study of the structure of superselection sectors by Doplicher, Haag and Roberts in an interacting model with nontrivial sectors. The existence of normal product states for the free Fermi field algebra and, thus, the verification of the funnel property for the associated net of local algebras are demonstrated.

1982-08-01

h-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash categories, Uniform bound and Effectiveeness

Jahn-Teller theorem, proposed in 1937, predicts a distortional instability for a molecule that has symmetry based degenerate electronic states. In 1939 Krishnan emphasized the importance of this theorem for the arrangement of water molecules around the transition metal or rare earth ions in aqueous solutions and hydrated saltes, in a short and interesting paper published in Nature by pointing out atleast four existing experimental results in support of the theorem. This paper of Krishnan has remained essentially unknown to the practitioners of Jahn-Teller effect, eventhough it pointed to the best experimental results that were available, in the 30's and 40's, in support of Jahn-Teller theorem. Some of the modern day experiments are also in conformity with some specific suggestions of Krishnan.

1998-01-01

A new proof of the Bianchi type IX attractor theorem

The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash diffeomorphism). The main tools used are semialgebraic triangulation and Nash approximation. One aspect of the algebraic nature of semialgebraic or Nash objects is that one can measure their complexities. We show h and s-cobordism theorems with a uniform bound on the complexity of the semialgebraic homeomorphism (or Nash diffeomorphism) obtained in terms of the complexity of the cobordism data. The uniform bound of semialgebraic h-cobordism cannot be recursive, which gives ...

2009-01-01

A new proof of the Bianchi type IX attractor theorem

We consider the dynamics toward the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The 'Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.

2009-04-07

A new proof of the Bianchi type IX attractor theorem

2009-04-07

A Nash-Moser theorem for singular evolution equations. Application to the Serre and Green-Naghdi equations

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.

2009-01-01

Virial estimator for dark energy

We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the equation, the second the behavior of the nonlinearities, and the third one assumes that an energy estimate can be found for the linearized system. We allow losses of derivatives in this energy estimate and therefore construct a solution by a Nash-Moser iterative scheme. As an application to this general theorem, we prove the well-posedness of the Serre and Green-Naghdi equation and discuss the problem of their validity as asymptotic models for the water-waves equations.

2007-01-01

The MacMahon Master Theorem for right quantum superalgebras and higher Sugawara operators for \\hat gl(m|n)

A new estimator of the local density of dark energy is suggested which comes from the virial theorem for non-relativistic gravitating systems embedded in the uniform dark energy background.

2011-01-01

Perception/Action: An Holistic Approach II

We prove an analogue of the MacMahon Master Theorem for the right quantum superalgebras. In particular, we obtain a new and simple proof of this theorem for the right quantum algebras. In the super case the theorem is then used to construct higher order Sugawara operators for the affine Lie superalgebra \\hat gl(m|n) in an explicit form. The operators are elements of a completed universal enveloping algebra of \\hat gl(m|n) at the critical level. They occur as the coefficients in the expansion of a noncommutative Berezinian and as the traces of powers of generator matrices. The same construction yields higher Hamiltonians for the Gaudin model associated with the Lie superalgebra gl(m|n).

2009-01-01

Science.gov (United States)

... And those who study cognition select problems (eg, tower of Hanoi, missionaries and cannibals, logic theorems) with minimal perceptual and motor ...

1993-10-12

On the Approach to Spherical Harmonics by Maxwell, Thomson and Tait

Fermion-boson symmetry through superluminal transformations

We present a unified self-consistent review of the approach to spherical harmonics developed in the second half of the 19th century by Maxwell and by Thomson and Tait. We remark how this spherical coordinate-free approach straightforwardly leads to physically very important results of the theory of solid and surface harmonics which become rather tedious to work out when using spherical coordinates and associated Legendre functions. These results include, among others, the addition theorem, spherical wave expansions, the construction of the standard set of normalized spherical harmonics, Y_lm - together with their rotational properties-, and recursion relations. We provide new proofs for Maxwell's theorem, the addition theorem and Hobson's theorem, respectively, using in the latter some elementary notions of the symbolic techniques proper of the theory of invariants. Also, we give an approach based on ...

2008-01-01

A stem cell niche dominance theorem

We consider the Pauli theorem on the spin-statistics connection for faster-than-light particles. As the consequence of the unlocalizability of tachyons in space we conclude that their spin-statistics correlations are inverted.

1985-08-01

UK PubMed Central (United Kingdom)

BackgroundMultilevelness is a defining characteristic of complex systems. For example, in the intestinal tissue the epithelial lining is organized into crypts that are maintained...Full Text Available

Intermittency and the central limit theorem

Inflation in Bianchi models and the cosmic no hair theorem in a brane world

Central limit theorem estimates of anomalous fractal dimensions of self-similar random cascades are studied. It is found that, in general, the normal approximation fails badly. A systematic series of approximations which converges to the exact result (both for the fractal dimensions and for the distribution itself) is derived for the {alpha}-model. Consequences for the 'empty bin effect' are indicated. (orig.).

1991-04-01

1 2 3 4 5 6

Infinitesimal symmetries and conservation laws of the DNLSE hierarchy and the Noether's theorem

The cosmic no hair theorem is studied in anisotropic brane worlds. Assuming anisotropic Bianchi models with an inflaton field it is shown that, during slow-roll inflation, anisotropy in all Bianchi models except a Bianchi type-IX universe washes out. Brane worlds admit both exponential and power law inflation. We consider here only exponential expansion of the universe. It is found that isotropization occurs much faster in a brane world than in the general theory of relativity.

2002-12-15

Global quantum gauge symmetry via reconstruction theorems

The hierarchy of integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of linearization of these equations and their conservation law in the terms of solutions of corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and conservation laws explicitly expressed through the variables of the nonlinear equations are derived. (author)

2007-08-15

Real Paley-Wiener theorems and local spectral radius formulas

In this paper we establish that every quantum field theory satisfying some basic axioms possesses a weak quasi Hopf algebra as gauge symmetry. We use a reconstruction theorem to find this symmetry algebra and show how it is sed to build a gauge covariant field algebra. We investigate the question of why this generality is necessary. The non-uniqueness of the reconstruction process is interpreted and a cohomological classification of possible global gauge symmetries is given. (author)

1996-12-21

Quantum adiabatic theorem for chemical reactions and systems with time-dependent orthogonalization

We systematically develop real Paley-Wiener theory for the Fourier transform on R^d for Schwartz functions, L^p-functions and distributions, in an elementary treatment based on the inversion theorem. As an application, we show how versions of classical Paley-Wiener theorems can be derived from the real ones via an approach which does not involve domain shifting and which may be put to good use for other transforms of Fourier type as well. An explanation is also given why the easily applied classical Paley-Wiener theorems are unlikely to be able to yield information about the support of a function or distribution which is more precise than giving its convex hull, whereas real Paley-Wiener theorems can be used to reconstruct the support precisely, albeit at the cost of combinatorial complexity. We indicate a possible application of real Paley-Wiener theory to partial differential equations in this vein ...

2008-01-01

Dixon's Theorem and random synchronization

A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the oscillating Schwinger Hamiltonian to establish the relationship between the internal (due to time-dependent eigenfunctions) and external (due to time-dependent Hamiltonian) time scales. We prove that this relationship needs to be taken as an independent quantum adiabatic approximation criterion. We give four examples, including logical expositions based on the spin-1/2 two-level system to address the gapped and gapless (due to energy level crossings) systems, as well as to understand how does this theorem allows one to study dynamical systems such as chemical reactions.

2011-01-01

A categorification of Morelli?s theorem

A transformation monoid on a set Omega is called synchronizing if it contains an element of rank 1 (that is, mapping the whole of Omega to a single point). In this paper, I tackle the question: given n and k, what is the probability that the submonoid of the full transformation monoid T_n generated by k random transformations is synchronizing? This question is analogous to Dixon's Theorem that two random permutations generate the symmetric or alternating group with high probability. Following the technique of Dixon's theorem, we need to analyse the maximal non-synchronizing submonoids of T_n. I develop a very close connection between transformation monoids and graphs, from which we obtain a description of non-synchronizing monoids as endomorphism monoids of graphs satisfying some very strong conditions. However, counting such graphs, and dealing with the intersections of their endomorphism monoids, seems difficult.

2011-01-01

British Library Electronic Table of Contents (United Kingdom)

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli?s description of the K-theory of a smooth projective toric variety (Morelli in Adv. Math. 100(2):154?182, 1993). Specifically, let X be a proper toric variety of dimension n and let Formula Not Shown be the Lie algebra of the compact dual (real) torus Formula Not Shown . Then there is a corresponding conical Lagrangian ??T ? M ? and an equivalence of triangulated dg categories Formula Not Shown , where Formula Not Shown is the triangulated dg category of perfect complexes of torus-equivariant coherent sheaves on X and Sh cc (M ?;?) is the triangulated dg category of complex of sheaves on M ? with co...

2011-01-01

Vector Boson Scattering in the Standard Model an Overview of Formulae

Exchange algebra and the Drinfeld-Sokolov theorem

Tree-level scattering amplitudes of longitudinally polarized electroweak vector bosons in the Standard Model are calculated using Mathematica package Feyncalc. The modifications of low-energy theorems for longitudinally polarized W and Z in the Standard Model are discussed.

1997-01-01

Examples of degenerated matter in astrophysics: white dwarf and neutron stars

We analyse the relation between the exchange algebra and the separation of the chiralities in classical Toda field theory. We show that there exists a conformally covariant Bloch wave basis such that the two chiralities commute. In terms of this basis we then reconstruct the periodic and local solution of Toda field theory. (orig.).

1991-01-01

Electroweak interactions and high-energy limit

Main features of star evolution are recalled. Then the general structure of white dwarf stars is examined. From the equation of state of an electron gas completely degenerated are deduced: mechanical equilibrium, Viriel theorem, mass-radius relationship and Chandrasekhar limit. These results are applied to neutron stars.

1982-06-01

Cavity detection by the electric method: the 3-dimensional case

A pedagogical introduction to the equivalence theorem for longitudinal vector bosons in electroweak theories is given and the problem of tree-level unitarity at high energies in models of electroweak interactions is briefly reviewed. To make the treatment self-containded, the basic of the Standard Model are summarized in an appendix.

1996-01-01

Roberts-type embeddings and conversion of transversal Tverberg's theorem

In this paper the authors prove a uniqueness theorem for the electric detection of cavities in a three dimensional solid from Cauchy data measured on the surface. The cavities, finite in number, are assumed to be insulating. The surfaces of the cavities are assumed to be smooth on the complement of a set that is, in some sense, negligible. (orig.)

2004-02-01

Low-energy Theorems for Vector Boson Scattering in SU(4)/SU(2) Model of Electroweak Symmetry Breaking

Central in the paper are two results on the existence of 'economical' embeddings in a Euclidean space. The first result (Corollary 1.4) states the existence of an embedding with image intersecting the large-dimensional planes in sets of 'controllable' dimension. The second result (Corollary 1.6) proves the existence of maps such that each small-dimensional plane contains 'controllably' many points of the image. Well known results of Noebeling-Pontryagin, Roberts, Hurewicz, Boltyanskii, and Goodsell can be obtained as consequences of these results. Their infinite-dimensional version concerning an embedding in a Hilbert space is also established (Theorem 1.8).

2005-12-31

Cosmic no-hair theorem in power-law inflation

Modifications of low-energy theorems for the scattering of longitudinally polarized W and Z bosons in an alternative model of electroweak symmetry breaking are discussed. The symmetry breaking pattern SU(4)/SU(2) leads to light (compared to 1 TeV) pseudo-Goldstone bosons. Their interactions with electroweak gauge bosons are described by chiral (or effective) lagrangian. Tree-level contribution of the pseudo-Goldstone bosons to the scattering amplitudes are computed. Comparison with the Standard Model is given.

1997-01-01

High air quality and low energy consumption. Performance of hybrid ventilation with CO2-sensors; Hoge luchtkwaliteit en lage energiebesparing. Goede prestaties van hybride ventilatie met CO2-sensoren

We prove a cosmic no-hair theorem for Bianchi models in power-law inflation. Provided that the potential of an inflaton {phi} is exp({minus}{lambda}{kappa}{phi}) with 0{le}{lambda}{lt} {radical}2/3 , we find that the isotropic power-law solution is the unique attractor for any initially expanding Bianchi-type models except type IX. For Bianchi type IX, this conclusion is also true if the initial ratio of the vacuum energy to the maximum three-curvature is larger than one half.

1992-02-15

Syzygy Theorems via comparison of order ideals on a hypersurface

The school building complex Waterland in The Hague, Netherlands, was built with a hybrid ventilation system. The indoor environment and energy consumption were monitored for one year. Air quality and thermal comfort are of a high quality and the consumption of energy for heating is circa 35% lower than normal. The Waterland project was one of eight demonstration projects, carried out within the framework of the ECBS-Annex 35: Hybrid ventilation in New and retrofitted Office Buildings. ECBS stands for the IEA-program Energy Conservation in Buildings and Community Systems. [Dutch] In ECBCs-annex 35 (ECBS staat voor het IEA-programma Energy Conservation in Buildings and Community Systems) is uitgebreid onderzoek gedaan naar hybride ventilatiesystemen in kantoren en scholen. Dit project heeft geleid tot acht internationale voorbeeldprojecten, waarvan scholencomplex Waterland te Den Haag er een van is. Het scholencomplex is in 2003 opgeleverd met een hybride ...

2005-11-01

British Library Electronic Table of Contents (United Kingdom)

We introduce a weak order ideal property that suffices for establishing the Evans-Griffith Syzygy Theorem. We study this weak order ideal property in settings that allow for comparison between homological algebra over a local ring R versus a hypersurface ring R =R/(x^n). Consequently we solve some relevant cases of the Evans-Griffith syzygy conjecture over local rings of unramified mixed characteristic p, with the case of syzygies of prime ideals of Cohen-Macaulay local rings of unramified mixed characteristic being noted. We reduce the remaining considerations to modules annihilated by p^s, s>0, that have finite projective dimension over a hypersurface ring.

2012-01-01

Quantum field theory of particles with braid group statistics in 2+1 dimensions

Ockham Efficiency Theorem for Stochastic Empirical Methods

The present thesis is concerned with the local quantum physics of relativistic particles and fields in three space-time dimensions, whose statistics is to be described by a representation of the braid group -- so-called plektons or, if the representation is Abelian, anyons. In particular the issue of the existence of free anyonic fields is addressed. In our context, these are operators affiliated with the 'local' field algebras and creating only single particle vectors from the vacuum. (Localizability here refers to regions extending to infinity in some spacelike direction.) Under a mild regularity condition for these fields, we can derive commutation relations which are not compatible with braid group statistics. Further, model-independent results concerning the PCT operator and the connection of spin and statistics are obtained. Assuming the observable algebra to satisfy the Bisognano-Wichmann theorem, a PCT theorem for plektons is derived. ...

1997-01-01

British Library Electronic Table of Contents (United Kingdom)

Ockham?s razor is the principle that, all other things being equal, scientists ought to prefer simpler theories. In recent years, philosophers have argued that simpler theories make better predictions, possess theoretical virtues like explanatory power, and have other pragmatic virtues like computational tractability. However, such arguments fail to explain how and why a preference for simplicity can help one find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new solution to that problem is the Ockham efficiency theorem (Kelly 2002, Minds Mach 14:485?505, 2004, Philos Sci 74:561?573, 2007a, b, Theor Comp Sci 383:270?289, c, d; Kelly and Glymour 2004), which states that scientists who heed Ockham?s razor retract their opinions less often and s...

2010-01-01

Linear family of Lie brackets on the space of matrices $Mat(n\\times m,\\K)$ and Ado's Theorem

Explicit Randomness is not Necessary when Modeling Probabilistic Encryption

In this paper we classify a linear family of Lie brackets on the space of rectangular matrices $Mat(n\\times m,\\K)$ and we give an analogue of the Ado's Theorem. We give also a similar classification on the algebra of the square matrices $Mat(n, \\K)$ and as a consequence, we prove that we can't built a faithful representation of the $(2n+1)$-dimensional Heisenberg Lie algebra $\\mathfrak{H}_n$ in a vector space $V$ with $\\dim V\\leq n+1$. Finally, we prove that in the case of the algebra of square matrices $Mat(n,\\K)$, the corresponding Lie algebras structures are a contraction of the canonical Lie algebra $\\mathfrak{gl}(n,\\K)$.

2008-01-01

1 2 3 4 5 6

Deformations of topological open strings

Although good encryption functions are probabilistic, most symbolic models do not capture this aspect explicitly. A typical solution, recently used to prove the soundness of such models with respect to computational ones, is to explicitly represent the dependency of ciphertexts on random coins as labels. In order to make these label-based models useful, it seems natural to try to extend the underlying decision procedures and the implementation of existing tools. In this paper we put forth a more practical alternative based on the following soundness theorem. We prove that for a large class of security properties (that includes rather standard formulations for secrecy and authenticity properties), security of protocols in the simpler model implies security in the label-based model. Combined with the soundness result of (\\textbf{?}) our theorem enables the translation of security results in unlabeled symbolic models to computational security.

2006-01-01

A sum rule approach to the violation of Dashen`s theorem; Une approache de la violation du theoreme de Dashen par les regles de somme

Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra - the complex of multilinear maps on the boundary Hilbert space. This complex is known to have the structure of a Gerstenhaber algebra (Deligne theorem), which is also found in closed string theory. Generalising the case of function algebras with a B-field, we identify the algebraic operations of the bulk sector, in terms of the mixed correlators. This gives a physical realisation of the Deligne theorem. We translate to the language of certain operads (spaces of d-discs with gluing) and d-algebras, and comment on generalisations, notably to the AdS/CFT correspondence. The formalism is applied to the topological A- and B-models on the disc. (author)

2001-01-01

The (2+1) Dirac Equations with $\\delta$ Potential

A classic sum rule by Das et al. is extended to seven of the low-energy constant K{sub i}, introduced by Urech, which parameterizes electromagnetic corrections at chiral order O(e{sup 2}p{sup 2}). Using the spurion formalism, a simple convolution representation is shown to hold and the structure in terms of the chiral renormalization scale, QCD renormalization scale and the QED gauge parameter is displayed. The role of the resonances is studied as providing rational interpolants to relevant QCD n-point functions in the Euclidean domain. A variety of asymptotic constraints must be implemented which have phenomenological consequences. A current assumption concerning the dominance of the lowest-lying resonances is shown clearly to fail in some cases. (author)

1999-10-01

Studying the triple-Higgs vertex in the process. gamma. gamma. yields HH at TeV energies

In this Letter the bound states of (2+1) Dirac equation with the cylindrically symmetric $\\delta (r-r_{0})$-potential are discussed. It is surprisingly found that the relation between the radial functions at two sides of $r_{0}$ can be established by an SO(2) transformation. We obtain a transcendental equation for calculating the energy of the bound state from the matching condition in the configuration space. The condition for existence of bound states is determined by the Sturm-Liouville theorem.

2001-01-01

Studying the triple-Higgs vertex in the process #gamma##gamma##->#HH at TeV energies

In the framework of the equivalence theorem the one-loop helicity amplitudes and cross section for the double Higgs production process {gamma}{gamma}{yields}HH are calculated. It is shown that the cross section is measurable at TeV {gamma}{gamma} colliders and is marginally sensitive to the triple-Higgs variation. (orig.).

1992-06-04

Some insights from total collapse

In the framework of the equivalence theorem the one-loop helicity amplitudes and cross section for the double Higgs production process #gamma##gamma##->#HH are calculated. It is shown that the cross section is measurable at TeV #gamma##gamma# colliders and is marginally sensitive to the triple-Higgs variation. (orig.).

On the homology of exotic Springer fibers

We discuss the Sundman-Weierstrass theorem of total collapse in its historical context. This remarkable and relatively simple result, a type of stability criterion, is at the crossroads of some interesting developments in the gravitation Newtonian N-body problem. We use it as motivation to explore the connections to such important concepts as integrability, singularities and tyipicality in order to gain some insight on the transition from a predominantly quantitative to a novel qualitative approach to dynamical problems that took place at the end of the 19th century.

2008-01-01

On the GBDT version of the B\\"acklund-Darboux transformation and its applications to the linear and nonlinear equations and Weyl theory

We determine the structure of the total homology groups of exotic Springer fibers as affine Weyl group representations. As applications, we provide single top/socle property of standard modules in the exotic Deligne-Langlands correspondence (except for root of unity case), an analogue of Verma's theorem, the coincidence of analytic/geometric gradings in the $C ^{\\infty}$-realization of anti-spherical modules of graded Hecke algebras of type $\\mathsf{BC}$ with unequal parameters, among others.

2011-01-01

Limit cycle's uniqueness for second order O.D.E.'s polynomial in $\\dot x$

A general theorem on the GBDT version of the B\\"acklund-Darboux transformation for systems rationally depending on the spectral parameter is treated and its applications to nonlinear equations are given. Explicit solutions of direct and inverse problems for Dirac-type systems, including systems with singularities, and for the system auxiliary to the $N$-wave equation are reviewed. New results on explicit construction of the wave functions for radial Dirac equation are obtained.

2009-01-01

Hamming Weights in Irreducible Cyclic Codes

We prove a uniqueness result for limit cycles of the second order ODE $\\ddot x + \\sum_{j=1}^{J}f_{j}(x)\\dot x^{j} + g(x) = 0$. We extend a uniqueness result proved in \\cite{CRV}. The main tool applied is an extension of Massera theorem proved in \\cite{GS}.

2010-01-01

Electromagnetic properties of generalized Majorana particles

Irreducible cyclic codes are an interesting type of codes and have applications in space communications. They have been studied for decades and a lot of progress has been made. The objectives of this paper are to survey and extend earlier results on the weight distributions of irreducible cyclic codes, present a divisibility theorem and develop bounds on the weights in irreducible cyclic codes.

2011-01-01

Cosmic no-hair in Brans-Dicke theory

We prove a theorem stating that a massive Majorana particle (a CPT-self-conjugate particle) with arbitrary spin J can possess only an anapole moment and multipoles of that. We also show that massless Majorana particles, except those of spin (1/2, do not have any single-photon electromagnetic form factor.

1989-02-20

Boundary string field theory of the D{bar D} system

In this short note we report our finding that within the context of alternative version of the Brans-Dicke theory (for #omega# #>=# -3/2, where #omega# is the Brans-Dicke parameter) the anisotropic Bianchi type cosmological models evolve towards the de Sitter isotropic universe. In short it is shown that during inflation there is no difference between the Brans-Dicke theory and General Relativity. Our result can thus be viewed as a generalization of the Wald's theorem for General Relativity. (author). 5 refs.

2009-04-07

Bosonic colored group field theory

We develop the boundary string field theory approach to tachyon condensation on the D{bar D} system. Particular attention is paid to the gauge fields, which combine with the tachyons in a natural way. We derive the RR couplings of the system and express the result in terms of Quillen's superconnection. The result is related to an index theorem, and is thus shown to be exact.

2001-05-15

Action and locality principle for noncommutative scalar field theories; Wirkungs- und Lokalitaetsprinzip fuer nichtkommutative skalare Feldtheorien

Bosonic colored group field theory is considered. Focusing first on dimension four, namely the colored Ooguri group field model, the main properties of Feynman graphs are studied. This leads to a theorem on optimal perturbative bounds of Feynman amplitudes in the ''ultraspin'' (large spin) limit. The results are generalized in any dimension. Finally, integrating out two colors we write a new representation, which could be useful for the constructive analysis of this type of models. (orig.)

2010-12-01

A new algebraic technique for polynomial-time computing the number modulo 2 of Hamiltonian decompositions and similar partitions of a graph's edge set

We develop a general framework for the formulation of the action principle and the noether theorem for classical noncommutative field theories. We give a concrete example of an algebra that fits into this framework. It describes a scalar field theory on noncommutative minkowski space. We develop a notion of locality for this algebra and investigate the locality properties of localised interaction terms. This leads us to the definition of local functionals on the field algebra. We propose a scheme for the quantisation of these functionals. (orig.) [German] Wir entwickeln eine allgemeinen rahmen, der es erlaubt, das wirkungsprinzip und das noether-theorem fuer klassische nichtkommutative feldtheorien zu formulieren. Als ein konkretes beispiel betrachten wir eine algebra, die sich in diesem rahmen einfuegt, und die eine skalare feldtheorie auf dem nichtkommutativen minkowski-raum beschreibt. Fuer diese algebra wird ein lokalitaetsbegriff ...

2003-12-01

A Numerical Algorithm for Determining the Contact Stress of Circular Crowned Roller Compressed between Two Flat Plates

In Graph Theory a number of results were devoted to studying the computational complexity of the number modulo 2 of a graph's edge set decompositions of various kinds, first of all including its Hamiltonian decompositions, as well as the number modulo 2 of, say, Hamiltonian cycles/paths etc. While the problems of finding a Hamiltonian decomposition and Hamiltonian cycle are NP-complete, counting these objects modulo 2 in polynomial time is yet possible for certain types of regular undirected graphs. Some of the most known examples are the theorems about the existence of an even number of Hamiltonian decompositions in a 4-regular graph and an even number of such decompositions where two given edges e and g belong to different cycles (Thomason, 1978), as well as an even number of Hamiltonian cycles passing through any given edge in a regular odd-degreed graph (Smith's theorem). The present article introduces a new algebraic technique which ...

2010-01-01

Science.gov (United States)

The main purpose of this paper is to explore a numerical algorithm for determining the contact stress when a circular crowned roller is compressed between two plates. To start with, the deformation curve on a plate surface will be derived by using the contact mechanical model. Then, the contact stress distribution along the roller which occurs on the plate surface is divided into three parts: from the center of contact to the edge, the edge and apart from the contact line. The first part is calculated by the elastic contact theorem for the contact subjected to nominal stress between non-crowned parts of roller and plates, the second part is obtained by the classical Hertzian contact solution for the contact between crowned parts of roller and plates, and the third part is simulated as exponential decay. In order to overcome the defect of the half space theorem, in which a plate with infinite thickness is assumed initially, a weighting method is ...

2007-01-01

Virtual and resonance levels in screened Coulomb potentials

Towards Antihydrogen Trapping and Spectroscopy at ALPHA

Two methods for computation of real, virtual and quasistationary energy eigenvalues are considered: summation of divergent perturbation series, solution of integral equations for t matrix on physical and nonphysical sheets of energy. The results of energy computation for s-, p- and d-states in potentials of a screened Coulomb type are presented. It is shown on an example of the Yukawa potential that the energy eigenvalues given by both these methods coincide with high precision. As an illustration the positions of real (deuteron) and virtual (singlet deuteron) poles of the np-scattering amplitude are calculated. For Yukawa type potentials the new theorem of symmetry for bound and virtual levels is discussed.

2003-09-01

Spontaneous radiation of an electron beam in a free-electron laser with a quadrupole wiggler

Spectroscopy of antihydrogen has the potential to yield high-precision tests of the CPT theorem and shed light on the matter-antimatter imbalance in the Universe. The ALPHA antihydrogen trap at CERN's Antiproton Decelerator aims to prepare a sample of antihydrogen atoms confined in an octupole-based Ioffe trap and to measure the frequency of several atomic transitions. We describe our techniques to directly measure the antiproton temperature and a new technique to cool them to below 10 K. We also show how our unique position-sensitive annihilation detector provides us with a highly sensitive method of identifying antiproton annihilations and effectively rejecting the cosmic-ray background.

2011-01-01

1 2 3 4 5 6

Sharp regularity for certain nilpotent group actions on the interval

A calculation is presented of spontaneous radiation emitted by an electron beam passing through a continuously rotating quadrupole magnetic undulator. It is shown that radiation spectrum emitted in forward direction of beam propagation has four peaks, corresponding to four betatron frequencies. Utilizing the Madey theorem, a stimulated emission is calculated and presented as gain versus frequency curves, for different values of the quadrupole magnetic field. A free-electron laser operating at two or three radiation frequencies with a quadrupole magnetic wiggler is suggested.

1986-09-01

Quasilinear theory of the 2D Euler equation

According to the classical Plante-Thurston Theorem, all nilpotent groups of $C^2$-diffeomorphisms of the closed interval are Abelian. Using techniques coming from the works of Denjoy and Pixton, Farb and Franks constructed a faithful action by $C^1$-diffeomorphisms of $[0,1]$ for every finitely-generated, torsion-free, non-Abelian nilpotent group. In this work, we give a version of this construction that is sharp in what concerns the H\\"older regularity of the derivatives. Half of the proof relies on results on random paths on Heisenberg-like groups that are interesting by themselves.

2011-01-01

On the Generic vanishing of certain Koszul cohomology groups

Motivated by the numerical investigations of Laval, Dubrulle & Nazarenko (1999), we develop a quasilinear theory of the 2D Euler equation and derive an integro-differential equation for the evolution of the coarse-grained vorticity. This equation respects all the invariance properties of the Euler equation and conserves angular momentum in a circular domain and linear impulse in a channel (as well as in an infinite domain). The explicit energy is not rigorously conserved as it is partly transfered into fine-grained fluctuations but the total energy is conserved. We prove a H-theorem for the Fermi-Dirac entropy and make the connection with statistical theories of 2D turbulence.

2000-01-01

Moderate Deviations for a Curie-Weiss model with dynamical external field

We propose a new approach to study Koszul cohomology of general $g^r_d$'s on general curves via degenerations and deformations. As an application of this new method, we prove projective normality for general line bundles $L$ on general curves with $h^1(L)\\le1$ and degree greater than roughly $(5/4)g$. This improves the bound in a classical theorem of Green and Lazarsfeld. Also we give some partial results on vanishing of higher syzygies for line bundles with $h^1(L)=1$.

2011-01-01

Incompatibility of the Copenhagen interpretation with quantum formalism and its reasons

In the present paper we prove moderate deviations for a Curie-Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard. The results extend those already obtained in the case of a constant external field by Eichelsbacher and L\\"owe. The Curie-Weiss model with dynamic external field is related to the so called dynamic Z-random walks. We also prove a moderate deviation result for the dynamic Z-random walk, completing the list of limit theorems for this object.

2011-01-01

Concentration of measures via size-biased couplings

It is proved the mathematical theorem, that the wave function describes the statistical ensemble of particles, but not a single particle. Supposition, that the wave function describes a single particle appears to be incompatible with formalism of quantum mechanics. One discusses the reasons, why this very simple statement has not been proved mathematically for many years. The reason lies in application of the trial and error methods for construction of the quantum mechanics. Application of this method as the main tool of investigation during eighty years generated "fitting mentality" of all microwold researchers.

2006-01-01

British Library Electronic Table of Contents (United Kingdom)

Let Y be a nonnegative random variable with mean?? and finite positive variance ? 2, and let Y s , defined on the same space as Y, have the Y size-biased distribution, characterized by Formula Not Shown Under a variety of conditions on Y and the coupling of Y and Y s , including combinations of boundedness and monotonicity, one sided concentration of measure inequalities such as Formula Not Shown hold for some explicit A and B. The theorem is applied to the number of bulbs switched on at the terminal time in the so called lightbulb process of Rao et?al. (Sankhy? 69:137?161, 2007).

2011-01-01

Atanassov's Intuitionistic Fuzzy Ideals of Gamma Semigroups

A neighborhood condition on all fractional $[a,b]$-factors

The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of gamma semigroups in order to obtain some characterization theorems. We also introduce the notion of Atanassov's intuitionistic fuzzy ideal extension in a gamma semigroup and investigate some of their important properties. A regular gamma semigroup has been characterized in terms of Atanasov's intutionistic fuzzy ideal. Characterization of prime ideal of a gamma semigroup has also been obtained in terms of Atanassov's intutionistic fuzzy ideal extension.

2011-01-01

A Remark on Gauge Transformations and the Moving Frame Method

In this note, we derive from Anstee's fractional $(g,f)$-factor theorem a similar characterization for the property of all fractional $(g,f)$-factors. Let $a

2011-01-01

Wave electromagnetic fields induced by instantaneous braking of charges

In this note we give a shorter proof of recent regularity results by Riviere and Riviere-Struwe. We differ from the mentioned articles only in using the direct method of Helein's moving frame to construct a suitable gauge transformation. Though this is neither new nor surprising, it enables us to describe a proof of regularity using besides the duality of Hardy- and BMO-space only elementary arguments of calculus of variations and algebraic identities. Moreover, we remark that in order to prove Hildebrandt's conjecture one can avoid the Nash-Moser imbedding theorem. There are no new results presented here, nor are there any techniques we could claim originality for.

2009-01-01

Valued Graphs and the Representation Theory of Lie Algebras

Exact expressions for wave electromagnetic fields during instantaneous braking of two differently charged discs uniformly moving in the opposite directions have been derived. Analysis of their properties has been made. It is shown that electromagnetic wave fields during instantaneous braking of charges have a tearing nature and the Umov-Poynting theorem in the integral form is realized only at a certain value of parameter #alpha# which determines charges rates at the moment of braking. The value of parameter #alpha# is in the ranges from 0.5 to #sq root#3/2. The wave field is formed already in the absence of motion of charged discs. It is a good example confirming the conclusion that in the case of nonstationary electromagnetic fields, performance of reaction force of the wave field can differ fram radiation energy.

The geometry emerging from the symmetries of a quantum system

Quivers (directed graphs) and species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their applications to the representation theory of associative algebras, Lie algebras, and quantum groups. In this paper, we discuss the most important results in the representation theory of species, such as Dlab and Ringel's extension of Gabriel's theorem, which classifies all species of finite and tame representation type. We also explain the link between species and K-species (where K is a field). Namely, we show that the category of K-species can be viewed as a subcategory of the category of species. Furthermore, we prove two results about the structure of the tensor ring of a species containing no oriented cycles that do not appear in the literature. Specifically, we prove that two such species have isomorphic tensor rings if and ...

2011-01-01

The Dissipative Merger Progenitors of Elliptical Galaxies

We investigate the relation between the symmetries of a quantum system and its topological quantum numbers, in a general C*-algebraic framework. We prove that, under suitable assumptions on the symmetry algebra, there exists a generalization of the Bloch-Floquet transform which induces a direct-integral decomposition of the algebra of observables. Such generalized transform selects uniquely the set of "continuous sections" in the direct integral, thus yielding a Hilbert bundle. The emerging geometric structure provides some topological invariants of the quantum system. Two running examples provide an Ariadne's thread through the paper. For the sake of completeness, we review two related theorems by von Neumann and Maurin and compare them with our result.

2009-01-01

Satisfying story of how it all began

We address the deviations of the scaling relations of elliptical galaxies from the expectations based on the virial theorem and homology, including the "tilt" of the "fundamental plane" and the steep decline of density with mass. We show that such tilts result from dissipative major mergers once the gas fraction available for dissipation declines with progenitor mass, and derive the scaling properties of the progenitors. We use hydrodynamical simulations to quantify the effects of major mergers with different gas fractions on the structural properties of galaxies. The tilts are driven by the differential shrinkage of the effective stellar radius as a function of dissipation in the merger, while the correlated smaller enhancements in internal velocity and stellar mass keep the slope of the velocity-stellar mass relation near V \\pr M_*^{1/4}. The progenitors match a straightforward model of disc formation in LCDM haloes. Their total to stellar mass ratio within the ...

2006-01-01

Revisited the mathematical derivation wall thickness measurement of pipe for radiography

{sup N}ow this 'Big Bang' idea seemed to me to be unsatisfactory...for it is an irrational process that cannot be described in scientific terms.' With this rather derisory remark (or at least so intended) in a 1950 radio broadcast, Fred Hoyle named the theory that rivalled his steady-state theory. The Big Bang has subsequently become the dominant paradigm in attempts to understand our universe. It is also one of the dominant ways in which popular-science writing seeks to persuade people to part with their cash. Simon Singh has rapidly made a name for himself as one of the leading popularizers of science, with his previous books Fermat's Last Theorem and The Code Book bringing accessible science to a wide audience . Big Bang brings him to a much busier marketplace, where he must compete both with other science writers and with working scientists. (U.K.)

2004-12-01

Perturbations of Schwarzschild Black Holes in Chern-Simons Modified Gravity

Wall thickness measurement of pipe is very important of the structural integrity of the industrial plant. However, the radiography method has an advantage because the ability of penetrating the insulated pipe. This will have economic benefit for industry. Moreover, the era of digital radiography has more advantages because the speed of radiographic work, less exposure time and no chemical used for film development. Either the conventional radiography or digital radiology, the wall thickness measurement is using the tangential radiography technique (TRT). In case, of a large diameter, pipe (more than inches) the determination maximum penetration wall thickness must be taken into the consideration. This paper is revisited the mathematical derivation of the determination of wall thickness measurement based on tangential radiography technique (TRT). The mathematical approach used in this derivation is the Pythagoras theorem and geometrical principles. In order to ...

2007-07-01

PCA consistency in high dimension, low sample size context

We study perturbations of a Schwarzschild black hole in Chern-Simons modified gravity. We begin by showing that Birkhoff's theorem holds for a wide family of Chern-Simons coupling functions, a scalar field present in the theory that controls the strength of the Chern-Simons correction to the Einstein-Hilbert action. After decomposing the perturbations in spherical harmonics, we study the linearized modified field equations and find that axial and polar modes are coupled, in contrast to general relativity. The divergence of the modified equations leads to the Pontryagin constraint, which forces the vanishing of the Cunningham-Price-Moncrief master function associated with axial modes. We analyze the structure of these equations and find that the appearance of the Pontryagin constraint yields an overconstrained system that does not allow for generic black hole oscillations. We illustrate this situation by studying the case characterized by a canonical choice of the ...

2007-01-01

Optimized pulse sequences for the suppression of decoherence in quantum information

Principal Component Analysis (PCA) is an important tool of dimension reduction especially when the dimension (or the number of variables) is very high. Asymptotic studies where the sample size is fixed, and the dimension grows [i.e., High Dimension, Low Sample Size (HDLSS)] are becoming increasingly relevant. We investigate the asymptotic behavior of the Principal Component (PC) directions. HDLSS asymptotics are used to study consistency, strong inconsistency and subspace consistency. We show that if the first few eigenvalues of a population covariance matrix are large enough compared to the others, then the corresponding estimated PC directions are consistent or converge to the appropriate subspace (subspace consistency) and most other PC directions are strongly inconsistent. Broad sets of sufficient conditions for each of these cases are specified and the main theorem gives a catalogue of possible combinations. In preparation for these results, we show that the ...

2009-01-01

On the Nature of the Cosmological Constant Problem

The dynamical decoupling (DD) aims at suppressing the decoherence by means of coherent control pulses. Even if devices exist where instantaneous pulses are an adequate approximation, experimentally a finite duration #tau#_p and a bounded amplitude are inevitable. They are the cause of additional errors which can be corrected by designing the pulse shape appropriately. The new pulse has the overall effect of an ideal, instantaneous pulse with the advantage of decoupling the spin (or qubit) from the bath up to the order O(#tau#_p"3). The limitation of the no-go theorem for #pi# pulses is avoided. Hence, the Uhrig sequence (UDD), originally thought for ideal #pi# pulses, works also for bounded control Hamiltonians. Numerical simulations show that concatenated sequences of real pulses are effective against general decoherence.

2010-03-21

On Bregman Distances and Divergences of Probability Measures

General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily conceived. On the other hand, experimental evidences show that there exists a non-zero cosmological constant, which implies in a deSitter space-time, not compatible with the assumed Minkowski structure. Such inconsistency is shown to be a consequence of the lack of a application independent curvature standard in Riemann's geometry, leading eventually to the cosmological constant problem in general relativity. We show how the curvature standard in Riemann's geometry can be fixed by Nash's theorem on locally embedded Riemannian geometries, which imply in the existence of extra dimensions. The resulting gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the ...

2009-01-01

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Mixmaster: fact and belief

The paper introduces scaled Bregman distances of probability distributions which admit non-uniform contributions of observed events. They are introduced in a general form covering not only the distances of discrete and continuous stochastic observations, but also the distances of random processes and signals. It is shown that the scaled Bregman distances extend not only the classical ones studied in the previous literature, but also the information divergence and the related wider class of convex divergences of probability measures. An information processing theorem is established too, but only in the sense of invariance w.r.t. statistically sufficient transformations and not in the sense of universal monotonicity. Pathological situations where coding can increase the classical Bregman distance are illustrated by a concrete example. In addition to the classical areas of application of the Bregman distances and convex divergences such as recognition, classification, ...

2009-01-01

Global exponential stability of periodic solution for shunting inhibitory CNNs with delays

We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. Surprisingly few facts are known about the 'Mixmaster' dynamics of these models, while at the same time most of the commonly held beliefs are rather vague. In this paper, we use Mixmaster facts as a base to build an infrastructure that makes it possible to sharpen the main Mixmaster beliefs. We formulate explicit conjectures concerning (i) the past asymptotic states of type IX solutions and (ii) the relevance of the Mixmaster/Kasner map for generic past asymptotic dynamics. The evidence for the conjectures is based on a study of the stochastic properties of this map in conjunction with dynamical systems techniques. We use a dynamical systems formulation, since this approach has so far been the only successful path to obtain theorems, but we also make comparisons with the 'metric' ...

2009-04-07

Global exponential stability of periodic solution for shunting inhibitory CNNs with delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence and stability of periodic solution for shunting inhibitory cellular neural networks (SICNNs) with delays x-bar {sub ij}(t)=-a{sub ij}(t)x{sub ij}(t)--bar B{sup kl}-bar Nr(i,j)B{sub ij}{sup kl}(t)f{sub ij}(x{sub kl}(t))x{sub ij}(t)--bar C{sup kl}-bar Nr(i,j)C{sub ij}{sup kl}(t)g{sub ij}(x{sub kl}(t-{tau}{sub kl}))x{sub ij}(t)+L{sub ij}(t)

2005-03-28

Equivariant cohomology of K-contact manifolds

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence and stability of periodic solution for shunting inhibitory cellular neural networks (SICNNs) with delays x-bar _i_j(t)=-a_i_j(t)x_i_j(t)--bar B"k"l-bar Nr(i,j)B_i_j"k"l(t)f_i_j(x_k_l(t))x_i_j(t)--bar C"k"l-bar Nr(i,j)C_i_j"k"l(t)g_i_j(x_k_l(t-#tau#_k_l))x_i_j(t)+L_i_j(t).

2005-03-28

Electron-phonon based local mode descriptions of displacive transformations

We investigate the equivariant cohomology of the natural torus action on a K-contact manifold and its relation to the topology of the Reeb flow. Using the contact moment map, we show that the equivariant cohomology of this action is Cohen-Macaulay, which is a generalization of equivariant formality for torus actions without fixed points. As a consequence, a generic component of the contact moment map is a perfect Morse-Bott function for the basic cohomology of the orbit foliation F of the Reeb flow. Assuming that the closed Reeb orbits are isolated, we show that the basic cohomology of F is trivial in odd degrees, and its dimension equals the number of closed Reeb orbits. We characterize the K-contact manifolds with minimal number of closed Reeb orbits as real cohomology spheres. We also prove a GKM type theorem for K-contact manifolds, which allows us to calculate the equivariant cohomology algebra of K-contact manifolds in presence of the nonisolated GKM ...

2011-01-01

D-branes and creation of strings

As a general approach to the problem of precursive behavior in alloys that undergo a displacive transformation, defect theories are becoming increasingly popular. However, the microscopic origin of the proposed defects is usually not considered. Yu and Anderson (1984) have argued that properties of strong-coupling superconductors, such as the A-15 compounds, imply a breakdown of Migdal's theorem (the adiabatic, or Born-Oppenheimer approximation for separation of electrons and phonons) in these systems. The electron-phonon coupling is so strong that it must be incorporated already in zeroth order. This is the basis for local phonon models, in which the electron-phonon coupling provides an effective double well potential for a localized group of atoms. The Yu-Anderson model and an analogous local Jahn-Teller model (Abell, 1983) are reviewed in connection with displacive transformations in strong-coupling alloys.

1986-01-01

Conjugate variables in quantum field theory: the basic case

We review two types of D-brane processes where open strings are created. In the first type, a closed string incident on a collection of D-branes is converted into a number of open strings running along them. For the case of threebranes we compare the leading absorption rate with that in semiclassical gravity, and find exact agreement. A supersymmetric non-renormalization theorem guarantees that this agreement survives all corrections in powers of the string coupling times the number of branes. The second type of process is creation of stretched open strings by crossing D-branes. We show that this is possible whenever a p-brane passes through an (8-p)-brane positioned orthogonally to it. The extra attractive force exerted by the stretched open string is crucial for finding that the net force cancels in this BPS system. (orig.)

1998-11-01

Brane-world Quantum Gravity

Within standard quantum field theory of one scalar field we define operators conjugate to the energy-momentum operators of the theory. They are singled out by calculational simplicity in Fock space. In terms of the underlying scalar field they are non-local. We establish their algebra where it turns out that time and space operators do not commute. Their transformation properties with respect to the conformal group are derived. Solving their eigenvalue problem permits to reconstruct the Fock space in terms of the eigenstates. It is indicated how Paulis theorem may be circumvented. As an application we form the analogue of S-matrices which yields information on the structure of the underlying spacetime. Similarly we define fields and look at their equations of motion.

2010-01-01

Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups

The Arnowitt-Deser-Misner canonical formulation of general relativity is extended to the covariant brane-world theory in arbitrary dimensions. The exclusive probing of the extra dimensions makes a substantial difference, allowing for the construction of a non-constrained canonical theory. The quantum states of the brane-world geometry are defined by the Tomonaga-Schwinger equation, whose integrability conditions are determined by the classical perturbations of submanifolds contained in the Nash's differentiable embedding theorem. In principle, quantum brane-world theory can be tested by current experiments in astrophysics and by near future laboratory experiments at Tev energy. The implications to the black-hole information loss problem, to the accelerating cosmology, and to a quantum mathematical theory of four-sub manifolds are briefly commented.

2007-01-01

Algebraic approach to solve tt dilepton equations

We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decompostion of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilising a certain lattice of "admissible subsets" of the vertices of C. We then characterise those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.

2011-01-01

Acoustic resonances in two-dimensional radial sonic crystal shells

The set of nonlinear equations describing the standard model kinematics of the top quark antiquark production system in the dilepton decay channel has at most a fourfold ambiguity due to two not fully reconstructed neutrinos. Its most precise solution is of major importance for measurements of top quark properties like the top quark mass and tt spin correlations. Simple algebraic operations allow one to transform the nonlinear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be analytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree 16. The number of its real solutions is determined analytically by means of Sturm's theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through ...

2005-11-01

A unified framework for biological evolution and stochastic quantization

Radial sonic crystals (RSC) are fluidlike structures infinitely periodic along the radial direction that verify the Bloch theorem and are possible only if certain specially designed acoustic metamaterials with mass density anisotropy can be engineered (see Torrent and Sanchez-Dehesa 2009 Phys. Rev. Lett. 103 064301). A comprehensive analysis of two-dimensional (2D) RSC shells is reported here. A given shell is in fact a circular slab with a central cavity. These finite crystal structures contain Fabry-Perot-like resonances and modes strongly localized at the central cavity. Semi-analytical expressions are developed to obtain the quality factors of the different resonances, their symmetry features and their excitation properties. The results reported here are completely general and can be extended to equivalent 3D spherical shells and to their photonic counterparts.

2010-07-15

3D Fourier synthesis of a new X-ray picture identical in projection to a previous picture

We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed which is related to a new type of stochastic quantization. We find that the probability distribution of the ensemble of particles can be decomposed into eigenfunctions associated to a discrete spectrum of eigenvalues. In absence of interactions between the particles, the out-of-equilibrium dynamics asymptotically relaxes towards the fundamental state. This phenomenon can be related with the Fisher theorem in biology. On the contrary, in presence of scattering processes the evolution reaches a steady state in which the distribution of the ensemble of particles is characterized by a Bose-Einstein statistics. In order to show a concrete example of this stochastic quantization we have solved explicitly the case in which the potential ...

2010-01-01

The clouds of physics and Einstein's last query: Can quantum mechanics be derived from general relativity?

A central problem in diagnostic radiology is to compare a new X-ray picture with a previous picture and from this comparison be able to decide if anatomical changes have occurred in the patient or not. It is of primary interest that these pictures are identical in projection. If not it is difficult to decide with confidence if differences between the pictures are due to anatomical changes or differences in their projection geometry. In this thesis we present a non invasive method that makes it possible to find the relative changes in the projection geometry between the exposure of a previous picture and a new picture. The method presented is based on the projection slice theorem (central section theorem). Instead of an elaborate search for a single new picture a pre-planned set of pictures are exposed from a circular orbit above the patient. By using 3D Fourier transform techniques we are able to synthesize a new X-ray picture from this set of ...

1993-11-01

Stabilization and limit theorems for geometric functionals of Gibbs point processes

Towards the end of the 19th century, Kelvin pronounced as the "clouds of physics" 1) the failure of the Michelson-Morely experiment to detect an ether wind, 2) the violation of the classical mechanical equipartition theorem in statistical thermodynamics. And he believed that the removal of these clouds would bring physics to an end. But as we know, the removal of these clouds led to the two great breakthoughts of modern physics: 1) The theory of relativity, and 2) to quantum mechanics. Towards the end of the 20th century more clouds of physics became apparent. They are 1) the riddle of quantum gravity, 2) the superluminal quantum correlations, 3) the small cosmological constant. Furthermore, there is the riddle of dark energy making up 70% of the physical universe, the non-baryonic cold dark matter making up 26% and the very small initial entropy of the universe. An attempt is made to explain the importance of these clouds for the future of physics. Conjectures for ...

2008-01-01

Research on ambient temperature passive magnetic bearings at the Lawrence Livermore National Laboratory

Given a Gibbs point process $\\P^{\\Psi}$ on $\\R^d$ having a weak enough potential $\\Psi$, we consider the random measures $\\mu_\\la := \\sum_{x \\in \\P^{\\Psi} \\cap Q_\\la} \\xi(x, \\P^{\\Psi} \\cap Q_\\la) \\delta_{x/\\la^{1/d}}$, where $Q_{\\la} := [-\\la^{1/d}/2,\\la^{1/d}/2]^d$ is the volume $\\la$ cube and where $\\xi(\\cdot,\\cdot)$ is a translation invariant stabilizing functional. Subject to $\\Psi$ satisfying a localization property and translation invariance, we establish weak laws of large numbers for $\\la^{-1} \\mu_\\la(f)$, $f$ a bounded test function on $\\R^d$, and weak convergence of $\\la^{-1/2} \\mu_\\la(f),$ suitably centered, to a Gaussian field acting on bounded test functions. The result yields limit laws for geometric functionals on Gibbs point processes including the Strauss and area interaction point processes as well as more general point processes defined by the Widom-Rowlinson and hard-core model. We provide applications to random sequential packing ...

2008-01-01

Partial Isometries of a Sub-Riemannian Manifold

Research performed at the Lawrence Livermore National Laboratory on the equilibrium and stability of a new class of ambient-temperature passive bearing systems is described. The basic concepts involved are: (1) Stability of the rotating system is only achieved in the rotating state. That is, disengaging mechanical systems are used to insure stable levitation at rest (when Earnshaw`s theorem applies). (2) Stable levitation by passive magnetic elements can be achieved if the vector sum of the force derivatives of the several elements of the system is net negative (i.e. restoring) for axial, transverse, and tilt-type perturbations from equilibrium. To satisfy the requirements of (2) using only permanent magnet elements we have employed periodic ``Halbach arrays.`` These interact with passive inductive loaded circuits and act as stabilizers, with the primary forces arising from axially symmetric permanent-magnet elements. Stabilizers and other elements needed to create ...

1997-04-01

On Sums of Generating Sets in (Z_2)^n

In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$. Then the pair $(H,g_H)$ defines a sub-Riemannian structure on $M$. We call a $C^1$-map $f:(M,H,g_H)\\to (N,h)$ into a Riemannian manifold $(N,h)$ a {\\em partial isometry} if the derivative map $df$ restricted to $H$ is isometric; in other words, $f^*h|_H=g_H$. The main result states that if $\\dim N>k$ then a smooth $H$-immersion $f_0:M\\to N$ satisfying $f^*h|_H

2010-01-01

Non local theories: New rules for old diagrams

Let A and B be two affinely generating sets of (Z_2)^n. As usual, we denote their Minkowski sum by A+B. How small can A+B be, given the cardinalities of A and B? We give a fairly tight answer to this question. Our bound is attained when both A and B are unions of cosets of a certain subgroup of (Z_2)^n. These cosets are arranged as Hamming balls, the smaller of which has radius 1. By similar methods, we reprove the Freiman-Ruzsa theorem in (Z_2)^n, with an optimal upper bound. Denote by F(K) the maximal spanning constant || / |A|, over all subsets A of (Z_2)^n with doubling constant |A+A| / |A| < K. We explicitly calculate F(K), and in particular show that 4^K / 4K < F(K) (1+o(1)) < 4^K / 2K. This improves the estimate F(K) = poly(K) 4^K, found recently by Green and Tao and by Konyagin.

2011-01-01

100

Intranuclear Cascade and Exciton Model calculation of 100-MeV #alpha#-particle-induced reactions on light nuclei

We show that a general variant of the Wick theorems can be used to reduce the time ordered products in the Gell-Mann and Low formula for a certain class on non local quantum field theories, including the case where the interaction Lagrangian is defined in terms of twisted products. The only necessary modification is the replacement of the Stueckelberg-Feynman propagator by the general propagator (the 'contractor' of Denk and Schweda) D(y-y';#tau#-#tau#')=(1)/i(#DELTA#_+(y-y')#theta#(#tau#-#tau#')+#DELTA#+(y'-y)#theta#(#tau#'-#tau#)), where the violations of locality and causality are represented by the dependence of #tau#,#tau#' on other points, besides those involved in the contraction. This leads naturally to a diagrammatic expansion of the Gell-Mann and Low formula, in terms of the same diagrams as in the local case, the only necessary modification concerning the Feynman rules. The ordinary local theory is easily recovered as a special case, and there is a ...

2004-08-01

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101

Theoretical interpretation of fast-charged-particle spectra, observed in the #alpha#-particle-induced reactions on the s-d shell nuclei (A = 24-28), in terms of the Intranuclear Cascade Model and the GDH exciton model (ALICE) is presented. The de-excitation of the excited residual nuclei is accounted for by the evaporation process. The theoretically predicted fast-proton and #alpha#' spectral shapes compare reasonably well with the corresponding measured spectra. However, the magnitude depends critically (as expected) on the reaction cross section employed by the model. As a first step to improve the model predictability of the reaction products, a closer look at the calculation of the #alpha#-particle reaction cross sections was undertaken. A microscopic approach using the optical theorem of Glauber's theory was employed to estimate the #alpha#-induced reaction cross sections for the light target nuclei under consideration. The calculated particle spectra were ...

102

Homotopy Normal Maps

Hilbert problem for a multiply connected circular domain and the analysis of the Hall effect in a plate

Normal maps between discrete groups $N\\rightarrow G$ were characterized[FS] as those which induce a compatible topological group structure on the homotopy quotient $EN\\times_N G$. Here we deal with topological group maps $N\\rightarrow G$ being normal in the same sense as above and hence forming a homotopical analogue to the inclusion of a topological normal subgroup in a reasonable way. We characterize these maps by a compatible simplicial loop space structure on $Bar_\\bullet(N,G)$, invariant under homotopy monoidal functors, e.g. Localizations and Completions. In the course of characterizing homotopy normality, we define a notion of a "homotopy action" similar to an $A_{\\infty}$ action on a space, but phrased in terms of Segal's 'special $\\Delta-$spaces' and seem to be of importance on its own right. As an application of the invariance of normal maps, we give a very short proof to a theorem of Dwyer and Farjoun namely that a localization by a suspended map ...

2010-01-01

103

Efficiently Simulating Higher-Order Arithmetic by a First-Order Theory Modulo

In this paper we analyze the Hilbert boundary-value problem of the theory of analytic functions for an $(N+1)$-connected circular domain. An exact series-form solution has already been derived for the case of continuous coefficients. Motivated by the study of the Hall effect in a multiply connected plate we extend these results by examining the case of discontinuous coefficients. The Hilbert problem maps into the Riemann-Hilbert problem for symmetric piece-wise meromorphic functions invariant with respect to a symmetric Schottky group. The solution to this problem is derived in terms of two analogues of the Cauchy kernel, quasiautomorphic and quasimultiplicative kernels. The former kernel is known for any symmetry Schottky group. We prove the existence theorem for the second, quasimultiplicative, kernel for any Schottky group (its series representation is known for the first class groups only). We also show that the use of an automorphic kernel requires the ...

2009-01-01

104

Dose planning and dose delivery in radiation therapy

Deduction modulo is a paradigm which consists in applying the inference rules of a deductive system (such as for instance natural deduction) modulo a rewrite system over terms and propositions. It has been shown that higher-order logic can be simulated into the first-order natural deduction modulo. However, a theorem stated by Goedel and proved by Parikh expresses that proofs in second-order arithmetic may be unboundedly shorter than proofs in first-order arithmetic, even when considering only formulae provable in first-order arithmetic. We investigate how deduction modulo can be used to translate proofs of higher-order arithmetic into first-order proofs without inflating their length. First we show how higher orders can be encoded through a quite simple (finite, terminating, confluent, left-linear) rewrite system. Then, a proof in higher-order arithmetic can be linearly translated into a proof in first-order arithmetic modulo this system. Second, in the ...

2008-01-01

105

A method has been developed for calibration of CT-numbers to volumetric electron density distributions using tissue substitutes of known elemental composition and experimentally determined electron density. This information have been used in a dose calculation method based on photon and electron interaction processes. The method utilizes a convolution integral between the photon fluence matrix and dose distribution kernels. Inhomogeneous media are accounted for using the theorems of Fano and O'Connor for scaling dose distribution kernels in proportion to electron density. For clinical application of a calculated dose plan, a method for prediction of accelerator output have been developed. The methods gives the number of monitor units that has to be given to obtain a certain absorbed dose to a point inside an irregular, inhomogeneous object. The method for verification of dose distributions outlined in this study makes it possible to exclude the treatment related ...

2008-08-01

106

Complex Gradient Systems

Bayesian Based Comment Spam Defending Tool

Let $M$ be a complex manifold of complex dimension $n+k$. We say that the functions $u_1,...s,u_k$ and the vector fields $\\xi_1,...,\\xi_k$ on $M$ form a \\emph{complex gradient system} if $\\xi_1,...,\\xi_k,J\\xi_1,...,J\\xi_k$ are linearly independent at each point $p\\in M$ and generate an integrable distribution of $TM$ of dimension $2k$ and $du_\\alpha(\\xi_\\beta)=0$, $\\d^c\\u_\\alpha(\\xi_\\beta)=\\delta_{\\alpha\\beta}$ for $\\alpha,\\beta=1,...,k$. We prove a Cauchy theorem for such complex gradient systems with initial data along a $\\CR-$submanifold of type $(\\CRdim,\\CRcodim)$. We also give a complete local characterization for the complex gradient systems which are \\emph{holomorphic} and \\emph{abelian}, which means that the vector fields $\\xi_\\alpha^c=\\xi_\\alpha-J\\xi_\\beta$, $\\alpha=1,...,k$ are holomorphic and satisfy $[\\xi_alpha^c,\\bar{\\xi_\\beta^c}]=0$ for each $\\alpha,\\beta=1,...,k$.

2011-01-01

107

A market power model with price caps and compact DC power flow constraints

Spam messes up user's inbox, consumes network resources and spread worms and viruses. Spam is flooding of unsolicited, unwanted e mail. Spam in blogs is called blog spam or comment spam.It is done by posting comments or flooding spams to the services such as blogs, forums,news,email archives and guestbooks. Blog spams generally appears on guestbooks or comment pages where spammers fill a comment box with spam words. In addition to wasting user's time with unwanted comments, spam also consumes a lot of bandwidth. In this paper, we propose a software tool to prevent such blog spams by using Bayesian Algorithm based technique. It is derived from Bayes' Theorem. It gives an output which has a probability that any comment is spam, given that it has certain words in it. With using our past entries and a comment entry, this value is obtained and compared with a threshold value to find if it exceeds the threshold value or not. By using this concept, we developed a software ...

2010-01-01

108

A characteristic ventricular shape in myelomeningocele-associated hydrocephalus? A CT stereology study

This paper presents a spatial gaming model with price caps for deregulated electricity markets. There has been heated debate on price caps that have been enforced in deregulated electricity markets. Opponents argue that price caps may send wrong economic signals while advocates argue that price caps are good for damping market power. This paper does not intend to take a stand in the argument. Given the fact that price caps are enforced in several deregulated regional electricity markets in the US, a logical step is to reflect this reality in gaining modeling. However, current gaining models have not included any price cap formulation. This paper is the first one to address the issue. DC power flow equations are used for representing the spatial nature of an electrical network. An algorithm is proposed to find a generalized Nash equilibrium under the enforcement of price caps based on the Kuhn-Tucker Vector Optimization Theorem. Case studies show the successful ...

2003-05-01

109

Measurement of the weak pion nucleon coupling constant, h1(pi), from backward pion photo-production near threshold on the proton

We measured the volume of the supratentorial ventricles in 39 consecutive children with myelomeningocele (MMC) and associated hydrocephalus, using a stereological method based on the Cavalieri theorem of systematic sampling. We distinguished the following groups: newborns before and after cerebrospinal fluid shunting (14), a somewhat larger group of newborns with an untreated MMC-associated hydrocephalus (25) and a group of shunted children at a mean age of 1.5 years (28). We paid special attention to the shape of the lateral ventricles, looking separately at the anterior and posterior halves. The measurements were compared with a healthy control group (10) and with children with hydrocephalus unrelated to MMC (15). The average volume ratio of the posterior to the anterior half of the lateral ventricles was 1.05 #+-# 0.39 in non-hydrocephalic children, 1.11 #+-# 0.55 in untreated hydrocephalic children without MMC, and 2.15 #+-# 0.65 in MMC-associated hydrocephalus ...

110

Genus 4 trigonal reduction of the Benney equations

The longest range weak pion-nucleon coupling constant, h¹/_n is important for nuclear parity violation. However, after considerable effort in the past two decades, its value is still poorly known largely due to many-body theoretical uncertainties. Prospects of a new measurement of h¹/_n in a theoretically clean process are presented. A measurement of the parity-violating asymmetry in pion photoproduction off the proton is related to h¹/_n in a low-energy theorem for the photon polarization asymmetry at threshold in the chiral limit. At present two completed experiments - photon circular polarization for ¹⁸F and the anapole moment of ¹³³Cs - have been interpreted to give very different values of ...

2003-05-01

111

On the Resolving Power of a Single Exact-Repeat Altimetric Satellite or a Coordinated Constellation of Satellites

It was shown by Gibbons and Tsarev (1996 Phys. Lett. A 211 19, 1999 Phys. Lett. A 258 263) that N-parameter reductions of the Benney equations correspond to particular N-parameter families of conformal maps. In recent papers (Baldwin and Gibbons 2003 J. Phys. A: Math. Gen. 36 8393-417, Baldwin and Gibbons 2004 J. Phys. A: Math. Gen. 37 5341-54), the present authors have constructed examples of such reductions where the mappings take the upper half p-plane to a polygonal slit domain in the #lambda#-plane. In those cases, the mapping function was expressed in terms of the derivatives of Kleinian #sigma# functions of hyperelliptic curves, restricted to the one-dimensional stratum #THETA#_1 of the #THETA#-divisor. This was done using an extension of the method given in Enolskii et al (2003 J. Nonlinear Sci. 13 157) extended to a genus 3 curve (Enolski V Z and Gibbons J Addition theorems on the strata of the theta divisor of genus three hyperelliptic curves, in ...

2006-04-07

112

Science.gov (United States)

It is proved that the mid-point grid, which is composed of samples obtained at ground track locations midway between crossover points (thus a subset of the full sampling), has the same resolving power as the full set; i.e., they resolve the same three-dimensional spectral space. The resolving power of the mid-point grid as derived previously by Tai (1995, 1998) is characterized by the Nyquist frequency ? c=? /T (where T is the repeat period of the exact-repeat satellite), and by (in local Cartesian coordinates) the zonal and meridional Nyquist wavenumber kc=2? /X and lc=2? /Y respectively (where X and Y are the east-west and north-south separation between adjacent parallel ground tracks). Here we re-derive this result in simplified terms. First, it is shown through the sampling theorem as demonstrated previously by Tai (1999) that even though samples of the real mid-point grid are not taken simultaneously, they resolve the same frequency range as that of a ...

2001-12-01

113

Measurement and analysis of neutron production cross sections and determination of some reaction rates for nuclear astrophysical calculations