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Fermat's last theorem

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The Yang-Mills equations are formulated in the form of generalized Maurer-Cartan equations, such that the corresponding algebraic operations are shown to satisfy the defining relations of homotopy Lie superalgebra.

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The authors derive in full details the Hamiltonian formulation of the N = 1D = 10 supergravity coupled to super Yang-Mills theory. In particular, they present the explicit form of the first class constraints and compute the constraints gauge algebra.

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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.

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By employing the higher dimensional version of the Wu-Yang Ansatz we obtain magnetically charged new black hole solutions in the Einstein-Yang-Mills-Lovelock (EYML) theory with second ($\\alpha2$) and third ($\\alpha3$)order parameters. These parameters, where $\\alpha2$ is also known as the Gauss-Bonnet parameter, modify the horizons (and the resulting thermodynamical properties) of the black holes. It is shown also that asymptotically, these parameters contribute to an effective cosmological constant -without cosmological constant- so that the solution behaves de-Sitter (Anti de-Sitter) like.

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A new classically stable model of spontaneous compactification is investigated. D=10 dimensional Einstein-Yang-Mills SU(3) x U(1) theory compactifies to CP(3) giving SU(4) x U(1) effective D=4 theory with no tachyons. An effective SU(4) coupling constant is calculated.

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We study the high energy behaviour of Yang-Mills theory under the inclusion of gravity. In the weak-gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.

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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 ...

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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.

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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.

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A method for systematically including topological degrees of freedom in perturbation theory is developed. This is not bound by the restrictions of semi-classical techniques. The Yang-Mills theory in three Euclidean dimensions is considered here. A well-defined separation of the topological and the ``spin wave'' degrees of freedom is obtained, motivated by a singular gauge. This has ``photons'' distorting the spherically symmetric magnetic fields of Dirac monopoles, and massless charged vector bosons ``W'' scattering off the latter. It is explicitly shown that the Dirac string does not contribute. The mode of the charged vector bosons with total angular momentum J=0 provides precisely the core to give a finite energy to the monopole. The radial equation for W is remarkably simplified and only two polarization states survive exactly for the anomalous magnetic moment required by the Yang-Mills interaction.

International Nuclear Information System (INIS)

Topological Chern-Simons theory coupled to matter fields is analysed in the framework of Dirac's method of quantising constrained systems in a general class of linear, non-local gauges. We show that in the weak coupling limit gauge invariant operators in the theory transform under an exchange according to a higher dimensional representation of the braid group which is built out of the fundamental representation matrices of the gauge group and thus behave like anyons. We also discover new solutions of the Yang-Baxter equation which emerges as a consistency condition on the structure functions of the operator algebra of the matter fields. (orig.).

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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.

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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.

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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).

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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 ...

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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

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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.

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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)

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Starting from the generalized Konishi anomaly equations at the non-perturbative level, we demonstrate that the algebraic consistency of the quantum chiral ring of the N=1 super Yang-Mills theory with gauge group U(N), one adjoint chiral superfield X and N_f<=2N flavours of quarks implies that the periods of the meromorphic one-form Tr dz/(z-X) must be quantized. This shows in particular that identities in the open string description of the theory, that follow from the fact that gauge invariant observables are expressed in terms of gauge variant building blocks, are mapped onto non-trivial dynamical equations in the closed string description.

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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.

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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...

Science.gov (United States)

... 14. Piatak, M. Jr., Saag, MS, Yang, LC, Clark, SJ, Kappes, JC, Luk, KC, Hahn, BH ... Wei, X., Ghosh, SK, Taylor, ME, Johnson, VA, Emini, EA, Deutsch, P., Lifson, JD ...

CERN Document Server

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.

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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.

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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.)

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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.

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We consider two-dimensional large N gauge theory with D adjoint scalars on a torus, which is obtained from a D+2 dimensional pure Yang-Mills theory on T^{D+2} with D small radii. The two dimensional model has various phases characterized by the holonomy of the gauge field around non-contractible cycles of the 2-torus. We determine the phase boundaries and derive the order of the phase transitions using a method developed in an earlier work (hep-th/0910.4526), which is nonperturbative in the 'tHooft coupling and uses a 1/D expansion. We embed our phase diagram in the more extensive phase structure of the D+2 dimensional Yang-Mills theory and match with the picture of a cascade of phase transitions found earlier in lattice calculations (hep-lat/0710.0098). We also propose a dual gravity system based on a Scherk-Schwarz compactification of a D2 brane wrapped on a 3-torus and find a phase structure which is similar to the phase diagram found in the ...

International Nuclear Information System (INIS)

We calculate the normalized factorial moments of multiplicity distributions through three models for elastic hadron scattering (Chou-Yang, Henzi-Valin and Menon-Pimentel). Connections between the moments and the inelastic overlap function and/or eikonal function are obtained by means of an impact parameter representation for the multiplicity distribution. The predictions are compared with experimental data on factorial moments from both inelastic and non-single-diffractive events. The model results present best agreement with the inelastic events and data favour the model by Henzi and Valin. (author)

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This monograph gives a detailed and pedagogical account of the geometry of rigid superspace and supersymmetric Yang-Mills theories. While the core of the text is concerned with the classical theory, the quantization and anomaly problem are briefly discussed following a comprehensive introduction to BRS differential algebras and their field theoretical applications. Among the treated topics are invariant forms and vector fields on superspace, the matrix-representation of the super-Poincare group, invariant connections on reductive homogeneous spaces and the supermetric approach. Various aspects of the subject are discussed for the first time in textbook and are consistently presented in a unified geometric formalism.

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In the early 1970s Yang and Menichelli demonstrated that direct laser illumination of low-density secondary explosive prr:ssings through a transparent window could produce detonation. 'The energy requirement for threshold initiation of detonation was reduced when a thin metal coating of metal covered the side of the window against which the low-density explosive was pressed. We have obtained experimental results that are in general agreement with the results of Renllund, Stanton and Trott (1 989) and recent: work by Nagayama, hou and Nakahara (2001). We report exploration of the effects of laser beam diameter, PEiTN density and specific surface area, and thickness of a titanium coating on the window.

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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.

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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...

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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.

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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)

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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.).

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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.

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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.

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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.

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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.

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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.)

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This Resource Letter provides a guide to the literature on Quantum Chromodynamics (QCD), the relativistic quantum field theory of the strong interactions. Journal articles, books, and other documents are cited for the following topics: quarks and color, the parton model, Yang-Mills theory, experimental evidence for color, QCD as a color gauge theory, asymptotic freedom, QCD for heavy hadrons, QCD on the lattice, the QCD vacuum, pictures of quark confinement, early and modern applications of perturbative QCD, the determination of the strong coupling and quark masses, QCD and the hadron spectrum, hadron decays, the quark-gluon plasma, the strong nuclear interaction, and QCD's role in nuclear physics. The letter {E} after an item indicates elementary level or material of general interest to persons becoming informed in the field. The letter {I}, for intermediate level, indicates material of a somewhat more specialized nature, and the letter {A} indicates rather ...

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We propose an extension of the su(2,2|4) superalgebra to incorporate the F1/D1 string charges in type IIB string theory on the AdS_5 X S^5 background, or the electro-magnetic charges in the dual super Yang-Mills theory. With the charges introduced, the superalgebra inevitably undergoes a noncentral extension, as noted recently in [1]. After developing a group theoretical method of obtaining the noncentral extension, we show that the charges form a certain nonunitary representation of the original unextended superalgebra, subject to some constraints. We solve the constraints completely and show that, apart from the su(2,2|4) generators, there exist 899 complex brane charges in the extended algebra. Explicitly we present all the super-commutators among them.

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In [W. Ye, F. Wu, H.W. Yang, Phys. Lett. B 647 (2007) 118] prescission protons and ? particles of high-isospin 206Pb were shown to be almost independent of the dissipation strength Formula Not Shown . Subsequently, in [P.N. Nadtochy, et al., Phys. Lett. B 685 (2010) 258] prescission light charged particles (LCPs) were shown to have approximately the same sensitivity as neutrons to Formula Not Shown for 206Pb and 204Hg nuclei. In this Letter we point out that the reason for the apparent contradictory conclusions is that the authors in the latter did not compute the changes in the absolute yields of prescission LCPs multiplicities with increasing Formula Not Shown and compare them with typical experimental uncertainties. It is shown that the expected changes are very small in the case of ne...

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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 ...

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 ...

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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.

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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.

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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 $h^1(L)=1$.

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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.

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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.

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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.

International Nuclear Information System (INIS)

Through the innovative design of a novel end plug scheme employing octopole MHD stabilization, the authors present the conceptual design of ''MINIMARS'', a small commercial fusion reactor based on the tandem mirror principle. The current baseline for MINIMARS has a net electric output of 600 MWe and they have configured the design for short construction times, factory-built modules, inherently safe blanket systems, and multiplexing in station sizes of #approx =# 600-2400 MWe. They demonstrate that the compact octopole end cell provides a number of advantages over the more conventional quadrupole (yin-yang) end cell encountered in the MARS tandem mirror reactor study, and enables ignition to be achieved with much shorter central cell lengths. Accordingly, being economic in small sizes, MINIMARS provides an attractive alternative to the more conventional larger conceptual fusion reactors encountered to date, and would contribute significantly to the lowering of ...

International Nuclear Information System (INIS)

The analytical treatment of the nonperturbative QCD dynamics is one of the main open questions of the strong interactions. Currently, it is only possible to get some qualitative information about this regime considering other QCD-like theories, as, for example, the N=4 super Yang-Mills theory, where one can perform calculations in the nonperturbative limit of large 't Hooft coupling using the anti-de Sitter space/conformal field theory (AdS/CFT). Recently, the high energy scattering amplitude was calculated in the AdS/CFT approach, applied to deep-inelastic scattering and confronted with the F_2 HERA data. In this work we extend the nonperturbative AdS/CFT inspired model for diffractive processes and compare its predictions with a perturbative approach based on the Balitsky-Kovchegov equation. We demonstrate that the AdS/CFT inspired model is not able to describe the current F_2"D"("3") HERA data and predicts a similar behavior to that from the Balitsky-Kovchegov ...

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The centre of the symmetric group algebra $\\mathbb{C}[\\mathfrak{S}_n]$ has been used successfully for studying important problems in enumerative combinatorics. These include maps in orientable surfaces and ramified covers of the sphere by curves of genus $g$, for example. However, the combinatorics of some equally important $\\mathfrak{S}_n$-factorization problems forces $k$ elements in $\\{1,...,n\\}$ to be distinguished. Examples of such problems include the star factorization problem, for which $k=1,$ and the enumeration of 2-cell embeddings of dipoles with two distinguished edges \\cite{VisentinWieler:2007} associated with Berenstein-Maldacena-Nastase operators in Yang-Mills theory \\cite{ConstableFreedmanHeadrick:2002}, for which $k=2.$ Although distinguishing these elements obstructs the use of central methods, these problems may be encoded algebraically in the centralizer of $\\mathbb{C}[\\mathfrak{S}_n]$ with respect to the subgroup $\\mathfrak{S}_{n-k}.$ ...

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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.

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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.

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{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.)

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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 ...

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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.

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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, ...

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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)

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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 ...

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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.)

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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.

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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 ...

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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 ...

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A series of first principles molecular dynamics and Monte Carlo simulations were carried out for liquid water to assess the validity and reproducibility of different sampling approaches. These simulations include Car-Parrinello molecular dynamics simulations using the program CPMD with different values of the fictitious electron mass in the microcanonical and canonical ensembles, Born-Oppenheimer molecular dynamics using the programs CPMD and CP2K in the microcanonical ensemble, and Metropolis Monte Carlo using CP2K in the canonical ensemble. With the exception of one simulation for 128 water molecules, all other simulations were carried out for systems consisting of 64 molecules. It is found that the structural and thermodynamic properties of these simulations are in excellent agreement with each other as long as adiabatic sampling is maintained in the Car-Parrinello molecular dynamics simulations either by choosing a sufficiently small fictitious mass in the microcanonical ensemble ...

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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 ...

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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 ...

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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.

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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 ...

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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 ...

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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 ...

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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 ...

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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 ...

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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 ...

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The absolute cross sections of "2"3Na(p,n)"2"3Mg, "2"7Al(p,n)"2"7Si and "3"0Si(#alpha#,n)"3"3S reactions were measured in the incident energy range of 5.05 to 5.80, 5.80 to 6.25 and 3.975 to 6.235 MeV respectively using a spherically shaped 4#pi# neutron detector. In the energy range 5.80 to 7.80 and 6.235 to 11.30 MeV the absolute cross sections of "2"3Na(p,n)"2"3Mg and "3"0Si-(#alpha#,n)"3"3S reactions were determined by optical model calculations. The cross sections of the inverse reactions "2"3Mg(n,p)"2"3Na and "3"3S(n,#alpha#)"3"0Si were also calculated by the same method for the neutron energy range of 10 keV to 7.50 MeV for each reaction. The cross section of the latter reaction in the neutron energy range of 10 keV to 840 keV was also determined from its inverse reaction "3"0Si(#alpha#,n)"3"3S by the application of the detailed balance theorem. The reactions for which the cross sections were determined are of importance in stellar evolution and ...