Gauge Space Research Articles

AN EKELAND TYPE VARIATIONAL PRINCIPLE ON GAUGE SPACES WITH APPLICATIONS TO FIXED POINT THEORY, DROP THEORY AND COERCIVITY

In this paper, a new Ekeland type variational principle on gauge spaces is established. As applications, we give Caristi-Kirk type �xed point theorems on gauge spaces, and Dane� s' drop theorem on semi- normed spaces. Also, we show that the Palais-Smale condition implies coercivity on semi-normed spaces.

Fixed-Point Results for Generalized Contractions on Ordered Gauge Spaces with Applications

The purpose of this paper is to present some fixed-point results for single-valued -contractions on ordered and complete gauge space. Our theorems generalize and extend some recent results in the literature. As an application, existence results for some integral equations on the positive real axis are given.

Flavored orbifold GUT — an SO(10) × S 4 model

Orbifold grand unified theories (GUTs) solve several problems in GUT model building. Therefore, it is intriguing to investigate similar constructions in the flavor context. In this paper, we propose that a flavor symmetry might emerge due to orbifold compactification of one orbifold and broken by boundary conditions of another orbifold. The combination of the orbifold parities in gauge and flavor space determines the zero modes. We demonstrate the construction in a supersymmetric (SUSY) SO(10) x S_4 orbifold GUT model, which predicts the tribimaximal mixing at leading order in the lepton sector as well as the Cabibbo angle in the quark sector.

Quarkyonic chiral spirals

We consider the formation of chiral density waves in Quarkyonic matter, which is a phase where cold, dense quarks experience confining forces. We model confinement following Gribov and Zwanziger, taking the gluon propagator, in Coulomb gauge and momentum space, as ∼ 1 / ( p → 2 ) 2 . We assume that the number of colors, N c , is large, and that the quark chemical potential, μ, is much larger than renormalization mass scale, Λ QCD . To leading order in 1 / N c and Λ QCD / μ , a gauge theory with N f flavors of massless quarks in 3 + 1 dimensions naturally reduces to a gauge theory in 1 + 1 dimensions, with an enlarged flavor symmetry of SU ( 2 N f ) . Through an anomalous chiral rotation, in two dimensions a Fermi sea of massless quarks maps directly onto the corresponding theory in vacuum. A chiral condensate forms locally, and varies with the spatial position, z, as 〈 ψ ¯ exp ( 2 i μ z γ 0 γ z ) ψ 〉 . Following Schön and Thies, we term this two-dimensional pion condensate a (Quarkyonic) chiral spiral. Massive quarks also exhibit chiral spirals, with the magnitude of the oscillations decreasing smoothly with increasing mass. The power law correlations of the Wess–Zumino–Novikov–Witten model in 1 + 1 dimensions then generate strong infrared effects in 3 + 1 dimensions.

The Hilbert space of the Chern–Simons theory on a cylinder: a loop quantum gravity approach

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern–Simons theory on a noncompact space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

Fixed point results for multivalued contractions on ordered gauge spaces

Abstract The purpose of this article is to present fixed point results for multivalued E ≤-contractions on ordered complete gauge space. Our theorems generalize and extend some recent results given in M. Frigon [7], S. Reich [12], I.A. Rus and A. Petruşel [15] and I.A. Rus et al. [16].

Transparent connections over negatively curved surfaces

Let $(M,g)$ be a closed oriented negatively curved surface. A unitary connection on a Hermitian vector bundle over $M$ is said to be transparent if its parallel transport along the closed geodesics of $g$ is the identity. We study the space of such connections modulo gauge and we prove a classification result in terms of the solutions of a certain PDE that arises naturally in the problem. We also show a local uniqueness result for the trivial connection and that there is a transparent $SU(2)$-connection associated to each meromorphic function on $M$.

Fibre Picard Operators on Gauge Spaces and Applications

The purpose of this paper is to prove some fibre Picard operator principles in gauge spaces. As application, the differentiability with respect to parameters of the solution of a Volterra functional-integral equation is discussed.

Spin Polarized Superfluid3He A1

Under applied magnetic field, the originally single superfluid 3 He transition near 3 mK in zero field splits into two transitions between which a new A 1 phase emerges. The two second order transitions are marked by abrupt changes in viscosity, zero sound attenuation and nuclear magnetic resonance. To date, the maximum magnetic field for producing A 1 phase is 15 T. The A 1 phase has been identified with a spin-polarized (ferromagnetic) superfluid system which breaks the relative symmetry between spin, orbit and gauge spaces. A superfluid mass current in A 1 is simultaneously a spin current resulting in the propagation of spin-entropy wave. Experiments with spin-entropy wave provide measurements of anisotropic superfluid density and strong coupling parameters, spin diffusion coefficient and texture transformations. Owing to the spin-polarized nature, superflows may be generated by applied magnetic field gradients and measured from the induced magnetic fountain pressure. The mechanical spin density detect...

Constructing the sobrification of an approach space via bicompletion

On every approach space X, we construct a compatible quasi-uniform gauge structure which turns out to be at the same time the coarsest functorial structure and the finest compatible totally bounded one. Based on the analogy with the classical Csaszar-Pervin quasi-uniform space, we call this the “Csaszar-Pervin” quasi-uniform gauge space. By means of the bicompletion of this Csaszar-Pervin quasi-uniform gauge space of a T0 approach space X, we succeed in constructing the sobrification of X.

Fixed point theorems for set-valued [formula omitted]-generalized contractions on gauge spaces

In this paper, we present a common fixed point theorem for a family of set-valued Φ -generalized contraction mappings on gauge spaces, which generalizes the main result from Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485–494].

Existence Principle for Advanced Integral Equations on Semiline

The continuation principle for generalized contractions in gauge spaces is used to discuss nonlinear integral equations with advanced argument.

Transition from Vibrational to Rotational Regimes in the Pairing Phase

An approximate solution at the critical point of the pairing transition from harmonic vibration (normal nuclear behavior) to deformed rotation (superconducting behavior) in gauge space is found by analytic solution of a collective pairing Hamiltonian. The eigenvalues are expressed in terms of the zeros of Bessel functions of integer order. Comparison of the results to the pairing bands based on the Pb isotopes suggests that this description may provide a simple approach to explaining the observed anharmonicities of the pairing vibrational structure around 208 Pb. The validity of the model is reinforced by comparing the results to an exact treatment of the pairing-phase transition in a two-level model.

Deformation theorems on non‐metrizable vector spaces and applications to critical point theory

AbstractLet E be a Banach space and Φ : E → ℝ a 𝒞1‐functional. Let 𝒫 be a family of semi‐norms on E which separates points and generates a (possibly non‐metrizable) topology 𝒯𝒫 on E weaker than the norm topology. This is a special case of a gage space, that is, a topological space where the topology is generated by a family of semi‐metrics. We develop some critical point theory for Φ : (E, 𝒫) → ℝ. In particular, we prove deformation lemmas where the deformations are continuous with respect to 𝒯𝒫. In applications this yields a gain in compactness when Φ does not satisfy the Palais–Smale condition because one can work with the weak topology.We also prove some foundational results on gage spaces. In particular, we introduce the concept of Lipschitz continuity in this setting and prove the existence of Lipschitz continuous partitions of unity. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Critical-Point Description of the Transition from Vibrational to Rotational Regimes in the Pairing Phase

An approximate solution at the critical point of the pairing transition from harmonic vibration to deformed rotation in gauge space is found by analytic solution of the collective pairing Hamiltonian. The eigenvalues are expressed in terms of the zeros of Bessel functions of integer order. The results are compared to the pairing bands based on the Pb isotopes.

Sleptonium at the linear collider and the slepton co-next-to-lightest supersymmetric particle scenario in gauge mediated symmetry breaking models

We discuss the possibility of formation and subsequent detection of a supersymmetric bound state composed of a slepton-antislepton pair at the next linear collider. The Green function method is used within a nonrelativistic approximation to estimate the threshold production cross section of the $2P$ bound state. The parameter space of gauge mediated symmetry breaking (GMSB) models allow a particular scenario in which a charged slepton (${\stackrel{\texttildelow{}}{e}}_{R},{\stackrel{\texttildelow{}}{\ensuremath{\mu}}}_{R}$ or ${\stackrel{\texttildelow{}}{\ensuremath{\tau}}}_{1}$) is the next-to-lightest supersymmetric particle (NLSP). Within this scenario the produced $2P$ bound-state decays, through a dipole transition, into the $1S$ ground-state with branching ratio $\ensuremath{\approx}100%$ emitting a very soft ($\ensuremath{\approx}1\text{ }\text{ }\mathrm{MeV}$) photon which goes undetected. The spectroscopy of the $1S$-state shows that it decays into two photons with $\mathrm{Br}\ensuremath{\approx}0.5$ up to ${m}_{\mathrm{NLSP}}\ensuremath{\approx}1\text{ }\text{ }\mathrm{TeV}$. Thus NLSP sleptonium threshold production gives rise to the signal ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}2P\ensuremath{\rightarrow}1S+``\mathrm{soft}\text{ }\text{ }\ensuremath{\gamma}''\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ which when compared with the standard model two-photon process (${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ ) has a statistical significance ($SS=$signal/noise) which, at an energy offset from threshold of $E=20\text{ }\text{ }\mathrm{GeV}$, goes from $SS=11$ to $SS=2$ when the mass of the NLSP ranges in the interval $[100,200]\text{ }\text{ }\mathrm{GeV}$.

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir–Keeler multivalued operators and admissible multivalued a α -contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485–494] and Rus, Petruşel, and Sîntămărian [I.A. Rus, A. Petruşel, A. Sîntămărian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947–1959].

Potential of Radar-Estimated Rainfall for Plant Disease Risk Forecast

Potential of Radar-Estimated Rainfall for Plant Disease Risk Forecast

Fixed point theory for generalized contractive maps of Meir–Keeler type

AbstractFixed point, domain invariance and coincidence results are presented for single‐valued generalized contractive maps of Meir–Keeler type defined on complete metric spaces (or more generally complete gauge spaces). The maps of Caristi type are also considered. In addition the random analogue of some of these fixed point results will be presented. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Random and deterministic fixed point theory for generalized contractive maps

Fixed point and homotopy results are presented for generalized contractions on complete gauge spaces. In addition we obtain random fixed point results for generalized contractions.