Monopoles on the Bryant–Salamon G2-manifolds

$G_2$-monopoles are solutions to gauge theoretical equations on noncompact $7$-manifolds of $G_2$ holonomy. We shall study this equation on the $3$ Bryant–Salamon manifolds. We construct examples of $G_2$-monopoles on two of these manifolds, namely the total space of the bundle of anti-self-dual two forms over the ${\mathbb{S}}^4$ and ${\mathbb{C}\mathbb{P}}^2$. These are the first nontrivial examples of $G_2$-monopoles.Associated with each monopole there is a parameter $m\in {\mathbb{R}}^{+}$, known as the mass of the monopole. We prove that under a symmetry assumption, for each given $m\in {\mathbb{R}}^{+}$ there is a unique monopole with mass $m$. We also find explicit irreducible $G_2$-instantons on ${\Lambda }_{-}^2\left({\mathbb{S}}^4\right)$ and on ${\Lambda }_{-}^2\left({\mathbb{C}\mathbb{P}}^2\right)$.The third Bryant–Salamon $G_2$-metric lives on the spinor bundle over the $3$-sphere. In this case we produce a vanishing theorem for monopoles.     

Optimal time travel in the Gödel universe

Using the theory of optimal rocket trajectories in general relativity, recently developed in Henriques and Natário (2011), we present a candidate for the minimum total integrated acceleration closed timelike curve in the Gödel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament’s conjectured value (Malament 1984), as was already implicit in the work of Manchak (Gen. Relativ. Gravit. 51–60, 2011); however, Malament’s conjecture does seem to hold for periodic closed timelike curves.     

Anomalous current algebras in the Skyrme model or chiral G×G with Wess-Zumino term

We deal with chiral G×G field theory with Wess-Zumino term (or the Skyrme model) specified in terms of its Goldstone fields. Working in four dimensions we derive the current of the Noether currents of the theory in the canonical formalism displaying its anomalous structure.     

A connection between the （G′/G）-expansion method and the truncated Painlev ＇e expansion method and its application to the mKdV equation

Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.     

A novel （G＇/G）-expansion method and its application to the Boussinesq equation

In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.     

Klein-Gordon and Weyl equations in the Gödel universe

Klein-Gordon and Weyl equations are investigated in the Gödel universe as the background metric. Both equations are solved, the Klein-Gordon equation for arbitrary coupling to the gravitational field.     

Search for the Multi-TeV Gamma Rays from the Shell-Like SNR G40.5-0.5 Using the Tibet Air Shower Array

Using observation data of the Tibet air shower array in different periods, a region with the highest excess of 4.4σ in the multi-TeV was detected from the SNR G40.5-0.5 direction, although statistically insignificant yet. The position of the highest excess is located around the EGRET unidentified source 3EG J1903 0550.     

Exact traveling wave solutions of an autonomous system via the enhanced (G′/G)-expansion method

Mathematical modeling of many autonomous physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear evolution equations plays a significant role in the study of nonlinear physical phenomena. In this article, the enhanced (G′/G)-expansion method has been applied for finding the exact traveling wave solutions of longitudinal wave motion equation in a nonlinear magneto-electro-elastic circular rod. Each of the obtained solutions contains an explicit function of the variables in the considered equations. It has been shown that the applied method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering fields.     

Exact solutions of the nonlinear differential-difference equations associated with the nonlinear electrical transmission line through a variable-coefficient discrete（G＇/G）-expansion method

We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete（G /G）-expansion method, we solve the nonlinear differential–difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.     

(G′/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics

In this paper, the (G′/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.     

Conserved charges and thermodynamics of the spinning Gödel black hole

We compute the mass, angular momenta, and charge of the G?del-type rotating black hole solution to five-dimensional minimal supergravity. A generalized Smarr formula is derived, and the first law of thermodynamics is verified. The computation rests on a new approach to conserved charges in gauge theories that allows for their computation at finite radius.     

A new application of the Gürsey and Radicati mass formula

We study the spin- and flavour-dependent SU(6) violations in the baryon spectrum by means of a Gürsey-Radicati mass formula. The average energy of each SU(6) multiplet is described using the SU(6)-invariant interaction given by a hypercentral potential containing a linear and a hyper-Coulomb term. We show that the nonstrange- and strange-baryon masses are, in general, fairly well reproduced and moreover that the Gürsey-Radicati formula holds in a satisfactory way also for the excited states up to 2 GeV.     

Search for neutrino oscillations at the nuclear power reactor in G?sgen

Summary The positron spectrum from the reaction was measured at two distances 37.9 m and 45.9 m from the core of the 2.8 GW power reactor in G?sgen (Switzerland). The data were analysed in terms of two neutrino oscillations of the disappearance type . No evidence for neutrino oscillations was found and limits on the oscillation parameters Δm ² and sin²2θ were derived.

---

Riassunto Si è misurato lo spettro dei positroni della reazione alle due distanze di 37.9 m e 45.9 dal nucleo del reattore di potenza di G?sgen (Svizzera). Si sono analizzati i dati in termini di due oscillazioni del tipo della sparizione . Non si è trovata alcuna prova di oscillazioni del neutrino e si sono dedotti limiti ai parametri di oscillazione Δm ² e sin²2θ.

---

Резюме Измерялся спектр позитронов из реакции на двух расстояниях 37.9 м и 45.9 м от активной зоны энергетического реактора в Гэсгене (Щвейцария). Полученные данные анализируются на основе двух нейтринных осцилляций исчезающего типа . Не было обнаружено доказательств для нейтринных осцилляций. Определяются пределы для параметров осцилляций Δm ² и sin²2θ.

     

Bianchi Type-III Cosmological Models with Gravitational Constant G and the Cosmological Constant ∧

Einstein field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for the Bianchi type-Ⅲ universe by assuming conservation law for the energy-momentum tensor. Exact solutions of the field equations are obtained by using the scalar of expansion proportional to the shear scalar θ∝σ, which leads to a relation between metric potential B = Cn, where n is a constant. The corresponding physical interpretation of the cosmological solutions are also discussed.     

Competition of the multiple Grtler modes in hypersonic boundary layer flows

Competition of multiple Grtler modes in hypersonic boundary layer flows are investigated with the local and marching methods.The wall-layer mode(mode W)and the trapped-layer mode(mode T)both occur in the compressible boundary layer where there exists a temperature adjustment layer near the upper edge.The mode T has the largest growth rate at a lower Grtler number while the mode W dominates at larger Grtler numbers.These two modes are both responsible for the flow transition in the hypersonic flows especially when Grtler number is in the high value range in which the crossover of these two modes takes place.Such high Grtler numbers are virtually far beyond the neutral regime.The nonparallel base flows,therefore,cease to influence the stability behavior of the Grtler modes.The effects of the Mach number on the multiple Grtler modes are studied within a chosen Mach number of 0.95,2,4 and 6.When the flow Mach number is sufficiently large,e.g.,Ma 4,the growth rate crossover of the mode T and mode W occurs both in the conventional G-βmap as well as on the route downstream for a fixed wavelength disturbance.Four particular regions(Region T,T-W,W-T and W)around the crossover point are highlighted with the marching analysis and the result matches that of the local analysis.The initial disturbance of a normal mode maintains the shape in its corresponding dominating region while a shape-transformation occurs outside this region.     

On the Euclidean approach to quantum field theory in Gödel space-time

Features of the quantum field theory in the background of the Gödel space-time are investigated. By using the Euclidean approach, a quantum field propagating in this background is found to possess a temperature proportional to the magnitude of the cosmic vorticity. However, in the semiclassical approximation, the Gödel solution does not present an intrinsic entropy.     

A connection between the(G'/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation

Recently the (G'/G)-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the (G'/G)-expansion method is a special form of the truncated Painlevé expansion method by introducing an intermediate expansion method. Then the generalized (G'/G)--(G'/G) expansion method is naturally derived from the standpoint of the nonstandard truncated Painlevé expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the (G'/G)-expansion method.     

The use of the Gáspár potential in theoretical investigations of the spectra of atoms and ions

The method of the use of theGáspár potential in theoretical investigations of the energy spectra of atoms and ions in the Hartree—Fock—Pauli approximation is described. The calculations of the energy spectra of a number of multiple-charged ions in the configurations 1s ²2s ²2p ²3s and 1s ²2s ²2p ²3d are presented as the examples and compared with the experimental data available.