Nonlocal Symmetry and Explicit Solution of the Alice-Bob Modified Korteweg-de Vries Equation

Nonlocal symmetry and explicit solution of the integrable Alice-Bob modified Korteweg-de Vries(ABm Kd V) equation is discussed, which has been established by the aid of the shifted parity and delayed time reversal to describe two-place events. Based on the Lax pair which contains the two-order partial derivative, the Lie symmetry group method is successfully applied to find the exact invariant solution for the AB-m Kd V equation with nonlocal symmetry by introducing one suitable auxiliary variable. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to some specific functions are derived. Figures show the physical phenomenon, that is, "the shifted parity and delayed time reversal to describe two-place events".     

The general solution of Bianchi type <Emphasis Type="Italic">V I I</Emphasis><Subscript><Emphasis Type="Italic">h</Emphasis></Subscript> vacuum cosmology

The theory of symmetries of systems of coupled, ordinary differential equations (ODE) is used to develop a concise algorithm in order to obtain the entire space of solutions to vacuum Bianchi Einstein’s field equations (EFEs). The symmetries used are the well known automorphisms of the Lie algebra for the corresponding isometry group of each Bianchi Type, as well as the scaling and the time re-parametrization symmetry. The application of the method to Type V I I _h results in (a) obtaining the general solution of Type V I I ₀ with the aid of the third Painlevé transcendental P _{I I I} ; (b) obtaining the general solution of Type V I I _h with the aid of the sixth Painlevé transcendental P _{V I} ; (c) the recovery of all known solutions (six in total) without a prior assumption of any extra symmetry; (d) The discovery of a new solution (the line element given in closed form) with a G ₃ isometry group acting on T ₃, i.e., on time-like hyper-surfaces, along with the emergence of the line element describing the flat vacuum Type V I I ₀ Bianchi Cosmology.     

Effective potential of composite fermionic fields in quantum electrodynamics in curved spacetime

The effective potential of composite fermions in quantum electrodynamics in curved spacetime is computed in the approximation linear in curvature. In the same approximation, the Schwinger-Dyson equations are obtained, and an exact solution which does not break chiral symmetry is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 96–101, September, 1990.The authors thank I. L. Bukhbinder and V. P. Gusykin for useful discussions.     

Energy radiated by an arbitrary material system

The solution of the Einstein field equations for the case of an arbitrary material system is analyzed on the basis of the asymptotic solutions found by Sachs for a radiative system devoid of symmetry. The tetrad formalism is used to find the energy and momentum of the system.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 3, pp.48–51, March, 1971.In conclusion the author thanks V. I. Rodichev and I. M. Dozmorov for valuable comments on this study.     

An extension of the SM based on effective Peccei–Quinn Symmetry

Peccei–Quinn (PQ) mechanism based on a chiral global U(1) symmetry is considered to be a simple and elegant solution for strong CP problem. The fact that the mechanism could be experimentally examined through the axion search makes it much more interesting and recently it causes a lot of attention again. However, it is also known that the mechanism is annoyed by two serious problems, that is, a domain wall problem and goodness of global symmetry. Any global symmetry is considered not to be exact due to the quantum effect of gravity. In this paper, we consider a solution to these problems, in which quark mass hierarchy and mixing, neutrino mass generation and existence of dark matter are closely related. In our solution, PQ symmetry is assumed to be induced through symmetry breaking at an intermediate scale of a local U(1) symmetry, and a global U(1) symmetry which plays a role of Froggatt–Nielsen symmetry . In the lepton sector, a remnant of the PQ symmetry controls neutrino mass generation and dark matter existence.     

Thermodynamic theory of finite ferroelectric crystals with surface energy

The phenomenological Landau theory of phase transition is generalized to finite ferroelectric crystals with surface energy. Restrictions of the expansion imposed by the symmetry of the surface are considered, and further analysis is devoted to a special case. The solution in the approximation of constant polarization is discussed. Single domain states of a plate are analysed in greater detail.The authors are very grateful to Dr. V.Janovec and Dr. J.Fousek of the Czechoslovak Academy of Sciences for helpful discussions. Thanks are due to Prof. L.Valenta for the valuable discussions dealing with the magnetical analogical problem.     

Mechanical properties of vanadium carbide and a ternary vanadium tungsten carbide

Ab initio total energy calculations are performed on non-stoichiometric vanadium carbide with supercells representing vacancy concentrations of V C_0.875 and V C_0.75. The V C_0.875 supercell retains a cubic symmetry whilst in the case of the V C_0.75 supercell C vacancies located in close proximity have the lowest energy configuration and the cubic lattice slightly distorts to a monoclinic symmetry. Using a stress–strain calculational procedure, the elastic constants of both the cubic and the monoclinic systems are deduced. In all cases C vacancies decrease the elastic moduli.A similar analysis is then applied to consider when W is incorporated into VC. In this case it is found that the elastic moduli increase with W content suggesting that a V-W-C alloy could have significant potential as a novel hard material.     

理论研究V2O6-的结构和电子性质

采用自旋非限制密度泛函(B3LYP)方法研究了V2O6-的结构和电子性质,得到的基态和前人的理论计算结果不同．V2O6-阴离子是具有C2v对称性的双重基态,而以前Vyboishchikov等人得到的结果为D2h对称性双重基态．V2O6中性分了是具有D2h对称性的开壳层单重基态,它的能量和三重态的非常接近,而Vyboishchikov等人和Calatayud等人分别得到D2h对称性的闭壳层单重基态和Cs对称性的三重基态．从该基态结果出发计算出的电子分离能和实验上的PES谱相符,相反前人得到的电子分离能和实验相差较大．     

Gravitational energy emitted by isolated material source. I

The solution is investigated of the Einstein field equations for the case of axial symmetry obtained by Van der Burg in 1966. We assume that the space-time is empty outside a time-similar world tube which contains all the field sources, and we shall concern ourselves with the void space-time region. The energy and the momentum of the system are obtained with the aid of the tetrad formalism; it is shown, moreover, that there is gravitational emission in the system.Translated from Izvestiya VUZ, Fizika, No. 12, pp. 101–104, December, 1971.In conclusion the author would like to express his thanks to V. I. Rodichev for his valuable comments on this work.     

Surface states ond-band metals

Electron surface states ond-band metals are investigated by the method of matching the crystal wave function to the outside solution at the surface. On a (100) surface of anfcc structure such a state is found near to the crossover of thes-band and thed-band of the same symmetry. In Ni this state lies 4–5 eV below the Fermi energy, for Cu 5–6 V beloweE _F. It explains the density of states anomaly seen in photoemission.     

Scattering and infinite dimensional symmetry schemes

We examine the recently proposed non-trivial binding of the Poincare group with internal symmetry groups, which leads to mass splitting without symmetry breaking, from the point of view of scattering. We give a very general realization of the corresponding infinite dimensional Lie algebra in the Fok space of asymptotic states built from two scalar nucleons. Assuming that the algebra describes the exact symmetry of theS-matrix we conclude that no elastic NN scattering exists.The author is indebted to Professor V. Votruba and Dr. J. Formánek for many stimulating discussions.     

Algebraic properties of the Dirac equation

The first-order symmetry operators of the Dirac equation are classified according to their tensor properties under transformations of the homogeneous Lorentz group; a minimal system of generators for the ring of symmetry operators of the free Dirac equation is obtained, and the physical meaning of the spin operators is considered; fields are found which admit symmetry operators of first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 84–89, February, 1972.The author is grateful to V. N. Shapovalov for discussions and valuable suggestions.     

The radial problem in gauge field theory models

The study of spontaneous symmetry breaking patterns in theories in which the ground state is determined by the minima of a potential invariant under the symmetry group of the system may be traced back to the solution of two classes of problems, that we shall quote in Tolédano and Dmitriev’s suggestive words [P. Tolédano, V. Dmitriev, Reconstructive Phase Transitions in Crystals and Quasicrystals, World Scientific, Singapore, 1996] as angular and radial problem, respectively. Whilst the former problem, i.e., the determination of the isotropy-type stratification, has been extensively treated both in condensed matter physics and in particle physics, the radial problem, in particular the construction of the phenomenological potential allowing the realization of all the symmetry allowed symmetry phases, has up to now substantially been disregarded in gauge field theory, because renormalizability limits to four the degree of the Higgs potential and it is widely thought that spontaneous radiative mass generation can anyway fix the issue. Through a rigorous analysis in the framework of geometric invariant theory (-matrix approach) we review these facts, focussing our attention on the role of radiative corrections. Then, we propose a way of reconciling renormalizability requirement and tree-level observability of all the phases allowed by the symmetry. The idea will be illustrated in simple extensions of two-Higgs-doublet SM, with additional scalar singlets and discrete symmetries. This will allow us to explain the rationale behind all the extensions of the Higgs sectors so far proposed to generate the observed Baryon asymmetry of our Universe at the EW Phase Transition.     

Infinite series symmetry reduction solutions to the modified KdV--Burgers equation

From the point of view of approximate symmetry, the modified Korteweg--de Vries--Burgers (mKdV--Burgers) equation with weak dissipation is investigated. The symmetry of a system of the corresponding partial differential equations which approximate the perturbed mKdV--Burgers equation is constructed and the corresponding general approximate symmetry reduction is derived; thereby infinite series solutions and general formulae can be obtained. The obtained result shows that the zero-order similarity solution to the mKdV--Burgers equation satisfies the Painlevé II equation. Also, at the level of travelling wave reduction, the general solution formulae are given for any travelling wave solution of an unperturbed mKdV equation. As an illustrative example, when the zero-order tanh profile solution is chosen as an initial approximate solution, physically approximate similarity solutions are obtained recursively under the appropriate choice of parameters occurring during computation.     

Family symmetry, gravity, and the strong CP problem

We show how in a class of models Peccei-Quinn symmetry can be realized as an automatic consequence of a gauged U(1) family symmetry. These models provide a solution to the strong CP problem either via a massless u-quark or via the DFSZ invisible axion. The local family symmetry protects against potentially large corrections to induced by quantum gravitational effects. In a supersymmetric extension, the “μ-problem” is shown to have a natural solution in the context of gravitationally induced operators. We also present a plausible mechanism which can explain the integ-generational mass hierarchy in such a context.     

Gaussian effective potential for theФ 4-theory in two dimensions at finite temperature

The Gaussian effective potential for the ground state of the ⁴-theory in 1+1 dimensions shows a symmetry breaking above a critical coupling constant. The restoration of the symmetry at high temperatures and the role of the renormalization are discussed.     

Density functional theory predictions for small radicals containing boron and aluminium: broken symmetry problems and solutions

Selected exchange-correlation functionals were employed to study certain radicals for which unrestricted (U) Hartree–Fock and post-Hartree–Fock methods showed spatial symmetry breakings. For AlO, BO₂ and BS₂ all functionals produced symmetry adapted solutions and predicted geometries and vibrational spectra in good accord with experiment. The USVWN and UB3LYP solutions for the D_∞h O–Al–O structure break spin symmetry. Mixing of these spin-unrestricted Kohn–Sham orbitals yielded stable solutions with reasonable geometries and energetics but with large errors for the vibrational spectra. Only UBHandHLYP results in a broken spatial symmetry solution and yields an anomalous vibrational spectrum. The UBLYP solution does not show a tendency to instability and predicts a D_infin;h O–Al–O species with a ²Π_g electronic state.     

Symmetry-increasing bifurcation of chaotic attractors

Bifurcation in symmetric is typically associated with spontaneous symmetry breaking. That is, bifurcation is associated with new solution having less symmetry.In this paper we show that symmetry-increasing bifurcation in the discrete dynamics of symmetric mappings is possible (and is perhaps generic). The reason for these bifurcations may be understood as follows. The existence of one attractor in a system with symmetry gives rise to a family of conjugate attractors all related by symmetry. Typically, in computer experiments, what we see is a sequence of symmetry-breaking bifurcations leading to the existence of conjugate chaotic attractors. As the bifurcation parameter is varied these attractors grow in size and merge leading to a single attractor having greater symmetry.We prove a theorem suggesting why this new attractor should have greater symmetry and present a number of striking examples of the symmetric patterns that can be formed by iterating the simplest mappings on the plane with the symmetry of the regular m-gon. In the last section we discuss period-doubling in the presence of symmetry.     

String dust solutions of the Einstein field equations with spherical or static cylindrical symmetry

The Einstein field equations are solved assuming spherical or static cylindrical symmetry and a string dust source. All solutions which may be matched onr =a to an external vacuum solution having the same symmetry are found.     

In situ observation on Au(1 0 0) surface in molten EMImBF4 by electrochemical atomic force microscopy (EC-AFM)

The Au(1 0 0) surface structure in contact with 1-ethyl-3-methylimidazolium tetrafluoroborate (EMImBF₄) has been observed using electrochemical atomic force microscopy (EC-AFM) under an electrochemically controlled potential. The AFM images, taken in EMImBF₄ in the potential range from −0.6 to 0.2 V vs. Ag/Ag(I), shows a fourfold symmetry with the distance between protrusions of ≈0.30-0.32 nm. This structure agrees well with the ideal surface structure of Au(1 0 0)-(1 × 1) and it is very similar to that previously obtained in a sulfuric acid aqueous solution.