On the nets of equi-conjugate pairs of curves in a Weyl hypersurface

In this paper, equi-conjugate pairs of curves in a hypersurfaceW _n(g_ij,T_k) are defined and the Chebyshev nets of the first kind, the second kind and the geodesic nets which are formed by the tangent vector fields of these pairs of curves are investigated.     

Extended Darboux function in a Weyl hypersurface

In this paper, by means of the prolonged differentiation, we introduce a pair of operators D andD ^* which enable us to extend the Darboux functions associated with a surface to the case of hypersurface in a Weyl space and discuss a few properties of these functions.     

Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions

In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ? × ? ^d with d ≥ 6. We prove the stability of solutions under the weak condition that the perturbation of the linear flow is small in certain space-time norms. As a by-product of our stability analysis, we also prove local well-posedness of solutions for which we only assume the smallness of the linear evolution. These results provide essential technical tools that can be applied towards obtaining the extension to high dimensions of the analysis of Kenig and Merle [17 Kenig , C.E. , Merle , F. ( 2008 ). Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation . Acta Math. 201 : 147 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]] of the dynamics of the focusing (NLW) below the energy threshold. By employing refined paraproduct estimates we also prove unconditional uniqueness of solutions for d ≥ 6 in the natural energy class. This extends an earlier result by Planchon [26 Planchon , F. ( 2003 ). On uniqueness for semilinear wave equations . Math. Z. 244 : 587 – 599 .[Web of Science ®] , [Google Scholar]].     

Negative energy blowup results for the focusing Hartree hierarchy via identities of virial and localized virial type

Abstract

We establish virial and localized virial identities for solutions to the Hartree hierarchy, an infinite system of partial differential equations which arises in mathematical modeling of many body quantum systems. As an application, we use arguments originally developed in the study of the nonlinear Schrödinger equation (see work of Zakharov, Glassey, and Ogawa–Tsutsumi) to show that certain classes of negative energy solutions must blowup in finite time. The most delicate case of this analysis is the proof of negative energy blowup without the assumption of finite variance; in this case, we make use of the localized virial estimates, combined with the quantum de Finetti theorem of Hudson and Moody and several algebraic identities adapted to our particular setting. Application of a carefully chosen truncation lemma then allows for the additional terms produced in the localization argument to be controlled.     

On the Chebyshev nets in a hypersurface of a Weyl space

In [1], Zlatanov introduced the Chebyshev vector fields of the first and second kind and the geodesic vector fields for an n-dimensional net in the Weyl spaceW _n . After having defined, in [2], the Chebyshev and geodesic curvatures of the lines of an arbitrary net,the b-nets and the c-nets, Tsareva and Zlatanov studied, among other things, some properties of the Chebyshev nets. In this paper, we consider an n-dimensional net in the hypersurfaceW _n of the Weyl SpaceW _n+1 and study some properties of the Chebyshev vector fields of the first and second kind and the geodesic vector fields of this net. Finally, two theorems concerning the b-nets and c-nets inW _n are obtained.     

On Fitting p-groups with all proper subgroups satisfying an outer commutator law

In this note we consider certain Fitting p-groups in which every proper subgroup satisfies an outer commutator identity and obtained some conditions for such groups to be imperfect. We also give an application of the main theorem to obtain an idea of the abundance of the groups under consideration.     

On an inverse scattering problem for a class Dirac operator with discontinuous coefficient and nonlinear dependence on the spectral parameter in the boundary condition

On the positive semi‐infinite interval, we obtained a generalization of the Marchenko method for a Dirac equation system with a discontinuous coefficient and a quadratic polynomial on a spectral parameter in the boundary condition. In this connection, we use an new integral representation of the Jost solution of equation systems, which does not have a ‘triangular’ form. The scattering function of the problem is defined, and its properties are examined. The Marchenko‐type main equation is obtained, and it is shown that the potential is uniquely recovered in terms the scattering function. Copyright © 2012 John Wiley & Sons, Ltd.     

On Groups with Certain Proper FC-Subgroups

Algebras and Representation Theory - Let G be a group. If for every proper normal subgroup N and element x of G with N〈x〉≠G, N〈x〉 is an FC-group, but G is not an...     

The smart meter and a smarter consumer: quantifying the benefits of smart meter implementation in the United States

The electric grid in the United States has been suffering from underinvestment for years, and now faces pressing challenges from rising demand and deteriorating infrastructure. High congestion levels in transmission lines are greatly reducing the efficiency of electricity generation and distribution. In this paper, we assess the faults of the current electric grid and quantify the costs of maintaining the current system into the future. While the proposed "smart grid" contains many proposals to upgrade the ailing infrastructure of the electric grid, we argue that smart meter installation in each U.S. household will offer a significant reduction in peak demand on the current system. A smart meter is a device which monitors a household's electricity consumption in real-time, and has the ability to display real-time pricing in each household. We conclude that these devices will provide short-term and long-term benefits to utilities and consumers. The smart meter will enable utilities to closely monitor electricity consumption in real-time, while also allowing households to adjust electricity consumption in response to real-time price adjustments.     

The structural, elastic and thermodynamic properties of thorium tetraboride

The structural, elastic and thermodynamic properties of thorium tetraboride (ThB₄) have been investigated by using first-principles plane-wave pseudopotential density functional theory with generalized gradient approximation. The behaviors of structural parameters under 0-70 GPa hydrostatic pressure are studied by means of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) geometry optimization scheme. By using the stress-strain method, single crystal elastic constants are calculated to test the mechanical stability of the crystal structure and to determine mechanical properties such as bulk modulus at each pressure. However, in order to study the thermodynamic properties of ThB₄, the quasi-harmonic Debye model is used. Then, the dependencies of bulk modulus, heat capacities, thermal expansions, Grüneisen parameters and Debye temperatures on the temperature and pressure are obtained in the whole pressure range 0-70 GPa and temperature range 0-1500 K.