THE GLOBAL AND LOCAL C^(2)-SOLUTIONS FOR THE WAVE EQUATION □u = G(u_t, Du) IN THREE SPACE DIMENSIONS

Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.

The Effects of Space Dimension and Temperature on the Cross Mating of Three Cryptic Species of the Bemisia tabaci Complex in China

The sweetpotato whitefly Bemisia tabaci（Homoptera：Aleyrodidae）is a destructive pest of agriculture and horticulture worldwide.Recent phylogenetic analysis using mitochondrial cytochrome oxidase 1 sequences indicates that this whitefly is a species complex including at least 24 morphologically indistinguishable but genetically distinct cryptic species.In this study,the inter-species crosses of Middle East-Asia Minor 1（MEAM1）,Mediterranean（MED）and Asia II 7 cryptic species,which were referred to as B,Q and Cv biotypes before,were conducted in two different devices,leaf cages（7 cm3）and cylinder cages（280 cm3）,and at three temperatures of 22,30 and 38°C.Results indicated that no female progeny were produced in the reciprocal cross between MEAM1×Asia II 7,between MED×Asia II 7 cryptic species neither in leaf cage nor in cylinder cages,while 0.81 and 1.37% of females in the offspring were recorded in the reciprocal cross between MEAM1×MED in leaf cage experiments.Approximately 0.95-0.98% female progeny were recorded in the reciprocal cross between MEAM1×MED at 30°C,0.77% female progeny were recorded in the single cross direction between MEAM1 × MED at 22°C,and no female progeny were found in their reciprocal cross at 38°C in leaf cage.Our findings indicated that neither space dimension nor temperature have a significant effect on the hybridization of different B.tabaci cryptic species.

PIECEWISE SMOOTH SOLUTION OF THE FIRST ORDER SEMILINEAR HYPERBOLIC SYSTEMS IN HIGHER SPACE DIMENSION

It is important to study the propagation and interaction of progressing waves of nonlinear equations in the class of piecewise smooth function. However, there has not been many works on that in multidimensional case. In 1985, J, Rauch & M. Reed have provad the existence and uniqueness of piecewise smooth solution for

A Creation Model from the Gell-Mann Standard Model to the Creation of Bio Cells: Based on the Assumption of Homogeneous 5D Space-Time Universe

In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to Tc in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition Tc upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schrödinger to most recently Geesink.

A Model of the Universe that Can Explain Dark Matter, Dark Energy, and the Fourth Space Dimension

This paper explains how a model of the universe can be constructed by incorporating time and space into geometry in a unique way to produce a 4-space dimension/1-time dimension model. The model can then show how dark matter can be the gravity that is produced by real matter that exists throughout our entire universe. The model can also show how dark energy is not an increase in energy that is causing the accelerated expansion of the universe, but is an accelerating decrease in matter throughout the universe as the stars and galaxies in the universe continue to convert matter into energy during their life cycles. And then the model can show how a fourth space dimension must exist in our universe to locate a point in space.

A Comparative Study on Two Techniques of Reducing the Dimension of Text Feature Space

With the development of large scale text processing, the dimension of text feature space has become larger and larger, which has added a lot of difficulties to natural language processing. How to reduce the dimension has become a practical problem in the field. Here we present two clustering methods, i.e. concept association and concept abstract, to achieve the goal. The first refers to the keyword clustering based on the co occurrence of

Modification of the Clarkson-Kruskal Direct Method for a Coupled System

A new idea is put forward to modify the Clarkson-Kruskal （CK） direct method. Using the usual CK direct method to a coupled KdV system, two types of usual similarity reductions can be obtained. However, the application of the modified CK direct method leads to three types of new similarity reductions different from the usual ones.

Principle for the Working of the Lithium-Ion Battery

The technological advances in Lithium-ion batteries have created many new applications, including electric vehicles. In this short note, we shall explain in simple terms the basic physics why and how it is possible to have high energy capacity in Lithium-ion batteries. However, heating has been a common problem and without appropriate design, they might give fire and explosion as reported.

Decay of a Mass-Less Field Far from Horizon of a Black Hole

Far from the horizon of a black hole of even space dimension n, a mass-less field decays as t1-2t-n in the time, where 1 is a harmonic mode of the sphere.

The Maximum Dissipative Extension of Schrodinger Operator

In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.

STABILITY OF DIFFERENCE SCHEMES FOR NONLINEAR PARABOLIC SYSTEMS WITH THREE DIMENSIONS

In this paper the existence of discrete vector solutions with bounded second order quotientsfor the difference systems of nonlinear parabolic system is established by the fixed point technique,and then the absolute and relative stability for the general difference schemes is justified in thesense of continuous dependence of the discrete vector solution of the difference schemes on thediscrete data of the original problems.

Global Existence of Small Solutions for Cubic Quasi-linear Klein-Gordon Systems in One Space Dimension

In this paper, we consider a system of two cubic quasi-linear Klein-Gordon equations with different masses for small, smooth, compactly supported Cauchy data in one space dimension. We show that such a system has global existence when the nonlinearities satisfy a convenient null condition. Our results extend the global existence proved by Sunagawa recently under the non-resonance assumption to that under the resonance assumption.

Hausdorff measure of sets of finite type of one-sided symbolic space

Some estimation formulae and a computation formula for the hausdorff meausre fo the sets of finite type of the one-sided symbolic space are given

Polynomial solutions of quasi-homogeneous partial differential equations

By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $\left\{ {\delta _\tau } \right\}{\text{ }}_{\tau< 0} $ given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or $m{\text{ = }}\sum\limits_{j = 1}^n {\alpha _j \alpha _j } $ for some $\alpha {\text{ = }}\left( {\alpha _1 ,{\text{ }} \ldots {\text{ }},\alpha _n } \right) \in l _ + ^n $ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ?n must be infinite