Die Zurückführung der Gleichungen eines rotationssymetrischen,statischen, inkompressiblen Plasmas von unendlicher Leitfähigkeit auf ein Randwertproblem

The equations of a rotationally symmetric, static, incompressible plasma with infinite conductivity are equivalent to an elliptic differential equation for the function where p means the pressure, ? the density, and Φ the potential of the external forces. Moreover this differential equality contains two arbitrary functions of ξ. When ξ_?² + ξ_?² < 0, both arbitrary functions can be computed from the boundary values of Hφ und H⊥ (the component of H , which is perpendicular to the boundary).     

Über ein weiteres Variationsprinzip im Zusammenhang mit kraftfreien Magnetfeldern

Im Anschluß an ein von Woltjer [1] diskutiertes Variationsproblem wird gezeigt: Die Euler-Lagrange-Gleichungen des Variationsproblems mit der Nebenbedingung wo H = rot A gesetzt ist, sind die Differentialgleichungen der kraftfreien Magnetfelder mit variablem α. Die Nebenbedingung läßt sich für alle Felder H erfüllen, die keinen singulären Punkt mit H = 0 in dem betrachteten Volumen V haben. In persuance of a variational principle discussed by Woltjer [1] it is shown that the Euler-Lagrange-equations of the variational problem with the secondary condition where H = rot A are the differential equations of the force-free magnetic fields with a variable scalar α. The secondary condition can be accomplished for all magnetic fields which do not contain singular points with H = 0 in the volume V under consideration.     

Zur unitarisierten Gravitationstheorie mit lang- und kurzrechweitigen Termen (mit ruhmasselosen und schweren Gravitonen)

In our papers, TREDER [1, 2] we have formulated a unified electrodynamics of the fourth order with bi-wave equations for the vector potential A. In this electrodynamics EINSTEIN ian photon and heavy W-mesons are the field quanta. In correspondence to this field theory we are able to formulate a unified theory of gravitation, too. The field equations for the gravitational metrics grr in this theory are corresponding with the EINSTEIN equations of General Relativity in the same way like the electromagnetic bi-wave equations are corresponding with the MAXWELL equations. The metric g_μν is a linear functional of an EINSTEIN ian long-range potential g_μν and of a subatomic short-range potential definierte Materie-Tensor die gemeinsame Quelle für alle drei Felder ist. Dann ist g1_μν, g2_μν und g_μν und es gelten die Funktional-Bedingungen wobei hier g2_μν Feldgleichungen vom “kosmologischen Typ” befriedigt. By these conditions, the short-range interaction becomes a repulsive force and the action of the NEWTON -EINSTEIN ian attraction and of the subatomic repulsion makes the matter point-like (as in the E.-I.-H.-method) but self-consistent. The gravitational metrics g2_μν become regulary. P. e., in the EINSTEIN approximation the field of a point-like mass M is given by a SCHWARZSCHILD     

On the Initial Boundary Value Problems for the Enskog Equation in Irregular Domains

The paper is concerned with the Enskog equation with a constant high density factor for large initial data in L ¹(R ⁿ). The initial boundary value problem is investigated for bounded domains with irregular boundaries. The proof of an H-theorem for the case of general domains and boundary conditions is given. The main result guarantees the existence of global solutions of boundary value problems for large initial data with all v-moments initially finite and domains having boundary with finite Hausdorff measure and satisfying a cone condition. Existence and uniqueness are first proved for the case of bounded velocities. The solution has finite norm where q = (t ₀, x) is taken on all possible n-dimensional planes Q(v) in R ^n+l intersecting a fixed point and orthogonal to vectors (1, v), v R ⁿ.     

New proofs of the existence of the Feigenbaum functions

A new proof of the existence of analytic, unimodal solutions of the Cvitanovi-Feigenbaum functional equation g(x) = –g(g(–x)),g(x) 1 - const|x|^r at 0, valid for all in (0, 1), is given, and the existence of the Eckmann-Wittwer functions [8] is recovered. The method also provides the existence of solutions for certain given values ofr, and in particular, forr=2, a proof requiring no computer.     

Identification of intra‐grain and grain boundary defects in polycrystalline Si thin films by electron paramagnetic resonance

We investigate the characteristics of intra‐grain and grain boundary defects in polycrystalline Si films, by employing quantitative electron paramagnetic resonance measurements on liquid phase crystallized layers with an average grain size of 200 µm and tailored solid phase crystallized Si layers with similar intra‐grain morphology but systematically varied grain sizes between 0.25 µm and 1 µm. The defect characteristics are found to be composed of two distinctive g ‐values of g = 2.0055 and 2.0032, which are attributed to grain boundary defects and intra‐grain defects, respectively. Additional hydrogenation leads to a reduction of the overall defect concentration, while a rapid thermal annealing process primarily heals intra‐grain defects.

     

Kinetic and mechanism of the homogeneous,unimolecular elimination of α,β‐unsaturated aldehydes in the gas phase

The gas phase thermal decarbonylation of α,β‐unsaturated aldehydes E‐2‐butenal and E‐3‐phenyl‐2‐methylpropenal was studied in a static system over the temperature range 380.5–490.0 °C and pressure range 55.5–150 Torr. The reactions are homogeneous and unimolecular and obey a first‐order rate law. The rate coefficient is represented by the following Arrhenius equations: The elimination products of 2‐butenal are propene and CO gas, while 3‐phenyl‐2‐methylpropenal produces α‐methylstyrene, cis‐trans‐β‐methylstyrene, indan, and CO gas. Kinetic and thermodynamic parameters suggest these elimination reactions to proceed through a three‐membered cyclic transition state type of mechanisms. However, a two steps mechanisms for the formation of a carbene type of intermediate through a four‐membered cyclic transition structure can not be overlooked. Copyright © 2007 John Wiley & Sons, Ltd.     

On diffuse reflection at the boundary for the Boltzmann equation and related equations

The paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities. The solutions obtained are proved to conserve mass at the boundary. After a preliminary study of the collisionless case, the main results obtained are existence for the Boltzmann equation in a DiPerna-Lions framework with the above boundary conditions in a bounded measure sense, and existence together with uniqueness for the BGK equation with Maxwellian diffusion on the boundary in anL framework.Deceased.     

Gravitationskollaps und Lichtgeschwindigkeit im Gravitationsfeld

An elementary criterion of the stability of a matter sphere against gravitational collapse is given by the circular velocity condition of POINCARÉ : In a space with a spherically symmetric gravitation potential ? (r) and with a spherically symmetric metric gik (e.g., a SCHWARZSCHILD space time) the circular velocity V^* of a particle on the surface r = R of the matter-sphere must be (This condition is a consequence of the virial theorem and of the POINCARÉ theorem.) - However, EINSTEIN 's axiom of causality implies that this velocity V^* must be smaller than the local velocity of light v: V^*2 < v². And this local velocity v is a function of the gravitation potential ?, too: v = v [?]. In the case of NEWTON 's or EINSTEIN 's theory the spherically symmetric gravitation potential is given by the NEWTON ian function ? = fM/r. In the special theory of relativity, we would have v = c (c = EINSTEIN 's fundamental velocity) and grr = 1. Therefore, the specialrelativistic stability condition is R > fMc^?2. - But in the NEWTON ian theory v is depending of the gravitation potential and depends of the boundary condition for the light propagation, also. According to the ansatz of LAPLACE (1799) we have: (emanation-theory of light). But, according to SOLDNER (1801), we have Therefore, we are finding in the case of LAPLACE the same condition R > fMc^?2 as in the SRT. But, in the case of SOLDER 's ansatz non condition for stability is resulting. - In the general relativistic theories the local velocity of light is given by EINSTEIN 's expression According to EINSTEIN 's theory of “static gravitation” (1911/12) we have grr = 1 and therefore the formula and according to the GRT (with - g_ω = grr^?1) we have the formula Therefore, the Hilbert-Laue condition r= R > 3fMc^?2 results as stability condition. From the gravo-optical point of view, in GRT and for the classical ansatz of LAPLACE “black-holes” with bounding states of light result for R ≤ 2fM^?2. But, no “black-holes” are existing according to SOLDNER 's ansatz. However, in GRT each black-hole must be a “collapsar”. But according to the classical theory of LAPLACE we have uncollapsed “black- holes” for the domain .     

Secondary Neutral Pion-nucleon Flux Ratio at the Top of the Atmosphere

The CERN Intersecting Storage Ring data on the inclusive reaction p + p → π° + X has been fitted with a phenomenological form where W_c(a,b,z) is the generalized confluent function defined by . M(a, b, z) being the well known Kummer's function. Using this form and primary proton spectrum of Goddard Space Flight Center Group the secondary neutral pion-nucleon flux ratio at the top of the atmosphere has been estimated. The derived result has been compared with those expected from p + p → π^± + X data, via different models.     

Periodic nonlinear waves on a half-line

Nontrivial solutions of the equationu _tt=u _xx–g(u) which are 2-periodic int and which decay asx are shown to exist ifg(a)=0 andg(0)>1. Breather-like solutions, which also decay asx –, can be interpreted as homoclinic solutions in thex-dynamics; their existence is still in question for generalg.     

Hierarchy of the non‐covalent interactions in the alanine‐based secondary structures. DFT study of the frequency shifts and electron‐density features

The alanine (Ala)‐based cluster models of C5, C7, and C10 H‐bonds are studied at the DFT/B3LYP level. CPMD/BLYP simulations of the infinite polyalanine α‐helix (C13 H‐bond) and the two‐stranded β‐sheets are performed. Combined use of frequency shifts and electron‐density features enable us to detect and describe quantitatively the non‐covalent interactions (H‐bonds) defining the intrinsic properties of Ala‐based secondary structures. The energies of the primary N? H O H‐bonds are decreasing in the following way: C13 > C5 ≥ C7 > C10. The energies of the secondary N? H O, N?H N, and H H interactions are comparable to those of the primary H‐bonds (～4.5 kcal/mol). Side chain–backbone C? H O interaction is found to be the weakest non‐covalent interaction in the considered species. Its energy is ～0.5 kcal/mol in the infinite polyalanine α‐helix. Quantum‐topological electron‐density analysis is found to be a powerful tool for the detection of secondary non‐covalent interactions (C?O H? C and H H) and bifurcated H‐bonds, while the frequency shift study is useful for the identification and characterization of primary or secondary H‐bonds of the N? H O type. Copyright © 2008 John Wiley & Sons, Ltd.     

The metal‐insulator transitions of VO2: A band theoretical approach

The results of first principles electronic structure calculations for the metallic rutile and the insulating monoclinic phase of vanadium dioxide are presented. In addition, the insulating phase is investigated for the first time. The density functional calculations allow for a consistent understanding of all three phases. In the rutile phase metallic conductivity is carried by metal orbitals, which fall into the one‐dimensional band, and the isotropically dispersing bands. Hybridization of both types of bands is weak. In the phase splitting of the band due to metal‐metal dimerization and upshift of the bands due to increased p‐d overlap lead to an effective separation of both types of bands. Despite incomplete opening of the optical band gap due to the shortcomings of the local density approximation, the metal‐insulator transition can be understood as a Peierls‐like instability of the band in an embedding background of electrons. In the phase, the metal‐insulator transition arises as a combined embedded Peierls‐like and antiferromagnetic instability. The results for VO₂ fit into the general scenario of an instability of the rutile‐type transition‐metal dioxides at the beginning of the d series towards dimerization or antiferromagnetic ordering within the characteristic metal chains. This scenario was successfully applied before to MoO₂ and NbO₂. In the compounds, the and bands can be completely separated, which leads to the observed metal‐insulator transitions.     

Kinetics and mechanisms of gas‐phase elimination of 2,2‐diethoxyethyl amine and 2,2‐diethoxy‐N,N‐diethylethanamine

The gas‐phase elimination kinetics of 2,2‐diethoxyethyl amine and 2,2‐diethoxy‐N,N‐diethylethanamine (320–380 °C; 40–150 Torr) in a seasoned reaction vessel are homogeneous, unimolecular and obey a first‐order rate law. These elimination processes involve two parallel reactions. The first gives ethanol and the corresponding 2‐ethoxyethenamine. The latter compound further decomposes to ethylene, CO and the corresponding amine. The second parallel reaction produce ethane and the corresponding ethyl ester of an α‐amino acid. The following Arrhenius expressions are given as: For 2,2‐diethoxyethyl amine For 2,2‐diethoxy‐N,N‐diethylethanamine Comparative kinetic and thermodynamic parameters of the overall, the parallel and the consecutive reactions lead to consider two types of mechanisms in terms of a concerted polar cyclic transition state structures. Copyright © 2008 John Wiley & Sons, Ltd.     

Über stationäre,rotierende, inkompressible Plasmen mit minimalen inneren Verlusten

The condition that the Ohmic and the friction losses are minimized leads to the assumption that both the magnetic field H and the velocity field v are Trkal-fields. . In the rotationally symmetric, stationary case the boundary conditions and the condition that the toroidal part of v and H should vanish on the boundary, lead to a linear eigenvalue problem for α, β which in case of a rectangular domain easily can be resolved. It follows: .     

Global existence and boundedness of large solutions to nonlinear equations of viscoelasticity with hardening

For the solutions of an initial-boundary value problem for the equations of viscoelasticity with isotropic hardening we derive a uniform bound under a growth condition for the nonlinearities in the case of one-space dimension. Global-in-time existence of solutions to large initial data is a consequence of the existence of this bound. In the most simple form, the equations we consider are with suitable functionsg ₁,g ₂,h satisfyingg ₂0 andXDedicated to Erhard Meister on the occasion of his sixtyfifth birthdayThis research was partially supported by the DFG-Forschergruppe Mathematische und Ingenieurwissenschaftliche Analyse bruchmechanischer und inelastischer Probleme     

Renormalons and analytic properties of the β function

The presence or absence of renormalon singularities in the Borel plane is shown to be determined by the analytic properties of the Gell-Mann-Low function β(g) and some other functions. A constructive criterion for the absence of singularities consists in the proper behavior of the β function and its Borel image at infinity, β(g) ∝ g^α and B(z) ∝ z^α with α ≤ 1. This criterion is probably fulfilled for the ?⁴ theory, quantum electrodynamics, and quantum chromodynamics, but is violated in the O(n)-symmetric sigma model with n → ∞.     

Positivity and self adjointness of theP(φ)2 Hamiltonian

We give a new proof that the locally correct HamiltonianH(g) is self adjoint, and that the vacuum energyE(g)=inf spectrumH(g) satisfies –O(D)E(g), where 0g1 andD=diam.supp.g.Supported in part by Air Force Office of Scientific Research, Contract AF 49(638) -1719.On leave at Princeton University. Alfred P. Sloan Foundation Fellow. Supported in part by Air Force Office of Scientific Research, Contract F44620-70-C-0030.     

Existence of solitary waves in higher dimensions

The elliptic equation u=F(u) possesses non-trivial solutions inR ⁿ which are exponentially small at infinity, for a large class of functionsF. Each of them provides a solitary wave of the nonlinear Klein-Gordon equation.This work was supported in part by NSF Grant MCS 75-08827     

Algebraic decomposition of the electromagnetic constitutive tensor. A step towards a pre‐metric based gravitation?

The aim of this paper is to provide an algebraic decomposition of the principal part of the electromagnetic constitutive tensor χ_μνρσ (a pre‐metric structure), in a sum of terms of the form where the Z_(i) are invariant scalars and g_μν(i)unimodular conformal metrics. If the space‐time is also equipped with a volume measure, such a decomposition is equivalent to a similar decomposition of the associated area metric, where the g_μν(i) are ordinary metrics. It has been recently argued [8] that, if such a particular decomposition should be available, it would then be possible to find a compatible connection and derived tensors.