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1.
For an annular cathode in a coaxial diode it has been shown that the averaged electric field strength at the end face of the cathode, En, depends on the edge thickness h as
. It has been found that the field strength varies with distance from the edge approximately as
. The problem of the electric field strength at the edge of the cathode in a magnetically insulated coaxial diode has been solved for the case where the cathode emissivity is limited with the use of a model assuming a given internal resistance of the voltage source. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 71–76, March, 2008.  相似文献   

2.
In this paper, we present several systematicways to find exact traveling-wave solutions of thesystems
where a, b, c, and d are real constants. These systems,derived by Bona, Saut and Toland for describingsmall-amplitude long waves in a water channel, areformally equivalent to the classical Boussinesq systemand correct through first order with regard to asmall parameter characterizing the typicalamplitude-todepth ratio. Exact solutions for a largeclass of systems are presented. The existence of theexact traveling-wave solutions is in general extremely helpful inthe theoretical and numerical study of thesystems.  相似文献   

3.
The Levinson theorem for the one-dimensional Schrödinger equation with both local and the nonlocal symmetric potentials is established by the Sturm–Liouville theorem. The critical case where the Schro;audinger equation has a finite zero-energy solution is also analyzed. It is shown that the number n + (n ) of bound states with even (odd) parity is related to the phase shift +(0)[(0)] of the scattering states with the same parity at zero momentum as
and
The problems on the positive-energy bound states and the physically redundant state related to the nonlocal interaction are also discussed.  相似文献   

4.
The mass and the total decay width of the W boson are measured with the L3 detector at the LEP e+e collider using W-boson pairs produced in 0.7 fb–1 of data collected at centre-of-mass energies between 161 and 209 GeV. Combining semi-leptonic and fully-hadronic final states, the mass and the width of the W boson are determined to be
where the first uncertainty is statistical and the second systematic.  相似文献   

5.
We consider a family of Hamiltonian systems
and we prove that it is integrable for . To show this we use the normal variational equation.  相似文献   

6.
We prove the existence of bubbling solutions for the following Chern-Simons-Higgs equation:
$ \Delta u +\frac{1}{\varepsilon^2} e^u(1-e^u) =4\pi \sum_{j=1}^N \delta_{p_j},\quad {\rm in} \, \Omega, $ \Delta u +\frac{1}{\varepsilon^2} e^u(1-e^u) =4\pi \sum_{j=1}^N \delta_{p_j},\quad {\rm in} \, \Omega,  相似文献   

7.
Maximal Inequalities for CIR Processes   总被引:1,自引:0,他引:1  
Let X be a Cox—Ingersoll—Ross (CIR) process given by
with X 0 = 0, where a, c>0, and B a standard Brownian motion starting at zero. We obtain some inequalities between the integral functional , t ⩾ 0 and the maximal process sup0⩽st X s , t ⩾ 0, where x↦ϕ(x) a nonnegative continuous function with some suitable conditions.  相似文献   

8.
According to the Einstein-Mayer theory of the Riemanniann space-time with Einstein-Cartan teleparallelism, the local Lorentz invariance is broken by the gravitational field defining Machian reference systems. This breaking of symmetry implies the occurrence of “hidden matter” in the Einstein equations of gravity. The hidden matter is described by the non-Lorentz-invariant energy-momentum tensor satisfying the relation . The tensor is formed from the Einstein-Cartan torsion field given by the anholonomy objects, FAik=2hA[i,k], and appears together with Hilbert’s energy-momentum tensor T* ik and Poincaré’s pressure λgik on the right-hand side of Einstein’s equations so that one has
According to this theory, in the universe and in cosmic systems one must excep “invisible masses” described by the Poincaré and Einstein-Cartan terms to exist. The torsion field FAik makes the space-time a Machian universe; it is of the same nature as the “weak interacting matter” discussed in astrophysics.  相似文献   

9.
Eigenvalue estimate for the Dirac–Witten operator is given on bounded domains (with smooth boundary) of spacelike spin hypersurfaces satisfying the dominant energy condition, under four natural boundary conditions (MIT, APS, modified APS and chiral conditions). Roughly speaking, any eigenvalue of the Dirac–Witten operator satisfies
where is the infimum of (the opposite of) the Lorentzian norm of the constraints vector. Equality cases are also investigated and lead to interesting geometric situations.   相似文献   

10.
It has been shown in E and Li (Comm. Pure. Appl. Math., 2007, in press) that the Andersen dynamics is uniformly ergodic. Exponential convergence to the invariant measure is established with an error bound of the form
where N is the number of particles, ν is the collision frequency and κ(ν)→const as ν→0. In this article we study the dependence on ν of the rate of convergence to equilibrium. In the one dimension and one particle case, we improve the error bound to be
In the d-dimension N-particle free-streaming case, it is proved that the optimal error bound is
It is also shown that as ν→∞, on the diffusive time scale, the Andersen dynamics converges to a Smoluchowski equation.  相似文献   

11.
We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action
with general F() and V(). The dynamical nature of each singularity is elucidated, and we show that both are, in general, dynamically unavoidable, reinforcing the unstable character of previous isotropic and homogeneous cosmological results obtained for the conformal coupling case.  相似文献   

12.
We find that the Laplace sequences of surfaces of period n in projective space P n–1 have two types, while type II occurs only for even n. The integrability condition of the fundamental equations of these two types have the same form
When all i = 1, the above equations become two-dimensional Toda equations. Darboux transformations are used to obtain explicit solutions to the above equations and the Laplace sequences of surfaces. Two examples in P 3 of types I and II are constructed.  相似文献   

13.
We consider the Zakharov equation in space dimension two
  相似文献   

14.
The properties of solutions of Einstein's equations for spherically symmetric gravitational fields are studied. The notions of R- and T-universe regions are introduced. T-regions are shown to be regions of essential instability in the distinguished direction of the flow of time. The geometrical properties and those of the deformation of reference frames in these regions are discussed. Birkhoff's theorem for the Schwarzschild field is stated more precisely. In a T-region of this field there exists a frame of reference with the interval in the form
where t is the time coordinate, r the radial space coordinate, γ the Newtonian gravitational constant, c the fundamental velocity and m the mass producing the field. In this system, by comparison with Schwarzschild's, the space and time coordinates have changed places. The properties of the motion of light rays and test particles in R- and T-regions are discussed. The conclusions should be taken into account in considering cosmological questions and in the investigation of superdense stellar configurations.  相似文献   

15.
We consider the Zakharov equation in space dimension two
  相似文献   

16.
This is the continuation of a series of articles concerning a class of quantum spin systems with Hamiltonian operators of the form
  相似文献   

17.
The mass and width of the W boson are measured using e+e → W+W events from the data sample collected by the OPAL experiment at LEP at centre-of-mass energies between 170 GeV and 209 GeV. The mass (mW) and width (ΓW) are determined using direct reconstruction of the kinematics of W+W → and W+W → events. When combined with previous OPAL measurements using W+W → events and the dependence on of the WW production cross-section at threshold, the results are determined to be
where the first error is statistical, the second systematic and the third due to uncertainties in the value of the LEP beam energy. By measuring in the channel using several different determinations of the direction of jets with differing sensitivities to soft particles, a limit is also obtained on possible final-state interactions due to colour reconnection effects inW+W → events. The consistency of the results for the W mass and width with those inferred from other electroweak parameters provides an important test of the Standard Model of electroweak interactions. Arrival of the final proofs: 28 November 2005 This paper is dedicated to the memory of Steve O'Neale  相似文献   

18.
In dimension n > 3 we show the existence of a compactly supported potential in the differentiability class , for which the solutions to the linear Schrödinger equation in,
fail to satisfy an evolution estimate of the form
This contrasts with known results in dimensions n ≤ 3, where a pointwise decay condition on V is generally sufficient to imply dispersive bounds.The obstructions in our example are generated by an expression with scaling law , which becomes dominant in the time interval .  相似文献   

19.
The irreducible R-matrices associated with the quantum Liouville and sine-Gordon equations were classified by the su(2) index l, 2l integer. We find that the associated quantum field theories must have the following equal time operator product expansions in the lattice approximation
  相似文献   

20.
The determinants of Laplacians acting in real line bundles over manifolds of the form
  相似文献   

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