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1.
In this paper, we deal with operators of the form
on the space ℝn. It is assumed that the principal part of L is a uniformly strongly elliptic operator and the coefficients c α,β with |α| + |β| < 2m are distributions. We find sufficient conditions on these coefficients (in terms of generalized Sobolev spaces with negative smoothness indices to which these coefficients belong) for the operator in question to be well defined in the sense of quadratic forms. Dedicated to the memory of B. M. Levitan Paper supported by RFBR under grant no. 04-01-00712.  相似文献   

2.
S. Rajasekar 《Pramana》2004,62(1):1-12
Integrability of a linearly damped two-coupled non-linear oscillators equation is investigated by employing the Painlevé analysis. The following two integrable cases are identified: (i)d = 0, α =β, δ_1 and δ_2 are arbitrary, (ii) d^2= 25α/6, α =β, δ_1 and δ_2 are arbitrary. Exact analytical solution is constructed for the integrable choices.  相似文献   

3.
We study amplitude-squared squeezing of the Hermitian operator Zθ=Z1 cosθ+Z2 sin θ, in the most general superposition state , of two coherent states and . Here operators Z1,2 are defined by , a is annihilation operator, θ is angle, and complex numbers C1,2 , α, β are arbitrary and only restriction on these is the normalization condition of the state . We define the condition for a state to be amplitude-squared squeezed for the operator Zθ if squeezing parameter , where N=a+a and . We find maximum amplitude-squared squeezing of Zθ in the superposed coherent state with minimum value 0.3268 of the parameter S for an infinite combinations with α- β= 2.16 exp [±i(π/4) + iθ/2], and with arbitrary values of (α+β) and θ. For this minimum value of squeezing parameter S, the expectation value of photon number can vary from the minimum value 1.0481 to infinity. Variations of the parameter S with different variables at maximum amplitude-squared squeezing are also discussed.  相似文献   

4.
If A q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ3 is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S 2 is the unit sphere in ℝ3, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D mD, 1≤ mM, distributed in an a priori given bounded domain D⊂ℝ3. The geometrical shape of a small particle D m is arbitrary, the boundary S m of D m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L 2(S 2× S 2) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential qL 2(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.  相似文献   

5.
Satish D Joglekar 《Pramana》1989,32(3):195-207
We discuss the general theory of renormalization of unbroken gauge theories in the nonlinear gauges in which the gauge-fixing term is of the form We show that higher loop renormalization modifiesfα [A] to contain ghost terms of the form and show how the corresponding ghost terms are deduced fromfα [A, c, c] uniquely. We show that the theory can be renormalized while preserving a modified form of BRS invariance by multiplicative and independent renormalizations onA, c, g, η, ζ, τ. We briefly discuss the independence of the renormalized S-matrix from η,ζ, τ.  相似文献   

6.
Let δ be a quasi-free derivation of the CAR algebra, and let be a closed *-derivation which is an extension of δ. We use Price's techniques from [6] to show that if the polynomials in the linear field operators a(f)→a * (f) in D( ) is a core for , then is quasi-free.  相似文献   

7.
Dirac’s large number hypothesis (LNH), in the formG/G 0=HH 0 −1 , is applied to the matter-dominated cosmological era, using the framework of the scale covariant theory (Canuto et al., 1977). We obtain explicit expressions forR andβ a as functions ofR E , whereR andR E are the scale factors of the cosmological Robertson-Walker metric, expressed in atomic and gravitational units, respectively, andβ a is the ratio between the rates of gravitational and atomic clocks. The parameters in these expressions are , the deceleration parameter in gravitational units, and (t 0)H 0 −1 where (t 0) is the present epoch value of the derivative ofβ a with respect to atomic time. We find that a necessary condition for the LNH to be compatible with a Robertson-Walker model is that (t 0)H 0 −12 1 . The only experimental values for (t 0) available at present are those based on the lengthening of the Moon’s period of revolution around the Earth, suggesting 0.86≥ (t 0)H 0 −1 ≥0.21; the more promising technique of radar ranging to the inner planets has not yet produced a value for (t 0). Using the lunar data, it follows that 0≤ ≲0.42 corresponding to an open universe (k=−1). Closed models (k=1, >1/2) are not compatible with the LNH since the required values of (t 0)H 0 −1 are more than an order of magnitude above the observational upper limit. Presented at the Dirac Symposium, Loyola University, New Orleans, 1981.  相似文献   

8.
We derive in 3+0 dimensions exact solutions of Liouville's equation 2=exp , by applying the Bäcklund transformation technique in conjunction with the principle of nonlinear superposition. The procedure, which is later extended to 3+1 dimensions, yield, as a byproduct, particular solutions of 2 and 2 =exp (2 +2 ).  相似文献   

9.
In this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G α is given by , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.   相似文献   

10.
The spinor approach of Witten and Nester is used to show that in ann-dimensional Lorentzian spaceV n , the conserved total energy-momentum vectorP is nonspace-like. It is shown thatP may be expressed in terms of an integral of an antisymmetric tensorE over ann – 2-dimensional subspace at space-like infinity inV n .E is expressed in terms of a spinor field inV n and its covariant derivatives. This tensor is a generalization of that used in the discussion of five-dimensional Lorentzian spaces.  相似文献   

11.
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   

12.
The influence of nuclear effects on the production of neutral strange particles (V 0) is investigated using the data obtained with SKAT propane-freon bubble chamber irradiated in the neutrino beam (with E v =3−30 GeV) at the Serpukhov accelerator. The mean multiplicity of V 0 particles in nuclear interactions, , is found to exceed significantly that in “quasideuteron” interactions, . The ratio of is larger than that for π mesons, . It is shown that the multiplicity gain of V 0 particles can be explained by intranuclear interactions of produced pions. The text was submitted by the authors in English.  相似文献   

13.
We calculate analytical contributions to then-loop asymptotic photon propagator from diagrams withn–1 electron loops, i.e. theO(1/N) terms in the largeN limit. The corresponding contributions to the on-shell -function, ()=6 log / logm reduced to rational combinations of s = p p s . For the -function of the MOM scheme (i.e. the Gell-Man-Low function) we obtain theO(1/N) terms of
  相似文献   

14.
A new modification of the least squares method (LSM) is proposed. The main idea is to consider the fitting parameters β i as independent random variables with a certain distribution density F1, β2, ..., β k ; φ1, ..., φ m ), which depends on a set of m experimental points φ j . Within this approach, the estimates of the parameters minimize squared deviations and are equivalent to means of the probability distribution = = ∫β i F1, β2, ..., β k ; φ1, ..., φ m )dβ1 dβ2...dβ k . Original Russian Text ? I.D. Gorlachev, B.B. Knyazev, A. Kuketayev, F.M. Pen’kov, 2009, published in Izvestiya Rossiiskoi Akademii Nauk. Seriya Fizicheskaya, 2009, Vol. 73, No. 2, pp. 257–260.  相似文献   

15.
The general theory of space tensors is applied to the study of a space-time manifoldsV 4 carrying a distinguished time-like congruence Γ. The problem is to determine a physically relevant spatial tensor analysis over (V 4, Γ), in order to proceed to a correct formulation of Relative Kinematics and Dynamics. This is achieved by showing that each choice of gives rise to a corresponding notion of ‘frame of reference’ associated with the congruence Γ. In particular, the frame of reference (Γ, ∇*) determined by the standard spatial tensor analysis is shown to provide the most natural generalization of the concept of frame of reference in Classical Physics. The previous arguments are finally applied to the study of geodesic motion inV 4. As a result, the general structure of the gravitational fields in the frame of reference (Γ, ∇*) is established. This work was assisted by funds from the C.N.R. under the aegis of the activity of the National Group for Mathematical Physics.  相似文献   

16.
The LHC (CMS) discovery potential in the search for supersymmetry and lepton-flavor violation in neutralino decays using the e ± μ + E T miss signature is studied. A detailed study is done for the CMS test points LM1-LM9. It is shown that, for the point LM1, it is possible to detect lepton-flavor violation in neutralino decays with lepton-flavor-violating branching Br( → μ± e ) ≥ 0.04 Br( → e + e , μ+ μ ) for an integral luminosity of 10 fb−1. The discovery potential in the mSUGRA-SUSY scenario with tan β = 10, sgn(μ) = + in the (m 0, m 1/2) plane using the e ± μ + E T miss signature is determined. The text was submitted by the authors in English.  相似文献   

17.
For M a factor of type III1 we can find for every automorphism group s that commutes with a modular automorphism group t and another modular automorphism group , an automorphism group that commutes with is connected with s by an inner cocycle.  相似文献   

18.
B K Barik  B B Deo 《Pramana》1985,25(6):663-671
A heavy quark antiquark potential is suggested connecting asymptotic freedom and quark confinement in a unified way. Theα g (q 2) calculated using Borel summation technique with three loop agrees with the two loopβ-function up tog 2/4π≅ 1.1 but changes appreciably afterg 2/4π=1.5. The potential so derived satisfactorily explains the and spectrum.  相似文献   

19.
For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p j eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p j eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x 2〉∼t α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.  相似文献   

20.
Let be a finite-dimensional complex simple Lie algebra and Uq( ) the associated quantum group (q is a nonzero complex number which we assume is transcendental). IfV is a finitedimensional irreducible representation of Uq( ), an affinization ofV is an irreducible representationVV of the quantum affine algebra Uq( ) which containsV with multiplicity one and is such that all other irreducible Uq( )-components ofV have highest weight strictly smaller than the highest weight ofV. There is a natural partial order on the set of Uq( ) classes of affinizations, and we look for the minimal one(s). In earlier papers, we showed that (i) if is of typeA, B, C, F orG, the minimal affinization is unique up to Uq( )-isomorphism; (ii) if is of typeD orE and is not orthogonal to the triple node of the Dynkin diagram of , there are either one or three minimal affinizations (depending on ). In this paper, we show, in contrast to the regular case, that if Uq( ) is of typeD 4 and is orthogonal to the triple node, the number of minimal affinizations has no upper bound independent of .As a by-product of our methods, we disprove a conjecture according to which, if is of typeA n,every affinization is isomorphic to a tensor product of representations of Uq( ) which are irreducible under Uq( ) (in an earlier paper, we proved this conjecture whenn=1).Both authors were partially supported by the NSF, DMS-9207701.  相似文献   

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