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71.
72.
Suppose that \(G =\mathbb{S}^1\) acts freely on a finitistic space X whose (mod p) cohomology ring is isomorphic to that of a lens space \(L^{2m-1}(p;q_1,\ldots,q_m)\) or \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\). The mod p index of the action is defined to be the largest integer n such that α n ?≠?0, where \(\alpha \,\epsilon\, H^2(X/G;\mathbb{Z}_p)\) is the nonzero characteristic class of the \(\mathbb{S}^1\)-bundle \(\mathbb{S}^1\hookrightarrow X\rightarrow X/G\). We show that the mod p index of a free action of G on \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\) is p???1, when it is defined. Using this, we obtain a Borsuk–Ulam type theorem for a free G-action on \(\mathbb{S}^1\times \mathbb{C}P^{m-1}\). It is note worthy that the mod p index for free G-actions on the cohomology lens space is not defined. 相似文献
73.
An n-dimensional pseudo-differential operator (p.d.o.) involving the n-dimensional Hankel transformation is defined. The symbol class H
m
is introduced. It is shown that p.d.o.’s associated with symbols belonging to this class are continuous linear mappings of
the n-dimensional Zemanian space Hm(In)H_\mu(I^n) into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o.
satisfies a certain L
1-norm inequality. 相似文献
74.
Complex dynamical invariants are searched out for two-dimensional complex potentials using rationalization method within the framework of an extended complex phase space characterized by x?=?x 1?+?i p 3,?y?=?x 2?+?i p 4, ?p x ?=?p 1?+?i x 3, ?p y ?=?p 2?+?i x 4. It is found that the cubic oscillator and shifted harmonic oscillator admit quadratic complex invariants. The obtained invariants may be useful for studying non-Hermitian Hamiltonian systems. 相似文献
75.
76.
D. J. SINGH A. KUMAR S. N. TIWARI 《International Journal of Computational Fluid Dynamics》2013,27(3):177-196
A numerical study is conducted to simulate the effects of extraneous shock impingement on a blunt body in viscous hypersonic flow. The interaction of extraneous shock with the leading-edge shock results in a very complex flow field that contains local regions of high pressure and intense heating. The heating and pressure can be orders of magnitude higher than the peak values in the absence of shock impingement. The flow field is calculated by solving thin-layer Navier-Stokes equations with a finite-volume flux splitting technique developed by van Leer. For a zero or small sweep of the body, a type IV interaction occurs, which produces a lambda shock structure with a supersonic jet embedded in the otherwise subsonic flow; for a moderate sweep of about 25°, a type V interaction occurs in which a subsonic shear layer sandwiched in supersonic flow is produced with a transmitted shock. In the present study, both type IV and type V interactions are investigated. Results of the present numerical investigation are compared with available experimental results. For the present conditions, the peak pressure is 2.2 times the unimpinged stagnation point pressure and the peak heating is 3 times the unimpinged stagnation point heating. The flow for a type IV interaction is found to be unsteady. 相似文献
77.
In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian amplitude equation using (G??/G)-expansion method, where G?=?G(??) satisfies a second-order linear ordinary differential equation (ODE). The travelling wave solutions expressed by hyperbolic, trigonometric and the rational functions are obtained. 相似文献
78.
PRAMOD KUMAR YADAWA 《Pramana》2011,76(4):613-619
The ultrasonic properties of the hexagonal closed packed structured Ni3Mo, Ni3Nb and Ni3Ta compounds were studied at room temperature for their characterization. For the investigations of ultrasonic properties,
the second-order elastic constants using Lennard–Jones potential were computed. The velocities V
1 and V
2 have minima and maxima respectively at 45° with the unique axis of the crystal, while V
3 increases with respect to angle with the unique axis of the crystal. The inconsistent behaviour of angle-dependent velocities
is associated with the action of second-order elastic constants. Debye average sound velocities of these compounds increase
with the angle and has maximum at 55° with the unique axis at room temperature. Hence, when a sound wave travels at 55° with
the unique axis of these materials, the average sound velocity is found to be maximum. The results achieved are discussed
and compared with the available experimental and theoretical results. 相似文献
79.
A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silicon tetrafluoride (SiF4) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums and mean excitation energies for the molecule. A pseudo-DOSD for SiF4 is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interaction of SiF4 with itself and with 43 other species and the triple-dipole dispersion energy coefficient C9 for (SiF4)3. 相似文献
80.
In this paper, we discuss a one parameter family of complex Born–Infeld solitons arising from a one parameter family of minimal surfaces. The process enables us to generate a new solution of the B–I equation from a given complex solution of a special type (which are abundant). We illustrate this with many examples. We find that the action or the energy of this family of solitons remains invariant in this family and find that the well-known Lorentz symmetry of the B–I equations is responsible for it. 相似文献