共查询到20条相似文献,搜索用时 15 毫秒
1.
Robert G. Payton 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,44(6):876-888
A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress
free crack. The resulting anti-plane wave motion problem has been solved in the form of a finite series representing the incident
and reflected pulses plus an integral representing the diffraction pulse. The series part of the solution has been previously
treated. In the present investigation the diffraction integral is integrated when λ (which measures the anisotropy of the
solid) is an odd integer number. The diffraction integral is also integrated when λ is half an odd integer, for the special
case in which the source lies in the plane of the crack and parallel to the crack edge. The displacement jump across the circular
diffraction wave front is given for unrestricted (positive) values of λ. 相似文献
2.
Fractional dimensions in semifields of odd order 总被引:1,自引:0,他引:1
A finite semifield D is considered a fractional dimensional semifield if it contains a subsemifield E such that λ := log|E||D| is not an integer. We develop spread-theoretic tools to determine when finite planes admit coordinatization by fractional
semifields, and to find such semifields when they exist. We use our results to show that such semifields exist for prime powers
3
n
whenever n is an odd integer divisible by 5 or 7. 相似文献
3.
S. Li 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2001,37(8):101-134
This paper is concerned with the diffraction problem in a transversely isotropic piezoelectric medium by a half-plane. The half-plane obstacle considered here is a semi-infinite slit, or a crack; both its surfaces are traction free and electric absorbent screens. In a generalized sense, we are dealing with the Sommerfeld problem in a piezoelectric medium.¶The coupled diffraction fields between acoustic wave and electric wave are excited by both incident acoustic wave as well as incident electric wave; and the sound soft and electric "blackness" conditions on the screens are characterized by a system of simultaneous Wiener-Hopf equations. Closed form solutions are sought by employing special techniques. Some interesting results have been obtained, such as mode conversions between acoustic wave and electric wave, novel diffraction patterns in the scattering fields, and the effect of electroacoustic head wave, as well as of surface wave-Bleustein-Gulyaev wave.¶Unlike the classical Sommerfeld problem, in which the only concern is the scattering field of electric wave, the strength of material, e.g. material toughness, is another concern here. From this perspective, relevant dynamic field intensity factors at the crack tip are derived explicitly. 相似文献
4.
Raffaele Mosca 《Graphs and Combinatorics》2002,18(2):367-379
Moving from a well known result of Hammer, Hansen, and Simeone, we introduce a new graph invariant, say λ(G) referring to any graph G. It is a non-negative integer which is non-zero whenever G contains particular induced odd cycles or, equivalently, admits a particular minimum clique-partition. We show that λ(G) can be efficiently evaluated and that its determination allows one to reduce the hard problem of computing a minimum clique-cover
of a graph to an identical problem of smaller size and special structure. Furthermore, one has α(G)≤θ(G)−λ(G), where α(G) and θ(G) respectively denote the cardinality of a maximum stable set of G and of a minimum clique-partition of G.
Received: April 12, 1999 Final version received: September 15, 2000 相似文献
5.
We provide some more explicit formulae to facilitate the computation of Ohtsuki’s rational invariants λ
n
of integral homology 3-spheres extracted from Reshetikhin-TuraevSU(2) quantum invariants. Several interesting consequences will follow from our computation of λ2. One of them says that λ2 is always an integer divisible by 3. It seems interesting to compare this result with the fact shown by Murakami that λ1 is 6 times the Casson invariant. Other consequences include some general criteria for distinguishing homology 3-spheres obtained
from surgery on knots by using the Jones polynomial.
The first author is supported in part by NSF and the second author is supported by an NSF Postdoctoral Fellowship. 相似文献
6.
Peter Hall 《Annals of the Institute of Statistical Mathematics》1980,32(1):351-362
The kernel method of density estimation is not so attractive when the density has its support confined to (0, ∞), particularly
when the density is unsmooth at the origin. In this situation the method of orthogonal series is competitive. We consider
three essentially different orthogonal series—those based on the even and odd Hermite functions, respectively, and that based
on Laguerre functions—and compare them from the point of view of mean integrated square error. 相似文献
7.
Åke Pleijel 《Arkiv f?r Matematik》1969,7(6):543-550
LetL be a formally selfadjoint differential operator andp a real-valued function, both ona≤x<∞. The deficiency indices are the numbers of solutions ofLu=λpu for Im λ>0 and for Im λ<0 which have a certain regularity atx=∞. (A) Ifp(x)≥0 this regularity means that the integral ofp(x)│u│2 converges at infinity. (B) Ifp changes its sign for arbitrarily large values ofx butL has a positive definite Dirichlet integral it is natural to relate the regularity to this integral. Weyl’s classical study
of the deficiency indices is reviewed for (A) with the help of elementary theory of quadratic forms. Individual bounds are
found for the deficiency indices also whenL is of odd order. It is then indicated how the method carriers over to (B). 相似文献
8.
Soliton solutions are found for nonlinear integro-differential equations with a type λ/(τ-τ′) kernel used to describe particle
tunneling and magnetic and superconducting vortices in a medium with nonlocal interaction. The Fourier transform method is
applied to derive asymptotic formulas for even and odd localized solutions. Analytical solutions are found for particular
parameter values. A complete pattern is constructed for the behavior of soliton solutions in an arbitrary range of the interaction
parameter λ by means of numerical calculations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 114, No. 3, pp. 366–379, March, 1998. 相似文献
9.
A mathematical program with a rational objective function may have irrational algebraic solutions even when the data are integral.
We suggest that for such problems the optimal solution will be represented as follows: If λ* denotes the optimal value there
will be given an intervalI and a polynomialP(λ) such thatI contains λ* and λ* is the unique root ofP(λ) inI. It is shown that with this representation the solutions to convex quadratic fractional programs and ratio games can be obtained
in polynomial time. 相似文献
10.
For a smooth irreducible complete algebraic curveC the “gaps” are the integersn such that every linear series of degreen has at least a base point. The Lüroth semigroup SC of a curveC is the subsemigroup ofN whose elements are not gaps. In this paper we deal with irreducible smooth curves of type (a, b) on a smooth quadricQ. The main result is an algorithm by which we can say if some integer λ∈N is a gap or is in SC. In the general case there are integers λ which are undecidable. For curves such as complete intersection, arithmetically
Cohen-Macaulay or Buchsbaum, we are able to describe explicitly “intervals” of gaps and “intervals” of integers which belong
to SC. For particular cases we can completely determine SC, by giving just the type of the curve (in particular the degree and the genus).
Work done with financial support of M.U.R.S.T. while the authors were members of G.N.S.A.G.A. of C.N.R. 相似文献
11.
In the paper [N. Gorenflo, A new explicit solution method for the diffraction through a slit, ZAMP 53 (2002), 877–886] the problem of diffraction through a slit in a screen has been considered for arbitrary Dirichlet data,
prescribed in the slit, and under the assumption that the normal derivative of the diffracted wave vanishes on the screen
itself. For this problem certain functions with the following properties have been constructed: Each function f is defined on the whole of R and on the screen the values f(x), |x| ≥ 1, are the Dirichlet data of the diffracted wave which takes on the Dirichlet data f(x), |x| ≤ 1, in the slit. The problem of expanding arbitrary Dirichlet data, prescribed in the slit, into a series of functions
of the considered form has been addressed, but not solved in a satisfactory way (only the application of the Gram-Schmidt
orthogonalization process to such functions has been proposed). In this continuation of the aforementioned paper we choose
the remaining degrees of freedom in the earlier given representations of such functions in a certain way. The resulting concrete
functions can be expressed by Hankel functions and explicitly given coefficients. We suggest the expansion of arbitrary Dirichlet
data, prescribed in the slit, into a series of these functions, here the expansion coefficients can be expressed explicitly
by certain moments of the expanded data. Using this expansion, the diffracted wave can be expressed in an explicit form. In
the future it should be examined whether similar techniques as those which are presented in the present paper can be used
to solve other canonical diffraction problems, inclusively vectorial diffraction problems. 相似文献
12.
Pirro Oppezzi 《Annali di Matematica Pura ed Applicata》1978,118(1):143-161
Summary I study an elliptic system, in the sense of Agmon-Douglis-Nirenberg, of partial differential equations with variable coefficients.
The matrix operator is of type P(D) + + λR(x, D) where λ εC, P(D) has constant coefficients, is elliptic, and his determinant admits a special elementary solution. On the coefficients
in R(x, D), sufficiently smooth, a certain behaviour at the infinity is assumed. For suitable known vectors f, the problem
P(D)u - λR(x, D)u=f is shown to be equivalent to a system of singular integral equations in special subspaces of [Wl,p]N, if N is the rank of the system, as is studied in [5]. This is possible when the unknown vector u belongs to a class that,
generally, is stricter than the one of existence and uniquencess for P(D) [4]. Then results on the solvability of the system
follow when λ is such that P(D+λR(x, D) is elliptic.
Entrata in Redazione l'8 giugno 1977.
Lavoro svolto nell'ambito del ? Laboratorio per la matematica applicata ? del C.N.R. presso l'Università di Genova. 相似文献
Entrata in Redazione l'8 giugno 1977.
Lavoro svolto nell'ambito del ? Laboratorio per la matematica applicata ? del C.N.R. presso l'Università di Genova. 相似文献
13.
A graph is called integral if all eigenvalues of its adjacency matrix consist entirely of integers. Recently, Csikvári proved the existence of integral trees of any even diameter. In the odd case, integral trees have been constructed with diameter at most 7. In this article, we show that for every odd integer n>1, there are infinitely many integral trees of diameter n. © 2011 Wiley Periodicals, Inc. J Graph Theory 相似文献
14.
Summary The time-dependent meandering of thin ocean jets in reduced gravity models has recently been shown to obey a natural coordinate
version of the standard modified Korteweg-deVries (mKdV) equation. The detachment of eddies from such a jet begins when different
segments of the jet path come into contact, causing the initially simply connected jet to “pinch” together. It is shown that
this pinching process is effected primarily by breather solutions to the mKdV equation. For a given initial condition the
solution will evolve into a dispersive wave train plus a finite number of breathers, the connectivity of which is determined
by a steepness parameter λ. Using the scattering transform for the mKdV equation the value(s) of λ can be calculated in a
straightforward manner, and the detachment (or lack thereof) of meanders can be forecast to a high degree of confidence by
calculating λ. Examples with simple meander disturbances show a remarkable degree of stability and resistance to detachment. 相似文献
15.
Arman Melkumyan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,58(2):330-349
The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium
is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation”
[15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means
of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion
between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield
structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details.
The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly.
Numerical analysis is presented. 相似文献
16.
Arman Melkumyan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,59(4):330-349
The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium
is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation”
[15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means
of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion
between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield
structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details.
The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly.
Numerical analysis is presented. 相似文献
17.
Carlo Magagna 《Monatshefte für Mathematik》2008,23(2):59-81
For a positive integer N, we define the N-rank of a non singular integer d × d matrix A to be the maximum integer r such that there exists a minor of order r whose determinant is not divisible by N. Given a positive integer r, we study the growth of the minimum integer k, such that A
k
− I has N-rank at most r, as a function of N. We show that this integer k goes to infinity faster than log N if and only if for every eigenvalue λ which is not a root of unity, the sum of the dimensions of the eigenspaces relative
to eigenvalues which are multiplicatively dependent with λ and are not roots of unity, plus the dimensions of the eigenspaces
relative to eigenvalues which are roots of unity, does not exceed d − r − 1. This result will be applied to recover a recent theorem of Luca and Shparlinski [6] which states that the group of rational
points of an ordinary elliptic curve E over a finite field with q
n
elements is almost cyclic, in a sense to be defined, when n goes to infinity. We will also extend this result to the product of two elliptic curves over a finite field and show that
the orders of the groups of
\Bbb Fqn-{\Bbb F}_{q^n}-
rational points of two non isogenous elliptic curves are almost coprime when n approaches infinity. 相似文献
18.
In the paper [N. Gorenflo, A new explicit solution method for the diffraction through a slit, ZAMP 53 (2002), 877–886] the problem of diffraction through a slit in a screen has been considered for arbitrary Dirichlet data,
prescribed in the slit, and under the assumption that the normal derivative of the diffracted wave vanishes on the screen
itself. For this problem certain functions with the following properties have been constructed: Each function f is defined on the whole of R and on the screen the values f(x), |x| ≥ 1, are the Dirichlet data of the diffracted wave which takes on the Dirichlet data f(x), |x| ≤ 1, in the slit. The problem of expanding arbitrary Dirichlet data, prescribed in the slit, into a series of functions
of the considered form has been addressed, but not solved in a satisfactory way (only the application of the Gram-Schmidt
orthogonalization process to such functions has been proposed). In this continuation of the aforementioned paper we choose
the remaining degrees of freedom in the earlier given representations of such functions in a certain way. The resulting concrete
functions can be expressed by Hankel functions and explicitly given coefficients. We suggest the expansion of arbitrary Dirichlet
data, prescribed in the slit, into a series of these functions, here the expansion coefficients can be expressed explicitly
by certain moments of the expanded data. Using this expansion, the diffracted wave can be expressed in an explicit form. In
the future it should be examined whether similar techniques as those which are presented in the present paper can be used
to solve other canonical diffraction problems, inclusively vectorial diffraction problems. 相似文献
19.
Mordechai Lewin 《Israel Journal of Mathematics》1974,18(4):345-347
It is shown that a graphG has all matchings of equal size if and only if for every matching setλ inG, G\V(λ) does not contain a maximal open path of odd length greater than one, which is not contained in a cycle. (V(λ) denotes the set of vertices incident with some edge ofλ.) Subsequently edge-coverings of graphs are discussed. A characterization is supplied for graphs all whose minimal covers
have equal size. 相似文献
20.
Palle E. T. Jorgensen Keri A. Kornelson Karen L. Shuman 《Journal of Fourier Analysis and Applications》2011,17(3):431-456
We study the harmonic analysis of Bernoulli measures μ
λ
, a one-parameter family of compactly supported Borel probability measures on the real line. The parameter λ is a fixed number in the open interval (0,1). The measures μ
λ
may be understood in any one of the following three equivalent ways: as infinite convolution measures of a two-point probability
distribution; as the distribution of a random power series; or as an iterated function system (IFS) equilibrium measure determined
by the two transformations λ(x±1). For a given λ, we consider the harmonic analysis in the sense of Fourier series in the Hilbert space L
2(μ
λ
). For L
2(μ
λ
) to have infinite families of orthogonal complex exponential functions e
2πis(⋅), it is known that λ must be a rational number of the form
\fracm2n\frac{m}{2n}, where m is odd. We show that
L2(m\frac12n)L^{2}(\mu_{\frac{1}{2n}}) has a variety of Fourier bases; i.e. orthonormal bases of exponential functions. For some other rational values of λ, we exhibit maximal Fourier families that are not orthonormal bases. 相似文献