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1.
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F n (f)}, where F n (x) = F(x) * δ n (x) and {δ n (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x ?s ln m |x| and x r is proved to exist and be equal to r m x ?rs ln m |x| for r, s, m = 2, 3…. 相似文献
2.
Emin Özçag 《Proceedings Mathematical Sciences》1999,109(1):87-94
The distributionF(x
+, −r) Inx+ andF(x
−, −s) corresponding to the functionsx
+
−r lnx+ andx
−
−s respectively are defined by the equations
(1) and
(2) whereH(x) denotes the Heaviside function. In this paper, using the concept of the neutrix limit due to J G van der Corput [1], we evaluate
the non-commutative neutrix product of distributionsF(x
+, −r) lnx+ andF(x
−, −s). The formulae for the neutrix productsF(x
+, −r) lnx
+ ox
−
−s, x+
−r lnx+ ox
−
−s andx
−
−s o F(x+, −r) lnx+ are also given forr, s = 1, 2, ... 相似文献
3.
Adem Kilicman 《Czechoslovak Mathematical Journal》2001,51(3):463-471
Let
,
be ultradistributions in
and let
and
where
is a sequence in
which converges to the Dirac-delta function
. Then the neutrix product
is defined on the space of ultradistributions
as the neutrix limit of the sequence
provided the limit
exist in the sense that
for all in
. We also prove that the neutrix convolution product
exist in
, if and only if the neutrix product
exist in
and the exchange formula
is then satisfied. 相似文献
4.
Truong et al. [7]proved that the weight distribution of a binary quadratic residue code C with length congruent to −1 modulo 8 can be determined by the weight distribution of a certain subcode of C containing only one-eighth of the codewords of C. In this paper, we prove that the same conclusion holds for any binary quadratic residue codes. 相似文献
5.
The non-commutative neutrix convolution product of the functions x
r cos–(x) and x
s cos+(x) is evaluated. Further similar non-commutative neutrix convolution products are evaluated and deduced. 相似文献
6.
《Optimization》2012,61(3-4):397-406
We give an asymptotic result for principal points of univariate distributions, as defined in Flury (1990). Principal points are a generalization of the mean and provide a natural way to approximate a continuous distribution. We show that for a given density $si:f$esi:it is asymptotically optimal to take the quantiles of the density proportional to$si:f$esi:i1/3 as principal points. 相似文献
7.
L. Loura 《Czechoslovak Mathematical Journal》2006,56(2):543-558
In this paper we use a duality method to introduce a new space of generalized distributions. This method is exactly the same
introduced by Schwartz for the distribution theory. Our space of generalized distributions contains all the Schwartz distributions
and all the multipole series of physicists and is, in a certain sense, the smallest space containing all these series.
To The Memory of Laurent Schwartz 相似文献
8.
Emin Özça? ?nci Ege Ha?met Gürçay 《Journal of Mathematical Analysis and Applications》2007,326(1):101-107
The distributions and were defined as the neutrix limit of the sequences and respectively for , see [J.D. Nicholos, B. Fisher, The distribution composition , J. Math. Anal. Appl. 258 (2001) 131-145; B. Fisher, On defining the distribution , Univ. u Novom Sadu Zb. Rad. Prirod. Mat. Fak. Ser. Mat. 15 (1985) 119-129]. We here consider these distributions when r=0. In other words, we define the sth powers of the Heaviside function H(x) in the distributional sense for negative integers. Further compositions are also considered. 相似文献
9.
Enkelejd Hashorva 《Extremes》2009,12(3):239-263
Let (S
1,S
2) = (R cos(Θ), R sin(Θ)) be a bivariate random vector with associated random radius R which has distribution function F being further independent of the random angle Θ. In this paper we investigate the asymptotic behaviour of the conditional
survivor probability when u approaches the upper endpoint of F. On the density function of Θ we impose a certain local asymptotic behaviour at 0, whereas for F we require that it belongs to the Gumbel max-domain of attraction. The main result of this contribution is an asymptotic
expansion of , which is then utilised to construct two estimators for the conditional distribution function . Furthermore, we allow Θ to depend on u.
相似文献
10.
It is shown that when the random vector X in Rn has a mean and when the conditional expectation E(u′X|v′X) = 0 for all vectors u, v Rn which satisfy u′v = 0, then the distribution of X is orthogonally invariant. A version of this characterization is also established when X does not have a mean vector. 相似文献
11.
Schwartz's almost periodic distributions are generalized to the case of Banach space valued distributions , and furthermore for a given arbitrary class A to for φ∈ test functions D(R,C)}. It is shown that this extension process is iteration complete, i.e. . Moreover the T from are characterized in various ways, also tempered distributions with P={X-valued functions of polynomial growth} are shown. Under suitable assumptions , , where for all h>0}, is defined with the corresponding extension of Mh. With an extension of the indefinite integral from to D′(R,X) a distribution analogue to the Bohl-Bohr-Amerio-Kadets theorem on the almost periodicity of bounded indefinite integrals of almost periodic functions is obtained, also for almost automorphic, Levitan almost periodic and recurrent functions, similar for a result of Levitan concerning ergodic indefinite integrals. For many of the above results a new (Δ)-condition is needed, we show that it holds for most of the A needed in applications. Also an application to the study of asymptotic behavior of distribution solutions of neutral integro-differential-difference systems is given. 相似文献
12.
S. G. Dani 《Journal of Theoretical Probability》1991,4(3):625-629
We give here a characterization of the Cauchy-type distributions onG/P, whereG is a semisimple Lie group andP is a parabolic subgroup. 相似文献
13.
C. Hipp 《Insurance: Mathematics and Economics》1985,4(4):227-232
New error bounds are derived for the approximation of aggregate claims distributions by compound Poisson distributions. These approximations can be recommended in most cases in which the normal approximation fails. 相似文献
14.
Hong Zang Tonghua Zhang Maoan Han 《Journal of Mathematical Analysis and Applications》2006,316(2):679-696
This paper concerns with the number of limit cycles for a cubic Hamiltonian system under cubic perturbation. The fact that there exist 9-11 limit cycles is proved. The different distributions of limit cycles are given by using methods of bifurcation theory and qualitative analysis, among which two distributions of eleven limit cycles are new. 相似文献
15.
We extend our work on the optimal mapping of distributions in three directions: (a) we consider any set-valued mapping, not just diffeomorphisms; (b) we distinguish between weak and strong optimality, and identify strong optimality with cyclic monotonicity; and (c) we prove that, under some restrictions, a weakly optimal mapping has the subgradient property. 相似文献
16.
Truc T. Nguyen Allan R. Sampson 《Annals of the Institute of Statistical Mathematics》1991,43(4):793-801
Several characterizations of multivariate stable distributions together with a characterization of multivariate normal distributions and multivariate stable distributions with Cauchy marginals are given. These are related to some standard characterizations of marcinkiewicz.Research supported, in part, by the Air Force Office of Scientific Research under Contract AFOSR 84-0113. Reproduction in whole or part is permitted for any purpose of the United States Government. 相似文献
17.
Ronald R. Yager 《Fuzzy Sets and Systems》1986,20(3):317-324
We suggest a modification of the definition of certainty associated with a possibility distribution so that we are assured that the certainty measure is always less than or equal to the possibility measure even in the face of subnormal distributions. We note that when the possibility distribution is normal this new definition reduces to the original definition of certainty. We use this new measure along with the definition of possibility measure to obtain measures of belief and plausibility in the fact of fuzzy information in the Mathematical Theory of Evidence. 相似文献
18.
R. M. Korwar 《Annals of the Institute of Statistical Mathematics》1989,41(2):305-321
This paper deals with a new system of discrete distributions. It also gives several characterizations of the Waring (and hence the Yule) distribution (and its truncated versions), the super-Poisson, the discrete uniform and other discrete distributions by using this system and other such systems existing in the literature, and linear regression. Continuous analogues of the above results are also briefly discussed. 相似文献
19.
On the jump behavior of distributions and logarithmic averages 总被引:1,自引:0,他引:1
Jasson Vindas Ricardo Estrada 《Journal of Mathematical Analysis and Applications》2008,347(2):597-606
The jump behavior and symmetric jump behavior of distributions are studied. We give several formulas for the jump of distributions in terms of logarithmic averages, this is done in terms of Cesàro-logarithmic means of decompositions of the Fourier transform and in terms of logarithmic radial and angular local asymptotic behaviors of harmonic conjugate functions. Application to Fourier series are analyzed. In particular, we give formulas for jumps of periodic distributions in terms of Cesàro–Riesz logarithmic means and Abel–Poisson logarithmic means of conjugate Fourier series. 相似文献
20.
S. Ya. Serovaiskii 《Mathematical Notes》1999,65(6):705-717
With the help of an iterative process, we define a fairly broad class of arithmetical distributions on which continuous operations
of addition, multiplication, and differentiation are defined. The multiplication of arithmetical distributions that we introduce
is made consistent with the known definitions of the product of distributions. The results obtained can be used to justify
the passage to the limit in the study of nonlinear problems of mathematical physics. Formalizing our approach, we describe
a construction of an extension of binary relations, which is called sequential extension, from a dense subset to the whole
topological space. These results are extended to operations of the first order. We show that the sequential extension of differentiation
from the set of infinitely differentiable functions to the set of distributions coincides up to isomorphism with the generalized
differentiation of distributions.
Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 836–853, June, 1999. 相似文献