共查询到20条相似文献,搜索用时 46 毫秒
1.
We construct an asymptotic formula for a sum function for
a
(), where
a
() is the sum of the ath powers of the norms of divisors of the Gaussian integer on an arithmetic progression 0 (mod ) and in a narrow sector 1 arg < 2. For this purpose, we use a representation of
a
(n) in the form of a series in the Ramanujan sums. 相似文献
2.
Toru Nakahara 《Monatshefte für Mathematik》1982,94(2):125-132
In this note we shall prove that there exist infinitely many cyclic biquadratic fieldsK whose integral bases are neither {1, , 2, } nor {1, , , 3) for any numbers , inK. Next, we shall construct infinitely many cyclic biquadratic fieldsK which have the index 1, but still have not the integral basis {1, , 2, 3) for every inK. Finally we shall give a class of biquadratic fields for a problem of Hasse concerning an integral basis. 相似文献
3.
LetN(x, n, ) denote the number of integer lattice points inside then-dimensional sphere of radius (an)1/2 with center at x. This numberN(x,n, ) is studied for fixed,n , andx varying. The average value (asx varies) ofN(x,n, ) is just the volume of the sphere, which is roughly of the form (2 e, )
n/2. it is shown that the maximal and minimal values ofN (x,n, ) differ from the everage by factors exponential inn, which is in contrast to the usual lattice point problems in bounded dimensions. This lattice point problem arose separately in universal quantization and in low density subset sum problems. 相似文献
4.
W. C. Stephen Suen 《Combinatorica》1993,13(2):209-229
We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let
i
be thei
th vertex encountered by DFS andL(i, m, n) be the height of
i
in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree. 相似文献
5.
Colin Mcdiarmid 《Mathematical Programming》1990,46(1-3):299-320
We investigate the decrease in potential at an iteration of Karmarkar's projective method for linear programming. For a fixed step length parameter (so that we must have 0 < 1) the best possible guarantee
n
() inn dimensional space is essentially ln 2 0.69; and to achieve this we must take about 1. Indeed we show the precise result that
n
() equals ln(1 +)-ln(1 –/(n – 1)) forn sufficiently large. If we choose an optimal step length at each iteration then this guarantee increases only to about
* 0.72. We also shed some light on the remarkable empirical observation that the number of iterations required seems scarcely to grow with the size of the problem. 相似文献
6.
V. A. Slousch 《Journal of Mathematical Sciences》2003,115(2):2272-2278
Let A be a self-adjoint elliptic second-order differential operator, let (, ) be an inner gap in the spectrum of A, and let B(t) = A + tW
*
W, where W is a differential operator of higher order. Conditions are obtained under which the spectrum of the operator B(t) in the gap (, ) is either discrete, or does not accumulate to the right-hand boundary of the spectral gap, or is finite. The quantity N(, A, W, ), (, ), > 0 (the number of eigenvalues of the operator B(t) passing the point (, ) as t increases from 0 to ) is considered. Estimates of N(, A, W, ) are obtained. For the perturbation W
*
W of a special form, the asymptotics of N(, A, W, ) as + is given. Bibliography: 5 titles. 相似文献
7.
A. B. Aleksandrov 《Journal of Mathematical Sciences》1993,63(2):115-129
Let be an inner function, let C, ¦¦=1. Then the harmonic function [(+)]/(–)] is the Poisson integral of a singular measure
D. N. Clark's known theorem enables us to identify in a natural manner the space H2 H2 with the space L2
(
).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 7–33, 1989. 相似文献
8.
Summary The aim of this paper is to generalize the well-known Eulerian numbers, defined by the recursion relationE(n, k) = (k + 1)E(n – 1, k) + (n – k)E(n – 1, k – 1), to the case thatn is replaced by . It is shown that these Eulerian functionsE(, k), which can also be defined in terms of a generating function, can be represented as a certain sum, as a determinant, or as a fractional Weyl integral. TheE(, k) satisfy recursion formulae, they are monotone ink and, as functions of , are arbitrarily often differentiable. Further, connections with the fractional Stirling numbers of second kind, theS(, k), > 0, introduced by the authors (1989), are discussed. Finally, a certain counterpart of the famous Worpitzky formula is given; it is essentially an approximation ofx
in terms of a sum involving theE(, k) and a hypergeometric function.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth. 相似文献
9.
Janet Heine Barnett 《Periodica Mathematica Hungarica》1995,30(3):171-176
It is consistent that 1(1,(:n))2 holds in any random extension for n finite and countable. 相似文献
10.
Kevin E. Osondu 《Semigroup Forum》1979,17(1):139-152
Let S be a cancellative semigroup which is a semilattice of left reversible semigroups S, . This article studies the relationship between the group of quotients G of S and the groups of quotients G of S, . It is shown that G is the maximum group homomorphic image of an inverse semigroup which is a semilattice of groups G (up to isomorphism).The technique used here which involves the use of Ore's quotients also applies to the study of the maximum group homomorphic image of a semigroup which is a semilattice of inverse semigroups. 相似文献
11.
V. L. Girko 《Journal of Mathematical Sciences》1993,66(4):2442-2447
For linear forms of regularized solutions (x, c)=Re c' · Re[I + i)+A'An
–1]–1 A'nb of systems of equations Ax=b, where A is an n×m matrix, x, c, b are vectors, and n is a sequence of constants, we propose the estimator
, where
is any measurable solution of the equation ()Re[1+1a(())]2+ (1–2)(1+1(gq()))=, a(y)=n–1 Sp[Iy+–1Zs'Zs+ iI]–1,
, i=nn
2n
–1sn
–1, n=mIn
2n
–1sn
–1, Xi are independent observations on the matrix A. Under certain conditions, it is proved that G8 is a consistent estimator for n and 0.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 111–119, 1988. 相似文献
12.
Dr. J. D. Stegeman 《Monatshefte für Mathematik》1976,82(4):337-340
It is proved that closed subgroups of
n
are Wiener-Ditkin sets for the Beurling algebrasL
1
(
n
), <1. 相似文献
13.
For a cardinal , we say that a subset B of a space X is C
-compact in X if for every continuous function
is a compact subset of
. If B is a C-compact subset of a space X, then (B, X) denotes the degree of C
-compactness of B in X. A space X is called -pseudocompact if X is C
-compact into itself. For each cardinal , we give an example of an -pseudocompact space X such that X × X is not pseudocompact: this answers a question posed by T. Retta in Some cardinal generalizations of pseudocompactness Czechoslovak Math. J. 43 (1993), 385–390. The boundedness of the product of two bounded subsets is studied in some particular cases. A version of the classical Glicksberg's Theorem on the pseudocompactness of the product of two spaces is given in the context of boundedness. This theorem is applied to several particular cases. 相似文献
14.
Littlewood-paley operators on the generalized Lipschitz spaces 总被引:3,自引:0,他引:3
Littlewood-Paley operators defined on a new kind of generalized Lipschitz spaces
0
,p
are studied. It is proved that the image of a function under the action of these operators is either equal to infinity almost everywhere or is in
0
,p
, where –n<<1 and 1<p<. 相似文献
15.
For the general fixed effects linear model:Y=X+, N(0,V),V0, we obtain the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionS in the class of all estimators under the loss function (d -S)D(d -S), whereD0 is known. For the general random effects linear model:
=XV
11
X+XV
12+V
21
X+V
220, we also get the necessary and sufficient conditions forLY+a to be admissible for a linear estimable functionS+Q in the class of all estimators under the loss function (d -S -Q)D(d -S -Q), whereD0 is known. 相似文献
16.
V. A. Derkach 《Mathematical Notes》1998,63(4):449-459
The Laguerre-Sonin polynomialsL
n
()
are orthogonal in linear spaces with indefinite inner product if<–1. We construct the completion () of this space and describe self-adjoint extensions of the Laguerre operatorl(y)=xy+(1+–x)y,<–1, in the space (). In particular, we write out the self-adjoint extension of the Laguerre operator whose eigenfunctions coincide with the Laguerre-Sonin polynomials and form an orthogonal basis in ().Translated fromMatematicheskie Zametki, Vol. 63, No. 4, pp. 509–521, April, 1998.This research was partially supported by the INTAS foundation under grant No. 93-02449. 相似文献
17.
Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation (-1)n(talphay(n))(n)+q(t)y = 0 (*) are established. In these criteria, equation (*) is viewed as a perturbation of the conditionally oscillatory equation (-1)n(talphay(n))(n) - µ,t2n-y = 0, where
n, is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed. 相似文献
18.
We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3. 相似文献
19.
The critical exponent of degenerate parabolic systems 总被引:1,自引:0,他引:1
Yuan-Wei Qi H. A. Levine 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1993,44(2):249-265
The Cauchy problemu
t=u
+v
p
,v
t
=v
+u
q
is studied, wherex R
N
, 0 <t < and ,,p andq, are positive exponents. It is proved that ifp,q 1 and 1 <pq < 1 + 2 max(p + ,q + )/n then every nontrivial non-negative solution is not global in time; whereaspq > 1 + 2 max(p + , q + )/n then there exist both positive global solutions and non-global solutions. In addition, the decaying in time of solutions tou
t,=u
inR
n
× (0, ), an equation which occurs naturally in our study of above systems, is studied and solutions with the fastest decaying in time are constructed. 相似文献
20.
Manabu Iwasa 《Annals of the Institute of Statistical Mathematics》1991,43(4):657-665
This paper discusses -admissiblility and d-admissiblity which are important concepts in studying the performance of statistical tests for composite hypotheses. A sufficient condition for -admissibility is presented. When =1/m, the Nomakuchi-Sakata test, which is uniformly more powerful than the likelihood ratio test for hypotheses min (1, 1) = 0 versus min (1, 1) > 0, is generalized for a class of distributions in an exponential family, and its unbiasedness and -admissibility are shown. Finally, the case of 1/m is discussed in brief. 相似文献