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1.
He-Jun Sun 《Ukrainian Mathematical Journal》2011,63(7):1154-1164
We investigate the Dirichlet weighted eigenvalue problem for a fourth-order elliptic operator with variable coefficients in
a bounded domain in
\mathbbRn {\mathbb{R}^n} . We establish a sharp inequality for its eigenvalues. It yields an estimate for the upper bound of the (k + 1)th eigenvalue in terms of the first k eigenvalues. Moreover, we also obtain estimates for some special cases of this problem. In particular, our results generalize
the Wang–Xia inequality (J. Funct. Anal., 245, No. 1, 334–352 (2007)) for the clamped-plate problem to a fourth-order elliptic operator with variable coefficients. 相似文献
2.
M. Yu. Shvaiko 《Journal of Mathematical Sciences》2011,176(4):548-560
We have proposed a modification of the methods for solving the system of integral equations [M. Ya. Leonov and N. Yu. Shvaiko,
“Complex plane deformation,” Dokl. Akad. Nauk SSSR,
159, No. 2, 1007–1010 (1964); N. Yu. Shvaiko, “On the theory of slip with smooth and singular loading surfaces,” Mat. Metody Fiz.-Mekh. Polya,
48, No. 3, 129–137 (2005)]. These equations describe the development of plane plastic deformation for simple and complex loading
processes. A characteristic feature of these equations lies in the presence of unknown functions both under the integral sign
and in the integration limits. We have written analytical solutions for monotone deformation and in a small neighborhood of
an angular point of the loading trajectory. For arbitrary piecewise smooth trajectories, we have reduced this problem to the
Cauchy problem for a first-order differential equation with known initial conditions. The results obtained simplify significantly
the construction of constitutive equations [(s)\dot]mn ~ [(e)\dot]mn {\dot{\sigma }_{mn}} \sim {\dot{\varepsilon }_{mn}} and their use in applied problems of the theory of plasticity as compared with [N. Yu. Shvaiko, “On the theory of slip with smooth and singular loading surfaces,” Mat. Metody Fiz.-Mekh. Polya,
48, No. 3, 129–137 (2005); N. Yu. Shvaiko, Complex Loading and Problems of Stability [in Russian], Izd. DGU, Dnepropetrovsk (1989)]. 相似文献
3.
Shaul K. Bar-lev Benzion Boukai 《Annals of the Institute of Statistical Mathematics》1986,38(1):277-283
Summary The null and nonnull distributions of the likelihood ratio statistics for testing the homogeneity ofk given populations, each associated with a nonregular density depending on two truncation parameters, are investigated. This
generalizes to the two-parameter case the work of Hogg (1956,Ann. Math. Statist.,27, 529–532), Barr (1966,J. Amer. Statist. Assoc.,61, 856–864) and Khatri and Jaiswal (1969,Aust. J. Statist.,11, 79–84; 1969, 1971,Ann. Inst. Statist. Math.,21, 127–136;23, 199–210). 相似文献
4.
W. R. Madych 《Journal d'Analyse Mathématique》2001,84(1):207-229
We consider certain aspects of the theory of interpolation via entire functions of exponential type, which include sampling
node sequences χ which can be highly irregular and data sequences {y(x)}xn∈χ which are not necessarily bounded. Under appropriate conditions, we show that there is an entire function of a suitable
exponential type which uniquely interpolates the data and indicate the validity of certain summabilty methods for the corresponding
Lagrange type interpolation series. Some of our results significantly extend the work of Schoenberg,Cardinal interpolation and spline functions VII: The behavior of cardinal spline interpolation as their degree tends to infinity, J. Analyse Math.27 (1974), 205–229. 相似文献
5.
This paper studies non-convex programming problems. It is known that, in statistical inference, many constrained estimation problems may be expressed as convex programming problems. However, in many practical problems, the objective functions are not convex. In this paper, we give a definition of a semi-convex objective function and discuss the corresponding non-convex programming problems. A two-step iterative algorithm called the alternating iterative method is proposed for finding solutions for such problems. The method is illustrated by three examples in constrained estimation problems given in Sasabuchi et al. (Biometrika, 72, 465472 (1983)), Shi N. Z. (J. Multivariate Anal., 50, 282-293 (1994)) and El Barmi H. and Dykstra R. (Ann. Statist., 26, 1878 1893 (1998)). 相似文献
6.
We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator
to a general quasilinear operator and remove a strong ellipticity assumption in Philippin (Maximum principles and eigenvalue
problems in partial differential equations (Knoxville, TN, 1987), Longman Sci. Tech., Pitman Res. Notes Math. Ser., Harlow,
175, pp. 34–48, 1988) and a growth assumption in Garofalo and Lewis (A symmetry result related to some overdetermined boundary
value problems, Am. J. Math. 111, 9–33, 1989) on the diffusion coefficient A, as well as a starshapedness assumption on Ω in Fragalà et al. (Overdetermined boundary value problems with possibly degenerate
ellipticity: a geometric approach. Math. Zeitschr. 254, 117–132, 2006). 相似文献
7.
A.S. Lewis 《Mathematical Programming》2003,97(1-2):155-176
Optimization problems involving the eigenvalues of symmetric and nonsymmetric matrices present a fascinating mathematical
challenge. Such problems arise often in theory and practice, particularly in engineering design, and are amenable to a rich
blend of classical mathematical techniques and contemporary optimization theory. This essay presents a personal choice of
some central mathematical ideas, outlined for the broad optimization community. I discuss the convex analysis of spectral
functions and invariant matrix norms, touching briefly on semidefinite representability, and then outlining two broader algebraic
viewpoints based on hyperbolic polynomials and Lie algebra. Analogous nonconvex notions lead into eigenvalue perturbation
theory. The last third of the article concerns stability, for polynomials, matrices, and associated dynamical systems, ending
with a section on robustness. The powerful and elegant language of nonsmooth analysis appears throughout, as a unifying narrative
thread.
Received: December 4, 2002 / Accepted: April 22, 2003
Published online: May 28, 2003
Key Words. eigenvalue optimization – convexity – nonsmooth analysis – duality – semidefinite program – subdifferential – Clarke regular
– chain rule – sensitivity – eigenvalue perturbation – partly smooth – spectral function – unitarily invariant norm – hyperbolic
polynomial – stability – robust control – pseudospectrum – H
∞
norm
Mathematics Subject Classification (2000): 90C30, 15A42, 65F15, 49K40 相似文献
8.
The limit as N → ∞ of the eigenvalue correlation function is studied in a neighborhood of zero for N × N Hermitian matrices
chosen at random from the Hilbert-Schmidt sphere of an appropriate radius. Dyson’s famous sin π(t1 − t2)/π(t1 − t2)-kernel asymptotic is extended to this class of matrix ensembles. Bibliography: 9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 68–80. 相似文献
9.
S. I. Kalmykov 《Journal of Mathematical Sciences》2009,157(4):623-631
The paper considers the equality cases in the rnajoration principle for meromorphic functions established earlier by V. N.
Dubinin and S. I. Kalmykov [Mat. Sb., 198, No. 12, 37–46 (2007)]. As corollaries of this principle, new inequalities for the coefficients and derivatives of polynomials
satisfying certain conditions on two intervals are obtained. Simple proofs of some Lukashov’s theorems on the derivatives
of rational functions on several intervals are provided. Bibliography: 13 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 357, 2008, pp. 143–157. 相似文献
10.
Kallol Paul 《Mathematica Slovaca》2010,60(1):121-128
One of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work [PAUL,
K.: Translatable radii of an operator in the direction of another operator, Scientae Mathematicae 2 (1999), 119–122] is studied in details. A necessary and sufficient condition for a unit vector f to be a stationary vector of the generalized eigenvalue problem Tf = λAf is obtained. Finally a theorem of Williams ([WILLIAMS, J. P.: Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129–136]) is generalized to obtain a translatable radius of an operator in the direction of another operator. 相似文献
11.
Summary We present a complete characterization of the class of (unbounded) sampling plans providing unbiased (sequential) estimation
of the reciprocal of the Bernoulli parameterp. This settles a conjecture set forth by Sinha and Sinha (1975,Ann. Inst. Statist. Math.,27, 245–258) regarding the nature of such plans as sought out by Gupta (1967,Ann. Inst. Statist. Math.,19, 413–416). Incidentally, a special type of sampling plans (termed ‘infinite-step generalizations of the inverse binomial
plans’), studied by Sinha and Bhattacharyya (1982, Institute of Statistics Mimeo Series, Raleigh), are seen to play a central
role in this study. 相似文献
12.
A. D. Kolesnik 《Ukrainian Mathematical Journal》2008,60(12):1915-1926
A symmetric random evolution X(t) = (X
1 (t), …, X
m
(t)) controlled by a homogeneous Poisson process with parameter λ > 0 is considered in the Euclidean space ℝ
m
, m ≥ 2. We obtain an asymptotic relation for the transition density p(x, t), t > 0, of the process X(t) as λ → 0 and describe the behavior of p(x, t) near the boundary of the diffusion domain in spaces of different dimensions.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1631 – 1641, December, 2008. 相似文献
13.
Kostaq Hila 《Mathematica Slovaca》2010,60(2):195-212
In this paper we obtain and establish some important results in ordered Γ-semigroups extending and generalizing those for
semigroups given in [PETRICH, M.: Introduction to Semigroups, Merill, Columbus, 1973] and for ordered semigroups from [KEHAYOPULU, N.: On weakly prime ideals of ordered semigroups, Math. Japon. 35 (1990), 1051–1056], [KEHAYOPULU, N.: On prime, weakly prime ideals in ordered semigroups, Semigroup Forum 44 (1992), 341–346] and [XIE, X. Y.—WU, M. F.: On quasi-prime, weakly quasi-prime left ideals in ordered semigroups, PU.M.A. 6 (1995), 105–120]. We introduce and give some characterizations about the quasi-prime and weakly quasi-prime left ideals of
ordered-Γ-semigroups. We also introduce the concept of weakly m-systems in ordered Γ-semigroups and give some characterizations of the quasi-prime and weakly quasi-prime left ideals by
weakly m-systems. 相似文献
14.
T. Shaposhnikova 《Journal of Mathematical Sciences》1995,75(3):1631-1645
The behavior of the solution of a boundary value problem for a parabolic equation with rapidly oscillating coefficientsɛ
−1
x,ɛ
−2k
t), (k⋝0) in a perforated domain for ε→0 is studied. Some estimates of the deviation of the solution and energy for the original
boundary value problem from the solution and energy of the corresponding homogenized problem are found. In this investigation
methods developed by Oleinik, Zhikov, Kozlov, Bensoussan, Lions, Papanikolaou, Cioranescu, and Paulin are used. Bibliography:
15 titles.
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 17, pp. 27–50, 1994. 相似文献
15.
We present various versions of generalized Aleksandrov–Bakelman–Pucci (ABP) maximum principle for L
p
-viscosity solutions of fully nonlinear second-order elliptic and parabolic equations with possibly superlinear-growth gradient
terms and unbounded coefficients. We derive the results via the “iterated” comparison function method, which was introduced
in our previous paper (Koike and Święch in Nonlin. Diff. Eq. Appl. 11, 491–509, 2004) for fully nonlinear elliptic equations. Our results extend those of (Koike and Święch in Nonlin. Diff. Eq.
Appl. 11, 491–509, 2004) and (Fok in Comm. Partial Diff. Eq. 23(5–6), 967–983) in the elliptic case, and of (Crandall et al. in Indiana Univ. Math. J. 47(4), 1293–1326, 1998; Comm. Partial Diff. Eq. 25, 1997–2053, 2000; Wang in Comm. Pure Appl. Math. 45, 27–76, 1992) and (Crandall and Święch in Lecture Notes in Pure and Applied Mathematics, vol. 234. Dekker, New York, 2003)
in the parabolic case.
Dedicated to Hitoshi Ishii on the occasion of his 60th birthday. 相似文献
16.
Solution of the spectral problem for the curl and Stokes operators with periodic boundary conditions
R. S. Saks 《Journal of Mathematical Sciences》2006,136(2):3794-3811
In this paper, we establish relations between eigenvalues and eigenfunctions of the curl operator and Stokes operator (with
periodic boundary conditions). These relations show that the curl operator is the square root of the Stokes operator with
ν = 1. The multiplicity of the zero eigenvalue of the curl operator is infinite. The space L
2(Q, 2π) is decomposed into a direct sum of eigenspaces of the operator curl. For any complex number λ, the equation rot
u + λu = f and the Stokes equation −ν(Δv + λ 2v) + ∇p = f, div v = 0, are solved. Bibliography: 15 titles.
Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 246–276. 相似文献
17.
Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1981,33(1):391-403
Summary Mises functional is extended for the two-sample problem. It is shown that the extended Mises functional also has the asymptotic
property given by von Mises (1947,Ann. Math. Statist.,18, 309–348) and by Filippova (1962,Theory Prob. Appl.,7, 24–57) in the one-sample case. Asymptotic behavior ofU-statistic in the two-sample case, the statistic of Cramér-von Mises type for testing homogeneity and so forth are investigated
as important examples of the theory.
The Institute of Statistical Mathematics 相似文献
18.
Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function 总被引:3,自引:0,他引:3
We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained
optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity
independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd–Omojokun class
of algorithms, each step is composed of a quasi-normal and a tangential step. Both steps are required to satisfy a decrease
condition for their respective trust-region subproblems. The proposed mechanism for accepting steps combines nonmonotone decrease
conditions on the constraint violation and/or the Lagrangian function, which leads to a flexibility and acceptance behavior
comparable to filter-based methods. We establish the global convergence of the method. Furthermore, transition to quadratic
local convergence is proved. Numerical tests are presented that confirm the robustness and efficiency of the approach.
Received: December 14, 2000 / Accepted: August 30, 2001 Published online: September 27, 2002
Key words. nonmonotone trust-region methods – sequential quadratic programming – penalty function – global convergence – equality constraints
– local convergence – large-scale optimization
Mathematics Subject Classification (2000): 65K05, 90C30 相似文献
19.
William J. McGraw 《Mathematische Annalen》2003,326(1):105-122
In a recent paper [Duke Math. J., 97, 219–233], Borcherds asks whether or not the spaces of vector valued modular forms associated to the Weil representation
have bases of modular forms whose Fourier expansions have only integer coefficients. We give an affirmative answer to Borcherds'
question. This strengthens and simplifies Borcherds' main theorem which is a generalization of a theorem of Gross, Kohnen,
and Zagier [Math. Ann., 278, 497–562].
Received: 27 September 2001 / Revised version: 22 July 2002 /
Published online: 28 March 2003
Mathematics Subject Classification (1991): 11F30; 11F27 相似文献
20.
For a system of n identical particles in a homogeneous magnetic field, the discrete spectrum of the Hamiltonian Hα, m on the subspaces of functions with permutational symmetry α and rotational (SO(2)) symmetry m is studied as m→∞. It is proved
that the discrete spectrum of the operator Hα,m contains only one eigenvalue if certain conditions are satisfied. The asymptotic behavior of this eigenvalue as m→∞ is found.
Bibliography: 7 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 197, pp. 28–41, 1992.
Translated by A. V. Lyakhovskaya 相似文献