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671.
Arrigo Cellina 《Proceedings of the American Mathematical Society》2002,130(2):413-418
This paper presents a necessary and sufficient condition on the convex function in order that continuous solutions to
satisfy a Strong Maximum Principle on any open connected .
satisfy a Strong Maximum Principle on any open connected .
672.
Zhenxiang Zhang. 《Mathematics of Computation》2002,71(240):1699-1734
The well-known Baillie-PSW probable prime test is a combination of a Rabin-Miller test and a ``true' (i.e., with The well-known Baillie-PSW probable prime test is a combination of a Rabin-Miller test and a ``true' (i.e., with ) Lucas test. Arnault mentioned in a recent paper that no precise result is known about its probability of error. Grantham recently provided a probable prime test (RQFT) with probability of error less than 1/7710, and pointed out that the lack of counter-examples to the Baillie-PSW test indicates that the true probability of error may be much lower.
and
Then we give explicit formulas to compute B and SB, and prove that, for odd composites ,
and point out that these are best possible. Finally, based on one-parameter quadratic-base pseudoprimes, we provide a probable prime test, called the One-Parameter Quadratic-Base Test (OPQBT), which passed by all primes and passed by an odd composite odd primes) with probability of error . We give explicit formulas to compute , and prove that
The running time of the OPQBT is asymptotically 4 times that of a Rabin-Miller test for worst cases, but twice that of a Rabin-Miller test for most composites. We point out that the OPQBT has clear finite group (field) structure and nice symmetry, and is indeed a more general and strict version of the Baillie-PSW test. Comparisons with Gantham's RQFT are given.
In this paper we first define pseudoprimes and strong pseudoprimes to quadratic bases with one parameter: , and define the base-counting functions:
and
Then we give explicit formulas to compute B and SB, and prove that, for odd composites ,
and point out that these are best possible. Finally, based on one-parameter quadratic-base pseudoprimes, we provide a probable prime test, called the One-Parameter Quadratic-Base Test (OPQBT), which passed by all primes and passed by an odd composite odd primes) with probability of error . We give explicit formulas to compute , and prove that
The running time of the OPQBT is asymptotically 4 times that of a Rabin-Miller test for worst cases, but twice that of a Rabin-Miller test for most composites. We point out that the OPQBT has clear finite group (field) structure and nice symmetry, and is indeed a more general and strict version of the Baillie-PSW test. Comparisons with Gantham's RQFT are given.
673.
674.
Yafang Gong 《分析论及其应用》2006,22(4)
Based on Bernstein's Theorem, Kalandia's Lemma describes the error estimate and the smoothness of the remainder under the second part of Holder norm when a Holder function is approximated by its best polynomial approximation. In this paper, Kalandia's Lemma is generalized to the cases that the best polynomial is replaced by one of its four kinds of Chebyshev polynomial expansions, the error estimates of the remainder are given out under Holder norm or the weighted Holder norms. 相似文献
675.
Super efficiency in convex vector optimization 总被引:17,自引:0,他引:17
We establish a Lagrange Multiplier Theorem for super efficiency in convex vector optimization and express super efficient solutions as saddle points of appropriate Lagrangian functions. An example is given to show that the boundedness of the base of the ordering cone is essential for the existence of super efficient points.Research is supported partially by NSERC.Research is supported partially by NSERC and Mount St. Vincent University grant. 相似文献
676.
677.
Thomas Dehn 《Journal of Computational and Applied Mathematics》1994,50(1-3):207-219
We consider the asymptotic behavior of the ratios qn+1(z)/qn(z) of polynomials orthonormal with respect to some positive measure μ. Let the recurrence coefficients n and βn converge to 0 and
, respectively. Then, qn+1(z)/qn(z) Φ(z),for n→∞ locally uniformly for
, where Φ maps
conformally onto the exterior of the unit disc (Nevai (1979)). We provide a new and direct proof for this and some related results due to Nevai, and apply it to convergence acceleration of diagonal Padé approximants. 相似文献
678.
A transversely isotropic material in the sense of Green is considered. A complete solution in terms of retarded potential
functions for the wave equations in transversely isotropic media is presented. In this paper we reduce the number of potential
functions to only one, and we discuss the required conditions. As a special case, the torsionless and rotationally symmetric
configuration with respect to the axis of symmetry of the material is discussed. The limiting case of elastostatics is cited,
where the solution is reduced to the Lekhnitskii–Hu–Nowacki solution. The solution is simplified for the special case of isotropy.
In this way, a new series of potential functions (to the best knowledge of the author) for the elastodynamics problem of isotropic
materials is presented This solution is reduced to a special case of the Cauchy–Kovalevski–Somigliana solution, if the displacements
satisfy specific conditions. Finally, Boggio's Theorem is generalized for transversely isotropic media which may be of interest
to the reader beyond the present application.
Dedicated to Morton E. Gurtin 相似文献
679.
In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation
where
(i) r,c ∈ C([t
0, ∞), ℝ := (− ∞, ∞)) and r(t) > 0 on [t
0, ∞) for some t
0 ⩾ 0;
(ii) Φ(u) = |u|p−2
u for some fixed number p > 1.
We also generalize some results of Hille-Wintner, Leighton and Willet. 相似文献