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This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis. 相似文献
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Mourad Kainane Mezadek Mohamed Kainane Mezadek Michael Reissig 《Mathematical Methods in the Applied Sciences》2020,43(6):3117-3147
In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity. 相似文献
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Efficient multicast search under delay and bandwidth constraints 总被引:1,自引:0,他引:1
The issue of a multicast search for a group of users is discussed in this study. Given the condition that the search is over
only after all the users in the group are found, this problem is called the Conference Call Search (CCS) problem. The goal
is to design efficient CCS strategies under delay and bandwidth constraints. While the problem of tracking a single user has
been addressed by many studies, to the best of our knowledge, this study is one of the first attempts to reduce the search
cost for multiple users. Moreover, as oppose to the single user tracking, for which one can always reduce the expected search
delay by increasing the expected search cost, for a multicast search the dependency between the delay and the search cost
is more complicated, as demonstrated in this study. We identify the key factors affecting the search efficiency, and the dependency
between them and the search delay. Our analysis shows that under tight bandwidth constraints, the CCS problem is NP-hard.
We therefore propose a search method that is not optimal, but has a low computational complexity. In addition, the proposed
strategy yields a low search delay as well as a low search cost. The performance of the proposed search strategy is superior
to the implementation of an optimal single user search on a group of users.
Amotz Bar-Noy received the B.Sc. degree in 1981 in Mathematics and Computer Science and the Ph.D. degree in 1987 in Computer Science, both
from the Hebrew University, Israel. From October 1987 to September 1989 he was a post-doc fellow in Stanford University, California.
From October 1989 to August 1996 he was a Research Staff Member with IBM T. J. Watson Research Center, New York. From February
1995 to September 2001 he was an associate Professor with the Electrical Engineering-Systems department of Tel Aviv University,
Israel. From September 1999 to December 2001 he was with AT research labs in New Jersey. Since February 2002 he is a Professor
with the Computer and Information Science Department of Brooklyn College - CUNY, Brooklyn New York.
Zohar Naor received the Ph.D. degree in Computer Science from Tel Aviv University, Tel Aviv, Israel, in 2000. Since 2003 he is with
the University of Haifa, Israel. His areas of interests include wireless networks, resource management of computer networks,
mobility, search strategies, and multiple access protocols. 相似文献
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杨晓光 《应用数学学报(英文版)》1997,13(4):337-341
1.IntroductionIntillspaperweanalyzetheconvergenceonmultiplicativeiterativealgorithmsfortheIninimizationofadiffcrentiablefunctiondefinedonthepositiveorthantofR".ThealgorithmissllggestedbyEggermolltl'],andisrelatedtotheEM[2](Expextation--Maximization)algoritllnlforPositronemissiontonlography[']andimagereconstructi..14].Wecollsidertheproblenl"linf(x)s.t.x20.Themultiplicativeiterativealgorithmshavethel'orlniforj=l,2,',n,withAhdeterminedthroughalinesearch.Whilelusem[5]establishedanelegantconv… 相似文献