Fixed points of the RSA encryption algorithm

In this paper the problem of the number of fixed points for an RSA algorithm is considered. This is an important question from the point of view of any cryptosystem. We have estimated the expected value of this number for randomly chosen RSA parameters. It turned out that it is O(ln²n), and the probability of finding such a point is O(ln²n/n). Thus, these values are really negligible, which had been intuitively expected.     

C-AMTE: A location mechanism for flexible cache management in chip multiprocessors

This paper describes Constrained Associative-Mapping-of-Tracking-Entries (C-AMTE), a scalable mechanism to facilitate flexible and efficient distributed cache management in large-scale chip multiprocessors (CMPs). C-AMTE enables fast locating of cache blocks in CMP cache schemes that employ one-to-one or one-to-many associative mappings. C-AMTE stores in per-core data structures tracking entries to avoid on-chip interconnect traffic outburst or long distance directory lookups. Simulation results using a full system simulator demonstrate that C-AMTE achieves improvement in cache access latency by up to 34.4%, close to that of a perfect location strategy.     

Anti-periodic fractional boundary value problems

We study a class of anti-periodic boundary value problems of fractional differential equations. Some existence and uniqueness results are obtained by applying some standard fixed point principles. Several examples are given to illustrate the results.     

Existence results for impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of mild solutions for nonlocal impulsive differential inclusions. On the basis of the fixed point theorems for multivalued maps and the technique of approximate solutions, new results are obtained. Examples are also provided to illustrate our results.     

Iterative methods for solving extended general mixed variational inequalities

In this paper, we introduce and consider a new class of mixed variational inequalities involving four operators, which are called extended general mixed variational inequalities. Using the resolvent operator technique, we establish the equivalence between the extended general mixed variational inequalities and fixed point problems as well as resolvent equations. We use this alternative equivalent formulation to suggest and analyze some iterative methods for solving general mixed variational inequalities. We study the convergence criteria for the suggested iterative methods under suitable conditions. Our methods of proof are very simple as compared with other techniques. The results proved in this paper may be viewed as refinements and important generalizations of the previous known results.     

On the generalized Hyers-Ulam stability of multi-quadratic mappings

A mapping f:Vⁿ?W, where V is a commutative group, W is a linear space, and n≥2 is an integer, is called multi-quadratic if it is quadratic in each variable. In this paper, we prove the generalized Hyers-Ulam stability of multi-quadratic mappings in Banach spaces and complete non-Archimedean spaces.     

Hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems

In this paper, we introduce a new iterative algorithm by hybrid method for finding a common element of the set of solutions of finite general mixed equilibrium problems and the set of solutions of a general variational inequality problem for finite inverse strongly monotone mappings and the set of common fixed points of infinite family of strictly pseudocontractive mappings in a real Hilbert space. Then we prove strong convergence of the scheme to a common element of the three above described sets. Our result improves and extends the corresponding results announced by many others.     

Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem

In this paper, we consider the following nonlinear fractional three-point boundary value problem

     

Data reductions, fixed parameter tractability, and random weighted d-CNF satisfiability

Data reduction is a key technique in the study of fixed parameter algorithms. In the AI literature, pruning techniques based on simple and efficient-to-implement reduction rules also play a crucial role in the success of many industrial-strength solvers. Understanding the effectiveness and the applicability of data reduction as a technique for designing heuristics for intractable problems has been one of the main motivations in studying the phase transition of randomly-generated instances of NP-complete problems.In this paper, we take the initiative to study the power of data reductions in the context of random instances of a generic intractable parameterized problem, the weighted d-CNF satisfiability problem. We propose a non-trivial random model for the problem and study the probabilistic behavior of the random instances from the model. We design an algorithm based on data reduction and other algorithmic techniques and prove that the algorithm solves the random instances with high probability and in fixed-parameter polynomial time O(dknm) where n is the number of variables, m is the number of clauses, and k is the fixed parameter. We establish the exact threshold of the phase transition of the solution probability and show that in some region of the problem space, unsatisfiable random instances of the problem have parametric resolution proof of fixed-parameter polynomial size. Also discussed is a more general random model and the generalization of the results to the model.     

第三代移动通信系统中的信道分配技术

移动通信系统发展至今信道分配技术一直都是热门话题,一个好的信道分配算法可以在特定的服务等级下(包括链路质量,新呼叫阻塞概率,切换失败概率)产生很高的频谱利用率。本文注重结合第三代移动通信系统对现有的信道分配技术进行综述并分析其优劣。