Fuzzy Weirstrass theorem and convex fuzzy mappings

The convexity and continuity of fuzzy mappings are defined through a linear ordering and a metric on the set of fuzzy numbers. The local-global minimum property of real-valued convex functions is extended to convex fuzzy mappings. It is proved that a strict local minimizer of a quasiconvex fuzzy mapping is also a strict global minimizer. Characterizations for convex fuzzy mappings and quasiconvex fuzzy mappings are given. In addition, the Weirstrass theorem is extended from real-valued functions to fuzzy mappings.     

Algebraic properties of cryptosystem PGM

In the late 1970s Magliveras invented a private-key cryptographic system calledPermutation Group Mappings (PGM). PGM is based on the prolific existence of certain kinds of factorization sets, calledlogarithmic signatures, for finite permutation groups. PGM is an endomorphic system with message space ℤ_|G| for a given finite permutation groupG. In this paper we prove several algebraic properties of PGM. We show that the set of PGM transformations ℐ _G is not closed under functional composition and hence not a group. This set is 2-transitive on ℤ_|G| if the underlying groupG is not hamiltonian and not abelian. Moreover, if the order ofG is not a power of 2, then the set of transformations contains an odd permutation. An important consequence of these results is that the group generated by the set of transformations is nearly always the symmetric group ℒ_|G|. Thus, allowing multiple encryption, any permutation of the message space is attainable. This property is one of the strongest security conditions that can be offered by a private-key encryption system. S. S. Magliveras was supported in part by NSF/NSA Grant Number MDA904-82-H0001, by U.S. West Communications, and by the Center for Communication and Information Science of the University of Nebraska.     

Rn 上的线性局部保控映射

设φ：Rn →Rn 是一个线性映射,对任意x∈Rn ,都存在与x有关的线性保控映射ψx ,使得φ（x）＝ψx（x）,则称φ是欧氏空间上的一个线性局部保控映射。线性保控映射是线性局部保控映射,其逆命题不成立。文中定义了两个与φ相关的Rn的子集Iφ和IIφ,如果任意Rn上的点都属于Iφ（或IIφ）,那么这个线性局部保控映射φ是线性保控映射。     

REMARKS ON JOHN DISKS

Let D■R2 be a Jordan domain,D*=R2\D,the exterior of D.In this article,the authors obtained the following results:(1)If D is a John disk,then D is an outer linearly locally connected domain;(2)If D* is a John disk,then D is an inner linearly locally connected domain;(3)A homeomorphism f:R 2 →R 2 is a quasiconformal mapping if and only if f(D)is a John disk for any John disk D■R 2 ;and(4)If D is a bounded quasidisk,then D is a John disk,and there exists an unbounded quasidisk which is not a John disk.     

Continuity versus Discretization

The threefold interest in architecture, biology and mathematics motivated us to examine and justify new architectural forms. We discuss some notions of rhythm: Euclidean, morphogenetic and morphologic. Contemporary relationships between structure and form are based on the generation of shape by technological processes, thus the resulting objects are restricted to their material expression. Here a phenomenological organisation of form and its continuity with the landscape arise out of the mathematical and architectural creativity. The use of the computer is applied from outside to inside instead from inside to outside; this means that we are dealing with the organisational processes via continuous methods instead of evolutionary processes given by computer simulations, known as genetic algorithms, where the resulting configurations are reduced to a matter of routine. The role of design as an aesthetic component innovates the theoretical framework of structural engineering to establish the architectural environments.     

广义混合均衡与不动点问题公共解的迭代算法

在Hilbert空间中,引入一种新的关于广义混合均衡问题的迭代方法,通过该迭代方法求得广义混合均衡问题的解集与非扩张映像的不动点集的公共解.并且在一定条件下,得到强收敛定理.所得结果改进和推广了这一领域内某些最新结果.     

Nonlinear Inverse Boundary-Value Problems of Conformal Mapping with a Controlling Potential

Some characteristic cases of formation of an ideal flow are described depending on preset values of controlling potential. Based on the modified G. Polozhii's method of summary mappings, the characteristic function of the flow is obtained. Examples of construction of a dynamic grid, field of velocities, and formation of different flows are given. Types of key problems of finding the values of controlling potential, which provide optimization of definite functionals are defined. An example of solution to one of them is presented.     

Iterated non-linear model predictive control based on tubes and contractive constraints

This paper presents a predictive control algorithm for non-linear systems based on successive linearizations of the non-linear dynamic around a given trajectory. A linear time varying model is obtained and the non-convex constrained optimization problem is transformed into a sequence of locally convex ones. The robustness of the proposed algorithm is addressed adding a convex contractive constraint. To account for linearization errors and to obtain more accurate results an inner iteration loop is added to the algorithm. A simple methodology to obtain an outer bounding-tube for state trajectories is also presented. The convergence of the iterative process and the stability of the closed-loop system are analyzed. The simulation results show the effectiveness of the proposed algorithm in controlling a quadcopter type unmanned aerial vehicle.     

Common fixed points of a countable family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the proposed iterative scheme under some control conditions.