On optimal interval quadrature formulae on classes of differentiable periodic functions

We solved the problem about the best interval quadrature formula on the class $W^r F$ of differentiable periodic functions with arbitrary permutation-invariant set $F$ of derivatives of order $r$. We proved that the formula with equal coefficients and $n$ node intervals, which have equidistant middle points, is the best on given class.

An Enhanced Multimedia Video Surveillance Security Using Wavelet Encryption Framework

Multimedia digital data include medical record and financial documents, which are not guaranteed with security. The concerns for security of multimedia digital data is been a widespread issue in the field of cybernetics. With increasing malwares in video payloads, the proposed study aims to reduce the embedding of malwares using Pseudo Arbitrary Permutation based Cellular Automata Encryption (PAP-CAE) System in video payloads. This method reduces the malware attacks and distortion rate by permuting the secret keys with Pseudo arbitrary permutation. Before the application of PAP-CAE, 2D wavelet transform is applied on the multimedia files that compresses the complex files into different scales and position to be transmitted via a network with reduced size. Simultaneously, it performs the process of decryption and decompression to retrieve the original files. The proposed method is evaluated against existing methods to test its efficacy in terms of detection accuracy, detection time of malwares and false positive rate. The result shows that the proposed method is effective against the detection of malwares in multimedia video files.

The Other Assignment For Problem Instances Esc 16b, Esc 16c And Esc 16h

The quadratic assigment problem (QAP) has remainedone of the great challenges in combinatorial optimization. In this paper I propose two programs, the MATLAB program for solving QAP, and the MATLAB program for checking objective value, if we input an arbitrary permutation, matrix flow and matrix distance. The first program using combination methods that combines random point strategy, forward exchange strategy , and backward exchange strategy. I‘ve tried my program to solve Esc 16b, Esc 16c and Esc 16h from QAPLIB (A Quadratic Assignment Problem Library). In the 500th iteration optimal value reached and I‘ve found the other assignment for problem instances Esc 16b, Esc 16c, and Esc 16h.

Class-preserving coleman automorphisms of permutational wreath products with 2-closed base groups

Let [Formula: see text] be a nontrivial [Formula: see text]-closed group and let [Formula: see text] be an arbitrary permutation group on a finite set [Formula: see text]. Let [Formula: see text] be the corresponding permutational wreath product of [Formula: see text] by [Formula: see text]. It is shown that every class-preserving Coleman automorphism of [Formula: see text]-power order of [Formula: see text] is inner. As a direct consequence, it is obtained that the normalizer property holds for [Formula: see text]. Further, it is shown that every class-preserving Coleman automorphism of [Formula: see text] is inner whenever [Formula: see text] is nilpotent. Our results generalize some known ones.

Chains of Length 2 in Fillings of Layer Polyominoes

The symmetry of the joint distribution of the numbers of crossings and nestings of length $2$ has been observed in many combinatorial structures, including permutations, matchings, set partitions, linked partitions, and certain families of graphs. These results have been unified in the larger context of enumeration of northeast and southeast chains of length $2$ in $01$-fillings of moon polyominoes. In this paper we extend this symmetry to fillings of a more general family—layer polyominoes, which are intersection-free and row-convex, but not necessarily column-convex. Our main result is that the joint distribution of the numbers of northeast and southeast chains of length $2$ over $01$-fillings is symmetric and invariant under an arbitrary permutation of rows.

LAYOUT OF AN ARBITRARY PERMUTATION IN A MINIMAL RIGHT TRIANGLE AREA

In VLSI layout of interconnection networks, routing two-point nets in some restricted area is one of the central operations. The main aim is usually minimization of the layout area, while reducing the number of wire bends is also very useful. In this paper, we consider connecting a set of N inputs on a line to a set of N outputs on a perpendicular line inside a right triangle shaped area, where the order of the outputs is a given permutation of the order of the corresponding inputs. Such triangles were used, for example, by Dinitz, Even, and Artishchev-Zapolotsky for an optimal layout of the Butterfly network. That layout was of a particular permutation, while here we solve the problem for an arbitrary permutation case. We show two layouts in an optimal area of ½ N2 + o(N2), with O (N) bends each. We prove that the first layout requires the absolutely minimum area and yields the irreducible number of bends, while containing knock-knees. The second one eliminates knock-knees, still keeping a constant number, 7, of bends per connection. As well, we prove a lower bound of 3N - o(N) for the number of bends in the worst case layout in an optimal area of ½ N2 + o(N2).

Arbitrary Size Benes Networks

The Benes network is a rearrangeable nonblocking network which can realize any arbitrary permutation. Overlall, the r-dimensional Benes network connects 2r inputs to 2r outputs through 2r - 1 levels of 2 × 2 switches. Each level of switches consists of 2r - 1 switches, and hence the size of the network has to be a power of two. In this paper, we extend Benes networks to arbitrary sizes. We also show that the looping routing algorithm used in Benes networks can be slightly modified and applied to arbitrary size Benes networks.