Abstract:
The Next Bit Test brie y states that a sequence is random if and only if, given any i bits of the sequence, it is not possible to predict the next bit of the sequence with a probability of success signicantly greater than 1=2. In 1996, Sadeghiyan and Mohajeri proposed a so-called \new universal test for bit strings", based on the theoretical next bit test. In this paper, we study dierent aspects of this test and show its weakness. Then, we improve it both theoretically and practically for better classication of the sequences. As a result, a Practical Next Bit (PNB) test is introduced in two Global and Local versions and a histogram, which gives an impression of the global evaluation of the underlying sequence. Testing samples of nonrandom sequences, using both the PNB test and the NIST Statistical Test Suite, indicates the superiority of the PNB test power over that of the NIST.

Keywords:
Next bit test

Random sequences
Statistical test.

Abstract:
Due to time-varying topological changes in a wireless ad hoc network, it is a challenging issue to provide stringent QoS requirements of most real-time applications. Each real-time application requires a specic set of QoS parameter guarantees (such as delay, jitter, packet loss. . . ). As multipath routing has the potential of reducing the congestion and increasing the throughput of the user trac in multi-hop wireless networks, it is assumed that multiple paths are available in advance between each source-destination pair. In the current work, those subsets of real-time applications (such as Video On Demand), which require minimized packet loss and a lower bound on the delivered bandwidth, are taken into account. Using a constrained optimization framework and trying to minimize the packet loss, an optimal rate is allocated to each source-destination path of the real-time application. Simulation results verify the enhanced performance of the proposed method in terms of the packet error rate.

Abstract:
Morphological ltering is a useful technique for the processing and analysis of binary and gray scale images. The extension of morphological techniques to color images is not a straightforward task because this extension stems from the multivariate ordering problem. Since multivariate ordering is ambiguous, existing approaches have used known vector ordering schemes for the color ordering purpose. In the last decade, many dierent color morphological operators have been introduced in the literature. Some of them have focused on noise suppression purposes. However, none has shown good performance, especially on edgy regions. In this paper, new color morphological operators, based on a fuzzy principle component analysis, are proposed for noise removal. These operators employ statistical information (obtained by applying a fuzzy clustering algorithm on the color space) to achieve the desired results for the denoising application. The performance of the proposed operators is compared with recent morphological operators, reported in the literature, for denoising purposes and the superiority of the proposed method is shown.

Keywords:
Color morphological operators

Noise suppression
Ordering
FPCA.

Abstract:
Heavily loaded stressed power systems exhibit complex nonlinear dynamic behavior, which cannot be analyzed and described accurately by conventional linear methods, such as eigen-analysis. A normal form of the vector elds theory, a well established mathematical method and the Modal Series technique (a relatively newly established approach) have been used as tools to analyze, characterize and quantify some of the stressed power system's sophisticated nonlinear behavior such as low frequency interarea oscillations. The normal form method has been used extensively in recent years for the analysis of nonlinear modal interaction and the role of this interaction in causing inter-area oscillations after the occurrence of large disturbances. However, the normal form has some shortcomings, which must be further highlighted. In this paper, some of these shortcomings are addressed by the use of simple examples. Linear modal, normal form and Modal Series methods are used to simulate a two-area, 4-machine power system test case and the results are compared with its accurate nonlinear simulation to asses the performance and accuracy of these three methods. It is shown that: 1) Normal form techniques cannot simulate stressed power systems well in some regions of its operating space, 2) In some regions of state space, even a linear modal method provides more accurate results than a normal form, and 3) Modal Series' results are consistently the most accurate of the three.

Keywords:
Power system dynamics

Normal forms method
Modal Series technique
Modal analysis; Nonlinear interaction.

Abstract:
The normalization theory in relational database design is a classical subject investigated in dierent papers. The results of these research works are the stronger normal forms such as 5NF, DKNF and 6NF. In these normal forms, there are less anomalies and redundancies, but it does not mean that these stronger normal forms are free of anomalies and redundancies. Each normal form discussion is based on a particular constraint. In this paper, we introduce relations which contain a new kind of constraint called \combinational constraint". We distinguish two important kinds of this constraints, namely Strong and Weak. Also we classify the Combinationally Constrained Relations as Single and Multiple. We introduce all kinds of such relations and specify them using their quantitative properties, formally. It can be shown that these relations are in 5NF or 6NF and still they contain redundancies and have some anomalies.

Keywords:
Relation

Constrained attribute
Free attribute
Combinational constraint
Combinationally constrained relation
Weak combinational constraint
Strong combinational constraint.

Abstract:
A simple process for the chemical vapor deposition of ultra SD single-wall carbon nanotubes has been developed. In this process, an iron nitrate nonahydrate solution in isopropyl alcohol with a concentration of (400 gr/milt) was used to catalyst nanoparticle formation on an oxidized silicon wafer. The oxide on the substrate was made of a thick layer of wet oxide sandwiched between two thin layers of dry oxide. The process results in semiconducting Single-Walled carbon NanoTubes (SWNTs) with diameters of less than 0.7 nm and more than a 1 ev band gap energy, which are amongst the smallest diameters of SWNTs ever reported.

Abstract:
In this paper, Quintic spline in o-step points is used for the solution of fourth-order boundary value problems. Spline relations and boundary formulas are developed and the convergence analysis of the given method is investigated. Numerical illustrations are given to show the applicability and eciency of our method.

Keywords:
Fourth-order ordinary dierential equation

Quintic spline
O-step points
Convergence analysis
Monotone matrix.

Abstract:
We study the problem of online coloring co-interval graphs. In this problem, a set of intervals on the real line is presented to the algorithm, one at a time, and upon receiving each interval I, the algorithm must assign I a color dierent from the colors of all previously presented intervals not intersecting I. The objective is to use as few colors as possible. It is known that the competitive ratio of the simple FIRST-FIT algorithm on the class of co-interval graphs is at most 2. We show that for the class of unit co-interval graphs, where all intervals have equal length, the 2-bound on the competitive ratio of FIRST-FIT is tight. On the other hand, we show that no deterministic online algorithm for coloring unit co-interval graphs can be better than 3/2-competitive. We then study the eect of randomization on our problem and show a lower bound of 4/3 on the competitive ratio of any randomized algorithm for the unit co-interval coloring problem. We also prove that for the class of general co-interval graphs, no randomized algorithm has a competitive ratio better than 3/2.

Keywords:
Online algorithms

Graph coloring
Co-interval graphs.