Ahmed Abbas Mohammed AL-Adilee

Encryption is one of many methods that have been used to secure storage and transmit images over unsecured and open networks. The asymmetric cryptography need more time for encryption and decryption. In this paper we suggested new method for image encryption that has the potential to overcome many of encryption problems. The proposed algorithm based on the concept of scrambling the positions of pixels, and changing the pixels intensity. The algorithm based on two major steps. The first one is scrambling image with uniform distribution for image data based on two dimension Cat map which improved for more secure by increasing the cycles of processing. While the second step is modifying a method of Shadow process algorithm. This modification makes the Shadow process suitable to work efficiently with images. The modified method uses image as a public key for encryption, and from the public key we derive the decryption key. The performance of proposed algorithm measures and gives high uncorrelated between adjacent pixels in encrypted image, high entropy and mostly uniform distribution, it gives better results compared with other works.

In this paper, we study a new type of sub-copulas, which is defined on quantum logic. We review the most common definitions, relations and properties of such functions. We extend the definition of what is recently called 2-dimensional QL-copula to n-dimensional QL-copula with respect to order difference instead of the summation approach, see [5]. We compose this paper to present an alternative interpretation of QL-copula rather thanthe one that we have already defined by AlAdilee and Nanasiova (2009) using an approach depends on definingsub-copulason quantum logic.

This paper devoted to review the most common principles and basic concepts of copula function. The main objective of this study is to make such approach in hand of Iraqi students, Iraqi researchers and Iraqi scientists, who are interested in modern topics of statistics so that they can find their way through this topic. We firstly demonstrate some basic definitions, properties and concepts related to copula function. Afterwards, we will present what is called the families of copula function and then demonstrate the methods of constructing copulas. We also prove some theorems that have been shown without proof in some papers.

Linear regression model is proposed to construct a proper estimation of parameters of Gumbel distribution as influences that effect on manufactured items, for example, bulbs, electrical machines, and so on. Such type of distributions and its properties that relevant to Gamma-distribution has been shown in this study. Some contributions of other extreme value distributions types such as Weibull distribution, and Fre ́chet distribution were introduced in general forms as models used for lifetime data. Maximum likelihood estimation (M.L.E) method was suggested to estimate the values of parameters because of its effective ability to obtain the best approximation for fitting data compared with other estimation methods like least square method, moments method, and other estimation methods. Another important fact of choosing this method is that this method regarded as a best method for small sample sizes.

This study concerned with comparing correlation coefficient (correlation) to copula functions (copulas) throughout their correlations, which are defined by means of their copulas . Indeed, it is an attempt to answer the following question, why copula functions (copula) is preferred in modern statistical inference to correlation?. We will discuss each topic individually, to make a right decision about the question above. For making our decision clear we have recalled some of the basic concepts related to correlation and copulas so that we can show the characteristics and differences of using each one.

Probability measure theory is the basis of many constructions in quantum structures. It can be understood as a mathematical model for the intuitive notion of uncertainty [6]. Without probability measure theory all the stochastic models in physics, biology and economics either would not have been developed or would not be rigorous. The modern period of probability measure theory is connected to the names such as S.N. Bernstein (1880-1968), E. Borel (1871-1956) and A.N. Kolmogorov (1903-1987). Moreover, in Physics, a probability space cannot solve the problem of incompatible elements which appears in the Von Neumann model (1932). For that reason, researchers, for example (Von Neumann) looked for new techniques that could explain the situation where the elements are either compatible or incompatible. In connection with classical concept of probability measure theory trying to solve problems of incompatible random events, many researchers suchas [1,10,11] have introduced equivalent approaches. One of these approaches is called the orthomodular lattice (OML). Many variant maps have been defined on an orthomodular lattice to solve different types of quantum structure problems. One of the basic multivariate functions that has been proposed in quantum logic is a function called s-map, which was introduced by Olga Nánásiová in 2003. This function plays a main role in our constructions.

A quantum logic is one of possible mathematical models for non-compatible random events. In this paper, we introduce and study functions called QL-copula and QL-co-copula on a quantum logic and we compare them with the classical definition of copula and co-copula, respectively. Finally, we show several examples of these functions by means of an s-map

This is a continuation of our previous work [1], where some problems were left open.We will consider the system of [0, 1]-valued functions as the MV-algebra M.Further we show that a slight modification of this model is possible also if νis additive, but not σ-additive.

measure differences on Quantum logic and orthomodular lattices

In this paper, we propose a new version of the Gumbel Distribution using a sine technique family. We discuss the key properties of this distribution, such as the probability density function, the cumulative distribution function, the survival function, the hazard function, the cumulative hazard, and the moments. Additionally, we present a method for estimating the distribution's parameters. We then analyze a dataset using the original and generalized distributions, comparing the results and using goodness-of-fit measures to determine which distribution best fits the data. Finally, we provide conclusions based on our findings, with many examples and valid comparisons applied on fuzzy data.