Grey system theory is a multidisciplinary scientific approach, which deals with systems that have partially unknown information (small sample and uncertain information). Grey modeling as an important component of such theory gives successful results with limited amount of data. Grey Models are divided into two types; univariate and multivariate grey models. The univariate grey model with one order derivative equation GM (1,1) is the base stone of the theory, it is considered the time series prediction model but it doesn’t take the relative factors in account. The traditional multivariate grey models GM(1,M) takes those factor in account but it has a complex structure and some defects in " modeling mechanism", "parameter estimation "and "model structure", So that traditional GM(1,M) submitted to many trials of optimizations to getting rid this defects. This research shows the characteristics of the traditional GM(1,M), the problems it suffer from, the method of getting rid of such problems and presents two optimized multivariable grey model of one order derivative equation. the first one is called the Optimized Grey Model abbreviated as OGM(1, M) by adding the linear correction term h1(M-1)and the grey action quantity term (h2) to the traditional model GM(1,M) the latter is called Optimized Background value Grey Model OBGM(1,M) by optimizing the Background value of the last model OGM(1,M). We use two A realistic data represents the water consumption in Baghdad at the period (2016-2022) to compare the two optimized models with the traditional represents the water consumption in Baghdad at the period (2016-2022)). we use the mean absolute percentage error (MAPE) and the determination coefficient R2. To compare the two optimized model with traditional one. The results show that the two optimized have less values than the those of the traditional model GM(I,M), and that verify the correctness of defects analysis of GM(1,M).
(25)
(17)
This work deals with kinetics and chemical equilibrium studies of esterification reaction of ethanol with acetic acid. The esterification reaction was catalyzed by an acidic ion exchange resin (Amberlyst- 15) using a batch stirred tank reactor. The pseudo-homogenous and Eley-Rideal models were successfully fitted with experimental data. At first, Eley-Rideal model was examined for heterogeneous esterification of acetic acid and ethanol. The pseudo-homogenous model was investigated with a power-law model. The apparent reaction order was determined to be (0.88) for Ethanol and (0.92) for acetic acid with a correlation coefficient (R2) of 0.981 and 0.988, respectively. The reaction order was determined to be 4.1087x10-3 L0.8/(mol0.8.min) with
... Show More
(9)
(3)
The result of a developed mathematical model for predicting the design
parameters of the fiber Raman amplifier (FRA) are demonstrated. The amplification
parameters are tested at different pump power with different fiber length. Recently,
the FRA employed in optical communication system to increase the repeater distance
as will as the capacity of the communication systems. The output results show, that
high Raman gain can be achieved by high pumping power, long effective area that
need to be small for high Raman gain. High-stimulated Raman gain coefficient is
recommended for high Raman amplifier gain, the low attenuation of the pump and the
transmitted signal in the fiber lead to high Raman gain.
In this research work, a simulator with time-domain visualizers and configurable parameters using a continuous time simulation approach with Matlab R2019a is presented for modeling and investigating the performance of optical fiber and free-space quantum channels as a part of a generic quantum key distribution system simulator. The modeled optical fiber quantum channel is characterized with a maximum allowable distance of 150 km with 0.2 dB/km at =1550nm. While, at =900nm and =830nm the attenuation values are 2 dB/km and 3 dB/km respectively. The modeled free space quantum channel is characterized at 0.1 dB/km at =860 nm with maximum allowable distance of 150 km also. The simulator was investigated in terms of the execution of the BB84 prot
... Show More
(5)
(5)
The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.
(12)
(9)
Values are penetrating or interfering in the lives of individuals and groups and are connected to them in the sense of life itself, because they are closely linked to the motives of behavior, hopes and goals, and can be said that values are everything. The concept of values is one of the concepts that have received the attention of researchers from different disciplines. This has resulted in a kind of confusion and variation in use from one specialization to the other, and uses multiple uses within one specialization. Therefore, there is no uniform definition of values because they relate to individuals. Individuals differ in many things, such as perception,
... Show More
In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a prior
... Show More
We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T-ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied. Abstract We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T- ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied.
(2)
(1)
Abstract
Characterized by the Ordinary Least Squares (OLS) on Maximum Likelihood for the greatest possible way that the exact moments are known , which means that it can be found, while the other method they are unknown, but approximations to their biases correct to 0(n-1) can be obtained by standard methods. In our research expressions for approximations to the biases of the ML estimators (the regression coefficients and scale parameter) for linear (type 1) Extreme Value Regression Model for Largest Values are presented by using the advanced approach depends on finding the first derivative, second and third.
MCA has gained a reputation for being a very useful statistical method for determining the association between two or more categorical variables and their graphical description. For performance this method, we must calculate the singular vectors through (SVD). Which is an important primary tool that allows user to construct a low-dimensional space to describe the association between the variables categories. As an alternative procedure to use (SVD), we can use the (BMD) method, which involves using orthogonal polynomials to reflect the structure of ordered categorical responses. When the features of BMD are combined with SVD, the (HD) is formed. The aim of study is to use alternative method of (MCA) that is appropriate with order
... Show More