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The Product of Automorphic Weighted Composition Operators on Hardy Space H <sup>2</sup>
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Abstract<p>Let <inline-formula> <tex-math><?CDATA $n\in {\mathbb{N}},{p}_{i}\in {\rm{U}},{\alpha }_{{P}_{i}}(z)=\frac{{p}_{i}-z}{1-{\bar{p}}_{i}z}(z\in {\rm{U}})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>n</mi> <mo>∈</mo> <mi>ℕ</mi> <mo>,</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>z</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mi>i</mi> </msub> <mi>z</mi> </mrow> </mfrac> <mo stretchy="false">(</mo> <mi>z</mi> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula>, and let <inline-formula> <tex-math><?CDATA ${f}_{1}\in {H}^{\infty },i=1,\ldots,n$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>∈</mo> <msup> <mi>H</mi> <mi>∞</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. We discuss the relation between the points <italic>p<sub>i</sub> </italic> in U and the functions <italic>f<sub>i</sub> </italic> in U and the properties of the product of automorphic weighted composition operators <inline-formula> <tex-math><?CDATA ${W}_{{f}_{1},{\alpha }_{{p}_{1}}}\,{W}_{{f}_{2},{\alpha }_{{p}_{2}}}\ldots {W}_{{f}_{i},{\alpha }_{pi}}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </msub> <mspace width="0.25em"></mspace> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>…</mo> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> on Hardy space H<sup>2</sup>. In fact, it is very nice connection between analytic function theory and operator theory. In this paper, we give the sufficient and necessary conditions to be normal, unitary, hermitian operator on <italic>H</italic> <sup>2</sup> and we shall present the shape of the numerical range of it.</p>
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Sat Feb 01 2020
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Composition effects on formation energies, electronic and vibrational properties of ZnCdS wurtzoid molecules: A DFT study
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Wed Mar 10 2021
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Fuzzy Subspaces For Fuzzy space of Orderings
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The purpose of this paper is to define fuzzy subspaces for fuzzy space of orderings and we prove some results about this definition in which it leads to a lot of new results on fuzzy space of orderings. Also we define the sum and product over such spaces such that: If f = < a1,…,an > and g = < b1,…bm>, their sum and product are f + g = < a1…,an, b1, …, bm> and f × g =. for all a1,…,an,b1,…,bm ? G

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Fri Sep 15 2023
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Al-academy
Employing digital marketing through communication in promoting the commercial product
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In recent years, the means of communication have achieved a great generality that made them occupy, in a short time, the first ranks among the most widely used social networks in the world, due to the many services and advantages offered by this network to its users. It has led to a leap in the field of visual communication, especially since it relies mainly on the image Its dimensions make it a means of communication and transfer of ideas and meanings between the peoples of the world, and it also allows the inclusion of digital advertising content using multimedia with a degree of professionalism in other social networks, which allowed the various segments of society the opportunity to invest this network in their businesses of differen

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Intelligent H2/H∞ Robust Control of an Active Magnetic Bearings System
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Abstract

Robust controller design requires a proper definition of uncertainty bounds. These uncertainty bounds are commonly selected randomly and conservatively for certain stability, without regard for controller performance.  This issue becomes critically important for multivariable systems with high nonlinearities, as in Active Magnetic Bearings (AMB) System. Flexibility and advanced learning abilities of intelligent techniques make them appealing for uncertainty estimation. The aim of this paper is to describe the development of robust H2/H controller for AMB based on intelligent estimation of uncertainty bounds using Adaptive Neuro Fuzzy Inference System (ANFIS).  Simulatio

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Publication Date
Tue Dec 15 2020
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Al-academy
Aesthetic and Functional Dimensions of the Industrial Product and their Influence on Construction of Consumer's Visual Impression: جاسم احمد زيدان
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  The visual impression represents a compound process of a group of concepts that might be secondary and interrelated to constitute, in reality, a cognitive image stored in the memory that can be retrieved according the implications of the situation in which the individual lives in his environment, as it awakens in him an image from the sub consciousness, thus it gets stimulated, and it is among the tangible things.
Since we live in our contemporary world under the development of knowledge, micro and wide technology of the devices, tools, materials, mechanisms, current developments and openness… etc. this transformation created visual impressions that the individual in general and the consumer in specific enjoys concerning his

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Tue Aug 15 2023
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The Aestheticof Balance And Its Relationship To The Design of The Industrial Product Shape
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The study tagged: (The aesthetics of balance and its relationship to the design of the body of the industrial product) discussed the role of balance in the design of industrial products of different shapes, colors and sizes, as well as their function. Based on the research problem that was determined by the following question: What is the relationship between balance and the design of the body of the industrial product? The aim of the research is to: reveal the statement of the effectiveness of the balance in the design of the industrial product body.
The study was defined in four chapters: in the first chapter, a problem, the importance, and the aim of the research were presented. The second chapter contained the theoretical framewor

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The effectiveness of prediction and clairvoyance and its functions in the inner space
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The research dealt with the effectiveness of prediction and foresight in design as a phenomenon that plays a role in the recipient's engagement with the design, as it shows the interaction between the recipient and the interior space. The designer is keen to diversify his formal vocabulary in a way that secures visual values that call for aesthetic integration, as well as securing mental and kinetic behavioral understanding in the interior space.
As the designer deals with a three-dimensional space that carries many visual scenes, the designer should not leave anything from it without standing on it with study and investigation, and puts the user as a basic goal as he provides interpretive data through prediction and foresight that le

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Publication Date
Sat Dec 31 2022
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EFFECT OF USING DIFFERENT LEVELS OF CAMEL FAT (HUMP FAT) ON PHYSIOCHEMICAL COMPOSITION OF SAUSAGE FROM BEEF CAMEL AND CHICKEN : EFFECT OF USING DIFFERENT LEVELS OF CAMEL FAT (HUMP FAT) ON PHYSIOCHEMICAL COMPOSITION OF SAUSAGE FROM BEEF CAMEL AND CHICKEN
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ABSTRACT

This study was conducted to determine the effect of various levels of hump fat (HF) used in manufacturing of camel, beef and chicken sausage to understand the effect of (HF) on physicochemical composition sausage, Different levels of hump fat (5, 7, and 10 %) were used, physicochemical compositions like (moisture, protein, fat, Ash, water holding capacity, shrinkage, cooking loss and pH) were determined. Results of the study revealed that moisture content showed high significant differences (P≤0.01)among treatments groups, Camel sausage and beef sausage tended to have highest values while chicken sausage reported the lowest value. The study showed no significant difference (P≤0.05) among the

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Approximated Methods for Linear Delay Differential Equations Using Weighted Residual Methods
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The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

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Publication Date
Mon Jun 30 2025
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Iraqi Journal Of Science
New Weighted Synthetic Oversampling Method for Improving Credit Card Fraud Detection
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The use of credit cards for online purchases has significantly increased in recent years, but it has also led to an increase in fraudulent activities that cost businesses and consumers billions of dollars annually. Detecting fraudulent transactions is crucial for protecting customers and maintaining the financial system's integrity. However, the number of fraudulent transactions is less than legitimate transactions, which can result in a data imbalance that affects classification performance and bias in the model evaluation results. This paper focuses on processing imbalanced data by proposing a new weighted oversampling method, wADASMO, to generate minor-class data (i.e., fraudulent transactions). The proposed method is based on th

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