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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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Publication Date
Wed Mar 24 2021
Journal Name
Indian Journal Of Forensic Medicine &amp; Toxicology
Study of Epstein - Barr virus Infection in Relation to the Immunohistochemical Expression of Bcl-2 gene in Tissues of Patients with Adenocarcinoma of the Colon
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Background: EBV infection in tissue micro-environment is challenged by the precisely regulated survivaland apoptosis mechanisms. Abnormal bcl-2 proto-oncogene expression in colonic carcinomas allowsaccumulation and propagation of these genetically altered cells.Objective: To analyze the relevant concordance of BCL-2 gene , EBNA1 s and LMP-1-EBV expression inissues from a group of Iraqi patients with colonic adenocarcinomas.Patients and Methods: One hundred (100) tissue biopsies, belonged to (40) patients with colorectalcancers, (40) patients with benign colon tumors, and (20) apparently normal colorectal control tissues,were enrolled in this study. The detection of EBNA1 s and LMP-1-EBV as well as BCL-2 was done byimmunohistochemist

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Publication Date
Wed Dec 12 2018
Journal Name
Iop Conference Series: Materials Science And Engineering
The performance of MnO<sub>2</sub>/graphite electrode for TOC removal from wastewater by indirect electrochemical oxidation process
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Electrochemical oxidation in the presence of sodium chloride used for removal of phenol and any other organic by products formed during the electrolysis by using MnO2/graphite electrode. The performance of the electrode was evaluated in terms fraction of phenol and the formed organic by products removed during the electrolysis process. The results showed that the electrochemical oxidation process was very effective in the removal of phenol and the other organics, where the removal percentage of phenol was 97.33%, and the final value of TOC was 6.985 ppm after 4 hours and by using a speed of rotation of the MnO2 electrode equal to 200 rpm.

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Publication Date
Fri Dec 07 2018
Journal Name
Asian Journal Of Pharmaceutical And Clinical Research
IMMUNOHISTOCHEMICAL EXPRESSION OF THE PROMISING THERAPEUTIC TARGET (HUMAN EPIDERMAL GROWTH FACTOR RECEPTOR 2/NEU) IN IRAQI PATIENTS WITH MEDULLOBLASTOMA
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Objectives: With the advent of ongoing novel modalities toward the treatment of human epidermal growth factor receptor 2 (HER2)/NEU - positive malignancies, the serious side effects of chemoradiotherapy have been minimized. Hence, this study was conducted to identify the patterns of immunohistochemical expression of the promising therapeutic target (HER2/NEU) among Iraqi patients with medulloblastoma in an attempt to provide basic histological information’s that would help in future clinical researches.Materials and Methods: In this retrospective study, 42 formalin - fixed paraffin - embedded tissue blocks represent cases of surgically removed medulloblastomas were retrieved from the archived materials in a specialized surgical ho

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Publication Date
Mon Apr 01 2019
Journal Name
Biochem. Cell. Arch
Improvement the surface properties of metal valves used in agriculture engine by using CO<inf>2</inf> laser beam
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Publication Date
Mon Apr 01 2019
Journal Name
Biochem. Cell. Arch
Association Of – 1195a/g Single Nucleotide Polymorphism Of Cyclooxygenase-2 Gene With The Severity Of Chronic Periodontitis In An Iraqi Population
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Chronic periodontitis (CP) is an inflammatory disease affecting tooth supporting structures in response to bacterial dental plaque causing irreversible tissue destruction. Cyclooxygenase-2 (COX-2) is an effective mediator in the pathogenesis of periodontitis. Polymorphisms in the COX-2 gene may contribute to its overexpression and increased disease susceptibility. To evaluate the association between -1195 A/G single nucleotide polymorphism (SNP) in the promotor area of the cyclooxygenase-2(COX-2) gene and severity of chronic periodontitis in a sample of Iraqi population. -1195A/ G COX-2 SNP was investigated in 70 chronic periodontitis (CP) cases and 30 healthy controls. CP cases composed of 2 subgroups (35 moderate CP cases and 35 severe CP

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Publication Date
Sun Dec 15 2019
Journal Name
Journal Of Baghdad College Of Dentistry
Angiopoietin-2 Immunohistochemical Expression in Oral Squamous cell Carcinoma
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Background: There are various secreted proteins affecting the prognosis of oral squamous cell carcinoma (OSCC) and one of them is Angiopoietin-2(Ang-2) which is thought to have an essential role in the development and progression of the tumor. Aim of the study: This study was conducted to determine the expression of (Ang-2) in (OSCC) to assess its correlations with clinicopathological parameters of the tumor. Material and Methods: 36 formalin- fixed, paraffin- embedded tissue blocks histologically diagnosed as OSCC were examined for Ang-2 immunohistochemical expression semi quantitively. Results: The expression of Ang-2 was significantly associated with histopathological grade (P value=0.023), while there is no significant association wi

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Publication Date
Fri Nov 18 2005
Journal Name
Acta Crystallographica Section E
Bis(μ3-4-bromo­phenyl­imido)tris­(tricarbonyl­ruthenium)(2 Ru—Ru)
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The title compound, [Ru3(μ3-NC6H4Br)2(CO)9], is a V-shaped triruthenium cluster, each side of the V being face-capped by a 4-bromo­phenyl­imide ligand. Each Ru atom is also ligated by three terminal carbonyl ligands. There are two molecules in the asymmetric unit with minor conformational differences.

Publication Date
Wed Mar 29 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Association between Gallstones and Diabetics Type 2 Iraqi Patients
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Gallstone disease is one of the most common complications among diabetic patients especially type 2 DM. Till now, there is no specific and certain factor that explain the incidence of gallstones among type 2 diabetic patients and many risk factors are taken collectively to estimate its intensity and severity compared to non diabetic counter parts. This clinical study was designed to evaluate and report the incidence and severity of gallstones among type 2 diabetics and non diabetics regarding certain factors. 20 diabetic females and 20 diabetic males were collected as patients′ group and have had gallstones while 20 females and 20 males who have had gallstones without diabetes mellitus type 2 were collected as controls′ group

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Publication Date
Wed Feb 01 2023
Journal Name
Baghdad Science Journal
Efficient Approach for Solving (2+1) D- Differential Equations
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     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

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Publication Date
Wed Dec 21 2016
Journal Name
Baghdad Science Journal
Synthesis, Spectral and Dyeing Performance Studies of 4-(2-Aminmo-5-nitro-phenylazo)-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one Complexes with Some Metal Ions
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The ligand 4-(2-aminmo-5-nitro-phenylazo)-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one derived from 4-aminoantipyrine and 4-nitroaniline was synthesized. The synthesized ligand was characterized by 1HNMR, FT-IR, UV-Vis spectra and (C.H.N) analysis. Complexes of (YIII and LaIII ) with the ligand were prepared in aqueous ethanol with a 1:2 M:L ratio and at optimum pH. The prepared complexes were characterized by using flame atomic absorption, FT-IR, UV-Vis spectra,(C.H.N) analysis and conductivity measurement. The stoichiometry of complexes was studied by the mole ratio and job methods. A concentration range (1×10-4 - 3×10-4 M) obeyed Beer's law, the complex solutions show high values of molar absorption. On the basis of physicochemical

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