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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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Mon Jul 01 2013
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Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
ON THE OCCURRENCE OF THE[ MONOGENEAN GYRODACTYLUS TAIMENI ERGENS, 1971 FOR THE FIRST TIME IN IRAQ ON GILLS OF THE COMMON CARP CYPRINUS CARPIO
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The monogenean Gyrodactylus taimeni Ergens, 1971 was recorded in this study for the first time in Iraq from gills of the common carp Cyprinus carpio Linnaeus, 1758. The description and measurements of this parasite as well as illustration were given. In addition, a list of species of Gyrodactylus so far recorded from C. carpio in Iraq is also included together with a list of all other hosts recorded for each gyrodactylid species.

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Sat Apr 01 2023
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Journal Of Legal, Ethical And Regulatory Issues
THE IMPACT OF THE ROLE OF THE ORTHODOX CHURCH ON THE POLITICS OF THE RUSSIAN FEDERATION
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The research tackles the nature of relationship between the Orthodox Church and the state in the Russian Federation. At the beginning of the nineties of the last century, the church had been performed a different role in its relationship with the state, and it had an effect over the internal and foreign policies for the Russian Federation. In political history of Russia, the church’s existence became an evident too much in comparing with the previous historical period, starting with the educational and political system, whether through a symbolic participating roles as what happened in the inauguration ceremony to take over responsibility of the head of state or taking actual roles such as influencing on the process of holding elections d

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The Impact of the Internationalization of the Libyan Crisis on the Future of the Political Settlement
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The internationalization of the Libyan crisis and its accompanying militarization of the conflict have played a vital role in hindering to reach a comprehensive political settlement solution in Libya. The increasing international greediness in the Libyan energy resources and the geopolitical importance of the Libyan State led to the involvement of many international and regional powers in this crisis and transformed the Libyan crisis into “proxy war”.  Moreover, the Turkish direct military intervention in the Libyan crisis is considered as one of the main constraints facing the international and regional efforts to settle the Libyan crisis as a result of the Turkish insistence on its military existence in Libya to preserve i

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Publication Date
Sun Feb 03 2019
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Journal Of Accounting And Financial Studies ( Jafs )
The effect of the Banking Capital on Finance Fixed Assets of the Bank: An Applied Study on a Sample of Iraqi Private Banks
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To the Banks capital several uses, including the protection of deposits and this was approved by the Basel Committee, And Finance long-term investments which intended to investment in fixed assets that are essential to the continuation of banking activity, Fixed assets not financed from the funds of the deposit, but the owner equity do this jop. the current research tries to prove the effect of banks capital on fixed assets for a sample of iraqi private banks (bank of baghdad and Iraqi middle east Investment bank), for the period from 2011 until 2014. The research concluded that the capital of bank of baghdad affect on his total fixed assets by (84%), and the capital of Iraqi middle east Investment bank affect on his total fixed assets b

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Evaluation and production of predictive maps on the impact of climate factors on the the land cover for the Baghdad city for the period (1999-2021)
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The general objective of the research is to better understand changes in land cover and their impact on climatic factors by measuring changes in land cover for the Baghdad city for the period 1999-2021 and evaluating changes in land cover and measuring changes in climatic factors (relative humidity and evaporation). This study from 1999 to 2021 and in two different seasons: the April of the growing season and August the dry season. When using the supervised classification method to determine the differences, the results showed remarkable changes, the study showed the spatial variations in LC from 1999 to 2021 as follows: increase in the vegetation and water bodies during April and decrease this in August while the soil and built up decreas

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Synthesis of Some Mixed ligands Complexes of (2-hydroxy benzaldine)-4-amino Antipyrine and 1,10-phenanthroline and Studying their antibacterial activity
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Complexes from the ligand (2-hydroxy benzaldine)-4-aminoantipyrine with some transition metal ions V(l?),Cr(lll),Fe(lll) and Co(ll) were prepared in the presence of the co-ligand 1,10-phenanthroline in alcoholic medium. These compounds were characterized by the available techniques: FT-IR ,UV-Visible ,magnetic susceptibility, Flame atomic absorption technique as well as elemental analysis and conductivity mesurments .From these spectral studies, a square pyramidal structure proposed for V(IV) complex and an octahedral geometry for Cr(III),Fe(III) and Co(II) complexes. The biological activity of the ligands and their complexes were evaluated by a gar plate diffusion technique against three human pathogenic bacterial strains: Pseudomonas ae

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Synthesis and Spectroscopic Studies of some Divalent Metall Ion Complexes of 3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid
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Synthesis and Spectroscopic Studies of some Divalent Metall Ion Complexes of 3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid
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3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid (HNP) a new ligand was synthesized by reaction of Tyrosine with (4-Nitrobenzoyl isothiocyanate) by using acetone as a solvent. The prepared ligand (HNP) has been characterized by elemental analysis (CHNS), infrared (FT-IR), electronic spectral (Ultraviolet visible) and(1H,13C-Nuclear Magnetic Resonance) spectra. Some Divalent metal ion complexes of (HNP) were prepared and spectroscopic studies by Fourier transform infrared (FTIR), electronic spectral(UV-Vis), molar conductance, magnetic susceptibility and atomic absorption. The results measured showed the formula of six prepared complexes were [M (HNP)2] (M+2 = Manganese, Cobalt, Nickel, Znic, Cadmium and Mercury),from the

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Evaluation of Interleukin-18 Serum Concentration and Gene Polymorphism (Rs1946518) in A Sample of Type-2 Diabetes Mellitus Patients from Iraq.
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Background Type two diabetes (T2DM) is characterized by insufficient insulin production and secretion. Additionally, the body develops insulin resistance which affects 90–95% of diabetics. Complex cytokines, receptors, genetic pathways, and the immune system are involved in T2DM. Interleukin-18 (IL-18) is one of the inflammatory cytokines associated with Type 2 diabetes. Environmental and genetic variables, including genetic polymorphisms, can increase T2DM risk and its consequences. Single nucleotide gene polymorphisms (SNPs) are important risk factors for diabetes that can be used to find the disease early and treat it better. Objective This study aimed to determine the levels of IL-18 in the serum of Iraqi patients with Type 2 diabetes

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Radiation shielding properties of Cd-Bi-Pb-Zn-borate glasses: influence of Bi<sub>2</sub>O<sub>3</sub> activation
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Abstract<p>We report the detail characterizations and <italic>γ</italic>-radiation protecting characteristics of some new types of cadmium (Cd)-bismuth (Bi)-lead (Pb)-zinc (Zn)-borate glasses of the form (70-x)B<sub>2</sub>O<sub>3</sub>-10ZnO-10PbO-10CdO-xBi<sub>2</sub>O<sub>3</sub> (with x = 0 to 20 mol%) synthesized via melt-quenching process. The influence of various Bi<sub>2</sub>O<sub>3</sub> contents on the <italic>γ</italic>-radiation shielding traits of the obtained glass samples was evaluated by exposing them at different <italic>γ</italic>-ray energies (0.356, 0.662, 1.173, and 1.33 MeV) whic</p> ... Show More
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