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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
Sun Mar 18 2018
Journal Name
International Journal Of Pharmaceutical Quality Assurance
The Role of Soluble L-Selectin with Polymorphism in Iraqi Arabs Patients with Diabetes Mellitus Type 2
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Diabetes mellitus type 2 [DMT2] is a disturbance of metabolism and complex diseases influenced by environmental, genetic agents, and linked with inflammation, happens when the pancreas either does not use the insulin as it should or the body does not make enough insulin, lead to insulin resistance [IR] alongside with gradual loss of ß-cell secretory ability. The aim of this study was to investigate the role of soluble L-selectin (sL-selectin) in diabetes mellitus type 2 patients in Iraqi Arabs patient. Study includes seventy six Iraqi Arabs patients (male and female) having newly diagnosed type 2 diabetes mellitus (T2DM), with Fifty three Iraqi Arabs healthy subjects matched in age, sex and ethnic group. Patients and healthy subjec

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Publication Date
Fri Apr 01 2022
Journal Name
Baghdad Science Journal
The Cut-off Values of Triglycerides - Glucose Index for Metabolic Syndrome Associated with Type 2 Diabetes Mellitus
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       The co-occurrence of metabolic syndrome with type 2 diabetes mellitus (T2DM) will potentiate the morbidity and mortality that may be associated with each case. Fasting triglycerides-glucose index (TyG index) has been recommended as a useful marker to predict metabolic syndrome. Our study aimed to introduce gender-specific cut-off values of triglycerides- glucose index   for diagnosing metabolic syndrome associated with type 2 diabetes mellitus. The data were collected from Baghdad hospitals between May - December 2019. The number of eligible participants was 424. National cholesterol education program, Adult Treatment Panel III criteria were used to define metabolic syndrome. Measurement of fasting blood glucose, lipid pro

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Publication Date
Sun Sep 07 2008
Journal Name
Baghdad Science Journal
The antiviral activity of the compound chalcone (4-ethoxy-2-hydroxy-4, 6-dimethoxy-chalcone) against rubella virus in vitro
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The studies on the antiviral compound chalcone in vitro in both tissue and organ culture systems against rubella virus glass that this compound relatively non toxic to the cell culture and organ culture of the concentration of 8 ug/ml or less, chalcone have significantly antiviral activity against rubella virus in tissue culture and organ culture. We find that a concentration of 0.03ug/ml or more inhibit the IOOTCID50 of rubella virus. The therapeutic index (TI) used in this study to evaluate the drug, the (TI) which is the ratio of the dose of drug which is just toxic (Maximum tolerated dose) to the dose which is just effective (Minimum effective dose). If this index is one or less it not possible to use the drug under the conditions outli

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Publication Date
Thu Apr 01 2021
Journal Name
Biochem. Cell. Arch.
AGE AND GENDER IMPACT ON GLYCAEMIC CONTROL, RENAL FUNCTION AND OXIDATIVE STRESS PARAMETERS IN IRAQI PATIENTS TYPE 2 DIABETES MELLITUS
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Type 2 daibetes mellitus (T2DM) is a global concern boosted by both population growth and ageing, the majority of affected people are aged between (40- 59 year). The objective of this research was to estimate the impact of age and gender on glycaemic control parameters: Fasting blood glucose (FBC), glycated hemoglobin (HbA1C), insulin, insulin resistance (IR) and insulin sensitivity (IS), renal function parameters: urea, creatinine and oxidative stress parameters: total antioxidant capacity (TAC) and reactive oxygen species (ROS). Eighty-one random samples of T2DM patients (35 men and 46 women) were included in this study, their average age was 52.75±9.63 year. Current study found that FBG, HbA1C and IR were highly significant (P<0.01) inc

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Publication Date
Tue Jan 01 2013
Journal Name
Chemical And Process Engineering Research
Synthesis and Characterization of Complexes of Schiff Base [1, 2-Diphenyl -2- 2-{[1-(3-Amino-Phenyl)-Ethylidene]-Hydrazono Methyl}-Phenol] with Mn(II), Fe(II), Co(II), Cu(II), Zn(II), Cd(II), Ni(II), and Hg(II) Ions
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The new tridentate Schiff base ligand (HL)namely 2-{[1-(3-amino-phenyl)-ethylidene]-hydrazono methyl}- phenol containing (N N O)as donors atoms was prepared in two steps:Step (1): By the reaction of 3- aminoacetophenone with hydrazine monohydrate under reflux in methanol and drops of glacial acetic acid gave the intermediate compound 3-(1- hydrazono ethyl)-phenol amine.Step (2): By the reaction of 3-(1-hydrazono ethyl)-phenol amine with salicyaldehyde under reflux in methanol, gave the ligand (HL).The prepared ligand was characterized by I.R, U.V-Vis,1H- 13C NMR spectra and melting point and reacted with some metal ions under reflux in methanol with (1:1) ratio gave complexes of the general formula: [MClL]. Where: M= Mn(II), Fe(II), Co(II),

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Publication Date
Mon Aug 07 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Science
Synthesis and Characterization of Tetradentate Complexes Type N2O2 From the Reaction of 2-Hydroxy -1, 2-Diphynel-Ethanone Oxime [H2L] With Mn II, Fe II, Co II, Ni II, Cu II and Hg II Ions
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Tetradentate complexes type [M (HL) 2] were prepared from the reaction of 2-hydroxy -1, 2-diphynel-ethanone oxime [H2L] and KOH with ( Mn II, Fe II, Co II, Ni II , Cu II and Hg II ), in methanol with (2:1) metal: ligand ratio. The general formula for Cu II and Mn II complexes are [M (HL) 2 Cl.H2O] K, for Co II [Co (HL) 2. H2O] and [M (HL) 2] for the rest of complexes. All compounds were characterised by spectroscopic methods, I.R, U.V-Vis, H.P.L.C, atomic absorption and conductivity measurements chloride content. From the data of these measurements, the proposed molecular structures for Fe II and Hg II complexes are tetrahedrals, while Mn II and Cu II complexes are octahedrals, Ni II complex adopting square planar structure and the complex

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Publication Date
Sun Mar 01 2009
Journal Name
Journal Of The College Of Basic Education, Al-mustansiriyah University
Artin Exponent for the special linear group SL(2,pk)where pk = 9,25 and 27
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Publication Date
Tue Dec 26 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Belief about Medications Among Type 2 Diabetic Patients Attending the National Diabetes Center in Iraq.
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Diabetes mellitus is a common health problem worldwide counting about 1.2 million cases in Iraq in 2015. Taking in account of the patient’s beliefs about the prescribed medication had been reported to be one of the most important factors that affects adherence where holding positive beliefs about medications is a prerequisite for intentional adherence. The aim of the current study was to investigate and assess beliefs about medicines among type 2 diabetic patients and to determine possible association between this belief and glycemic control as well as some patient-specific factors. This study is a cross-sectional study carried out on 380 (mean age 56.58± 10.06 years) already diagnosed T2DM patients who attended the National Diabetes

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Publication Date
Wed Mar 29 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Correlation between Serum Total Adiponectin and Hemoglobin in Type 2 Diabetic Patients without Microalbuminuria
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Low serum total adiponectin is associated with a high incidence of type 2 diabetes or coronary artery disease in the general population. Paradoxically, serum total adiponectin is elevated in patients with chronic kidney disease (CKD), such as overt diabetic nephropathy. The current study aimed to investigate whether or not  anemia to be dependently associated with serum level of total adiponectin in  non-albuminuric male patients with type 2 diabetes . The study included 42 type 2 diabetic male patients. Anemia was defined as hemoglobin (Hb) below 14.0g/dL. All the patients were without microalbuminuria, to exclude diabetic nephropathy. The diabetic patients were divided into 2 groups according to the hemoglobin level in ad

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Publication Date
Tue Mar 30 2021
Journal Name
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Electrochemical Polymerization and Biological Activity of 4-(Nicotinamido)-4-Oxo-2-Butenoic Acid as An Anticorrosion Coating on A 316L Stainless Steel Surface
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In this study, poly4-(nicotinamido)-4-oxo-2-butenoic acid (PNOE) was prepared by the electro polymerization of 4-(nicotinamido)-4-oxo-2-butenoic acid (NOE) monomer on a 316 stainless steel (St.St) which acts as an anticorrosion coating.  Fourier transforms infrared (FTIR), atomic force microscopy (AFM), scanning electron microscopy (SEM), and cyclic voltammetry were used to diagnose the structure and the properties of the prepared polymer layer. The corrosion behavior of the uncoated and coated 316  St.St were evaluated by using an electro chemical polarization technique in 0.2 M hydrochloric acid  solution as a corrosive medium at a temperature range of 293 to 323 K. Nano materials, such as nano ZnO and graphene were added in di

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