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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 Jan 01 2025
Journal Name
Medical Journal Of Babylon
Study Effect of Periostin Level in Obese Iraqi Females Patients with Type 2 Diabetes Mellitus
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Abstract<sec> <title>Background:

Obesity has been connected to a higher risk of acquiring a number of diseases, including cancer, type 2 diabetes mellitus (T2DM), hypertension, and cardiovascular disease. Periostin is a crucial regulator of the growth and maintenance of bones, teeth, and the heart.

Objectives:

The aim of the study was to estimate the level of (periostin, glycated hemoglobin [HbA1c], fasting serum [FBG], total cholesterol [TC], high-density lipoprotein [HDL], low-density lipoprotein [LDL], and triglycerides [TG]) in diabetic Ira

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
SYNTHESIS AND ANTIMICROBIAL ACTIVITY OF SOME (2-AMINO-5-THIOL-1, 3, 4-THIADIAZOLE DERIVATIVES
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Five derivatives of thiadiazole were prepared with aldehydes and alkyl halides, compoundA: 2-amino-5-thiol-1,3,4- thiadiazole, compound B :2-(o-hydroxybenzylidine)amino-5-thiol-1,3,4-thiadiazole, compoundC: 2(2-butan-lidine)amino-5-thiol-1,3,4-thiadiazole, compound E: 2- amino-5-(2-Propanylthio)-1,3,4-thiadiazol) and compound F:2(o-chlorobenzylamino)-5-(2-propanyl thio)-1,3,4 thiadiazol. All prepared compounds were diagnosed by (IR) and (UV) Spectroscopy. All of those compounds were screened for their anti-microbial activity in vitro. The results show that most of the compounds A, B, C exhibited moderate to good activity against Gram-positive bacteria and the same compound exhibit low to moderate activity on most gram-negative bacte

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Publication Date
Mon Oct 01 2018
Journal Name
Data In Brief
Chemical and structural data of (1, 2, 3-triazol-4-yl) pyridine-containing coordination compounds
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The data presented in this paper are related to the research article entitled “Novel dichloro(bis{2-[1-(4-methylphenyl)-1H-1,2,3-triazol-4-yl-κN3 ]pyridine-κN})metal(II) coordination compounds of seven transition metals (Mn, Fe, Co, Ni, Cu, Zn and Cd)” (Conradie et al., 2018) [1]. This paper presents characterization and structural data of the 2-(1-(4-methyl-phenyl)-1H-1,2,3-triazol-1-yl)pyridine ligand (L2 ) (Tawfiq et al., 2014) [2] as well as seven dichloro(bis{2- [1-(4-methylphenyl)-1H-1,2,3-triazol-4-yl-κN3 ]pyridine-κN})metal (II) coordination compounds, [M(L2 )2Cl2], all containing the same ligand but coordinated to different metal ions. The data illustrate the shift in IR, UV/VIS, and NMR (for diamagnetic complexes) peaks wh

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Publication Date
Tue Jun 30 2015
Journal Name
Al-kindy College Medical Journal
Evidence Based Updating of HbA1c Targets: Global Guidelines forGlycemic Control in Type 2 Diabetes Mellitus
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Background:Measurement of hemoglobin A1c (A1C) is a renowned tactic for gauging long-term glycemic control, and exemplifies an outstanding influence to the quality of care in diabetic patients.The concept of targets is open to criticism; they may be unattainable, or limit what could be attained, and in addition they may be economically difficult to attain. However, without some form of targeted control of an asymptomatic condition it becomes difficult to promote care at allObjectives: The present article aims to address the most recent evidence-based global guidelines of A1C targets intended for glycemic control in Type 2 Diabetes Mellitus (T2D).Key messages:Rationale for Treatment Targets of A1C includesevidence for microvascular and ma

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Publication Date
Sat Sep 01 2018
Journal Name
Polyhedron
Novel dichloro (bis {2-[1-(4-methylphenyl)-1H-1, 2, 3-triazol-4-yl-κN3] pyridine-κN}) metal (II) coordination compounds of seven transition metals (Mn, Fe, Co, Ni, Cu, Zn and Cd)
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Publication Date
Sat Jun 25 2022
Journal Name
International Journal Of Drug Delivery Technology
Assessment of Serum Levels of the WNT Pathway Antagonist (Dickkopf-1) in a Sample of Type 2 Diabetic Patients with Retinopathy using Two Groups of Antidiabetics
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Objectives: Dickkopf-1 (DKK-1) is WNT/b-catenin pathway antagonist which plays a detrimental role in the development of diabetic retinopathy (DR). This research aimed to assess serum DKK-1 levels in diabetic patients who have and have not developed DR and, compare them with the control subjects finding out whether we can use it as an indicator for DR early diagnosis and to find out which one of the widely used two groups of antidiabetic treatments had the greater effect on this biomarker and hence on the progression of DR. Methods: The study participants were divided into two subgroups: First, 70 patients (36 male, 34 female) with type 2 diabetes mellitus, among them 35 patients diagnosed with DR and 35 with no evidence of DR, and s

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Publication Date
Sun Jun 16 2019
Journal Name
Al–bahith Al–a'alami
News frames for the phenomenon of terrorism in international satellite channels directed in Arabic An analytical study of the main news bulletins in the Russian channel today 1/2/31/5/2018
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International satellite channels in Arabic are targeted to the region with their news bulletins and their innovative programs, attracting the interest of the Arab viewers in their news articles and programs with new ideas and methods as well as high technology in the production and synthesis of videos. Therefore, they work on framing the above, And the media policy that governs, so focused the problem of the study to try to answer the question of the President is how to frame the international satellite channels in Arabic to the phenomenon of terrorism? What are the aspects that are working to highlight and aspects that try to hide? The study adopted the survey methodology for the main news bulletins in the Russian channel today for the

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Publication Date
Wed Feb 01 2023
Journal Name
Baghdad Science Journal
Synthesis, Theoretical Study, and Biological Evaluation of Some Metal Ions with Ligand "Methyl -6-[2-(4-Hydroxyphenyl) -2-((1-Phenylethylidene) Amino) Acetamido] -2,2-Dimethyl-5—Oxo-1-Thia-4-Azabicyclo [3.2.0] Heptane-3-Carboxyylate
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Schiff base (methyl 6-(2- (4-hydroxyphenyl) -2- (1-phenyl ethyl ideneamino) acetamido) -3, 3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0] heptane-2-carboxylate)Co(II), Ni(II), Cu (II), Zn (II), and Hg(II)] ions were employed to make certain complexes. Metal analysis M percent, elemental chemical analysis (C.H.N.S), and other standard physico-chemical methods were used. Magnetic susceptibility, conductometric measurements, FT-IR and UV-visible Spectra were used to identified. Theoretical treatment of the generated complexes in the gas phase was performed using the (hyperchem-8.07) program for molecular mechanics and semi-empirical computations. The (PM3) approach was used to determine the heat of formation (ΔH˚f), binding energy (ΔEb

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Publication Date
Wed Feb 01 2023
Journal Name
Baghdad Science Journal
Synthesis, Theoretical Study, and Biological Evaluation of Some Metal Ions with Ligand "Methyl -6-[2-(4-Hydroxyphenyl) -2-((1-Phenylethylidene) Amino) Acetamido] -2,2-Dimethyl-5—Oxo-1-Thia-4-Azabicyclo [3.2.0] Heptane-3-Carboxyylate
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Schiff base (methyl 6-(2- (4-hydroxyphenyl) -2- (1-phenyl ethyl ideneamino) acetamido) -3, 3-dimethyl-7-oxo-4-thia-1-azabicyclo[3.2.0] heptane-2-carboxylate)Co(II), Ni(II), Cu (II), Zn (II), and Hg(II)] ions were employed to make certain complexes. Metal analysis M percent, elemental chemical analysis (C.H.N.S), and other standard physico-chemical methods were used. Magnetic susceptibility, conductometric measurements, FT-IR and UV-visible Spectra were used to identified. Theoretical treatment of the generated complexes in the gas phase was performed using the (hyperchem-8.07) program for molecular mechanics and semi-empirical computations. The (PM3) approach was used to determine the heat of formation (ΔH˚f), binding energy (ΔEb), an

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Publication Date
Mon Jan 17 2011
Journal Name
مجلة كلية التربية
Synthesis and Characterization of Complexes of [(N,N- -Bis(2- Hydroxy Ethyl) Glycine] with Some Metal Salts
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Some transition metal ions (Cr +3, Co+2 , Ni+2,Cu+2, Zn+2,Ag + ,Cd+2 ) complexes of [(N, N- - Bis(2- hydroxy ethyl) Glycine] (Bicine) have been synthesized and characterized by FTIR ,UV-Visble spectroscopy, atomic absorption, magnetic susceptibility, conductivity measurements and study of the nature of the complexes formed in ethanolic solution following the moleratio method. From the results obtained the following general formola have been given for the prepared complexes [M m+ (Bicine)n]. XH2O