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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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AN EXPERIMENTAL STUDY OF THE EFFECT OF VORTEX GENERATOR ON THE FLAT-PLATE BOUNDARY LAYER: AN EXPERIMENTAL STUDY OF THE EFFECT OF VORTEX GENERATOR ON THE FLAT-PLATE BOUNDARY LAYER
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This paper is dealing with an experimental study to show the influence of the geometric characteristics of the vortex generators VG son the thickness of the boundary layer (∂) and drag coefficients (CD) of the flat plate. Vortex generators work effectively on medium and high angles of attack, since they are "hidden" under the boundary layer and practically ineffective at low angles.

            The height of VGs relative to the thickness of the boundary layer enables us to study the efficacy of VGs in delaying boundary layer separation. The distance between two VGs also has an effect on the boundary layer if we take into

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Publication Date
Tue Nov 24 2015
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The Impact of External Environment Factors on the Quality of Educational Services (An Empirical Study): The Impact of External Environment Factors on the Quality of Educational Services (An Empirical Study)
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This research aims to identify the role of external environment factors on the quality of educational services, from the academic point of view, where the distribution of a questionnaire to a random sample of (100) university professors, and then analyzing a model, and test the validity of this model using structural modeling (SEM) (Structural Equation Modeling).
And then test the relationships between variables using the software of Statistical Package for Social Sciences (SPSS V.18), the research found a number of conclusions, the most important conclusion is: the external environment factors has significant impact on the quality of educational services.

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Publication Date
Thu Jan 26 2006
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(OC-6-13)-Bis[5-bromo-2-(4-bromo­phenyl­diazenyl)phen­yl]dicarbonyl­ruthenium(II) with mutually transN-donor atoms
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The title compound, [Ru(C12H7Br2N2)2(CO)2], possesses a distorted octa­hedral environment about the Ru atom, with two cyclo­metallated 4,4′-dibromo­azobenzene ligands and two mutually cis carbonyl ligands. The donor atoms are arranged such that the N atoms are mutually trans and the aryl C atoms are trans to carbonyl ligands.

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Synthesis and biological studies for some heterocyclic compounds derived from 2-Morpholino-1,8- naphthyridine-4-carboxylic acid
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New heterocyclic compounds derived from 2-Morpholino-1,8-naphthyridine-4-carboxylic acid such as oxadiazolo, thiadiazolo – thione and triazolo-thione have been prepared and characterized on the basis of IR and 1H NMR spectra data. The hydrizide compound was utilized as a starting material for preparing of these compounds. The second part of this study involves the biological studies of some of these naphthyridine derivatives by using three different kinds of bacteria namely: Staphylococcus aureus, Pseudomonas aeruglnosa and Escherichia coli. The data indicated that some of these compounds have a good activity against the tested bacteria in comparison to antibiotics.

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Thu Mar 30 2023
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Ultrafast lithium disilicate veneer debonding time assisted by a CO<sub>2</sub> laser with temperature control
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We report on using a CO2 (10.6 µm) laser to debond the lithium disilicate veneers. Sixty-four sound human premolar teeth and 64 veneer specimens were used in the study. The zigzag movement via CO2 laser handpiece along with an air-cooled jet to prevent temperature elevation above the necrosis temperature limit (5.5 C°) was applied. The optimal deboning irradiation time was super-fast, at about 5 seconds at 3 Watt CO2 laser power. It is 20 times less than any previously published work for veneers debonding. The enamel beneath the debonded veneers has been assessed by atomic force microscopy (AFM) and shear stress technique as criteria for the easiness of debonding. The

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Relation between Serum Leptin, Lipid Profiles and other biomarkers levels in patients with type 2 diabetic nephropathy
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Background: In advanced diabetes mellitus, serum levels of the most hormones are altered due to several interplaying mechanisms. Objective: To assess the relation of serum leptin and lipid profile in type 2 diabetic nephropathy. Patients and Method: Serum leptin levels and its relation to lipid profile were estimated in 62 patients with type 2 diabetic nephropathy attending the National Diabetes Center in Al- Mustansiriya University, and (26) healthy individuals considered as control group. The diabetic patients were classified into three groups, (24) pathients with normoalbuminuria (21) patients with microalbuminuria and (17) patients with macroalbuminuria. Fasting plasma glucose, serum creatinine, Hb A1c %, lipid profile (Total c

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Association between Serum Leptin Level and Insulin Resistance in Acromegalic Iraqi Patients with Type 2 Diabetes Mellitus
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SYNTHESIS, SPECTROSCOPIC, CHARACTERIZATION AND BIOLOGICAL STUDIES FOR NEW COMPLEXES WITH N1, N5-BIS (3-HYDROXYPHENYL)- 2-OXOPENTANEDIAMIDE
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New complexes have been prepared from the new ligand [N1,N5-bis(3-hydroxyphenyl)-2- oxopentanediamide] derived from 2-Oxoglutaric acid and 3-aminophenol. Accordingly its binudear Mn(II),Co(II),Ni(II),Pd(II) and VO(II) complexes were prepared.. These compounds have been characterized by FT-IR, UV-Vis,Mass, 1H-NMR spectra, TGA curve, Chloride containing ,Molar conductance and atomic absorption. The characterization results gave binuclear complexes and pentadentate coordination and tetrahedral geometry for each Cobalt, Nickel, Manganese and Copper complexes otherwise Palladium complex gave a square planar geometry and Vanadium complex gave a square pyramidal geometry and the ligand is tetradentate. The biological activities for the new compoun

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Peer Support for Type 2 Diabetes Management in Low- and Middle-Income Countries (LMICs): A Scoping Review
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Background: Although there is evidence of peer support in high-income countries, the use of peer support as an intervention for cardiometabolic disease management, including type 2 diabetes (T2DM), in low- and middle-income countries (LMICs), is unclear. Methods: A scoping review methodology was used to search the databases MEDLINE, Embase, Emcare, PsycINFO, LILACS, CDSR, and CENTRAL. Results: Twenty-eight studies were included in this scoping review. Of these, 67% were developed in Asia, 22% in Africa, and 11% in the Americas. The definition of peer support varied; however, peer support offered a social and emotional dimension to help individuals cope with negative emotions and barriers while promoting disease management. Conclusio

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