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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 May 01 2019
Journal Name
Research Journal Of Chemistry And Environment
Synthesis and Characterization of New Complexes of 2- (Benzo[d]Thiazol-2-ylAmino)-2-(5-Chloro-2-Hydroxy Phenyl) Acetonitrile Ligand with Some Divalent Transition Metal Ions
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A series of metal ion complexes of some divalent transition metal ions having the general composition [ML2Cl2]nH2O with 2-(benzo[d]thiazol-2-ylamino)-2- (5-chloro-2-hydroxy phenyl) acetonitrile ligand has been prepared from 5-chloro-2-hydroxy-benzaldehyde and benzo[d]thiazol-2-amine. Existence of cyanide as potassium cyanide in acidic medium was considered, characterized by elemental chemical analysis, conductance of molarity, magnetic susceptibility measurements, FTIR electronic spectral studies and mole ratio method. FTIR indicates the participation of amino and acetonitrile nitrogen which is coordinated with the central metal ion.

Publication Date
Fri Jan 03 2020
Journal Name
Chalcogenide Letters
THE EFFECT OF Ag CONTENT AND HEAT TREATMENT ON STRUCTURAL AND MORPHOLOGICAL PROPERTIES OF THIN (Cu1-xAgx)2 ZnSnSe4 FILMS
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(Cu1-x,Agx)2ZnSnSe4 alloys have been fabricated with different Ag content(x=0, 0.1, and 0.2) successfully from their elements. Thin films of these alloys have been deposited on coring glass substrate at room temperature by thermal evaporation technique under vacuum of 10-5Torr with thickness of 800nm and deposition rate of 0.53 nm/sec. Later, films have been annealed in vacuum at (373, and 473)K, for one hour. The crystal structure of fabricated alloys and as deposited thin films had been examined by XRD analysis, which confirms the formation of tetragonal phase in [112] direction, and no secondary phases are founded. The shifting of main polycrystalline peak (112) to lower Bragg’s angle as compared to Cu2ZnSnSe4 angle refers to incorpora

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Publication Date
Fri May 31 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Fibrewise locally micro sliceable and fibrewise locally micro-section able micro-topological space
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The primary objective of this research be to develop a novel thought of fibrewise micro—topological spaces over B. We present the notions from fibrewise micro closed, fibrewise micro open, fibrewise locally micro sliceable, and fibrewise locally micro-section able micro topological spaces over B. Moreover, we define these concepts and back them up with proof and some micro topological characteristics connected to these ideas, including studies and fibrewise locally micro sliceable and fibrewise locally micro-section able micro topological spaces, making it ideal for applications where high-performance processing is needed. This paper will explore the features and benefits of fibrewise locally micro-sliceable and fibrewise locally

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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space
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      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

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Publication Date
Tue Nov 03 2015
Journal Name
Journal Of Natural Sciences Research
Implementation of remote sensing for vegetation studying using vegetation indices and automatic feature space plot
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Publication Date
Sun Dec 25 2022
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Epicatechin product of Camellia sinensis leaves detection by thin layer chromatography and high performance liquid chromatography
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The current study performed in order to detect and quantify epicatechin in two tea samples of Camellia sinensis (black and green tea) by thin layer chromatography (TLC) and high performance liquid chromatography (HPLC). Extraction of epicatechin from black and green tea was done by using two different methods: maceration (cold extraction method) and decoction (hot extraction method). Qualitative and quantitative determinations of epicatechin in two tea samples were investigated. Epicatechin identification was made by utilizing preliminary chemical tests and TLC. This identification was also boosted by HPLC and then quantified epicatechin in all ethyl acetate fractions of two tea samples. This research revealed the existence of epica

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Publication Date
Thu Aug 02 2018
Journal Name
Association Of Arab Universities Journal Of Engineering Sciences
Performance Study for Mixed Transforms Generated by Tensor Product in Image Compression and Processing
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In all applications and specially in real time applications, image processing and compression plays in modern life a very important part in both storage and transmission over internet for example, but finding orthogonal matrices as a filter or transform in different sizes is very complex and importance to using in different applications like image processing and communications systems, at present, new method to find orthogonal matrices as transform filter then used for Mixed Transforms Generated by using a technique so-called Tensor Product based for Data Processing, these techniques are developed and utilized. Our aims at this paper are to evaluate and analyze this new mixed technique in Image Compression using the Discrete Wavelet Transfo

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Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
The substitutions of Strontium by yttrium and their effects on Bi<sub>2</sub>Sr<sub>2</sub>-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10</sub>+<sub>δ</sub> superconducting compound
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Abstract<p>Superconducting compound Bi<sub>2</sub>Sr2-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> were Synthesized by method of solid state reaction, at 1033 K for 160 hours temperature of the sintering at normal atmospheric pressure where substitutions Yttrium oxide with Strontium. When Y2O3 concentration (0.0, 0.1, 0.2, 0.3, 0.4 and 0.5). All specimens of Bi<sub>2</sub>Sr<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconducting compounds were examined. The resistivity of electrical was checked by the four point probe technique, It was found th</p> ... Show More
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Publication Date
Wed May 01 2024
Journal Name
Biology
Lysophosphatidylcholine Acetyltransferase 2 (LPCAT2) Influences the Gene Expression of the Lipopolysaccharide Receptor Complex in Infected RAW264.7 Macrophages, Depending on the E. coli Lipopolysaccharide Serotype
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Escherichia coli (E. coli) is a frequent gram-negative bacterium that causes nosocomial infections, affecting more than 100 million patients annually worldwide. Bacterial lipopolysaccharide (LPS) from E. coli binds to toll-like receptor 4 (TLR4) and its co-receptor’s cluster of differentiation protein 14 (CD14) and myeloid differentiation factor 2 (MD2), collectively known as the LPS receptor complex. LPCAT2 participates in lipid-raft assembly by phospholipid remodelling. Previous research has proven that LPCAT2 co-localises in lipid rafts with TLR4 and regulates macrophage inflammatory response. However, no published evidence exists of the influence of LPCAT2 on the gene expression of the LPS receptor complex induced by smooth or rough b

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Publication Date
Mon Apr 01 2024
Journal Name
Indonesian Journal Of Chemistry
Synthesis, Structure and Biological Activity Studies of New Metal Ion Complexes Based on 3-[(3-Hydroxynaphthalene-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one
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In the present study, a novel ligand (L) made of 2-hydroxynaphthaldehyde and 3-hydrazone-1,3-dihydro-indole-2-one(3-[(3-hydroxynaphthalen-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one). The ligand was characterized by FTIR, UV-vis, mass, 1H-NMR, 13C-NMR, and CHN elemental analysis. New complexes of this ligand were created by treating methanol and a drop of DMF solution of the produced ligand with the hydrated metal salts of Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) in a molar ratio of 2:1 (L:M). As a result, complexes have been emerged and identified FTIR, UV-vis, C.H.N., chloride-containing, molar conductance, magnetic susceptibility, and atomic absorption. The characterization result for each complex indicated complexes wi

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