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The Well-Posed Operators with Their Spectra in L^pw-Spaces

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Advances in Pure Mathematics 2023年第6期13卷 347-368页

作者： sobhy el-sayed ibrahim Faculty of Basic Education Department of Mathematics Public Authority of Applied Education and Training Kuwait Kuwait

In this paper, we have considered the general ordinary quasi-differential operators generated by a general quasi-differential expression τp,q in Lpw-spaces of order n with complex coefficients and its formal adjoint τ+q',p' in Lpw-spaces for arbitrary p,q∈[1,∞). We have proved in the case of one singular end-point that all well-posed extensions of the minimal operator T0 (τp,q) generated by such expression τp,q and their formal adjoint on the interval [a,b) with maximal deficiency indices have resolvents which are Hilbert-Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions can be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while others are new.

关键词： Quasi-Differential Expressions Regular and Singular Endpoints Minimal and Maximal Operators Regularly Solvable Operators Well-Posed Operators Deficiency Indices

On the Spectra of General Ordinary Quasi-Differential Operators and Their L²_w-Solutions

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Advances in Pure Mathematics 2022年第3期12卷 186-205页

作者： sobhy el-sayed ibrahim Department of Mathematics Faculty of Basic Education Public Authority of Applied Education and Training Kuwait City Kuwait

In this paper, we consider the general ordinary quasi-differential expression τ of order n with complex coefficients and its formal adjoint τ+ on the interval [a,b). We shall show in the case of one singular end-point and under suitable conditions that all solutions of a general ordinary quasi-differential equation are in the weighted Hilbert space provided that all solutions of the equations and its adjoint are in . Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions may be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while the others are new.

关键词： General Ordinary Quasi-Differential Expressions Regular and Singular End-Points Singular Differential Operators Essential Spectra Point Spectra and Regularity Fields

The Products of Regularly Solvable Operators with Their Spectra in Direct Sum Spaces

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Advances in Pure Mathematics 2013年第4期3卷 415-429页

作者： sobhy el-sayed ibrahim Department of Mathematics Faculty of Science Benha University Benha Egypt

In this paper, we consider the general quasi-differential expressions each of order n with complex coefficients and their formal adjoints on the interval (a,b). It is shown in direct sum spaces of functions defined on each of the separate intervals with the cases of one and two singular end-points and when all solutions of the equation and its adjoint are in (the limit circle case) that all well-posed extensions of the minimal operator have resolvents which are HilbertSchmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. These results extend those of formally symmetric expression studied in [1-10] and those of general quasi-differential expressions in [11-19].

关键词： Product of Quasi-Differential Expressions Regular and Singular Endpoints Regularly Solvable Operators Essential Spectra Hilbert-Schmidt Integral Operators

On the Product of Integro Differential Equations and Their Solutions in Direct Sum Spaces

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Journal of Mathematics and System Science 2013年第5期3卷 231-245页

作者： sobhy el-sayed ibrahim College of Basic Education Department of Mathematics Al-Ardiya area Kuwait

In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.

关键词： Quasi-integro differential equation product differential expressions direct sum spaces bounded and square integrablesolutions.

Facile synthesis of graphene anchored rare earth doped mixed metal ferrite nanorods:A potential candidate for azo dye mineralization

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Journal of Rare Earths 2024年第5期42卷 907-916,I0004页

作者： Tehmina Kousar Muhammad Aadil Sonia Zulfiqar sobhy Mibrahim Sidra Mubeen Warda Hassan Kashuf Shafiq Farzana Mahmood Institute of Chemical Sciences Bahauddin Zakariya UniversityMultan60800Pakistan Department of Chemistry Rahim Yar Khan CampusThe Islarnia University of BahawalpurRahim Yar Khan64200Pakistan Department of Chemistry Faculty of ScienceUniversity of Ostrava30.Dubna 22Ostrava70103Czech Republic Department of Chemical and Biological Engineering Iowa State UniversitySweeney Hall618 Bissell RoadAmeslowa50011United States Department of Biochemistry College of ScienceKing Saud UniversityPO.Box 2455Riyadh11451Saudi Arabi Department of Chemistry The Women University Multan66000Pakistan

Bandgap tuning using rare earth metals as dopants in ferrite-based photocatalytic materials has received a lot of interest because the Fermi 4f energy of these metals generates a sub-energy state in the bandgap generated by the overlapping of Fe-3d and O-2p ***,dysprosium-doped cobalt-nickel mixed ferrite(D-CNFO)and its graphene-reinforced composite(D-CNFO@G)were prepared and an ideal photocatalyst material for azo dye mineralization was proposed.A cost-effective combination of wetchemical and ultrasonication methods was used to prepare the doped and composite *** characterization methodologies were used to scrutinize the optical,compositional,structural,morphological,and photocatalytic characteristics of as-prepared *** X-ray diffraction analysis identified the spinel phase's(cubic)structure,while the electronic spectroscopy examination confirmed the prepared samples'rod-like *** UV/visible absorbance spectrum shows the higher light harvesting behavior of the D-CNFO@G in the visible *** mineralization performance of the DCNFO and D-CNFO@G composites was analyzed using Congo-red(an anionic dye),a well-known azo *** D-CNFO@G sample removes Congo-red dye at a rate almost 2.4%faster than the D-CNFO *** experiment involving trapping free radicals indicates that hydroxyl radical play s a crucial role in dye *** the D-CNFO@G catalyst is magnetic and can be isolated easily from the photocatalytic system,it shows an awkward cycle activity of more than 96%after five mineralization *** asprepared D-CNFO@G composite is proved as an excellent option for azo dye mineralization because of the combined impacts of rare earth doping,graphene reinforcement and nanotechnology.

关键词： azo-dye Composite Graphene Dy-doped Nanotechnology Rare earths

Transient elastography and diffusion-weighted magnetic resonance imaging for assessment of liver fibrosis in children with chronic hepatitis C

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World Journal of Virology 2024年第3期13卷 89-97页

作者： Mohamed A el-Guindi Alif A Allam Ahmed A Abdel-Razek Gihan A sobhy Menan E Salem Mohamed A Abd-Allah Mostafa M Sira Pediatric Hepatology Gastroenterology and NutritionNational Liver InstituteMenoufia UniversityShebin El-Koom 32511MenoufiaEgypt Department of Diagnostic Radiology Mansoura Faculty MedicineMansoura 13551Egypt

BACKGROUND Chronic hepatitis C(CHC)is a health burden with consequent morbidity and *** biopsy is the gold standard for evaluating fibrosis and assessing disease severity and prognostic purposes *** altern-atives for liver biopsy such as transient elastography(TE)and diffusion-weighted magnetic resonance imaging(DW-MRI)are critical *** To evaluate TE and DW-MRI as noninvasive tools for predicting liver fibrosis in children with *** This prospective cross-sectional study initially recruited 100 children with CHC virus ***-four children completed the full set of investigations including liver stiffness measurement(LSM)using TE and measurement of apparent diffusion coefficient(ADC)of the liver and spleen using *** biopsies were evaluated for fibrosis using Ishak scoring *** and liver and spleen ADC were compared in different fibrosis stages and correlation analysis was performed with histopathological findings and other laboratory *** Most patients had moderate fibrosis(73.5%)while 26.5%had mild *** had severe fibrosis or *** majority(68.8%)had mild activity,while only 7.8%had moderate *** scores had a significant direct correlation with LSM(P=0.008)and were negatively correlated with both liver and spleen ADC but with no statistical significance(P=0.086 and P=0.145,respectively).Similarly,histopatho-logical activity correlated significantly with LSM(P=0.002)but not with liver or spleen ADC(P=0.84 and 0.98 respectively).LSM and liver ADC were able to significantly discriminate F3 from lower fibrosis stages(area under the curve=0.700 and 0.747,respectively)with a better performance of liver *** TE and liver ADC were helpful in predicting significant fibrosis in children with chronic hepatitis C virus infection with a better performance of liver ADC.

关键词： Apparent diffusion coefficient Chronic hepatitis C Diffusion-weighted magnetic resonance imaging Liver fibrosis Liver stiffness Transient elastography

Ameliorative effect of Morus alba leaves extract against developmental retinopathy in pups of diabetic and aluminum intoxicated pregnant albino rats

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Asian Pacific Journal of Tropical Biomedicine 2015年第4期5卷 300-309页

作者： Hassan el-Sayyed Gamal Badawy sobhy Hassab elnabi ibrahim el-elaimy Eman Al Shehari Department of Zoology Faculty of Science Mansoura University Department of Zoology Faculty of Science Menoufiya University

Objective: To investigate the possible ameliorative effect of crude water extract of Morus alba(M. alba) leaves on retinopathy of rat pups maternally subjected to diabetes and/or Al ***: Both control and experimental groups were subjected to certain integrated approaches, namely, biochemical assessments, light microscopic investigation, transmission electron microscopic investigation, single cell gel electrophoresis(comet assay) and determination of DNA ***: The retina of pups of diabetic and/or Al-intoxicated mothers exhibited abnormal alterations in retinal cell layers including retinal pigmented epithelium, photoreceptor inner segment and ganglion cells. Increased incidence of DNA fragmentation and apoptosis were evident in pups of diabetic and/or Al-intoxicated mothers. However, retina of pups maternally received M. alba extract plus diabetes or Al-intoxicated alone or in combination showed marked amelioration. Less degree of ameliorations was seen in retina of pups maternally subjected to combined treatment. Furthermore, application of crude water extract of *** resulted in amelioration of the alterations of maternal serum glucose as well as Al ***: Based on the results of the present study, M. alba extract is effective against experimentally diabetic and Al-induced developmental retinopathy.

关键词： Morus alba Retinopathy Aluminum Diabetes TEM Comet assay

Prying Force Assessment Using Nonlinear Finite element Model

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Journal of Civil Engineering and Architecture 2010年第7期4卷 56-65页

作者： Hesham sobhy sayed Mohammed Hassanien Serror Department of Structural Engineering Faculty of Engineering Cairo University Giza Egypt

Steel connection design using pre-tensioned bolts depends significantly on the value of the Prying forces exerted from the end plate. The Egyptian Code ECP （205） suggested a formula that can determine the Prying force value. In this research, the Prying force is numerically computed in a T-Stub connection using nonlinear finite element techniques. The model uses plane stress four node elements with two degrees of freedom per node to simulate the flange of the T-Stub. The bolts are simulated using a truss element with large deformation capability to allow modeling of the pretension force. Surface to surface gap elements are used in order to simulate the contact between the T-Stub and the supporting element. Parametric study on the end plate thickness, bolt size, bolt arrangement and pretension forces is performed in order to calibrate the Code formula. The parametric study covers all the practical ranges of the variables. The study revealed that the Code formula, inaccurately, determines the Prying force in a certain range. Moreover, a new equation for the prying force is developed using regression analysis on the finite element results.

关键词： Prying force finite element regression analysis new equation code requirements

Development of Primary Percutaneous Coronary Intervention as a National Reperfusion Strategy for Patients with ST-elevation Myocardial Infarction and Assessment of Its Use in Egypt

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Cardiovascular Innovations and Applications 2020年第2期4卷 269-278页

作者： Mohamed sobhy Ahmed elshal Noha Ghanem Hosam Hasan-Ali Nabil Farag Nireen Okasha el sayed Farag Mohamed Sadaka Hisham Abo el Enein Sameh Salama Hazem Khamis Khaled Shokry Hany Ragy Amany elshorbagy Radwa Mehanna Cardiology Department Faculty of MedicineAlexandria University HospitalAlexandriaEgypt International Center for Organization and Marketing AlexandriaEgypt Cardiology Department Faculty of Medicine Assiut University HospitalAssiut GovernorateEgypt Cardiology Department Faculty of Medicine Ain Shams University HospitalHeliopolisEgypt Cardiology Department Nasser InstituteCairoEgypt Cardiology Department Faculty of MedicineZagazig University HospitalZagazigEgypt Cardiology Department Faculty of MedicineBanha University HospitalBanhaEgypt Cardiology Department Faculty of MedicineKasr El Ainy HospitalKasr Al AinyEgypt Cardiology Department Wady El Nile HospitalZeitounEgypt Cardiology Department Military HospitalHeliopolisCairoEgypt Cardiology Department National Heart InstituteHeliopolisCairoEgypt Physiology Department Faculty of MedicineAlexandria UniversityAlexandriaEgypt

Objective:Early treatment of acute ischemia of the heart by performing immediate percutaneous coronary intervention(PCI)to restore blood fl ow in patients with the clinical presentation of an acute coronary syndrome and more specifi cally with ST-elevation myocardial infarction(STEMI)can save *** study aims to identify the mean time(door to balloon time and fi rst contact to balloon time)to primary PCI for STEMI patients and to assess the percentage of primary PCI and its success rate in ***:A registry study of patients presenting to cardiac centers in Egypt was designed,where patients’basic characteristics,the treatment strategy,and the door to balloon time and the fi rst contact to balloon time were ***:One thousand six hundred fi fty STEMI patients with a mean age of 57 years were included in the *** transfer for primary PCI was the most used treatment strategy,representing 74.6%of all treatment strategies *** door to balloon time and the fi rst contact to balloon time were 50 and 60 minutes,respectively,with a primary PCI success rate of 65.1%.Conclusion:The registry study results showed a marked improvement by implementation of the best treatment strategy with respect to the time factor to achieve a better outcome for STEMI patients in Egypt.

关键词： ST-elevation myocardial infarction primary percutaneous coronary intervention door to balloon time fi rst medical contact to balloon time