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On the Cauchy Problem for Some Parabolic Partial Differential Equations with Time Delays
Mahmoudm El-Borai ...et al KYUNGPOOK UNIVERSITY 1997 Kyungpook mathematical journal Vol.37 No.1
The Cauchy problem for some parabolic partial differential equations of higher orders and with time delays is considered. The existence and uniqueness theorems of this problem is studied. Some smoothness properties with respect to the parameters of these delay partial differential equations are considered.
On the Asymptotic Behaviour of Some Nonlinear Parabolic Systems
Mahmoud M. El-Borai ...et al KYUNGPOOK UNIVERSITY 1997 Kyungpook mathematical journal Vol.37 No.1
We study the existence and uniqueness and asymptotic behaviour of the solutions of the Cauchy problem for some non-linear parabolic systems of the form. ◁수식삽입▷(원문을 참조하세요) x ∈ Rⁿ^(n) , u , f_(i) ∈ R^(υ) , i = 1, 2, 3, where Rⁿ is the n-dimensional Euclidean space and (A_(α), |α|≤ 2m) is a family of square matrices whose elements are suffciently smooth functions on Rⁿ ×[0, ∞). It is supposed that f₁(x, t, 0) = 0 and f₃(x, t, u) ≤Θ(t) for all x ∈ Rⁿ, t ∈ [0, ∞), |u| < M; whereΘ(t) ∈ L₁[0, ∞). The considered problem is solved under a suitable condition on f₂ by using Liapunov function.
ON A DISCUSSION OF NONLINEAR INTEGRAL EQUATIONOF TYPE VOLTERRA-HAMMERSTEIN
M. M. EL-Borai,M. A. Abdou,M. M. EL-Kojok 한국수학교육학회 2008 純粹 및 應用數學 Vol.15 No.1
Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Hammerstein. Also, the nor- mality and continuity of the integral operator are discussed. A numerical method is used to obtain a system of nonlinear integral equations in position. The solution is obtained, and many applications in one, two and three dimensionals are considered.
ON A DISCUSSION OF NONLINEAR INTEGRAL EQUATION OF TYPE VOLTERRA-FREDHOLM
M. M. EL-Borai,M. A. Abdou,M. M. EL-Kojok 한국산업응용수학회 2006 Journal of the Korean Society for Industrial and A Vol.10 No.2-1
Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Fredholm. Also, the normality and continuity of the integral operator are discussed. The solution is obtained, and many applications in one, two and three dimensionals are considered.
E. H. Borai,E. M. El Afifi,A. M. Shahr El-Din 한국화학공학회 2017 Korean Journal of Chemical Engineering Vol.34 No.4
This work is directed for removal of the nondesired species (228Ra, 226Ra, 223Ra, 210Pb, Th(IV) and Fe(III)) in the rare earth chloride (RECl3) liquor before separation of Ln(III). The different factors affecting elimination of radium-isotopes, lead (210Pb), Th(IV) and Fe(III) from the RECl3 liquor, have been investigated and optimized. The results indicated that the activity concentration of radionuclides in RECl3 liquor was above the safe limits required during the separation process of Ln(III). Adjustment of pH 3±0.1 leads to eliminate 14±1% of radionuclides and Th(IV), and 40±3% of Fe(III), while 12±1% of Ln(III) was lost. The developed method shows that more than 95% of the nondesired species was selectively removed when the liquor was eliminated by potassium sulfate or sulfuric acid solutions in presence of Ba/Pb-carrier (1 : 1). About 20-83% of Ln(III) was lost when the non-desired species removed by sodium or ammonium sulfate or potassium chromate solutions. Fe(III) interfered with Ln(III) when radionuclides and Th(IV) were eliminated by 2.6M H2SO4 in presence of Ba/Pb-carrier. Finally, use of 0.23M K2SO4 or 2.6M H2SO4 was efficient to reduce level of 228Ra, 226Ra, 223Ra and 210Pb to the safe limits in viewpoint of radiation protection. In addition, the interfered Th(IV) and Fe(III) were also eliminated efficiently from RECl3 liquor before the chemical processing of Ln(III).
Rizk, Hala F.,El-Badawi, Mahmoud A.,Ibrahim, Seham A.,El-Borai, Mohamed A. Korean Chemical Society 2010 대한화학회지 Vol.54 No.6
Coupling of 5-amino-1,3-diaryl-pyrazoles 1a-c with diazonium salts of different aryl amines gave a series of novel 1,3-diaryl-5-amino-4-arylazopyrazoles 3a-l. Such compounds could be also obtained by reaction of 5-amino-1,3-diaryl-4-nitroso- 1H-pyrazoles 2a-c with different aryl amines in alkaline medium. Oxidation of azo derivatives 3a-l with cupric acetate, in dimethyl formamide and stream of air, gave 2,4,6-triaryl-2,4-dihydropyrazolo [4,3-d]-1,2,3-triazoles 4a-l. and the fluorescence properties of the cyclic triazoles were studied. Diazotization of 5-amino-1,3-diaryl-1H-pyrazoles 1a-c by sodium nitrite in ortho-phosphoric acid followed by coupling with some aryl amines gave o-aminoazo compounds 5a-f. Cyclisation of compounds 5a-f in pyridine and cupric acetate gave the corresponding triazoles 6a-f. The coupling of compounds 6a-f with different aryl diazonium salts gave compounds 7a-j. The synthesized dyes were applied to polyesters as disperse dyes and the fastness properties were evaluated. 5-Amino-1,3-diaryl-pyrazoles 1a-c 와 다양한 aryl amine의diazonium salts를 반응시켜서 1,3-diaryl-5-amino-4-arylazopyrazoles 3a-l을 합성하였으며, 몇 가지 화합물은 5-amino-1,3-diaryl-4-nitroso-1H-pyrazoles 2a-c와 aryl amine의 diazonium salts를 반응시켜서 얻었다. 합성한 azo 유도체 화합물 3a-l을 DMF 용매 속에서 cupric acetate와 산화반응시켜서 2,4,6-triaryl-2,4-dihydropyrazolo [4,3-d]-1,2,3-triazoles 4a-l을 합성하였으며, 합성한 cyclic triazoles에 대한 형광 특성을 측정하였다. 한편, Diazotization of sodium nitrite/ortho-phosphoric acid 조건에서 5-amino-1,3-diaryl-1H-pyrazoles 1a-c를 diazotization화 반응시킨 다음에, aryl amines과 반응시켜서 o-aminoazo compounds 5a-f를 합성하였다. 합성한 화합물 5a-f를 pyridine/cupric acetate 반응 조건에서 반응시켜서 triazole 6a-f들을 합성하였으며, 얻어진 화합물 6a-f을 aryl diazonium salts과 반응시켜서 화합물 7a-j을 합성하였다. 합성한 염료 화합물을 polyesters에 분산염료와 정착성을 측정하였다.
Reduced Fertility and Fecundity among Patients with Bipolar I Disorder and Schizophrenia in Egypt
Hader Mansour,Kareem Kandil,Warda Fathi,Mai Elassy,Ibtihal Ibrahim,Hala Salah,Amal Yassin,Hanan Elsayed,Salwa Tobar,Hala El-Boraie,Ahmed Eissa,Mohamed Elhadidy,Nahed E. Ibrahim,Wafaa El-Bahaei,Vishwaj 대한신경정신의학회 2011 PSYCHIATRY INVESTIGATION Vol.8 No.3
Objective To evaluate reproduction among patients with bipolar I disorder (BP1) or schizophrenia (SZ) in Egypt. Methods BP1 patients (n=113) were compared with community based, demographically balanced controls (n=124) and SZ patients (n=79, DSM-IV). All participants were evaluated using structured interviews and corroborative data were obtained from relatives. Standard indices of procreation were included in multivariate analyses that incorporated key demographic variables. Results Control individuals were significantly more likely to have children than BP1 or SZ patients (controls 46.8%, BP1 15.9%, SZ 17.7%), but the BP1-SZ differences were non-significant. The average number of children for BP1 patients (0.37±0.9) and SZ patients (0.38±0.9) was significantly lower than for controls (1.04±1.48) (BP1 vs controls, p<0.001; SZ vs controls, p<0.001). The frequency of marriages among BP1 patients was nominally higher than the SZ group, but was significantly lower than controls (BP1: 31.9% SZ: 27.8% control: 57.3%). Even among married individuals, BP1 (but not SZ) patients were childless more often than controls (p=0.001). The marital fertility, i.e., the average number of children among patients with conjugal relationships for controls (1.8±1.57) was significantly higher than BP1 patients (1.14±1.31, p=0.02), but not significantly different from SZ patients (1.36±1.32, p=0.2). Conclusion Selected reproductive measures are significantly and substantially reduced among Egyptian BP1 patients. The reproductive indices are similar among BP1 and SZ patients, suggesting a role for general illness related variables. Regardless of the cause/s, the impairment constitutes important, under-investigated disability. Objective To evaluate reproduction among patients with bipolar I disorder (BP1) or schizophrenia (SZ) in Egypt. Methods BP1 patients (n=113) were compared with community based, demographically balanced controls (n=124) and SZ patients (n=79, DSM-IV). All participants were evaluated using structured interviews and corroborative data were obtained from relatives. Standard indices of procreation were included in multivariate analyses that incorporated key demographic variables. Results Control individuals were significantly more likely to have children than BP1 or SZ patients (controls 46.8%, BP1 15.9%, SZ 17.7%), but the BP1-SZ differences were non-significant. The average number of children for BP1 patients (0.37±0.9) and SZ patients (0.38±0.9) was significantly lower than for controls (1.04±1.48) (BP1 vs controls, p<0.001; SZ vs controls, p<0.001). The frequency of marriages among BP1 patients was nominally higher than the SZ group, but was significantly lower than controls (BP1: 31.9% SZ: 27.8% control: 57.3%). Even among married individuals, BP1 (but not SZ) patients were childless more often than controls (p=0.001). The marital fertility, i.e., the average number of children among patients with conjugal relationships for controls (1.8±1.57) was significantly higher than BP1 patients (1.14±1.31, p=0.02), but not significantly different from SZ patients (1.36±1.32, p=0.2). Conclusion Selected reproductive measures are significantly and substantially reduced among Egyptian BP1 patients. The reproductive indices are similar among BP1 and SZ patients, suggesting a role for general illness related variables. Regardless of the cause/s, the impairment constitutes important, under-investigated disability.