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Register a new userThe Estimations of Modulus of Derivatives in some Classes of Univalent Functions
تقدير طويلات المشتقات في بعض فضاءات التوابع المتباينة
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ليكن فضاء التوابع التحليلية و المتباينة في قرص الواحدة من المستوي العقدي التي تحقق الشرط باستخدام نظرية دو برانج تم البرهان ، من أجل توابع هذا الفضاء، على صحة التقديرات الآتية: و من أجل توابع الفضاء ( أسرة التوابع التحليلية المحدبة و المتباينة في قرص الواحدة) تم البرهان على صحة التقديرات الآتية.
Let denote the class of functions that are analytic and univalent in the unit disk such that: Using De Brange Theorem it has been shown for the functinos of this class that the the following estimations are true: For the Subclass ( e.i. The Class of Convex functionswhdch in analytic and univalent in unit disk) the following estimations are true.
References used
(ALEKSANDROV,I. Boundary Values of Functional on the Class of Holomorphic Functions Univalent in a Circle. Sibirsk, Mat. Z. 4 , (1963
BADDOUR,H. ARMALE, H. The estimation of Modules of Fifth Derivative for the Analytic and Univalent Functions. Damascus Univ. Journal v10. No. (37-38) 1994
BIEBERBACH, L. Uber die Koeffizienten derjenigen Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, Sitzungs -berichte Preussische Akademie der Wissenschaften, 1916, 940-955
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مفهوم التابع لعدة متحولات
التمثيل البياني لتابع لمتحولين
نهايات التوابع لمتحولين واستمرارها
النهايات
النهايات التكرارية
الاستمرار
المشتقات الجزئية
التفاضل التام
التفاضل التام من المراتب العليا
الجاكوبي (Jacobian)
التوابع الشعاعية (Vec
tor functions)
المنحنيات الفراغية (Space curves)
السطوح (Surfaces)
المؤثر التفاضلي الموجه (Differential vector operator)
تدرج التابع السلمي (Gradient of scalar function)
خواص شعاع التدرج (Properties of the gradient)
تباعد الحقل الشعاعي(Divergence of vector field)
المعنى الفيزيائي للتباعد
دوران الحقل الشعاعي (Curl of vector field)
المعنى الهندسي للدوران
This research aimed to define a new class of complex functions , which depends in its definition on the definition of famous Holder class. We studied the relation between the new and Holder classes, then we proved some properties of the class.
We fi
nally applied this study to approximate the class of complex functions on closed curves , which belong to a wide class of curves.
In this research two Indomethacin derivatives were
synthesized, Indomethacin ethyl ester was synthesized by
The Direct Esterification method by reacting indomethacin
with ethanol within different conditions of time, molar
ratios and solvents in a
cidic medium using homogeneous
acid catalysts such as sulfuric acid and methane sulfuric
acid and heterogeneous acid catalysts such as amberlyst-
15. Then indomethacin acid hydrazide was synthesized by
condensing the previous ester with hydrazine hydrate and
the best conditions were studied of time, molar ratios,
solvents and different temperatures without using any
catalyst.
The purpose of this research is toextendsome results introduced by Rockafellar[19] in finite-dimensioal spaces to general Banach space using the Housdoroff distance convergent instead of epigraphical convergent .These results are aplicationsto study
the second-order epi-derivatives of function to classeand to study the second-order epi-derivatives of sum two convex functionand to studythe second-order epi-derivatives of Moreau-Yosida approximate function alsoto study ofthe second-order epi-derivatives of composition convex function with linear operator .
Unit testing is a practical approach for increasing the correctness
and quality of software; but writing unit test code is exhausting and
tedious job; and requires a great deal of time and effort. So even
with the use of frameworks for writing and
running unit test such as
JUnit this will need a great deal of time and effort. As a
consequence, there is a pressure in writing testing code. So we
present in this paper a new method to generate unit testing
automatically in order to speed up the testing process and reduce
the cost. We have implemented this method on the Java
programming language, where we write a new specification called
JFS describes the behavior of the function in terms of input and
output. This specification is written inside the code class and is
independent of the code, and it can be written before starting the
code phase and thus achieve the principle TDD Test-Driven
Development which is based on written test-first in order to
improve the development process. After writing specification we
will generate test classes for the execution of unit testing (we used
JUnit as framework to execute unit testing) based on the new
specification.
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