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Solvability and Construction of a Solution to the Fredholm Integral Equation of the First Kind

Journal of Applied Mathematics and Physics 2024年第2期12卷 720-735页

作者： aisag.liev serikbai Nurmagambetov Dias Sevryugin Ilya Differential Equations and Control Theory Al-Farabi Kazakh National University Almaty Kazakhstan Department of Mathematics Prairie View A&M University Prairie View USA

The issues of solvability and construction of a solution of the Fredholm integral equation of the first kind are considered. It is done by immersing the original problem into solving an extremal problem in Hilbert space. Necessary and sufficient conditions for the existence of a solution are obtained. A method of constructing a solution of the Fredholm integral equation of the first kind is developed. A constructive theory of solvability and construction of a solution to a boundary value problem of a linear integrodifferential equation with a distributed delay in control, generated by the Fredholm integral equation of the first kind, has been created.

关键词： Integral Equations Solvability Solution Construction Controllability Minimizing Sequences

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Renal venous hypertension

引用

World Journal of Hypertension 2016年第1期6卷 60-65页

作者： Makhmud Muslimovich Аliev Rustam Zafarjanovich Yuldashev Gulnora Srajitdinovna Аdilova Аvazjon Аbdunomonovich Dekhqonboev Department of Pediatric Surgery Republican Specialized Scientific Practical Medical Centre of Pediatrics

Renal venous hypertension usually seen in young, otherwise healthy individuals and can lead to significant overall morbidity. Aside from clinical findings and physicalexamination, diagnosis can be made with ultrasound, computed tomography, or magnetic resonance conventional venography. Symptoms and haemodynamic significance of the compression determine the ideal treatment method. This review of the literature discusses normal and pathological developmental aspects of renocaval venous segment and related circulatory disorders, summarizes congenital and acquired changes in left renal vein and their impact on development of renal venous hypertension. Also will be discussed surgical tactics of portosystemic shunting and their potential effects on renal hemodynamics.

关键词： Renal venous hypertension Nutcracker syndrome Kidney Portal hypertension Splenorenal shunts

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