Infinite Product Form of the Solution of the Aftereffect Problem with One Turning Point

2015 ◽  
Vol 7 (1) ◽  
pp. 97-105
2011 ◽  
Vol 54 (3) ◽  
pp. 506-518 ◽  
Author(s):  
A. Neamaty ◽  
S. Mosazadeh

AbstractIn this paper, we are going to investigate the canonical property of solutions of systems of differential equations having a singularity and turning point of even order. First, by a replacement, we transform the system to the Sturm–Liouville equation with turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm–Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm–Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.


2003 ◽  
Author(s):  
Shi-Jian Luo ◽  
Ming-Xi Tang ◽  
Shang-Shang Zhu ◽  
John Hamilton Frazer ◽  
Shou-Qian Sun ◽  
...  

1999 ◽  
pp. 95
Author(s):  
Editorial board Of the Journal

In the 10th issue of the Bulletin “Ukrainian Religious Studies” in the rubric “Scientific Reports and Announcements” there are in particular the following papers: “Religious Studies and Theology” by A.Kolodny, “Activity of the Orthodox Mission in Ukraine on the Turning Point of the XIX-XXth Centuries” by G.Nadtoka, “Religion in the Spiritual Heritage of V.Lypinsky” by L.Kondratyk, “Church as a Factor of the Self-identification of the Nation in the Cultural and Civilization Environment” by O.Nedavnya, “The Problems of Development of The Social Teaching of the Catholicism” by V.Sergyiko, “The God-Thunder Perun in the Pagan World-outlook of the Ancient Rus’” by N.Fatyushyna and other papers


2017 ◽  
Vol 26 (4) ◽  
pp. 391-410 ◽  
Author(s):  
David McCrone

The Brexit referendum in 2016 was a major turning-point in British and Scottish politics, reflected in a majority for Leave in England, but for Remain in Scotland. This article uses the British and Scottish Social Surveys for 2016 to explain Scottish-English differences, and finds that there were broad similarities in terms of social and demographic characteristics, and in terms of social values (‘authoritarians’ voting for Leave). Being ‘English’, however, was much more significant than being ‘Scottish’ in accounting for Brexit vote. The association between Brexit vote and constitutional preferences, notably voting intention in a future Scottish Independence Referendum, is far less clear-cut. Brexit promises to be a political game-changer, but in ways which are complex and unpredictable.


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