scholarly journals The nonlocal by time problem for evolutionary singular equations of infinite order

Author(s):  
V.V. Gorodetskii ◽  
◽  
G.P. Verezhak ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Hanna Verezhak ◽  
Vasyl Gorodetskyi

In this paper, we establish the correct solvability of a nonlocal multipoint in time problem for the evolutionary equation of a parabolic type with the Bessel operator of infinite order in the case where the initial function is an element of the space of generalized functions of type S∘′.


2019 ◽  
Vol 12 (03) ◽  
pp. 1950037 ◽  
Author(s):  
Zinovii Nytrebych ◽  
Oksana Malanchuk

The problem with local nonhomogeneous two-point in time conditions for homogeneous PDE of the second order in time and, generally, infinite order in spatial variables is investigated. This problem is degenerated namely its characteristic determinant is identically zero. The condition of existence of a solution of the degenerate problem is established. Also, we proposed the differential-symbol method of constructing the solution of the problem in the classes of entire functions. Some examples of solving the degenerate two-point in time problems are presented.


2021 ◽  
Vol 71 (5) ◽  
pp. 1125-1132
Author(s):  
Zinovii Nytrebych ◽  
Oksana Malanchuk

Abstract We investigate the problem with local homogeneous two-point conditions with respect to time for nonhomogeneous PDE of second order in time variable and generally infinite order in spatial variables in the case when the characteristic determinant of the problem identically equals zero. We establish the nonexistence conditions of solution of this problem in the class of entire functions.


2007 ◽  
Vol 30 (4) ◽  
pp. 51 ◽  
Author(s):  
A. Baranchuk ◽  
G. Dagnone ◽  
P. Fowler ◽  
M. N. Harrison ◽  
L. Lisnevskaia ◽  
...  

Electrocardiography (ECG) interpretation is an essential skill for physicians as well as for many other health care professionals. Continuing education is necessary to maintain these skills. The process of teaching and learning ECG interpretation is complex and involves both deductive mechanisms and recognition of patterns for different clinical situations (“pattern recognition”). The successful methodologies of interactive sessions and real time problem based learning have never been evaluated with a long distance education model. To evaluate the efficacy of broadcasting ECG rounds to different hospitals in the Southeastern Ontario region; to perform qualitative research to determine the impact of this methodology in developing and maintaining skills in ECG interpretation. ECG rounds are held weekly at Kingston General Hospital and will be transmitted live to Napanee, Belleville, Oshawa, Peterborough and Brockville. The teaching methodology is based on real ECG cases. The audience is invited to analyze the ECG case and the coordinator will introduce comments to guide the case through the proper algorithm. Final interpretation will be achieved emphasizing the deductive process and the relevance of each case. An evaluation will be filled out by each participant at the end of each session. Videoconferencing works through a vast array of internet LANs, WANs, ISDN phone lines, routers, switches, firewalls and Codecs (Coder/Decoder) and bridges. A videoconference Codec takes the analog audio and video signal codes and compresses it into a digital signal and transmits that digital signal to another Codec where the signal is decompressed and retranslated back into analog video and audio. This compression and decompression allows large amounts of data to be transferred across a network at close to real time (384 kbps with 30 frames of video per second). Videoconferencing communication works on voice activation so whichever site is speaking has the floor and is seen by all the participating sites. A continuous presence mode allows each site to have the same visual and audio involvement as the host site. A bridged multipoint can connect between 8 and 12 sites simultaneously. This innovative methodology for teaching ECG will facilitate access to developing and maintaining skills in ECG interpretation for a large number of health care providers. Bertsch TF, Callas PW, Rubin A. Effectiveness of lectures attended via interactive video conferencing versus in-person in preparing third-year internal medicine clerkship students for clinical practice examinations. Teach Learn Med 2007; 19(1):4-8. Yellowlees PM, Hogarth M, Hilty DM. The importance of distributed broadband networks to academic biomedical research and education programs. Acad Psychaitry 2006;30:451-455


2020 ◽  
Vol 59 (1) ◽  
pp. 243-251
Author(s):  
Josh Lofy ◽  
Vladimir Gasparian ◽  
Zhyrair Gevorkian ◽  
Esther Jódar

AbstractIn the present work, we study the rotations of the polarization of light propagating in right and left-handed films and layered structures. Through the use of complex values representing the rotations we analyze the transmission (Faraday effect) and reflections (Kerr effect) of light. It is shown that the real and imaginary parts of the complex angle of Faraday and Kerr rotations are odd and even functions for the refractive index n, respectively. In the thin film case with left-handed materials there are large resonant enhancements of the reflected Kerr angle that could be obtained experimentally. In the magnetic clock approach, used in the tunneling time problem, two characteristic time components are related to the real and imaginary portions of the complex Faraday rotation angle . The complex angle at the different propagation regimes through a finite stack of alternating right and left-handed materials is analyzed in detail. We found that, in spite of the fact that Re(θ) in the forbidden gap is almost zero, the Im(θ) changes drastically in both value and sign.


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