Correct Solvability of a Nonlocal Multipoint (in Time) Problem for One Class of Evolutionary Equations

2013 ◽  
Vol 65 (3) ◽  
pp. 377-392 ◽  
Author(s):  
V. V. Horodets’kyi ◽  
O. V. Martynyuk ◽  
R. I. Petryshyn
Keyword(s):  
Evolutionary Equations ◽  
Correct Solvability ◽  
Time Problem

A Multipoint (In Time) Problem for One Class of Pseudodifferential Evolutionary Equations

2018 ◽  
Vol 70 (3) ◽  
pp. 385-409
Author(s):  
V. V. Gorodetskii ◽  
R. I. Petrishin ◽  
A. P. Verezhak
Keyword(s):  
Evolutionary Equations ◽  
Time Problem

scholarly journals A Nonlocal in Time Problem for Evolutionary Singular Equations in Generalized Spaces of Type S∘

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Hanna Verezhak ◽  
Vasyl Gorodetskyi
Keyword(s):  
Initial Function ◽  
Infinite Order ◽  
Parabolic Type ◽  
Generalized Functions ◽  
Bessel Operator ◽  
Evolutionary Equation ◽  
Correct Solvability ◽  
Singular Equations ◽  
Time Problem ◽  
Space Of Generalized Functions

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∘′.

scholarly journals NONLOCAL BY TIME PROBLEM FOR SOME DIFFERENTIAL-OPERATOR EQUATION IN SPACES OF S AND S TYPES

2021 ◽  
Vol 9 (2) ◽  
pp. 53-69
Author(s):  
S. Bodnaruk ◽  
V. Gorodetskyi ◽  
R. Kolisnyk ◽  
N. Shevchuk
Keyword(s):  
Fundamental Solution ◽  
Initial Function ◽  
Fourier Transforms ◽  
Nonlocal Condition ◽  
Adjoint Operator ◽  
Generalized Function ◽  
Transform Method ◽  
Correct Solvability ◽  
Time Problem ◽  
Sigma 1

In the theory of fractional integro-differentiation the operator $A := \displaystyle \Big(I-\frac{\partial^2}{\partial x^2}\Big)$ is often used. This operator called the Bessel operator of fractional differentiation of the order of $ 1/2 $. This paper investigates the properties of the operator $B := \displaystyle \Big(I-\frac{\partial^2}{\partial x^2}+\frac{\partial^4}{\partial x^4}\Big)$, which can be understood as a certain analogue of the operator $A$. It is established that $B$ is a self-adjoint operator in Hilbert space $L_2(\mathbb{R})$, the narrowing of which to a certain space of $S$ type (such spaces are introduced in \cite{lit_bodn_2}) matches the pseudodifferential operator $F_{\sigma \to x}^{-1}[a(\sigma) F_{x\to \sigma}]$ constructed by the function-symbol $a(\sigma) = (1+\sigma^2+\sigma^4)^{1/4}$, $\sigma \in \mathbb{R}$ (here $F$, $F^{-1}$ are the Fourier transforms). This approach allows us to apply effectively the Fourier transform method in the study of the correct solvability of a nonlocal by time problem for the evolution equation with the specified operator. The correct solvability for the specified equation is established in the case when the initial function, by means of which the nonlocal condition is given, is an element of the space of the generalized function of the Gevrey ultradistribution type. The properties of the fundamental solution of the problem was studied, the representation of the solution in the form of a convolution of the fundamental solution of the initial function is given.

45. Education at distance: Broadcasting ECG rounds to Southeastern Ontario (BESO Project). An innovative approach for teaching electrocardiography

2007 ◽  
Vol 30 (4) ◽  
pp. 51 ◽  
Author(s):  
A. Baranchuk ◽  
G. Dagnone ◽  
P. Fowler ◽  
M. N. Harrison ◽  
L. Lisnevskaia ◽  
...  
Keyword(s):  
Health Care ◽  
Real Time ◽  
Digital Signal ◽  
Teaching Methodology ◽  
Care Providers ◽  
Long Distance ◽  
Medicine Clerkship ◽  
Time Problem ◽  
The Impact ◽  
Ecg Interpretation

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

scholarly journals Faraday and Kerr Effects in Right and Left-Handed Films and Layered Materials

2020 ◽  
Vol 59 (1) ◽  
pp. 243-251
Author(s):  
Josh Lofy ◽  
Vladimir Gasparian ◽  
Zhyrair Gevorkian ◽  
Esther Jódar
Keyword(s):  
Kerr Effect ◽  
Tunneling Time ◽  
The Real ◽  
Left Handed ◽  
Faraday Rotation Angle ◽  
Time Problem ◽  
Kerr Angle ◽  
Polarization Of Light ◽  
Effect Of Light ◽  
Forbidden Gap

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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