A generalized delta derivative on time scale with applications

2020 ◽  
Vol 43 (15) ◽  
pp. 9046-9079
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scale ◽  
Delta Derivative

scholarly journals Solving Riccati type q-Difference Equations via Difference Transform Method

2021 ◽  
Vol 26 (4) ◽  
Author(s):  
Ayad Raisan Khudair ◽  
Ahmed Y. Abdulmajeed
Keyword(s):  
Difference Equations ◽  
Positive Constant ◽  
Time Scale ◽  
Taylor Formula ◽  
Transform Method ◽  
Quantum Calculus ◽  
The Difference ◽  
Delta Derivative

In this paper, we deal on the time scale that its delta derivative of graininess function is a nonzero positive constant. Based on the Taylor formula for this time scale, we investigate the difference transform method (DTM). This method has been applied successfully to solve Riccati type difference equations in quantum calculus. To demonstrate the ability and efficacy of this method, some examples have been provided.

DIFFERENTIATING SOLUTIONS OF A BOUNDARY VALUE PROBLEM ON A TIME SCALE

2016 ◽  
Vol 94 (1) ◽  
pp. 101-109 ◽  
Author(s):  
LEE H. BAXTER ◽  
JEFFREY W. LYONS ◽  
JEFFREY T. NEUGEBAUER
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Time Scale ◽  
Variational Equation ◽  
Boundary Value ◽  
Dynamic Boundary ◽  
Delta Derivative ◽  
General Time

We show that the solution of the dynamic boundary value problem $y^{{\rm\Delta}{\rm\Delta}}=f(t,y,y^{{\rm\Delta}})$, $y(t_{1})=y_{1}$, $y(t_{2})=y_{2}$, on a general time scale, may be delta-differentiated with respect to $y_{1},~y_{2},~t_{1}$ and $t_{2}$. By utilising an analogue of a theorem of Peano, we show that the delta derivative of the solution solves the boundary value problem consisting of either the variational equation or its dynamic analogue along with interesting boundary conditions.

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

The E-ring: interactions with plasma and implications for its evolution

1984 ◽  
Vol 75 ◽  
pp. 599-602
Author(s):  
T.V. Johnson ◽  
G.E. Morfill ◽  
E. Grun
Keyword(s):  
Time Scale ◽  
Particle Density ◽  
High Energy ◽  
Particle Removal ◽  
Density Region ◽  
Drag Forces ◽  
Orbit Evolution ◽  
History Of ◽  
Ring Particle ◽  
Ring Material

A number of lines of evidence suggest that the particles making up the E-ring are small, on the order of a few microns or less in size (Terrile and Tokunaga, 1980, BAAS; Pang et al., 1982 Saturn meeting; Tucson, AZ). This suggests that a variety of electromagnetic and plasma affects may be important in considering the history of such particles. We have shown (Morfill et al., 1982, J. Geophys. Res., in press) that plasma drags forces from the corotating plasma will rapidly evolve E-ring particle orbits to increasing distance from Saturn until a point is reached where radiation drag forces acting to decrease orbital radius balance this outward acceleration. This occurs at approximately Rhea's orbit, although the exact value is subject to many uncertainties. The time scale for plasma drag to move particles from Enceladus' orbit to the outer E-ring is ~104yr. A variety of effects also act to remove particles, primarily sputtering by both high energy charged particles (Cheng et al., 1982, J. Geophys. Res., in press) and corotating plasma (Morfill et al., 1982). The time scale for sputtering away one micron particles is also short, 102 - 10 yrs. Thus the detailed particle density profile in the E-ring is set by a competition between orbit evolution and particle removal. The high density region near Enceladus' orbit may result from the sputtering yeild of corotating ions being less than unity at this radius (e.g. Eviatar et al., 1982, Saturn meeting). In any case, an active source of E-ring material is required if the feature is not very ephemeral - Enceladus itself, with its geologically recent surface, appears still to be the best candidate for the ultimate source of E-ring material.

The long-term instability of the new generation hydrogen masers

2020 ◽  
pp. 35-38
Author(s):  
S.I. Donchenko ◽  
I.Y. Blinov ◽  
I.B. Norets ◽  
Y.F. Smirnov ◽  
A.A. Belyaev ◽  
...  
Keyword(s):  
Time Scale ◽  
Frequency Difference ◽  
Clock Frequency ◽  
Quantum Frequency ◽  
Frequency Standards ◽  
Quantum Frequency Standards ◽  
New Generation ◽  
Atomic Time

The latest changes in the algorithm for the formation of the international atomic time scale TAI are reported in terms of estimating the weights of the clocks involved in the formation of TAI. Studies of the characteristics of the long-term instability of new-generation hydrogen masers based on processing the results of the clock frequency difference with respect to TAI are performed. It has been confirmed that at present, new-generation hydrogen masers show significantly less long-term instability in comparison with quantum frequency standards ofsimilar and other types.

Multiple Behavioral Effects by Different Essential Oils Diffused Personally in the Second Time Scale

2018 ◽  
Vol 138 (8) ◽  
pp. 354-355
Author(s):  
Aya Fujita ◽  
Sho Kitabatake ◽  
Kazuko Yamagishi ◽  
Shuji Fujita
Keyword(s):  
Essential Oils ◽  
Time Scale ◽  
Behavioral Effects
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