scholarly journals Steffensen's Integral Inequality on Time Scales

2007 ◽  
Vol 2007 ◽  
pp. 1-11 ◽  
Author(s):  
Umut Mutlu Ozkan ◽  
Hüseyin Yildirim
Keyword(s):  
Time Scales ◽  
Integral Inequality

scholarly journals Properties of Some Partial Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Time Scales ◽  
Point Theorem ◽  
Integral Inequality ◽  
Dynamic Equation ◽  
Dynamic Equations ◽  
Banach Fixed Point Theorem

The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.

scholarly journals Integral Inequality of Hardy-Type on Time Scales

2019 ◽  
Vol 09 (06) ◽  
pp. 534-543
Author(s):  
Emmanuella Ehui Aribike ◽  
Yisa Oluwatoyin Anthonio ◽  
Kamilu Rauf ◽  
Michael Oyelami Ajisope
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Hardy Type

scholarly journals Oscillation criteria for a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zhiyu Zhang ◽  
Ruihua Feng
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Dynamic Equations ◽  
Riccati Transformation ◽  
Third Order ◽  
Oscillation Criteria ◽  
Delay Dynamic Equations

AbstractIn this paper, we study the oscillation of a class of third-order Emden–Fowler delay dynamic equations with sublinear neutral terms on time scales. By using Riccati transformation and integral inequality, we establish several new theorems to ensure that each solution of the equation oscillates or asymptotically approaches zero, and the results in the literature are supplemented and extended. Examples are given to illustrate our main results.

scholarly journals Boundedness of the Solutions to Certain Delay Dynamic Integrodifferential Systems on Time Scales

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Min Fan ◽  
Yazhou Tian
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Boundedness Of Solutions ◽  
Delay Integral Inequality

In this paper, the bounds on the solutions of certain delay dynamic integrodifferential systems on time scales are considered. Based on a new Gronwall-Bellman type delay integral inequality, we can estimate the boundedness of solutions to integrodifferential systems. At the end, an example is presented to state the main results.

scholarly journals On Inequality Applicable to Partial Dynamic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Deepak B. Pachpatte
Keyword(s):  
Time Scales ◽  
Integral Inequality ◽  
Dynamic Equations

The main objective of the paper is to study new integral inequality on time scales which is used for the study of some partial dynamic equations. Some applications of our results are also given.

LVSEM: Past Present and Future

1990 ◽  
Vol 48 (1) ◽  
pp. 364-365
Author(s):  
James B. Pawley
Keyword(s):  
Field Emission ◽  
Line Width ◽  
Time Scales ◽  
Silicon Oxide ◽  
Beam Current ◽  
High Brightness ◽  
High Beam ◽  
Fixed Charges ◽  
Beam Voltage ◽  
Deposited Metal

Past: In 1960 Thornley published the first description of SEM studies carried out at low beam voltage (LVSEM, 1-5 kV). The aim was to reduce charging on insulators but increased contrast and difficulties with low beam current and frozen biological specimens were also noted. These disadvantages prevented widespread use of LVSEM except by a few enthusiasts such as Boyde. An exception was its use in connection with studies in which biological specimens were dissected in the SEM as this process destroyed the conducting films and produced charging unless LVSEM was used.In the 1980’s field emission (FE) SEM’s came into more common use. The high brightness and smaller energy spread characteristic of the FE-SEM’s greatly reduced the practical resolution penalty associated with LVSEM and the number of investigators taking advantage of the technique rapidly expanded; led by those studying semiconductors. In semiconductor research, the SEM is used to measure the line-width of the deposited metal conductors and of the features of the photo-resist used to form them. In addition, the SEM is used to measure the surface potentials of operating circuits with sub-micrometer resolution and on pico-second time scales. Because high beam voltages destroy semiconductors by injecting fixed charges into silicon oxide insulators, these studies must be performed using LVSEM where the beam does not penetrate so far.

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