scholarly journals Some new dynamic inequality on time scales in three variables

2017 ◽  
Vol 11 (6) ◽  
pp. 1135-1140
Author(s):  
Deepak B. Pachpatte
2015 ◽  
Vol 48 ◽  
pp. 162-169 ◽  
Author(s):  
S.H. Saker ◽  
R.R. Mahmoud ◽  
A. Peterson

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sarah Sarfaraz ◽  
Naveed Ahmad ◽  
Ghaus ur Rahman

Abstract In this paper, we develop a fundamental dynamic inequality, a generalization of comparison theorem and reproduce the proofs of some nonlinear integral Pachpatte’s inequalities by using their continuous analogue. We also unify and extend these improved integral Pachpatte’s inequalities and their corresponding discrete analogues on arbitrary time scales. The results are used to make qualitative analysis of higher order dynamic equations.


2019 ◽  
Vol 13 (3) ◽  
pp. 819-838
Author(s):  
Samir Saker ◽  
Mahmoud Osman ◽  
Mario Krnic

In this paper, we establish some new reverse dynamic inequalities and use them to prove some higher integrability theorems for decreasing functions on time scales. In order to derive our main results, we first prove a new dynamic inequality for convex functions related to the inequality of Hardy, Littlewood and P?lya, known from the literature. Then, we prove a refinement of the famous Hardy inequality on time scales for a class of decreasing functions. As an application, our results are utilized to formulate the corresponding reverse integral and discrete inequalities, which are essentially new.


Author(s):  
James B. Pawley

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.


2013 ◽  
Vol 40 (3) ◽  
pp. 185-203
Author(s):  
Dhahri Maher ◽  
Bellakhel Ghazi ◽  
Chahed Jamel

Author(s):  
Joe H. Chow ◽  
Petar V. Kokotovic
Keyword(s):  

Author(s):  
Joshua M. Epstein

This part describes the agent-based and computational model for Agent_Zero and demonstrates its capacity for generative minimalism. It first explains the replicability of the model before offering an interpretation of the model by imagining a guerilla war like Vietnam, Afghanistan, or Iraq, where events transpire on a 2-D population of contiguous yellow patches. Each patch is occupied by a single stationary indigenous agent, which has two possible states: inactive and active. The discussion then turns to Agent_Zero's affective component and an elementary type of bounded rationality, as well as its social component, with particular emphasis on disposition, action, and pseudocode. Computational parables are then presented, including a parable relating to the slaughter of innocents through dispositional contagion. This part also shows how the model can capture three spatially explicit examples in which affect and probability change on different time scales.


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