scholarly journals Some Steffensen-type inequalities over time scale measure spaces

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 4095-4106
Author(s):  
A.A. El-Deeb ◽  
Mario Krnic
Keyword(s):  
Time Scale ◽  
Classical Setting ◽  
Measure Spaces ◽  
Scale Measure ◽  
Scale Spaces ◽  
Finite Measures ◽  
Over Time ◽  
General Time

In this paper we study some new dynamic Steffensen-type inequalities on a general time scale. More precisely, we deal with time scale spaces with positive ?-finite measures. As an application, our results are compared with some previous results known from the literature. It turns out that our results generalize some previously known Steffensen-type inequalities in a classical setting.

scholarly journals Some new dynamic Steffensen-type inequalities on a general time scale measure space

2021 ◽  
Vol 7 (3) ◽  
pp. 4326-4337
Author(s):  
Ahmed A. El-Deeb ◽  
◽  
Inho Hwang ◽  
Choonkil Park ◽  
Omar Bazighifan ◽  
...  
Keyword(s):  
Time Scale ◽  
Measure Space ◽  
Finite Measure ◽  
Special Cases ◽  
Scale Measure ◽  
New Inequalities ◽  
General Time

<abstract><p>Our work is based on the multiple inequalities illustrated by Josip Pečarić in 2013, 1982 and Srivastava in 2017. With the help of a positive $ \sigma $-finite measure, we generalize a number of those inequalities to a general time scale measure space. Besides that, in order to obtain some new inequalities as special cases, we also extend our inequalities to discrete and continuous calculus.</p></abstract>

scholarly journals On a first-order semipositone boundary value problem on a time scale

2014 ◽  
Vol 8 (2) ◽  
pp. 269-287
Author(s):  
Christopher Goodrich
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Difference Equations ◽  
Dynamic Equation ◽  
Time Scale ◽  
Boundary Value ◽  
First Order ◽  
General Time

We consider the existence of a positive solution to the first-order dynamic equation y?(t)+p(t)y?(t) = ?f (t, y?(t)), t?(a, b)T, subject to the boundary condition y(a) = y(b) + ?T1,T2 F(s, y(s)) ?s for ?1,?2 ? [a,b]T. In this setting, we allow f to take negative values for some (t; y). Our results generalize some recent results for this class of problems, and because we treat the problem on a general time scale T we provide new results for this problem in the case of differential, difference, and q-difference equations. We also provide some discussion of the applicability of our results.

Decisions and the Uncertainty of Behaviour

Behaviour ◽  
1973 ◽  
Vol 45 (1-2) ◽  
pp. 83-103 ◽  
Author(s):  
◽  
Marian Dawkins
Keyword(s):  
Time Scale ◽  
The Other ◽  
Drinking Behaviour ◽  
Temporal Patterning ◽  
Domestic Chicks ◽  
Decision Structure ◽  
Videotape Analysis ◽  
Behavioural Sequence ◽  
Different Parts ◽  
Over Time

AbstractBehaviour can be described in terms of its changing uncertainty or decision structure over time. Such a description is economical, maximally informative and may well be of importance neurophysiologically. We try to show that the methods which are normally used to detect temporal patterning between already recognized behavioural acts can also be used on a finer time scale to detect moment to moment patterns of posture within those acts. From such analyses, it is possible to calculate the 'decisioniness' or 'uncertainty' of different parts of the behavioural sequence. We illustrate this by an attempt to describe the decision structure of the drinking behaviour of domestic chicks, using frame by frame videotape analysis. For example, it appears that the first downstroke phase of each drink is more uncertain as to outcome than the other phases, suggesting that 'decisions' are taken during the downstroke. We end with an attempt to plot a continuous graph of behaviour uncertainty against time sampled at 50 msec intervals.

Geologic Time

2021 ◽  
pp. 47-68
Author(s):  
Elisabeth Ervin-Blankenheim
Keyword(s):  
Time Scale ◽  
Sedimentation Rates ◽  
Charles Lyell ◽  
Geologic Time ◽  
The Bible ◽  
The Earth ◽  
Time To Build ◽  
Over Time

The time scale of geology—the first overarching precept in geology—and its development are the focus of this chapter. How did geologists determine the great age of the Earth through the spatial nature of geologic units and changes in fossils over time? There was no guidebook to the process of unraveling the Earth’s biography, and the discoveries proceeded step by step using observation and the development of hypotheses. Scientists such as Abraham Werner established principles to place rocks in order relative to one another, providing the beginning of understanding strata, their composition, sources, and life within them. Early estimates of the age of the Earth were on the order of thousands of years, carefully calculated based on the generations in the Bible. However, geologists such as James Hutton and Charles Lyell realized that the probable age of the Earth was much greater by examining the time it would take for processes, like sedimentation rates for a layer of sand or mud to be deposited to occur. From these observations, they deduced it would take orders of magnitude more time to build up great masses of rock layers, and the time scale of geology was extended millions of years.

Analysis of follow-up data

2020 ◽  
pp. 93-118
Author(s):  
Bendix Carstensen
Keyword(s):  
Data Collection ◽  
Time Scale ◽  
Poisson Regression ◽  
Time Dependent ◽  
Follow Up Study ◽  
Dependent Variables ◽  
The Status ◽  
Over Time

This chapter assesses the analysis and representation of follow-up data. follow-up refers to the process of monitoring persons over time for occurrence of a (set of) prespecified event(s). Practical data collection is often via look-up in registers or databases. The basic requirements for recordings in a follow-up study include date of entry to the study, date of exit from the study, and the status of the person at the exit date. The chapter then explains the likelihood from a follow-up study and why one can analyse rates using Poisson regression. The likelihood contribution from a single person's follow-up can be subdivided in contributions from subintervals of the follow-up. The chapter details the task of splitting the follow-up time along a time-scale. Finally, it considers time-dependent variables.

p-type in ZnO:N by codoping with Cr

2003 ◽  
Vol 786 ◽  
Author(s):  
E. Kaminska ◽  
A. Piotrowska ◽  
J. Kossut ◽  
R. Butkute ◽  
W. Dobrowolski ◽  
...  
Keyword(s):  
Time Scale ◽  
Room Temperature ◽  
Surface Passivation ◽  
Hole Concentration ◽  
Rf Sputtering ◽  
Zno Films ◽  
Type Conductivity ◽  
Chromium Doping ◽  
P Type ◽  
Over Time

ABSTRACTWe report on the fabrication of p-ZnO films by thermal oxidation of Zn3N2 deposited by reactive rf sputtering. With additional chromium doping we achieved p-type conductivity with the hole concentration ∼5×1017cm−3 and the mobility of 23.6 cm2/Vs at room temperature. We developed a method of surface passivation of p-ZnO that maintains its p-type conductivity over time-scale of months.

scholarly journals Some Dynamic Hilbert-Type Inequalities on Time Scales

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1410 ◽  
Author(s):  
Ghada AlNemer ◽  
Mohammed Zakarya ◽  
Hoda A. Abd El-Hamid ◽  
Praveen Agarwal ◽  
Haytham M. Rezk
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Discrete Inequalities ◽  
Hilbert Type ◽  
General Time

Throughout this article, we will demonstrate some new generalizations of dynamic Hilbert type inequalities, which are used in various problems involving symmetry. We develop a number of those symmetric inequalities to a general time scale. From these inequalities, as particular cases, we formulate some integral and discrete inequalities that have been demonstrated in the literature and also extend some of the dynamic inequalities that have been achieved in time scales.

Topological measure spaces: two counter-examples

1975 ◽  
Vol 78 (1) ◽  
pp. 95-106 ◽  
Author(s):  
D. H. Fremlin
Keyword(s):  
Radon Measures ◽  
Topological Measure ◽  
Measure Spaces ◽  
Finite Measures ◽  
Nikodym Theorem

The ‘Radon measures’ of N. Bourbaki(1) enjoy many striking properties. Among the most important of these is the ‘strong Radon-Nikodým theorem’ that the dual of L1-(μ) can always be identified with L∞(μ) ((1), chap. 5, §5, no. 8, theorem 4). As this is certainly not true of non-σ-finite measures in general, it is natural to ask what are the special properties on which it relies.

scholarly journals Worn Out or Worn In?

2021 ◽  
Author(s):  
◽  
Ross Ernest Stevens
Keyword(s):  
Time Scale ◽  
The Body ◽  
Design Concept ◽  
Specific Site ◽  
Soft Body ◽  
The Core ◽  
The Future ◽  
The Creation ◽  
Initial Concept ◽  
Over Time

<p>Worn out or worn in started with the creation of a building. For an industrial designer, this was unfamiliar territory. Through working with a specific site came the recognition of the potential of weathering to add a unique quality to the design that goes beyond its initial concept. The inclusion of this potential in the design required a projection into the future and an acceptance of the inevitability of influences that could not be fully controlled. Rain, sun, footprints and cobwebs would all add or subtract to the initially simplistic design concept. It was another realm of design: a 4 dimensional one. Where does the equivalent of weathering exist within the familiar scale of mass produced products? It is in the interaction between the body and the products through use. The potential of this interaction to add another dimension to a design forms the core of this research. The body is a complex site: fluid, directed, precarious, yet nurturing. While it may at first seem unreasonable that the soft body could erode hard, seemingly durable materials, the evidence is all around us. Though it works at a time scale that is almost invisible to our everyday perception, over time the evidence is recorded in our products. Through research by reading, observing, designing, making and unmaking products, the concept of designs embedded within products has emerged. Like a box of chocolates with a series of layers, this research addresses how the wearing away of one layer can reveal the existence of another.</p>

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