scholarly journals Some Gronwall–Bellman Inequalities on Time Scales and Their Continuous Forms: A Survey

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 198
Author(s):  
Francesca Barich
Keyword(s):  
Time Scales ◽  
Main Part ◽  
The Third ◽  
Continuous Form ◽  
Linear And Nonlinear

Some generalizations of the Gronwall–Bellman (G–B) inequality are presented in this paper in continuous form and on time scales. After S. Hilger introduced the time scales theory in 1988, over the years many mathematicians have studied new versions of this inequality according to new results; the purpose of this paper is to present some of them. Therefore, in the Introduction, some generalizations of G–B inequality in continuous forms, linear and nonlinear are presented. In the second section, some important and interesting results on time scales theory are given. In the third and main part of our paper, G–B inequalities on time scales and their possible connection with G–B inequalities presented in the introduction are investigated. In particular, in the third section of this work, more attention is given to G–B type inequalities on time scales discussed in the last four years.

scholarly journals Delta-Nabla Type Maximum Principles for Second-Order Dynamic Equations on Time Scales and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-28
Author(s):  
Jiang Zhu ◽  
Dongmei Liu
Keyword(s):  
Time Scales ◽  
Initial Value Problems ◽  
Second Order ◽  
Dynamic Equations ◽  
Maximum Principles ◽  
Uniqueness Theorems ◽  
Initial Value ◽  
Approximation Theorems ◽  
Construction Techniques ◽  
Linear And Nonlinear

Some delta-nabla type maximum principles for second-order dynamic equations on time scales are proved. By using these maximum principles, the uniqueness theorems of the solutions, the approximation theorems of the solutions, the existence theorem, and construction techniques of the lower and upper solutions for second-order linear and nonlinear initial value problems and boundary value problems on time scales are proved, the oscillation of second-order mixed delat-nabla differential equations is discussed and, some maximum principles for second order mixed forward and backward difference dynamic system are proved.

scholarly journals Frontex activities on the Western Balkan route during the migrant crisis (2015-…)

2020 ◽  
Vol 8 (2) ◽  
pp. 97-111
Author(s):  
Patryk Bukowski
Keyword(s):  
European Union ◽  
Main Part ◽  
Statistical Data ◽  
Coast Guard ◽  
The European Union ◽  
The Third ◽  
Current Activity ◽  
The Subject ◽  
Normative Perspective

According to the title, the subject of this article is the activity of Frontex (European Border and Coast Guard Agency) on the Western Balkan route during the migrant crisis, the escalation of which took place in mid-2015. The main part of the text has been divided into four parts. In the first part of the article, the author briefly described the genesis of Frontex and its current activity in the normative perspective. In the second part, the author characterised the determinants of the migrant crisis, focusing on the challenges for the European Union which the crisis generated. In the third part, the author described the course of the Western Balkan route and analysed statistical data on the population migrating that route. In the fourth and last part, the author analysed Frontex’s activity on the Western Balkan route, describing the determinants of the actions taken.

Inverse semigroups generated by a pair of subgroups

1977 ◽  
Vol 77 (1-2) ◽  
pp. 9-22 ◽  
Author(s):  
D. B. McAlister
Keyword(s):  
Inverse Semigroup ◽  
Free Product ◽  
Homomorphic Image ◽  
Main Part ◽  
Structure Theorem ◽  
Inverse Semigroups ◽  
Infinite Cyclic Group ◽  
The Third ◽  
Group A ◽  
Maximum Group

SynopsisThe aim of this paper is to describe the free product of a pair G, H of groups in the category of inverse semigroups. Since any inverse semigroup generated by G and H is a homomorphic image of this semigroup, this paper can be regarded as asking how large a subcategory, of the category of inverse semigroups, is the category of groups? In this light, we show that every countable inverse semigroup is a homomorphic image of an inverse subsemigroup of the free product of two copies of the infinite cyclic group. A similar result can be obtained for arbitrary cardinalities. Hence, the category of inverse semigroups is generated, using algebraic constructions by the subcategory of groups.The main part of the paper is concerned with obtaining the structure of the free product G inv H, of two groups G, H in the category of inverse semigroups. It is shown in section 1 that G inv H is E-unitary; thus G inv H can be described in terms of its maximum group homomorphic image G gp H, the free product of G and H in the category of groups, and its semilattice of idempotents. The second section considers some properties of the semilattice of idempotents while the third applies these to obtain a representation of G inv H which is faithful except when one group is a non-trivial finite group and the other is trivial. This representation is used in section 4 to give a structure theorem for G inv H. In this section, too, the result described in the first paragraph is proved. The last section, section 5, consists of examples.

scholarly journals Discovery of a soft X-ray lag in the ultraluminous X-ray source NGC 1313 X-1

2019 ◽  
Vol 491 (4) ◽  
pp. 5172-5178 ◽  
Author(s):  
E Kara ◽  
C Pinto ◽  
D J Walton ◽  
W N Alston ◽  
M Bachetti ◽  
...  
Keyword(s):  
Time Scales ◽  
Timing Analysis ◽  
Lag Time ◽  
Accretion Disc ◽  
Causal Connection ◽  
Energy Bands ◽  
X Ray ◽  
Accretion Flow ◽  
Radiative Processes ◽  
The Third

ABSTRACT Ultraluminous X-ray sources (ULXs) provide a unique opportunity to probe the geometry and energetics of super-Eddington accretion. The radiative processes involved in super-Eddington accretion are not well understood, and so studying correlated variability between different energy bands can provide insights into the causal connection between different emitting regions. We present a spectral-timing analysis of NGC 1313 X-1 from a recent XMM–Newton campaign. The spectra can be decomposed into two thermal-like components, the hotter of which may originate from the inner accretion disc, and the cooler from an optically thick outflow. We find correlated variability between hard (2–10 keV) and soft (0.3–2 keV) bands on kilosecond time-scales, and find a soft lag of ∼150 s. The covariance spectrum suggests that emission contributing to the lags is largely associated with the hotter of the two thermal-like components, likely originating from the inner accretion flow. This is only the third ULX to exhibit soft lags. The lags range over three orders of magnitude in amplitude, but all three are ∼5–20 per cent of the corresponding characteristic variability time-scales. If these soft lags can be understood in the context of a unified picture of ULXs, then lag time-scales may provide constraints on the density and extent of radiatively driven outflows.

scholarly journals Remarks on Giovanni Sartor's Paper, The Logic of Proportionality: Reasoning with Non-Numerical Magnitudes

2013 ◽  
Vol 14 (8) ◽  
pp. 1457-1461
Author(s):  
Wojciech Załuski
Keyword(s):  
Conceptual Framework ◽  
Main Part ◽  
Strict Sense ◽  
Teleological Reasoning ◽  
The Third ◽  
Numerical Magnitudes ◽  
Goal Adoption ◽  
Constituent Elements ◽  
The Impact ◽  
Special Case

In his brilliant paper The Logic of Proportionality: Reasoning with Non-Numerical Magnitudes, Professor Sartor provides a multi-layered analysis of proportionality based on a model of teleological reasoning governed by value-norms, arguing that this kind of reasoning is quantitative but non-numerical, i.e., operates on magnitudes to which no symbolic numerals are assigned. The analysis pursued by Professor Sartor can be divided into three parts. In the first part, drawing on the theory of bounded rationality, Professor Sartor develops a model of teleological reasoning (of which proportionality reasoning is a special case) distinguishing its four stages: Value-adoption, goal-adoption, plan-adoption, and action-adoption. In the second part, he introduces and develops in great and illuminating detail a distinction between value-norms and action-norms. In the third—main—part, Professor Sartor makes the basic claim of his paper that proportionality reasoning (i.e., reasoning aimed at establishing whether a given legislative norm interfering with some constitutionally protected right is “proportional”), involving the assessment of the impact of choices upon relevant values, is quantitative but not based on numerical magnitudes, and develops a conceptual framework for reconstructing this reasoning and explicating its constituent elements (suitability, necessity, and balancing in the strict sense). Each of these parts abounds with valuable analyses and precious insights and would deserve a separate commentary, yet I shall confine myself mainly to the analysis of the third part, in which he develops his basic claim. I shall focus in the first place on two interpretive problems my reading of Professor Sartor's paper has given rise to, though some of my remarks will concern also more technical matters.

Experiment and m.h.d. theory of stability and relaxation in toroidal discharges

1981 ◽  
Vol 300 (1456) ◽  
pp. 525-533 ◽  
Keyword(s):  
Field Line ◽  
Time Scales ◽  
Solar Flares ◽  
Magnetic Energy ◽  
Self Control ◽  
Control Mechanisms ◽  
High Current ◽  
Linear And Nonlinear ◽  
Ideal Magnetohydrodynamic ◽  
Good Agreement

The experimental behaviour of plasma instabilities in high-current discharges is found to be in good agreement with the predictions of linear and nonlinear magnetohydrodynamic theory. Observations show that on time-scales comparable with the Alfven transit time there are rapidly growing ideal magnetohydrodynamic perturbations whereas experiments on longer time-scales show the growth and saturation of resistive instabilities which involve changes in field line topology. The plasmas are observed to exhibit self-control mechanisms which are related to the relaxation of configurations to states of lower magnetic energy. Rapid magnetic field line reconnection phenomena, as in solar flares, are observed.

scholarly journals Съвременни аспекти на регулирането на финансовите пазари (Contemporary Aspects of Financial Markets Regulation)

2020 ◽  
pp. 14-28
Keyword(s):  
Financial Markets ◽  
Main Part ◽  
Banking Sector ◽  
Financial Derivatives ◽  
The Third ◽  
Banking Regulations ◽  
Scientific Project ◽  
Alternative Finance ◽  
Global Financial System ◽  
Financial Markets Regulation

Contemporary Aspects of Financial Markets Regulation The article reflects the work and results under a university scientific project (UNWE, 2017- 2019) bearing the same title. The choice of the specific aspects to be explored is based on the market developments post-2008, when the world was already affected by the Global financial and economic crisis. The banking sector regulation is a subject of the first main part, as the banks were in the epicenter of the financial collapse in 2008 and afterwards, when many weaknesses and gaps in banking regulations became evident. The second main part of the article is about the financial derivatives market – those financial instruments were defined as drivers of the globalization of the crisis. The developments on the financial derivatives market, including its regulation, have a great impact on the global financial system and most notably on its stability. The third main part of the article treats the problems of alternative finance, as a forceful process of circumventing traditional banking is taking place. This is a new field, based on financial innovation, and its regulation is a contemporary matter. The fourth part is about the regulatory reforms of the Bulgarian financial market, given in perspective for a EU member state and respectively the effects for the national economy.

scholarly journals The lighthouse after Coase: Alternative ways to provide goods and func-tions of state

2021 ◽  
pp. 247-264
Author(s):  
Grigoriy Kalyagin
Keyword(s):  
Economic Theory ◽  
Political Economy ◽  
Public Goods ◽  
Public Good ◽  
Main Part ◽  
Special Role ◽  
The Third ◽  
Club Good ◽  
Xix Century ◽  
Further Development

This article attempts to answer the question of what determines the choice of the method to provide one or another public good. Why is one good given as a private one, another one as a club good, the third one as a purely public good, and the fourth one as a mix of different forms. In fact, this question includes the question of what the state should (and should not) do. The main part of the article presents a review of the discussion concerning the good, which played a special role in economic theory - the lighthouses. Although the classics of political economy of XIX - early XX centuries considered them as a striking example of pure public goods, the famous article by R. Coase [Coase, 1974] concludes that the services of lighthouses in England and Wales were not funded from general taxes, that is, they were not provided as public goods until the second third of XIX century. Further development of this discussion, which is still incomplete and relevant, leads to the understanding that lighthouse services are provided in different countries and/ or at different times as goods of various types. The same applies to almost any other goods. The concrete way of providing this good depends not only on the country and time, but also on how to estimate the specific offenses it provides. We conclude that there exist no private, public, etc. benefits by themselves, and a socially effective way of delivering benefits depends on the technologies and institutions available in the society.

scholarly journals Mathematical Modeling for Prediction of Heating and Air-Conditioning Energies of Multistory Buildings in Duhok City

2018 ◽  
Vol 7 (4) ◽  
pp. 153
Author(s):  
Neven E. Zaya ◽  
Lokman H. Hassan ◽  
Halis Bilgil
Keyword(s):  
Air Conditioning ◽  
Perfect Matching ◽  
Nonlinear Models ◽  
The Other ◽  
Multistory Buildings ◽  
The Third ◽  
The Common ◽  
Linear And Nonlinear ◽  
Predicted Values ◽  
Building Walls

Present endeavor is devoted to estimate the air-conditioning and heating energies or loads of modern buildings in Duhok City, Iraq using new mathematical models. Many parameters have been considered in current modeling, namely, area of building, number of storeys and types of the common materials of the building walls. Regression analysis is performed to formulate new mathematical linear and nonlinear models for the loads. In addition, Fuzzy logic is utilized in the third model employing Sugeno's regulation. The outcomes reveal that the reasonable matching is achieved between the proposed models and mechanical engineering analytical solutions of heating and air-conditioning standards. Consequently, high correlation coefficient as more than 85% is determined between the predicted values of the models and analytical results. The linear model shows perfect matching with the analytical outputs more than the other proposed mathematical formulations.

scholarly journals MUA'LLAGAT ZOHAYR IBN ABI SOLMA: ELEGANT PIECE OF ARABIC POETRY (1)

2021 ◽  
Vol 3 (1) ◽  
pp. 1-11
Author(s):  
Yahya Saleh Hasan Dahami ◽  
Abdullah Al Ghamdi
Keyword(s):  
Main Part ◽  
Arabic Language ◽  
Courtly Love ◽  
Arabic Literature ◽  
Love Poetry ◽  
Arabic Poetry ◽  
The Third ◽  
Critical Methodology ◽  
Classical Poetry ◽  
Classical Arabic

Zohayr ibn Abi Solma is identified as an eminent poet who produced poetry distinguished with preeminence in courtly and virtuous love. The study employs an analytical and critical methodology, attempting to elucidate the influence of virtuous love narrated by the poet in the first verse lines of his great Mua'llagah. It commences with a terse introductory synopsis shedding light on the importance of classical Arabic and its involvement with poetry. The paper attempts to prove, via the poetry of Zohayr ibn Abi Solma, the greatness of the Arabic classical poetry and demonstrate the aptitudes of the poet through his Mua'llagah. It is divided into four main parts. The first part deals with the greatness of the Arabic language then it moves to the second section that focuses on Arabic Poetry: Treasure of Wisdom. The third one sheds light on the poet's 'The Man and the Poet', and the last main part goes with an analytical and critical endeavor of the first ten verse lines of Al-Mua'llagah of Zohayr. It comes to an end with a conclusion. Keywords: Arabic Literature, Arabic Poetry, Courtly Love Poetry, Courteous Arabic Poetry, Umm Awfa, Virtuous Poetry.

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