scholarly journals Majorization, “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law

2018 ◽  
Vol 16 (1) ◽  
pp. 1357-1373 ◽  
Author(s):  
Naveed Latif ◽  
Đilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Green Functions ◽  
The Real ◽  
Utility Distribution ◽  
Definition Of

AbstractIn this paper, we consider the definition of “useful” Csiszár divergence and “useful” Zipf-Mandelbrot law associated with the real utility distribution to give the results for majorizatioQn inequalities by using monotonic sequences. We obtain the equivalent statements between continuous convex functions and Green functions via majorization inequalities, “useful” Csiszár functional and “useful” Zipf-Mandelbrot law. By considering “useful” Csiszár divergence in the integral case, we give the results for integral majorization inequality. Towards the end, some applications are given.

scholarly journals Hermite–Hadamard-type inequalities for the interval-valued approximately h-convex functions via generalized fractional integrals

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Dafang Zhao ◽  
Muhammad Aamir Ali ◽  
Artion Kashuri ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarikaya
Keyword(s):  
Convex Functions ◽  
Fractional Integrals ◽  
Special Cases ◽  
Definition Of ◽  
The Given ◽  
Class Of Functions ◽  
Interval Valued ◽  
New Inequalities

Abstract In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called “interval-valued approximately h-convex functions”. We establish some inequalities of Hermite–Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302, 2018 and H. Budak et al. in Proc. Am. Math. Soc., 2019). We also discussed some special cases from our main results.

scholarly journals Levinson-type inequalities via new Green functions and Montgomery identity

2020 ◽  
Vol 18 (1) ◽  
pp. 632-652 ◽  
Author(s):  
Muhammad Adeel ◽  
Khuram Ali Khan ◽  
Ðilda Pečarić ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Green Functions ◽  
Montgomery Identity ◽  
Data Points

Abstract In this study, Levinson-type inequalities are generalized by using new Green functions and Montgomery identity for the class of k-convex functions (k ≥ 3). Čebyšev-, Grüss- and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, a new functional is introduced based on {\mathfrak{f}} divergence and then some estimates for new functional are obtained. Some inequalities for Shannon entropies are obtained too.

Successive coefficients of close-to-convex functions

2020 ◽  
Vol 32 (5) ◽  
pp. 1131-1141 ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Real Axis ◽  
Convex Functions ◽  
Positive Direction ◽  
The Real ◽  
Coefficient Problems ◽  
The Difference

AbstractIn this paper we discuss coefficient problems for functions in the class {{\mathcal{C}}_{0}(k)}. This family is a subset of {{\mathcal{C}}}, the class of close-to-convex functions, consisting of functions which are convex in the positive direction of the real axis. Our main aim is to find some bounds of the difference of successive coefficients depending on the fixed second coefficient. Under this assumption we also estimate {|a_{n+1}|-|a_{n}|} and {|a_{n}|}. Moreover, it is proved that {\operatorname{Re}\{a_{n}\}\geq 0} for all {f\in{\mathcal{C}}_{0}(k)}.

On modified Green functions in exterior problems for the Helmholtz equation

1982 ◽  
Vol 383 (1785) ◽  
pp. 313-332 ◽  
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Present Note ◽  
Boundary Integral ◽  
Green Functions ◽  
Exterior Problems ◽  
The Green Function ◽  
Definition Of

The question of non-uniqueness in boundary integral equation formu­lations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of co­efficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.

scholarly journals Imagology of Iranians in One Thousand Nights and One Night

2016 ◽  
Vol 4 (1) ◽  
pp. 74
Author(s):  
Ehsan Ghabool ◽  
Mina Ravansalar
Keyword(s):  
Comparative Literature ◽  
Literary Work ◽  
Real Image ◽  
Economic Prosperity ◽  
Literary Works ◽  
Arabic Translation ◽  
The Real ◽  
Similarities And Differences ◽  
Definition Of

Imagology is a branch of comparative literature which explores the image of one nation in the literature of another nation. One Thousand Nights and One Night is among the important books which can show the image of different nations and people such as Indians, Iranians and Arabs. Since the oldest version of the book is in Arabic, it is considered an Arabic literary work though it was translated from a Persian tale in the first place. On this basis the study of the image of Iranians in One Thousand Nights and One Night can be included under the definition of imagology. In this article, first we explain, analyze and study the image of Iranians in the book One Thousand Nights and One Night with respect to 1. anthropology (including entertainments, personification of animals, disapprobation of lies and betrayal of spouses), 2. religious and mythical beliefs (including the belief in daevas and jinnis, magic, fire-worshipping and similar plots), 3. politics (emphasizing the position of vizier and his family in government), 4. economics (emphasizing economic prosperity), then we will compare the collected information with the image of Iranians in credited works and in this way we will identify the similarities and differences of Iranians’ image in One Thousand Nights and One Night and the above-said literary works. Finally we come to this conclusion that the similarities belong to the real image of Iranians in the pre-Islamic days and that differences show the image of post-Islamic Iran which is added through Arabic translation.

scholarly journals Some remarks on incomplete gamma type function γ*(α, x_)

Filomat ◽  
2015 ◽  
Vol 29 (1) ◽  
pp. 125-131 ◽  
Author(s):  
Emin Özcağ ◽  
İnci Egeb
Keyword(s):  
Recurrence Relation ◽  
Real Line ◽  
Summable Function ◽  
Type Function ◽  
The Real ◽  
Definition Of ◽  
Derivatives Of

The incomplete gamma type function ?*(?, x_) is defined as locally summable function on the real line for ?>0 by ?*(?,x_) = {?x0 |u|?-1 e-u du, x?0; 0, x > 0 = ?-x_0 |u|?-1 e-u du the integral divergining ? ? 0 and by using the recurrence relation ?*(? + 1,x_) = -??*(?,x_) - x?_ e-x the definition of ?*(?, x_) can be extended to the negative non-integer values of ?. Recently the authors [8] defined ?*(-m, x_) for m = 0, 1, 2,... . In this paper we define the derivatives of the incomplete gamma type function ?*(?, x_) as a distribution for all ? < 0.

scholarly journals Problemy z granicami wypowiedzeń w polszczyźnie mówionej – uwagi wstępne

2015 ◽  
Author(s):  
Michał Szczyszek
Keyword(s):  
Spoken Language ◽  
Specific Task ◽  
The Real ◽  
Definition Of ◽  
Task Oriented ◽  
Theoretical Reflection ◽  
Innovative Concept

The article discusses the problems associated with segmented into separate sentences the stream of spoken language. There are both: theoretical problems (what is utterance?, what are its boundaries?, what are the theoretical proposals for the segmentation of utterances?), and practical problems (where is the real border between the two utterances in spoken language?, what criteria of segmentation stream of spoken language can be used?). The language material – which is the basis for the research presented in this article – comes from twenty task-oriented dialogue sessions with the participation of forty speakers performing a specific task. As a result of the analysis, based on available positions and theoretical reflection I managed to develop a tool for syntactical segmentation of the stream of spoken language. This tool can be presented in the form of a new (innovative) concept of definition of the utterance.

The Concept of Land Real Estate in the Act on Real Estate Management

2020 ◽  
Vol 2(22) ◽  
pp. 37-46
Author(s):  
Michał Kiedrzynek
Keyword(s):  
Real Estate ◽  
Civil Law ◽  
The Real ◽  
The Real Estate ◽  
The Subject ◽  
Estate Management ◽  
Definition Of ◽  
Real Estate Management

The management of public real estate has been regulated in many legal acts, among which the Act of August 21, 1997 on real estate management plays the greatest role. The definitions contained in it are intended to explain the most important concepts related to the subject of this act. However, with regard to the definition of land real estate, we are dealing with a repetition of what was defined by the provisions of civil law. Such a situation raises justified interpretation doubts, which may have significant consequences in the application of this act. The existence of two definitions for the same object is undesirable and the Real Estate Management Act should be amended in this respect by including an appropriate reference to the provisions of civil law.

Essentialism and Prejudice

2020 ◽  
pp. 95-98
Author(s):  
Philippe Rochat
Keyword(s):  
Real World ◽  
Implicit Beliefs ◽  
The Real ◽  
Actual Experience ◽  
Immediate Experience ◽  
Definition Of ◽  
Default Assumption

Humans can’t help but generalize in ways that are rarely, if ever, dictated by reason and prudence. We jump quickly to confirmatory and reassuring conclusions with a propensity to invent things in reference to worlds that only exist in our minds. Rather than being just games of the imagination, these inventions actually influence, often unbeknownst to us (subliminally), our attitudes and actions in the real world, in particular our discriminatory attitudes and actions toward people. Our innate propensity to chunk, cluster, and categorize things corresponds with our propensity to reproduce patterns of reality that are constructed based on ready-made or default implicit beliefs (i.e., stereotyping). Furthermore, the built-in default assumption that things and people have essential, nonobvious characteristics (definition of essentialism) allows for the immediate experience of favorable or unfavorable feelings toward people or things prior to, or not based on, actual experience (i.e. the definition of prejudice).

Social Media as Public Political Instrument

2020 ◽  
pp. 158-174
Author(s):  
Ikbal Maulana
Keyword(s):  
Social Media ◽  
Real Problem ◽  
Political Pressure ◽  
The Real ◽  
The Public ◽  
Real People ◽  
Political Forces ◽  
Single Voice ◽  
Political Legitimation ◽  
Definition Of

Due to its large number public cannot gather in one place and speak as a single voice, and consequently it cannot represent itself. However, public is always needed as political legitimation, therefore political forces compete to make their own definitions of public and use them as the basis of political claims. To make their definition of public close to the real people, democratic mechanisms have been developed. Once in a number of years, people elect candidates who will represent and govern them. But, most of the time they will be silent and ignored by the changing dynamics of politics. Conventional media does not help the public much to express its voice. Most often it becomes the tool of the elite for indoctrination or the mobilizing of bias. However, social media might empower people, because it allows them to voice their own concerns and to have conversation with each other. But, to have a real impact, the conversation must be directed to solve a real problem. Leadership is required to mobilize people's voice virtually and then turn it into a real political pressure.

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