The packing measure of the graphs and level sets of certain continuous functions

1988 ◽  
Vol 104 (2) ◽  
pp. 347-360 ◽  
Author(s):  
Fraydoun Rezakhanlou
Keyword(s):  
Continuous Function ◽  
Level Sets ◽  
Continuous Functions ◽  
Packing Dimension ◽  
Packing Measure ◽  
Occupation Measure ◽  
Weierstrass Function ◽  
Local Growth ◽  
Almost All ◽  
The Relationship

AbstractThe relationship between the local growth of a continuous function and the packing measure of its level sets and of its graph is studied. For the Weierstrass function with b an integer such that b ≥ 2 and with 0 < α < 1, and for x ∈ Range (W) outside a set of first category, the level set W−1(x) has packing dimension at least 1 − α. Furthermore, for almost all x ∈ Range (W), the packing dimension of f is at most 1 − α. Finer results on the occupation measure and the size of the graph of a continuous function satisfying the Zygmund Λ-condition are obtained.

Some properties of maximal measures on compact convex sets

1983 ◽  
Vol 94 (2) ◽  
pp. 297-305 ◽  
Author(s):  
C. J. K. Batty
Keyword(s):  
Continuous Function ◽  
State Space ◽  
Convex Sets ◽  
Convex Set ◽  
Compact Convex ◽  
Continuous Functions ◽  
Regularity Conditions ◽  
Maximal Measure ◽  
Compact Convex Set ◽  
Almost All

AbstractLet be a maximal measure on a compact convex set K, K* be the state space of the space of all continuous functions f: KK ℝ which are affine in the first variable, 1 be the -algebra on K generated by the Baire sets and the compact extremal subsets of K, and = {BeK1}. Then(i) For any fixed continuous function g:K ℝ and -almost all x in K, there is a closed face of K containing x on which g is constant.(ii) The image of under the map :KK* defined by f, (x) = f(x, x) is the unique maximal measure on K* representing its barycentre(iii) induces a measure on (eK) satisfying certain regularity conditions.

scholarly journals Forms of supra g#α -Continuous Functions

2019 ◽  
Vol 8 (10S) ◽  
pp. 251-257
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Normal Space ◽  
Relationship Of ◽  
The Relationship

This paper encompasses and particularly throws light on the new classes of functions called strongly supra -Continuous and perfectly supra - continuous functions and to analyze some of the unique properties and relations amid them. Subsequently, the conception of almost supra -continuous function is also conferred and the relationship of these functions with other functions were investigated and portrayed. Furthermore, a mildly supra -normal space have been defined and analyzed.

Contemporary Qur'anic Studies in Iran and its Relationship with Qur'anic Studies in the West

2012 ◽  
Vol 14 (1) ◽  
pp. 45-72
Author(s):  
Morteza Karimi-Nia
Keyword(s):  
Islamic Law ◽  
Human Sciences ◽  
The West ◽  
Communications Technologies ◽  
Religious Learning ◽  
The Status ◽  
Islamic Republic Of Iran ◽  
Almost All ◽  
The Impact ◽  
The Relationship

The status of tafsīr and Qur'anic studies in the Islamic Republic of Iran has changed significantly during recent decades. The essay provides an overview of the state of Qur'anic studies in Iran today, aiming to examine the extent of the impact of studies by Western scholars on Iranian academic circles during the last three decades and the relationship between them. As in most Islamic countries, the major bulk of academic activity in Iran in this field used to be undertaken by the traditional ʿulamāʾ; however, since the beginning of the twentieth century and the establishment of universities and other academic institutions in the Islamic world, there has been increasing diversity and development. After the Islamic Revolution, many gradual changes in the structure and approach of centres of religious learning and universities have occurred. Contemporary advancements in modern sciences and communications technologies have gradually brought the institutions engaged in the study of human sciences to confront the new context. As a result, the traditional Shīʿī centres of learning, which until 50 years ago devoted themselves exclusively to the study of Islamic law and jurisprudence, today pay attention to the teaching of foreign languages, Qur'anic sciences and exegesis, including Western studies about the Qur'an, to a certain extent, and recognise the importance of almost all of the human sciences of the West.

Almost Somewhat Near Continuity and Near Regularity

2021 ◽  
Vol 7 (1) ◽  
pp. 88-99
Author(s):  
Zanyar A. Ameen
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
One To One ◽  
Nearly Continuous

AbstractThe notions of almost somewhat near continuity of functions and near regularity of spaces are introduced. Some properties of almost somewhat nearly continuous functions and their connections are studied. At the end, it is shown that a one-to-one almost somewhat nearly continuous function f from a space X onto a space Y is somewhat nearly continuous if and only if the range of f is nearly regular.

Industrial districts and local governance in the Italian experience

1999 ◽  
Vol 18 (2) ◽  
pp. 131-139
Author(s):  
Maurizio Mistri
Keyword(s):  
Political Behavior ◽  
Political Attitudes ◽  
Local Governance ◽  
Dynamic Processes ◽  
Industrial Districts ◽  
Small Enterprises ◽  
Local Growth ◽  
Italian Experience ◽  
The Law ◽  
The Relationship

This paper focuses on the problem of the governance of industrial districts in Italy. The analysis begins with an assessment of the dynamic processes that characterize the development of industrial districts, particularly as concerns the elements of a cultural nature. The relationship between local political attitudes and forms of local growth is considered, generally revealing how in the various practical examples there is a convergence between models of political behavior and the needs of the system of small enterprises. The paper ends with a brief discussion of the law 317/91, designed to establish the responsibilities and roles of the industrial districts.

scholarly journals Double parton distributions in the pion from lattice QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Gunnar S. Bali ◽  
Luca Castagnini ◽  
Markus Diehl ◽  
Jonathan R. Gaunt ◽  
Benjamin Gläßle ◽  
...  
Keyword(s):  
Spatial Distribution ◽  
Lattice Qcd ◽  
Quark Mass ◽  
Matrix Elements ◽  
Parton Distributions ◽  
Almost All ◽  
The Relationship

Abstract We perform a lattice study of double parton distributions in the pion, using the relationship between their Mellin moments and pion matrix elements of two local currents. A good statistical signal is obtained for almost all relevant Wick contractions. We investigate correlations in the spatial distribution of two partons in the pion, as well as correlations involving the parton polarisation. The patterns we observe depend significantly on the quark mass. We investigate the assumption that double parton distributions approximately factorise into a convolution of single parton distributions.

scholarly journals Bayonet-shaped language development in autism with regression: a retrospective study

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
David Gagnon ◽  
Abderrahim Zeribi ◽  
Élise Douard ◽  
Valérie Courchesne ◽  
Borja Rodríguez-Herreros ◽  
...  
Keyword(s):  
Language Development ◽  
Linear Models ◽  
Autism Spectrum ◽  
Early Language ◽  
Verbal Iq ◽  
Logistic Regression Models ◽  
Language Level ◽  
Language Outcome ◽  
Almost All ◽  
The Relationship

Abstract Background Language delay is one of the major referral criteria for an autism evaluation. Once an autism spectrum diagnosis is established, the language prognosis is among the main parental concerns. Early language regression (ELR) is observed by 10–50% of parents but its relevance to late language level and socio-communicative ability is uncertain. This study aimed to establish the predictive value of ELR on the progression of language development and socio-communicative outcomes to guide clinicians in addressing parents’ concerns at the time of diagnosis. Methods We used socio-communicative, language, and cognitive data of 2,047 autism spectrum participants from the Simons Simplex Collection, aged 4–18 years (mean = 9 years; SD = 3.6). Cox proportional hazard and logistic regression models were used to evaluate the effect of ELR on language milestones and the probability of using complex and flexible language, as defined by the choice of ADOS module at enrollment. Linear models were then used to evaluate the relationship of ELR and non-verbal IQ with socio-communicative and language levels. Results ELR is associated with earlier language milestones but delayed attainment of fluent, complex, and flexible language. However, this language outcome can be expected for almost all autistic children without intellectual disability at 18 years of age. It is mostly influenced by non-verbal IQ, not ELR. The language and socio-communicative level of participants with flexible language, as measured by the Vineland and ADOS socio-communicative subscales, was not affected by ELR. Limitations This study is based on a relatively coarse measure of ultimate language level and relies on retrospective reporting of early language milestones and ELR. It does not prospectively document the age at which language catches up, the relationship between ELR and other behavioral areas of regression, nor the effects of intervention. Conclusions For autistic individuals with ELR and a normal level of non-verbal intelligence, language development follows a “bayonet shape” trajectory: early first words followed by regression, a plateau with limited progress, and then language catch up.

Actual Challenges, Risks and Security Safety

2020 ◽  
Vol 1 (1) ◽  
pp. 65-83
Author(s):  
Božidar Forca ◽  
Dragoljub Sekulović ◽  
Igor Vukonjanski
Keyword(s):  
National Security ◽  
Modern World ◽  
Security Strategy ◽  
Theoretical Understanding ◽  
National Security Strategy ◽  
Security Challenges ◽  
Wide Range ◽  
The Subject ◽  
Almost All ◽  
The Relationship

Security is one of the most common terms in the modern world. This statement is supported by the fact that the term security is used in a wide range of areas. The subject of this paper is national security and the challenges, risks and threats to that security in contemporary international relations. The purpose of the work is twofold. First, to show the diversity of theoretical understanding of the term challenge, risk and threat by various authors. On the other hand, the overriding goal is to analyze the relationship to the challenges, risks and threats in different countries. When it comes to national security, challenges, risks and threats, most often, are identified in a document called the national security strategy. This document, as one of the highest in the hierarchy of political acts of every state, when it comes to security, is passed by almost all modern states of the world. The analysis of numerous national security strategies has revealed that it is possible to identify: 1) the challenges, risks and threats that appear in all strategies, 2) the challenges, risks and threats of security that appear in most strategies, and 3) the challenges, risks and threats of security which are country specific.

scholarly journals An Analysis of the Post-War Community Relations between Buddhists and Muslims in Sri Lanka: A Muslim’s Perspective

2016 ◽  
Vol 9 (6) ◽  
pp. 42
Author(s):  
Ahmad Sunawari Long ◽  
Khaidzir Hj. Ismail ◽  
Kamarudin Salleh ◽  
Saadiah Kumin ◽  
Halizah Omar ◽  
...  
Keyword(s):  
Sri Lanka ◽  
Total Population ◽  
Community Relations ◽  
Religious Groups ◽  
Islam And Christianity ◽  
Post War ◽  
Almost All ◽  
Religious Aspects ◽  
The Relationship ◽  
Community Relationship

Sri Lanka is a multi-ethnic, multi-religious country comprising four of the world’s major religions: Buddhism, Hinduism, Islam and Christianity. Buddhists are the predominant ethnic group, constituting 70.19% of the total population, while Muslims make up the second largest minority in the country. There are many records in the history to prove well the cordial relationship between Buddhists and Muslims in Sri Lanka. However, in the past couple of years, particularly during the aftermath of the civil war, tension may be observed in the relationship between these two religious groups. This is due to a campaign undertaken by a several Buddhist nationalist groups whose intensions are to create a division among these respective societies. These groups have been carrying protests against Muslim social, cultural and religious aspects, including issuing Halal certification, slaughtering of cattle, conducting prayer services, etc. Moreover, they have disseminated misinterpretations about Muslims and Islam with derogatory speeches among the Buddhist public, for the purpose of accomplishing above division. Given the above backdrop, this paper attempts to determine the post-war relationship between Muslims and Buddhists in the country, including major interrupting factors, through analyzing Muslims’ point of views. According to the results, there is no remarkable fluctuation in the relationships between Muslims and Buddhists, and Muslims have posited that there are several social, cultural and religious practices them that act as significant barriers to maintaining a better community relationship with Buddhists, such as slaughtering of cattle for meals. Therefore, almost all of the Muslims have been demanding proper guidelines regarding the slaughtering of cattle, the Niqabs (face cover of Muslim women), and other factors related to interrupting a better interaction with the Buddhists for better cordiality, within the context of Sri Lanka.

scholarly journals A note on weakly θ-continuous functions

1989 ◽  
Vol 12 (1) ◽  
pp. 9-13 ◽  
Author(s):  
M. Mrševic ◽  
I. L. Reilly
Keyword(s):  
Continuous Function ◽  
Continuous Functions ◽  
Topological Spaces ◽  
New Class ◽  
Weakly Continuous ◽  
Class Of Functions

Recently a new class of functions between topological spaces, called weaklyθ-continuous functions, has been introduced and studied. In this paper we show how an appropriate change of topology on the domain of a weaklyθ-continuous function reduces it to a weakly continuous function. This paper examines some of the consequences of this result.

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