On A Sequence of Cantor Fractals

In this paper we discuss some topological and geometrical properties of terms in a sequence of Cantor fractals and the limit of the sequence in order to obtain an exact relation between positive real numbers and Hausdorff dimensions of fractals of Euclidean spaces

On Operator-valued Semicircular Random Variables

In this paper, we discuss some special properties of operator- valued semicircular random variables including representation of the Cauchy transform of a compactly supported probability measure in terms of their operator-valued Cauchy transforms and existence of nonzero discrete part of their associated distributions.Comment: 14 page

A Classification of Elements of Function Space F(R,R)F(\mathbb{R},\mathbb{R})

In this paper, we classify the function space of all real-valued functions on R denoted as F(R, R) into 28 distinct blocks. Each block contains elements that share common features in terms of the cardinality of their sets of continuity and differentiability. Alongside this classification, we introduce the concept of the Connection, which reveals a special relationship structure between four wellknown real-valued functions in real analysis: the Cantor function, Dirichlet function, the Thomae function, and the Weierstrass function. Despite the significance of this field, several perspectives remain unexplore

A Multilevel Analysis of the Contribution of Individual, Socioeconomic and Geographical Factors on Kindergarten Children’s Developmental Health: A Saskatchewan Province-Wide Study

In current literature of child public health, a growing number of studies has been dedicated to early childhood development with a focus on child developmental health measured via the teacher completed Early Development Instrument (EDI). Using multilevel modeling as the optimal statistical method to analyze hierarchical EDI data, this study determines the strength of the effect and significance of predictors of children’s 5 EDI outcomes, vulnerability, and the multiple vulnerability by taking into account the hierarchy present in its design. In addition, this study conducts an extensive epidemiological review of the risk factors associated with a child’s developmental health at each level of the hierarchy, at cross-levels of the hierarchy and their variations across different levels of the hierarchy. This cross-sectional study considered 9045 Saskatchewan children who were ages 4-8 years in the 2008-2009 school years. Individual child characteristics, EDI domains, and vulnerability data were collected by the Ministry of Education teachers in the provincial 2008 EDI project; neighborhood contextual Census data were compiled by SPHERU staff at the University of Saskatchewan. Multilevel linear and logistic models were used to analyze the data. According to the results, individual characteristics, such as being Aboriginal, an ESL learner, male, and being absent from school; neighborhood characteristics such as income inequality; and geographical characteristics such as living in a large city have negative effects on EDI scores and exacerbating the odds of vulnerability. Compounding effects of Aboriginal-special skills, large city-Aboriginal, and large city-neighborhood median income were positive on the above outcomes with considerable either significance or strength, while those of neighborhood income inequality-Aboriginal, and large city-neighborhood income inequality were negative with notable significance and strength. Furthermore, neighborhood contextual variables contribute to a considerable proportion of health outcome variations and the results associated with neighborhood income inequality give further evidence of the income inequality hypothesis. The findings of this study recommend provincial child public health policy makers’ extended attention to Aboriginal children, children with ESL status, those children living in neighborhoods with high income inequality and children from Regina

Cayley's hyperdeterminant: a combinatorial approach via representation theory

Cayley's hyperdeterminant is a homogeneous polynomial of degree 4 in the 8 entries of a 2 x 2 x 2 array. It is the simplest (nonconstant) polynomial which is invariant under changes of basis in three directions. We use elementary facts about representations of the 3-dimensional simple Lie algebra sl_2(C) to reduce the problem of finding the invariant polynomials for a 2 x 2 x 2 array to a combinatorial problem on the enumeration of 2 x 2 x 2 arrays with non-negative integer entries. We then apply results from linear algebra to obtain a new proof that Cayley's hyperdeterminant generates all the invariants. In the last section we show how this approach can be applied to general multidimensional arrays.Comment: 20 page

Some Results on the Distributions of Operator Valued Semicircular Random Variables

The operator-valued free central limit theorem and operator-valued semi-circular random variables were first introduced by D. Voiculescu in 1995 as operator-valued free analogues of the classical central limit theorem and normal random variables, respectively. In 2007, R. Speicher and others showed that the operator-valued Cauchy transform of the semicircular distribution satisfies a functional equation involving the variance of the semicircular distribution. In this thesis, we consider a non - commutative probability space (A;E_B;B) where in which A is a unital C -algebra, B is a C -subalgebra of A containing its unit and E_B A B is a conditional expectation. For a given B−valued self-adjoint semicircular random variable s > A with variance ; it is still an open question under what conditions the distribution of s has an atomic part. We provide a partial answer in terms of properties of when B is the algebra of n × n complex matrices. In addition, we show that for a given compactly supported probability measure its associated Cauchy transform can be represented in terms of the operator-valued Cauchy transforms of a sequence of finite dimensional matrix-valued semicircular random variables in two ways. Finally, we give another representation of its Cauchy transform in terms of operator-valued Cauchy transform of an in finite dimensional matrix-valued semicircular random variable

Explaining the Opportunities and Challenges of the Law on Dissemination and Free Access to Information in Iran from the Perspective of Lawyers

The right to have free access to information is one of the most underlying examples of the first generation of human rights. Also, it is a requirement of realization of citizenship rights and one of the vital issues in the principle of democratic participation discourse. Due to the importance of this issue, the approval of the Law on Dissemination and Free Access to Information in 2009 in Iran can be a vital step toward the achievement of free access to information, transparency, and favorable democracy. The purpose of this study is to explain the challenges and opportunities of the Law on Dissemination and Free Access to Information in Iran. Hence, by referring to scholars in the field of law, formal and natural evaluation of Law on Dissemination and Free Access to Information was done. The method in this study is data-based, and deep interviews are used to analyze the different aspects of this issue. The statistical population in this study consists of scholars and experts of the law. The results obtained from the interviews led to the identification of three opportunities including good democracy and governance, prevention and fight against corruption and revival and implementation of the citizenship document. Besides, five vital challenges were identified in the section of interviewing with lawyers: the ambiguity of law exceptions, lack of sanction of law, ambiguity in the concept of access to information, the challenge of dissemination system and access to information, and parallel laws challenges. According to the identified challenges and opportunities, it seems that the efforts of Ministries of Culture and Arts, Communications and Technology, Education, and National Media, and revision of legal articles concerning these challenges can be the proper solution to these problems

Digital Entrepreneurship

This open access book explores the global challenges and experiences related to digital entrepreneurial activities, using carefully selected examples from leading companies and economies that shape world business today and tomorrow. Digital entrepreneurship and the companies steering it have an enormous global impact; they promise to transform the business world and change the way we communicate with each other. These companies use digitalization and artificial intelligence to enhance the quality of decisions and augment their business and customer operations. This book demonstrates how cloud services are continuing to evolve; how cryptocurrencies are traded in the banking industry; how platforms are created to commercialize business, and how, taken together, these developments provide new opportunities in the digitalized era. Further, it discusses a wide range of digital factors changing the way businesses operate, including artificial intelligence, chatbots, voice search, augmented and virtual reality, as well as cyber threats and data privacy management. “Digitalization mirrors the Industrial Revolution’s impact. This book provides a complement of perspectives on the opportunities emanating from such a deep seated change in our economy. It is a comprehensive collection of thought leadership mapped into a very useful framework. Scholars, digital entrepreneurs and practitioners will benefit from this timely work.” Gina O’Connor, Professor of Innovation Management at Babson College, USA “This book defines and delineates the requirements for companies to enable their businesses to succeed in a post-COVID19 world. This book deftly examines how to accomplish and achieve digital entrepreneurship by leveraging cloud computing, AI, IoT and other critical technologies. This is truly a unique “must-read” book because it goes beyond theory and provides practical examples.” Charlie Isaacs, CTO of Customer Connection at Salesforce.com, USA "This book provides digital entrepreneurs useful guidance identifying, validating and building their venture. The international authors developed new perspectives on digital entrepreneurship that can support to create impact ventures.” Felix Staeritz, CEO FoundersLane, Member of the World Economic Forum Digital Leaders Board and bestselling author of FightBack, German

Depression and Anxiety in Iranian Mothers of Children with Epilepsy

How to Cite this Article: Soltanifar A, Ashrafzadeh F, Mohareri F, Mokhber N. Depression and Anxiety in Iranian Mothers ofChildren with Epilepsy. Iranian Journal of Child Neurology 2012;6(1):29-34. ObjectiveEpilepsy is a common neurological disorder in children. Parents with epileptic children have many psychosocial care needs. So the main goal of this study was to evaluate depression and anxiety in Iranian mothers with epileptic children.Materials & MethodsWe identified 30 mothers of children with epilepsy and 30 mothers of children without epilepsy with children aged between 8 and 12 years who met the study criteria. In all children with epilepsy, the mothers were the main caregivers and all these children lived in two-parent families. Children in the control group were in the same age. Ninety-eight percent of children in the control group lived in two-parent families with the mother as the main caregiver. All mothers fulfilled the Beck Depression Inventory (BDI) and Spielberger State-Trait Anxiety Inventory.ResultsAccording to these data, BDI scores were significantly higher in the mothers of epileptic children (mean of Beck score=16.5) compared to the control group (mean of Beck score=9.8). The total, Spielberger State-Trait Anxiety Inventory scores for mothers of children with epilepsy were 100.3, 51.7 and 48.6. However, these scores in the control group were 86.9, 45.1 and 41.8. These differences were statistically significant.In a second analysis, using the demographic data, we did not find any statistically significant relation between anxiety or depression and the mothers’ job, children’s medication and other demographic variables.ConclusionNeurologists and psychiatrists need to develop better programs for adequate management of psychiatric disorders in mothers with epileptic children. References 1. Cowan LD. The epidemiology of the epilepsies inchildren. 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