The detection of outliers for the standard least squares regression model is a problem which has ... more The detection of outliers for the standard least squares regression model is a problem which has been extensively studied. LAD regression diagnostics offers alternative approaches whose main feature is the robustness. The robustness of LAD regression to outliers are very ...
Between the dawn of the Internet through year 2003, there were just a few dozens exabytes of info... more Between the dawn of the Internet through year 2003, there were just a few dozens exabytes of information on the Web. Today, that much information is created weekly. The opportunity to capture the opinions of the general public about social events, political movements, company strategies, marketing campaigns, and product preferences has raised increasing interest both in the scientific community, for the exciting open challenges, and in the business world, for the remarkable fallouts in social media marketing and financial forecast. Keeping up with the ever-growing amount of unstructured information on the Web, however, is a formidable task. Unlike standard statistical approaches, sentic computing relies on a vector space model of affective common-sense knowledge to work with natural language at concept-level. The well-known noisiness of common-sense data sources, however, is a major factor in jeopardizing the efficiency of analogical reasoning in the vector space. In this work, it i...
Spatial statistics may be defined as that part of statistics in which the information re-garding ... more Spatial statistics may be defined as that part of statistics in which the information re-garding the observations takes into account a positional variable. Generally when a prob-lem concerns a space in two dimension, a bidimensional surface and a two co-ordinates system are ...
A positive integer m is said to be a practical number if every integer n; with 1 n oe(m); is a su... more A positive integer m is said to be a practical number if every integer n; with 1 n oe(m); is a sum of distinct positive divisors of m: In this note we prove two conjectures of Margenstern: (i) every even positive integer is a sum of two practical numbers; (ii) there exist infinitely many practical numbers m such that m \Gamma 2 and m+ 2 are also practical.
In this paper we study some structure properties of primitive weird numbers in terms of their fac... more In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield primitive weird numbers of the form $mp_1\dots p_k$ for a suitable deficient positive integer $m$ and primes $p_1,\dots,p_k$ and generalize a recent technique developed for generating primitive weird numbers of the form $2^np_1p_2$. The same techniques can be used to search for odd weird numbers, whose existence is still an open question.
ABSTRACT Text A weird number is a number n for which σ(n)>2nσ(n)>2n and such that n... more ABSTRACT Text A weird number is a number n for which σ(n)>2nσ(n)>2n and such that n is not a sum of distinct proper divisors of n . In this paper we prove that n=2kpqn=2kpq is weird for a quite large set of primes p and q. In particular this gives an algorithm to generate very large primitive weird numbers, i.e., weird numbers that are not multiple of other weird numbers. Assuming classical conjectures on the gaps between consecutive primes, this also would prove that there are infinitely many primitive weird numbers, a question raised by Benkoski and Erdős in 1974. Video For a video summary of this paper, please visit http://youtu.be/OS93l3a_Mjo.
A new family of sequences is proposed. An example of sequence of this family is more accurately s... more A new family of sequences is proposed. An example of sequence of this family is more accurately studied. This sequence is composed by the integers n for which the sum of binary digits is equal to the sum of binary digits of n^2. Some structure and asymptotic properties are proved and a conjecture about its counting function is discussed.
In this paper, we examine the attitudes toward integrating work and family in a sample of 247 tea... more In this paper, we examine the attitudes toward integrating work and family in a sample of 247 teachers in Switzerland and Israel. More particularly, we focus on the national context’s role in mediating the relations between professional and private spheres. The data were collected by a questionnaire implemented and administered in the two countries. The analysis reveals differences between Israeli and Swiss teachers regarding the importance of attribution to life roles and their attitudes toward conflict and facilitation. Findings suggest new insights into the consideration of cultural elements in shaping the teachers’ attitudes toward the integration of family and work.
This textbook is an introduction to simulation techniques. After a short review of elements of pr... more This textbook is an introduction to simulation techniques. After a short review of elements of probability theory, the authors present various methods of generation of a large number of random variables. Next, the transformations of uniformly distributed random variables are considered that allow one to generate samples of random variables with given distribution. Testing the hypotheses about the distribution of a sample is the topic of next chapter. Finally, the Monte Carlo method with applications is presented. The textbook is devoted to nonspecialists: mathematicians having no deep knowledge of statistics, engineers, computer scientists, etc. Contents: 1. Introduction. 2. Elements of probability theory. 3. Random numbers. 4. Transformations of variables and simulation of samples. 5. Hypothesis testing and random numbers. 6. Monte Carlo method and its applications. 7. Computer-aided simulation.Reviewer: Vigirdas Mackevičius (Vilnius)
A positive integer m is said to be practical if every integer n 2 (1; m) is a sum of distinct pos... more A positive integer m is said to be practical if every integer n 2 (1; m) is a sum of distinct positive divisors of m: In this paper we give an equivalent deenition of practical number, and describe some arithmetical properties of practical numbers showing a remarkable analogy with primes. We give an improvement of the estimate of the gap between consecutive practical numbers and prove the existence of innn-itely many practical numbers in suitable binary recurrence sequences, including the sequences of Fibonacci, Lucas and Pell.
A weird number is a number n for which σ ( n ) > 2 n and such that n is not a sum of distinct ... more A weird number is a number n for which σ ( n ) > 2 n and such that n is not a sum of distinct proper divisors of n. In this paper we prove that n = 2 k p q is weird for a quite large set of primes p and q. In particular this gives an algorithm to generate very large primitive weird numbers, i.e., weird numbers that are not multiple of other weird numbers. assuming classical conjectures on the gaps between consecutive primes, this also would prove that there are infinitely many primitive weird numbers, a question raised by Benkoski and Erdős in 1974.
The detection of outliers for the standard least squares regression model is a problem which has ... more The detection of outliers for the standard least squares regression model is a problem which has been extensively studied. LAD regression diagnostics offers alternative approaches whose main feature is the robustness. The robustness of LAD regression to outliers are very ...
Between the dawn of the Internet through year 2003, there were just a few dozens exabytes of info... more Between the dawn of the Internet through year 2003, there were just a few dozens exabytes of information on the Web. Today, that much information is created weekly. The opportunity to capture the opinions of the general public about social events, political movements, company strategies, marketing campaigns, and product preferences has raised increasing interest both in the scientific community, for the exciting open challenges, and in the business world, for the remarkable fallouts in social media marketing and financial forecast. Keeping up with the ever-growing amount of unstructured information on the Web, however, is a formidable task. Unlike standard statistical approaches, sentic computing relies on a vector space model of affective common-sense knowledge to work with natural language at concept-level. The well-known noisiness of common-sense data sources, however, is a major factor in jeopardizing the efficiency of analogical reasoning in the vector space. In this work, it i...
Spatial statistics may be defined as that part of statistics in which the information re-garding ... more Spatial statistics may be defined as that part of statistics in which the information re-garding the observations takes into account a positional variable. Generally when a prob-lem concerns a space in two dimension, a bidimensional surface and a two co-ordinates system are ...
A positive integer m is said to be a practical number if every integer n; with 1 n oe(m); is a su... more A positive integer m is said to be a practical number if every integer n; with 1 n oe(m); is a sum of distinct positive divisors of m: In this note we prove two conjectures of Margenstern: (i) every even positive integer is a sum of two practical numbers; (ii) there exist infinitely many practical numbers m such that m \Gamma 2 and m+ 2 are also practical.
In this paper we study some structure properties of primitive weird numbers in terms of their fac... more In this paper we study some structure properties of primitive weird numbers in terms of their factorization. We give sufficient conditions to ensure that a positive integer is weird. Two algorithms for generating weird numbers having a given number of distinct prime factors are presented. These algorithms yield primitive weird numbers of the form $mp_1\dots p_k$ for a suitable deficient positive integer $m$ and primes $p_1,\dots,p_k$ and generalize a recent technique developed for generating primitive weird numbers of the form $2^np_1p_2$. The same techniques can be used to search for odd weird numbers, whose existence is still an open question.
ABSTRACT Text A weird number is a number n for which σ(n)>2nσ(n)>2n and such that n... more ABSTRACT Text A weird number is a number n for which σ(n)>2nσ(n)>2n and such that n is not a sum of distinct proper divisors of n . In this paper we prove that n=2kpqn=2kpq is weird for a quite large set of primes p and q. In particular this gives an algorithm to generate very large primitive weird numbers, i.e., weird numbers that are not multiple of other weird numbers. Assuming classical conjectures on the gaps between consecutive primes, this also would prove that there are infinitely many primitive weird numbers, a question raised by Benkoski and Erdős in 1974. Video For a video summary of this paper, please visit http://youtu.be/OS93l3a_Mjo.
A new family of sequences is proposed. An example of sequence of this family is more accurately s... more A new family of sequences is proposed. An example of sequence of this family is more accurately studied. This sequence is composed by the integers n for which the sum of binary digits is equal to the sum of binary digits of n^2. Some structure and asymptotic properties are proved and a conjecture about its counting function is discussed.
In this paper, we examine the attitudes toward integrating work and family in a sample of 247 tea... more In this paper, we examine the attitudes toward integrating work and family in a sample of 247 teachers in Switzerland and Israel. More particularly, we focus on the national context’s role in mediating the relations between professional and private spheres. The data were collected by a questionnaire implemented and administered in the two countries. The analysis reveals differences between Israeli and Swiss teachers regarding the importance of attribution to life roles and their attitudes toward conflict and facilitation. Findings suggest new insights into the consideration of cultural elements in shaping the teachers’ attitudes toward the integration of family and work.
This textbook is an introduction to simulation techniques. After a short review of elements of pr... more This textbook is an introduction to simulation techniques. After a short review of elements of probability theory, the authors present various methods of generation of a large number of random variables. Next, the transformations of uniformly distributed random variables are considered that allow one to generate samples of random variables with given distribution. Testing the hypotheses about the distribution of a sample is the topic of next chapter. Finally, the Monte Carlo method with applications is presented. The textbook is devoted to nonspecialists: mathematicians having no deep knowledge of statistics, engineers, computer scientists, etc. Contents: 1. Introduction. 2. Elements of probability theory. 3. Random numbers. 4. Transformations of variables and simulation of samples. 5. Hypothesis testing and random numbers. 6. Monte Carlo method and its applications. 7. Computer-aided simulation.Reviewer: Vigirdas Mackevičius (Vilnius)
A positive integer m is said to be practical if every integer n 2 (1; m) is a sum of distinct pos... more A positive integer m is said to be practical if every integer n 2 (1; m) is a sum of distinct positive divisors of m: In this paper we give an equivalent deenition of practical number, and describe some arithmetical properties of practical numbers showing a remarkable analogy with primes. We give an improvement of the estimate of the gap between consecutive practical numbers and prove the existence of innn-itely many practical numbers in suitable binary recurrence sequences, including the sequences of Fibonacci, Lucas and Pell.
A weird number is a number n for which σ ( n ) > 2 n and such that n is not a sum of distinct ... more A weird number is a number n for which σ ( n ) > 2 n and such that n is not a sum of distinct proper divisors of n. In this paper we prove that n = 2 k p q is weird for a quite large set of primes p and q. In particular this gives an algorithm to generate very large primitive weird numbers, i.e., weird numbers that are not multiple of other weird numbers. assuming classical conjectures on the gaps between consecutive primes, this also would prove that there are infinitely many primitive weird numbers, a question raised by Benkoski and Erdős in 1974.
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