One-sided L\'{e}vy stable distributions

In this paper, we show new representations of one-sided L\'{e}vy stable distributions for irrational L\'{e}vy indices of the type $\left(\frac{p}{q}\right)^{\frac{l_{2}}{l_{1}}}$ which are not covered in \cite{pg1} : for rational L\'{e}vy indices. Furthermore, other equivalent representations for a distribution of a rational L\'{e}vy index is described. We also give a simplest proof for the formulae which cover the cases for rational L\'{e}vy indices. Finally we introduce the concepts of L\'{e}vy smashing and L\'{e}vy-smashed gamma stochastic processes.Comment: Welcome for comment

General relations between sums of squares and sums of triangular numbers

Let = ( 1, · · · , m) be a partition of k. Let r (n) denote the number of solutions in integers of 1x21 + · · · + mx2 m = n, and let t (n) denote the number of solutions in non negative integers of 1x1(x1 +1)/2+· · ·+ mxm(xm +1)/2 = n. We prove that if 1 k 7, then there is a constant c , depending only on , such that r (8n + k) = c t (n), for all integers n

The Role of Gender Dynamics in the Relationship between Parental Maltreatment and Juvenile Theft in South Korea

Juvenile theft is the leading crime among adolescents in Korea and is a serious social concern. The present study is an examination of youth theft in the framework of general strain theory, which asserts that criminal behavior occurs as a response to various strains, such as parental abuse and neglect. To test the role of parent-youth gender dynamics in the relationship between parental strain and youth theft, the current study analyzed a community-based sample of youth offenders and non-offenders in Korea (N = 374) using multivariate logistic regression models with interaction terms. Paternal physical abuse and maternal neglect predicted greater youth involvement in theft behavior. Regarding parent-youth gender dynamics, there was no difference in the role of maternal or paternal maltreatment in predicting theft behavior in sons or daughters. The exception was fathers' neglect, in which daughters showed higher odds of theft engagement than did sons who experienced even greater paternal neglect. The findings underscored the distinct and detrimental role of parental maltreatment in adolescent theft. The results supported the need to reach out to parents in consideration of the youth's gender and provided important implications for guiding current social services in preventing juvenile theft in Korea

Validation of the South Korean Version of the Beliefs about Emotions Scale

Background Beliefs about the unacceptability of experiencing or expressing negative emotions can contribute to diverse psychological symptoms and associated with poor treatment outcomes and low treatment attempts. The Beliefs about Emotions Scale (BES) was developed to assess such beliefs based on the cognitive-behavioral models; however, no study has reported on the psychometric properties of the BES in Korea. The present study aimed to cross-culturally adapt and validate the BES for the Korean population (BES-K). Methods The BES-K was administered to 592 Korean adults (323 men and 269 women) aged 20–59 years. Exploratory and confirmatory factor analysis were used to assess the factor model of the scale. Pearson correlation coefficients were used to evaluate the relationships between the BES-K and other psychological measures. Results The result showed a two-factor model of the BES-K, with Factor 1 relating to Interpersonal and Factor 2 representing Intrapersonal aspects. The scale had significant yet moderately low correlations with measures of depression, anxiety, and difficulties in emotion regulation. Conclusion The BES-K is a useful instrument in evaluating the beliefs about emotions in the Korean population