This thesis is concerned with the development and application of categorical tools in the study of the cluster algebras of S. Fomin and A. Zelevinsky. C. Amiot’s generalized cluster category is a triangulated category which has been used, in the case where it is Hom-finite, to categorify a certain class of cluster algebras, using cluster characters in the sense of Y. Palu. In this thesis, we ge...

We present a new skew-normal distribution, denoted by NSN($lambada$). We first derive the density and moment generating function of NSN($lambada$). The properties of SN($lambada$), the known skew-normal distribution of Azzalini, and NSN($lambada$) are compared with each other. Finally, a numerical example for testing about the parameter $lambada$ in NSN($lambada$) is given. ...

This research is based on cases of hail that caused flooding in Binjai City May 22, 2022. study aims to see the correlation and regression Atmospheric Stability index value cloud top temperature data from Himawari-8 satellite imagery. So ERA-5 reanalysis can be used obtain temperatures predicting events. The indices this are CAPE, KI TTI. located with testing 00UTC – 24UTC Supported form sea su...

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

In this thesis some aspects of process capability analysis are considered. Process capability analysis deals with how to assess the capability of manufacturing processes. Based on the process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability ...

In group-living species with male dominance hierarchies where receptive periods of females do not overlap, high male reproductive skew would be predicted. However, the existence of female multiple mating and alternative male mating strategies can call into question single-male monopolization of paternity in groups. Ring-tailed lemurs (Lemur catta) are seasonally breeding primates that live in m...

Let $S(G^{sigma})$ be the skew-adjacency matrix of the oriented graph $G^{sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $sigma$ to each of its edges. The skew energy of an oriented graph $G^{sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{sigma})$. Two oriented graphs are said to be skew equienergetic iftheir skew energies...

It is well-known that the skew-normal distribution can provide an alternative model to the normal distribution for analyzing asymmetric data. The aim of this paper is to propose two goodness-of-fit tests for assessing whether a sample comes from a multivariate skew-normal (MSN) distribution. We address the problem of multivariate skew-normality goodness-of-fit based on the empirical Laplace tra...