Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

Our goal from this work is to find the linear prediction of the sum of two Poisson process
) ( ) ( ) ( t Y t X t Z + = at the future time 0 ), ( ≥ + τ τ t Z and that is when we know the values of
) (t Z in the past time and the correlation function ) (τ βz

This Book is intended to be a textbook studied for undergraduate course in financial statistics/ department of Financial Sciences and Banking. This book is designed to be used in semester system. To achieve the goals of the book, it is divided into the following chapters. Chapter one introduces basic concepts. Chapter two devotes to frequency distribution and data representation. Chapter three discusses central tendency measures (all types of means, mode, and median). Chapter four deals with dispersion Measures (standard deviation, variance, and coefficient of variation). Chapter five concerned with correlation and regression analysis. While chapter six concerned with testing Hypotheses (One population mean test, Two "independent" populati

Crime is considered as an unlawful activity of all kinds and it is punished by law. Crimes have an impact on a society's quality of life and economic development. With a large rise in crime globally, there is a necessity to analyze crime data to bring down the rate of crime. This encourages the police and people to occupy the required measures and more effectively restricting the crimes. The purpose of this research is to develop predictive models that can aid in crime pattern analysis and thus support the Boston department's crime prevention efforts. The geographical location factor has been adopted in our model, and this is due to its being an influential factor in several situations, whether it is traveling to a specific area or livin

Bis-anthraquinones with a unique molecular backbone, (+)-2,2’-epicytoskyrin A (epi) and (+)-1,1′-bislunatin (bis), was produced by endophytic fungi Diaporthe sp GNBP-10 associated with Gambir plant (Uncaria gambier). Epi and bis possess robust antimicrobial activity toward various pathogens. This study focus on knowing the optimum condition of epi and bis production from Diaporthe sp GNBP-10. A series of culture media with various nutrient compositions was investigated in epi and bis production. The content of epi and bis was determined by measuring the area under the curve from TLC-densitometric (scanner) experiment. The linear regression analysis was then applied to obtain the results. The optimi

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

In this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.

Watermelon is known to be infested by multiple insect pests both simultaneously and in sequence. Interactions by pests have been shown to have positive or negative, additive or non additive, compensatory or over compensatory effects on yields. Hardly has this sort of relationship been defined for watermelon vis-à-vis insect herbivores. A 2-year, 2-season (4 trials) field experiments were laid in the Research Farm of Federal University Wukari, to investigate the interactive effects of key insect pests of watermelon on fruit yield of Watermelon in 2016 and 2017 using natural infestations. The relationship between the dominant insect pests and fruit yield were determined by correlation (r) and linear regression (simple and multiple) analys