‏‎for the first time nakayama introduced qf-ring. in 1967 carl. faith and elbert a. walker showed that r is qf-ring if and only if each injective right r-module is projective if and only if each injective left r-modules is projective. in 1987 s.k.jain and s.r.lopez-permouth proved that every ring homomorphic images of r has the property that each cyclic s-module is essentialy embeddable in dire...

the space now known as complete erdos space ec was introduced by paul erdos in 1940 as the closed subspace of the hilbert space ?2 consisting of all vectors such that every coordinate is in the convergent sequence {0} ? { 1 n : n ? n}. in a solution to a problem posed by lex g. oversteegen we present simple and useful topological characterizations of ec. as an application we determine the ...

magnetic resonance imaging (mri) is a notable medical imaging technique that makes of phenomenon of nuclear magnetic resonance. because of the resolution and the technology being harmless, mri has considered as the most desirable imaging technique in clinical applications. the visual quality of mri plays an important role in accuracy of medical delineations that can be seriously degraded by exi...

in chapter 1, charactrizations of fragmentability, which are obtained by namioka (37), ribarska (45) and kenderov-moors (32), are given. also the connection between fragmentability and its variants and other topics in banach spaces such as analytic space, the radone-nikodym property, differentiability of convex functions, kadec renorming are discussed. in chapter 2, we use game characterization...

adolescents and young adults and their problems is an issue whose importance is obvious to anyone because youth are the founders of our countrys future and requires proper planning to be on leisure. given the importance of leisure,this study to investigate needs assessment and planning how adolescents and young adults spend their leisure time in urban of case study of high school girls and boys...

the main objective in sampling is to select a sample from a population in order to estimate some unknown population parameter, usually a total or a mean of some interesting variable. a simple way to take a sample of size n is to let all the possible samples have the same probability of being selected. this is called simple random sampling and then all units have the same probability of being ch...

let h be a separable hilbert space and let b be the set of bessel sequences in h. by using several interesting results in operator theory we study some topological properties of frames and riesz bases by constructing a banach space structure on b. the convergence of a sequence of elements in b is de_ned and we determine whether important properties of the sequence is preserved under the con...