In this paper we prove a discrete version of Tanaka’s Theorem [19] for the Hardy-Littlewood maximal operator in dimension n = 1, both in the non-centered and centered cases. For the non-centered maximal operator f M we prove that, given a function f : Z→ R of bounded variation, Var(f Mf) ≤ Var(f), where Var(f) represents the total variation of f . For the centered maximal operator M we prove th...

Uptil now most of the work is done on image, video, audio.but today the Database watermarking becomes the research topic because of the increasing the use of relational database systems. Which deals with the legal issue of copyright protection of database systems. .Watermarking is an information hiding technique which is used to embed a mark within some host content. In this paper,we have focus...

Our aim is to show that it is impossible to find a bound for the power of the first fixed point of the aleph function. 0 Introduction אα is called a fixed point of the א-function if אα = α. It is called the first fixed point if α is the least ordinal such that אα = α. More constructive, the first repeat point of the א-function is the limit of the following sequence א0,אא0 ,אאא0 ,אאאא0 , . . . T...

Heat stroke is hardly seen in Malaysia. However, it occurs commonly in Saudi Arabia during the Haj season. Many Malaysian pilgrims are affected every year and some die. Having faced this environmental hazard for eight years, the Malaysian Medical Mission, sent each year to look after our pilgrims, modified its treatment strategy in 1988 and successfully decreased the overall morbidity and morta...