to demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the banach-zareckitheorem is presented on the basis of the radon-nikodym theoremwhich emphasizes on measure-type properties of the lebesgueintegral. the banach-zarecki theorem says that a real-valuedfunction $f$ is absolutely continuous on a finite closed intervalif and only if it is continuo...

transfusion of blood products from an infected person with aids, is meant to infect recipient. blood products such as whole blood, red blood cells, platelets, plasma, frozen blood precipitate, factor viii, factor ix, can be infected with hiv. transmissions from blood factors can be seen in plasma from thousands of donors that were collected in a container and were used to treat hemophilia. bloo...

A number p is a safe prime if both p and (p − 1)/2 are prime. This note describes a method of generating safe primes that is considerably faster than repeatedly generating random primes q until p = 2q + 1 is also prime.

Transformational approach requires to write transformation functions that ensure properties C1 and C2. Proving these conditions on complex typed objects is a serious bottleneck for the application of this approach. We propose to use a theorem prover to assist the development of safe transformation functions. In this paper, we present how we have designed in that way a set of safe transformation...

this paper gives a short survey of some of the known results generalizing the theorem, credited to i. schur, that if the central factor group is finite then the derived subgroup is also finite.

in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

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