Almost every, essentially: Given a Lebesgue measure space (X,B, μ), a property P (x) predicated of elements of X is said to hold for almost every x ∈ X, if the set X \ {x : P (x) holds} has zero measure. Two sets A,B ∈ B are essentially disjoint if μ(A ∩B) = 0. Conservative system: Is an infinite measure preserving system such that for no set A ∈ B with positive measure are A,T−1A,T−2A, . . . p...

In Mexico, there are important elements within the built and sculptural heritage, characterized by a rich variety of cultures that left vestiges. Due to age various elements, it is necessary carry out restoration processes include partial replacement components others physically compatible. This same putty can be used make models elaboration pieces allow making them known or preserving them. Re...

Two plane graphs with the same vertex set are compatible if their union is again a plane graph. We consider bichromatic plane straight-line graphs with vertex set S consisting of the same number of red and blue points, and (perfect) matchings which are compatible to them. For several different classes C of graphs, we present lower and upper bounds such that any given graph G(S) ∈ C admits a com...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

We construct both randomizable and strongly existentially unforgeable structure-preserving signatures for messages consisting of many group elements. To sign a message consisting of N = mn group elements we have a verification key size of m group elements and signatures contain n+2 elements. Verification of a signature requires evaluating n+1 pairing product equations. We also investigate the c...

We develop the mathematical theory of algebra functions on for a finite alphabet , such that the functions are level-compatible when they are restricted to the different levels according to . We shall first establish the fundamentals and the structure of such function spaces and the related properties, and propose and study the all important level-preserving transformers there. We shall then lo...

in this research, the methodology of which is descriptive-inferential, our problem is the role of the unity of divine acts in mulla sadra’s transcendent philosophy and the evaluation of his arguments on it. in this regard, after explaining the concept of “unity of divine acts”, we show that since the boundaries of sadra’s philosophical system approaches speculative mysticism, sadra’s system in ...