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...

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...

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 ...

As modeling details can have a large impact on planner performance, domain transformation has been a traditional subject of interest in the planning community not only between languages, but also within languages. Herein, we automate an intra-language transformation method that has as yet been applied only manually, and that has never been formally described: action schema splitting, which tran...

The distribution of Coxeter descents and block number over the set fully commutative elements in hyperoctahedral group B n , FC ( ) is studied this paper. We prove that associated Chow quasi-symmetric generating function equal to a non-negative sum products two Schur functions. proof involves decomposition into disjoint union two-sided Barbash–Vogan combinatorial cells, type extension Rubey’s d...