‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

The aim of this paper is to show that under some mild conditions a functional equation of multiplicative $(alpha,beta)$-derivation is superstable on standard operator algebras. Furthermore, we prove that this generalized derivation can be a continuous and an inner $(alpha,beta)$-derivation.

Let T be a triangular ring. An additive map δ from T into itself is said to be Jordan derivable at an element Z ∈ T if δ(A)B +Aδ(B) + δ(B)A+Bδ(A) = δ(AB+BA) for any A,B ∈ T with AB + BA = Z. An element Z ∈ T is called a Jordan all-derivable point of T if every additive map Jordan derivable at Z is a Jordan derivation. In this paper, we show that some idempotents in T are Jordan all-derivable po...

This paper establishes a relation between the notion of a codifferential category and the more classic theory of Kähler differentials in commutative algebra. A codifferential category is an additive symmetric monoidal category with a monad T , which is furthermore an algebra modality, i.e. a natural assignment of an associative algebra structure to each object of the form T (C). Finally, a codi...

This paper presents a formula to predict expected response to one generation of truncation selection for a dichotomous trait under polygenic additive inheritance. The derivation relies on the threshold liability concept and on the normality assumption of the joint distribution of additive genetic values and their predictors used as selection criteria. This formula accounts for asymmetry of resp...

The derivation and analysis of optimum multiuser detectors for additive-rate and additive-light Poisson multiple-access channels are studied. The observed point process models the output of an ideal photodetector illuminated by several synchronous or asynchronous users who modulate coherent light of the same frequency. Dynamic programmingbased decision rules for the asynchronous multiple-access...

In this work, we study the formal connections between non-linear Fokker-Planck Equation associated with non-additive entropy and Boltzmann correlation functional. The collisional term following $q$-algebra is adopted. derivation of Equation, two constraints are imposed on final result: i) that entropic index $q$ a characteristic parameter systems value does not change time, ii) for $q \rightarr...