On additive functions with a non-decreasing normal order

On the Normal Order of Arithmetic Functions.

Decreasing Functions with Applications

The theory of increasing positively homogeneous functions deened on the positive orthant is applied to the class of decreasing functions. A multiplicative version of the inf-convolution operation is studied for decreasing functions. Modiied penalty functions for some constrained optimization problems are introduced which are in general nonlinear with respect to the objective function of the ori...

On construction of non-normal Boolean functions

Given two non-weakly k-normal Boolean functions on n variables a method is proposed to construct a non-weakly (k + 1)-normal Boolean function on (n + 2)variables.

Modified Maximum Likelihood Estimation in First-Order Autoregressive Moving Average Models with some Non-Normal Residuals

When modeling time series data using autoregressive-moving average processes, it is a common practice to presume that the residuals are normally distributed. However, sometimes we encounter non-normal residuals and asymmetry of data marginal distribution. Despite widespread use of pure autoregressive processes for modeling non-normal time series, the autoregressive-moving average models have le...

Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements

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...