In the present paper terminology “total” is used for a generalization of the Burkill integral and multiplicative integral, respectively. The functions, the totals of which are considered, take their values from a Banach algebra B with a unity. This means a Banach space B in which for every pair f ∈ B, g ∈ B a product fg ∈ B is defined such that ‖fg‖ ≤ ‖f‖ ‖g‖ and if h ∈ B, then f(g + h) = fg + ...

We show that a completely multiplicative automatic function, which dos not have 0 as value, is almost periodic.

Linear discrete-time systems with stochastic uncertainties in their state-space model are considered. The problem of dynamic output-feedback control is solved via a new approach, for both the finite horizon and the stationary cases. In both cases, a cost function is defined which is the expected value of the standard H∞ performance index with respect to the uncertain parameters. An example is g...

In this paper we investigate multiplicative noise models in the context of continuous optimization. We illustrate how some intrinsic properties of the noise model imply the failure of reasonable search algorithms for locating the optimum of the noiseless part of the objective function. Those findings are rigorously investigated on the (1 + 1)-ES for the minimization of the noisy sphere function...

abstract various mathematical water uptake models have been introduced for plants response to combined drought and salinity stress. the reduction functions are classified as additive, multiplicative and conceptual models. in this study six different macroscopic reduction functions, namely; van genuchten (additive and multiplicative), dirksen et al., van dam et al, skaggs et al and homaee were e...

We introduce a class of multiplicative functions in which each function satisfies some statistic conditions, and then prove that the above are not correlated with finite degree polynomial nilsequences. Besides, we give two applications this result. One is twisting coefficients automorphic L-function on G L m ( ⩾ 2 ) $GL_m (m \geqslant 2)$ nilsequences has logarithmic decay; other mean value Möb...

We study succinct representations of a convex univariate function φ over a finite domain. We show how to construct a succinct representation, namely a piecewise-linear function φ̄ approximating φ when given a black box access to an L-approximation oracle φ̃ of φ (the oracle value is always within a multiplicative factor L from the true value). The piecewise linear function φ̄ has few breakpoints (...

Permutations over F22k with low differential uniform, high algebraic degree and high nonlinearity are of great cryptographical importance since they can be chosen as the substitution boxes (S-boxes) for many block ciphers. A well known example is that the Advanced Encryption Standard (AES) chooses a differentially 4-uniform permutation, the multiplicative inverse function, as its S-box. In this...