The stochastic Fokas system (SFS), driven by multiplicative noise in the Itô sense, was investigated this study. Novel trigonometric, rational, hyperbolic, and elliptic solutions are found using a modified mapping method. Because is used to explain nonlinear pulse propagation monomode optical fibers, provided may be utilized analyze broad range of critical physical phenomena. In order impacts n...

‎Bucket recursive trees are an interesting and natural‎ ‎generalization of ordinary recursive trees and have a connection‎ to mathematical chemistry‎. ‎In this paper‎, ‎we give the lower and upper bounds for the moment generating‎ ‎function and moments of the multiplicative Zagreb indices in a‎ ‎randomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$‎. Also, ‎we consi...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called ΣΠΣ circuits, we show that there is a tight connection between error correcting codes and circuits computing functions with high nonlinearity. Combining this with known coding theo...

We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L1 setting requiring no growth assumptions on the nonline...

In this paper, regular fast algorithms for discrete cosine transform (DCT) and discrete sine transform (DST) of types II–IV are proposed and mapped onto pipeline architectures. The algorithms are based on the factorization of transform matrices described earlier by Wang. The regular structures of the algorithms are advantageous when mapping them onto hardware although such algorithms do not rea...

The Cayley–Dickson loop Qn is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley–Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). We establish that the inner mapping group Inn(Qn) is an elementary abelian 2-group of order 2 −2 and describe the multiplicati...

The differential uniformity of a mapping F : F2n → F2n is defined as the maximum number of solutions x for equations F (x+a)+F (x) = b when a ̸= 0 and b run over F2n . In this paper we study the question whether it is possible to determine the differential uniformity of a mapping by considering not all elements a ̸= 0, but only those from a special proper subset of F2n \ {0}. We show that the ans...