Let $X\subset {\mathbb{P}}^n$ be an integral and non-degenerate $m$-dimensional variety. For any $P\in {\mathbb{P}}^n$ the $X$-rank $r_X(P)$ is the minimal cardinality of $S\subset X$ such that $P\in \langle S\rangle$. Here we study the pairs $(X,P)$ such that $r_X(P)\ge n+2-m$, i.e. $r_X(P)=n+2-m$. These pairs exist only in positive characteristic, with $X$ strange and $P$ a strange point of $X$.

The main purpose of this paper is to prove that some hyperspaces of a non-metric chainable continuum have the fixed point property.

We generalize atomic decomposition for Banach spaces and called it $T$-atomic decomposition. A necessary condition for $T$-atomic decomposition is given. A characterization for a triangular atomic decomposition is also given. Finally, as an application of triangular atomic decompositions, we prove that if a Banach space has a triangular atomic decomposition, then it also has an approximative atomic decomposition, an atomic decomposition and a fusion Banach frame.

We give a generalization of error-correcting code construction from $C_{ab}$ curves by working with towers of algebraic function fields. The towers are constructed recursively, using defining equations of $C_{ab}$ curves. In order to estimate the parameters of the corresponding one-point Goppa codes, one needs to calculate the genus. Instead of using the Hurwitz genus formula, for which one needs to know about ramification behavior, we use the Riemann-Roch theorem to get an upper bound for the genus by counting the number of Weierstrass gap numbers associated to a particular divisor. We provide a family of examples of towers which meet the bound.

In this short note we provide an extension of a convolution identity for exchangeable dependent risks, which is motivated by an elegant proof of Panjer’s algorithm derived in Mikosch (2006).

We determine some stability results concerning the cubic functional equation in non-Archimedean fuzzy normed spaces. Our result can be regarded as a generalization of the stability phenomenon in the framework of $ℒ$-fuzzy normed spaces.

In this note we wish to implement some very technical consequences due to professor(s) P.J. Basser and Sinisa Pajevic [5] to discuss the spectral decomposition of $4$th-order Douglas tensor in ${}^{*}\text{P}$-Finsler manifold. Actually, throughout the article, we have just reviewed the results of [5] for a particular $4$th-order covariance Douglas tensor, most often enunciated in Finslerian geometry. Moreover, spectral decomposition techniques have been studied for isotropic Douglas tensor.