In this paper we give an alternative proof of the construction of n-dimensional ordinal sums given in Mesiar and Sempi \cite{mesiar}, we also provide a new methodology to construct n-copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in \cite{durante08} and \cite{durante09}. Finally, we use the gluing method of Siburg and Stoimenov \cite{siburg} and its generalization in Mesiar {et al.} \cite{mesiarjagr} to give an alternative method of patchwork construction of n-copulas, which can be also used in composition with our patchwork method.
The concept of an n-equidistant polygonal fuzzy number is introduced to avoid the complexity of the operations between fuzzy numbers. Firstly, the properties of linear operations and the convergence of n-equidistant polygonal fuzzy numbers are discussed, the method how to change a fuzzy number into an n-equidistant polygonal fuzzy number is shown. Next, for given a µ-integrable polygonal fuzzy valued function, an n-equidistant polygonal fuzzy valued function is constructed. By introducing the definition of K-quasi-additive integral and Kintegral norm, the universal approximation of polygonal fuzzy neural network are studied. The final result indicates that the polygonal fuzzy neural network still possess universal approximation to an integrable system.
A tree is classified as being type I provided that there are two or more Perron branches at its characteristic vertex. The question arises as to how one might construct such a tree in which the Perron branches at the characteristic vertex are not isomorphic. Motivated by an example of Grone and Merris, we produce a large class of such trees, and show how to construct others from them. We also investigate some of the properties of a subclass of these trees. Throughout, we exploit connections between characteristic vertices, algebraic connectivity, and Perron values of certain positive matrices associated with the tree.
A construction of cell algebras is introduced and some of their properties are investigated. A particular case of this construction for lattices of nets is considered.
We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.
A surjective bounded homomorphism fails to preserve n-weak amenability, in general. We however show that it preserves the property if the involved homomorphism enjoys a right inverse. We examine this fact for certain homomorphisms on several Banach algebras.
The paper deals with a description of a constructive neural network based on gradient initial setting of its weights. The network has been used as a pattern classifier of two dimensional patterns but it can be generally used to n x m associative problems. A network topology, processes of learning and retrieving, experiments and comparison to other neural networks are described.
Ground beetles (Carabidae: Coleoptera) are predators of the seed of herbaceous plants scattered on the ground, but prefer that of certain species. Foraging beetles encounter both freshly dispersed and seed exhumed from the soil bank. The predation on seed from the soil bank has never been studied and the effect of burial on seed acceptability is unknown. The preferences of two generalist granivorous carabids, Harpalus affinis and Pseudoophonus rufipes, were investigated by offering them fresh (stored frozen after dispersal) and buried (for 6 months in the soil under field conditions) seed of six common weed species. Significantly more of the buried seed of Tripleurospermum inodorum and significantly less of that of Taraxacum officinale was eaten than fresh seed. For four other weed species the consumption of both kinds of seed did not differ. The preferences were similar in both species of carabid. The change in preference probably occurred because the seed of T. officinale was partially decayed and the repellent surface of T. inodorum seed abraded. Provided the seed in the soil bank does not decay it may have a similar or better food value for carabids than fresh seed.
For every product preserving bundle functor $T^\mu $ on fibered manifolds, we describe the underlying functor of any order $(r,s,q), s\ge r\le q$. We define the bundle $K_{k,l}^{r,s,q} Y$ of $(k,l)$-dimensional contact elements of the order $(r,s,q)$ on a fibered manifold $Y$ and we characterize its elements geometrically. Then we study the bundle of general contact elements of type $\mu $. We also determine all natural transformations of $K_{k,l}^{r,s,q} Y$ into itself and of $T(K_{k,l}^{r,s,q} Y)$ into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from $Y$ to $K_{k,l}^{r,s,q} Y$.
The P3 intersection graph of a graph G has for vertices all the induced paths of order 3 in G. Two vertices in P3(G) are adjacent if the corresponding paths in G are not disjoint. A w-container between two different vertices u and v in a graph G is a set of w internally vertex disjoint paths between u and v. The length of a container is the length of the longest path in it. The w-wide diameter of G is the minimum number l such that there is a w-container of length at most l between any pair of different vertices u and v in G. Interconnection networks are usually modeled by graphs. The w-wide diameter provides a measure of the maximum communication delay between any two nodes when up to w − 1 nodes fail. Therefore, the wide diameter constitutes a measure of network fault tolerance. In this paper we construct containers in P3(G) and apply the results obtained to the study of their connectivity and wide diameters.