In this paper we introduce continuous $g$-Bessel multipliers in Hilbert spaces and investigate some of their properties. We provide some conditions under which a continuous $g$-Bessel multiplier is a compact operator. Also, we show the continuous dependency of continuous $g$-Bessel multipliers on their parameters.

We propose a new method called C-SOM using a Self-Organizing Map (SOM) for function approximation. C-SOM takes care about the output values of the «win-ning» neuron's neighbors of the map to compute the output value associated with the input data. Our work extends the standard SOM with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve its gen...

the notion of a probabilistic metric  space  corresponds to thesituations when we do not know exactly the  distance.  probabilistic metric space was  introduced by karl menger. alsina, schweizer and sklar gave a general definition of  probabilistic normed space based on the definition of menger [1]. in this note we study the pn spaces which are  topological vector spaces and the open mapping an...

We introduce a model of reproduction in which the genotypephenotype (G-P) map is able to evolve. In this model, Each organism implements a G-P map, determining how the organism is encoded in its genome. Crucially, it also determines how the G-P map itself is encoded. We call these maps ‘self-encoding’. We relate this model to recent artificial life research, and back to the seminal work of John...

In this paper, we study the existence and uniqueness of fixed points for mappings with respect to a $wt$-distance in $b$-metric spaces endowed with a graph. Our results are significant, since we replace the condition of continuity of mapping with the condition of orbitally $G$-continuity of mapping and we consider $b$-metric spaces with graph instead of $b$-metric spaces, under which can be gen...

This work describes the characterisation and culture performance of a novel, orbitally shaken, single-use photobioreactor (SUPBr) system for microalgae cultivation. The SUPBr mounted on an orbitally shaken platform was illuminated from below. Investigation of fluid hydrodynamics indicated a range of different flow regimes and the existence of 'in-phase' and 'out-of-phase' conditions. Quantifica...

An N-dimensional real representation E of a finite group G is said to have the “Borsuk-Ulam Property” if any continuous G-map from the (N + 1)-fold join of G (an N-complex equipped with the diagonal G-action) to E has a zero. This happens iff the “Van Kampen characteristic class” of E is nonzero, so using standard computations one can explicitly characterize representations having the B-U prope...

Some operator inequalities for synchronous functions that are related to the c̆ebys̆ev inequality are given. Among other inequalities for synchronous functions it is shown that ‖φ (f (A) g (A))− φ (f (A))φ (g (A))‖ ≤ max {∥∥φ (f2 (A))− φ (f (A))∥∥ , ∥∥φ (g2 (A))− φ (g (A))∥∥} whereA is a self-adjoint and compact operator on B (H ), f, g ∈ C (sp (A)) continuous and non-negative functions and φ : B...

Let f be a continuous map of an interval into itself having periodic points of period 2n for all n ≥ 0 and no other periods. It is shown that every neighborhood of f contains a map g such that the set of periods of the periodic points of g is finite. This answers a question posed by L. S. Block and W. A.