Hilbert’s machine is a supertask machine inspired by Hilbert’s Hotel whose functioning leads to a contradiction that compromises the Axiom of Infinity. 1. Hilbert’s Machine In the following conceptual discussion we will make use of a theoretical device that will be referred to as Hilbert’s machine, composed of the following elements (see Figure 1): (1) An infinite tape similar to those of Turin...

Abstract Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, alienation problem between Drygas’ and exponential Cauchy functional equations, which is expressed equation f ( x + y ) g...

In the case of equation (1.2) condition (1.4) coincides with the known Kruzhkov entropy condition [9]. If the function g(u) strictly increases then any weak solution of (1.1) is an entropy solution of this equation as well (cf. [2]) but for degenerate equations this may be violated and, in particular, entropy condition (1.4) is necessary for the uniqueness of solution to the Cauchy problem for ...

After brieey reviewing the interrelation between Riesz-bases, biorthogonality and a certain stability notion for multiscale basis transformations we establish a basic stability criterion for a general Hilbert space setting. An important tool in this context is a strengthened Cauchy inequality. It is based on direct and inverse estimates for a certain scale of spaces induced by the underlying mu...

This paper draws on the theory of soft $A$-metric space using points sets and concept spaces. new has great importance as a type generalisation metric spaces since it includes various known In this paper, we introduce examine relations with Then, basic properties these spaces: Hausdorffness, Cauchy sequence, convergence.

Given a smooth projective variety X X over number field alttext="k"> k encoding="application/x-tex">k...

Let k be an integer. Two vertex k-colorings of a graph are adjacent if they differ on exactly one vertex. A graph is k-mixing if any proper k-coloring can be transformed into any other through a sequence of adjacent proper k-colorings. Any graph is (tw + 2)-mixing, where tw is the treewidth of the graph (Cereceda 2006). We prove that the shortest sequence between any two (tw + 2)-colorings is a...

In this paper, determining the operator norm, we give certain characterizations of matrix transformations from space $ \left\vert \overline N_p^{\phi }\right\vert _{k}$, all series summable by absolute weighted mean summability method, to one classical sequence spaces $c_{0},c,l_{\infty }.$ Also, obtain necessary and sufficient conditions for each in these classes be compact establish a number ...

In this paper, we introduce the concept of Kaleva-Seikkala’s type fuzzy b -metric spaces as a generalization notion id="M3"> and metric spaces. such spaces, establish Banach type, Reich Chatterjea fixed-point theorems, which improve relevant results in Two technical lemmas are employed to ensure that Picard sequence is C...