Journal of AppliedMath

On wavelet type Chlodovsky Bézier operators

2025-07-01T07:19:05+00:00

This paper mainly deals with Chlodovsky Bézier variants constructed via compactly supported Daubechies wavelets. We estimate the convergence rate of the aforementioned operators at a fixed point x₀> 0 at which the one-sided limits exist of the target function f. It is evident that the class of operators under consideration encompasses at least the classical version of the Chlodovsky operators along with their B ézier and Kantorovich variants. Therefore, our findings broaden and build upon previous results on Chlodovsky, Chlodovsky Bézier, Chlodovsky-Kantorovich Bézier operators presented in the literature.

Model validation based on value-of-information theory

2025-07-03T00:40:34+00:00

The modeling and simulation community has devoted considerable attention to the question of model validity as a condition for the use of a model in an engineering decision-making process. Their work has focused on the concept of “accuracy”, loosely defined as the difference between a model-computed result and a real-world result. The objective of this paper is to introduce an alternative approach, based on classical decision theory, that focuses on the value of the information that a model provides to the decision-making process. This is a significant departure from the current approach to model validation, and it derives from the preference, “I want the best outcome that I can get”. Use is made of an example case that results in a paradox to illustrate weaknesses in the accuracy-focused approach. Instead of advocating the use of a model based on its accuracy, this work advocates using a model if it adds value to the overall application, thus relating validation directly to system performance. The approach fills significant gaps in the current theory, notably providing a clearly defined validity metric and a mathematically rigorous rationale for the use of this metric.

The new Generalized Schwarzschild-spacetimes trivial Ricci solitons and the new smooth metric space

2025-07-23T03:30:59+00:00

The Ricci flow of the Generalized-Schwarzschild spacetimes is newly studied. The soliton configurations are newly stated as trivial Ricci soliton of (Generalized)-Schwarzschild spacetimes. The new smooth metric space is written; the majorization theorem for the distance is given. The application of harmonic maps is presented. The definition of topological soliton as a Schwarzschild soliton of complete Riemannian manifold is newly provided with. New theorems about Generalized-Schwarzschild solitons which are extended from those about the Kaehler solitons are proven; the new theorems are given, which allow one to establish the differences with respect to Kaehler solitons. The new properties of the Generalized Schwarzschild metric are studied. As results, smooth metric spaces are newly exposed as ones endowed with bounded Bakry-Emery curvature; the initial conditions are newly studied: the weight function is majorized as consisting of a polynomial function of the distance(s) (from the initial condition) at most.The Generalized-Schwarzschild metric is now newly proven to be descending from a smooth function. The initial conditions are newly studied to depend only on the spherical neighborhood of the point. The trivial expanding Ricci Kaehler soliton is newly proven to be a Generalized-Schwarzschild soliton; accordingly, this soliton is newly proven to have only one end.

A new quantum computational set-up for algebraic topology via simplicial sets

2025-07-01T06:55:34+00:00

In this paper, a quantum computational framework for algebraic topology based on simplicial set theory is presented. This extends previous work, which was limited to simplicial complexes and aimed mostly at topological data analysis. The proposed set-up applies to any parafinite simplicial set and proceeds by associating with it a finite dimensional simplicial Hilbert space, whose simplicial operator structure is studied in some depth. It is shown in particular how the problem of determining the simplicial set’s homology can be solved within the simplicial Hilbert framework. Further, the conditions under which simplicial set theoretic algorithms can be implemented in a quantum computational setting with finite resources are examined. Finally a quantum algorithmic scheme capable of computing the simplicial homology spaces and Betti numbers of a simplicial set combining a number of basic quantum algorithms is outlined.