International Journal of Open Problems in Computer Science and Mathematics

Some new parametric integral formulas depending on an adjustable function

2025-07-02T11:29:18+00:00

This article presents new integral formulas based on a single adjustable function and one or two minimally restricted parameters. These formulas are not found in previous literature. They are notable for their simplicity and their links to key mathematical constants and special functions.

On Spectral Properties of Orthogonal Isometries

2025-07-17T20:50:26+00:00

Isometries are special mappings with a property of distance preservation. This property makes them unique and interesting in-terms of characterization. However, it is very difficult to do characterizations of properties of isometires in a general Banach space setting due to the intricate underlying structures in Banach spaces. In this paper, we characterize spectral properties of isometries and in particular when they are orthogonal. We show that orthogonal isometries preserve distance even when they are subjected to direct sum decomposition.

New two-parameter integral formulas proved via the digamma function

2025-08-07T15:15:24+00:00

This paper presents new integral formulas involving two parameters: an integer parameter and a real parameter. These formulas are notable for their generality, as well as for the method of proof, which relies on the properties of the digamma function. Detailed derivations are provided, offering a fresh perspective compared to more conventional techniques. Additionally, the paper proposes an open problem concerning the possibility of proving these results using standard integral calculus methods.

Achromatic Numbers of $n$-Complete Starfish and $SF(n, 1)$ Graphs

2025-09-09T07:31:55+00:00

The achromatic number of a graph is the largest number of colors that can be assigned to each vertex of the graph such that adjacent vertices are assigned different colors and any two different colors are assigned to some pair of adjacent vertices. In this paper, we find exact values of the achromatic numbers of $n$-complete starfish graphs, and bounds on the achromatic numbers of $SF(n, 1)$ graphs when $n$ is a natural number and $n\geq 3$.

On Spectra of Symmetrized Two-Sided Multiplication Operators Implemented by Orthogonal Isometries

2025-08-15T21:47:12+00:00

Characterization of Symmetrized Two-Sided Multiplication Operators have been done over years in-terms of their properties which include numerical ranges and norms among others. However, characterizing the spectrum and norms have not been exhausted still remains interesting. There exists an open question requiring the determination of the norms of elementary operators in a general Banach space setting. Since there is a strong relation ship between the norm and spectral radius, it is in the interest of this study to characterize spectral properties of Symmetrized Two-Sided Multiplication Operators as an avenue that can help in solving the general problem.

Dynamical Analysis and Modeling of COVID-19 and Related Diseases under Comorbidity in Complex Domains

2025-09-22T12:23:31+00:00

The COVID-19 infection is known for causing more challenges to people with underlying health conditions such as cardiovascular, cerebrovascular and diabetes among others. Due to these complications and outbreak of diseases, there is need to formulate a model for comorbidities. Those who have these two or more diseases died at higher rate, four times, compared to those who are suffering from one disease. For diabetes and COVID-19 infected patients, mortality rate is higher, this means the rate of recovery is low and more resources are used towards patients with diabetes and COVID-19 comorbidity. Containment measures for COVID-19 such as quarantine and social distancing may lead to a decline in exercising and lack of a balanced diet, which are key for managing diabetic complications such as vision loss and kidney failure. This note provides a dynamical analysis comparing the rate of recovery and death rate that is high in those co-morbidities compared to those who do not have co-morbidities, all under vaccinations.

New Look of Trigonometric and Hyperbolic Inequalities

2025-09-29T11:05:53+00:00

In this paper, we introduce a new approach for families to parameter dependent inequalities. Depending on the values of the different parameters these inequalities are extending the classical ones.

Study of a particular class of integrals

2025-10-01T13:45:32+00:00

This paper investigates a specific class of integrals that produce interesting results, including evaluations involving fundamental mathematical constants. Rigorous proofs are provided, and several directions for future research are proposed.