International Journal of Mathematics and Mathematical Sciences

In analytic geometry, Bézout’s theorem stated the number of intersection points of two algebraic curves and Fulton introduced the intersection multiplicity of two curves at some point in local case. It is meaningful to give the exact expression of the intersection multiplicity of two curves at some point. In this paper, we mainly express the intersection multiplicity of two curves at some point in and under fold point, where . First, we give a sufficient and necessary condition for the coincidence of the intersection multiplicity of two curves at some point and the smallest degree of the terms of these two curves in . Furthermore, we show that two different definitions of intersection multiplicity of two curves at a point in are equivalent and then give the exact expression of the intersection multiplicity of two curves at some point in under fold point.

Fractional-order derivative modeling continues to receive great interest among researchers across the globe. In this study, Tuberculosis-COVID-19 coinfection is studied using Atangana–Baleanu fractional-order derivatives defined in Caputo sense. We confirmed the existence and singularity of the solution and investigated the model’s equilibrium points. Additionally, we examined the model’s stability in terms of the Ulam–Hyers and generalized Ulam–Hyers stability criteria. The basic reproduction number was calculated using the next-generation matrix approach. We also looked into the model’s disease-free equilibrium point’s regional stability. Numerical scheme for simulating the fractional-order system with Mittag–Leffler Kernels are presented. Numerical simulations are given to validate the model. Results of the simulation showed a decline in the number of COVID-19 infections within the population when the fractional operator was reduced.

In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3-variables quadratic functional equation in the setting of 2-Banach space. Also, we obtain some hyperstability results for the 3-variables quadratic functional equation. The results obtained in this paper extend several known results of the literature to the setting of 2-Banach space.

In this paper, we prove that the characteristic of a minimal ideal and a minimal generalized ideal, which is meant to be one of minimal left ideal, minimal right ideal, bi-ideal, quasi-ideal, and -ideal in a ring, is either zero or a prime number . When the characteristic is zero, then the minimal ideal (minimal generalized ideal) as additive group is torsion-free, and when the characteristic is , then every element of its additive group has order . Furthermore, we give some properties for minimal ideals and for generalized ideals which depend on their characteristics.

Stated choice experiments are increasingly becoming popular due to their ability to optimize information gain with limited resources. Many designs have been developed for the selection of various attributes and their levels to form choice sets. One such design is blocked fractional factorial design (BFFD). Stated choice experiments for symmetric attributes of 4 choice sets of sizes 2 and 4 and 8 choice sets of sizes 2 and 4 were developed using BFFDs. Generators for the stated choice set of sizes 2 and 4 with resolution three, four, and five were developed. The alias structures and confounding effects for the designs were derived, as well as their clear effects if any for estimation. The -efficiency was used to compute the efficiencies of the proposed designs since it has better statistical properties. The computed efficiencies for the proposed designs reveal that 4 choice sets of size 4 designs are more efficient. Finally, a practical application of the proposed method was carried out for four choice sets of size 4 using design with attributes and levels of service quality in public transport.

The aim of this research is to study the effects of thermal radiation and chemical reaction on hydromagnetic fluid flow in a cylindrical collapsible tube with an obstacle. The fluid flow is governed by continuity, momentum, energy, and concentration equations. Similarity transformation has been used to convert the obtained PDEs into ODEs. The collocation method has been used to numerically solve the ODEs. The method has been implemented in MATLAB using the bvp4c inbuilt function. The effects of the nondimensional parameters on velocity, temperature, and concentration have been presented graphically. Additionally, the skin-friction coefficient, the Nusselt number, and the Sherwood number have been discussed and are presented in a tabular form. The findings demonstrated that increasing the Reynolds number causes a rise in the fluid temperature and velocity. The fluid velocity decreases as the Hartmann number and the weight of the obstacle increase but increases with increasing Grashof numbers. The temperature of the fluid increases as the radiation parameter, or Eckert number, increases, but decreases as the Prandtl number increases. As the Soret number rises, so do the fluid’s temperature and concentration distribution. With an increase in the unsteadiness parameter, the fluid velocity and the concentration distribution decrease, whereas the opposite is seen in temperature. As the Schmidt number, the concentration Grashof number, and the chemical reaction parameter increase, the fluid’s concentration decreases. There is an increase in skin-friction coefficient with increasing Prandtl number, Eckert number, Soret number, thermal Grashof number, concentration Grashof number, thermal radiation parameter, Hartmann number, and unsteadiness parameter, while a decrease is observed with increasing Reynolds number. The Nusselt number increases with an increase in the Prandtl number, Eckert number, thermal radiation parameter, Hartmann number, and unsteadiness parameter. A slight decrease in the Nusselt number has been observed with increasing thermal Grashof number. The Sherwood number decreases with increasing Prandtl number, chemical reaction parameter, and thermal radiation parameter but increases with increasing Schmidt number, Eckert number, and Soret number. The research has the potential for a wide range of applications including but not limited to the medical field and other physical sciences.