Journal of Mathematics

The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.

In this study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya-like triangles to make it easier to examine the basic properties of these numbers. With the help of the properties obtained in this study, we defined a number sequence containing the new type of Leonardo numbers created by choosing the coefficients from the bicomplex numbers. Furthermore, we gave the relationship of this newly defined sequence with the Fibonacci sequence. We also provided some important identities in the literature provided by the elements of this sequence described in this paper.

The world economy is affected by fluctuations in the price of crude oil, making precise and effective forecasting of crude oil prices essential. In this study, we propose a combined forecasting scheme, which combines a quadratic decomposition and optimized support vector regression (SVR). In the decomposition part, the original crude oil price series are first decomposed using empirical modal decomposition (CEEMDAN), and then the residuals of the first decomposition (RES) are decomposed using variational modal decomposition (VMD). Additionally, this work proposes to optimize the support vector regression model (SVR) by the seagull optimization algorithm (SOA). Ultimately, the empirical investigation created the feature-variable system and predicted the filtered features. By computing evaluation indices like MAE, MSE, , and MAPE and validating using Brent and WTI crude oil spot, the prediction errors of the CEEMDAN -RES.-VMD -SOA-SVR combination prediction model presented in this paper are assessed and compared with those of the other twelve comparative models. The empirical evidence shows that the combination model being proposed in this paper outperforms the other related comparative models and improves the accuracy of the crude oil price forecasting model.

The main purpose of this article is to use some identities of the classical Gauss sums, the properties of character sums, and Dedekind sums (modulo an odd prime) to study the computational problem of one-kind mean values related to Dedekind sums and give some interesting identities for them.

The Hyers–Ulam stability of multi-coefficients Pexider additive functional inequalities in Banach spaces is investigated. In order to do this, the fixed point method and the direct method are used.

This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.