Vediyappan Govindan, Selvam Arunachalam, Dumitru Baleanu
et al.
Fractional calculus concept has proven to be a great, powerful, and effective tool in analyzing mathematical models across diverse various fields of scientific and engineering domains. A significant feature of this article is to investigate the novel Human T-cell Lymphotropic Virus (HTLV)/Human Papillomavirus (HPV)/Human Immunodeficiency Virus (HIV) multi-infection model, along with a computational numerical study and stability analysis to describe the modified Atangana-Baleanu-Caputo fractional order framework. The model performed stability analysis based on the Ulam-Hyers stability concept can be established by using the solution of existence and uniqueness conditions derived from the fixed-point techniques for the recommended problem. The multi-infection dynamical system behavior is expressed on the approximate solution of a two-step Lagrange interpolation polynomials numerical scheme utilizing a modified Atangana-Baleanu-Caputo fractional order framework, with all implementation and simulations conducted in Matrix Laboratory (MATLAB). Overall judgment shows that the numerical results of the recommended method significantly impact the multi-infection model behavior.
There are three main constructions of supercharacter theories for a group G. The first, defined by Diaconis and Isaacs, comes from the action of a group A via automorphisms on our given group G. Another general way to construct a supercharacter theory for G, defined by Diaconis and Isaacs, uses the action of a group A of automor- phisms of the cyclotomic field Q[ζ|G|]. The third, defined by Hendrickson, is combining a supercharacter theories of a normal subgroup N of G with a supercharacter theory of G/N . In this paper we construct a supercharacter theory from an arbitrary set of normal subgroups of G. We show that when we consider the set of all normal subgroups of G, the corresponding supercharacter theory is related to a partition of G given by certain values on the central primitive idempotents. Also, we show the supercharacter theories that we construct can not be obtained via automorphisms or a single normal subgroup.
The dual stable Grothendieck polynomials are a deformation of the Schur functions, originating in the study of the K-theory of the Grassmannian. We generalize these polynomials by introducing a countable family of additional parameters such that the generalization still defines symmetric functions. We outline two self-contained proofs of this fact, one of which constructs a family of involutions on the set of reverse plane partitions generalizing the Bender-Knuth involutions on semistandard tableaux, whereas the other classifies the structure of reverse plane partitions with entries 1 and 2.
We present a way to normalize a combinatorial Morse function into an integer-valued canonical representative of the set of discrete Morse functions inducing a given gradient field.
We classify the $Q$-multiplicity-free skew Schur $Q$-functions. Towards this result, we also provide new relations between the shifted Littlewood-Richardson coefficients.
We study an extension of the chip-firing game. A given set of admissible moves, called Yamanouchi moves, allows the player to pass from a starting configuration $\alpha$ to a further configuration $\beta$. This can be encoded via an action of a certain group, the toppling group, associated with each connected graph. This action gives rise to a generalization of Hall-Littlewood symmetric polynomials and a new combinatorial basis for them. Moreover, it provides a general method to construct all orthogonal systems associated with a given random variable.