East West Math

THE HIT PROBLEM OF FIVE VARIABLES IN THE DEGREE THIRTY

Nguyen Sum — 2023-05-11

Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] over the
prime field of two elements, F2, with the degree of each xi being 1. We
study the hit problem, set up by Frank Peterson, of finding a minimal set
of generators for Pk as a module over the mod-2 Steenrod algebra, A. In
this paper, we explicitly determine a minimal set of A-generators for Pk
in the case k = 5 and the degree 2d+1 − 2 with d 6 4.

SOME UNIQUENESS THEOREMS FOR HOLOMORPHIC CURVES ON ANNULUS SHARING HYPERSURFACES IN GENERAL POSITION

Ha Tran Phuong — 2023-05-11

Recently H. T. Phuong and L. Vilaisavanh proved a second main theorem for algebraically non-degenerate holomorphic curves on annulus intersecting hypersurfaces. Based on this theorem, here we prove some uniqueness theorems for holomorphic curves on annulus in the case of hypersurfaces in general position in complex projective.

A NOTE ON CENTRAL IDEMPOTENTS IN GROUP RING OF SYMMETRIC GROUP OVER Zn

Anuradha Sabharwal — 2023-05-11

The number of central idempotents in group ring Zn[S3] have been determined. Furthermore, some explicit form of central idempotents have also been obtained.

ALL MAXIMAL UNIT-REGULAR SIBMONOIDS OF RELHYP((2),(2))

Pornpimol Kunama — 2023-05-11

Relational hypersubstitutions for algebraic systems are mappings which map operation symbols to terms and map relation symbols to relational terms preserving arities. The set of all relational hypersubstitutions for
algebraic systems (Relhyp(τ, τ 0)) together with a binary operation defined on this set forms a monoid. In this paper, we determine all maximal unit-regular submonoids of this monoid of type ((2),(2)).

FORWARD PROBLEM FOR POLLUTION CONTROL BASED ON STREETER-PHELPS EQUATION

Tran Thi Nang — 2023-05-11

The relationship between the discharger and the water quality of the receptor streams was described by a mathematical equation, for the first time introduced in the early 20th century, known as the Streeter – Phelps equation. There have been many follow-up studies to develop this work; however, most of these stopped in the case of steady-state flows and discharges. The expansion through the unsteady case is unnoticed. In this study, the Streeter-Phelps equation is considered in its most general form, accounting for the temporal variation of both the flow and the discharger over time. This study inherits the previous studies but considers for the case of an unstead discharger, especially when the pollutant concentration in the wastewater exceeds the allowable standard. The mathematical model Streeter – Phelps is applied in the case of insteady of the waste discharger. The results show that the error with other products like MIKE is in the range of less than 10%. This result allows the application of the Streeter - Phelps model to the pollution control problem.