Table of Content
Volume 8, Number 3 (2025)-Table of Contents
Open AccessArticleSome New Coincidence Point Results in B-Metric Spaces using a Simulation Function
Abderrahmane Boudraa, Taieb Hamaizia*
Annals of Communications in Mathematics 2025
8 (3)
343-349
DOI: https://doi.org/10.62072/acm.2025.080301
ABSTRACT. In this paper, we prove a coincidence point theorem in the context of b-metric spaces. The result is achieved by extending the known conditions of existence and uniqueness through the use of simulation functions. An example is also provided to support the obtained result.
Open AccessArticleInferior Semigroups and Ideals
G. Muhiuddin*, Young Bae Jun
Annals of Communications in Mathematics 2025
8 (3)
350-362
DOI: https://doi.org/10.62072/acm.2025.080302
ABSTRACT. Inferior semigroups, left (right) inferior ideals and inferior quasi-ideals in semi-groups are introduced, and several properties are investigated. Characterizations of inferior semigroups and ideals are considered, and relations between inferior semigroups, inferior ideals and inferior quasi-ideals are discussed. Characteristic inferior mappings and inferior products of inferior mappings are introduced. Using these notions, related properties on inferior semigroups, left (right) inferior ideals and inferior quasi-ideals are investigated. A regular semigroup is characterized by an inferior quasi-ideal.
Open AccessArticleOn Some Connections Between Hilbert and Hardy Type Integral Inequalities
Christophe Chesneau
Annals of Communications in Mathematics 2025
8 (3)
363-378
DOI: https://doi.org/10.62072/acm.2025.080303
ABSTRACT. This article investigates some new connections between the Hilbert and Hardy integral inequalities. In particular, two general theorems are established, both based on integral terms derived from those used in these two famous inequalities. They have the property of depending on two functions and one modulable parameter. Applications and examples are given to specific cases combining Hilbert and Hardy type integral inequalities. Emphasis is placed on a particular weighted integral term, showing how our results can be used to improve what can be obtained with some classical integral inequalities in the literature.
Open AccessArticleExploring Ideals of Semiring with Involution
M. Murali Krishna Rao, Noorbhasha Rafi*
Annals of Communications in Mathematics 2025
8 (3)
379-385
DOI: https://doi.org/10.62072/acm.2025.080304
ABSTRACT. In this paper, we introduce the notion of involution in semirings. We define bi-ideal, quasi ideal, interior ideal, bi-quasi interior ideal, and bi-interior ideals of semirings with involution and study their properties.
Open AccessArticleOn Some Trigonometric and Inverse Trigonometric Integral Formulas
Christophe Chesneau
Annals of Communications in Mathematics 2025
8 (3)
386-392
DOI: https://doi.org/10.62072/acm.2025.080305
ABSTRACT. This paper presents a new collection of trigonometric and inverse trigonometric integral formulas based on a known integral result. Some of these formulas evaluate to zero, while others are notable for their connection to well-known mathematical constants, such as π,√ 2, and the Catalan constant. Comprehensive proofs are provided for all results, and an open problem is posed to inspire further investigation.
Open AccessArticleTribonacci Cordial Labeling of Some Snake Graphs
Ariel C. Pedrano*, Melaine Vieve S. Gudin
Annals of Communications in Mathematics 2025
8 (3)
393-405
DOI: https://doi.org/10.62072/acm.2025.080306
ABSTRACT. An injective function f : V (G) → {T0, T1, T2, . . . , Tn}, where n = |V (G)| − 1, is said to be a Tribonacci cordial labeling if the induced function f ∗ E(G) →{0, 1} defined by f∗(uv) = (f(u) + f(v)) mod 2 satisfies the condition |ef (0) − ef (1)| ≤ 1 where ef (0) is the number of edges with label 0 and ef (1) is the number of edges with label 1. A graph that admits a tribonacci cordial labeling is called a Tribonacci cordial graph. In this paper, we determined the Tribonacci Cordial Labeling of Triangular Snake Graph T Sn, Double Triangular Snake Graph D(T Sn), Quadrilateral Snake Graph QSn, Double Quadrilateral Snake Graph D(QSn), and Cycle Quadrilateral Snake Graph C(QSn).
Open AccessArticleSolution of the Millennium Problem for the Navier-Stokes Equations
Alexander G. Ramm
Annals of Communications in Mathematics 2025
8 (2)
406-409
DOI: https://doi.org/10.62072/acm.2025.080307
ABSTRACT. One of the millennium problems can be stated as follows: can there be smooth, not vanishing identically initial data for the Navier-Stokes equations in R such that the corresponding solution to the NSP (Navier-Stokes problem) exists for all times t ≥ 0? We prove that such a solution does not exist.
Open AccessArticleFuzzy Bi-Quasi-Interior Ideals of Semirings
Ganesh Kumar Reddi, M. Murali Krishna Rao, Rajendra Kumar Kona*, Vineela B
Annals of Communications in Mathematics 2025
8 (3)
410-424
DOI: https://doi.org/10.62072/acm.2025.080308
ABSTRACT.In this paper, we introduce the notion of a fuzzy bi-quasi interior ideal as a generalization of fuzzy ideals, fuzzy bi-quasi ideals, fuzzy quasi-interior ideals and fuzzy bi-interior ideals of a semiring. We prove that every fuzzy right quasi-interior ideal of a semiring is a fuzzy bi-quasi interior ideal and a fuzzy bi-quasi interior ideal is a fuzzy right tri-ideal of a semiring. We characterize the regular semiring in terms of fuzzy bi-quasi interior ideals and study some of the properties.
Open AccessArticleSubexponential Computation of Truncated Theta Series
Francesco Sica
Annals of Communications in Mathematics 2025
8 (3)
425-430
DOI: https://doi.org/10.62072/acm.2025.080309
ABSTRACT. We describe an algorithm to compute in $O(e^{c\sqrt{ k\log k}})$ binary operations, for some absolute constant $c>0$, expressions like $\sum_{1\leq n\leq 2^\alpha} e^{\frac{2\pi i n^2}{2^k}} n^a$ and $\sum_{\substack{1\leq n\leq 2^\alpha\\ 1\leq m\leq 2^\beta}} e^{\frac{2\pi i nm}{2^k}} n^a m^b$ where $\alpha,\beta= O(k)$ and $a,b$ are fixed (small) nonnegative integers. The error terms in these computations are $O(e^{-c k})$.