General Mathematics
In this paper, we study the concept of complex fuzzy soft matrices. The application of complex fuzzy soft matrices in signals and systems via the cross product of complex fuzzy soft matrices and Fourier transform was carried out. In this…
The so-called Ahmed integral $$ \int_{0}^{1}\frac{\arctan\left(\sqrt{2+x^{2}}\right)}{(1+x^{2})\sqrt{2+x^{2}}}\,\mathrm{d} x=\frac{5\pi^{2}}{96}, $$ has attracted considerable interest since its appearance in the "American Mathematical…
We study the Borwein--Bailey--Girgensohn sinusoidal series S_BBG = sum_{n=1}^\infty (1/n) * ((2+sin n)/3)^n, originally posed as an open problem by Borwein, Bailey, and Girgensohn, whose convergence was established by Boppana using the…
The main focus of the present paper is the following inequality $\left( \sqrt{bc}-a\right) m_a+ \left(\sqrt{ac}-b\right)m_b+\left(\sqrt{ab}-c\right)m_c \geq 0,$ where $a,b,c$ are the sides of a non-degenerate triangle and $m_a,m_b,m_c,$ the…
In 2016, Dannan and Sitnik established the notable Damascus inequality, which features a symmetric structure under a multiplicative constraint. In this study, we consider the natural generalisation of this inequality by characterising all…
The sequence $F_{dn+h}$ and its convolutions have (for $h=0$) been studied in a recent paper at the arxiv [arXiv:2603.08636]. The instance with general $h$ is more involved and uses Chebyshev polynomials.
Triangle centers are usually studied individually or through special geometric relationships, but little attention has been given to global structure among them. In this paper we introduce several natural ways to order triangle centers,…
In this paper, we present a fixed point method for high-precision computation of number $\pi$ based on the sine function. Let $P\in \mathbb{N}$. We define the function: \[ S\left(x\right) =x+\sum_{k=1}^{P}\left(\prod_{\ell=1}^{k-1}\frac…
We present an algebraic generalization of Euler's theorem for quadrilaterals. Starting from the parallelogram identity in an inner product space, we derive Apollonius' identity and obtain Euler's quadrilateral identity in a unified vector…
We present a rigorous analytic proof of a generalized continued fraction (GCF) identity for the transcendental constant $8/\pi^2$, a result recently conjectured via the algorithmic framework of the Ramanujan Machine. Distinct from canonical…
In the study of linear dispersive media it is of primary interest to gain knowledge of the impulse response of the material. The standard approach to compute the response involves a Laplace transform inversion, i.e., the solution of a…
The article presents a generalization of the classical Hardy-Littlewood conjecture concerning the density of prime tuples to the case of tuples consisting of almost-prime numbers (numbers with a specified quantity of prime divisors). The…
Complex systems consist of interacting units whose interactions may be pairwise, involving two units, or higher-order, involving more than two units simultaneously. Graphs capture pairwise interactions and represent such systems as…
We study orthogonal polynomial systems arising from general pre-Hilbert inner products on polynomial spaces, beyond the classical framework of measures. To each such inner product we associate a canonical Laplacian defined from an abstract…
To address the limitations of conventional critically sampled graph filter banks in joint time-vertex signal processing, which require decomposing the joint graph into bipartite subgraphs and thus cannot fully exploit all temporal and…
In this paper we study the even monic degree-8 cuboid polynomial $P_{a,u}(t)$ introduced by R.A. Sharipov in the first-cuboid specialization of his cuboid equations. For nonzero integers $a,u$ with $u^2\neq a^2$ we prove that $P_{a,u}(t)$…
Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker…
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
In many practical applications, signals and environments are time- varying, which makes fixed filters unreliable. Adaptive filtering, on the other hand, updates in real time to suppress noise, track nonstationary signals, and identify…
The basic power function $t_n(x)=x^n$ is in some sense a classical limit for large $x$, of the monictised Chebyshev polynomial of the first kind $T_n(x)/2^{n-1}$. A theorem of Ritt says they are the only two families of polynomials $p_n(x)$…