综合数学
Here, we introduce a novel method for obtaining chaotic dynamics based on the Montgomery conjecture for the pair correlation of zeros of the Riemann zeta function. Motivated by the conjecture, we present a recursive relation that reveals…
Pausinger recently investigated a special determinant involving prime numbers. In this short note we point out that this type of determinants was already known in linear algebra and its computation is unrelated to prime numbers.
We are looking for integer numbers $g_{j}$ and $x_{j}$ ($j=1,...,n$) such that the sums $T_{\pi} := \sum_{j=1}^{n} g_{j} \cdot x_{\pi\left( j\right) }$ are different for all permutations $\pi\in S_{n}$ and $\max\left\{T_{\pi}:\pi\in…
In this paper we study the best approximation of a fixed fuzzy-number-valued continuous function to a subset of fuzzy-number-valued continuous functions. We also introduce a method to measure the distance between a fuzzy-number-valued…
In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the…
We extend Cardaliaguet-Euvrard neural network operators to the context of fuzzy number valued continuous functions and study their behaviour. We focus on level continuous, sendograph continuous and endograph continuous functions and obtain…
In this paper, we investigate the properties of Clifford prolate spheroidal wave functions (CPSWFs) through their associated eigenvalues. We prove that the expansion coefficients in CPSWFs series decay as both the order and the homogeneity…
This work develops an operator-theoretic and dynamical framework inspired by the Riemann--von Mangoldt formula, chaotic dynamics, and random-matrix models for the Riemann zeta function, without attempting to prove the Riemann Hypothesis.…
We obtain closed form of some infinite series involving derivatives of an analogue of the Riemann xi function for Dedekind zeta function and nontrivial zeros of Dedekind zeta function assuming the Extended Riemann Hypothesis. Conversely, we…
This paper builds on the research initiated by Boyadzhiev, but introduces generalized harmonic numbers, \[ H_n(\alpha)= \sum_{k=1}^n \frac{\alpha^{k}}{k}, \] which enable the derivation of new identities as well as the reformulation of…
We are concerned with the Steiner chains consisting of four circles. More precisely, we deal with the so-called complex moments of Steiner 4-chains introduced in a recent paper by J.Lagarias, C.Mallows and A.Wilks. We compute the invariant…
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies…
Let M be a smooth closed (compact without boundary) Riemannian manifold of dimension n and P a q-dimensional smooth submanifold of M. U will denote the tubular neighborhood of P in M. Let E be a smooth vector bundle over M. Here we will…
In this paper, the fuzzy Hausdorff distance is studied, and also the fuzzy equidistant set for two points of a fuzzy metric space is introduced. Here, the fuzzy metric space has been redefined using recently developed fuzzy geometry, and…
We have proved in this paper that numbers can be expressed in algebraic form using one variable and two real rational quantities and thus sum of three cubes can also be expressed in algebraic form as a cubic polynomial. Using skeletal or…
The standard Laplacian $-\triangle_{\mathbb R^n}$ in $L^2(\mathbb R^n)$ is self-adjoint and translation invariant on the finite-dimensional linear space $\mathbb R^n$. In this paper, we define a translation invariant operator…
The counting function for the numbers satisfying the Collatz conjecture is studied. A related exponential congruence equation is investigated, yielding a method to construct its solutions from free variables, and enabling us to find at…
We give two low-complexity algorithms, one for dimensionality reduction and one for dimensionality increase, which are applicable to any dataset, regardless of whether the set has an intrinsic dimension or not. The corresponding methods…
It is argued that for certain meromorphic functions $u:\cal{R}\rightarrow\cal{R}$ and analytic function $ A_1$ and for any integrable function $F$, as long as it converges as a Cauchy Principal Value,, $$\int_{-\infty}^{\infty}A_1(x)F[u(x)]…
In this paper, we presents novel and sharp bounds on the Albertson index of trees, revealing deep connections between degree sequences and graph irregularity where the Albertson index of Caterpillar tree satisfy \[…