In this paper we present not only some properties related to bi-warped product submanifolds of locally conformal almost cosymplectic manifolds, but also we show how the squared norm of the second fundamental form and the bi-warped product's warping functions are related when the bi-warped product submanifold has a proper slant submanifold as a base or fiber.

In this article, we consider the uniqueness problem of the non-linear differential polynomial $(f^{n}P(f)H[f])^{(k)}$, where $f(z)$ is a transcendental meromorphic function. With the concept of share a small function with finite weight. We obtain some results which extend and improve some results due to Pulak Sahoo and Biswajit Saha (Acta Mathematica Vietnamica. 41, 25–36 (2016)).

We describe a generalization of Lipschitz spaces under fractional convolution and discuss some basic properties of these spaces. The aim of this work is to introduce and study a linear space $A_{p}^{lip_{\left( \alpha ,1\right) }^{\beta }}\left(\mathbb{R}^{d}\right) $ of functions $h$ belonging to Lipschitz space under fractional convolution whose fractional Fourier transforms $\mathcal{F}{_{\beta }}h$ belongs to {Lebesgue spaces}. We show that this space\ becomes a Banach algebra with the sum norm ${\left\Vert h\right\Vert }_{lip_{\left( \alpha,1\right) }^{\beta },p}={\left\Vert h\right\Vert _{\left( \alpha ,1\right)_{\beta }}} +{\left\Vert \mathcal{F}{{_{\beta }}h}\right\Vert _{p}}$ {and } $\Theta $ (fractional convolution) convolution operation. Also we indicate that this space becomes an essential Banach module over ${{L^{1}}\left(\mathbb{R}^{d}\right)}$ with $\Theta$ convolution.

Let $(F_n)_{n\geq 0}$ be a Fibonacci sequence. A non-negative integer whose digits are all equal is called a repdigit and any non-zero repdigit is of the form $ a \left( \dfrac{10^d-1}{9} \right)$ where $ 1 \leq a \leq 9$ and $ 1 \leq d .$ In this paper, we search all repdigits that can be written as products of three Fibonacci numbers. As a mathematical expression, we find all non-negative integer solutions $(n,m,l,a,d)$ of the Diophantine equation $ F_nF_mF_l =a \left( \dfrac{10^d-1}{9} \right),$ $ 1 \leq l \leq m \leq n$ and $1 \leq a \leq 9$.

In this paper, evolution equations of framed curves are investigated in 4-dimensional Euclidean space. Also, inextensible flows of these curves in 4-dimensional Euclidean space are researched. After that evolution equations for framed curvatures are obtained.

In this paper, we discuss the uniqueness of meromorphic functions that share one finite value DM (different multiplicities) with first derivative in an angular domain.

The main motivation of this paper is to investigate the geometric properties of non unique fixed points of self-mappings via simulation functions. Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a geometric figure. In this paper, we consider the set of simulation functions for geometric applications in the fixed point theory both on metric and some generalized metric spaces ($S$-metric spaces and $b$-metric spaces).

In the paper, we introduce the notion of unique range sets for the class of derivatives of meromorphic functions and hence show that the existing least cardinality for unique range sets can be significantly reduced for this special class of meromorphic functions along with some relaxed sharing conditions. Moreover, we prove two theorems in this regard to the most general setting in order to incorporate all possible classes of finite sets for the uniqueness of derivatives of meromorphic functions. Finally, in the application section, we have exhibited a number of examples to justify the far-reaching applications of our main results.

In this paper, we define a new adapted trihedron called q-geodesic trihedron. Using this frame, we construct q-offsets and q-Mannheim offsets of ruled surfaces. We present theorems for q-offsets and q-Mannheim offsets to be developable. Finally, we illustrate the theory with some examples.

For a crossed module ${\bf G}_*$ and abelian crossed module ${\bf A}_*$ equipped with an action of ${\bf G}_*$ we construct a truncated cochain complex $C^*({\bf G}_*, {\bf A}_*)$. We show that the corresponding cohomology groups ${\sf H}^i({\bf G}_*,{\bf A}_*)$, $0\leq i \leq 2$ have several nice properties and can be considered as a "cocycle" description of cotriple cohomology of crossed modules first introduced in \cite{ccg}, and further studied in [9], [15].

In this paper, motivated by the definition of Strong Uniqueness Polynomial for Meromorphic Functions (SUPM) as introduced by Fujimoto earlier, we have strived on the utmost generalization of the same definition and thus presented a new extended version of it namely Strong Uniqueness Polynomial for Meromorphic Functions in the Wider Sense (SUPMWS). In fact, in the last section of this article, under a remark, we have exhibited that this extension is viable, thereby justifying the introduction of the new definition. Using the SUPMWS, we also delve into investigating the generation of unique range sets with finite weight. This implies that the new definition can be effectively employed to establish unique range sets with certain characteristics, which could be significant in various applications and mathematical contexts. Our results will conveniently improve and extend a series of results in the literature.

We show that in many classical characterization theorems involving parapolar spaces, we can lift the assumption of having only symplecta of finite rank. At the same time, we present an example of a parapolar space of infinite symplectic rank which shows that this is not possible in all characterizations.