11,823 Results Found

In this paper, a subclass of complex-valued harmonic univalent functions defined by a generalized linear operator is introduced. Some interesting results such as coefficient bounds, compactness, and other properties of this class are obtained.

This article presents a q-generalized linear operator in Geometric Function Theory (GFT) and investigates its application to classes of analytic bounded functions of complex order $S_q(c;M)$ and $C_q(c;M)$ where $0\&l$...

According to the spatial dimension, equation type, and time sequence, the latest progress in controllability of stochastic linear systems and some unsolved problems are introduced. Firstly, the exact controllability of stochastic linear systems in fi...

We shall present some more generalized and further refinements of reversed AM-GM operator inequalities for positive linear maps due to Xue’s and Ali’s publications.

The authors of the present paper previously proved the Ulam stability for the n-th-order linear differential operator with constant coefficients. They obtained its best Ulam constant for the case of distinct roots of the characteristic equation. Howe...

The aim of the present paper is to introduce and study some new subclasses of p-valent functions by making use of a linear q-differential Borel operator.We also deduce some properties, such as inclusion relationships of the newly introduced classes a...

The results from this paper are related to the geometric function theory. In order to obtain them, we use the technique based on differential subordination, one of the newest techniques used in the field, also known as the technique of admissible fun...

The linear differential operator with constant coefficients $D\left(y\right)=y^{\left(n\right)}+a_1{y}^{(n-1)}+\dots +a_{n}y,y\in {\mathcal{C}}^n(\mathbb{R},X)$ acting in a Banach space X is Ulam stable if and only if its characteristic equation has no roots on the imaginary axis. We prove that if...

In this paper, we first introduce a linear integral operator ${\Im }_p(a,c,\mu )(\mu >0;a,c\in \mathbb{R};c>a>-\mu p;p\in {\mathbb{N}}^{+}:=\{1,2,3,\dots \}),$ which is somewhat related to a rather specialized form of the Riemann–Liouville fractional...

While over a hundred articles discuss second-order differential inequalities and subordinations in the complex plane, very few address the relatively unexplored classes of third-order fuzzy differential subordination and superordination. This paper b...

In this paper, we define three subclasses ${\mathcal{M}}_{p,\alpha }^{n,q}(\eta ,A,B),{\mathcal{I}}_{p,\alpha }^n(\lambda ,\mu ,\gamma ),$, R${}_p^{n,q}(\lambda ,\mu ,\gamma )$ connected with a q-analogue of linear differential operator ${\mathcal{D}}_{\alpha ,p,\mathcal{G}}^{n,q}$ which consist of functions $\mathcal{F}$ of the form...

In this paper, we obtain a result on Ulam stability for a second order differential operator acting on a Banach space. The result is connected to the existence of a global solution for a Riccati differential equation and some appropriate conditions o...

The concept of subordination is expanded in this study from the fuzzy sets theory to the geometry theory of analytic functions with a single complex variable. This work aims to clarify fuzzy subordination as a notion and demonstrate its primary attri...

The present paper deals with estimates for differences of certain positive linear operators defined on bounded or unbounded intervals. Our approach involves Baskakov type operators, the kth order Kantorovich modification of the Baskakov operators, th...

This paper explores the application of Hilbert topological spaces and linear operator algebra in the modelling and analysis of OFDM signals and wireless channels, where the channel is considered as a linear time-invariant (LTI) system. The wireless c...

We prove that a linear operator of a complex Banach space has a shadowable point if and only if it has the shadowing property. In addition, every equicontinuous linear operator does not have the shadowing property and its spectrum is contained in the...

A graph has genus k if it can be embedded without edge crossings on a smooth orientable surface of genus k and not on one of genus $k-1$ . A mapping of the set of graphs on n vertices to itself is called a linear operator if the image of...

Basic neural network operators are interpreted as positive linear operators and the related general theory applies to them. These operators are induced by a symmetrized density function deriving from the parametrized and deformed hyperbolic tangent a...

We prove a theorem that describes all possible tensor-valued natural operations in the presence of a linear connection and an orientation in terms of certain linear representations of the special linear group. As an application of this result, we pro...

We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating the theoreti...

If a graph can be embedded in a smooth orientable surface of genus g without edge crossings and can not be embedded on one of genus $g-1$ without edge crossings, then we say that the graph has genus g. We consider a mapping on the set o...

This manuscript determines the set of Pareto optimal solutions of certain multiobjective-optimization problems involving continuous linear operators defined on Banach spaces and Hilbert spaces. These multioptimization problems typically arise in engi...

The main objective of our paper is to focus on the study of sequences (finite or countable) of groups and hypergroups of linear differential operators of decreasing orders. By using a suitable ordering or preordering of groups linear differential ope...

We study some properties of arctic rank of Boolean matrices. We compare the arctic rank with Boolean rank and term rank of a given Boolean matrix. Furthermore, we obtain some characterizations of linear operators that preserve arctic rank on Boolean...

Let H be an infinite-dimensional separable complex Hilbert space and $B\left(H\right)$ the algebra of all bounded linear operators on H. In this paper, we characterized the linear maps $\varphi :B\left(H\right)\to B\left(H\right)$, which are surjective up to compact operators preserving...

One of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analys...

In the present paper, we investigate the influence of the choice of continuous linear operator for obtaining the approximate periodic solutions of ordinary second-order differential equations. In most of these problems, the periods are unknown, and t...

Basic fuzzy multicomposite neural network operators are interpreted as fuzzy positive linear operators, and the related general fuzzy theory is applied. These fuzzy operators are defined by the composition of seven well-known activation functions. We...

In this article, we study the JF iterative algorithm to approximate the fixed points of a non-linear operator that satisfies condition (E) in uniformly convex Banach spaces. Further, some weak and strong convergence results are presented for the same...

We introduce the notion of the interval-valued linear Diophantine fuzzy set, which is a generalized fuzzy model for providing more accurate information, particularly in emergency decision-making, with the help of intervals of membership grades and no...

In this work, we study a linear operator f on a pre-Euclidean space $\mathcal{V}$ by using properties of a corresponding graph. Given a basis $\mathcal{B}$ of $\mathcal{V}$, we present a decomposition of $\mathcal{V}$ as an orthogonal direct sum of certain linear subspaces ${\left\{U_i\right\}}_{i\in I}$, each one a...

Multi-composite activated neural network operators can be understood as positive linear operators, allowing them to be analyzed using standard, established theory. Formed by composing multiple general activation functions, these operators act upon co...

The concept of linear Diophantine fuzzy set (LDFS) theory with its control parameters is a strong model for machine learning and data-driven multi-criteria decision making (MCDM). The sine-trigonometric function (STF) has two significant features, pe...

Active distribution grids require analysis methods that combine physical fidelity with low computational cost for repeated screening, optimization workflows, and operational decision support. Local linearized power-flow models can support these tasks...

Due to booming economic development over the past decades, energy demands in most of China’s provincial power grids have increased sharply, and it has become challenging to guarantee the energy balance at peak periods. In many provincial electr...

Reliability and vulnerability (RV) are two very important performance measures but, due to their stage-inseparable nature, they cannot be explicitly incorporated in stochastic dynamic programming (SDP), which is extensively used in reservoir operatio...

In this paper, the authors introduce the Orlicz spaces corresponding to the Young function and, by virtue of the equivalent theorem between the modified K-functional and modulus of smoothness, establish the direct, inverse, and equivalent theorems fo...

As interest in Moon exploration grows, and efforts to establish an orbiting outpost intensify, accurate modeling of spacecraft dynamics in cislunar space is becoming increasingly important. Contrary to satellites in Low Earth Orbit (LEO), where it ta...

With the support of cloud computing technology, it is easier for financial institutions to obtain more key information about the whole industry chain. However, the massive use of financial data has many potential risks. In order to better cope with t...

In the present paper we study a class of Toeplitz operators called concentration operators that are self-adjoint and compact in the linear canonical Dunkl setting. We show that a finite vector space spanned by the first eigenfunctions of such operato...

In this manuscript, we combine the notion of linear Diophantine fuzzy set (LDFS), uncertain linguistic set (ULS), and complex fuzzy set (CFS) to elaborate the notion of complex linear Diophantine uncertain linguistic set (CLDULS). CLDULS refers to tr...

Free-piston linear generators (FPLGs) have attractive application prospects for hybrid electric vehicles (HEVs) owing to their high-efficiency, low-emissions and multi-fuel flexibility. In order to achieve long-term stable operation, the hybrid syste...

We analyze several factors that affect the linear output range of CMOS image sensors, including charge transfer time, reset transistor supply voltage, the capacitance of integration capacitor, the n-well doping of the pinned photodiode (PPD) and the...

The variable-flux memory machine (VFMM) can perform flexible online PM flux adjustment by utilizing a magnetizing current pulse, effectively extending the machine operation range. However, the continuous flux adjustment (CFA) method generally suffers...

This paper presents linear programming (LP) formulations for short-term energy time-shift operational scheduling with energy storage systems (ESSs) in power grids. In particular, it is shown that the conventional nonlinear formulations for electric b...

A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class of PDEs reads: $\frac{\partial p}{\partial t}-{\sum }_{j=0}^m\left({\sum }_{r=0}^{n_j}{a}_{jr}\left(t\right)x^r\right)\frac{\partial j_p}{\partial x^j}=0$ F-operato...

Nowadays, there is an ever-increasing diversity of materials available, each with its own set of features, capabilities, benefits, and drawbacks. There is no single definitive criteria for selecting the perfect biomedical material; designers and engi...

The inherent variability and unpredictability of renewable energy output pose significant challenges to power grid stability. Pumped Storage Power Stations (PSPS) play a pivotal role in mitigating these challenges, enhancing the grid’s reliabil...

The symmetrical linear Diophantine fuzzy Hamacher aggregation operators play a fundamental role in many decision-making applications. The selection of a cyber security system is of paramount importance for maintaining digital assets. It necessitates...

In this paper, we define a modified and generalized analytic Feynman integral associated with the bounded linear operator on abstract Wiener spaces. We then prove its existence. We also establish some modified and generalized analytic Feynman integra...