The aim of this paper is to investigate when a linear normed space is an inner product space. Several conditions in a linear normed space are formulated with the help of inequalities. Some of them are from the literature and others are new. We prove...
In this paper, we introduce an inner product on abelian groups and, after investigating the basic properties of the inner product, we first show that each inner product group is a torsion-free abelian normed group. We give examples of such groups and...
In this paper, we prove the Chebyshev-Steffensen inequality involving the inner product on the real m-space. Some upper bounds for the weighted Chebyshev-Steffensen functional, as well as the Jensen-Steffensen functional involving the inner product u...
Inner product encryption, first introduced by Katz et al., is a type of predicate encryption in which a ciphertext and a private key correspond to an attribute vector and a predicate vector, respectively. Only if the attribute and predicate vectors s...
In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, Möbius, Proper Velocity, and Chen’s gyrogroups. This leads to the study of...
The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies o...
The purpose of this paper is to prove certain refinements of Ostrowski’s inequality in an inner product space. We study extensions of Ostrowski type inequalities in a 2-inner product space. Finally, some applications which are related to the Chebyshe...
With the rise of technology in recent years, more people are studying distributed system architecture, such as the e-government system. The advantage of this architecture is that when a single point of failure occurs, it does not cause the system to...
With the recent advances in mobile technologies, biometric verification is being adopted in many smart devices as a means for authenticating their owners. As biometric data leakage may cause stringent privacy issues, many proposals have been offered...
First, we show that the non-trivial fuzzy inner product space under the linearity condition does not exist, which means a fuzzy inner product space with linearity produces only a crisp real number for each pair of vectors. If the positive-definitenes...
The aim of this article is to establish several estimates of the triangle inequality in a normed space over the field of real numbers. We obtain some improvements of the Cauchy–Schwarz inequality, which is improved by using the Tapia semi-inner...
In this paper, we propose a definition for a semi-inner product in the space of p-summable sequences equipped with an n-norm. Using this definition, we introduce the concepts of pn-orthogonality and the pn-angle between two vectors in the s...
Within the framework of 6G networks, the rapid proliferation of Internet of Things (IoT) devices, coupled with their decentralized and heterogeneous characteristics, presents substantial security challenges. Conventional centralized systems face sign...
In recent years, data mining technology has become increasingly popular, evolving into an independent discipline as research deepens. This study constructs and optimizes an association rule algorithm based on the Boolean vector (BV) inner product and...
By mimicking the hierarchical structure of human brain, deep spiking neural networks (DSNNs) can extract features from a lower level to a higher level gradually, and improve the performance for the processing of spatio-temporal information. Due to th...
The paper is concerned with complex fuzzy numbers and complex fuzzy inner product spaces. In the classical complex number set, a complex number can be expressed using the Cartesian form or polar form. Both expressions are needed because one expressio...
Studies in adults showed differential neural processing between overt and inner speech. So far, it is unclear whether inner and overt speech are processed differentially in children. The present study examines the pre-activation of the speech network...
Understanding the impacts of regional climate change on crop production will benefit strategic decisions for future agricultural adaptation in China. In this study, the climatic production potential of potato over the past 61 years in Inner Mongolia...
Speech production not only relies on spoken (overt speech) but also on silent output (inner speech). Little is known about whether inner and overt speech are processed differently and which neural mechanisms are involved. By simultaneously applying e...
There is increasing focus on the difficult challenge of realizing coordinated development of production, living and ecological spaces within the regional development process. An ecological–production–living space evaluation index system w...
The rapidly increasing expansion of distributed energy resources (DER), such as renewable energy systems and energy storage systems into the electric power system and the integration of advanced information and communication technologies enable DER o...
Production efficiency is a standard to evaluate the high-quality development of animal husbandry. As an important tool for herdsmen to collect and use information for animal husbandry production and innovation, the internet is not only an inner motiv...
22 August 2019
With the supply of water, energy and food facing severe challenges, there has been an increased recognition of the importance of studying the regional water–energy–food nexus. In this paper, Inner Mongolia, including 12 cities in China, w...
Rapid urbanization is causing ecological and environmental issues to worsen. The stability of the ecosystem function of the farming–pastoral ecotone (FPE) in Inner Mongolia is essential to ensuring the sustained growth of the nearby cities, act...
Grassland ecosystems are a significant part of the global ecosystem and support the livelihoods of millions of people. The Inner Mongolia grassland is the largest temperate grassland in the world, and an important ecological barrier for China, but du...
This paper investigates how two fundamental consumer characteristics, self-esteem (inner-self) and status seeking (outer-self), influence consumers’ purchasing behaviors of CSR (Corporate Social Responsibility) products via two mediating effect...
As a key task in machine learning, data classification is essential to find a suitable coordinate system to represent the data features of different classes of samples. This paper proposes the mutual-energy inner product optimization method for const...
We study the sequence of polynomials {Sn}n≥0 that are orthogonal with respect to the general discrete Sobolev-type inner product ⟨f,g⟩s=∫f(x)g(x)dμ(x)+∑j=1N∑k=0djλj,kf(k)(cj)g(k)(cj), where μ is a finite Bore...
In this contribution we consider sequences of monic polynomials orthogonal with respect to the Sobolev-type inner product f,g=⟨uM,fg⟩+λTjf(α)Tjg(α), where uM is the Meixner linear operator, λ∈R+, j∈N,...
In the domain of functional magnetic resonance imaging (fMRI) data analysis, given two correlation matrices between regions of interest (ROIs) for the same subject, it is important to reveal relatively large differences to ensure accurate interpretat...
This work aims to develop a new class of accretive mappings and investigate its associated class of proximal mappings. This new class of accretive mappings is known as generalized (Hk,φ)-η-accretive mappings. Further, the research work includ...
A unitary-evolution process leading to an ultimate collapse and to a complete loss of observability alias quantum phase transition is studied. A specific solvable N−state model is considered, characterized by a non-stationary non-Hermitian Hami...
In this study, we first generalize the Lorentzian inner and vector products, and then we define the generalized split quaternions by means of the generalized Lorentzian inner and vector products. Next, on any hyperboloid of one or two sheets, which i...
We present a generalization of Bregman divergences in finite-dimensional symplectic vector spaces that we term symplectic Bregman divergences. Symplectic Bregman divergences are derived from a symplectic generalization of the Fenchel–Young ineq...
Strip roads serve to enable silviculture operations, maintain biodiversity, and decrease damages to the soil and environment. At the same time, strip roads decrease the productive area. The aim of this study is to evaluate the influence of strip road...
The aim of the paper is to construct a secondary characteristic homomorphism for Lie pseudoalgebras. The case of inner product modules is under consideration.
In Internet of Things (IoT) systems in which a large number of IoT devices are connected to each other and to third-party servers, it is crucial to verify whether each device operates appropriately. Although anomaly detection can help with this verif...
There are two main strategies for improving the projection-based reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, constructing ROM bases that yie...
Leaf area index (LAI) is a key indicator of vegetation structure and function, and its products have a wide range of applications in vegetation condition assessment and usually act as important input parameters for ecosystem modeling. Grassland plays...
Vectors are almost always introduced as objects having magnitude and direction. Following that idea, textbooks and courses introduce the concept of a vector norm and the angle between two vectors. While this is correct and useful for vectors in two-...
Let (X,d) be a metric linear space and a∈X. The point a divides the space into three sets: Ha = {x ∈ X: d(0,x) < d(x,a)}, Ma = {x ∈ X: d(0,x) = d(x,a)} and La = {x ∈ X: d(0,x) > d(x,a)}. If the distance is generated by a nor...
Zero-Knowledge Proof is widely used in blockchains. For example, zk-SNARK is used in Zcash as its core technology to identifying transactions without the exposure of the actual transaction values. Up to now, various range proofs have been proposed, a...
Let Gp(x,y,z)=∥x+y+z∥p+∥z∥p−∥x+z∥p−∥y+z∥p be defined on a normed space X. The special case G2(x,y,z)=0,∀z∈X, where X is a real normed linear space, coincides with the trapezoid o...
Access and utilization of data are central to the cloud computing paradigm. With the advent of the Internet of Things (IoT), the tendency of data sharing on the cloud has seen enormous growth. With data sharing comes numerous security and privacy iss...
Crowdsourcing enables requesters to publish tasks to a platform and workers are rewarded for performing tasks of interest. It provides an efficient and low-cost way to aggregate data and solve problems that are difficult for computers but simple for...
In this article, we established new results related to a 2-pre-Hilbert space. Among these results we will mention the Cauchy-Schwarz inequality. We show several applications related to some statistical indicators as average, variance and standard dev...
8 January 2022
Rural areas are crucial to the realization of sustainable development goals (SDGs). Rural social capital is indispensable for these areas to fulfil the SDGs. As China pursues rural revitalization, it is essential to achieve the sustainable developmen...
A quasi-least-squares (QLS) mixed finite element method (MFE) based on the L2-inner product is utilized to solve an incompressible magnetohydrodynamic (MHD) model. These models are associated with the three unknown terms, i.e., fluid velocity, fluid...
Herders’ living strategy is a function of the capitals at their disposal which also serve as a buffering mechanism when shocks arise. An insight into the connection between livelihood strategies and capitals owned by herders provides guidance t...
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a time-independent Hilbe...
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