Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environmen...Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environment, which current methods cannot effectively address. A normbased adaptive coefficient zeroing neural network(NACZNN) model to solve the TDARE problem is proposed.展开更多
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers ...The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.展开更多
We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be ...We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .展开更多
In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better...In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.展开更多
We are all witnesses to the widespread use of wireless LANs (WLAN) and their easy implementation in indoor environments. Wi-Fi is the most popular technology for the WLAN. However, interference caused by building mate...We are all witnesses to the widespread use of wireless LANs (WLAN) and their easy implementation in indoor environments. Wi-Fi is the most popular technology for the WLAN. However, interference caused by building materials is a common, yet often overlooked, contributor to poor Wi-Fi performance. This interference occurs due to the nature of radio wave propagation and the characteristics of the wireless communication system. Therefore, during the implementation of these networks, one must consider the quasi-static nature of the Wi-Fi signal and its dependence on the influence of various building materials on the propagation of these waves. This paper presents the effects of building materials and structures on indoor environments for Wi-Fi 2.4 GHz and 5 GHz. To establish the interdependencies between factors influencing electric field levels, measurements were conducted in an experimental Wi-Fi network at different distances from the access point (AP). The results obtained show that the electric field strength of the Wi-Fi signal decreases depending on the distance, the building materials, and the transmitted frequency. Concrete material had the most significant impact on the strength of the electric field in Wi-Fi, while glass had a relatively minor effect on reducing it. Wi-Fi operates within the radio frequency spectrum, typically utilizing frequencies in the 2.4 GHz and 5 GHz bands. Additionally, measurements revealed that Wi-Fi signal penetration is more pronounced at lower frequencies (2.4 GHz) as opposed to the Wi-Fi signal 5 GHz. The findings can be used to address the impact of building materials and structures on indoor radio wave propagation, ultimately ensuring seamless Wi-Fi signal coverage within buildings.展开更多
基金supported in part by the Natural Science Foundation of Guangdong Province,China(2021A 1515011847)Postgraduate Education Innovation Project of Guangdong Ocean University(202214,202250,202251,202159,202160)+1 种基金the Special Project in Key Fields of Universities in Department of Education of Guangdong Province(2019KZDZX1036)the Key Laboratory of Digital Signal and Image Processing of Guangdong Province(2019GDDSIPL-01)。
文摘Dear Editor, The time-dependent algebraic Riccati equation(TDARE) problem is applied to many optimal control industrial applications. It is susceptible to interference from measurement noises in the virtual environment, which current methods cannot effectively address. A normbased adaptive coefficient zeroing neural network(NACZNN) model to solve the TDARE problem is proposed.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
文摘The superiority of hypothetical quantum computers is not due to faster calculations but due to different scheme of calculations running on special hardware. At the same time, one should realize that quantum computers would only provide dramatic speedups for a few specific problems, for example, factoring integers and breaking cryptographic codes in the conventional quantum computing approach. The core of quantum computing follows the way a state of a quantum system is defined when basic things interact with each other. In the conventional approach, it is implemented through the tensor product of qubits. In the suggested geometric algebra formalism simultaneous availability of all the results for non-measured observables is based on the definition of states as points on a three-dimensional sphere, which is very different from the usual Hilbert space scheme.
文摘We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .
基金partially supported by the Natural Sciences and Engineering Research Council of Canada(2019-03907)。
文摘In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
文摘We are all witnesses to the widespread use of wireless LANs (WLAN) and their easy implementation in indoor environments. Wi-Fi is the most popular technology for the WLAN. However, interference caused by building materials is a common, yet often overlooked, contributor to poor Wi-Fi performance. This interference occurs due to the nature of radio wave propagation and the characteristics of the wireless communication system. Therefore, during the implementation of these networks, one must consider the quasi-static nature of the Wi-Fi signal and its dependence on the influence of various building materials on the propagation of these waves. This paper presents the effects of building materials and structures on indoor environments for Wi-Fi 2.4 GHz and 5 GHz. To establish the interdependencies between factors influencing electric field levels, measurements were conducted in an experimental Wi-Fi network at different distances from the access point (AP). The results obtained show that the electric field strength of the Wi-Fi signal decreases depending on the distance, the building materials, and the transmitted frequency. Concrete material had the most significant impact on the strength of the electric field in Wi-Fi, while glass had a relatively minor effect on reducing it. Wi-Fi operates within the radio frequency spectrum, typically utilizing frequencies in the 2.4 GHz and 5 GHz bands. Additionally, measurements revealed that Wi-Fi signal penetration is more pronounced at lower frequencies (2.4 GHz) as opposed to the Wi-Fi signal 5 GHz. The findings can be used to address the impact of building materials and structures on indoor radio wave propagation, ultimately ensuring seamless Wi-Fi signal coverage within buildings.
