We consider a two-component reaction-diffusion system with a nonlocal reaction term. A necessary condition and a sufficient condition for the internal stabilizability to zero of one of the two components of the soluti...
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We consider a two-component reaction-diffusion system with a nonlocal reaction term. A necessary condition and a sufficient condition for the internal stabilizability to zero of one of the two components of the solution while preserving the nonnegativity of both components have been established in [6]. In case of stabilizability, a feedback stabilizing control of harvesting type has been indicated. The rate of stabilization (for the indicated feedback control) is given by the principal eigenvalue of a certain non-selfadjoint operator. A large principal eigenvalue leads to a fast stabilization. The first main goal of this article is to approximate this principal eigenvalue. This is done in two steps. First, we investigate the large-time behavior of the solution to a logistic population dynamics with migration, and next we derive as a consequence a method to approximate the principal eigenvalue. The other main goal is to derive a conceptual iterativealgorithm to improve the position of the support of the control in order to get a faster stabilization. Our results apply to prey-predator systems.
The rheological properties of cement-based materials (CBM) significantly influence their workability and application in construction. Despite the common use of coaxial cylinder rheometers for measuring these propertie...
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The rheological properties of cement-based materials (CBM) significantly influence their workability and application in construction. Despite the common use of coaxial cylinder rheometers for measuring these properties, challenges arise, particularly at low shear rates due to plug flow within the tested samples. This study aims to investigate the impact of plug flow on rheological property measurements of CBM and proposes strategies to enhance measurement accuracy. An image analysis method and a novel numerical iteration algorithm were proposed in this study to address plug flow effects. Three series fresh cement paste with different fluidities were prepared to conduct the rheological tests. Through the image analysis method, actual shear radii at different rotor speeds were measured. The corresponding rheological parameters were determined and compared using the complete shear assumption, the image analysis method, and numerical iteration algorithm, respectively. The results indicated the great influence of plug flow on rheological results, especially at low shear rates and low fluidities, highlighting the need for its consideration in rheological parameters calculations. Moreover, the proposed numerical iteration algorithm was verified to calculate the incomplete shear state of CBM and improve the measurement accuracy of rheological parameters. The extensions and limitations of the numerical iteration algorithm in its application were discussed further.
Sensor placement optimisation is an important problem in the field of structural health monitoring (SHM). Many researchers solve this problem by focusing only on the network requirements, without considering the civil...
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Sensor placement optimisation is an important problem in the field of structural health monitoring (SHM). Many researchers solve this problem by focusing only on the network requirements, without considering the civil engineering requirements. However, there are researchers that optimise the sensor placement considering network and civil requirements. Unfortunately, those researchers did not address minimising the number of sensors. As a result, in this research we study the problem of minimising the number of sensors for SHM in wireless sensors networks satisfying both civil and network requirements. The authors' contribution in this work is showing the mathematical model of the mentioned problem. Then, solve the problem using different methods: exhaustive search, genetic algorithm (GA), and a numerical iterative algorithm that applies binary search (BS). The problem is solved using different number of sensors as well as different placements in many conducted experiments. The obtained results showed that minimising the number of sensors becomes more significant with big structures. Furthermore, the BS algorithm is the best to use to solve the problem for small buildings. However, for larger buildings, there is a trade-off between the performance, and time complexity, where the BS gives optimal solution, but GA gives better time execution.
Estimating the optimal order of fractional accumulating operator and the optimal initial value are two inherent problems in studies of fractional grey models. To find the optimal order of fractional accumulating opera...
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ISBN:
(纸本)9781665440899
Estimating the optimal order of fractional accumulating operator and the optimal initial value are two inherent problems in studies of fractional grey models. To find the optimal order of fractional accumulating operator, numerical iteration algorithm is applied in this paper. It is used in applications compared with the other two existing optimization algorithm (genetic algorithm and particle swarm optimization algorithm), which proves that the numerical iteration algorithm is simpler than the other two algorithms and has the same accuracy. At the same time, this paper proposes a numerical method to find the optimal initial condition and gives a proof. And based on methods mentioned previously, a novel fractional-order grey discrete model with initial value optimization is proposed. In order to test the new model, per capita power consumption in southern Jiangsu province is employed. Results show that the new fractional-order discrete grey model proposed in this paper is better than the competitive grey model in predicting and fitting periods.
Positronium (Ps) lifetime imaging is gaining attention to bring out additional biomedical information from positron emission tomography (PET). The lifetime of Ps in vivo can change depending on the physical and chemic...
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Positronium (Ps) lifetime imaging is gaining attention to bring out additional biomedical information from positron emission tomography (PET). The lifetime of Ps in vivo can change depending on the physical and chemical environments related to some diseases. Due to the limited sensitivity, Ps lifetime imaging may require merging some voxels for statistical accuracy. This paper presents a method for separating the lifetime components in the voxel to avoid information loss due to averaging. The mathematics for this separation is the inverse Laplace transform (ILT), and the authors examined an iterativenumerical ILT algorithm using Tikhonov regularization, namely CONTIN, to discriminate a small lifetime difference due to oxygen saturation. The separability makes it possible to merge voxels without missing critical information on whether they contain abnormally long or short lifetime components. The authors conclude that ILT can compensate for the weaknesses of Ps lifetime imaging and extract the maximum amount of information.
Estimating the optimal order of fractional accumulating operator and the optimal initial value are two inherent problems in studies of fractional grey *** find the optimal order of fractional accumulating operator,num...
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Estimating the optimal order of fractional accumulating operator and the optimal initial value are two inherent problems in studies of fractional grey *** find the optimal order of fractional accumulating operator,numerical iteration algorithm is applied in this *** is used in applications compared with the other two existing optimization algorithm(genetic algorithm and particle swarm optimization algorithm),which proves that the numerical iteration algorithm is simpler than the other two algorithms and has the same *** the same time,this paper proposes a numerical method to find the optimal initial condition and gives a *** based on methods mentioned previously,a novel fractional-order grey discrete model with initial value optimization is *** order to test the new model,per capita power consumption in southern Jiangsu province is *** show that the new fractional-order discrete grey model proposed in this paper is better than the competitive grey model in predicting and fitting periods.
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