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1 – 10 of 19It is extremely difficult to establish a variational principle for plasma. Kalaawy obtained a variational principle by using the semi-inverse method in 2016, and Li and He…
Abstract
Purpose
It is extremely difficult to establish a variational principle for plasma. Kalaawy obtained a variational principle by using the semi-inverse method in 2016, and Li and He suggested a modification in 2017. This paper aims to search for a generalized variational formulation with a free parameter.
Design/methodology/approach
The semi-inverse method is used by suitable construction of a trial functional with some free parameters.
Findings
A modification of Li-He’s variational principle with a free parameter is obtained.
Originality/value
This paper suggests a new approach to construction of a trial-functional with some free parameters.
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Tarikul Islam and Armina Akter
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to…
Abstract
Purpose
Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional
Design/methodology/approach
The rational fractional
Findings
Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.
Originality/value
The rational fractional
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In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).
Abstract
Purpose
In this paper, the author presents a hybrid method along with its error analysis to solve (1+2)-dimensional non-linear time-space fractional partial differential equations (FPDEs).
Design/methodology/approach
The proposed method is a combination of Sumudu transform and a semi-analytc technique Daftardar-Gejji and Jafari method (DGJM).
Findings
The author solves various non-trivial examples using the proposed method. Moreover, the author obtained the solutions either in exact form or in a series that converges to a closed-form solution. The proposed method is a very good tool to solve this type of equations.
Originality/value
The present work is original. To the best of the author's knowledge, this work is not done by anyone in the literature.
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This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and…
Abstract
Purpose
This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.
Design/methodology/approach
The functional analysis method is the a priori estimate method or energy inequality method.
Findings
The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.
Research limitations/implications
The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.
Originality/value
The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.
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Kai Zheng, Xianjun Yang, Yilei Wang, Yingjie Wu and Xianghan Zheng
The purpose of this paper is to alleviate the problem of poor robustness and over-fitting caused by large-scale data in collaborative filtering recommendation algorithms.
Abstract
Purpose
The purpose of this paper is to alleviate the problem of poor robustness and over-fitting caused by large-scale data in collaborative filtering recommendation algorithms.
Design/methodology/approach
Interpreting user behavior from the probabilistic perspective of hidden variables is helpful to improve robustness and over-fitting problems. Constructing a recommendation network by variational inference can effectively solve the complex distribution calculation in the probabilistic recommendation model. Based on the aforementioned analysis, this paper uses variational auto-encoder to construct a generating network, which can restore user-rating data to solve the problem of poor robustness and over-fitting caused by large-scale data. Meanwhile, for the existing KL-vanishing problem in the variational inference deep learning model, this paper optimizes the model by the KL annealing and Free Bits methods.
Findings
The effect of the basic model is considerably improved after using the KL annealing or Free Bits method to solve KL vanishing. The proposed models evidently perform worse than competitors on small data sets, such as MovieLens 1 M. By contrast, they have better effects on large data sets such as MovieLens 10 M and MovieLens 20 M.
Originality/value
This paper presents the usage of the variational inference model for collaborative filtering recommendation and introduces the KL annealing and Free Bits methods to improve the basic model effect. Because the variational inference training denotes the probability distribution of the hidden vector, the problem of poor robustness and overfitting is alleviated. When the amount of data is relatively large in the actual application scenario, the probability distribution of the fitted actual data can better represent the user and the item. Therefore, using variational inference for collaborative filtering recommendation is of practical value.
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Fong Yew Leong, Dax Enshan Koh, Wei-Bin Ewe and Jian Feng Kong
This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular…
Abstract
Purpose
This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.
Design/methodology/approach
The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.
Findings
Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.
Practical implications
Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.
Originality/value
This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.
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Getahun Bekele Wega and Habtu Zegeye
Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The…
Abstract
Our purpose of this study is to construct an algorithm for finding a zero of the sum of two maximally monotone mappings in Hilbert spaces and discus its convergence. The assumption that one of the mappings is
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