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The present paper is in two folds. In the first fold, we prove the Lipschitz continuity of the proximal mapping associated with a general strongly H-monotone mapping and compute an estimate of its Lipschitz constant under some mild assumptions imposed on the mapping H involved in the proximal mapping. We provide two examples to show that a maximal monotone mapping need not be a general H-monotone for a single-valued mapping H from a Banach space to its dual space. A class of multi-valued nonlinear variational inclusion problems is considered, and by using the notion of proximal mapping and Nadler's technique, an iterative algorithm with mixed errors is suggested to compute its solutions. Under some appropriate hypotheses imposed on the mappings and parameters involved in the multi-valued nonlinear variational inclusion problem, the strong convergence of the sequences generated by the proposed algorithm to a solution of the aforesaid problem is verified. The second fold of this paper investigates and analyzes the notion of Cn-monotone mappings defined and studied in [S.Z. Nazemi, A new class of monotone mappings and a new class of variational inclusions in Banach spaces, J. Optim. Theory Appl. 155(3)(2012) 785-795]. Several comments related to the results and algorithm appeared in the above mentioned paper are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Yosida approximation operator associated with H- monotone operator in Hilbert spaces and prove some of its important properties. In addition, we consider a system of generalized nonlinear variational inclusions involving Yosida approximation operator and establish its equivalence with the fixed point problems using resolvent operator technique. This alternative equivalent formulation is employed to propose an iterative algorithm for solving this system of generalized nonlinear variational inclusions. Further, we discuss the existence of solution and convergence analysis of the proposed iterative algorithm under suitable conditions. Finally, we present a numerical example in support of the results proved and demonstrate the convergence result using MATLAB. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) offer a new approach to wireless communication, leveraging their high mobility, flexibility, and visual communication capabilities. Ambient backscatter communication enables Internet of Things devices to transmit data by reflecting and modulating ambient radio waves, eliminating the need for additional wireless channels, and reducing energy consumption and cost for sensors. However, passive ambient backscatter communication has limitations such as limited range and poor communication quality. By utilizing UAVs as communication nodes, these limitations can be overcome, expanding the communication range and improving the quality of communication. Although some research has been conducted on combining UAVs and ambient backscatter, several challenges remain. One key challenge is the strong direct link interference in ambient backscatter under UAV conditions, which significantly affects communication quality. In this paper, we propose an intelligent backward and forward straight link interference cancellation algorithm based on NOMA decoding technique to enhance ambient backscatter communication quality under UAV conditions and extract more ambient energy for UAV energy supply. The paper includes theoretical derivation, algorithm description, and simulation analysis to validate the error bit rate of labeled information bits. The results demonstrate that the forward algorithm reduces the error bit rate by approximately 20% under low signal-to-noise ratio (SNR) conditions, while the backward algorithm reduces the error bit rate under high SNR conditions. The combination of the forward and backward algorithms reduces the error bit rate under both high and low SNR conditions. The proposed method contributes to improving the quality of ambient backscatter communication in UAV settings. [ABSTRACT FROM AUTHOR]

Panel data model with fixed effects is widely used in economic and administrative applications. However, the presence of factors: measurement errors, data variability and outliers may potentially decrease the accuracy of the model prediction. In this paper, we use panel interval-valued data to represent measurement errors and data volatility of observations. Further, we propose a corresponding panel interval-valued data model with fixed effects, in which both the response and explanatory variables are interval-valued data. To reduce the impact of outliers on our model, we propose a robust estimation method based on the iterative weighted least squares technique. Later, Monte Carlo simulation and empirical application demonstrate that our model is a suitable tool for analyzing the behaviour of panel interval-valued data. [ABSTRACT FROM AUTHOR]

In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm's effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel high-order structure-preserving numerical scheme for solving the damped nonlinear space fractional Schrödinger equation (DNSFSE) in two spatial dimensions. The main idea of constructing new algorithm consists of two parts. Firstly, we introduce an auxiliary exponential variable to transform the original DNSFSE into a modified one. The modified DNSFSE subjects to the conservation of mass and energy, which is crucial to develop structure-preserving numerical schemes. Secondly, we construct a high-order numerical differential formula to approximate the Riesz derivative in space, which contributes to a semi-discrete difference scheme for the modified DNSFSE. Combining the semi-discrete scheme with the variant Crank–Nicolson method in time, we can obtain the fully-discrete difference scheme for solving the modified DNSFSE. The advantage of the proposed scheme is that a fourth-order convergent accuracy can be achieved in space while maintaining the conservation of mass and energy. Subsequently, we conduct a detailed study on the boundedness, uniqueness, and convergence of solution for fully-discrete scheme. Furthermore, an improved efficient iterative algorithm is proposed for the fully-discrete scheme, which has the advantage of maintaining the same convergence order as the original difference scheme. Finally, extensive numerical results are reported to further verify the correctness of theoretical analysis and the effectiveness of the proposed numerical algorithm. [ABSTRACT FROM AUTHOR]

The receding contact problem between a graded piezoelectric layer and a homogeneous piezoelectric substrate is considered in this paper. It is assumed that the gradation of the elastic piezoelectric graded layer is of exponential type through its thickness. Using standard Fourier transform, the contact problem is converted to a system of two singular integral equations in which the contact pressures and the electric charge displacement in addition to the contact dimensions are the unknowns. The integral equations are then solved numerically using Gauss–Jacobi integration formula. The primary objective of this paper is to investigate the effect of material gradation on the contact pressure, electric charge distribution and on the length of the receding contact. The main findings of the paper are that the inhomogeneity parameter has a strong effect on the contact pressure and the electric charge distribution at the receding contact interface. It is concluded that a softer FGPM in + z direction results in lower contact pressure and electric displacement. [ABSTRACT FROM AUTHOR]

This paper studies the multiple-sets split feasibility problem in Hilbert spaces. To solve this problem, we propose a new algorithm and establish a strong convergence theorem for it. Our scheme combines the hybrid projection method with the proximal point algorithm. We show that the iterative method converges strongly under weaker assumptions than the ones used recently by Yao et al. (Optimization 69(2):269–281, 2020). We also study an application to the split feasibility problem and give a strong convergence result to the minimum-norm solution to the problem. Thereafter, some numerical examples are conducted in order to illustrate the convergence analysis of the considered methods as well as compare our results to the related ones introduced by Buong (Numer Algorithms 76:783–798, 2017) and Yao et al. (2020). We end this paper by considering an application of our method to a class of optimal control problems and compare our result with the one introduced by Anh et al. (Acta Math Vietnam 42:413–429, 2017). [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative algorithm for finding a common solution for variational inclusion problem and fixed point problem in real Hilbert spaces. This method can be implemented more easily without the prior knowledge of the Lipschitz constant of component operators. The algorithm uses variable step-sizes which are updated at each iteration by a simple computation. In additional, weak and strong convergence results of the proposed algorithm are obtained under some mild conditions. Then, we establish the linear rate of convergence for the proposed algorithm. Finally, an example is given to illustrate the convergence of the algorithm. [ABSTRACT FROM AUTHOR]

To improve the estimation efficiency of high-dimensional regression problems, penalized regularization is routinely used. However, accurately estimating the model remains challenging, particularly in the presence of correlated effects, wherein irrelevant covariates exhibit strong correlation with relevant ones. This situation, referred to as correlated data, poses additional complexities for model estimation. In this paper, we propose the elastic-net multi-step screening procedure (EnMSP), an iterative algorithm designed to recover sparse linear models in the context of correlated data. EnMSP uses a small repeated penalty strategy to identify truly relevant covariates in a few iterations. Specifically, in each iteration, EnMSP enhances the adaptive lasso method by adding a weighted l 2 penalty, which improves the selection of relevant covariates. The method is shown to select the true model and achieve the l 2 -norm error bound under certain conditions. The effectiveness of EnMSP is demonstrated through numerical comparisons and applications in financial data. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel Halpern-type algorithm and prove that the sequence generated by the algorithm converges strongly to the common element of the set of fixed points of the two firmly nonexpansive mappings and the solution set of zero points of the monotone inclusion problems on Hadamard manifolds, the main results in this paper extended and improved some recent related results. [ABSTRACT FROM AUTHOR]

The multi-beam array stitching test system (MASTS) based on the Hartmann principle is employed to measure the aberrations in large-aperture optical systems. As each small-aperture and ideal parallel beam traverses the optical system, it is converged into a spot at the focal plane of the optical system. The centroid position of the spot contains the information about the wavefront slope of the sub-aperture at that specific location in the optical system. Scanning the optical system with this small-aperture beam across the entire aperture of the optical system, we can yield the aberration information to be tested. To mitigate pointing errors induced by scanning motion and accurately obtain the aberration signals of the optical system, nine beams are integrated into a 3 × 3 multi-beam array system, and their directions are aligned to be identical. However, achieving complete alignment in the same direction for all nine beams is a challenging task, resulting in errors due to their pointing differences within the array. This paper introduces an iterative algorithm designed to obtain high-precision multi-beam pointing errors and to reconstruct the wavefront of the optical system under test. This enables a more accurate measurement of wavefront aberrations in the optical system to be tested. Firstly, simulation models were implemented to validate the algorithm's feasibility. Additionally, a scanning optical measurement system with a multi-beam array was developed in our lab, and the iterative algorithm was applied to process our experimental data. The results were then compared with interferometer data, demonstrating that our algorithm is feasible for MASTS to measure aberrations in large-aperture optical systems with high accuracy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find the approximate series solution of IVPs on nonlinear differential equations (NDEs) and on systems of NDEs via an iterative algorithm that can be easily exhibited through MATLAB code. We propose a modified iterative scheme based on the DGJM method of solving functional equations of the form u = f + N(u), and we observe that the method is far better than those existing in the literature. For the sake of illustration, series solutions to a few physical equations proposed by Klien-Gordon, Allen- Cahn and Benjamin-Bona-Mahony are provided along with the MATLAB code used for computation. Moreover, graphs are used to validate the efficacy of the method. [ABSTRACT FROM AUTHOR]

To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network defined on the whole problem domain. In such a partitioned neural network approach, suitable interface conditions or subdomain boundary conditions are combined to obtain a convergent approximate solution. However, there has been no rigorous study on the convergence and parallel computing enhancement on the partitioned neural network approach. In this paper, iterative algorithms are proposed to enhance parallel computation performance in the partitioned neural network approximation. Our iterative algorithms are based on classical additive Schwarz domain decomposition methods. For the proposed iterative algorithms, their convergence is analyzed under an error assumption on the local and coarse neural network solutions. Numerical results are also included to show the performance of the proposed iterative algorithms. [ABSTRACT FROM AUTHOR]

In this paper, algorithms for finding common solutions of strong vector equilibrium and fixed point problems of multivalued mappings are considered. First, a Minty vector equilibrium problem is introduced and the relationship between the Minty vector equilibrium problem and the strong equilibrium problem is discussed. Then, by applying the Minty vector equilibrium problem, projection iterative methods are proposed and some convergence results are established in Hilbert spaces. The main results obtained in this paper develop and improve some recent works in this field. [ABSTRACT FROM AUTHOR]

This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of obstacles and takes the joint blockage phenomenon into account. We show on a couple of simple instances that the Laplace transforms of total interference satisfies a functional equation that can be solved efficiently by an iterative scheme. This is used to analyze the coverage probability of the receiver and the effect of blockage correlation and penetration loss in both dense and sparse blockage environments. Furthermore, this model is used to investigate the effect of blockage correlation on user beamforming techniques. Another functional equation and its associated iterative algorithm are proposed to derive the coverage performance of the best beam selection in this context. In addition, the conditional coverage probability is also derived to evaluate the effect of beam switching. The results not only show that beam selection is quite efficient for multi-beam terminals, but also show how the correlation brought by blockages can be leveraged to accelerate beam sweeping and pairing. [ABSTRACT FROM AUTHOR]

This paper presents a new sufficiently descent algorithm for system of nonlinear equations where the underlying operator is pseudomonotone. The conditions imposed on the proposed algorithm to achieve convergence are Lipschitz continuity and pseudomonotonicity which is weaker than monotonicity assumption forced upon many algorithms in this area found in the literature. Numerical experiments on selected test problems taken from the literature validate the efficiency of the new algorithm. Moreover, the new algorithm demonstrates superior performance in comparison with some existing algorithms. Furthermore, the proposed algorithm is applied to reconstruct some disturbed signals. [ABSTRACT FROM AUTHOR]

This paper considers various hybrid methods for solving a system of nonlinear equations. Extensive numerical experiments confirm the research hypothesis that one particular form of hybridization of the conjugate gradient algorithm with Newton's method outperforms other hybrid strategies considered in the paper. [ABSTRACT FROM AUTHOR]

The main contribution of this work is the construction of a new iterative algorithm with the help of the notion of resolvent operator associated with an $ \widehat{A} $-maximal $ m $-relaxed $ \eta $-accretive mapping for solving a new class of set-valued variational-like inclusion problems in the setting of Banach spaces. The convergence analysis of the iterative sequences generated by our proposed iterative algorithm is studied under some appropriate conditions. The main attention of the final section is paid to the investigating and analysis of the notion of $ (H(.,.), \eta) $-accretive operator introduced and studied by Wang and Ding (2010). In the light of the considered conditions for an $ (H(.,.), \eta) $-accretive operator, we point out that every $ (H(.,.), \eta) $-accretive operator is actually an $ \widehat{A} $-maximal $ m $-relaxed $ \eta $-accretive mapping and is not a new one. Finally, our paper is closed with some important comments regarding $ (H(.,.), \eta) $-accretive operator and the derived results related to it in the literature. [ABSTRACT FROM AUTHOR]

Background: With the development of low‐dose computed tomography (CT), incomplete data reconstruction has been widely concerned. The total variation (TV) minimization algorithm can accurately reconstruct images from sparse or noisy data. Purpose: However, the traditional TV algorithm ignores the direction of structures in images, leading to the loss of edge information and block artifacts when the object is not piecewise constant. Since the anisotropic information can facilitate preserving the edge and detail information in images, we aim to improve the TV algorithm in terms of reconstruction accuracy via this approach. Methods: In this paper, we propose an adaptive‐weighted high order total variation (awHOTV) algorithm. We construct the second order TV‐norm using the second order gradient, adapt the anisotropic edge property between neighboring image pixels, adjust the local image‐intensity gradient to keep edge information, and design the corresponding Chambolle‐Pock (CP) solving algorithm. Implementing the proposed algorithm, comprehensive studies are conducted in the ideal projection data experiment where the Structural similarity (SSIM), Root Mean Square Error (RMSE), Contrast to noise ratio (CNR), and modulation transform function (MTF) curves are utilized to evaluate the quality of reconstructed images in statism, structure, spatial resolution, and contrast, respectively. In the noisy data experiment, we further use the noise power spectrum (NPS) curve to evaluate the reconstructed images and compare it with other three algorithms. Results: We use the 2D slice in the XCAT phantom, 2D slice in TCIA Challenge data and FORBILD phantom as simulation phantoms and use real bird data for real verification. The results show that, compared with the traditional TV and FBP algorithms, the awHOTV has better performance in terms of RMSE, SSIM, and Pearson correlation coefficient (PCC) under the projected data with different sparsity. In addition, the awHOTV algorithm is robust against the noise of different intensities. Conclusions: The proposed awHOTV method can reconstruct the images with high accuracy under sparse or noisy data. The awHOTV solves the strip artifacts caused by sparse data in the FBP method. Compared with the TV method, the awHOTV can effectively suppress block artifacts and has good detail protection ability. [ABSTRACT FROM AUTHOR]

Poisson surface reconstruction (PSR) remains a popular technique for reconstructing watertight surfaces from 3D point samples thanks to its efficiency, simplicity, and robustness. Yet, the existing PSR method and subsequent variants work only for oriented points. This paper intends to validate that an improved PSR, called iPSR, can completely eliminate the requirement of point normals and proceed in an iterative manner. In each iteration, iPSR takes as input point samples with normals directly computed from the surface obtained in the preceding iteration, and then generates a new surface with better quality. Extensive quantitative evaluation confirms that the new iPSR algorithm converges in 5--30 iterations even with randomly initialized normals. If initialized with a simple visibility based heuristic, iPSR can further reduce the number of iterations. We conduct comprehensive comparisons with PSR and other powerful implicit-function based methods. Finally, we confirm iPSR's effectiveness and scalability on the AIM@SHAPE dataset and challenging (indoor and outdoor) scenes. Code and data for this paper are at https://github.com/houfei0801/ipsr. [ABSTRACT FROM AUTHOR]

In this work we reflect a new system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. By using resolvent operator technique, we offer an iterative algorithm for figuring out the approximate solution of the said system. The motive of this paper is to review the convergence analysis of a system of generalized nonlinear variational inclusion problems in 2-uniformly smooth Banach spaces. The proposition used in this paper can be considered as an extension of propositions for examining the existence of solution for various classes of variational inclusions considered and studied by many authors in 2-uniformly smooth Banach spaces. [ABSTRACT FROM AUTHOR]

The present paper is concerned with exploiting an iterative decoupling algorithm to address the problem of third-order tensor deblurring. The regularized deblurring problem, which is mathematically given by the sum of a fidelity term and a regularization term, is decoupled into an observation fidelity and a denoiser model steps. One basic advantage of the iterative decoupling algorithm is that the deblurring problem is supervised by the efficiency of the denoiser model. Thus, we consider a patch-based weighted low-rank tensor with sparsity prior. Numerical tests to image deblurring are given to demonstrate the efficiency of the proposed decoupling based algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safeguarding strategy and its Hessian matrix is positive and definite throughout the iteration process. Numerical experiments are conducted on a range of test problems, with 120 instances to demonstrate the efficacy of the proposed algorithm by comparing it with existing techniques in the literature. However, the results obtained validate the effectiveness of the proposed method in terms of the standard metrics of comparison. Additionally, the proposed approach is applied to address motion-control problems in a robotic model, resulting in favorable outcomes in terms of the robot's motion characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we prove that a three-step iterative algorithm converges strongly to the solution of a functional Volterra integral equation of the second kind. We also show the solution presented in the convergence theorem can obtain by removing a strong restriction imposed on the control sequence. Finally, we analyse the data-dependence result by using this iterative algorithm, and to support obtained result we give an example. [ABSTRACT FROM AUTHOR]

Feature selection aims at selecting representative features from the original high-dimensional feature set, and it has drawn much attention in most real-world applications like data mining and pattern recognition. This paper studies feature selection problem from the viewpoint of feature self-representation. Traditionally, feature self-representation is only performed on the whole-level reconstruction, whereas the feature selection ability is insufficient owing to the intra-class variations. To address this problem, we propose a new feature selection method, i.e., class-level regularized self-representation (CLRSR). In the proposed method, a class-level reconstruction term is designed to reduce intra-class variations of the samples from different categories. By jointly optimizing the whole-level reconstruction and the class-level reconstruction, CLRSR is able to select more discriminative and informative features. Moreover, an iterative algorithm is proposed to minimize cost function of CLRSR, and its convergence is proven in theory. By comparing with several state-of-the-art feature selection methods, experimental evaluations on six benchmark datasets have verified effectiveness and superiority of CLRSR. [ABSTRACT FROM AUTHOR]

The paper is devoted to the introduction of a new class of generalized set-valued nonlinear variational-like inequality problems in the setting of Banach spaces. By means of the notion of P- η -proximal mapping, we prove its equivalence with a class of generalized implicit Wiener–Hopf equations and employ the obtained equivalence relationship and Nadler's technique to suggest a new iterative algorithm for finding an approximate solution of the considered problem. The existence of solution and the strong convergence of the sequences generated by our proposed iterative algorithm to the solution of our considered problem are verified. The problem of finding a common element of the set of solutions of a generalized nonlinear variational-like inequality problem and the set of fixed points of a total asymptotically nonexpansive mapping is also investigated. The final section deals with the investigation and analysis of the main results appeared in Kazmi and Bhat (Appl Math Comput 166:164–180, 2005) and some comments relating to them are given. The results presented in this article extend and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

Motivated by the nature of observed responses in real world situations, we propose an iterative algorithm for estimating population column proportions of a n × k Bernoulli random matrix (X) in survey type designs. The Perron-Frobenius theorem is used to establish the limiting form of the proposed estimator in the iteration process, where pj, j = 1 , ... , k , is given by the row sum of the Perron projection of XtX or X t (1 n − X). An asymptotic distribution of the proposed estimator is provided in this paper. [ABSTRACT FROM AUTHOR]

The paper considers an inverse problem of determining the coefficients in the model of small transverse vibrations of a homogeneous finite string one end of which is placed in a moving medium and the other is free. The vibrations are simulated by a hyperbolic equation on an interval. One boundary condition has a nonclassical form. Additional data for solving the inverse problem are the values of the solution of the forward problem with a known fixed value of the spatial argument. In the inverse problem, it is required to determine the function in the nonclassical boundary condition and a functional factor on the right-hand side of the equation. Uniqueness and existence theorems for the inverse problem are proved. For the forward problem, conditions for unique solvability are established in a form that simplifies the analysis of the inverse problem. For the numerical solution of the inverse problem, an algorithm is proposed for the stage-by-stage separate reconstruction of the sought-for functions using the method of successive approximations for integral equations. [ABSTRACT FROM AUTHOR]

Backscatter communication is a promising technology for the Internet of Things (IoT) systems with low-energy consumption, in which the data transmission of the backscatter devices relies on reflecting the incident signal. However, limited by the low power characteristic of the reflected signal from backscatter devices, achieving efficient data collection for the widely distributed backscatter devices is a thorny problem. Considering that unmanned aerial vehicles (UAVs) have flexible deployment capability, employing UAVs in a backscatter communication network can achieve feasible data collection for backscatter devices. In this paper, we consider a UAV-aided backscatter system and introduce Non-orthogonal multiple access (NOMA) to enable the UAV to collect signals from multiple backscatter devices simultaneously. We formulate an optimization problem to maximize the communication throughput of the considered system by jointly designing the backscatter device matching, the trajectory of the UAV, and the reflection coefficients of the backscatter devices, which is a non-convex optimization problem and challenging to solve. Hence, we decouple the original problem into three sub-problems and propose an efficient iterative algorithm based on Block Coordinate Descent (BCD) to solve them. In detail, a game-based matching algorithm is designed to ensure the transmission needs of remote backscatter devices. The UAV trajectory and reflection coefficients of backscatter devices are optimized through the Successive Convex Approximation (SCA) algorithm and relaxation algorithm. By iterative optimization of the sub-problems, the original problem is solved. The simulation results show that the proposed scheme can obtain a significant throughput gain compared to benchmark schemes. [ABSTRACT FROM AUTHOR]

Abstract Unmanned aerial vehicles (UAVs) offer a new approach to wireless communication, leveraging their high mobility, flexibility, and visual communication capabilities. Ambient backscatter communication enables Internet of Things devices to transmit data by reflecting and modulating ambient radio waves, eliminating the need for additional wireless channels, and reducing energy consumption and cost for sensors. However, passive ambient backscatter communication has limitations such as limited range and poor communication quality. By utilizing UAVs as communication nodes, these limitations can be overcome, expanding the communication range and improving the quality of communication. Although some research has been conducted on combining UAVs and ambient backscatter, several challenges remain. One key challenge is the strong direct link interference in ambient backscatter under UAV conditions, which significantly affects communication quality. In this paper, we propose an intelligent backward and forward straight link interference cancellation algorithm based on NOMA decoding technique to enhance ambient backscatter communication quality under UAV conditions and extract more ambient energy for UAV energy supply. The paper includes theoretical derivation, algorithm description, and simulation analysis to validate the error bit rate of labeled information bits. The results demonstrate that the forward algorithm reduces the error bit rate by approximately 20% under low signal-to-noise ratio (SNR) conditions, while the backward algorithm reduces the error bit rate under high SNR conditions. The combination of the forward and backward algorithms reduces the error bit rate under both high and low SNR conditions. The proposed method contributes to improving the quality of ambient backscatter communication in UAV settings.

This paper focuses on investigating the problem of finding a common element of the set of solutions of a generalized nonlinear implicit variational-like inclusion problem involving an $ (A,\eta) $ (A , η) -maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. and the set of fixed points of a total asymptotically nonexpansive mapping. To achieve such a purpose, a new iterative algorithm is constructed. Applying the concepts of graph convergence and generalized resolvent operator associated with an $ (A,\eta) $ (A , η) -maximal m-relaxed monotone mapping in the sense of L.-G.-s.i.p. As an application of the obtained equivalence relationship, the strong convergence of the sequence generated by our proposed iterative algorithm to a point belonging to the intersection of the two sets mentioned above is proved. [ABSTRACT FROM AUTHOR]

In this paper an iterative method is proposed to solve a partial differential equation (PDE) with free boundary arising from pricing corporate bond with credit grade migration risk. A iterative algorithm is designed to construct two sequences of fixed internal boundary problems, which produce two weak solution sequences. It is proved that both weak solution sequences are convergent. In each iteration step, an implicit-upwind difference scheme is used to solve the fixed internal boundary problem. It is shown that the scheme is stable and first-order convergent. Numerical experiments verify that the limit of the weak solution sequence is the solution of the free boundary problem. This method simplifies the free boundary problem solving, ensures the stability of the discrete scheme and reduces the amount of calculation. [ABSTRACT FROM AUTHOR]

In this paper, an implicit viscosity iterative algorithm for nonexpansive mappings is proposed and investigated on Hadamard manifolds. A convergence theorem of a fixed point of a nonexpansive mapping is established on Hadamard manifolds. It is proved that the fixed point also solves a variational inequality. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to construct a new iterative algorithm using the notion of P-η-resolvent operator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved. [ABSTRACT FROM AUTHOR]

In this manuscript, using (H-η-accretive mappings we study the existence of common solution of a system of generalized mixed variational-like inclusion problems and the set of fixed point problems in q-uniformly smooth Banach spaces. The method used in this paper can be considered as an extension of methods for studying the existence of common solution for various classes of variational inclusions considered and studied by many authors in q-uniformly smooth Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, GNSS interferometric reflectometry (GNSS-IR) is firstly proposed to estimate ground surface subsidence caused by underground coal mining. Ground subsidence on the main direction of a coal seam is described by using the probability integral model (PIM) with unknown parameters. Based on the laws of reflection in geometric optics, model of GNSS signal-to-noise (SNR) observation for the tilt surface, which results from differential subsidence of ground points, is derived. Semi-cycle SNR observations fitting method is used to determine the phase of the SNR series. Phase variation of the SNR series is used to calculate reflector height of ground specular reflection point. Based on the reflector height and ground tilt angle, an iterative algorithm is proposed to determine coefficients of PIM, and thus subsidence of the ground reflection point. By using the low-cost navigational GNSS receiver and antenna, an experimental campaign was conducted to validate the proposed method. The results show that, when the maximum subsidence is 3076 mm, the maximum relative error of the proposed method-based subsidence estimation is 5.5%. This study also suggests that, based on the proposed method, the navigational GNSS instrument can be treated as a new type of sensor for continuously measuring ground subsidence deformation in a cost-effective way. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate some inequalities involving the p-weighted geometric operator mean A ♯ p B = A 1 / 2 ( A − 1 / 2 B A − 1 / 2 ) p A 1 / 2 , where p ∈ [0, 1] is a real number and A, B are two positive invertible operators acting on a Hilbert space. As applications, we obtain some inequalities about the so-called Tsallis relative operator entropy. We also give some inequalities involving the Heinz operator mean. Our results refine some inequalities existing in the literature. In a second part, we construct iterative algorithms converging to A ♯ p B with a high rate of convergence. Some relationships involving A ♯ p B are deduced. Numerical examples illustrating the theoretical results are also discussed. [ABSTRACT FROM AUTHOR]

In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables. [ABSTRACT FROM AUTHOR]

Capacitated two-stage time minimization transportation problem is an important optimization problem arising in industries. In literature, there is only one approach to solving this problem, but it has a deficiency of resulting in memory overflow in implementation on computer for large scale instances. In this paper, this problem is reduced to a series of finding the feasible flow in a network with lower and upper arc capacities, and two iterative algorithms are proposed as more robust solution method for this problem as compared to the existing approach. It is proved that both iterative algorithms find the optimal solution to this problem in a polynomial time. Due to fully utilizing the network structure characteristics inherent to this problem, both iterative algorithms have the advantage of easy implementation on computer and high computational efficiency, and successfully overcome the deficiency of existing approach. Computational experiments validate that as compared to the existing approach, both iterative algorithms are efficient and more robust method to solve this problem, where one iterative algorithm significantly outperforms the other in terms of computational time, especially for large scale instances. [ABSTRACT FROM AUTHOR]

This paper deals with the study of mixed variational-like inclusions involving Yosida approximation operator (MVLIYAO) and η-proximal mapping in Banach spaces. It is investigated that (MVLIYAO) is equivalent to fixed point problems in Banach spaces. Using this equivalence, a new iterative algorithm is proposed to find the solution of (MVLIYAO). A numerical example is provided to support our main result by using the MATLAB program. [ABSTRACT FROM AUTHOR]

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