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Background: The variational method, a quantum mechanical approach, estimates effective charge distributions and ground-state energy by minimizing the Hamiltonian's expectation value using trial wave functions with adjustable parameters. This method provides valuable insights into system behavior and is widely used in theoretical chemistry and physics. This paper aims to investigate ground-state energies and isoelectronic sequences using the variational method, introducing a novel approach for analyzing multi-electron systems. This technique allows for determining effective charge values and ground-state energies for 2–5 electrons sequence up to Z ≤ 20. Hydrogenic wave functions are used as a trial wave function to calculate effective charge in 1 s, 2 s, and 2p states. Two varying parameters were used to calculate an approximate wave function for the system. These values are then used in non-relativistic Hamiltonian with electron–electron interaction terms to calculate the ground-state energy of an atom. Result: The results align with the reported experimental values, showing a marginal 1% error. Conclusion: A Python algorithm is established based on the variational principle. It was found that, based on a few selected parameters in scripting the program, a very promising result was obtained. Furthermore, adding more variational parameters can minimize the difference between experimental and theoretical values, and this technique can be extended to elements with higher atomic numbers. [ABSTRACT FROM AUTHOR]

A novel and efficient modeling approach has been developed for simulating the responses of triaxial induction logging (TIL) in layered biaxial anisotropic (BA) formations. The core of this innovative technique lies in analytically calculating the primary fields within a homogeneous medium and approximating the scattered fields within layered formations. The former involves employing a two-level subtraction technique. Initially, the first-level subtraction entails altering the direction of the Fourier transform to mitigate the integral singularity of the spectral fields, particularly in high-angle and horizontal wells. Conversely, the second-level subtraction aims to further optimize integral convergence by creating an equivalent unbounded transverse isotropic (TI) formation and eliminating the corresponding spectral fields. With the two-level subtractions, the convergence of the spectral field has been enhanced by more than six orders of magnitude. Additionally, a strict recursive algorithm and approximation method are developed to compute the scattered fields in layered biaxial anisotropic media. The rigorous algorithm is based on a modified amplitude propagator matrix (MAPM) approach and serves as the benchmark for the approximation method. In contrast, the approximation method exploits the similarity between the spectral scattered field of the TI medium and the BA medium, establishing corresponding equivalent layered TI models for each magnetic component. Since the scattered field in TI models only involves a one-dimensional semi-infinite integral, the computational complexity is significantly reduced. Numerical simulation examples demonstrate that the new simulation method is at least two orders of magnitude faster than the current modeling approach while maintaining computational precision error within 0.5%. This significantly improved simulation efficiency provides a solid foundation for expediting the logging data processing. [ABSTRACT FROM AUTHOR]

Abstract Background The variational method, a quantum mechanical approach, estimates effective charge distributions and ground-state energy by minimizing the Hamiltonian's expectation value using trial wave functions with adjustable parameters. This method provides valuable insights into system behavior and is widely used in theoretical chemistry and physics. This paper aims to investigate ground-state energies and isoelectronic sequences using the variational method, introducing a novel approach for analyzing multi-electron systems. This technique allows for determining effective charge values and ground-state energies for 2–5 electrons sequence up to Z ≤ 20. Hydrogenic wave functions are used as a trial wave function to calculate effective charge in 1 s, 2 s, and 2p states. Two varying parameters were used to calculate an approximate wave function for the system. These values are then used in non-relativistic Hamiltonian with electron–electron interaction terms to calculate the ground-state energy of an atom. Result The results align with the reported experimental values, showing a marginal 1% error. Conclusion A Python algorithm is established based on the variational principle. It was found that, based on a few selected parameters in scripting the program, a very promising result was obtained. Furthermore, adding more variational parameters can minimize the difference between experimental and theoretical values, and this technique can be extended to elements with higher atomic numbers.

When pairwise comparisons are used to express preferences for alternatives or judgments on criteria's importance, several methods can be used to derive priorities in multi-criteria decision-making. In the case of inconsistency, different methods give different results.

The deneutrosophication process is a process transforming from neutrosophic values to crisp output values. It is the final step for the operations within a neutrosophic set and system. Neutrosophic set theories are a generalization of intuitionistic fuzzy and fuzzy set theories, focusing on truth, indeterminacy, and falsity memberships independently. However, it isn't easy to generate a geometrical model such as a Bézier surface by using neutrosophic set theory through the deneutrosophication process. Therefore, this paper used an average of triangular footprint method in the deneutrosophication process to construct the neutrosophic Bézier surface (NBS) models by using approximation methods. Before generating the model, the neutrosophic control net (NCN) must first be introduced using the deneutrosophication process. After that, the NCN will be blended with the Bernstein basis function to generate the NBS approximation model. Next, some numerical examples of NBS will be provided. Finally, the deneutrosophication of NBS approximation models will be visualized, and its algorithm will be shown. [ABSTRACT FROM AUTHOR]

We use the approximation method of Razborov to analyze the locality barrier which arose from the investigation of the hardness magnification approach to complexity lower bounds. Adapting a limitation of the approximation method obtained by Razborov, we show that in many cases it is not possible to combine the approximation method with typical (localizable) hardness magnification theorems to derive strong circuit lower bounds. In particular, one cannot use the approximation method to derive an extremely strong constant-depth circuit lower bound and then magnify it to an NC 1 lower bound for an explicit function. To prove this, we show that lower bounds obtained by the approximation method are in many cases localizable in the sense that they imply lower bounds for circuits which are allowed to use arbitrarily powerful oracles with small fan-in. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the delayed-advanced Kaldorian business cycle model and consider how time-delay and time-advance affect economic fluctuations. Given the asymptotic stability of the original Kaldor model, we first show that an approximated Kaldor model by a Taylor series expansion can accurately describe the dynamics of the delayed Kaldor model. We also confirm that the delay has a destabilizing effect. When time-delay is replaced with time-advance, we have an advanced Kaldor model. Taking the advanced capital stock formulation, we derive the stability conditions and find that the time-advance has a stabilizing effect. Lastly, we examine these opposite-signed effects in a modified delayed-advanced model. [ABSTRACT FROM AUTHOR]

In this research, we offer a new proximal point technique for approximating a common member of the set of all solutions of the convex minimization problems in the setting of CAT(1) spaces. We further show that, in some modest circumstances, the resulting process is convergent. Our results extend and enhance other related results in the literature. [ABSTRACT FROM AUTHOR]

In order to expand the range of techniques used to explore the efficiency of gamma ray shielding materials, the feasibility of cubic spline and Akima interpolation methods in predicting of the mass attenuation coefficients (MACs) values was examined A series of Li2O–Fe2O3–In2O3–Bi2O3–P2O5 glasses were proposed, and their mass attenuation coefficients were calculated using the two methods and compared with that estimated using the standard Phy-X software to check their accuracy. The tested energies were divided into a set of 42 discrete energy ranges, where at each range four coefficients were determined for each glass using MATLAB. The CS and Akima interpolation values were then graphed as a function of energy alongside the theoretical MAC values, demonstrating a strong agreement between the two methods and the Phy-X values. For example, the Phy-X value for the S1 glass at 0.2600 MeV is equal to 0.1208 cm2/g, while the CS and Akima interpolation values are 0.1208 and 0.1217 cm2/g, respectively. Because of the excellent predictive abilities of these methods, both the CS and Akima interpolation mathematical models are useful tools to anticipate MAC values at any energy within the range of the given data set. [ABSTRACT FROM AUTHOR]

In certain situations, probability computations can become complex, particularly when dealing with compound distributions. This computational complexity can be simplified by using approximation techniques such as the "saddle-point" approximation. In this paper, the authors have proposed the bivariate compound zero-truncated Poisson-Gamma distribution. This distribution is obtained by compounding the zero-truncated Poisson distribution with independent Gamma variates. To demonstrate the effectiveness of the proposed approach, the authors have provided an illustrative example to showcase the approximate computation of the bivariate compound zerotruncated Poisson-Gamma distribution. Furthermore, an extensive simulation study has been conducted to evaluate the performance of the proposed saddle-point approximation. The results indicate that the proposed saddle-point approximation is an excellent approximation of the distribution function of the bivariate compound zero-truncated Poisson-Gamma distribution which validates the effectiveness of the proposed approach. The high accuracy of the saddle-point approximation method is demonstrated by comparisons among saddle-point approximations, normal approximations, and exact calculations. [ABSTRACT FROM AUTHOR]

Anaerobic digestion (AD) is a promising technology for renewable energy production from organic waste. In order to maximize the produced biogas quantity and quality, this paper deals with the optimization of the AD process in a CSTR bioreactor of a full-scale biogas plant. For this purpose, a novel approach was adopted coupling, a highly complex BioModel for AD simulation, and a gradient-based optimization method. In order to improve AD performance, the dosages of various types of biological additives, the dosages of inorganic additives, and the temperature in the bioreactor were optimized in three different scenarios. The best biogas quality was obtained using multi-objective optimization, where the objective function involves the following two conflicting objectives: the maximization of biogas production and minimization of the needed heating energy. The obtained results show that, potentially, the content of C H 4 can be increased by 11%, while the contents of H 2 , H 2 S , and N H 3 can be reduced by 30%, 20%, and 81% when comparing the simulation results with the experimental data. The obtained results confirm the usefulness of the proposed approach, which can easily be adapted or upgraded for other bioreactor types. [ABSTRACT FROM AUTHOR]

We deal with the nonlinear parabolic problems given by the fractional N-Laplacian operator and time derivative of functions on the fractional Orlicz–Sobolev spaces. We get a result which shows existence of a weak solution for these fractional N-Laplacian heat flows. We obtain this result by using the approximation method. We first obtain a unique sequence of the approximating weak solutions from the difference fractional N-Laplacian problems, and then get some sequences of the variant approximating weak solutions. We next show the convergence of the sequences of the approximating weak solutions to the limits and the limit of some sequence of the approximating weak solutions is a weak solution of this problem. [ABSTRACT FROM AUTHOR]

The effect of a permanent magnetic field on the crystallization of calcium carbonate from carbonate aqueous solutions was studied. Based on the equations for the first- and second-order dissociation constants of carbonic acid, the stability constants of NaCO3- and NaHCO30 complexes, the mass balance and electroneutrality equations, the values of the system components and the ratio between the components of the carbonate subsystem were determined, and it was established that the main species in experimental conditions are СО32-, NaСО3- and HСО3- and the main components of the carbonate subsystem are СО32- (86.7%) and HСО3- (13.19%). Studies have shown that with a significant excess of CO32- over HCO3- ions in the solution at temperatures of 18-20˚C, calcite and vaterite are most likely formed. During the crystallization of calcium carbonate from an aqueous carbonate solution in a magnetic field of 125-250 mT, the size of the crystallites increases significantly compared to the absence of a magnetic field.

A novel and efficient modeling approach has been developed for simulating the responses of triaxial induction logging (TIL) in layered biaxial anisotropic (BA) formations. The core of this innovative technique lies in analytically calculating the primary fields within a homogeneous medium and approximating the scattered fields within layered formations. The former involves employing a two-level subtraction technique. Initially, the first-level subtraction entails altering the direction of the Fourier transform to mitigate the integral singularity of the spectral fields, particularly in high-angle and horizontal wells. Conversely, the second-level subtraction aims to further optimize integral convergence by creating an equivalent unbounded transverse isotropic (TI) formation and eliminating the corresponding spectral fields. With the two-level subtractions, the convergence of the spectral field has been enhanced by more than six orders of magnitude. Additionally, a strict recursive algorithm and approximation method are developed to compute the scattered fields in layered biaxial anisotropic media. The rigorous algorithm is based on a modified amplitude propagator matrix (MAPM) approach and serves as the benchmark for the approximation method. In contrast, the approximation method exploits the similarity between the spectral scattered field of the TI medium and the BA medium, establishing corresponding equivalent layered TI models for each magnetic component. Since the scattered field in TI models only involves a one-dimensional semi-infinite integral, the computational complexity is significantly reduced. Numerical simulation examples demonstrate that the new simulation method is at least two orders of magnitude faster than the current modeling approach while maintaining computational precision error within 0.5%. This significantly improved simulation efficiency provides a solid foundation for expediting the logging data processing.

In this paper, using the approximation method and the technique of weak noncompactness, we obtain some results regarding the existence of the solution for the sum of a multivalued operator and a single-valued operator in the weak topology. In addition, an application of integral inclusion is presented that explains our theory. This study extends some previously known single-valued Krasnosel'skii-type theorems to multivalued versions under weak topology. [ABSTRACT FROM AUTHOR]

We use an approximation method to prove the existence of nontrivial weak solutions for two nonlocal inhomogeneous elliptic problems in a bounded domain Ω of R n (n ≥ 1) under weak conditions on the diffusion coefficients M, N : (0 , + ∞) → R and some hypotheses on the n × n matrix function a and the functions f, g : Ω × R → R that we will give below. Moreover, the existence of a positive solution is obtained for each problem by imposing some additional conditions on Ω , a, f, g and using a bootstrap argument. [ABSTRACT FROM AUTHOR]

In this paper, we devote to studying the existence of normalized solutions for the following Schrödinger equation with Sobolev critical nonlinearities. $ \begin{align*} &\left\{\begin{array}{ll} -\Delta u = \lambda u+\mu\lvert u \rvert^{q-2}u+\lvert u \rvert^{p-2}u&{\mbox{in}}\ \mathbb{R}^N,\\ \int_{\mathbb{R}^N}\lvert u\rvert^2dx = a^2, \end{array}\right. \end{align*} $ where $ N\geqslant 3 $, $ 2 < q < 2+\frac{4}{N} $, $ p = 2^* = \frac{2N}{N-2} $, $ a, \mu > 0 $ and $ \lambda\in\mathbb{R} $ is a Lagrange multiplier. Since the existence result for $ 2+\frac{4}{N} < p < 2^* $ has been proved, using an approximation method, that is let $ p\rightarrow 2^* $, we obtain that there exists a mountain-pass type solution for $ p = 2^* $.

To run a successful cattle business, you will have to select a cattle market where the cattle trader will purchase the cattle to be delivered whenever the customers need them, however, there are so many problems in the distribution of cattle to various markets. Hence, the objective of this paper was to evaluate the transportation problem models on cattle business in Niger state, Nigeria at a minimum cost using Russell's Approximation Method by selecting seven cattle markets (Bangi, Beji, Ibeto, Kawon-Kontagora, Kuta, Mariga and Tungar-Malam) in Niger state for distribution to some selected locations in Akure, Ibadan, Ilorin, Ijebu-Ode, Lagos and Oshogbo in the South Western part of Nigeria at a minimum cost. The Russell's Approximation method is used to find the Initial Basic Feasible Solution (N36, 703, 723.98). The optimality method is tested via Stepping Stone Method and found it to be not optimal. Furthermore, the optimal solution is found using MS Excel solver. The minimum cost of transportation is found to be N36, 159,785.13. [ABSTRACT FROM AUTHOR]

Anaerobic digestion (AD) is a promising technology for renewable energy production from organic waste. In order to maximize the produced biogas quantity and quality, this paper deals with the optimization of the AD process in a CSTR bioreactor of a full-scale biogas plant. For this purpose, a novel approach was adopted coupling, a highly complex BioModel for AD simulation, and a gradient-based optimization method. In order to improve AD performance, the dosages of various types of biological additives, the dosages of inorganic additives, and the temperature in the bioreactor were optimized in three different scenarios. The best biogas quality was obtained using multi-objective optimization, where the objective function involves the following two conflicting objectives: the maximization of biogas production and minimization of the needed heating energy. The obtained results show that, potentially, the content of CH4 can be increased by 11%, while the contents of H2, H2S, and NH3 can be reduced by 30%, 20%, and 81% when comparing the simulation results with the experimental data. The obtained results confirm the usefulness of the proposed approach, which can easily be adapted or upgraded for other bioreactor types.

To run a successful cattle business, you will have to select a cattle market where the cattle trader will purchase the cattle to be delivered whenever the customers need them, however, there are so many problems in the distribution of cattle to various markets. Hence, the objective of this paper was to evaluate the transportation problem models on cattle business in Niger state, Nigeria at a minimum cost using Russell’s Approximation Method by selecting seven cattle markets (Bangi, Beji, Ibeto, Kawon-Kontagora, Kuta, Mariga and Tungar-Malam) in Niger state for distribution to some selected locations in Akure, Ibadan, Ilorin, Ijebu-Ode, Lagos and Oshogbo in the South Western part of Nigeria at a minimum cost. The Russell’s Approximation method is used to find the Initial Basic Feasible Solution (N36, 703, 723.98). The optimality method is tested via Stepping Stone Method and found it to be not optimal. Furthermore, the optimal solution is found using MS Excel solver. The minimum cost of transportation is found to be N36, 159,785.13.

In this paper, we devote to studying the existence of normalized solutions for the following Schrödinger equation with Sobolev critical nonlinearities. { − Δ u = λ u + μ | u | q − 2 u + | u | p − 2 u in R N , ∫ R N | u | 2 d x = a 2 , where N ⩾ 3 , 2 < q < 2 + 4 N , p = 2 ∗ = 2 N N − 2 , a , μ > 0 and λ ∈ R is a Lagrange multiplier. Since the existence result for 2 + 4 N < p < 2 ∗ has been proved, using an approximation method, that is let p → 2 ∗ , we obtain that there exists a mountain-pass type solution for p = 2 ∗ . [ABSTRACT FROM AUTHOR]

Improving the performance and speed of encryption algorithms is an important issue in cryptography. One of these improvements is the use of the RNS system. In the research, the RNS system and how to retrieve numbers from the RNS system to WNS weight number system or (decimal number) where discussed in several ways, and after performing multiplication operations, giving illustrative examples and making comparisons between methods. [ABSTRACT FROM AUTHOR]

We prove an existence result for strong solutions $u\in W^{2,q}\left(\Omega\right) $ of singular semilinear elliptic problems of the form $-\Delta u=g\left( \cdot,u\right) $ in $\Omega,$ $u=\tau$ on $\partial\Omega,$ where $1

Summary: This paper presents the digital realization of the fractional‐order PI (FOPI) controller fractional integrator element using the improved constant phase approximation method. A new pole‐zero rationalization approach is proposed within the bandwidth of the Bode phase plot. The voltage source inverter fed induction motor fractional‐order model has been identified. A novel mathematical FOPI controller design procedure for the identified FO plant model has been proposed. The designed FOPI controller fractional integrator element is implemented using the constant phase approximation method. A detailed comparative performance study of the proposed approximation method with the existing Charef, Oustaloup, and refined Oustaloup methods has been carried out using the Bode, Nyquist, and Nichols plots. The proposed FOPI controller is placed in the speed feedback loop of the rotor field‐oriented control algorithm of IM. To confirm the proposed FOPI controller approximation method's robustness, a hardware study is carried out on the laboratory hardware‐in‐loop (HIL) platform. In addition, variation in the number of pole‐zero pair's effect on the speed tracking performance, robustness against parameter and load variations are also analyzed. [ABSTRACT FROM AUTHOR]

The article considers the possibility of a practical assessment of the filtration situation in the rock bases of high concrete dams under construction and in operation. Amethod that allows obtaining online a general picture of the filtration state at the base of a concrete dam based on an array of readings from a piezometric observation network is proposed. The wide possibilities of analysing the results obtained for assessing the stress-strain state (SSS) of the dam-rock massif system containing a dam with a reservoir are shown. [ABSTRACT FROM AUTHOR]

The graph coloring problem, an NP-hard combinatorial optimization problem, is required in some engineering applications. This research focuses on the requirement of designing a new particle swarm optimization model to minimize the search space and generations. This stochastic method is developed using divide and conquer with improved strategies to offset the problems in the well-known existing ways. The divide and conquer strategy splits the vertex set of graph G into two subsets, and then, the subsets are solved to reduce the search space. The advanced neighborhood search operator is applied to a particle for a fixed number of iterations to improve its position to obtain the best neighborhood. The modified turbulent strategy is designed to overcome the problem of getting a divergent solution. The iterative fitness assessment and walking one strategy are applied to identify the maximum conflicting vertices and assign a set of valid colors. The behavioral analysis of this stochastic search model reveals that premature convergence is primarily caused by the decrease in the velocity of particles in the search space that leads to a total implosion and, ultimately, fitness stagnation of the swarm. The lazy particles are driven out for exploring new search spaces to avoid premature convergence. The experimental results of this method have revealed that a better near-optimal solution is obtained for some of the critical benchmark graphs compared with the state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following Schrödinger–Poisson system with perturbation:

A deterministic annealing (DA) method is presented for solving the multi-robot routing problem with min–max objective. This is an NP-hard problem belonging to the multi-robot task allocation set of problems where robots are assigned to a group of sequentially ordered tasks such that the cost of the slowest robot is minimized. The problem is first formulated in a matrix form where the optimal solution of the problem is the minimum-cost permutation matrix without any loops. The solution matrix is then found using the DA method is based on mean field theory applied to a Potts spin model which has been proven to yield near-optimal results for NP-hard problems. Our method is bench-marked against simulated annealing and a heuristic search method. The results show that the proposed method is promising for small-medium sized problems in terms of computation time and solution quality compared to the other two methods. [ABSTRACT FROM AUTHOR]

The transportation problem is an optimization problem related to determining the transportation plan that will ensure the transportation of products from supply points to demand points with minimum total cost. Although this problem can be modeled as a linear programming model because of its special structure, it is usually solved in two phases: finding the initial basic solution and finding the optimal solution. Thus, finding a good initial solution is important, especially in large problems since it will reduce the number of steps required in the second phase. To date, many approaches have been developed to find the initial basic solution. In this study, a new method called avoid maximum cost method is proposed for determining the initial basic solution of the transportation problem. The advantage of this algorithm is that it is easy to understand and implement. The avoid maximum cost method is applied to test problems and compared with six well-known initial solution methods. The results show that the proposed method produces a consistent and very good initial basic feasible solution. In addition, because of its simplicity, this method can be used as an alternative method for an initial basic feasible solution besides well-known methods in teaching. [ABSTRACT FROM AUTHOR]

The goal of this research is to develop a high-performance fractionalized proportional--integral--derivative (FPID) controller based on Henry Gas Solubility Optimization (HGSO) for controlling the speed of a direct current (DC) motor. The suggested HGSOA-based Fractionalized PID technique with Matsuda approximation method was used to obtain the optimal FPID controller by minimising the integral of time multiplied absolute error (ITAE) as the objective function. Index of performance and disturbance rejection analyses, as well as transient and frequency responses, were all employed to validate the suggested approach's effectiveness. The proposed HGSO-FPID controller with Matsuda approximation was then compared not only to the original HGSO algorithm-tuned PID controller, but also to other controllers tuned by cutting-edge meta-heuristic algorithms such as Atom Search Optimization algorithm (ASO), Grey Wolf Optimization algorithm (GWO), Particle Swarm Optimisation (PSO), Invasive Weed Optimisation (IWO), and stochastic fractal search (SFS). The results showed that the proposed HGSOA-FPID controller has better performance with lower settling time, Ts which 0.1003 s, with lower rise time, Tr which is 0.0579 s, negligible overshoot, D which is 0.0052% and strong output disturbance rejection when compared to the performance of the other controllers. [ABSTRACT FROM AUTHOR]

Under differential privacy, to solve the optimal publishing problem with multiple consistency constraints, an approximation method of multiple consistency constraints was proposed by the theoretical analysis of the principle of optimal consistency release.The main idea was to divide the consistency constraint problem into several consistency constraint sub-problems and then achieve the original problem's optimal consistency release by solving each consistency constraint sub-problem repeatedly and independently.The advantage was that after the consistency constraint problem divided, the sub-problems were often easier to solve, or the technology to achieve optimal and consistent release of sub-problems is quite mature.Therefore more complex differential privacy optimal release problem could be solved.After analysis, the approximation method's convergence was fully demonstrated, ensuring that any partition of consistency constrained sub-problems can always achieve the optimal consistency release of the original problem.Furthermore, taking the sales histogram publishing as an example, based on the approximation method of multiple consistency constraints, a parallel algorithm was designed with optimal consistency release under differential privacy.The experimental results show that the algorithm's efficiency is 400 times higher than that of the general solution, and the algorithm can process millions of large-scale data.

Abstract This paper deals with nonlocal fractional p-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractional p-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next show that there exists a limit sequence of a sequence of weak solutions for finite-dimensional problems, and this limit sequence is a sequence of the solutions of our problems. We get this result by the estimate of the energy functional and the compactness property of continuous embedding inclusions between some special spaces.

This article introduces a variation of the p-center problem (PCP), called distributionally robust conditional vertex p-center problem. This problem differs from the conventional PCP in the sense that (i) some key centers in a given set of candidates are designated, and (ii) a distributionally robust optimization (DRO) method is developed. We present a distributionally robust chance-constrained model to formulate this problem. In terms of tractability, we propose a safe tractable approximation method to reformulate the original DRO model as mixed-integer second-order cone programs under the bounded and Gaussian perturbation ambiguous sets. We further use the branch-and-cut algorithm to solve the tractable counterpart models. The application of the DRO model is illustrated for locating emergency rescue stations in the high-speed railway network by two different sized case studies. Finally, we demonstrate the advantages of the DRO model in comparison with the traditional robust optimisation model and the nominal stochastic programming model. [ABSTRACT FROM AUTHOR]

In this paper, a new two-steps design strategy is introduced for the optimal rational approximation of the fractional-order Butterworth filter. At first, the weighting factors of the summation between the ${n}^{\text {th}}$ -order and the $(n + 1)^{\text {th}}$ -order Butterworth filters are optimally determined. Subsequently, this model is employed as an initial point for another optimization routine, which minimizes the magnitude-frequency error relative to the $(n+\alpha)^{\text {th}}$ -order, where $\alpha \in (0, 1)$ , Butterworth filter. The proposed approximant demonstrates improved performance about the magnitude mean squared error compared to the state-of-the-art design for six decades of bandwidth, but the introduced approach does not require a fractional-order transfer function model and the approximant of the $s^\alpha $ operator. The proposed strategy also avoids the use of the cascading technique to yield higher-order fractional-order Butterworth filter models. The performance of the proposed $1.5^{\text {th}}$ -order Butterworth filter in follow-the-leader feedback topology is verified through SPICE simulations and its hardware implementation based on Analog Devices AD844AN-type current feedback operational amplifier.

We prove an existence result for strong solutions u∈W2,q(Ω) of singular semilinear elliptic problems of the form -Δu=g(⋅,u) in Ω, u=τ on ∂Ω, where 1

Neutrosophic concept is known undirected graph theory to involve with complex logistic networks, not clearly given and unpredictable real life situations, where fuzzy logic malfunctions to model. The transportation objective is to ship all logistic nodes in the network. The logistic network mostly experiences in stable condition, but for some edges found to be volatile. The weight of these erratic edges may vary at random (bridgelifting/bascule, ad hoc accident on road, traffic condition) In this article, we propose an approximation algorithm for solving minimum spanning tree (MST) of an undirected neutrosophic graphs (UNG), in which the edge weights represent neutrosophic values. The approximation upon the balanced score calculation is introduced for all known configurations in alternative MST. As the result, we further compute decisive threshold value for the weak weights amid minimum cost pre-computation. If the threshold triggers then the proper MST can direct the decision and avoid post-computation. The proposed algorithm is also related to other existing approaches and a numerical analysis is presented. [ABSTRACT FROM AUTHOR]

Oscillations may cause both economic and technical problems such as a reduction in overall system reliability. Therefore, detecting and preventing oscillatory behavior that affects power systems is important. This paper proposes an oscillation recognition method that includes monitoring and extracting features in a recursive and sequential manner in a time-series measurement in power systems. We propose a geometric feature extraction process for recognizing oscillations by constructing an average system and Poincaré map for time-series measurement. The proposed process provides the features of a system's damping and frequency of oscillation, and the developed monitoring systems are based on nonlinear dynamics. The circulating oscillatory behavior is represented on a finite-integer-delay embedded time-series plane, extracted by a Poincaré map construction, and examined directly along the trajectory to monitor the features of the oscillation according to damping and frequency. Oscillatory behavior recognition is tested on IEEE's second benchmark system for subsynchronous resonance to verify the fast extraction of oscillation components. In addition, a case study for Korean power systems with a high penetration of renewable energy and application on actual measurement data is carried out to demonstrate the practical application of the process.

In this paper, we introduce a new accelerated iterative method for finding a common fixed point of a countable family of nonexpansive mappings in the Hilbert spaces framework. Using our main result, we obtain a new accelerated image restoration iterative method for solving a minimization problem in the form of the sum of two proper lower semi-continuous and convex functions. As applications, we apply our algorithm to solving image restoration problems. [ABSTRACT FROM AUTHOR]

Couette–Poiseuille (C–P) flow, which is driven by drag from a moving wall and a pressure gradient, can exist in different states depending on the relative strengths of the two above-mentioned factors. Of particular interest is the onset of flow reversal, which is characterized kinematically by a zero shear rate on the stationary wall. This study presents two different methods for obtaining the critical conditions for the onset of flow reversal in C–P flows. In the first method, exact values of the critical flow rate and pressure gradient are computed by solving a pair of algebraic equations derived from the Weissenberg–Rabinowitsch relation. Using this method, the difficulty in solving the nonlinear differential equation is avoided. In the second method, estimates of the critical conditions are obtained analytically by locally approximating the given fluid as a power-law fluid. To evaluate the prediction accuracy, the methods are applied to the C–P flows of Carreau–Yasuda and Bingham–Carreau–Yasuda fluids. It is demonstrated that the relative errors remained reasonably low in most system parameter ranges, except in cases where the flow curve in the log–log scale is highly nonlinear. [ABSTRACT FROM AUTHOR]

Mining frequent itemsets in transaction databases is an important task in many applications. It becomes more challenging when dealing with a large transaction database because traditional algorithms are not scalable due to the limited main memory. In this paper, we propose a new approach for the approximately mining of frequent itemsets in a big transaction database. Our approach is suitable for mining big transaction databases since it uses the frequent itemsets from a subset of the entire database to approximate the result of the whole data, and can be implemented in a distributed environment. Our algorithm is able to efficiently produce high-accurate results, however it misses some true frequent itemsets. To address this problem and reduce the number of false negative frequent itemsets we introduce an additional parameter to the algorithm to discover most of the frequent itemsets contained in the entire data set. In this article, we show an empirical evaluation of the results of the proposed approach. [ABSTRACT FROM AUTHOR]

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Since the development of recurrence plots (RP) and recurrence quantification analysis (RQA), there has been a growing interest in many areas in studying physical systems using recursion techniques. In particular, as part of the RQAs, we observed the development of the concept of recurrence microstates, defined as small blocks obtained from a recurrence graph. It can be shown that some other RQAs can be calculated as a function of recurrence microstates, and the probabilities of occurrences of these microstates can define an information entropy, the so-called entropy of recurrence microstates. It was also observed that recurrence microstates and recurrence entropy can distinguish between correlated and uncorrelated stochastic and deterministic states, due to their symmetry properties. In this paper we propose analytical expressions for calculating the entropy of recurrence microstates, avoiding the need to sample a large set of recurrence microstates. The results can be particularly important in quantifying small amounts of data, where significant sampling of microstates may not be possible. In this paper we propose analytical expressions to compute the entropy of recurrence microstates avoiding the need to sample a large set of recurrence microstates. We show that our results are accurate for cases where the probability distribution function is known. For other situations, the results can be calculated approximately. Another important fact is that the approximate results can be generalized to any size of microstate, making them a powerful tool for calculating the entropy of recurrence. Our approximate methods allow us to know what these properties are and how to exploit this quantifier in the best possible way, with minimal memory usage. Finally, we show that our analytical results are in remarkable agreement with numerical simulations. • We can approximate the recurrence microstates entropy with only a few relevant microstates. • The approximation scheme is capable of extract information from short time series. • We developed a framework for obtaining analytically the probabilities of any recurrence microstate. [ABSTRACT FROM AUTHOR]

Analyzing throughput is very important for the design, optimization, and management of production lines. In this paper, we present an efficient throughput analysis approach for production lines with merging, splitting, and recirculating topologies. In particular, we define a decomposition regulation based on queue modules for the decomposition of the various topologies, and we improve an iterative approximation method for calculating and iterating the queue module state probabilities until the throughput of the production line is obtained. To decrease the computation time and automate the calculation process of the queue module state probabilities, we build a queue module database that includes the solution equations of common queue module state probabilities. The numerical examples show that our approach calculates the throughput of production lines with merging, splitting, and recirculating topologies with high accuracy (≥90%) and efficiency (completed in ten min). Our contribution is an efficient throughput evaluation methodology that can be used to rapidly estimate the performance and the cost of production lines with various topologies in the conceptual design phase of production lines in the industry.

This paper deals with nonlocal fractional p-Laplacian problems with difference. We get a theorem which shows existence of a sequence of weak solutions for a family of nonlocal fractional p-Laplacian problems with difference. We first show that there exists a sequence of weak solutions for these problems on the finite-dimensional subspace. We next show that there exists a limit sequence of a sequence of weak solutions for finite-dimensional problems, and this limit sequence is a sequence of the solutions of our problems. We get this result by the estimate of the energy functional and the compactness property of continuous embedding inclusions between some special spaces. [ABSTRACT FROM AUTHOR]

We consider a class of mathematical programs with complementarity constraints (MPCC) where the objective function involves a non-Lipschitz sparsity-inducing term. Due to the existence of the non-Lipschitz term, existing constraint qualifications for locally Lipschitz MPCC cannot ensure that necessary optimality conditions hold at a local minimizer. In this paper, we present necessary optimality conditions and MPCC-tailored qualifications for the non-Lipschitz MPCC. The proposed qualifications are related to the constraints and the non-Lipschitz term, which ensure that local minimizers satisfy these necessary optimality conditions. Moreover, we present an approximation method for solving the non-Lipschitz MPCC and establish its convergence. Finally, we use numerical examples of sparse solutions of linear complementarity problems and the second-best road pricing problem in transportation science to illustrate the effectiveness of our approximation method for solving the non-Lipschitz MPCC. [ABSTRACT FROM AUTHOR]