Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Multifractal estimation of NMR T_(2) cut-off value in low-permeability rocks considering spectrum kurtosis: SMOTE-based oversampling integrated with machine learning

The transverse relaxation time (T_(2)) cut-off value plays a crucial role in nuclear magnetic resonance for identifying movable and immovable boundaries, evaluating permeability, and determining fluid saturation in petrophysical characterization of petroleum reservoirs. This study focuses on the systematic analysis of T_(2) spectra and T_(2) cut-off values in low-permeability reservoir rocks. Analysis of 36 low-permeability cores revealed a wide distribution of T_(2) cut-off values, ranging from 7 to 50 ms. Additionally, the T_(2) spectra exhibited multimodal characteristics, predominantly displaying unimodal and bimodal morphologies, with a few trimodal morphologies, which are inherently influenced by different pore types. Fractal characteristics of pore structure in fully water-saturated cores were captured through the T_(2) spectra, which were calculated using generalized fractal and multifractal theories. To augment the limited dataset of 36 cores, the synthetic minority oversampling technique was employed. Models for evaluating the T_(2) cut-off value were separately developed based on the classified T_(2) spectra, considering the number of peaks, and utilizing generalized fractal dimensions at the weight <0 and the singular intensity range. The underlying mechanism is that the singular intensity and generalized fractal dimensions at the weight <0 can detect the T_(2) spectral shift. However, the T_(2) spectral shift has negligible effects on multifractal spectrum function difference and generalized fractal dimensions at the weight >0. The primary objective of this work is to gain insights into the relationship between the kurtosis of the T_(2) spectrum and pore types, as well as to predict the T_(2) cut-off value of low-permeability rocks using machine learning and data augmentation techniques.

THE OPTIMAL STRATEGY FOR INSURANCE COMPANY UNDER THE INFLUENCE OF TERMINAL VALUE

This paper considers a model of an insurance company which is allowed to invest a risky asset and to purchase proportional reinsurance. The objective is to find the policy which maximizes the expected total discounted dividend pay-out until the time of bankruptcy and the terminal value of the company under liquidity constraint. We find the solution of this problem via solving the problem with zero terminal value. We also analyze the influence of terminal value on the optimal policy.

Value Composition and Optimal Utilization of Religious Cultural Landscape Resources

Multiple value structure of religious cultural landscape resources influences and determines development and regulation of cultural landscape resources. In the multiple value structure consisting of cultural inheritance, spiritual needs, industrial expansion, leisure and entertainment, development and utilization of religious cultural landscape resources should adhere to scientific classification, relatively independent policy orientation, make and implement specific countermeasures, so as to meet various requirements of the public and other relevant subjects using more refined and improved policy measures, and to realize the optimal utilization and comprehensive value of religious cultural landscapes.

THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION

The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.

The Optimal Inventory Policy for Reusable Items with Random Planning Horizon Considering Present Value

We discuss five areas of inventory model, including reusable raw material, EPQ model, optimization, random planning horizon and present value. In the traditional EPQ model, the stock-holding cost of raw material was not counted as a part of relevant cost. We explored the possibility of reducing a company’s impact on the environment and increasing their competitiveness by recycling their repair and waste disposal. The products are manufactured with reusable raw material. Our analysis takes into account the time value, and the present value method is applied to determine the optimal inventory policies for reusable items with random planning horizon. Results show how the heuristic approach can achieve global optimum. Numerical examples are given to validate the proposed system.

Optimal Allocation of Public Transport Hub Based on Load Loss Value and the Economy of Distribution Network

The rapid development of electric buses has brought a surge in the number of bus hubs and their charging and discharging capacities.Therefore,the location and construction scale of bus hubs will greatly affect the operation costs and benefits of an urban distribution network in the future.Through the scientific and reasonable planning of public transport hubs on the premise of meeting the needs of basic public transport services,it can reduce the negative impact of electric bus charging loads upon the power grids.Furthermore,it can use its flexible operation characteristics to provide flexible support for the distribution network.In this paper,taking the impact of public transport hub on the reliability of distribution network as the starting point,a three-level programming optimization model based on the value and economy of distribution network load loss is proposed.Through the upper model,several planning schemes can be generated,which provides boundary conditions for the expansion of middle-level optimization.The normal operation dispatching scheme of public transport hub obtained from the middle-level optimization results provides boundary conditions for the development of lower level optimization.Through the lower level optimization,the expected load loss of the whole distribution system including bus hub under the planning scheme given by the upper level can be obtained.The effectiveness of the model is verified by an IEEE-33 bus example.

Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

Optimality for Henig Proper Efficiency in Vector Optimization Involving Dini Set-Valued Directional Derivatives

This note studies the optimality conditions of vector optimization problems involving generalized convexity in locally convex spaces. Based upon the concept of Dini set-valued directional derivatives, the necessary and sufficient optimality conditions are established for Henig proper and strong minimal solutions respectively in generalized preinvex vector optimization problems.

Numerical solutions of second order initial value problems of Bratu-type via optimal homotopy asymptotic method

We present the optimal homotopy asymptotic method (OHAM) to find the numerical solution of the second order initial value problems of Bratu-type. We solve some examples to illustrate the validity and efficiency of the method.

DERNNet:Dual Encoding Recurrent Neural Network Based Secure Optimal Routing in WSN

A Wireless Sensor Network(WSN)is constructed with numerous sensors over geographical regions.The basic challenge experienced while designing WSN is in increasing the network lifetime and use of low energy.As sensor nodes are resource constrained in nature,novel techniques are essential to improve lifetime of nodes in WSN.Nodes energy is considered as an important resource for sensor node which are battery powered based.In WSN,energy is consumed mainly while data is being transferred among nodes in the network.Several research works are carried out focusing on preserving energy of nodes in the network and made network to live longer.Moreover,this network is threatened by attacks like vampire attack where the network is loaded by fake traffic.Here,Dual Encoding Recurrent Neural network(DERNNet)is proposed for classifying the vampire nodes s node in the network.Moreover,the Grey Wolf Optimization(GWO)algorithm helps for transferring the data by determining best solutions to optimally select the aggregation points;thereby maximizing battery/lifetime of the network nodes.The proposed method is evaluated with three standard approaches namely Knowledge and Intrusion Detection based Secure Atom Search Routing(KIDSASR),Risk-aware Reputation-based Trust(RaRTrust)model and Activation Function-based Trusted Neighbor Selection(AF-TNS)in terms of various parameters.These existing methods may lead to wastage of energy due to vampire attack,which further reduce the lifetime and increase average energy consumed in the network.Hence,the proposed DERNNet method achieves 31.4%of routing overhead,23%of end-to-end delay,78.6%of energy efficiency,94.8%of throughput,28.2%of average latency,92.4%of packet delivery ratio,85.2%of network lifetime,and 94.3%of classification accuracy.

Novel Discrete Particle Swarm Optimization Based on Huge Value Penalty for Solving Engineering Problem

For the purpose of solving the engineering constrained discrete optimization problem, a novel discrete particle swarm optimization（DPSO） is proposed. The proposed novel DPSO is based on the idea of normal particle swarm optimization（PSO）, but deals with the variables as discrete type, the discrete optimum solution is found through updating the location of discrete variable. To avoid long calculation time and improve the efficiency of algorithm, scheme of constraint level and huge value penalty are proposed to deal with the constraints, the stratagem of reproducing the new particles and best keeping model of particle are employed to increase the diversity of particles. The validity of the proposed DPSO is examined by benchmark numerical examples, the results show that the novel DPSO has great advantages over current algorithm. The optimum designs of the 100-1 500 mm bellows under 0.25 MPa are fulfilled by DPSO. Comparing the optimization results with the bellows in-service, optimization results by discrete penalty particle swarm optimization（DPPSO） and theory solution, the comparison result shows that the global discrete optima of bellows are obtained by proposed DPSO, and confirms that the proposed novel DPSO and schemes can be used to solve the engineering constrained discrete problem successfully.

Dynamic monitoring of menopause hormone therapy and defining the cut-off value of endometrial thickness during uterine bleeding

The aim of this study was to evaluate the effects of low-dose tibolone therapy on ovarian area, uterine volume and endometrial thickness, and define the cut-off value of endometrial thickness for curettage during uterine bleeding. We followed 619 postmenopausal women, aged 40-60 years, for two years. There were 301 subjects in the low-dose tibolone treatment group and 318 subjects in the control group. The ovarian area, uterine volume and endometrial thickness in all participants were measured by transvaginal ultrasound prior to, one and two years post enrollment, respectively. Endometrial specimens were collected from all subjects with abnormal uterine bleeding during the follow-up period. We found that the uterine volume in the treatment group was greater than that in the control group, and the difference was significant （P〈0.05）, but there were no significant differences in ovarian area and endometrial thickness between the two groups （P〉0.05）. When the cut-off value for endometrial thickness was 7.35 ram, the sensitivity and specificity were 100% and 79.07%, respectively, and 85.71% and 93.02% when 7.55 mm was set as the cut-offduring tibolone therapy. The results indicate that low-dose tibolone therapy may postpone uterine atrophy and the cut-off value of endometrial thickness may be appropriately adjusted for curettage.

P2P transaction method for distributed energy prosumers based on reputation value

Adding a reputation incentive system to peer-to-peer(P2P)energy transactions can encourage prosumers to regulate their trading behavior,which is important for ensuring the efficiency and reliability of P2P transactions.This study proposed a P2P transaction mechanism and game optimization model for prosumers involved in distributed energy sources considering reputation-value incentives.First,the deviation of P2P transactions and the non-consumption rate of distributed renewable energy in P2P transactions were established as indicators to quantify the influencing factors of the reputation value,and a reputation incentive model of P2P transactions for prosumers was constructed.Then,the penalty coefficient was applied to the cost function of the prosumers,and a non-cooperative game model of P2P transactions based on the complete information of multi-prosumers was established.Furthermore,the Nash equilibrium problem was transformed into a nonlinear optimization problem by constructing the modified optimal reaction function,and the Nash equilibrium solution of the game was obtained via a relaxation algorithm.Finally,the modified IEEE 33-node test system based on electricity market P2P and an IEEE 123-node test system were used to analyze and verify the cost and P2P participation of prosumers considering the reputation value.The results show that the addition of the reputation incentive system can encourage prosumers to standardize their interactive transaction behavior and actively participate in P2P transactions.It can also improve the operation efficiency of the power grid and promote the perfection of the P2P transaction mechanism.

Optimal Portfolio Selection with Delay under the Framework of Uncertainty Theory

This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.

Cut-off Values of Diagnostic Indices to Detect Iron Deficiency in Chinese Breast-fed Infants

Iron deficiency anemia is one of the most prevalent nutritional deficiency worldwide. The commonly used cut-off values for identifying iron deficiency are extrapolated from older children and may not be suitable for infants. Therefore, our study aimed to establish appropriate cut-off values for the evaluation of iron status in Chinese infants. Pregnant women who delivered at 〉37 gestational weeks with normal iron status were recruited. Later, infants with normal birth weight and who were breastfed in the first 4 months were selected. Blood samples were collected to assess hemoglobin, serum ferritin, soluble transferrin receptor, mean corpuscular volume and free erythrocyte protoporphyrin. Cut-offs of all iron indices were determined as the limit of 95% confidence interval.

CONE-DIRECTED CONTINGENT DERIVATIVES AND GENERALIZED PREINVEX SET-VALUED OPTIMIZATION

By using cone-directed contingent derivatives, the unified necessary and sufficient optimality conditions are given for weakly and strongly minimal elements respectively in generalized preinvex set-valued optimization.

Series-parallel Hybrid Vehicle Control Strategy Design and Optimization Using Real-valued Genetic Algorithm

Despite the series-parallel hybrid electric vehicle inherits the performance advantages from both series and parallel hybrid electric vehicle, few researches about the series-parallel hybrid electric vehicle have been revealed because of its complex co nstruction and control strategy. In this paper, a series-parallel hybrid electric bus as well as its control strategy is revealed, and a control parameter optimization approach using the real-valued genetic algorithm is proposed. The optimization objective is to minimize the fuel consumption while sustain the battery state of charge, a tangent penalty function of state of charge（SOC） is embodied in the objective function to recast this multi-objective nonlinear optimization problem as a single linear optimization problem. For this strategy, the vehicle operating mode is switched based on the vehicle speed, and an ＂optimal line＂ typed strategy is designed for the parallel control. The optimization parameters include the speed threshold for mode switching, the highest state of charge allowed, the lowest state of charge allowed and the scale factor of the engine optimal torque to the engine maximum torque at a rotational speed. They are optimized through numerical experiments based on real-value genes, arithmetic crossover and mutation operators. The hybrid bus has been evaluated at the Chinese Transit Bus City Driving Cycle via road test, in which a control area network-based monitor system was used to trace the driving schedule. The test result shows that this approach is feasible for the control parameter optimization. This approach can be applied to not only the novel construction presented in this paper, but also other types of hybrid electric vehicles.