Neutrality Criteria for Stability Analysis of Dynamical Systems through Lorentz and Rossler Model Problems

Two methods of stability analysis of systems described by dynamical equations are being considered. They are based on an analysis of eigenvalues spectrum for the evolutionary matrix or the spectral equation and they allow determining the conditions of stability and instability, as well as the possibility of chaotic behavior of systems in case of a stability loss. The methods are illustrated for nonlinear Lorenz and Rossler model problems.

Problem-solving model guided by stimulus-organism-response theory:State of mind and coping styles of depressed mothers after cesarean delivery

BACKGROUND The use of a problem-solving model guided by stimulus-organism-response(SOR)theory for women with postpartum depression after cesarean delivery may inform nursing interventions for women with postpartum depression.AIM To explore the state of mind and coping style of women with depression after cesarean delivery guided by SOR theory.METHODS Eighty postpartum depressed women with cesarean delivery admitted to the hospital between January 2022 and October 2023 were selected and divided into two groups of 40 cases each,according to the random number table method.In the control group,the observation group adopted the problem-solving nursing model under SOR theory.The two groups were consecutively intervened for 12 weeks,and the state of mind,coping styles,and degree of post-partum depression were analyzed at the end of the intervention.RESULTS The Edinburgh Postnatal Depression Scale and Hamilton Depression Scale-24-item scores of the observation group were lower than in the control group after care,and the level of improvement in the state of mind was higher than that of the control group(P<0.05).The level of coping with illness in the observation group after care(26.48±3.35)was higher than that in the control group(21.73±3.20),and the level of avoidance(12.04±2.68)and submission(8.14±1.15)was lower than that in the control group(15.75±2.69 and 9.95±1.20),with significant differences(P<0.05).CONCLUSION Adopting the problem-solving nursing model using SOR theory for postpartum depressed mothers after cesarean delivery reduced maternal depression,improved their state of mind,and coping level with illness.

An Efficient Three-Dimensional Coupled Normal Mode Model and Its Application to Internal Solitary Wave Problems

We present an efficient three-dimensional coupled-mode model based on the Fourier synthesis technique. In principle, this model is a one-way model, and hence provides satisfactory accuracy for problems where the forward scattering dominates. At the same time, this model provides an efficiency gain of an order of magnitude or more over two-way coupled-mode models. This model can be applied to three-dimensional range-dependent problems with a slowly varying bathymetry or internal waves. A numerical example of the latter is demonstrated in this work. Comparisons of both accuracy and efficiency between the present model and a benchmark model are also provided.

Social Problems Caused by the Model

While achieving successes,the neoliberalist economic development model hasalso given rise to a series of grave problems,especially problem of social injusticeand polarization,which have begun to threaten Latin America’s social security andstability.

Parallel optimization of underwater acoustic models:A survey

Underwater acoustic models are effective tools for simulating underwater sound propagation.More than 50 years of research have been conducted on the theory and computational models of sound propagation in the ocean.Unfortunately,underwater sound propagation models were unable to solve practical large-scale three-dimensional problems for many years due to limited computing power and hardware conditions.Since the mid-1980s,research on high performance computing for acoustic propagation models in the field of underwater acoustics has flourished with the emergence of high-performance computing platforms,enabling underwater acoustic propagation models to solve many practical application problems that could not be solved before.In this paper,the contributions of research on high-performance computing for underwater acoustic propagation models since the 1980s are thoroughly reviewed and the possible development directions for the future are outlined.

ON THE CLOSURE PROBLEM OF TURBULENCE MODEL THEORY

It is a wrong viewpoint that the turbulence closure problem is due to thenon-linearity, of N-S equation, because if we omit the non-linear terms in N-Sequation,many, physical quantities can not be obtained other than the mean-values. Inthis paper, we proof that the closure problem of turbulence be induced by lack ofstatistical disiribution in present turbulence theory. And the restriction of turbulencemodel theory and shortcoming of direct numerical simulation of N-S to solve theturbulence have been pointed out.

The Win-Win-Win Papakonstantinidis Model in the Ultimatum Game

In this article it is investigated the case of a three-part ultimatum game,where the proposer makes repeated sharing suggestions to the responder and a"third".This"third"is the regulatory factor of recurring bids,at a rate-at each time of the immediately preceding.This article answers to question like"what share would the proposer be willing to give to the responder in the case of three taking part in the ultimatum game?"Which would be moral and which fair?At which point of distribution would it be accepted by the responder?A Chi Square(x^(2))test is used.For this reason,after investigating the social integration factors through the literature,two small surveys trying to identify the distribution rate are conducted.We conclude that a share 0.40 could be accepted by the responder and the"third".

A New Fractional Model for the Falling Body Problem

Recently, a conformable fractional derivative has been proposed to calculate the derivative of non-integer order of time functions. It has been shown that this new fractional derivative definition obeys many advantages over the preceding definitions. For mathematical models in applied sciences and to preserve the dimensionality of the physical quantities, an auxiliary parameter （~r） which has the dimension of seconds should be implemented in the fractional derivative definition. We obtain analytic solutions for the resulting conformable fractional differential equations describing the vertical velocity and the height of the falling body. It is shown that the dimensions of velocity and height are always correct without any restrictions on the auxiliary parameter cr which contradicts with the results in the literature when applying the Caputo definition to the same problem. This may open the door for many future works either to describe the role of such an auxiliary parameter or to derive a more suitable definition for the fractional derivative.

A New Searching Strategy for the Lost Plane Based on RBF Neural Network Model and Global Optimization Model

In this paper, we construct two models for the searching task for a lost plane. Model 1 determines the searching area. We predict the trajectory of floats generated after the disintegration of the plane by using RBF neural network model, and then determine the searching area according to the trajectory. With the pass of time, the searching area will also be constantly moving along the trajectory. Model 2 develops a maritime search plan to achieve the purpose of completing the search in the shortest time. We optimize the searching time and transform the problem into the 0-1 knapsack problem. Solving this problem by improved genetic algorithm, we can get the shortest searching time and the best choice for the search power.

Data-Driven Load Forecasting Using Machine Learning and Meteorological Data

Electrical load forecasting is very crucial for electrical power systems’planning and operation.Both electrical buildings’load demand and meteorological datasets may contain hidden patterns that are required to be investigated and studied to show their potential impact on load forecasting.The meteorological data are analyzed in this study through different data mining techniques aiming to predict the electrical load demand of a factory located in Riyadh,Saudi Arabia.The factory load and meteorological data used in this study are recorded hourly between 2016 and 2017.These data are provided by King Abdullah City for Atomic and Renewable Energy and Saudi Electricity Company at a site located in Riyadh.After applying the data pre-processing techniques to prepare the data,different machine learning algorithms,namely Artificial Neural Network and Support Vector Regression(SVR),are applied and compared to predict the factory load.In addition,for the sake of selecting the optimal set of features,13 different combinations of features are investigated in this study.The outcomes of this study emphasize selecting the optimal set of features as more features may add complexity to the learning process.Finally,the SVR algorithm with six features provides the most accurate prediction values to predict the factory load.

Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow

The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.

CLASSICAL VERIGIN PROBLEM AS A LIMIT CASE OF VERIGIN PROBLEM WITH SURFACE TENSION AT FREE BOUNDARY

In this paper we consider Verigin problem with surfaCe tension at freeboundary:where Ω1(t),Ω2(t) are regions of water and oil respectivelyl Γt is a free boundarybetween Ω1(t) and Ω2(t).Let Ω=Ω1(t) ∪Γt∪Ω1(t) be a bounded annular domainin R2, Ω2(t) is inside. nt is a normal of Γt, Pointing inwards Ω2(t),P1 and P2 arepressures of water and oil, μ1 and μ2 are viscosities of water and oil respectively, k isthe permeability, φ is the porosity, K and Vn are the curvature and the normal velocityof Γt in the direction of nt.We prove that the classical Verigin problem is the limit case(s-0) of Veriginproblem with surfaCe tension at free boundary.

Developments of parabolic equation method in the period of 2000–2016

Parabolic equation （PE） method is an efficient tool for modelling underwater sound propagation, particularly for problems involving range dependence. Since the PE method was first introduced into the field of underwater acoustics, it has been about 40 years, during which contributions to extending its capability has been continuously made. The most recent review paper surveyed the contributions made before 1999. In the period of 2000-2016, the development of PE method basically focuses on seismo-acoustic problems, three-dimensional problems, and realistic applications. In this paper, a review covering the contribution from 2000 to 2016 is given, and what should be done in future work is also discussed.

The Positive Research of Human Capital Structure and the Disparity Problem of Area in Our Country

The factors that influence the economic growth are various and complicated.This paper has especially probed into calculating and impact on regional economic growth of the human capital structure. First, on the basis of considering human capital quality, we use Gini coefficient law to calculate human capital structure coefficient of our country＇s each province （municipal or district）; Second, according to the result of calculating of human capital structure coefficient, considering input of material capital, average education level and so on at the same time, we set up regional economic growth model and use the panel data to examine the model. The result indicates the human capital structure coefficient of each province （municipal or district）in inverse proportion to economic growth （- 0. 108）. The last is the conclusion of this text.

Direct adaptive regulation of unknown nonlinear systems with analysis of the model order problem

A new method for the direct adaptive regulation of unknown nonlinear dynamical systems is proposed in this paper,paying special attention to the analysis of the model order problem.The method uses a neurofuzzy (NF) modeling of the unknown system,which combines fuzzy systems (FSs) with high order neural networks (HONNs).We propose the approximation of the unknown system by a special form of an NF-dynamical system (NFDS),which,however,may assume a smaller number of states than the original unknown model.The omission of states,referred to as a model order problem,is modeled by introducing a disturbance term in the approximating equations.The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties.An adaptive modification method,termed ‘parameter hopping’,is incorporated into the weight estimation algorithm so that the existence and boundedness of the control signal are always assured.The applicability and potency of the method are tested by simulations on well known benchmarks such as ‘DC motor’ and ‘Lorenz system’,where it is shown that it performs quite well under a reduced model order assumption.Moreover,the proposed NF approach is shown to outperform simple recurrent high order neural networks (RHONNs).

Implementation of a new network equilibrium model of travel choices

This paper develops a new combined network equilibrium model by using more behaviorally sound mathematical forms to represent the four travel choices（i.e., trip frequency,destination, mode, and route） in a conventional travel demand forecasting process. Trip frequency choice relates to the traveler decision on “making a trip” or “not making a trip”so it is given by a binary logit model. Destination choice is formulated as a parameterized dogit model of which the captivity parameters（expressed as functions of independent variables） allow individual travelers to be captive to specific destinations. Mode choice is given by a two-level nested logit model to avoid IIA restriction. Trip assignment is based on Wardrop＇s “user-optimized” principle. All model forms describing travel choices are in response to the level of services incurred by the transportation system. Through the introduction of inclusive values, the traveler decisions concerning trip frequency, destination, mode, and route choices are inherently interrelated and jointly determined.To obtain solutions of the new combined model, it was reformulated as an equivalent convex programming problem with linear constraints, a great advantage from the computational aspects. The model was applied empirically to a transportation network in New Jersey. The application results show that the new model is consistently better than the commonly used logit combined model in reproducing the observed trip flows from origin zones, origin to destination（O-D） trip flows, O-D trip flows by mode, and trip flows on the network links.

Solving the maximal matching problem with DNA molecules in Adleman-Lipton model

The maximal matching problem （MMP） is to find maximal edge subsets in a given undirected graph, that no pair of edges are adjacent in the subsets. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications in optimal combination and linear programming fields. It can be difficultly solved by the electronic computer in exponential level time. Meanwhile in previous studies deoxyribonucleic acid （DNA） molecular operations usually were used to solve NP-complete continuous path search problems, e.g. HPP, traveling salesman problem, rarely for NP-hard problems with discrete vertices or edges solutions, such as the minimum vertex cover problem, graph coloring problem and so on. In this paper, we present a DNA algorithm for solving the MMP with DNA molecular operations. For an undirected graph with n vertices and m edges, we reasonably design fixed length DNA strands representing vertices and edges of the graph, take appropriate steps and get the solutions of the MMP in proper length range using O（n^3） time. We extend the application of DNA molecular operations and simultaneously simplify the complexity of the computation.

h-P Finite Element Approximation for Full-Potential Electronic Structure Calculations

The(continuous) finite element approximations of different orders for the computation of the solution to electronic structures were proposed in some papers and the performance of these approaches is becoming appreciable and is now well understood.In this publication,the author proposes to extend this discretization for full-potential electronic structure calculations by combining the refinement of the finite element mesh,where the solution is most singular with the increase of the degree of the polynomial approximations in the regions where the solution is mostly regular.This combination of increase of approximation properties,done in an a priori or a posteriori manner,is well-known to generally produce an optimal exponential type convergence rate with respect to the number of degrees of freedom even when the solution is singular.The analysis performed here sustains this property in the case of Hartree-Fock and Kohn-Sham problems.

THE STUDY OF RETRIEVAL THEORY AND METHODS FROM SATELLITE REMOTE SENSING FOR METEOROLOGICAL PARAMETERS OVER EASTERN ASIA-PARTI:ISPRM AND SRRM

A review of ten-year's practice in developing the improved simultaneous physical retrieval method(ISPRM)is given in the hope that some creative ideas can be drawn from it.The improvement upon the SPRM is associated with the under-determinedness of this ill-posed inverse problem.In our experiment,the precondition is observed that prior information must be independent of the satellite measurements.The well-posed retrieval theory has told us that the forward process is fundamental for the retrieval,and it is the bridge between the input of satellite radiance and the output of retrievals.In order to obtain a better result from the forward process. the full advantage of every prior information available must be taken.It is necessary to turn the ill- posed inverse problem into the well-posed one.Then by using the Ridge regression or Bayes algorithm to find the optimal combination among the first guess,the theoretical analogue information and the satellite observations,the impact of the under-determinedness of this inverse problem on the numerical solution is minimized.