Game Theory Based Model for Predictive Analytics Using Distributed Position Function

This paper presents a game theory-based method for predicting the outcomes of negotiation and group decision-making problems. We propose an extension to the BDM model to address problems where actors’ positions are distributed over a position spectrum. We generalize the concept of position in the model to incorporate continuous positions for the actors, enabling them to have more flexibility in defining their targets. We explore different possible functions to study the role of the position function and discuss appropriate distance measures for computing the distance between the positions of actors. To validate the proposed extension, we demonstrate the trustworthiness of our model’s performance and interpretation by replicating the results based on data used in earlier studies.

Weak Fault Feature Extraction of the Rotating Machinery Using Flexible Analytic Wavelet Transform and Nonlinear Quantum Permutation Entropy

Addressing the challenges posed by the nonlinear and non-stationary vibrations in rotating machinery,where weak fault characteristic signals hinder accurate fault state representation,we propose a novel feature extraction method that combines the Flexible Analytic Wavelet Transform(FAWT)with Nonlinear Quantum Permutation Entropy.FAWT,leveraging fractional orders and arbitrary scaling and translation factors,exhibits superior translational invariance and adjustable fundamental oscillatory characteristics.This flexibility enables FAWT to provide well-suited wavelet shapes,effectively matching subtle fault components and avoiding performance degradation associated with fixed frequency partitioning and low-oscillation bases in detecting weak faults.In our approach,gearbox vibration signals undergo FAWT to obtain sub-bands.Quantum theory is then introduced into permutation entropy to propose Nonlinear Quantum Permutation Entropy,a feature that more accurately characterizes the operational state of vibration simulation signals.The nonlinear quantum permutation entropy extracted from sub-bands is utilized to characterize the operating state of rotating machinery.A comprehensive analysis of vibration signals from rolling bearings and gearboxes validates the feasibility of the proposed method.Comparative assessments with parameters derived from traditional permutation entropy,sample entropy,wavelet transform(WT),and empirical mode decomposition(EMD)underscore the superior effectiveness of this approach in fault detection and classification for rotating machinery.

Seismic risk evaluation for a planning mountain tunnel using improved analytical hierarchy process based on extension theory

Seismic risk evaluation(SRE) in early stages(e.g., project planning and preliminary design)for a mountain tunnel located in seismic areas has the same importance as that in final stages(e.g.,performance-based design, structural analysis, and optimization). SRE for planning mountain tunnels bridges the gap between the planning on the macro level and the design/analysis on the micro level regarding the risk management of infrastructural systems. A transition from subjective or qualitative description to objective or quantitative quantification of seismic risk is aimed to improve the seismic behavior of the mountain tunnel and thus reduce the associated seismic risk. A new method of systematic SRE for the planning mountain tunnel was presented herein. The method employs extension theory(ET)and an ET-based improved analytical hierarchy process. Additionally, a new risk-classification criterion is proposed to classify and quantify the seismic risk for a planning mountain tunnel. This SRE method is applied to a mountain tunnel in southwest China, using the extension model based on matter element theory and dependent function operation.The reasonability and flexibility of the SRE method for application to the mountain tunnel are illustrated.According to different seismic risk levels and classification criteria, methods and measures for improving the seismic design are proposed, which can reduce the seismic risk and provide a frame of reference for elaborate seismic design.

Analytical Theory of the Geodesic Acoustic Mode in the Small and Large Orbit Drift Width Limits and its Application in a Study of Plasma Shaping Effect

Analytical theories of the geodesic acoustic mode （GAM） are reviewed in the small- and large-orbit drift width limits, respectively. Different physics pictures in these two limits are displayed. As an example, these two analytical methods are employed to investigate the plasma shaping effect on the frequency and collisionless damping rate of the GAM.

OLD AND RECENT RESULTS IN THE ANALYTIC THEORY OF DIRICHLET SERIES:A SURVEY

This survey is dedicated to the memory of Professor Jiarong Yu,who recently passed away.It is concerned by a topic of which he was fond,an interest shared by myself:the analytic theory of Dirichlet series.

Using Extension Theory and Fuzzy Analytic Hierarchy Process on Heterogeneous Wireless Network Selection Algorithm

In order to solve the problem that determining decision factors weights is of subjectivity in heterogeneous wireless network selection algorithm, a network selection algorithm based on extension theory and fuzzy analytic hierarchy process (FAHP) is proposed in this paper. In addition, user and operator codetermine the optimal network using the proposed algorithm, which can give consideration to user and operator benefits. The fuzzy judgment matrix is constructed by membership degree of decision factors which is calculated according to extension theory. The comprehensive weight of each decision factor is obtained using FAHP. Finally, the optimal network is selected through total property value ranking of each candidate network under user preference and operator preference. The simulation results show that the proposed algorithm can select the optimal network efficiently and accurately, satisfy user preference, and implement load balance between networks.

AN ANALYTICAL SOLUTION OF RECTANGULAR LAMINATEDPLATES BY HIGHER-ORDER THEORY

On the basis of the Reddy's higher-order theory of composites, this paper introduces a displacement function Phi into it and transforms its three differential equations for symmetric cross-ply composites into only one eight-order differential equation generated by the displacement-function. When a proper Phi is chosen, both solutions are obtained, namely, the Navier-type solution of simply supported rectangular laminated plates and the Levy-type solution with the boundary condition where two opposite edges are simply supported and remains are arbitrary. The numerical examples show that the present results coincide well with the existing results in the references, thus validating that the present solving method is reliable. The higher-order theory of Reddy is simpler in calculation but has higher precision than the first-order shear deformation theory because the former has fewer unknows than the latter and requires no shear coefficients.

Unified analytical solution for deep circular tunnel with consideration of seepage pressure,grouting and lining

A new unified analytical solution is presented for predicting the range of plastic zone and stress distributions around a deep circular tunnel in a homogeneous isotropic continuous medium. The rock mass, grouting zone and lining are assumed as elastic-perfectly plastic and governed by the unified strength theory(UST). This new solution has made it possible to consider the interaction between seepage pressure, lining, grouting and rock mass, and the intermediate principal stress effect together. Moreover, parametric analysis is carried out to identify the influence of the related parameters on the plastic zone radius. Under the given conditions, the results show that the plastic zone radius decreases with an increasing cohesion, internal friction angle and hydraulic conductivity of lining and unified failure criterion parameter, respectively; whereas the plastic zone radius increases with the growth of elasticity modulus of lining. Comparison of results from the new solution and the other published one shows well agreement and provides confidence in the new solution proposed.

Methods of analytical mechanics for solving differential equations of first order

A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton-Noether method, the Lagrange-Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.

An analytical symplectic approach to the vibration analysis of orthotropic graphene sheets

A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach. A Hamiltonian system is established by introducing a total unknown vector consisting of the displacement amplitude, rotation angle, shear force, and bending moment. The high-order governing differential equation of the vibration of SLGSs is transformed into a set of ordinary differential equations in symplectic space. Exact solutions for free vibration are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary conditions. Vibration modes are expressed in terms of the symplectic eigenfunctions. In the numerical examples, comparison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given. A parametric study of the natural frequency is also included.

Analytical solution of velocity distribution for flow through submerged large deflection flexible vegetation

An analytical solution for predicting the vertical distribution of streamwise mean velocity in an open channel flow with submerged flexible vegetation is proposed when large bending occurs. The flow regime is separated into two horizontal layers： a vegetation layer and a free water layer. In the vegetation layer, a mechanical analysis for the flexible vegetation is conducted, and an approximately linear relationship between the drag force of bending vegetation and the streamwise mean flow velocity is observed in the case of large deflection, which differes significantly from the case of rigid upright vegetation. Based on the theoretical analysis, a linear streamwise drag force-mean flow velocity expression in the momentum equation is derived, and an analytical solution is obtained. For the free water layer, a new expression is presented, replacing the traditional logarithmic velocity distribution, to obtain a zero velocity gradient at the water surface. Finally, the analytical predictions are compared with published experimental data, and the good agreement demonstrates that this model is effective for the open channel flow through the large deflection flexible vegetation.

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot＇s dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot＇s dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.

The molecular structure and analytical potential energy function of HCO （X^2A＇）

In this paper the equilibrium structure of HCO has been optimized by using density functional theory （DFT）/ B3P86 method and CC-PVTZ basis. It has a bent （Cs, X^2A＇） ground state structure with an angle of 124.4095 °. The vibronic frequencies and force constants have also been calculated. Based on the principles of atomic and molecular reaction statics, the possible electronic states and reasonable dissociation limits for the ground state of HCO molecule have been determined. The analytic potential energy function of HCO （X^2A＇） molecule has been derived by using the many-body expansion theory. The contour lines are constructed, which show the static properties of HCO （X^2A＇）, such as the equilibrium structure, the lowest energies, etc. The potential energy surface of HCO （X^2A＇） is reasonable and very satisfactory.

Analytical Framework for Market-oriented DSR Flexibility Integration and Management

Integration and management of the flexibility of Demand Side Resources (DSR) in today’s energy systems plays a significant role in building up a sustainable society. However, the challenges of understanding, predicating and handling the uncertainties associated this subject to a great extent hamper its development. In this paper, an analytical framework based on a multi-portfolio setup in presence of a deregulated power market is proposed to address such challenges by adopting the thinking in modern portfolio theory (MPT). A Numerical example that targets on analyzing the risk and return for various flexibility pricing strategies are presented to illustrate some features of the framework.

Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading

This paper presents an analytical solution for one-dimensional consolidation of soft soil under some common types of cyclic loading such as trapezoidal cyclic loading, based on the assumptions proposed by Davis and Raymond (1965) that the decrease in permeability is proportional to the decrease in compressibility during the consolidation process of the soil and that the distribution of initial effective stress is constant with depth. It is verified by the existing analytical solutions in special cases. Using the solution obtained, some diagrams are prepared and the relevant consolidation behavior is investigated.

An analytical approximation of focusing-wave-induced load on a semi-submerged cylinder

Owing to the complexity of the physical mechanisms of rouge waves,the theoretical study of the rogue-wavestructure interaction problems still makes little progress.However,for regular-shaped structures,it is possible to give a theoretical analysis,if a relatively simple model of the rogue waves is used.The wave load,induced by a focusing wave which is known as an intuitive basic model of the rouge waves,upon a semi-submerged cylinder is studied analytically.The focusing wave is approximate by the Gauss envelope wave,an ideal model which contains most features of the rogue wave.The diffraction velocity potential is derived through the separation of flow field,and the formulas of the horizontal force and bending moment are proposed.The derived formulas are simplified appropriately,and validated through comparison against numerical results.In addition,the influence of parameters,such as the focusing degree,the submerging depth and the wave focusing position,is thoroughly investigated.

Modeling of metal–oxide semiconductor: Analytical bond-order potential for cupric oxide

Atomistic potentials for cupric element and cupric oxide are derived based on the analytical bond-order scheme that was presented by Brenner [Brenner D W, Erratum： Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films, Phys. Rev. B 1992, 46 1948]. In this paper, for the pure cupric element, the energy and structural parameters for several bulk phases as well as dimmer structure are well reproduced. The reference data are taken from our density functional theory calculations and the available experiments. The model potential also provides a good description of the bulk properties of various solid structures of cupric oxide compound structures, including cohesive energies, lattice parameters, and elastic constants.

Model-element Analytic Method for Plastic Forming of Material

MEM(model element method) is proposed to resolve the present difficulties and problems in CAE about plastic forming of material.There are four advantages when MEM is integrated with FEM(finite element method) and UBM(upper boundary element method).First,it can make full use of their own advantages and overcome their own disadvantages;second,it can analyse material plastic fluid expediently;third,it can optimize design;finally,it can improve technological content and application effect of CAE software.Based on introducing the principle of MEM briefly,features and applications of MEM are pointed out.In conclusion,a new analysis method for plastic forming comes forth.