This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the prop...This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.展开更多
In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetr...In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.展开更多
Motivation of this paper is an open problem exposed by B. Beauzamy .Let M be a 3×3 matrix and d(M) is the distance to the diagonal algebra. Let α(M)= sup {‖P ⊥MP‖∶P is a projection in the diagonal algeb...Motivation of this paper is an open problem exposed by B. Beauzamy .Let M be a 3×3 matrix and d(M) is the distance to the diagonal algebra. Let α(M)= sup {‖P ⊥MP‖∶P is a projection in the diagonal algebra} and then call K(M)=d(Μ)α(M) the distance coefficient of M. The following results are obtained: (1) If M has two zero entries apart from its diagonal, then K(M)322; (2) If M has one zero entry apart from its diagonal, then K(M)4132; (3) If M is arbitrary, then K(M)32.展开更多
In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access...In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.展开更多
The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicula...The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicular to its hole and the other to its side wall. Until now, there has not been a program to calculate the input impedance or its equivalent electromagnetic parameters for the later case. In this paper, an approach for analyzing the reflection characteristics of the impregnated honeycomb when its side wall faces the incident plane wave is proposed. Experiments prove it an effective, accurate and fast solution to this subject.展开更多
Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone,surface detection of signature noble gas radioisotopes is considered a positive identification of ...Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone,surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions(UNEs).However,the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved,including the generation of complex fracture networks,reactivation of natural fractures and faults,and thermo-hydro-mechanical-chemical(THMC)coupling of radionuclide gas transport in the subsurface.In this study,we provide an experimental investigation of hydro-mechanical(HM)coupling among gas flow,stress states,rock deformation,and rock damage using a unique multi-physics triaxial direct shear rock testing system.The testing system also features redundant gas pressure and flow rate measurements,well suited for parameter uncertainty quantification.Using porous tuff and tight granite samples that are relevant to historic UNE tests,we measured the Biot effective stress coefficient,rock matrix gas permeability,and fracture gas permeability at a range of pore pressure and stress conditions.The Biot effective stress coefficient varies from 0.69 to 1 for the tuff,whose porosity averages 35.3%±0.7%,while this coefficient varies from 0.51 to 0.78 for the tight granite(porosity<1%,perhaps an underestimate).Matrix gas permeability is strongly correlated to effective stress for the granite,but not for the porous tuff.Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event:(1)The porous tuff shows apparent fracture dilation or compression upon stress changes,which does not necessarily change the gas permeability;(2)The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement;and(3)Hydromechanical coupling among stress states,rock damage,and gas flow appears to be stronger in tight granite than in porous tuff.展开更多
Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate ...Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate dynamical model of industrial robots,which greatly hinders the realization of a stable,fast and accurate trajectory tracking control.Therefore,the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method.Moreover,an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory.The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved.With the SCARA robot as the research object,the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.展开更多
文摘This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.
基金Supported by CNPq-Conselho Nacional de Desenvolvimento Cient'fico e Tecnológico
文摘In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.
文摘Motivation of this paper is an open problem exposed by B. Beauzamy .Let M be a 3×3 matrix and d(M) is the distance to the diagonal algebra. Let α(M)= sup {‖P ⊥MP‖∶P is a projection in the diagonal algebra} and then call K(M)=d(Μ)α(M) the distance coefficient of M. The following results are obtained: (1) If M has two zero entries apart from its diagonal, then K(M)322; (2) If M has one zero entry apart from its diagonal, then K(M)4132; (3) If M is arbitrary, then K(M)32.
文摘In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.
文摘The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicular to its hole and the other to its side wall. Until now, there has not been a program to calculate the input impedance or its equivalent electromagnetic parameters for the later case. In this paper, an approach for analyzing the reflection characteristics of the impregnated honeycomb when its side wall faces the incident plane wave is proposed. Experiments prove it an effective, accurate and fast solution to this subject.
基金supported by the Laboratory Directed Research&Development(LDRD)program at the Los Alamos National Laboratory(LANL)(Grant No.20220019DR).
文摘Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone,surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions(UNEs).However,the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved,including the generation of complex fracture networks,reactivation of natural fractures and faults,and thermo-hydro-mechanical-chemical(THMC)coupling of radionuclide gas transport in the subsurface.In this study,we provide an experimental investigation of hydro-mechanical(HM)coupling among gas flow,stress states,rock deformation,and rock damage using a unique multi-physics triaxial direct shear rock testing system.The testing system also features redundant gas pressure and flow rate measurements,well suited for parameter uncertainty quantification.Using porous tuff and tight granite samples that are relevant to historic UNE tests,we measured the Biot effective stress coefficient,rock matrix gas permeability,and fracture gas permeability at a range of pore pressure and stress conditions.The Biot effective stress coefficient varies from 0.69 to 1 for the tuff,whose porosity averages 35.3%±0.7%,while this coefficient varies from 0.51 to 0.78 for the tight granite(porosity<1%,perhaps an underestimate).Matrix gas permeability is strongly correlated to effective stress for the granite,but not for the porous tuff.Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event:(1)The porous tuff shows apparent fracture dilation or compression upon stress changes,which does not necessarily change the gas permeability;(2)The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement;and(3)Hydromechanical coupling among stress states,rock damage,and gas flow appears to be stronger in tight granite than in porous tuff.
基金the Beijing Municipal Scienceand Technology Project (No.KM202111417006)the Academic Research Projects of Beijing Union University (Nos.ZK10202305 and ZK80202004)the Beijing Municipal Science and Technology Project (No.KM202111417005)。
文摘Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate dynamical model of industrial robots,which greatly hinders the realization of a stable,fast and accurate trajectory tracking control.Therefore,the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method.Moreover,an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory.The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved.With the SCARA robot as the research object,the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.
