Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth m...Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.展开更多
The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so t...The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.展开更多
In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, ...In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.展开更多
Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,...Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,where the range of p is different from(1,∞),and we isolate the right class of weights introduced by Auscher and Martell.In this work,we use good-λ inequality with two parameters through the weighted boundedness of Riesz transforms ▽L^(-1/2).Our result recovers,in some sense,a previous result of Hofmann.展开更多
Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted...Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.展开更多
1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive defi...1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive definite matrix exists one and only onesquare root which is a symmetric positive definite matrix,too（e.g.see[5]）.Higham[4]studied carefully the relation of a real nonsingular matrix between its real square rootsand its eigenvalues.Alefeld and Schneider[1]pointed out that for any nonsingular M-ma-trix there is one and only one M-matrix as its square root.In this paper,we study on展开更多
Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generate...Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generated by the Kato square root v/L and a Lipschitz function, which recovers a previous result of Calderon, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.展开更多
Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato ...Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln（Rn）（n> 2）,is bounded from the homogenous Sobolev space L1p（Rn） to Lp（Rn）（p-（L） <p<p+（L））.展开更多
The effectiveness of using an Ensemble Square Root Filter（EnSRF） to assimilate real Doppler radar observations on convective scale is investigated by applying the technique to a case of squall line on 12July 2005 in...The effectiveness of using an Ensemble Square Root Filter（EnSRF） to assimilate real Doppler radar observations on convective scale is investigated by applying the technique to a case of squall line on 12July 2005 in midwest Shandong Province using the Weather Research and Forecasting（WRF） model.The experimental results show that：（1） The EnSRF system has the potential to initiate a squall line accurately by assimilation of real Doppler radar data.The convective-scale information has been added into the WRF model through radar data assimilation and thus the analyzed fields are improved noticeably.The model spin-up time has been shortened,and the precipitation forecast is improved accordingly.（2） Compared with the control run,the deterministic forecast initiated with the ensemble mean analysis of EnSRF produces more accurate prediction of microphysical fields.The predicted wind and thermal fields are reasonable and in accordance with the characteristics of convective storms.（3） The propagation direction of the squall line from the ensemble mean analysis is consistent with that of the observation,but the propagation speed is larger than the observed.The effective forecast period for this squall line is about 5-6 h,probably because of the nonlinear development of the convective storm.展开更多
Animals grouping together is one of the most interesting phenomena in population dynamics and different functional responses as a result of prey-predator forming groups have been considered by many authors in their mo...Animals grouping together is one of the most interesting phenomena in population dynamics and different functional responses as a result of prey-predator forming groups have been considered by many authors in their models. In the present paper we have considered a model for one prey and two competing predator populations with time lag and square root functional response on account of herd formation by prey. It is shown that due to the inclusion of another competing predator, the underlying system without delay becomes more stable and limit cycles do not occur naturally. However, after considering the effect of time lag in the basic system, limit cycles appear in the case of all equilibrium points when delay time crosses some critical value. From the numerical simulation, it is observed that the length of delay is minimum when only prey population survives and it is maximum when all the populations coexist.展开更多
The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle nu...The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers N_A and N_B with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of N_A and N_B.展开更多
This research presents the square root sum of squares response of displacements and tunnel moments under the Kobe and Loma Prieta seismic excitations with a peak ground acceleration of 0.05 g for various dry relative ...This research presents the square root sum of squares response of displacements and tunnel moments under the Kobe and Loma Prieta seismic excitations with a peak ground acceleration of 0.05 g for various dry relative densities of local sand in Bangladesh.For this reason,a one-dimensional gravitational shake table test was performed after calibration to determine the seismic performance of the concrete tunnel-sand-pile interaction model.A vertical 40 kg load was applied on each pile cap along with the seismic excitations.The experimental results obtained were compared with the previous numerical study conducted by using field data so as to better interpret the variations of results.In the case of vertical sand displacement,the ratio between the previous field data obtained through numerical study and the present study is found to be 0.96.Moreover,the experimental results were compared with the 3D full-scale numerical analysis results of Plaxis considering the Mohr-Coulomb constitutive model of sand.Variations of experimental and numerical results show a satisfactory level of alignment with the previously published work.According to the shake table test results,the lateral displacement of the tunnel is greater than the vertical displacement because of the transverse directional seismic excitation on the tunnel body.The minimum difference between lateral and vertical displacements of the tunnel is found to be 31%for a relative density of 27%under the Loma Prieta earthquake.However,this research may be advanced in the future by considering various peak ground accelerations,tunnel-pile clearance,and geometric properties.展开更多
The significant role of square root mapping in probability,statistics,physics,architecture and engineering motivates us to emphasize on a new radical functional equation arising from a square root and reciprocal squar...The significant role of square root mapping in probability,statistics,physics,architecture and engineering motivates us to emphasize on a new radical functional equation arising from a square root and reciprocal square root mappings.The interesting attribute of this equation is that it has both a square root mapping and a reciprocal square root mapping as solutions.We establish that the hyperstabilities of this equation exist using a fixed point alternative theorem.It is also demonstrated with an example that the stability may fail in special cases.展开更多
Selecting the optimal model helps decision-makers to reduce the uncertainty in the slope calculation process.The uncertainty quantification process using root-mean-square error(RMSE)has limitations.It can obscure loca...Selecting the optimal model helps decision-makers to reduce the uncertainty in the slope calculation process.The uncertainty quantification process using root-mean-square error(RMSE)has limitations.It can obscure local uncertainty features and neglect the statistical characteristics of uncertainty,which may hinder decision-makers'understanding and model selection.展开更多
For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself ...For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.展开更多
Caprock is a water-saturated formation with a sufficient entry capillary pressure to prevent the upward migration of a buoyant fluid. When the entry capillary pressure of caprock is smaller than the pressure exerted b...Caprock is a water-saturated formation with a sufficient entry capillary pressure to prevent the upward migration of a buoyant fluid. When the entry capillary pressure of caprock is smaller than the pressure exerted by the buoyant CO2plume, CO2gradually penetrates into the caprock. The CO2penetration depth into a caprock layer can be used to measure the caprock sealing efficiency and becomes the key issue to the assessment of caprock sealing efficiency. On the other hand, our numerical simulations on a caprock layer have revealed that a square root law for time and pore pressure exists for the CO2penetration into the caprock layer. Based on this finding, this study proposes a simple approach to estimate the CO2penetration depth into a caprock layer. This simple approach is initially developed to consider the speed of CO2invading front. It explicitly expresses the penetration depth with pressuring time, pressure difference and pressure magnitude. This simple approach is then used to fit three sets of experimental data and good fittings are observed regardless of pressures, strengths of porous media, and pore fluids(water,hydrochloric acid, and carbonic acid). Finally, theoretical analyses are conducted to explore those factors affecting CO2penetration depth. The effects of capillary pressure, gas sorption induced swelling, and fluid property are then included in this simple approach. These results show that this simple approach can predict the penetration depth into a caprock layer with sufficient accuracy, even if complicated interactions in penetration process are not explicitly expressed in this simple formula.展开更多
FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem（SLAM）. However, in this framework there are two important potential limitatio...FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem（SLAM）. However, in this framework there are two important potential limitations, the particle depletion problem and the linear approximations of the nonlinear functions. To overcome these two drawbacks, this paper proposes a new FastSLAM algorithm based on revised genetic resampling and square root unscented particle filter（SR-UPF）. Double roulette wheels as the selection operator, and fast Metropolis-Hastings（MH） as the mutation operator and traditional crossover are combined to form a new resampling method. Amending the particle degeneracy and keeping the particle diversity are both taken into considerations in this method. As SR-UPF propagates the sigma points through the true nonlinearity, it decreases the linearization errors. By directly transferring the square root of the state covariance matrix, SR-UPF has better numerical stability. Both simulation and experimental results demonstrate that the proposed algorithm can improve the diversity of particles, and perform well on estimation accuracy and consistency.展开更多
The solutions of the nonlinear singular integral equation,t 6 L,are considered,where L is a closed contour in the complex plane,b≠0 is a constant and f(t)is a polynomial.It is an extension of the results obtained in[...The solutions of the nonlinear singular integral equation,t 6 L,are considered,where L is a closed contour in the complex plane,b≠0 is a constant and f(t)is a polynomial.It is an extension of the results obtained in[1]when f(t)is a constant.Certain special cases are illustrated.展开更多
Recovering an unknown high dimensional low rank matrix from a small set of entries is widely spread in the fields of machine learning,system identification and image restoration,etc.In many practical applications,the ...Recovering an unknown high dimensional low rank matrix from a small set of entries is widely spread in the fields of machine learning,system identification and image restoration,etc.In many practical applications,the few observations are always corrupted by noise and the noise level is also unknown.A novel model with nuclear norm and square root type estimator has been proposed,which does not rely on the knowledge or on an estimation of the standard deviation of the noise.In this paper,we firstly reformulate the problem to an equivalent variable separated form by introducing an auxiliary variable.Then we propose an efficient alternating direction method of multipliers(ADMM)for solving it.Both of resulting subproblems admit an explicit solution,which makes our algorithm have a cheap computing.Finally,the numerical results show the benefits of the model and the efficiency of the proposed method.展开更多
基金This research was supported by the National Basic Research Program of China （Grant No. 2007CB209603）, Key Project of the National Natural Science Foundation （Grant No. 40830424）, State Key Laboratory of Geological Processes and Mineral Resources Geo-detection Laboratory of the Ministry of Education for their sponsorship （GPMR 200633, GDL0801）.
文摘Improving the focusing capability of pre-stack time migration allows the imaged section to reflect structural characteristics, depth, and interface shape and it is a key step for the preparation of the initial depth migration velocity model. The traditional symmetrical travel time equation is derived based on the assumption of a layered model. It is difficult to achieve the desired effect of focusing in media with strong lateral variation. The nonsymmetrical travel time equation based on Lie algebra and a pseudo-differential operator contains a lateral velocity derivative which can improve the focusing capability even in strongly lateral variable media and also the computation precision of the weight coefficients for relative amplitude preservation. Compared with the symmetrical methods, the nonsymmetrical method is more effective. In this paper, we describe several key steps of nonsymmetric pre-stack travel time calculation and present some test results using synthetic and real data.
基金Supported by the National Natural Science Foundation of China (10161009)
文摘The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.
基金The project supported by National Natural Science Foundation of China under Grant No. 10571166
文摘In classical statistics, the Fisher information is unique in the sense that it is essentially the only monotone Riemannian metric on the space of probability densities. In quantum theory, this uniqueness breaks down, and there are many natural quantum analogues of the Fisher information, among which two particular versions distinguish themselves by their intuitive and informational significance： The first has its origin in the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurement, and is defined via the square root of the density operator. The second arises from Helstrom＇s study of quantum detection in 1967, and is defined via the symmetric logarithmic derivative. The aim of this paper Js to compare these two versions of quantum Fisher information, and to establish two informational inequalities relating them.
基金supported by NSFC(1187109611471033)+4 种基金supported by NSFC(113710571147103311571160)SRFDP(20130003110003)the Fundamental Research Funds for the Central Universities(2014KJJCA10)。
文摘Let L=-div(A▽) be a second order divergence form elliptic operator with bounded measurable coefficients in R^(n).We establish weighted L^(p) norm inequalities for commutators generated by √L and Lipschitz functions,where the range of p is different from(1,∞),and we isolate the right class of weights introduced by Auscher and Martell.In this work,we use good-λ inequality with two parameters through the weighted boundedness of Riesz transforms ▽L^(-1/2).Our result recovers,in some sense,a previous result of Hofmann.
基金supported by the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the National Natural Science Foundation of China(12071431)+1 种基金the Fundamental Research Funds for the Central Universities(lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
基金The second author is supported by Xiamen University,China
文摘1 IntroductionLet A∈C<sup>n×n</sup>, B∈C<sup>n×n</sup>.We say B is a square root of A if A=B×B i.e.A=B<sup>2</sup>.It is well-known that any symmetric positive definite matrix exists one and only onesquare root which is a symmetric positive definite matrix,too（e.g.see[5]）.Higham[4]studied carefully the relation of a real nonsingular matrix between its real square rootsand its eigenvalues.Alefeld and Schneider[1]pointed out that for any nonsingular M-ma-trix there is one and only one M-matrix as its square root.In this paper,we study on
基金supported by NSF of China(Grant No.11471033)supported by NSF of China(Grant Nos.11371057,11571160)+4 种基金NCET of China(Grant No.NCET-11-0574)the Fundamental Research Funds for the Central Universities(FRF-TP-12-006B)the Fundamental Research Funds for the Central Universities(Grant No.2014KJJCA10)SRFDP of China(Grant No.20130003110003)supported by NSF(Grant No.DMS 1101244)
文摘Let L = -div（AV） be a second order divergence form elliptic operator, and A be an accretive, n × n matrix with bounded measurable complex coefficients in R^n. We obtain the Lp bounds for the commutator generated by the Kato square root v/L and a Lipschitz function, which recovers a previous result of Calderon, by a different method. In this work, we develop a new theory for the commutators associated to elliptic operators with Lipschitz function. The theory of the commutator with Lipschitz function is distinguished from the analogous elliptic operator theory.
基金supported by National Natural Science Foundation of China (Grant No. 11471033)Program for New Century Excellent Talents in University of China (Grant No. NCET-11-0574)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. FRF-BR-17-001B)the Fundamental Research Funds for Doctoral Candidate of University of Science and Technology Beijing (Grant No. FRF-BR-17018)
文摘Let L=-div（A▽） be a second-order divergent-form elliptic operator,where A is an accretive n×n matrix with bounded and measurable complex coefficients on Herein,we prove that the commutator [b,L1/2]of the Kato square root L1/2 and b with ▽b∈Ln（Rn）（n> 2）,is bounded from the homogenous Sobolev space L1p（Rn） to Lp（Rn）（p-（L） <p<p+（L））.
基金Supported by the National Natural Science Foundation of China(41105067)National High Technology Research and Development Program of China(2013AA09A506-5)Special Scientific Reserch Fund of Marin Public Welfare Profession of China(201305032-2)
文摘The effectiveness of using an Ensemble Square Root Filter（EnSRF） to assimilate real Doppler radar observations on convective scale is investigated by applying the technique to a case of squall line on 12July 2005 in midwest Shandong Province using the Weather Research and Forecasting（WRF） model.The experimental results show that：（1） The EnSRF system has the potential to initiate a squall line accurately by assimilation of real Doppler radar data.The convective-scale information has been added into the WRF model through radar data assimilation and thus the analyzed fields are improved noticeably.The model spin-up time has been shortened,and the precipitation forecast is improved accordingly.（2） Compared with the control run,the deterministic forecast initiated with the ensemble mean analysis of EnSRF produces more accurate prediction of microphysical fields.The predicted wind and thermal fields are reasonable and in accordance with the characteristics of convective storms.（3） The propagation direction of the squall line from the ensemble mean analysis is consistent with that of the observation,but the propagation speed is larger than the observed.The effective forecast period for this squall line is about 5-6 h,probably because of the nonlinear development of the convective storm.
文摘Animals grouping together is one of the most interesting phenomena in population dynamics and different functional responses as a result of prey-predator forming groups have been considered by many authors in their models. In the present paper we have considered a model for one prey and two competing predator populations with time lag and square root functional response on account of herd formation by prey. It is shown that due to the inclusion of another competing predator, the underlying system without delay becomes more stable and limit cycles do not occur naturally. However, after considering the effect of time lag in the basic system, limit cycles appear in the case of all equilibrium points when delay time crosses some critical value. From the numerical simulation, it is observed that the length of delay is minimum when only prey population survives and it is maximum when all the populations coexist.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11372122,11274393,11574404,and 11275279the Open Project Program of State Key Laboratory of Theoretical Physics,Institute of Theoretical Physics,Chinese Academy of Sciences,China+1 种基金the National Basic Research Program of China(2013CB933601)Guangdong Natural Science Foundation(2016A030313313)
文摘The coupled Gross–Pitaevskii equations for two-species BEC have been solved analytically under the Thomas-Fermi approximation(TFA). Based on the analytical solution, two formulae are derived to relate the particle numbers N_A and N_B with the root mean square radii of the two kinds of atoms. Only the case that both kinds of atoms have nonzero distribution at the center of an isotropic trap is considered. In this case the TFA has been found to work nicely. Thus, the two formulae are applicable and are useful for the evaluation of N_A and N_B.
文摘This research presents the square root sum of squares response of displacements and tunnel moments under the Kobe and Loma Prieta seismic excitations with a peak ground acceleration of 0.05 g for various dry relative densities of local sand in Bangladesh.For this reason,a one-dimensional gravitational shake table test was performed after calibration to determine the seismic performance of the concrete tunnel-sand-pile interaction model.A vertical 40 kg load was applied on each pile cap along with the seismic excitations.The experimental results obtained were compared with the previous numerical study conducted by using field data so as to better interpret the variations of results.In the case of vertical sand displacement,the ratio between the previous field data obtained through numerical study and the present study is found to be 0.96.Moreover,the experimental results were compared with the 3D full-scale numerical analysis results of Plaxis considering the Mohr-Coulomb constitutive model of sand.Variations of experimental and numerical results show a satisfactory level of alignment with the previously published work.According to the shake table test results,the lateral displacement of the tunnel is greater than the vertical displacement because of the transverse directional seismic excitation on the tunnel body.The minimum difference between lateral and vertical displacements of the tunnel is found to be 31%for a relative density of 27%under the Loma Prieta earthquake.However,this research may be advanced in the future by considering various peak ground accelerations,tunnel-pile clearance,and geometric properties.
基金Supported by the Science and Engineering Research Board(SERB),India(MTR/2020/000534).
文摘The significant role of square root mapping in probability,statistics,physics,architecture and engineering motivates us to emphasize on a new radical functional equation arising from a square root and reciprocal square root mappings.The interesting attribute of this equation is that it has both a square root mapping and a reciprocal square root mapping as solutions.We establish that the hyperstabilities of this equation exist using a fixed point alternative theorem.It is also demonstrated with an example that the stability may fail in special cases.
基金supported by the National Key Research and Development Program of China:Core Technologies and Software Systems of Geospatial Intelligence(Project No.:2021YFB3900900).
文摘Selecting the optimal model helps decision-makers to reduce the uncertainty in the slope calculation process.The uncertainty quantification process using root-mean-square error(RMSE)has limitations.It can obscure local uncertainty features and neglect the statistical characteristics of uncertainty,which may hinder decision-makers'understanding and model selection.
基金funded by Prince Sultan University,Riyadh,Saudi Arabia。
文摘For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.
基金the financial support from the Creative Research and Development Group Program of Jiangsu Province(2014-27)the National Science Fund for Distinguished Young Scholars(Grant No.51125017)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD2014)
文摘Caprock is a water-saturated formation with a sufficient entry capillary pressure to prevent the upward migration of a buoyant fluid. When the entry capillary pressure of caprock is smaller than the pressure exerted by the buoyant CO2plume, CO2gradually penetrates into the caprock. The CO2penetration depth into a caprock layer can be used to measure the caprock sealing efficiency and becomes the key issue to the assessment of caprock sealing efficiency. On the other hand, our numerical simulations on a caprock layer have revealed that a square root law for time and pore pressure exists for the CO2penetration into the caprock layer. Based on this finding, this study proposes a simple approach to estimate the CO2penetration depth into a caprock layer. This simple approach is initially developed to consider the speed of CO2invading front. It explicitly expresses the penetration depth with pressuring time, pressure difference and pressure magnitude. This simple approach is then used to fit three sets of experimental data and good fittings are observed regardless of pressures, strengths of porous media, and pore fluids(water,hydrochloric acid, and carbonic acid). Finally, theoretical analyses are conducted to explore those factors affecting CO2penetration depth. The effects of capillary pressure, gas sorption induced swelling, and fluid property are then included in this simple approach. These results show that this simple approach can predict the penetration depth into a caprock layer with sufficient accuracy, even if complicated interactions in penetration process are not explicitly expressed in this simple formula.
基金supported by National Natural Science Foundation of China(No.61101197)Research Fund for the Doctoral Program of Higher Education of China(No.20093219120025)
文摘FastSLAM is a popular framework which uses a Rao-Blackwellized particle filter to solve the simultaneous localization and mapping problem（SLAM）. However, in this framework there are two important potential limitations, the particle depletion problem and the linear approximations of the nonlinear functions. To overcome these two drawbacks, this paper proposes a new FastSLAM algorithm based on revised genetic resampling and square root unscented particle filter（SR-UPF）. Double roulette wheels as the selection operator, and fast Metropolis-Hastings（MH） as the mutation operator and traditional crossover are combined to form a new resampling method. Amending the particle degeneracy and keeping the particle diversity are both taken into considerations in this method. As SR-UPF propagates the sigma points through the true nonlinearity, it decreases the linearization errors. By directly transferring the square root of the state covariance matrix, SR-UPF has better numerical stability. Both simulation and experimental results demonstrate that the proposed algorithm can improve the diversity of particles, and perform well on estimation accuracy and consistency.
文摘The solutions of the nonlinear singular integral equation,t 6 L,are considered,where L is a closed contour in the complex plane,b≠0 is a constant and f(t)is a polynomial.It is an extension of the results obtained in[1]when f(t)is a constant.Certain special cases are illustrated.
基金Supported by the National Natural Science Foundation of China(Grant No.11971149,12101195,12071112,11871383)Natural Science Foundation of Henan Province for Youth(Grant No.202300410146).
文摘Recovering an unknown high dimensional low rank matrix from a small set of entries is widely spread in the fields of machine learning,system identification and image restoration,etc.In many practical applications,the few observations are always corrupted by noise and the noise level is also unknown.A novel model with nuclear norm and square root type estimator has been proposed,which does not rely on the knowledge or on an estimation of the standard deviation of the noise.In this paper,we firstly reformulate the problem to an equivalent variable separated form by introducing an auxiliary variable.Then we propose an efficient alternating direction method of multipliers(ADMM)for solving it.Both of resulting subproblems admit an explicit solution,which makes our algorithm have a cheap computing.Finally,the numerical results show the benefits of the model and the efficiency of the proposed method.
