Quantum confinement is recognized to be an inherent property in low-dimensional structures.Traditionally,it is believed that the carriers trapped within the well cannot escape due to the discrete energy levels.However...Quantum confinement is recognized to be an inherent property in low-dimensional structures.Traditionally,it is believed that the carriers trapped within the well cannot escape due to the discrete energy levels.However,our previous research has revealed efficient carrier escape in low-dimensional structures,contradicting this conventional understanding.In this study,we review the energy band structure of quantum wells along the growth direction considering it as a superposition of the bulk material dispersion and quantization energy dispersion resulting from the quantum confinement across the whole Brillouin zone.By accounting for all wave vectors,we obtain a certain distribution of carrier energy at each quantized energy level,giving rise to the energy subbands.These results enable carriers to escape from the well under the influence of an electric field.Additionally,we have compiled a comprehensive summary of various energy band scenarios in quantum well structures relevant to carrier transport.Such a new interpretation holds significant value in deepening our comprehension of low-dimensional energy bands,discovering new physical phenomena,and designing novel devices with superior performance.展开更多
In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and dualit...In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.展开更多
Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of ...Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.展开更多
We study the interaction between dark energy （DE） and dark matter in the scope of anisotropic Bianchi type-I space-time. First we derive the general form of the DE equation of state （EoS） parameter in both non-int...We study the interaction between dark energy （DE） and dark matter in the scope of anisotropic Bianchi type-I space-time. First we derive the general form of the DE equation of state （EoS） parameter in both non-interacting and interacting cases and then we examine its future by applying a hyperbolic scale factor. It is shown that in the non-interacting case, depending on the value of the anisotropy parameter K, the DE EoS parameter varies from phantom to quintessence whereas in the interacting case the EoS parameter varies in the quintessence region. However, in both cases, the DE EoS parameter ωde ultimately （i.e. at z ： -1） tends to the cosmological constant （ωde = -1）. Moreover, we fix the cosmological bound on the anisotropy parameter K by using recent observational data about the Hubble parameter.展开更多
In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum like...In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.展开更多
The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential v...The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.展开更多
This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of t...This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.展开更多
We have studied Locally Rotationally Symmetric (LRS) Bianchi type-I cosmological model filled with anisotropic fluid in general theory of relativity. The solutions of the field equations are obtained by using special ...We have studied Locally Rotationally Symmetric (LRS) Bianchi type-I cosmological model filled with anisotropic fluid in general theory of relativity. The solutions of the field equations are obtained by using special form of deceleration parameter which gives early deceleration and late time accelerating cosmological model. The geometrical and physical aspect of the model is also studied.展开更多
Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential includ...Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential included with a real number. The relation between the deceleration parameter and Hubble parameter and average scale factor is used in that cosmological model. The effect of the viscosity on the entropy of the universe is utilized by energy momentum tensor with bulk viscous terms in a conservative manner. We obtained a formula for calculating the entropy of the universe in terms of viscosity and used it to compare to the study. Also, various physical and kinematical properties have been discussed.展开更多
Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confiden...Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.展开更多
基金the National Natural Science Foundation of China(Grant Nos.61991441 and 62004218)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB01000000)Youth Innovation Promotion Association of Chinese Academy of Sciences(Grant No.2021005).
文摘Quantum confinement is recognized to be an inherent property in low-dimensional structures.Traditionally,it is believed that the carriers trapped within the well cannot escape due to the discrete energy levels.However,our previous research has revealed efficient carrier escape in low-dimensional structures,contradicting this conventional understanding.In this study,we review the energy band structure of quantum wells along the growth direction considering it as a superposition of the bulk material dispersion and quantization energy dispersion resulting from the quantum confinement across the whole Brillouin zone.By accounting for all wave vectors,we obtain a certain distribution of carrier energy at each quantized energy level,giving rise to the energy subbands.These results enable carriers to escape from the well under the influence of an electric field.Additionally,we have compiled a comprehensive summary of various energy band scenarios in quantum well structures relevant to carrier transport.Such a new interpretation holds significant value in deepening our comprehension of low-dimensional energy bands,discovering new physical phenomena,and designing novel devices with superior performance.
基金Foundation item： Supported by the National Natural Science Foundation of China（60574075） University, engaged in optimization theory and application.
文摘In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.
文摘Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms;therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.
基金a research fund from the Mahshahr Branch of Islamic Azad University under the project entitled "Interacting Viscous Dark Energy And Cold Dark Matter In An Anisotropic Universe"
文摘We study the interaction between dark energy （DE） and dark matter in the scope of anisotropic Bianchi type-I space-time. First we derive the general form of the DE equation of state （EoS） parameter in both non-interacting and interacting cases and then we examine its future by applying a hyperbolic scale factor. It is shown that in the non-interacting case, depending on the value of the anisotropy parameter K, the DE EoS parameter varies from phantom to quintessence whereas in the interacting case the EoS parameter varies in the quintessence region. However, in both cases, the DE EoS parameter ωde ultimately （i.e. at z ： -1） tends to the cosmological constant （ωde = -1）. Moreover, we fix the cosmological bound on the anisotropy parameter K by using recent observational data about the Hubble parameter.
文摘In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.
文摘The exact solutions of the Einstein field equations for dark energy (DE) in Locally Rotationally Symmetric (LRS) Bianchi type-I metric under the assumption on the anisotropy of the fluid are obtained for exponential volumetric expansion within the frame work of Lyra manifold for uniform and time varying displacement field. The isotropy of the fluid and space is examined.
基金supported by the National Natural Science Foundation of China(7117116470471057)
文摘This paper proposes a simple constant-stress accel- erated life test （ALT） model from Burr type XII distribution when the data are Type-I progressively hybrid censored. The maximum likelihood estimation （MLE） of the parameters is obtained through the numerical method for solving the likelihood equations. Approxi- mate confidence interval （CI）, based on normal approximation to the asymptotic distribution of MLE and percentile bootstrap Cl is derived. Finally, a numerical example is introduced and then a Monte Carlo simulation study is carried out to illustrate the pro- posed method.
文摘We have studied Locally Rotationally Symmetric (LRS) Bianchi type-I cosmological model filled with anisotropic fluid in general theory of relativity. The solutions of the field equations are obtained by using special form of deceleration parameter which gives early deceleration and late time accelerating cosmological model. The geometrical and physical aspect of the model is also studied.
文摘Bianchi Type-I cosmological model in the presence of Saez-Ballester theory gravitation is studied. An exact solution of the field equation is given by considering the cosmological model yield a metric potential included with a real number. The relation between the deceleration parameter and Hubble parameter and average scale factor is used in that cosmological model. The effect of the viscosity on the entropy of the universe is utilized by energy momentum tensor with bulk viscous terms in a conservative manner. We obtained a formula for calculating the entropy of the universe in terms of viscosity and used it to compare to the study. Also, various physical and kinematical properties have been discussed.
基金Supported by National Natural Science Foundation of China(Grant No.11901058).
文摘Firstly, the maximum likelihood estimate and asymptotic confidence interval of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left censored samples, furthermore, the asymptotic confidence interval of reliability function is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian estimates of the unkown parameter and reliability function are obtained, and the expected mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to calculate the mean values and relative errors of the estimates. Finally, an example of life data is analyzed by using the statistical method in this paper.
