Background: A novel approach to modelling individual tree growth dynamics is proposed. The approach combines multiple imputation and copula sampling to produce a stochastic individual tree growth and yield projection...Background: A novel approach to modelling individual tree growth dynamics is proposed. The approach combines multiple imputation and copula sampling to produce a stochastic individual tree growth and yield projection system. Methods: The Nova Scotia, Canada permanent sample plot network is used as a case study to develop and test the modelling approach. Predictions from this model are compared to predictions from the Acadian variant of the Forest Vegetation Simulator, a widely used statistical individual tree growth and yield model. Results: Diameter and height growth rates were predicted with error rates consistent with those produced using statistical models. Mortality and ingrowth error rates were higher than those observed for diameter and height, but also were within the bounds produced by traditional approaches for predicting these rates. Ingrowth species composition was very poorly predicted. The model was capable of reproducing a wide range of stand dynamic trajectories and in some cases reproduced trajectories that the statistical model was incapable of reproducing. Conclusions: The model has potential to be used as a benchmarking tool for evaluating statistical and process models and may provide a mechanism to separate signal from noise and improve our ability to analyze and learn from large regional datasets that often have underlying flaws in sample design.展开更多
The deformation and failure of coal and rock is energy-driving results according to thermodynamics.It is important to study the strain energy characteristics of coal-rock composite samples to better understand the def...The deformation and failure of coal and rock is energy-driving results according to thermodynamics.It is important to study the strain energy characteristics of coal-rock composite samples to better understand the deformation and failure mechanism of of coal-rock composite structures.In this research,laboratory tests and numerical simulation of uniaxial compressions of coal-rock composite samples were carried out with five different loading rates.The test results show that strength,deformation,acoustic emission(AE)and energy evolution of coal-rock composite sample all have obvious loading rate effects.The uniaxial compressive strength and elastic modulus increase with the increase of loading rate.And with the increase of loading rate,the AE energy at the peak strength of coal-rock composites increases first,then decreases,and then increases.With the increase of loading rate,the AE cumulative count first decreases and then increases.And the total absorption energy and dissipation energy of coal-rock composite samples show non-linear increasing trends,while release elastic strain energy increases first and then decreases.The laboratory experiments conducted on coal-rock composite samples were simulated numerically using the particle flow code(PFC).With careful selection of suitable material constitutive models for coal and rock,and accurate estimation and calibration of mechanical parameters of coal-rock composite sample,it was possible to obtain a good agreement between the laboratory experimental and numerical results.This research can provide references for understanding failure of underground coalrock composite structure by using energy related measuring methods.展开更多
The deep cement mixing(DCM)is used to improve the capacity and reduce the settlement of the soft ground by forming cemented clay columns.The investigation on the mechanical behaviour of the DCM samples is limited to e...The deep cement mixing(DCM)is used to improve the capacity and reduce the settlement of the soft ground by forming cemented clay columns.The investigation on the mechanical behaviour of the DCM samples is limited to either laboratory-prepared samples or in-situ samples under unconfined compression.In this study,a series of drained and undrained triaxial shearing tests was performed on the in-situ cored DCM samples with high cement content to assess their mechanical behaviours.It is found that the drainage condition affects significantly the stiffness,peak and residual strengths of the DCM samples,which is mainly due to the state of excess pore water pressure at different strain levels,i.e.being positive before the peak deviatoric stress and negative after the peak deviatoric stress,in the undrained tests.The slope of the failure envelope changes obviously with the confining pressures,being steeper at lower stress levels and flatter at higher stress levels.The strength parameters,effective cohesion and friction angle obtained from lower stress levels(c′0 andφ′0)are 400 kPa and 58°,respectively,which are deemed to be true for design in most DCM applications where the in-situ stress levels are normally at lower values of 50-200 kPa.Additionally,the computed tomography(CT)scanning system was adopted to visualize the internal structures of DCM samples.It is found that the clay pockets existing inside the DCM samples due to uneven mixing affect markedly their stress-strain behaviour,which is one of the main reasons for the high variability of the DCM samples.展开更多
In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals ...In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.展开更多
Riparian areas are unique although often small component of the overall watershed landscape. The structure of riparian forests along Erdaobai River on the north slope of Changbai Mountain were investigated by using fi...Riparian areas are unique although often small component of the overall watershed landscape. The structure of riparian forests along Erdaobai River on the north slope of Changbai Mountain were investigated by using field data collected from eight sampling transects perpendicular to the Erdaobai River channel. Two kinds of species-area saturation curves were used to examine the relationship between species number and minimum sampling area. The results showed that riparian gymnosperms accounted for a high proportion of all gymnosperms in the Changbai Mountain Nature Reserve while riparian ferns and angiosperms accounted for a relatively low proportion. The average minimum sampling areas of riparian forest that included 60%, 80%, and 90% of the community species pool were about 85, 185, and 328 m 2 , respectively; while those for nonriparian forest were about 275, 390, and 514 m 2 , correspondingly.展开更多
The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower...The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.展开更多
It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the pro- priety of the posterior in the nonparame...It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the pro- priety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance compo- nents and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.展开更多
The size and form of sampling units-SU have always been variables considered in planning and structuring forest inventories, being performed in forests or in plantations. The experimental work outlined to deal with th...The size and form of sampling units-SU have always been variables considered in planning and structuring forest inventories, being performed in forests or in plantations. The experimental work outlined to deal with the problem was conducted in an area of araucaria forest, in Sao Joao de Triunfo, PR, Brazil. The forms of sampling units circle, square and rectangular were evaluated, whose areas ranged from 200 m2 to 1000 m2. Time was recorded using a stopwatch and computed separately for locomotion and measurement. The power model was used to adjust the relations of the times of locomotion and measurement, as well as a hyperbolic one for the coefficient of variation, all taking as function of the SUs sizes. To achieve the analytical solution for the optimum size of the SU, it was necessary simulating the behavior of the three functions until the size of 10,000 m2. By taking the derivative of the combined function it was found the maximum point, which allowed optimizing the size of the SU in 600 m2 for the structured experimental conditions. This result proved the formulated hypothesis, performing even a critical analysis of the inclusion of other relevant variables, such as size of the area to be inventoried, number of SUs performed in one day of work, average distance between the SUs, average speeds for locomotion between SUs and for taking all respective measurements.展开更多
The drive towards shorter design cycles for analog integrated circuits has given impetus to the development of Field Programmable Analog Arrays(FPAAs),which are the analogue counterparts of Field Programmable Gate Arr...The drive towards shorter design cycles for analog integrated circuits has given impetus to the development of Field Programmable Analog Arrays(FPAAs),which are the analogue counterparts of Field Programmable Gate Arrays(FPGAs).In this paper,we present a new design methodology which using FPAA as a powerful analog front-end processing platform in the smart sensory microsystem.The proposed FPAA contains 16 homogeneous mixed-grained Configurable Analog Blocks(CABs) which house a variety of processing elements especially the proposed fine-grained Core Configurable Amplifiers(CCAs).The high flexible CABs allow the FPAA operating in both continuous-time and discrete-time approaches suitable to support variety of sensors.To reduce the nonideal parasitic effects and save area,the fat-tree interconnection network is adopted in this FPAA.The functionality of this FPAA is demonstrated through embedding of voltage and capacitive sensor signal readout circuits and a configurable band pass filter.The minimal detectable voltage and capacitor achieves 38 uV and 8.3 aF respectively within 100 Hz sensor bandwidth.The power consumption comparison of CCA in three applications shows that the FPAA has high power efficiency.And the simulation results also show that the FPAA has good tolerance with wide PVT variations.展开更多
Recently,the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential equations.However,for some cases of high-dimensional systems,such tech...Recently,the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential equations.However,for some cases of high-dimensional systems,such technique may be time-consuming and inaccurate.In this paper,the authors put forward a pre-training physics-informed neural network with mixed sampling(pPINN)to address these issues.Just based on the initial and boundary conditions,the authors design the pre-training stage to filter out the set of the misfitting points,which is regarded as part of the training points in the next stage.The authors further take the parameters of the neural network in Stage 1 as the initialization in Stage 2.The advantage of the proposed approach is that it takes less time to transfer the valuable information from the first stage to the second one to improve the calculation accuracy,especially for the high-dimensional systems.To verify the performance of the pPINN algorithm,the authors first focus on the growing-and-decaying mode of line rogue wave in the Davey-Stewartson I equation.Another case is the accelerated motion of lump in the inhomogeneous Kadomtsev-Petviashvili equation,which admits a more complex evolution than the uniform equation.The exact solution provides a perfect sample for data experiments,and can also be used as a reference frame to identify the performance of the algorithm.The experiments confirm that the pPINN algorithm can improve the prediction accuracy and training efficiency well,and reduce the training time to a large extent for simulating nonlinear waves of high-dimensional equations.展开更多
We estimated the proportion of hatchery and natural fall spawning chum salmon returning to the Amur River using chemical markers specific to hatchery-origin fry.We used otolith microchemistry technique to identify fis...We estimated the proportion of hatchery and natural fall spawning chum salmon returning to the Amur River using chemical markers specific to hatchery-origin fry.We used otolith microchemistry technique to identify fish with artificial origin among returning spawners.First,we found that juveniles of artificial origin had higher values of the Sr:Ca molar ratio of the otoliths’edge zone compared with juveniles of natural origin,what can be related to the use of rearing feed produced from raw materials of marine origin rich in strontium.Then we observed that most of the spawners from Anyuisky Hatchery and from the Amur River mouth at the start of the spawning migration has also the higher value of Sr:Ca molar ratio of the juvenile zone of otoliths.Also,adults with higher values of the Sr:Ca molar ratio are characterized by a skewed right in the peak of the age distribution.Both,the age structure and phenological shift in the time of spawning migration of individuals with higher value of the used chemical marker corresponds to results of studies on hatchery-produced chum salmon completed at different parts on Northern Pacific.The results of this study will be used in the management of Amur fall chum salmon fisheries,and also demonstrates the necessity of the development of specific measures for increasing the survival of juvenile anadromous salmonids released at large rivers and exposed to prolonged freshwater migration to the ocean.As a further application of the methodology,we plan to identify the markers specific to each of the hatcheries and main spawning tributaries belonging to Amur River catchments.This will be an important step in the evaluation of the contribution of different stocks in mixed fisheries and also in the estimation of the effect of hatchery releases on naturally spawning stocks of Amur fall chum.Following to,our results may indicate the applicability of this approach for the determination of artificial-origin fish in a mixed sample of the Amur fall chum salmon.展开更多
Suppose {Xn} be a sequence of stationary and φ-mixed random variables (for example, see Ref. [1]), the common unknown probability density of Xn′s is f(x). For each n≥1, the kernel estimators of f(x), based on...Suppose {Xn} be a sequence of stationary and φ-mixed random variables (for example, see Ref. [1]), the common unknown probability density of Xn′s is f(x). For each n≥1, the kernel estimators of f(x), based on X1′,X2′…… XN′, are defined as:展开更多
We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the f...We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.展开更多
文摘Background: A novel approach to modelling individual tree growth dynamics is proposed. The approach combines multiple imputation and copula sampling to produce a stochastic individual tree growth and yield projection system. Methods: The Nova Scotia, Canada permanent sample plot network is used as a case study to develop and test the modelling approach. Predictions from this model are compared to predictions from the Acadian variant of the Forest Vegetation Simulator, a widely used statistical individual tree growth and yield model. Results: Diameter and height growth rates were predicted with error rates consistent with those produced using statistical models. Mortality and ingrowth error rates were higher than those observed for diameter and height, but also were within the bounds produced by traditional approaches for predicting these rates. Ingrowth species composition was very poorly predicted. The model was capable of reproducing a wide range of stand dynamic trajectories and in some cases reproduced trajectories that the statistical model was incapable of reproducing. Conclusions: The model has potential to be used as a benchmarking tool for evaluating statistical and process models and may provide a mechanism to separate signal from noise and improve our ability to analyze and learn from large regional datasets that often have underlying flaws in sample design.
基金Projects(51774196,51804181,51874190)supported by the National Natural Science Foundation of ChinaProject(2019GSF111020)supported by the Key R&D Program of Shandong Province,ChinaProject(201908370205)supported by the China Scholarship Council。
文摘The deformation and failure of coal and rock is energy-driving results according to thermodynamics.It is important to study the strain energy characteristics of coal-rock composite samples to better understand the deformation and failure mechanism of of coal-rock composite structures.In this research,laboratory tests and numerical simulation of uniaxial compressions of coal-rock composite samples were carried out with five different loading rates.The test results show that strength,deformation,acoustic emission(AE)and energy evolution of coal-rock composite sample all have obvious loading rate effects.The uniaxial compressive strength and elastic modulus increase with the increase of loading rate.And with the increase of loading rate,the AE energy at the peak strength of coal-rock composites increases first,then decreases,and then increases.With the increase of loading rate,the AE cumulative count first decreases and then increases.And the total absorption energy and dissipation energy of coal-rock composite samples show non-linear increasing trends,while release elastic strain energy increases first and then decreases.The laboratory experiments conducted on coal-rock composite samples were simulated numerically using the particle flow code(PFC).With careful selection of suitable material constitutive models for coal and rock,and accurate estimation and calibration of mechanical parameters of coal-rock composite sample,it was possible to obtain a good agreement between the laboratory experimental and numerical results.This research can provide references for understanding failure of underground coalrock composite structure by using energy related measuring methods.
基金funded by the Environment and Conservation Fund(Grant Nos.2020-170 and 2021-156)the National Natural Science Foundation of China(Grant No.42102327).
文摘The deep cement mixing(DCM)is used to improve the capacity and reduce the settlement of the soft ground by forming cemented clay columns.The investigation on the mechanical behaviour of the DCM samples is limited to either laboratory-prepared samples or in-situ samples under unconfined compression.In this study,a series of drained and undrained triaxial shearing tests was performed on the in-situ cored DCM samples with high cement content to assess their mechanical behaviours.It is found that the drainage condition affects significantly the stiffness,peak and residual strengths of the DCM samples,which is mainly due to the state of excess pore water pressure at different strain levels,i.e.being positive before the peak deviatoric stress and negative after the peak deviatoric stress,in the undrained tests.The slope of the failure envelope changes obviously with the confining pressures,being steeper at lower stress levels and flatter at higher stress levels.The strength parameters,effective cohesion and friction angle obtained from lower stress levels(c′0 andφ′0)are 400 kPa and 58°,respectively,which are deemed to be true for design in most DCM applications where the in-situ stress levels are normally at lower values of 50-200 kPa.Additionally,the computed tomography(CT)scanning system was adopted to visualize the internal structures of DCM samples.It is found that the clay pockets existing inside the DCM samples due to uneven mixing affect markedly their stress-strain behaviour,which is one of the main reasons for the high variability of the DCM samples.
基金Supported by the National Natural Science Foundation of China(11271088,11361011,11201088)the Natural Science Foundation of Guangxi(2013GXNSFAA019004,2013GXNSFAA019007,2013GXNSFBA019001)
文摘In this paper, we obtain the joint empirical likelihood confidence regions for a finite number of quantiles under strong mixing samples. As an application of this result, the empirical likelihood confidence intervals for the difference of any two quantiles are also obtained.
基金supported by the Ministry of Science and Technology of the People's Republic of China (2006BAD03A09)the Special Fund of State Key Laboratory of Urban and Regional Ecology
文摘Riparian areas are unique although often small component of the overall watershed landscape. The structure of riparian forests along Erdaobai River on the north slope of Changbai Mountain were investigated by using field data collected from eight sampling transects perpendicular to the Erdaobai River channel. Two kinds of species-area saturation curves were used to examine the relationship between species number and minimum sampling area. The results showed that riparian gymnosperms accounted for a high proportion of all gymnosperms in the Changbai Mountain Nature Reserve while riparian ferns and angiosperms accounted for a relatively low proportion. The average minimum sampling areas of riparian forest that included 60%, 80%, and 90% of the community species pool were about 85, 185, and 328 m 2 , respectively; while those for nonriparian forest were about 275, 390, and 514 m 2 , correspondingly.
基金The NSF (11201001,11171001,11126176) of Chinathe NSF (1208085QA03) of Anhui Province+2 种基金Provincial Natural Science Research Project (KJ2010A005) of Anhui CollegesDoctoral Research Start-up Funds Projects of Anhui Universitythe Students’ Innovative Training Project (2012003) of Anhui University
文摘The strong consistency of M estimator of regression parameter in linear model for φ-mixing samples is discussed by using the classic Rosenthal type inequality. We get the strong consistency of M estimator under lower moment condition, which generalizes and improves the corresponding ones for independent sequences.
基金supported by the Natural Science Foundation of China(11201345,11271136)
文摘It is well known that spline smoothing estimator relates to the Bayesian estimate under partially informative normal prior. In this paper, we derive the conditions for the pro- priety of the posterior in the nonparametric mixed effects model under this class of partially informative normal prior for fixed effect with inverse gamma priors on the variance compo- nents and hierarchical priors for covariance matrix of random effect, then we explore the Gibbs sampling procedure.
文摘The size and form of sampling units-SU have always been variables considered in planning and structuring forest inventories, being performed in forests or in plantations. The experimental work outlined to deal with the problem was conducted in an area of araucaria forest, in Sao Joao de Triunfo, PR, Brazil. The forms of sampling units circle, square and rectangular were evaluated, whose areas ranged from 200 m2 to 1000 m2. Time was recorded using a stopwatch and computed separately for locomotion and measurement. The power model was used to adjust the relations of the times of locomotion and measurement, as well as a hyperbolic one for the coefficient of variation, all taking as function of the SUs sizes. To achieve the analytical solution for the optimum size of the SU, it was necessary simulating the behavior of the three functions until the size of 10,000 m2. By taking the derivative of the combined function it was found the maximum point, which allowed optimizing the size of the SU in 600 m2 for the structured experimental conditions. This result proved the formulated hypothesis, performing even a critical analysis of the inclusion of other relevant variables, such as size of the area to be inventoried, number of SUs performed in one day of work, average distance between the SUs, average speeds for locomotion between SUs and for taking all respective measurements.
基金Supported by the CAS/SAFEA International Partnership Program for Creative Research Teams,National High Technology Research and Develop Program of China(2012AA012301)National Science and Technology Major Project of China(2013ZX03006004)
文摘The drive towards shorter design cycles for analog integrated circuits has given impetus to the development of Field Programmable Analog Arrays(FPAAs),which are the analogue counterparts of Field Programmable Gate Arrays(FPGAs).In this paper,we present a new design methodology which using FPAA as a powerful analog front-end processing platform in the smart sensory microsystem.The proposed FPAA contains 16 homogeneous mixed-grained Configurable Analog Blocks(CABs) which house a variety of processing elements especially the proposed fine-grained Core Configurable Amplifiers(CCAs).The high flexible CABs allow the FPAA operating in both continuous-time and discrete-time approaches suitable to support variety of sensors.To reduce the nonideal parasitic effects and save area,the fat-tree interconnection network is adopted in this FPAA.The functionality of this FPAA is demonstrated through embedding of voltage and capacitive sensor signal readout circuits and a configurable band pass filter.The minimal detectable voltage and capacitor achieves 38 uV and 8.3 aF respectively within 100 Hz sensor bandwidth.The power consumption comparison of CCA in three applications shows that the FPAA has high power efficiency.And the simulation results also show that the FPAA has good tolerance with wide PVT variations.
文摘Recently,the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential equations.However,for some cases of high-dimensional systems,such technique may be time-consuming and inaccurate.In this paper,the authors put forward a pre-training physics-informed neural network with mixed sampling(pPINN)to address these issues.Just based on the initial and boundary conditions,the authors design the pre-training stage to filter out the set of the misfitting points,which is regarded as part of the training points in the next stage.The authors further take the parameters of the neural network in Stage 1 as the initialization in Stage 2.The advantage of the proposed approach is that it takes less time to transfer the valuable information from the first stage to the second one to improve the calculation accuracy,especially for the high-dimensional systems.To verify the performance of the pPINN algorithm,the authors first focus on the growing-and-decaying mode of line rogue wave in the Davey-Stewartson I equation.Another case is the accelerated motion of lump in the inhomogeneous Kadomtsev-Petviashvili equation,which admits a more complex evolution than the uniform equation.The exact solution provides a perfect sample for data experiments,and can also be used as a reference frame to identify the performance of the algorithm.The experiments confirm that the pPINN algorithm can improve the prediction accuracy and training efficiency well,and reduce the training time to a large extent for simulating nonlinear waves of high-dimensional equations.
基金support of the grant of the Ministry of Science and Higher Education of the Russian Federation project No.2019-0858"Biogeochemical and geochemical studies of landscapes in the conditions of the development of mineral deposits,the search for new methods of monitoring and forecasting the State of the environment".
文摘We estimated the proportion of hatchery and natural fall spawning chum salmon returning to the Amur River using chemical markers specific to hatchery-origin fry.We used otolith microchemistry technique to identify fish with artificial origin among returning spawners.First,we found that juveniles of artificial origin had higher values of the Sr:Ca molar ratio of the otoliths’edge zone compared with juveniles of natural origin,what can be related to the use of rearing feed produced from raw materials of marine origin rich in strontium.Then we observed that most of the spawners from Anyuisky Hatchery and from the Amur River mouth at the start of the spawning migration has also the higher value of Sr:Ca molar ratio of the juvenile zone of otoliths.Also,adults with higher values of the Sr:Ca molar ratio are characterized by a skewed right in the peak of the age distribution.Both,the age structure and phenological shift in the time of spawning migration of individuals with higher value of the used chemical marker corresponds to results of studies on hatchery-produced chum salmon completed at different parts on Northern Pacific.The results of this study will be used in the management of Amur fall chum salmon fisheries,and also demonstrates the necessity of the development of specific measures for increasing the survival of juvenile anadromous salmonids released at large rivers and exposed to prolonged freshwater migration to the ocean.As a further application of the methodology,we plan to identify the markers specific to each of the hatcheries and main spawning tributaries belonging to Amur River catchments.This will be an important step in the evaluation of the contribution of different stocks in mixed fisheries and also in the estimation of the effect of hatchery releases on naturally spawning stocks of Amur fall chum.Following to,our results may indicate the applicability of this approach for the determination of artificial-origin fish in a mixed sample of the Amur fall chum salmon.
文摘Suppose {Xn} be a sequence of stationary and φ-mixed random variables (for example, see Ref. [1]), the common unknown probability density of Xn′s is f(x). For each n≥1, the kernel estimators of f(x), based on X1′,X2′…… XN′, are defined as:
基金supported by the Natural Science Foundation of Xinjiang Uygur Autonomous Region of China(2019D01A05)supported by the NSFC(11571132)。
文摘We consider the interior inverse scattering problem for recovering the shape of a penetrable partially coated cavity with external obstacles from the knowledge of measured scattered waves due to point sources.In the first part,we obtain the well-posedness of the direct scattering problem by the variational method.In the second part,we establish the mathematical basis of the linear sampling method to recover both the shape of the cavity,and the shape of the external obstacle,however the exterior transmission eigenvalue problem also plays a key role in the discussion of this paper.