This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
Interval-valued pre-aggregation functions are a hot topic in the research of aggregation functions and have received considerable attention in recent years.As a special class of interval-valued pre-aggregation functio...Interval-valued pre-aggregation functions are a hot topic in the research of aggregation functions and have received considerable attention in recent years.As a special class of interval-valued pre-aggregation functions,(light)interval-valued pre-t-norms were initially proposed by Wang and Hu,but their properties were not further discussed by the authors.The main purpose of this paper is to study in depth the properties and generation of(light)intervalvalued pre-t-norms.Firstly,several properties of(light)interval-valued pre-t-norms and their relationship with(light)pre-t-norms are presented.Then,two different generation methods for(light)interval-valued pre-t-norms are introduced.Finally,it demonstrates a specific application of(light)interval-valued pre-t-norms in constructing interval-valued directional monotonic fuzzy implications,namely,using the(light)interval-valued pre-t-norm IT,interval-valued fuzzy negations IN,and(light)interval-valued pre-t-conorm IS to construct interval-valued QL-directional monotonic operations.展开更多
This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case ...This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).展开更多
Seabed soils’stress-strain relationships are nonlinear,and the complexity associated with soil constitutive behavior increases substantially as the loading becomes reversed.This study focuses on the constitutive beha...Seabed soils’stress-strain relationships are nonlinear,and the complexity associated with soil constitutive behavior increases substantially as the loading becomes reversed.This study focuses on the constitutive behavior of cohesive seabed soils under monotonic and cyclic wave loadings.The theoretical framework developed is based on Bounding Surface Plasticity,where soil strain-hardening is addressed through a proposed hardening law to calculate plastic strains and their evolution during the loading history.Considering clays and clay-like cohesive soils located mainly on the surface of the seabed,the plastic hardening modulus is updated using deviatoric plastic strains,and a new degradation function,which is a novel contribution in the study,is developed and incorporated into the theoretical framework.The proposed model,whose mathematical formulation is more practical and simpler compared to other similar models for cohesive seabed soils,is integrated into a computer program using an explicit numerical scheme.Then,several drained and undrained monotonic and cyclic triaxial tests for normally and over-consolidated clays are simulated to verify the proposed constitutive formulation.Results indicate that simulations of cyclic triaxial tests using the proposed model successfully capture the essential static and dynamic behavior of cohesive seabed soils,including large number of load cycles.The proposed model stands out with its predictive power and the simplification advantage it brings to the theory through the hardening law compared to previous models,as successfully demonstrated in this study.The proposed model can be used in solving coastal and offshore geotechnical engineering problems with high accuracy.展开更多
This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Ya...This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Yan et al.(Math.Model.Anal.,19,537-555,2014).展开更多
On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial ...On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.展开更多
In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coeffi...In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.展开更多
This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tai...This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.展开更多
In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(...In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(4)(50x+41)^(2),x>0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).展开更多
This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having...This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.展开更多
In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-subspaces. For a generalized ordered （GO）-space X, we also show that X is mon...In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-subspaces. For a generalized ordered （GO）-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X＊ is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.展开更多
Monotonic lateral load model tests were carried out on steel skirted suction caissons embedded in the saturated medium sand to study the bearing capacity. A three-dimensional continuum finite element model was develop...Monotonic lateral load model tests were carried out on steel skirted suction caissons embedded in the saturated medium sand to study the bearing capacity. A three-dimensional continuum finite element model was developed with Z_SOIL software. The numerical model was calibrated against experimental results. Soil deformation and earth pressures on skirted caissons were investigated by using the finite element model to extend the model tests. It shows that the ＂skirted＂ structure can significantly increase the lateral capacity and limit the deflection, especially suitable for offshore wind turbines, compared with regular suction caissons without the ＂skirted＂ at the same load level. In addition, appropriate determination of rotation centers plays a crucial role in calculating the lateral capacity by using the analytical method. It was also found that the rotation center is related to dimensions of skirted suction caissons and loading process, i.e. the rotation center moves upwards with the increase of the ＂skirted＂ width and length; moreover, the rotation center moves downwards with the increase of loading and keeps constant when all the sand along the caisson＇s wall yields. It is so complex that we cannot simply determine its position like the regular suction caisson commonly with a specified position to the length ratio of the caisson.展开更多
This paper presents a model to simulate the monotonic and cyclic behaviours of weakly cemented sands.An elastoplastic constitutive model within the framework of bounding surface plasticity theory is adopted to predict...This paper presents a model to simulate the monotonic and cyclic behaviours of weakly cemented sands.An elastoplastic constitutive model within the framework of bounding surface plasticity theory is adopted to predict the mechanical behaviour of soft sandstone under monotonic and cyclic loadings. In this model, the loading surface always passes through the current stress state regardless of the type of loading. Destruction of the cementation bonds by plastic deformation in the model is considered as the primary mechanism responsible for the mechanical degradation of loosely cemented sands/weak rock.To model cyclic response, the unloading plastic and elastic moduli are formulated based on the loading/reloading plastic and elastic moduli. The proposed model was implemented in FLAC2D and evaluated against laboratory triaxial tests under monotonic and cyclic loadings, and the model results agreed well with the experimental observations. For cyclic tests, hysteresis loops are captured with reasonable accuracy.展开更多
The modified suction caisson(MSC) is a novel type of foundation for ocean engineering, consisting of a short external closed-top cylinder-shaped structure surrounding the upper part of the regular suction caisson(RSC)...The modified suction caisson(MSC) is a novel type of foundation for ocean engineering, consisting of a short external closed-top cylinder-shaped structure surrounding the upper part of the regular suction caisson(RSC). The MSC can provide larger lateral bearing capacity and limit the deflection compared with the RSC. Therefore, the MSC can be much more appropriate to use as an offshore wind turbine foundation. Model tests on the MSC in saturated sand subjected to monotonic lateral loading were carried out to investigate the effects of external structure sizes on the sand surface deformation and the earth pressure distribution along the embedded depth. Test results show that the deformation range of the sand surface increases with the increasing width and length of the external structure. The magnitude of sand upheaval around the MSC is smaller than that of the RSC and the sand upheaval value around the MSC in the loading direction decreases with the increasing external structure dimensions. The net earth pressure in the loading direction acting on the internal compartment of the MSC is smaller than that of the RSC at the same embedded depth. The maximum net earth pressure acting on the external structure outer wall in the loading direction is larger than that of the internal compartment, indicating that a considerable amount of the lateral load and moment is resisted by the external skirt structure.展开更多
In this study the stress–strain characteristics of sand-ground rubber mixtures are investigated in the sandlike zone,at different confining pressures,using hollow cylinder specimens subjected to torsional monotonic a...In this study the stress–strain characteristics of sand-ground rubber mixtures are investigated in the sandlike zone,at different confining pressures,using hollow cylinder specimens subjected to torsional monotonic and cyclic loading.Under monotonic loading a mixture of sand-ground rubber with 10% and 25% rubber content show more contraction behaviour than that observed in a pure sand specimen.Phase transformation point in these mixtures are located on a larger shear strain.As expected,the shear strength of specimens decreases with increase of ground rubber content.However,with increasing of effective confining pressure,the loss in shear strength of the mixture is decreased.In addition,a mixture with 25% ground rubber shows a smaller loss in shear strength compared to a mixture with 10% ground rubber mixture.Under cyclic loading mixtures with 10% and 25% ground rubber have similar liquefaction resistance,especially at confining pressures of 110 k Pa and 260 k Pa.Therefore,by using of the mixture with 25% ground rubber,a larger volume of scrap tires could be recycled.The addition of ground rubber to sand would affect the shear strain variation and excess pore water pressure trends,and this effect was further intensified with increasing ground rubber percentage.展开更多
In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma fu...In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].展开更多
The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizonta...The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.展开更多
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金the National Natural Science Foundation of China(Grant No.12171294)。
文摘Interval-valued pre-aggregation functions are a hot topic in the research of aggregation functions and have received considerable attention in recent years.As a special class of interval-valued pre-aggregation functions,(light)interval-valued pre-t-norms were initially proposed by Wang and Hu,but their properties were not further discussed by the authors.The main purpose of this paper is to study in depth the properties and generation of(light)intervalvalued pre-t-norms.Firstly,several properties of(light)interval-valued pre-t-norms and their relationship with(light)pre-t-norms are presented.Then,two different generation methods for(light)interval-valued pre-t-norms are introduced.Finally,it demonstrates a specific application of(light)interval-valued pre-t-norms in constructing interval-valued directional monotonic fuzzy implications,namely,using the(light)interval-valued pre-t-norm IT,interval-valued fuzzy negations IN,and(light)interval-valued pre-t-conorm IS to construct interval-valued QL-directional monotonic operations.
基金Supported by the National Natural Science Foundation of China(12071162)the Natural Science Foundation of Fujian Province(2021J01302)the Fundamental Research Funds for the Central Universities(ZQN-802)。
文摘This paper deals with the monotonicity of limit wave speed c0(h)to a perturbed g KdV equation.We show the decrease of c0(h)by combining the analytic method and the numerical technique.Our results solve a special case of the open question presented by Yan et al.,and the method potentially provides a way to study the monotonicity of c0(h)for general m∈N^(+).
基金funded by the Istanbul Technical University Research Projects Unit(BAP)with project number 37606.
文摘Seabed soils’stress-strain relationships are nonlinear,and the complexity associated with soil constitutive behavior increases substantially as the loading becomes reversed.This study focuses on the constitutive behavior of cohesive seabed soils under monotonic and cyclic wave loadings.The theoretical framework developed is based on Bounding Surface Plasticity,where soil strain-hardening is addressed through a proposed hardening law to calculate plastic strains and their evolution during the loading history.Considering clays and clay-like cohesive soils located mainly on the surface of the seabed,the plastic hardening modulus is updated using deviatoric plastic strains,and a new degradation function,which is a novel contribution in the study,is developed and incorporated into the theoretical framework.The proposed model,whose mathematical formulation is more practical and simpler compared to other similar models for cohesive seabed soils,is integrated into a computer program using an explicit numerical scheme.Then,several drained and undrained monotonic and cyclic triaxial tests for normally and over-consolidated clays are simulated to verify the proposed constitutive formulation.Results indicate that simulations of cyclic triaxial tests using the proposed model successfully capture the essential static and dynamic behavior of cohesive seabed soils,including large number of load cycles.The proposed model stands out with its predictive power and the simplification advantage it brings to the theory through the hardening law compared to previous models,as successfully demonstrated in this study.The proposed model can be used in solving coastal and offshore geotechnical engineering problems with high accuracy.
基金Supported by the National Natural Science Foundation of China (12071162)the Natural Science Foundation of Fujian Province (2025J01168)。
文摘This paper concerns the monotonicity of limit wave speed c0(h) for the perturbed g Kd V equation with general even m.We show that c0(h) is decreasing.Our results give partial answer to the open problem presented by Yan et al.(Math.Model.Anal.,19,537-555,2014).
文摘On the basis of the paoers[3—7],this paper study the monotonicity problems for the positive semidefinite generalized inverses of the positive semidefinite self-conjugate matrices of quaternions in the Lowner partial order,give the explicit formulations of the monotonicity solution sets A{1;≥,T_1;≤B^(1)}and B{1;≥,T_2≥A^(1)}for the(1)-inverse,and two results of the monotonicity charac teriaztion for the(1,2)-inverse.
基金supported by the National Science Foundation of China(11271248 and 11302002)the National Science Research Project of Anhui Educational Department(KJ2012Z127)the PhD research startup foundation of Anhui Normal University
文摘In Orlicz-Lorentz sequence space Aψ,w with the Orlicz norm, uniform monotonic- ity, points of upper local uniform monotonicity and lower local uniform monotonicity are characterized. Moreover, the monotonicity coefficient in Aψ,w are discussed.
基金The National Natural Science Foundation of China(No.11001052,11171065)the National Science Foundation of Jiangsu Province(No.BK2011058)the Science Foundation of Nanjing University of Posts and Telecommunications(No.JG00710JX57)
文摘This paper considers the upper orthant and extremal tail dependence indices for multivariate t-copula. Where, the multivariate t-copula is defined under a correlation structure. The explicit representations of the tail dependence parameters are deduced since the copula of continuous variables is invariant under strictly increasing transformation about the random variables, which are more simple than those obtained in previous research. Then, the local monotonicity of these indices about the correlation coefficient is discussed, and it is concluded that the upper extremal dependence index increases with the correlation coefficient, but the monotonicity of the upper orthant tail dependence index is complex. Some simulations are performed by the Monte Carlo method to verify the obtained results, which are found to be satisfactory. Meanwhile, it is concluded that the obtained conclusions can be extended to any distribution family in which the generating random variable has a regularly varying distribution.
文摘In this paper,we study the completely monotonic property of two functions involving the functionΔ(x)=[ψ′(x)]2+ψ″(x)and deduce the double inequality x^(2)+3x+3/3x^(4)(2x+1)^(2)<Δ(x)<625x^(2)+2275x+5043/3x^(4)(50x+41)^(2),x>0which improve some recent results,whereψ(x)is the logarithmic derivative of the Gamma function.Also,we deduce the completely monotonic degree of a function involvingψ′(x).
文摘This paper investigates Buck＇s question about which class of spaces is strongly monotonically T2,and if other properties are combined with strongly monotonically T2,which class of spaces could be got. Based on having a cushioned pair-base space and compact strongly monotonically T2 space,some results （Theorems 1--3） are obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11271036)Beijing Natural Science Foundation(Grant No.1102002)Doctoral Fund of Innovation of Beijing University of Technology
文摘In the first part of this note, we mainly prove that monotone metacompactness is hereditary with respect to closed subspaces and open Fσ-subspaces. For a generalized ordered （GO）-space X, we also show that X is monotonically metacompact if and only if its closed linearly ordered extension X＊ is monotonically metacompact. We also point out that every non-Archimedean space X is monotonically ultraparacompact. In the second part of this note, we give an alternate proof of the result that McAuley space is paracompact and metacompact.
基金financially supported by the National Natural Science Foundation of China(Grant No.51078227)Shandong Natural Science Foundation(Grant No.ZR2009FM003)
文摘Monotonic lateral load model tests were carried out on steel skirted suction caissons embedded in the saturated medium sand to study the bearing capacity. A three-dimensional continuum finite element model was developed with Z_SOIL software. The numerical model was calibrated against experimental results. Soil deformation and earth pressures on skirted caissons were investigated by using the finite element model to extend the model tests. It shows that the ＂skirted＂ structure can significantly increase the lateral capacity and limit the deflection, especially suitable for offshore wind turbines, compared with regular suction caissons without the ＂skirted＂ at the same load level. In addition, appropriate determination of rotation centers plays a crucial role in calculating the lateral capacity by using the analytical method. It was also found that the rotation center is related to dimensions of skirted suction caissons and loading process, i.e. the rotation center moves upwards with the increase of the ＂skirted＂ width and length; moreover, the rotation center moves downwards with the increase of loading and keeps constant when all the sand along the caisson＇s wall yields. It is so complex that we cannot simply determine its position like the regular suction caisson commonly with a specified position to the length ratio of the caisson.
基金Funding for this project has been provided by BP Canada and the Nature Science and Engineering Research Council of Canada(NSERC)
文摘This paper presents a model to simulate the monotonic and cyclic behaviours of weakly cemented sands.An elastoplastic constitutive model within the framework of bounding surface plasticity theory is adopted to predict the mechanical behaviour of soft sandstone under monotonic and cyclic loadings. In this model, the loading surface always passes through the current stress state regardless of the type of loading. Destruction of the cementation bonds by plastic deformation in the model is considered as the primary mechanism responsible for the mechanical degradation of loosely cemented sands/weak rock.To model cyclic response, the unloading plastic and elastic moduli are formulated based on the loading/reloading plastic and elastic moduli. The proposed model was implemented in FLAC2D and evaluated against laboratory triaxial tests under monotonic and cyclic loadings, and the model results agreed well with the experimental observations. For cyclic tests, hysteresis loops are captured with reasonable accuracy.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51639002 and 51379118)the SDUST Research Fund(Grant No.2015KYTD104)
文摘The modified suction caisson(MSC) is a novel type of foundation for ocean engineering, consisting of a short external closed-top cylinder-shaped structure surrounding the upper part of the regular suction caisson(RSC). The MSC can provide larger lateral bearing capacity and limit the deflection compared with the RSC. Therefore, the MSC can be much more appropriate to use as an offshore wind turbine foundation. Model tests on the MSC in saturated sand subjected to monotonic lateral loading were carried out to investigate the effects of external structure sizes on the sand surface deformation and the earth pressure distribution along the embedded depth. Test results show that the deformation range of the sand surface increases with the increasing width and length of the external structure. The magnitude of sand upheaval around the MSC is smaller than that of the RSC and the sand upheaval value around the MSC in the loading direction decreases with the increasing external structure dimensions. The net earth pressure in the loading direction acting on the internal compartment of the MSC is smaller than that of the RSC at the same embedded depth. The maximum net earth pressure acting on the external structure outer wall in the loading direction is larger than that of the internal compartment, indicating that a considerable amount of the lateral load and moment is resisted by the external skirt structure.
文摘In this study the stress–strain characteristics of sand-ground rubber mixtures are investigated in the sandlike zone,at different confining pressures,using hollow cylinder specimens subjected to torsional monotonic and cyclic loading.Under monotonic loading a mixture of sand-ground rubber with 10% and 25% rubber content show more contraction behaviour than that observed in a pure sand specimen.Phase transformation point in these mixtures are located on a larger shear strain.As expected,the shear strength of specimens decreases with increase of ground rubber content.However,with increasing of effective confining pressure,the loss in shear strength of the mixture is decreased.In addition,a mixture with 25% ground rubber shows a smaller loss in shear strength compared to a mixture with 10% ground rubber mixture.Under cyclic loading mixtures with 10% and 25% ground rubber have similar liquefaction resistance,especially at confining pressures of 110 k Pa and 260 k Pa.Therefore,by using of the mixture with 25% ground rubber,a larger volume of scrap tires could be recycled.The addition of ground rubber to sand would affect the shear strain variation and excess pore water pressure trends,and this effect was further intensified with increasing ground rubber percentage.
文摘In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].
基金Supported by the National Natural science Foundation of China(10701035)ChenGuang Project of Shang-hai Education Development Foundation(2007CG33)a Special Fund for Young Teachers in Shanghai Universities(79001320)
文摘The single-index model with monotonic link function is investigated. Firstly, it is showed that the link function h（.） can be viewed by a graphic method. That is, the plot with the fitted response y on the horizontal axis and the observed y on the vertical axis can be used to visualize the link function. It is pointed out that this graphic approach is also applicable even when the link function is not monotonic. Note that many existing nonparametric smoothers can also be used to assess h（.）. Therefore, the I-spline approximation of the link function via maximizing the covariance function with a penalty function is investigated in the present work. The consistency of the criterion is constructed. A small simulation is carried out to evidence the efficiency of the approach proposed in the paper.
