We present an application of short-pulse laser-generated hard x rays for the diagnosis of indirectly driven double shell targets. Coneinserted double shell targets were imploded through an indirect drive approach on t...We present an application of short-pulse laser-generated hard x rays for the diagnosis of indirectly driven double shell targets. Coneinserted double shell targets were imploded through an indirect drive approach on the upgraded SG-II laser facility. Then, based on thepoint-projection hard x-ray radiography technique, time-resolved radiography of the double shell targets, including that of their near-peakcompression, were obtained. The backlighter source was created by the interactions of a high-intensity short pulsed laser with a metalmicrowire target. Images of the target near peak compression were obtained with an Au microwire. In addition, radiation hydrodynamicsimulations were performed, and the target evolution obtained agrees well with the experimental results. Using the radiographic images, arealdensities of the targets were evaluated.展开更多
We will consider an extension of a direct method due to Griewank and Reddien for the computation of double symmetry-breaking turning points which arise in the two-parameter dependent nonlinear problem of the form f(x,...We will consider an extension of a direct method due to Griewank and Reddien for the computation of double symmetry-breaking turning points which arise in the two-parameter dependent nonlinear problem of the form f(x,λ,μ)= 0. The method proposed could produce an extended system which does not introduce the null vectors as variables, and could therefore reduce the computational effort and storage. One numerical example is presented to demonstrate that the method is efficient.展开更多
We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vec...We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.展开更多
Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance ...Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.展开更多
The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional(3D)stagnation point body is studied under a microgravity environment.The effects of g-jitter and thermal radiation e...The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional(3D)stagnation point body is studied under a microgravity environment.The effects of g-jitter and thermal radiation exist under the microgravity environment,where there is a gravitational field with fluctuations.The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition.With the semi-similar transformation technique,the dimensional system of equations is reduced into a dimensionless system of equations,where the dependent variables of the problem are lessened.A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method,which is an implicit finite difference approach.The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics,the heat transfer properties,and the concentration distributions.The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body,where the stagnation point is located.The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied,where the fluctuating range becomes smaller when the oscillation frequency increases.Moreover,the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux,and the thermal radiation could increase the heat transfer properties.展开更多
To better reflect the psychological behavior characteristics of loss aversion,this paper builds a double reference point decision making method for dynamic multi-attribute decision-making(DMADM)problem,taking bottom-l...To better reflect the psychological behavior characteristics of loss aversion,this paper builds a double reference point decision making method for dynamic multi-attribute decision-making(DMADM)problem,taking bottom-line and target as reference pints.First,the gain/loss function is given,and the state is divided according to the relationship between the gain/loss value and the reference point.Second,the attitude function is constructed based on the results of state division to establish the utility function.Third,the comprehensive utility value is calculated as the basis for alternatives classification and ranking.Finally,the new method is used to evaluate the development level of smart cities.The results show that the new method can judge the degree to which the alternatives meet the requirements of the decision-maker.While the new method can effectively screen out the unsatisfactory alternatives,the ranking results of other alternatives are consistent with those of traditional methods.展开更多
In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered B...In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.展开更多
We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems...We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems to determine double high order S-breaking bifurcation points. and we could also show that there exist two quadratic pitchfork bifurcation point paths passing through the point being considered.展开更多
The "double low-points" anomaly in daily variation of vertical geomagnetic component was observed on May 9, 2008 at 13 geomagnetic observatories belonging to the geomagnetic observatory network center of China Earth...The "double low-points" anomaly in daily variation of vertical geomagnetic component was observed on May 9, 2008 at 13 geomagnetic observatories belonging to the geomagnetic observatory network center of China Earthquake Administration. These observatories distribute roughly on three belts with the intersection in western Sichuan. On May 12, three days after the anomaly appearance, the great Ms8.0 Wenchuan earthquake occurred. The "double low-points" anomaly in daily variation of vertical geomagnetic component is an anomalous phenomenon of regional geomagnetism, which does exist objectively. The possible cause is the change of extrinsic eddy current system resulting in geomagnetic daily quiet variation (Sq), or the delay of several hours between the intrinsic and the extrinsic eddy current systems. The relationship between the "double low-points" anomaly of daily geomagnetic variation and the earthquake reveals that the former possibly reflects the accelerative alteration of earthquake gestation in the deep Earth.展开更多
AIM: To present an inclusion criterion for patients who have suffered bilateral amputation in order to be treated with the supplementary resuscitation treatment which is hereby proposed by the author.METHODS: This wor...AIM: To present an inclusion criterion for patients who have suffered bilateral amputation in order to be treated with the supplementary resuscitation treatment which is hereby proposed by the author.METHODS: This work is based on a Retrospective Cohort model so that a certainly lethal risk to the control group is avoided.RESULTS: This paper presents a hypothesis on acupunctural PC-9 Zhong chong point, further supported by previous statistical work recorded for the K-1 Yong quan resuscitation point.CONCLUSION: Thanks to the application of the resuscitation maneuver herein proposed on the previously mentioned point, patients with bilateral amputation would have another alternative treatment available in case basic and advanced CPR should fail.展开更多
Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent ...Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent decades.The reported research presents the double snap-through mechanism applied to a hemispheric point absorber type wave energy converter(WEC)to improve the energy absorption perfomance.The double snap-through mechanism comprises four oblique springs mounted in an X-configuration.This provides the WEC with different dynamic stability behaviors depending on the particular geometric and physical parameters employed.The efficiency of these different WEC behaviors(linear,bistable,and tristable)was initially evaluated under the action of regular waves.The results for bistable or tristable responses indicated significant improvements in the WEC's energy capture efficiency.Furthermore,the WEC frequency bandwidth was shown to be significantly enlarged when the tristable mode was in operation.However,the corresponding tristable trajectory showed intra-well behavior in the middle potential well,which induced a more severe low-energy absorption when a small wave amplitude acted on the WEC compared to when the bistable WEC was employed.Nevertheless,positive effects were observed when appropriate initial conditions were imposed.The results also showed that for bistable or tristable responses,a suitable spring stiffness may cause the buoy to oscillate in high energy modes.展开更多
Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning poin...Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning points and triple S bieaking turning points,one ts quadratic turning pornt path and one is quadratic pitch fork bifurcation point path.Some simple regular extended systems to corn pute double and triple S-breaking turning points are proposed.Numerical examples are also展开更多
In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,...In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].展开更多
In the investigation, the complex geometric domain is a concave geometrical pattern. Due to the symmetric character, the left side of the geometric pattern,?i.e.?the L-shaped region is calculated in the study. The gov...In the investigation, the complex geometric domain is a concave geometrical pattern. Due to the symmetric character, the left side of the geometric pattern,?i.e.?the L-shaped region is calculated in the study. The governing equation is expressed with?Laplace?equations. And the analysis is solved by eigenfunction expansion and point-match method. Besides, visual?C++?helps obtain the results of numerical calculation. The local values and the mean values of the function are also discussed in this study.展开更多
Wind loads have instantaneity and turbulence characteristics that will lead to pointing errors in antenna structures,and these errors cannot be ignored in high-frequency observations.Using the Tianma 65 m radio telesc...Wind loads have instantaneity and turbulence characteristics that will lead to pointing errors in antenna structures,and these errors cannot be ignored in high-frequency observations.Using the Tianma 65 m radio telescope(TMRT)as an example object,the pointing errors caused by wind loads are investigated using an accelerometer system.First,the resonant frequency range of the antenna structure is used for reference to acquire useful signals through the bandpass filtering method.Then,the direct current(DC)component of these signals is filtered out using the fast discrete Fourier transform method,and the baseline of the acceleration is corrected using the least-squares method.Finally,the acceleration integral is solved approximately using the discrete trapezoidal area method,and the structural vibration displacement of the antenna is determined using a double integral of acceleration.The pointing errors are then obtained based on the displacement relationship between the primary and subreflector surfaces.When the wind speed is 3.2 m/s,the antenna pitch angle is 61.7°and the wind direction angle is 80°,the generated pitch pointing error is 3.05'',and the azimuth pointing error is 1.14''.These results are consistent with those obtained via inclinometer measurements,thus validating the signal processing method and the pointing error calculation method proposed in this paper.The research methods and data analysis results reported here provide a basis for further wind-induced pointing error correction studies.展开更多
基金supported by the National Key R&D Program of China(Grant Nos.2022YFA1603300 and 2022YFA1603200)the Science Challenge Project(Grant No.TZ2018005)in China+1 种基金the National Natural Science Foundation of China(Grant Nos.11805188 and 12175209)the Laser Fusion Research Center Funds for Young Talents(Grant No.RCFPD6-2022-1).
文摘We present an application of short-pulse laser-generated hard x rays for the diagnosis of indirectly driven double shell targets. Coneinserted double shell targets were imploded through an indirect drive approach on the upgraded SG-II laser facility. Then, based on thepoint-projection hard x-ray radiography technique, time-resolved radiography of the double shell targets, including that of their near-peakcompression, were obtained. The backlighter source was created by the interactions of a high-intensity short pulsed laser with a metalmicrowire target. Images of the target near peak compression were obtained with an Au microwire. In addition, radiation hydrodynamicsimulations were performed, and the target evolution obtained agrees well with the experimental results. Using the radiographic images, arealdensities of the targets were evaluated.
基金This work was supported by Natural Science Foundation of Guangdong
文摘We will consider an extension of a direct method due to Griewank and Reddien for the computation of double symmetry-breaking turning points which arise in the two-parameter dependent nonlinear problem of the form f(x,λ,μ)= 0. The method proposed could produce an extended system which does not introduce the null vectors as variables, and could therefore reduce the computational effort and storage. One numerical example is presented to demonstrate that the method is efficient.
文摘We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.
基金supported by NSFC(51105131)Excellent Youth Foundation of Henan Scientific Committee(124100510002)Creative Talent Foundation in University of Henan Province(2011HASTIT016)
文摘Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.
基金Project supported by the Ministry of Education(MOE)and Research Management Centre,Universiti Teknologi Malaysia(Nos.5F166,5F004,07G70,07G72,07G76,and 07G77)。
文摘The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional(3D)stagnation point body is studied under a microgravity environment.The effects of g-jitter and thermal radiation exist under the microgravity environment,where there is a gravitational field with fluctuations.The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition.With the semi-similar transformation technique,the dimensional system of equations is reduced into a dimensionless system of equations,where the dependent variables of the problem are lessened.A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method,which is an implicit finite difference approach.The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics,the heat transfer properties,and the concentration distributions.The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body,where the stagnation point is located.The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied,where the fluctuating range becomes smaller when the oscillation frequency increases.Moreover,the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux,and the thermal radiation could increase the heat transfer properties.
基金supported in part by the National Natural Science Foundation of China under Grant 62003379Natural Science Foundation of Guangdong Province under Grant 2018A030313317+3 种基金Special Research Project on the Prevention and Control of COVID-19 Epidemic in Colleges and Universities of Guangdong under Grant 2020KZDZX1118Guangzhou Science and Technology Program under Grant 202002030246Research Project and Development Plan for Key Areas of Guangdong Province under Grant 2020B0202080002Guangzhou Key Research Base of Humanities and Social Sciences(Research Center of Agricultural Products Circulation in Guangdong-Hong Kong-Macao Greater Bay Area).
文摘To better reflect the psychological behavior characteristics of loss aversion,this paper builds a double reference point decision making method for dynamic multi-attribute decision-making(DMADM)problem,taking bottom-line and target as reference pints.First,the gain/loss function is given,and the state is divided according to the relationship between the gain/loss value and the reference point.Second,the attitude function is constructed based on the results of state division to establish the utility function.Third,the comprehensive utility value is calculated as the basis for alternatives classification and ranking.Finally,the new method is used to evaluate the development level of smart cities.The results show that the new method can judge the degree to which the alternatives meet the requirements of the decision-maker.While the new method can effectively screen out the unsatisfactory alternatives,the ranking results of other alternatives are consistent with those of traditional methods.
基金Funded by the Natural Science Foundation of China (No. 10171070)
文摘In this paper, a new concept of double coupled fixed point for multi-valued mixed increasing operators is given and some new double coupled fixed point theorems for multi-valued mixed increasing operators in ordered Banach spaces are also given. These results extend and generalize some results of Huang and Fang.
文摘We consider double high order S-breaking bifurcation points of two-Parameter dependent nonlinear problems with Z_2×Z_2-symmetry. Because of the underlying symmetry we could propose some regular extended systems to determine double high order S-breaking bifurcation points. and we could also show that there exist two quadratic pitchfork bifurcation point paths passing through the point being considered.
文摘The "double low-points" anomaly in daily variation of vertical geomagnetic component was observed on May 9, 2008 at 13 geomagnetic observatories belonging to the geomagnetic observatory network center of China Earthquake Administration. These observatories distribute roughly on three belts with the intersection in western Sichuan. On May 12, three days after the anomaly appearance, the great Ms8.0 Wenchuan earthquake occurred. The "double low-points" anomaly in daily variation of vertical geomagnetic component is an anomalous phenomenon of regional geomagnetism, which does exist objectively. The possible cause is the change of extrinsic eddy current system resulting in geomagnetic daily quiet variation (Sq), or the delay of several hours between the intrinsic and the extrinsic eddy current systems. The relationship between the "double low-points" anomaly of daily geomagnetic variation and the earthquake reveals that the former possibly reflects the accelerative alteration of earthquake gestation in the deep Earth.
文摘AIM: To present an inclusion criterion for patients who have suffered bilateral amputation in order to be treated with the supplementary resuscitation treatment which is hereby proposed by the author.METHODS: This work is based on a Retrospective Cohort model so that a certainly lethal risk to the control group is avoided.RESULTS: This paper presents a hypothesis on acupunctural PC-9 Zhong chong point, further supported by previous statistical work recorded for the K-1 Yong quan resuscitation point.CONCLUSION: Thanks to the application of the resuscitation maneuver herein proposed on the previously mentioned point, patients with bilateral amputation would have another alternative treatment available in case basic and advanced CPR should fail.
基金supported by the China Scholarship Council under Grant No.201600090258the National Key Research and Development Program of China under Grant No.2016YFC0303700the 111 Project under Grant No.B18054。
文摘Lower efficiencies induce higher energy costs and pose a barrier to wave energy devices'commercial applications.Therefore,the efficiency enhancement of wave energy converters has received much attention in recent decades.The reported research presents the double snap-through mechanism applied to a hemispheric point absorber type wave energy converter(WEC)to improve the energy absorption perfomance.The double snap-through mechanism comprises four oblique springs mounted in an X-configuration.This provides the WEC with different dynamic stability behaviors depending on the particular geometric and physical parameters employed.The efficiency of these different WEC behaviors(linear,bistable,and tristable)was initially evaluated under the action of regular waves.The results for bistable or tristable responses indicated significant improvements in the WEC's energy capture efficiency.Furthermore,the WEC frequency bandwidth was shown to be significantly enlarged when the tristable mode was in operation.However,the corresponding tristable trajectory showed intra-well behavior in the middle potential well,which induced a more severe low-energy absorption when a small wave amplitude acted on the WEC compared to when the bistable WEC was employed.Nevertheless,positive effects were observed when appropriate initial conditions were imposed.The results also showed that for bistable or tristable responses,a suitable spring stiffness may cause the buoy to oscillate in high energy modes.
基金This work is supported by NSFC amd Slate Major Key Project for Baslc Research
文摘Making use of the Z2×Z2 symmetry,we could study the structure near multiple S-treaking turning points.In particular,we show that there exist two kinds of singular point path through double S breaking turning points and triple S bieaking turning points,one ts quadratic turning pornt path and one is quadratic pitch fork bifurcation point path.Some simple regular extended systems to corn pute double and triple S-breaking turning points are proposed.Numerical examples are also
文摘In this paper, some approximation formulae for a class of convolution type double singular integral operators depending on three parameters of the type(T_λf)(x, y) = ∫_a^b ∫_a^b f(t, s)K_λ(t-x,s-y)dsdt, x,y ∈(a,b), λ ∈ Λ [0,∞),(0.1)are given. Here f belongs to the function space L_1( <a,b >~2), where <a,b> is an arbitrary interval in R. In this paper three theorems are proved, one for existence of the operator(T_λf)(x, y) and the others for its Fatou-type pointwise convergence to f(x_0, y_0), as(x,y,λ) tends to(x_0, y_0, λ_0). In contrast to previous works, the kernel functions K_λ(u,v)don't have to be 2π-periodic, positive, even and radial. Our results improve and extend some of the previous results of [1, 6, 8, 10, 11, 13] in three dimensional frame and especially the very recent paper [15].
文摘In the investigation, the complex geometric domain is a concave geometrical pattern. Due to the symmetric character, the left side of the geometric pattern,?i.e.?the L-shaped region is calculated in the study. The governing equation is expressed with?Laplace?equations. And the analysis is solved by eigenfunction expansion and point-match method. Besides, visual?C++?helps obtain the results of numerical calculation. The local values and the mean values of the function are also discussed in this study.
基金provided by the TMRT operators during the observations.This work was supported by the National Key Basic Research and Development Program(2018YFA0404702)the National Natural Science Foundation of China(U1631114,11873015,and 11203062)+2 种基金the CAS Key Technology Talent Program,the Knowledge Innovation Program of CAS(KJCX1-YW-18)the Scientific Program of Shanghai Municipality(08DZ1160100)the Key Laboratory for Radio Astronomy of CAS,the Key Laboratory of Planetary Sciences of CAS,and the CAS Scholarship.
文摘Wind loads have instantaneity and turbulence characteristics that will lead to pointing errors in antenna structures,and these errors cannot be ignored in high-frequency observations.Using the Tianma 65 m radio telescope(TMRT)as an example object,the pointing errors caused by wind loads are investigated using an accelerometer system.First,the resonant frequency range of the antenna structure is used for reference to acquire useful signals through the bandpass filtering method.Then,the direct current(DC)component of these signals is filtered out using the fast discrete Fourier transform method,and the baseline of the acceleration is corrected using the least-squares method.Finally,the acceleration integral is solved approximately using the discrete trapezoidal area method,and the structural vibration displacement of the antenna is determined using a double integral of acceleration.The pointing errors are then obtained based on the displacement relationship between the primary and subreflector surfaces.When the wind speed is 3.2 m/s,the antenna pitch angle is 61.7°and the wind direction angle is 80°,the generated pitch pointing error is 3.05'',and the azimuth pointing error is 1.14''.These results are consistent with those obtained via inclinometer measurements,thus validating the signal processing method and the pointing error calculation method proposed in this paper.The research methods and data analysis results reported here provide a basis for further wind-induced pointing error correction studies.