In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown...In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.展开更多
Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively...Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.展开更多
In this paper, the authors study a class of Finsler metric defined by a Rieman- nian metric and a 1-form. We find a necessary and sufficient condition for the metric to be prejectively flat.
In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential...In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.展开更多
In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai...In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai 0=1,2,4） are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.展开更多
In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessa...In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.展开更多
In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4...In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.展开更多
In this paper, we study spherically symmetric Finsler metrics. Analyzing the solution of the projectively fiat equation, we construct a new class of projectively flat Finsler metrics.
In this paper,we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics.Further,we discover that some of these metrics actually have the zero flag cur...In this paper,we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics.Further,we discover that some of these metrics actually have the zero flag curvature.展开更多
In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat ...In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.展开更多
In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.
In recent years,the demand for synchronous acquisition of three-dimensional(3D)shape and col-or texture has surged in fields such as cultural heritage preservation and healthcare.Addressing this need,this paper propos...In recent years,the demand for synchronous acquisition of three-dimensional(3D)shape and col-or texture has surged in fields such as cultural heritage preservation and healthcare.Addressing this need,this paper proposes a novel method for simultaneous 3D shape and color texture capture.First,a linear model correlating camera exposure time with grayscale values is established.Through exposure time calibration,the projected red,green and blue(RGB)light and white-light grayscale values captured by a monochrome cam-era are aligned.Then,three sets of color fringes are projected onto the object to identify optimal pixels for 3D reconstruction.And,three pure-color patterns are projected to synthesize the color texture.Experimental res-ults show that this method effectively achieves synchronous 3D shape and color texture acquisition,offering high speed and precision,and avoids color crosstalk interference common in 3D reconstruction of colored ob-jects using a monochrome camera.展开更多
Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):...Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):=D_(λ)^(b)(A)/K b(PPλ).We mainly verify that D_(λ-sg)^(b)(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too.展开更多
In this paper,we study and characterize locally projectively flat singular square metrics with constant flag curvature.First,we obtain the sufficient and necessary conditions that singular square metrics are locally p...In this paper,we study and characterize locally projectively flat singular square metrics with constant flag curvature.First,we obtain the sufficient and necessary conditions that singular square metrics are locally pro jectively flat.Furthermore,we classify locally pro jectively flat singular square metrics with constant flag curvature completely.展开更多
China and Laos are close neighbors with a long-standing friendship.Since the early 2000s,China has supported Laos'economic and social development through wide-ranging cooperation projects,all guided by the vision ...China and Laos are close neighbors with a long-standing friendship.Since the early 2000s,China has supported Laos'economic and social development through wide-ranging cooperation projects,all guided by the vision of a community with a shared future.As this vision takes deeper root,many aid projects have moved from blueprint to reality,delivering tangible benefits across towns and villages and improving the lives of ordinary Lao people while further strengthening bilateral ties.展开更多
Projections of future urban land change are essential for a range of sustainability assessments,including those related to biodiversity loss,carbon emissions,and agricultural land conversion.However,to what extent and...Projections of future urban land change are essential for a range of sustainability assessments,including those related to biodiversity loss,carbon emissions,and agricultural land conversion.However,to what extent and where current projections agree or disagree remains unknown.Here,we systematically compare existing global projections that are consistent with the Shared Socioeconomic Pathways.We find that the total global urban land area is expected to increase by 112%between 2020 and 2100(averaged across all projections),with a coefficient of variation of 0.81.This variation is mostly caused by the selection of the underlying drivers that are included in the different models.Regionally,the highest average growth rates are found in sub-Saharan Africa(+679%to+730%),while this region also has the highest variation across projections(coefficient of variation ranging from 2.02 to 2.18).When ranking scenarios within a study from the highest to the lowest projected increase in urban land,rankings are relatively similar for regions in the Global North,but not for regions in the Global South.The large disagreement across projections can lead to high uncertainties in assessments of future urban land change impacts,which can undermine the effectiveness of long-term planning,policymaking,and resource management decisions.展开更多
This study provides potential climate projections for Central Asia(CA)based on multi-regional climate model(RCM)outputs from the Coordinated Regional Climate Downscaling Experiment for Central Asia(CORDEX-CAII).Despit...This study provides potential climate projections for Central Asia(CA)based on multi-regional climate model(RCM)outputs from the Coordinated Regional Climate Downscaling Experiment for Central Asia(CORDEX-CAII).Despite some systematic biases,all RCMs effectively capture the main features of observed temperature and precipitation means and extremes over CA,with notable variations in model performance due to differences in the driving global climate models and the RCMs themselves.Overall,REMO consistently outperforms ALARO in simulating temperature-related indices,and ALARO-0 provides more accurate simulations for precipitation-related indices,and the multimodel ensemble(MME)tends to outperform individual RCMs.Under the representative concentration pathway(RCP)scenarios of RCP2.6 and RCP8.5,the MME results indicate a clear warming trend across CA for all temperature-related indices,except for the diurnal temperature range,with annual temperatures projected to increase by 0.15℃/10 yr and 0.53℃/10 yr,respectively.Both scenarios exhibit similar spatial distributions in projected annual precipitation,characterized by peak increases of~0.2 mm per day in northern CA.The number of consecutive dry days is projected to slightly increase under RCP8.5,while it is expected to slightly decrease under RCP2.6.This study improves our understanding of the applicability of RCMs in CA and provides reliable projections of future climate change.展开更多
Climate models are essential for understanding past,present,and future changes in atmospheric circulation,with circulation modes providing key sources of seasonal predictability and prediction uncertainties for both g...Climate models are essential for understanding past,present,and future changes in atmospheric circulation,with circulation modes providing key sources of seasonal predictability and prediction uncertainties for both global and regional climates.This study assesses the performance of models participating in phase 6 of the Coupled Model Intercomparison Project in simulating interannual variability modes of Northern Hemisphere 500-hPa geopotential height during winter and summer,distinguishing predictable(potentially predictable on seasonal or longer timescales)and unpredictable(intraseasonal and essentially unpredictable at long range)components,using reanalysis data and a variance decomposition method.Although most models effectively capture unpredictable modes in reanalysis,their ability to reproduce dominant predictable modes-specifically the Pacific-North American pattern,Arctic Oscillation,and Western Pacific Oscillation in winter,and the East Atlantic and North Atlantic Oscillations in summer-varies notably.An optimal ensemble is identified to distinguish(a)predictable-external modes,dominated by external forcing,and(b)predictable-internal modes,associated with slow internal variability,during the historical period(1950-2014)and the SSP5-8.5 scenario(2036-2100).Under increased radiative forcing,the leading winter/summer predictable-external mode exhibits a more uniform spatial distribution,remarkably larger trend and annual variance,and enhanced height-sea surface temperature(SST)covariance under SSP5-8.5 compared to historical conditions.The dominant winter/summer predictable-internal modes also exhibit increased variance and height-SST covariance under SSP5-8.5,along with localized changes in spatial configuration.Minimal changes are observed in spatial distribution or variance for dominant winter/summer unpredictable modes under SSP5-8.5.This study,from a predictive perspective,deepens our understanding of model uncertainties and projected changes in circulations.展开更多
基金Supported by the National Natural Science Foundation of China(12061061)Young Talents Team Project of Gansu Province(2025QNTD49)+1 种基金Lanshan Talents Project of Northwest Minzu University(Xbmulsrc202412)Longyuan Young Talents of Gansu Province。
文摘In this article,we first establish a recollement related to projectively coresolved Gorenstein flat(PGF)complexes.Secondly,we define and study PGF dimension of complexes,we denote it PG F(X)for a complex X.It is shown that the PGF(X)is equal to the infimum of the set{supA|there exists a diagram of morphisms of complexes A←G→X,such that G→X is a special PGF precover of X and G→A is a PGF almost isomorphism}.
文摘Abstract In this article, the author studies the projectively flat Matsumoto metric F=α^2/（α -β）, where α=√αijy^iy^j is a Riemannian metric and β =biy^i is 1-form. Theyconclude that α is locally projectively fiat and β is paralled with respect to α. And get the same result for the higher order approximate Matsumoto metric.
基金Supported by the National Natural Science Foundation of China (Grant No.11071005)
文摘In this paper, the authors study a class of Finsler metric defined by a Rieman- nian metric and a 1-form. We find a necessary and sufficient condition for the metric to be prejectively flat.
基金Project (No. 10571154) supported by the National Natural ScienceFoundation of China
文摘In this paper, we study a class of Finsler metric in the form F=αexp(β/α)+εβ, where α is a Riemannian metric and β is a 1-form, ε is a constant. We call F exponential Finsler metric. We proved that exponential Finsler metric F is locally projectively flat if and only if α is projectively flat and β is parallel with respect to α. Moreover, we proved that the Douglas tensor of expo-nential Finsler metric F vanishes if and only if β is parallel with respect to α. And from this fact, we get that if exponential Finsler metric F is the Douglas metric, then F is not only a Berwald metric, but also a Landsberg metric.
文摘In this paper, we consider some polynomial （a,fl）-metrics, and discuss the sufficient and necessary conditions for a Finsler metric in the form F=α＋α1β＋α2β^2/α＋α4β^4/α^3 to be projectively flat, where ai 0=1,2,4） are constants with a1≠0, a is a Riemannian metric and β is a 1-form. By analyzing the geodesic coefficients and the divisibility of certain polynomials, we obtain that there are only five projectively flat cases for metrics of this type. This gives a classification for such kind of Finsler metrics.
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study a class of special Finsler metrics F called arctangent Finsler metric, which is a special （α, β）-metric, where a is a Riemannian metric and β is a 1-form, We obtain a sufficient and necessary condition that F is locally projectively fiat if and only if α and β satisfy two special equations. Furthermore we give the non-trivial solutions for F to be locally projectively fiat. Moreover, we prove that such projectively fiat Finsler metrics with constant flag curvature must be locally Minkowskian.
基金Project (No. 10571154) supported by the National Natural Science Foundation of China
文摘In this work, we study the Asanov Finsler metric F=α（β^2/α^2＋gβ/α＋1）^1/2exp{（G/2）arctan[β/（hα）＋G/2]}, where α=（αijy^iy^i）^1/2 is a Riemannian metric and β=by^i is a 1-fom, g∈（-2,2）, h=（1-g^2/4）^1/2, G=g/h. We give the necessary and sufficient condition for Asanov metric to be locally projectively flat, i.e., α is projectively flat and ,Sis parallel with respect to α. Moreover, we proved that the Douglas tensor of Asanov Finsler metric vanishes if and only if β is parallel with respect to α.
基金Supported by the National Natural Science Foundation of China(Grant No.11071005)
文摘In this paper, we study spherically symmetric Finsler metrics. Analyzing the solution of the projectively fiat equation, we construct a new class of projectively flat Finsler metrics.
基金supported by the National Natural Science Foundation of China(Grant Nos.10371138&10471001).
文摘In this paper,we find some solutions to a system of partial differential equations that characterize the projectively flat Finsler metrics.Further,we discover that some of these metrics actually have the zero flag curvature.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10571154).
文摘In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, form, and ∈ and k≠0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘In this paper, we study a special class of two-dimensional Finsler metrics defined by a Riemannian metric and 1-form. We classify those which are locally projectively flat with constant flag curvature.
文摘In recent years,the demand for synchronous acquisition of three-dimensional(3D)shape and col-or texture has surged in fields such as cultural heritage preservation and healthcare.Addressing this need,this paper proposes a novel method for simultaneous 3D shape and color texture capture.First,a linear model correlating camera exposure time with grayscale values is established.Through exposure time calibration,the projected red,green and blue(RGB)light and white-light grayscale values captured by a monochrome cam-era are aligned.Then,three sets of color fringes are projected onto the object to identify optimal pixels for 3D reconstruction.And,three pure-color patterns are projected to synthesize the color texture.Experimental res-ults show that this method effectively achieves synchronous 3D shape and color texture acquisition,offering high speed and precision,and avoids color crosstalk interference common in 3D reconstruction of colored ob-jects using a monochrome camera.
文摘Let A be a Grothendieck category.Theλ-pure singularity category D_(λ-sg)^(b)(A)of A is a Verdier quotient of the boundedλ-pure derived category D_(λ)^(b)(A)by a thick subcategory K^(b)(PPλ),i.e.,D_(λ-sg)^(b)(A):=D_(λ)^(b)(A)/K b(PPλ).We mainly verify that D_(λ-sg)^(b)(A)is triangle equivalent to another quotient category under a special condition.And we also prove that a triangle equivalence between special homotopy categories induces aλ-pure derived equivalence,and it induces aλ-pure singular equivalence too.
基金Supported by the National Natural Science Foundation of China(Grant No.11871126)the Science Foundation of Chongqing Normal University(Grant No.17XLB022)。
文摘In this paper,we study and characterize locally projectively flat singular square metrics with constant flag curvature.First,we obtain the sufficient and necessary conditions that singular square metrics are locally pro jectively flat.Furthermore,we classify locally pro jectively flat singular square metrics with constant flag curvature completely.
基金supported by the Yunnan Provincial Philosophy and Social Science Planning Projectthe Yunnan Academy of Social Sciences。
文摘China and Laos are close neighbors with a long-standing friendship.Since the early 2000s,China has supported Laos'economic and social development through wide-ranging cooperation projects,all guided by the vision of a community with a shared future.As this vision takes deeper root,many aid projects have moved from blueprint to reality,delivering tangible benefits across towns and villages and improving the lives of ordinary Lao people while further strengthening bilateral ties.
基金supported by the Netherlands Organization for Scientific Research NWO in the form of a VIDI grant(Grant No.VI.Vidi.198.008).
文摘Projections of future urban land change are essential for a range of sustainability assessments,including those related to biodiversity loss,carbon emissions,and agricultural land conversion.However,to what extent and where current projections agree or disagree remains unknown.Here,we systematically compare existing global projections that are consistent with the Shared Socioeconomic Pathways.We find that the total global urban land area is expected to increase by 112%between 2020 and 2100(averaged across all projections),with a coefficient of variation of 0.81.This variation is mostly caused by the selection of the underlying drivers that are included in the different models.Regionally,the highest average growth rates are found in sub-Saharan Africa(+679%to+730%),while this region also has the highest variation across projections(coefficient of variation ranging from 2.02 to 2.18).When ranking scenarios within a study from the highest to the lowest projected increase in urban land,rankings are relatively similar for regions in the Global North,but not for regions in the Global South.The large disagreement across projections can lead to high uncertainties in assessments of future urban land change impacts,which can undermine the effectiveness of long-term planning,policymaking,and resource management decisions.
基金jointly supported by the Second Tibetan Plateau Scientific Expedition and Research Program[grant number 2019QZKK0103]the National Natural Science Foundation of China[grant number 42293294]the China Meteorological Administration Climate Change Special Program[grant number QBZ202303]。
文摘This study provides potential climate projections for Central Asia(CA)based on multi-regional climate model(RCM)outputs from the Coordinated Regional Climate Downscaling Experiment for Central Asia(CORDEX-CAII).Despite some systematic biases,all RCMs effectively capture the main features of observed temperature and precipitation means and extremes over CA,with notable variations in model performance due to differences in the driving global climate models and the RCMs themselves.Overall,REMO consistently outperforms ALARO in simulating temperature-related indices,and ALARO-0 provides more accurate simulations for precipitation-related indices,and the multimodel ensemble(MME)tends to outperform individual RCMs.Under the representative concentration pathway(RCP)scenarios of RCP2.6 and RCP8.5,the MME results indicate a clear warming trend across CA for all temperature-related indices,except for the diurnal temperature range,with annual temperatures projected to increase by 0.15℃/10 yr and 0.53℃/10 yr,respectively.Both scenarios exhibit similar spatial distributions in projected annual precipitation,characterized by peak increases of~0.2 mm per day in northern CA.The number of consecutive dry days is projected to slightly increase under RCP8.5,while it is expected to slightly decrease under RCP2.6.This study improves our understanding of the applicability of RCMs in CA and provides reliable projections of future climate change.
基金supported by the National Natural Science Foundation of China(Grant Nos.U2342210 and 42275043)the National Institute of Natural Hazards,Ministry of Emergency Management of China(Grant Nos.J2223806,ZDJ2024-25 and ZDJ2025-34)。
文摘Climate models are essential for understanding past,present,and future changes in atmospheric circulation,with circulation modes providing key sources of seasonal predictability and prediction uncertainties for both global and regional climates.This study assesses the performance of models participating in phase 6 of the Coupled Model Intercomparison Project in simulating interannual variability modes of Northern Hemisphere 500-hPa geopotential height during winter and summer,distinguishing predictable(potentially predictable on seasonal or longer timescales)and unpredictable(intraseasonal and essentially unpredictable at long range)components,using reanalysis data and a variance decomposition method.Although most models effectively capture unpredictable modes in reanalysis,their ability to reproduce dominant predictable modes-specifically the Pacific-North American pattern,Arctic Oscillation,and Western Pacific Oscillation in winter,and the East Atlantic and North Atlantic Oscillations in summer-varies notably.An optimal ensemble is identified to distinguish(a)predictable-external modes,dominated by external forcing,and(b)predictable-internal modes,associated with slow internal variability,during the historical period(1950-2014)and the SSP5-8.5 scenario(2036-2100).Under increased radiative forcing,the leading winter/summer predictable-external mode exhibits a more uniform spatial distribution,remarkably larger trend and annual variance,and enhanced height-sea surface temperature(SST)covariance under SSP5-8.5 compared to historical conditions.The dominant winter/summer predictable-internal modes also exhibit increased variance and height-SST covariance under SSP5-8.5,along with localized changes in spatial configuration.Minimal changes are observed in spatial distribution or variance for dominant winter/summer unpredictable modes under SSP5-8.5.This study,from a predictive perspective,deepens our understanding of model uncertainties and projected changes in circulations.
