Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected...Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected 2n-manifolds M and L, n > 1. A corollary is that each (n ? 1)-connected 2n-manifold admits selfmaps of degree larger than 1, n > 1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms; in particular, there is a map f : M → L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.展开更多
The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity d...The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.展开更多
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the co...The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.展开更多
BACKGROUND： It has been proved that brain electrical activity mapping （BEAM） and transcranial Doppler （TCD） detection can reflect the function of brain cell and its diseased degree of infant patients with moderat...BACKGROUND： It has been proved that brain electrical activity mapping （BEAM） and transcranial Doppler （TCD） detection can reflect the function of brain cell and its diseased degree of infant patients with moderate to severe hypoxic-ischemic encephalopathy （HIE）. OBJECTIVE： To observe the abnormal results of HIE at different degrees detected with BEAM and TCD in infant patients, and compare the detection results at the same time point between BEAM, TCD and computer tomography （CT） examinations. DESIGN ： Contrast observation SETTING： Departments of Neuro-electrophysiology and Pediatrics, Second Affiliated Hospital of Qiqihar Medical College. PARTICIPANTS： Totally 416 infant patients with HIE who received treatment in the Department of Newborn Infants, Second Affiliated Hospital of Qiqihar Medical College during January 2001 and December 2005. The infant patients, 278 male and 138 female, were at embryonic 37 to 42 weeks and weighing 2.0 to 4.1 kg, and they were diagnosed with CT and met the diagnostic criteria of HIE of newborn infants compiled by Department of Neonatology, Pediatric Academy, Chinese Medical Association. According to diagnostic criteria, 130 patients were mild abnormal, 196 moderate abnormal and 90 severe abnormal. The relatives of all the infant patients were informed of the experiment. METHOOS： BEAM and TCD examinations were performed in the involved 416 infant patients with HIE at different degrees with DYD2000 16-channel BEAM instrument and EME-2000 ultrasonograph before preliminary diagnosis treatment （within 1 month after birth） and 1,3,6,12 and 24 months after birth, and detected results were compared between BEAM, TCD and CT examinations. MAIN OUTCOME MEASURES： Comparison of detection results of HIE at different time points in infant patients between BEAM. TCD and CT examinations. RESULTS： All the 416 infant patients with HIE participated in the result analysis. （1） Comparison of the detected results in infant patients with mild HIE at different time points after birth between BEAM, TCD and CT examinations： BEAM examination showed that the recovery was delayed, and the abnormal rate of BEAM examination was significantly higher than that of CT examination 1 and 3 months after birth [55.4%（72/130）vs. 17.0% （22/130 ）,x^2=41.66 ;29.2% （ 38/130 ） vs. 6.2% （ 8/130 ）, x^2=23.77, P 〈 0.01 ], exceptional patients had mild abnormality and reached the normal level in about 6 months. TCD examination showed that the disease condition significantly improved and infant patients with HIE basically recovered 1 or 2 months after birth, while CT examination showed that infant patients recovered 3 or 4 months after birth. （2） Comparison of detection results of infant patients with moderate HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination 1,3,6 and 12 months after birth [90.8% （178/196）,78.6% （154/196）,x^2=4.32,P 〈 0.05;64.3% （126/196）,43.9% （86/196） ,x^2=16.44 ;44.9% （88/196） ,22.4% （44/196）,x^2=22.11 ;21.4% （42/196）, 10.2% （20/196）,x^2=9.27, P 〈 0.01]. BEAM examination showed that there was still one patient who did not completely recovered in the 24^th month due to the relatives of infant patients did not combine the treatment,. TCD examination showed that the abnormal rate was 23.1%（30/196）in the 1^st month after birth, and all the patients recovered to the normal in the 3^rd month after birth, while CT examination showed that mild abnormality still existed in the 24^th month after birth （1.0% ,2/196）. （3） Comparison of detection results of infant patients with severe HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination in the 1^st, 3^rd, 6^th and 12^th months after birth[86.7% （78/90）,44.4% （40/90）,x^2=35.53;62.2% （56/90）,31.1% （28/90）,x^2=17.51 ;37.8% （34/90）,6.7% （6/90）, x^2=27.14, P 〈 0.01]. BEAM examination showed that mild abnormality still existed in 4 infant patients in the 24^th month after birth. TCD examination showed that the abnormal rate was 11.1% （10/90） in the 3^rd month after birth, and all the infant patients recovered in the 6^th month after birth. CT examination showed that the abnormal rate was 6.7%（6/90） in the 12^th month after birth, and all of infant patients recovered to the normal in the 24^th month after birth.CONCLUSION ： BEAM is the direct index to detect brain function of infant patients with HIE, and positive reaction is still very sensitive in the tracking detection of convalescent period. The positive rate of morphological reaction in CT examination is superior to that in TCD examination, and the positive rate is very high in the acute period of HIE in examination.展开更多
提出一种预估计混叠度的PEMAP(pre-estimated MAP (maximum a posteriori))算法,用于卫星图像的地面超分辨率处理.它通过频域分析确定卫星图像的混叠度,将其作为先验信息在空域控制MAP估计的循环迭代,联合估计帧间位移和高分辨率图像....提出一种预估计混叠度的PEMAP(pre-estimated MAP (maximum a posteriori))算法,用于卫星图像的地面超分辨率处理.它通过频域分析确定卫星图像的混叠度,将其作为先验信息在空域控制MAP估计的循环迭代,联合估计帧间位移和高分辨率图像.该算法克服了最大后验概率MAP算法的盲目性和不稳定性,使其适应性更好.实际的卫星图像处理显示了较好的处理效果.展开更多
In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt dom...In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.展开更多
Hydrogeological map is one of the important carriers of groundwater related information.It directly reflects the hydrogeological conditions and previous investigation and research results of a mapping area.The hydroge...Hydrogeological map is one of the important carriers of groundwater related information.It directly reflects the hydrogeological conditions and previous investigation and research results of a mapping area.The hydrogeological map of China is a map reflecting the characteristics of hydrogeology and groundwater dynamics on a national scale.On the basis of the hydrogeological map of China(1:4000000)compiled in 1988,this map compilation attempted to update and enhance the existing map,with the latest survey results from the project of National Investigation and Evaluation of Groundwater Resources and Environmental Problems led by China Geological Survey.Task of the mapping program included redefining groundwater types,quantifying the classification standard of the groundwater and adding the pore-fissure water in laterite layer of hilly basin.The multilayer structures for porous,karst and porous-fractured groundwater and their water-rich grades are reflected on the map.Based on the comprehensive summary of the latest hydrogeological data of China,this research conducts an in-depth analysis of the regional distribution characteristics of groundwater in China,utilizes a digital mapping process and establishes a cartographic database for the purpose of further use.With the enrichment of the content and the continuous improvement of cognitive level,mapping content can be updated quickly,which has practical significance for the concept of surveying and mapping and scientific popularization.展开更多
The Brouwer degree of every isoparametric gradient map has been given by using moving frame. It has been used to construct the harmonic representations of the elements of homotopy groups of the spheres.
Let M,N be oriented closed manifolds of dimension n.Denote the Brouwer degree ofa smooth map g: M→N by deg（g）.It is well known that deg（g）=sum from x∈g<sup>-1</sup>（y） sign dg<sub>x</sub&g...Let M,N be oriented closed manifolds of dimension n.Denote the Brouwer degree ofa smooth map g: M→N by deg（g）.It is well known that deg（g）=sum from x∈g<sup>-1</sup>（y） sign dg<sub>x</sub>,where yis a regular value of g.When M=N=S<sup>n+1</sup>,the homotopy class [g]∈multiply from n+1 S<sup>n+1</sup>≌Z is deter-mined by the Brouwer degree of g.Since finding a harmonic representative of an elementin multiply from n+1 S<sub>n+1</sub> is important（see refs.[1—3]）,it is necessary to calculate the Brouwer degree ofa map.展开更多
We determine the set of degrees between some classes of oriented closed （n - 1）-connected 2n-manifolds by using the arithmetic theory of quadratic forms.
E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixe...E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.展开更多
By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？
Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mappi...Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mapping （see Ning et al. （2017））. In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan＇s theorem.展开更多
文摘Thom–Pontrjagin constructions are used to give a computable necessary and sufficient condition for a homomorphism ? : H n (L;Z) → H n (M;Z) to be realized by a map f : M → L of degree k for closed (n ? 1)-connected 2n-manifolds M and L, n > 1. A corollary is that each (n ? 1)-connected 2n-manifold admits selfmaps of degree larger than 1, n > 1. In the most interesting case of dimension 4, with the additional surgery arguments we give a necessary and sufficient condition for the existence of a degree k map from a closed orientable 4-manifold M to a closed simply connected 4-manifold L in terms of their intersection forms; in particular, there is a map f : M → L of degree 1 if and only if the intersection form of L is isomorphic to a direct summand of that of M.
基金funded by the Natural Science Foundation Committee,China(41364001,41371435)
文摘The degree of spatial similarity plays an important role in map generalization, yet there has been no quantitative research into it. To fill this gap, this study first defines map scale change and spatial similarity degree/relation in multi-scale map spaces and then proposes a model for calculating the degree of spatial similarity between a point cloud at one scale and its gener- alized counterpart at another scale. After validation, the new model features 16 points with map scale change as the x coordinate and the degree of spatial similarity as the y coordinate. Finally, using an application for curve fitting, the model achieves an empirical formula that can calculate the degree of spatial similarity using map scale change as the sole independent variable, and vice versa. This formula can be used to automate algorithms for point feature generalization and to determine when to terminate them during the generalization.
文摘The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued (S) and (S), type mappings and the concepts of the limits of multivalued (S) and (S) + type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for (S) type mapping and the degree for (S)+ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations (see part 3) and to obtain some new fixed point theorems in part 4.
文摘BACKGROUND： It has been proved that brain electrical activity mapping （BEAM） and transcranial Doppler （TCD） detection can reflect the function of brain cell and its diseased degree of infant patients with moderate to severe hypoxic-ischemic encephalopathy （HIE）. OBJECTIVE： To observe the abnormal results of HIE at different degrees detected with BEAM and TCD in infant patients, and compare the detection results at the same time point between BEAM, TCD and computer tomography （CT） examinations. DESIGN ： Contrast observation SETTING： Departments of Neuro-electrophysiology and Pediatrics, Second Affiliated Hospital of Qiqihar Medical College. PARTICIPANTS： Totally 416 infant patients with HIE who received treatment in the Department of Newborn Infants, Second Affiliated Hospital of Qiqihar Medical College during January 2001 and December 2005. The infant patients, 278 male and 138 female, were at embryonic 37 to 42 weeks and weighing 2.0 to 4.1 kg, and they were diagnosed with CT and met the diagnostic criteria of HIE of newborn infants compiled by Department of Neonatology, Pediatric Academy, Chinese Medical Association. According to diagnostic criteria, 130 patients were mild abnormal, 196 moderate abnormal and 90 severe abnormal. The relatives of all the infant patients were informed of the experiment. METHOOS： BEAM and TCD examinations were performed in the involved 416 infant patients with HIE at different degrees with DYD2000 16-channel BEAM instrument and EME-2000 ultrasonograph before preliminary diagnosis treatment （within 1 month after birth） and 1,3,6,12 and 24 months after birth, and detected results were compared between BEAM, TCD and CT examinations. MAIN OUTCOME MEASURES： Comparison of detection results of HIE at different time points in infant patients between BEAM. TCD and CT examinations. RESULTS： All the 416 infant patients with HIE participated in the result analysis. （1） Comparison of the detected results in infant patients with mild HIE at different time points after birth between BEAM, TCD and CT examinations： BEAM examination showed that the recovery was delayed, and the abnormal rate of BEAM examination was significantly higher than that of CT examination 1 and 3 months after birth [55.4%（72/130）vs. 17.0% （22/130 ）,x^2=41.66 ;29.2% （ 38/130 ） vs. 6.2% （ 8/130 ）, x^2=23.77, P 〈 0.01 ], exceptional patients had mild abnormality and reached the normal level in about 6 months. TCD examination showed that the disease condition significantly improved and infant patients with HIE basically recovered 1 or 2 months after birth, while CT examination showed that infant patients recovered 3 or 4 months after birth. （2） Comparison of detection results of infant patients with moderate HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination 1,3,6 and 12 months after birth [90.8% （178/196）,78.6% （154/196）,x^2=4.32,P 〈 0.05;64.3% （126/196）,43.9% （86/196） ,x^2=16.44 ;44.9% （88/196） ,22.4% （44/196）,x^2=22.11 ;21.4% （42/196）, 10.2% （20/196）,x^2=9.27, P 〈 0.01]. BEAM examination showed that there was still one patient who did not completely recovered in the 24^th month due to the relatives of infant patients did not combine the treatment,. TCD examination showed that the abnormal rate was 23.1%（30/196）in the 1^st month after birth, and all the patients recovered to the normal in the 3^rd month after birth, while CT examination showed that mild abnormality still existed in the 24^th month after birth （1.0% ,2/196）. （3） Comparison of detection results of infant patients with severe HIE at different time points between BEAM, TCD and CT examinations： The abnormal rate of BEAM examination was significantly higher than that of CT examination in the 1^st, 3^rd, 6^th and 12^th months after birth[86.7% （78/90）,44.4% （40/90）,x^2=35.53;62.2% （56/90）,31.1% （28/90）,x^2=17.51 ;37.8% （34/90）,6.7% （6/90）, x^2=27.14, P 〈 0.01]. BEAM examination showed that mild abnormality still existed in 4 infant patients in the 24^th month after birth. TCD examination showed that the abnormal rate was 11.1% （10/90） in the 3^rd month after birth, and all the infant patients recovered in the 6^th month after birth. CT examination showed that the abnormal rate was 6.7%（6/90） in the 12^th month after birth, and all of infant patients recovered to the normal in the 24^th month after birth.CONCLUSION ： BEAM is the direct index to detect brain function of infant patients with HIE, and positive reaction is still very sensitive in the tracking detection of convalescent period. The positive rate of morphological reaction in CT examination is superior to that in TCD examination, and the positive rate is very high in the acute period of HIE in examination.
文摘提出一种预估计混叠度的PEMAP(pre-estimated MAP (maximum a posteriori))算法,用于卫星图像的地面超分辨率处理.它通过频域分析确定卫星图像的混叠度,将其作为先验信息在空域控制MAP估计的循环迭代,联合估计帧间位移和高分辨率图像.该算法克服了最大后验概率MAP算法的盲目性和不稳定性,使其适应性更好.实际的卫星图像处理显示了较好的处理效果.
基金supported by the National Natural Science Foundation of China(11001246,11101139)Zhejiang Innovation Project(T200905)
文摘In this note, the author introduces some new subcIasses of starlike mappings S^＊Ωn1p2,…,pn（β,A,B）={f∈H（Ω）：｜itanβ＋（1-itanβ）2/p（z）аp/аz（z）Jf^-1（z）f（z）-1-AB/1-B^2｜〈B-A/1-B^2},on Reinhardt domains Ωn1p2,…,pn=z∈C^n：｜z1｜^2＋n∑j=2｜zj｜^pj〈1}where - 1≤A〈B〈1,q=min{p2,…,pn}≥1,l=max{p2,…,pn}≥2 and β ∈（-π/2,π/2）.Some different conditions for P are established such that these classes are preserved under the following modified Roper-Suffridge operator F（z）=（f（z1）＋f＇（z1）Pm（z0）,（f＇（z1））^1/mz0）＇where f is a normalized biholomorphic function on the unit disc D, z = （z1,z0） ∈Ωn1p2,…,pn,z0=（z2,…,zn）∈ C^n-1.Another condition for P is also obtained such that the above generalized Roper-Suffridge operator preserves an almost spirallike function of type/3 and order β These results generalize the modified Roper-Suffridge extension oper-ator from the unit ball to Reinhardt domains. Notice that when p2 = p3 …=pn = 2,our results reduce to the recent results of Feng and Yu.
文摘Hydrogeological map is one of the important carriers of groundwater related information.It directly reflects the hydrogeological conditions and previous investigation and research results of a mapping area.The hydrogeological map of China is a map reflecting the characteristics of hydrogeology and groundwater dynamics on a national scale.On the basis of the hydrogeological map of China(1:4000000)compiled in 1988,this map compilation attempted to update and enhance the existing map,with the latest survey results from the project of National Investigation and Evaluation of Groundwater Resources and Environmental Problems led by China Geological Survey.Task of the mapping program included redefining groundwater types,quantifying the classification standard of the groundwater and adding the pore-fissure water in laterite layer of hilly basin.The multilayer structures for porous,karst and porous-fractured groundwater and their water-rich grades are reflected on the map.Based on the comprehensive summary of the latest hydrogeological data of China,this research conducts an in-depth analysis of the regional distribution characteristics of groundwater in China,utilizes a digital mapping process and establishes a cartographic database for the purpose of further use.With the enrichment of the content and the continuous improvement of cognitive level,mapping content can be updated quickly,which has practical significance for the concept of surveying and mapping and scientific popularization.
基金Project supported by the National Natural Science Foundation of China,the State Education Commission Foundation of China and the Foundation of the Chinese Academy of Sciences.
文摘The Brouwer degree of every isoparametric gradient map has been given by using moving frame. It has been used to construct the harmonic representations of the elements of homotopy groups of the spheres.
文摘Let M,N be oriented closed manifolds of dimension n.Denote the Brouwer degree ofa smooth map g: M→N by deg（g）.It is well known that deg（g）=sum from x∈g<sup>-1</sup>（y） sign dg<sub>x</sub>,where yis a regular value of g.When M=N=S<sup>n+1</sup>,the homotopy class [g]∈multiply from n+1 S<sup>n+1</sup>≌Z is deter-mined by the Brouwer degree of g.Since finding a harmonic representative of an elementin multiply from n+1 S<sub>n+1</sub> is important（see refs.[1—3]）,it is necessary to calculate the Brouwer degree ofa map.
基金Supported by Morningside Center of Mathematics, National Natural Science Foundation of China (Grant Nos. 10325105 and 10531060)KRF (2003-070-C00001)
文摘We determine the set of degrees between some classes of oriented closed （n - 1）-connected 2n-manifolds by using the arithmetic theory of quadratic forms.
基金Supported in part by Education Ministry,Anhui Province,China(No:2003kj047zd)
文摘E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.
基金The third author is partially supported by National Natural Science Foundation of China （Grant No. 10631060） and Ph.D. grant of the Ministry of Education of China （Grant No. 5171042-055）
文摘By constructing certain maps, this note completes the answer of the question： For which closed orientable 3-manifold N, is the set of mapping degrees D（M, N） finite for any closed orientable 3-manifold M？
基金supported by National Natural Science Foundation of China(Grant Nos.11501058 and 11431013)the Fundamental Research Funds for the Central Universities(Grant No.0208005202035)Key Research Program of Frontier Sciences,Chinese Academy of Sciences(Grant No.QYZDY-SSW-SYS001)
文摘Let Gi be a closed Lie subgroup of U（n）, Ωi be a bounded Gi-invariant domain in Cn which contains 0, and （9（Cn）Gi = C, for i= 1,2. If f ： f21 →2 is abiholomorphism, and f（0） = 0, then f is a polynomial mapping （see Ning et al. （2017））. In this paper, we provide an upper bound for the degree of such polynomial mappings. It is a natural generalization of the well-known Cartan＇s theorem.
