The study aimed to examine the applicability of carbon nanoparticles as a tracer for lymph node mapping and the related factors of lymph node and No.8p subgroup metastasis in patients with gastric cancer.Clinical data...The study aimed to examine the applicability of carbon nanoparticles as a tracer for lymph node mapping and the related factors of lymph node and No.8p subgroup metastasis in patients with gastric cancer.Clinical data of 50 patients with gastric cancer,who had not received treatment preoperatively and underwent gastrectomy in Department of Gastrointestinal Surgery,Wuhan Union Hospital,between October 2014 and August 2015,were retrospectively analyzed.These patients were found to have no distant metastasis preoperatively.Thirty-five out of 50 patients were subjected to lymphatic mapping technique using carbon nanoparticles as the tracer,and the rest 15 cases did not experience the lymphatic mapping and served as controls.The sensitivity,specificity,false positive rate and false negative rate were calculated according to the number of lymph nodes,and the staining and metastasis condition of lymph nodes.The diagnostic value of carbon nanoparticles on metastatic lymph nodes was evaluated.The relationship between the metastasis of lymph nodes or subgroup No.8p lymph nodes and clinicopathologic features was analyzed by χ^2-test or Fisher's exact test.All patients underwent D2 surgery(lymph node dissection including all the group 1 and group 2 nodes) plus the dissection of the subgroup No.8p lymph nodes.It was found that the average number of harvested lymph nodes in lymphatic mapping technique group(45.7±14.5) was greater than that in control group(39.2±11.7),but the difference was not significantly different(P=0.138〉0.05).The success rate,the accuracy,sensitivity,specificity and false negative rate was 97%,57%,28%,62% and 72% respectively.The metastasis of lymph nodes was correlated to the depth of cancer invasion(T stage)(P=0.004〈0.05),and the metastasis of No.8p lymph nodes was correlated to the extent of lymph node involvement(N stage)(P=0.007〈0.05).Six cases had lymph node metastasis in subgroup No.8p,and their TNM stages and clinical stages were as follows:T1N2M0 ⅡA,T3N3M0 ⅢB,T4 a N3M0 ⅢC,T4 a N3M0 ⅢC,T4 a N3M0 ⅢC,and T4 b N3M0 ⅢC.In conclusion,our study indicated that carbon nanoparticles failed to show good selectivity for metastatic lymph nodes;the result of lymphatic mapping does not achieve a satisfactory performance;the incidence of lymph node metastasis may increase,accompanying with the increase of the depth of cancer invasion;No.8p lymph node metastasis tends to occur for gastric carcinoma patients with the extent of lymph node metastasis over N2 stage.展开更多
The discovery and application of environment-sensitive genic male sterile(EGMS) rice germplasm provide an easy method for hybrid rice breeding and have made great contributions to hybrid rice production. Typically, th...The discovery and application of environment-sensitive genic male sterile(EGMS) rice germplasm provide an easy method for hybrid rice breeding and have made great contributions to hybrid rice production. Typically, the photoperiod-and thermosensitive GMS(P/TGMS) lines utilized in two-line hybrid systems are male sterile under long day or/and high temperature but fertile under short day or/and low temperature conditions. However, Yannong S(Yn S), a reverse TGMS(rTGMS) line, is sterile under low temperature(<29℃) and fertile under high temperature(>29.5℃). Here, we report a genetic study on the rTGMS trait in Yn S. Interestingly, the F1 plants of the cross between Yn S and a cultivar, L422, were male sterile at 22℃ and completely fertile at 27℃. Moreover, the segregation ratio of fertile and sterile individuals in Yn S/L422 F2 populations changed from 1:3.05 to 2.95:1 when the ambient temperature increased, showing that the rTGMS trait exhibits semidominance in Yn S. We further found a locus on chromosome 10, termed RTMS10, which controls the rTGMS trait in Yn S. We then finely mapped RTMS10 to a ~68 kb interval between markers ID13116 and ID1318 by Yn S/L422 BC6 F2 populations. A near iso-genic line(NIL) NL1 from the BC6 F3 generation was developed and the pollen of NL1 became abnormal from the meiosis stage under low temperature. In summary, we identified an rTGMS locus, RTMS10, and provided co-segregated markers, which could help to accelerate molecular breeding of rTGMS lines and better understand the rTGMS trait in rice.展开更多
Recently,convolutional neural network(CNN)-based visual inspec-tion has been developed to detect defects on building surfaces automatically.The CNN model demonstrates remarkable accuracy in image data analysis;however...Recently,convolutional neural network(CNN)-based visual inspec-tion has been developed to detect defects on building surfaces automatically.The CNN model demonstrates remarkable accuracy in image data analysis;however,the predicted results have uncertainty in providing accurate informa-tion to users because of the“black box”problem in the deep learning model.Therefore,this study proposes a visual explanation method to overcome the uncertainty limitation of CNN-based defect identification.The visual repre-sentative gradient-weights class activation mapping(Grad-CAM)method is adopted to provide visually explainable information.A visualizing evaluation index is proposed to quantitatively analyze visual representations;this index reflects a rough estimate of the concordance rate between the visualized heat map and intended defects.In addition,an ablation study,adopting three-branch combinations with the VGG16,is implemented to identify perfor-mance variations by visualizing predicted results.Experiments reveal that the proposed model,combined with hybrid pooling,batch normalization,and multi-attention modules,achieves the best performance with an accuracy of 97.77%,corresponding to an improvement of 2.49%compared with the baseline model.Consequently,this study demonstrates that reliable results from an automatic defect classification model can be provided to an inspector through the visual representation of the predicted results using CNN models.展开更多
In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n|zi|p〈1,1〈p〈+∞. It is proved that for such f,| | |f||(z)|≤1-||f(z)||^2/1-|z|^2,z∈D. Th...In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n|zi|p〈1,1〈p〈+∞. It is proved that for such f,| | |f||(z)|≤1-||f(z)||^2/1-|z|^2,z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.展开更多
Mind map has been widely recognized as an effective teaching and learning tool in all levels of education. This paper, based on the writer’s teaching practice, aimed to investigate the potential use of mind map in En...Mind map has been widely recognized as an effective teaching and learning tool in all levels of education. This paper, based on the writer’s teaching practice, aimed to investigate the potential use of mind map in English intensive reading classes of college students, and found that it could help students to understand and memorize the main ideas and important details of reading materials in a systematical way.展开更多
In this paper some theorems on fixed points of pair of asymptotically regularmappings in p-uniformly convex Banach space are proved For these mappings somefixed point theorems in a Hilbert space.in Lp spaces in Hardy ...In this paper some theorems on fixed points of pair of asymptotically regularmappings in p-uniformly convex Banach space are proved For these mappings somefixed point theorems in a Hilbert space.in Lp spaces in Hardy spaces Hp and in Sobolev spaces Hpk for 1<P<+∞ and K>0 are also established.Thus resultsof Gornicki Kruppel and others are extended.展开更多
In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this i...In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this iteration scheme is equivalent to the convergency of some other implicit Kirk-type iteration (implicit Kirk-Noor, implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class of maps. Some numerical examples were considered to show that the equivalence of convergence results to the fixed point is true. The results unify most equivalence results in literature.展开更多
We introduce a new family of classes of operators termed as *p-paranormal operator, classes *A(p,p);p > 0 and *A(p,q);p, q > 0, parallel to p-paranormal operator and classes A(p,p);p> 0 and A(p,q);p, q > 0...We introduce a new family of classes of operators termed as *p-paranormal operator, classes *A(p,p);p > 0 and *A(p,q);p, q > 0, parallel to p-paranormal operator and classes A(p,p);p> 0 and A(p,q);p, q > 0 introduced by M. Fujii, D. Jung, S. H. Lee, M. Y. Lee and R. Nakamoto [1]. We present a necessary and sufficient condition for p-hyponormal operator T∈B(H)to be *p-paranormal and the monotonicity of *A(p,q). We also present an alternative proof of a result of M. Fujii, et al. [1, Theorem 3.4].展开更多
Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are...Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.展开更多
In this paper, by initiative research on local spectral theory of total class wF(p, r, q) operators, we get some important results. Such as total class wF(p, r,q) operators is normaloid operator, the local spectra...In this paper, by initiative research on local spectral theory of total class wF(p, r, q) operators, we get some important results. Such as total class wF(p, r,q) operators is normaloid operator, the local spectral subspace of total class wF(p, r, q) operators is equal to the space EλH(Eλ the Reisz idempotent, with respect to λ1, of T), total class wF(p, r, q) operators has finite ascent, and so on.展开更多
Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These i...Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.展开更多
In this article, we give an operator transform T (*) from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ...In this article, we give an operator transform T (*) from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ(T ) = σ( T (*)) and σa(T )/{0} = σa( T (*))/{0}, in case T belongs to class A. Next, we obtain some relations between T and T (9).展开更多
Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximat...Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M≃G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk≃(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK≃(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.展开更多
Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p- class group of type (2,2,2) , ...Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p- class group of type (2,2,2) , resp. (3,3), form periodic sequences in the descendant tree of the elementary Abelian root , resp. . The particular vertex of the periodic sequence which occurs as the p-class tower group G of an assigned field K is determined uniquely by the p-class number of a quadratic, resp. cubic, auxiliary field k, associated unambiguously to K. Consequently, the hard problem of identifying the p-class tower group G is reduced to an easy computation of low degree arithmetical invariants.展开更多
Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an ...Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.展开更多
The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in...The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.展开更多
Zeolite P was synthesized through hydrothermal method based on a kind of Class C fly ash(FA). X-ray diffraction(XRD), scanning electron microscopy(SEM), and Brunauer–Emmett–Teller(BET) were used to analyze and chara...Zeolite P was synthesized through hydrothermal method based on a kind of Class C fly ash(FA). X-ray diffraction(XRD), scanning electron microscopy(SEM), and Brunauer–Emmett–Teller(BET) were used to analyze and characterize the synthetic sample. The kinetics and thermodynamics of copper and nickel ions removed by the zeolite samples were experimentally explored in detail. The results of kinetic treatment showed the second-order exchange second-order saturation model(SESSM) can well describe the removal process of copper ions, while the first-order empirical kinetic model(FEKM) is the best kinetic model for nickel ions. Langmuir and Freundlich isotherms were used to fit the equilibrium concentration of Cu(Ⅱ) or Ni(Ⅱ) under certain conditions. Whether for copper or nickel ion, the Langmuir model is in good agreement with the experimental equilibrium concentration.The apparent theoretical removal capacities for Cu(Ⅱ) and Ni(Ⅱ) can reach to 138.1 mg·g^(-1) and 77.0 mg·g^(-1),respectively.展开更多
文摘The study aimed to examine the applicability of carbon nanoparticles as a tracer for lymph node mapping and the related factors of lymph node and No.8p subgroup metastasis in patients with gastric cancer.Clinical data of 50 patients with gastric cancer,who had not received treatment preoperatively and underwent gastrectomy in Department of Gastrointestinal Surgery,Wuhan Union Hospital,between October 2014 and August 2015,were retrospectively analyzed.These patients were found to have no distant metastasis preoperatively.Thirty-five out of 50 patients were subjected to lymphatic mapping technique using carbon nanoparticles as the tracer,and the rest 15 cases did not experience the lymphatic mapping and served as controls.The sensitivity,specificity,false positive rate and false negative rate were calculated according to the number of lymph nodes,and the staining and metastasis condition of lymph nodes.The diagnostic value of carbon nanoparticles on metastatic lymph nodes was evaluated.The relationship between the metastasis of lymph nodes or subgroup No.8p lymph nodes and clinicopathologic features was analyzed by χ^2-test or Fisher's exact test.All patients underwent D2 surgery(lymph node dissection including all the group 1 and group 2 nodes) plus the dissection of the subgroup No.8p lymph nodes.It was found that the average number of harvested lymph nodes in lymphatic mapping technique group(45.7±14.5) was greater than that in control group(39.2±11.7),but the difference was not significantly different(P=0.138〉0.05).The success rate,the accuracy,sensitivity,specificity and false negative rate was 97%,57%,28%,62% and 72% respectively.The metastasis of lymph nodes was correlated to the depth of cancer invasion(T stage)(P=0.004〈0.05),and the metastasis of No.8p lymph nodes was correlated to the extent of lymph node involvement(N stage)(P=0.007〈0.05).Six cases had lymph node metastasis in subgroup No.8p,and their TNM stages and clinical stages were as follows:T1N2M0 ⅡA,T3N3M0 ⅢB,T4 a N3M0 ⅢC,T4 a N3M0 ⅢC,T4 a N3M0 ⅢC,and T4 b N3M0 ⅢC.In conclusion,our study indicated that carbon nanoparticles failed to show good selectivity for metastatic lymph nodes;the result of lymphatic mapping does not achieve a satisfactory performance;the incidence of lymph node metastasis may increase,accompanying with the increase of the depth of cancer invasion;No.8p lymph node metastasis tends to occur for gastric carcinoma patients with the extent of lymph node metastasis over N2 stage.
基金funded by the Key Research and Development Program of Anhui Province,China(201904a06020016 and 202104g01020013)the National Natural Science Foundation of China(31101204)the Program of Rice Genetic Breeding Key Laboratory of Anhui Province,China(SDKF-201903)。
文摘The discovery and application of environment-sensitive genic male sterile(EGMS) rice germplasm provide an easy method for hybrid rice breeding and have made great contributions to hybrid rice production. Typically, the photoperiod-and thermosensitive GMS(P/TGMS) lines utilized in two-line hybrid systems are male sterile under long day or/and high temperature but fertile under short day or/and low temperature conditions. However, Yannong S(Yn S), a reverse TGMS(rTGMS) line, is sterile under low temperature(<29℃) and fertile under high temperature(>29.5℃). Here, we report a genetic study on the rTGMS trait in Yn S. Interestingly, the F1 plants of the cross between Yn S and a cultivar, L422, were male sterile at 22℃ and completely fertile at 27℃. Moreover, the segregation ratio of fertile and sterile individuals in Yn S/L422 F2 populations changed from 1:3.05 to 2.95:1 when the ambient temperature increased, showing that the rTGMS trait exhibits semidominance in Yn S. We further found a locus on chromosome 10, termed RTMS10, which controls the rTGMS trait in Yn S. We then finely mapped RTMS10 to a ~68 kb interval between markers ID13116 and ID1318 by Yn S/L422 BC6 F2 populations. A near iso-genic line(NIL) NL1 from the BC6 F3 generation was developed and the pollen of NL1 became abnormal from the meiosis stage under low temperature. In summary, we identified an rTGMS locus, RTMS10, and provided co-segregated markers, which could help to accelerate molecular breeding of rTGMS lines and better understand the rTGMS trait in rice.
基金supported by a Korea Agency for Infrastructure Technology Advancement(KAIA)grant funded by the Ministry of Land,Infrastructure,and Transport(Grant 22CTAP-C163951-02).
文摘Recently,convolutional neural network(CNN)-based visual inspec-tion has been developed to detect defects on building surfaces automatically.The CNN model demonstrates remarkable accuracy in image data analysis;however,the predicted results have uncertainty in providing accurate informa-tion to users because of the“black box”problem in the deep learning model.Therefore,this study proposes a visual explanation method to overcome the uncertainty limitation of CNN-based defect identification.The visual repre-sentative gradient-weights class activation mapping(Grad-CAM)method is adopted to provide visually explainable information.A visualizing evaluation index is proposed to quantitatively analyze visual representations;this index reflects a rough estimate of the concordance rate between the visualized heat map and intended defects.In addition,an ablation study,adopting three-branch combinations with the VGG16,is implemented to identify perfor-mance variations by visualizing predicted results.Experiments reveal that the proposed model,combined with hybrid pooling,batch normalization,and multi-attention modules,achieves the best performance with an accuracy of 97.77%,corresponding to an improvement of 2.49%compared with the baseline model.Consequently,this study demonstrates that reliable results from an automatic defect classification model can be provided to an inspector through the visual representation of the predicted results using CNN models.
基金supported by National Natural Science Foundations of China(11011373,11201199,11271333)Zhejiang Provincial Natural Science Foundation of China(LY14A010008)
文摘In this note, we consider a holomorphic mapping f from the unit disk C in C to p-ball B^p = {z∈C^n;i=1∑n|zi|p〈1,1〈p〈+∞. It is proved that for such f,| | |f||(z)|≤1-||f(z)||^2/1-|z|^2,z∈D. The extremal problem is also discussed when p is an even number. This result extends some related results on Schwarz lemma.
文摘Mind map has been widely recognized as an effective teaching and learning tool in all levels of education. This paper, based on the writer’s teaching practice, aimed to investigate the potential use of mind map in English intensive reading classes of college students, and found that it could help students to understand and memorize the main ideas and important details of reading materials in a systematical way.
文摘In this paper some theorems on fixed points of pair of asymptotically regularmappings in p-uniformly convex Banach space are proved For these mappings somefixed point theorems in a Hilbert space.in Lp spaces in Hardy spaces Hp and in Sobolev spaces Hpk for 1<P<+∞ and K>0 are also established.Thus resultsof Gornicki Kruppel and others are extended.
文摘In this paper, a modified implicit Kirk-multistep iteration scheme and a strong convergence result for a general class of maps in a normed linear space was established. It was also shown that the convergence of this iteration scheme is equivalent to the convergency of some other implicit Kirk-type iteration (implicit Kirk-Noor, implicit Kirk-Ishikawa and implicit Kirk-Mann iterations) for the same class of maps. Some numerical examples were considered to show that the equivalence of convergence results to the fixed point is true. The results unify most equivalence results in literature.
文摘We introduce a new family of classes of operators termed as *p-paranormal operator, classes *A(p,p);p > 0 and *A(p,q);p, q > 0, parallel to p-paranormal operator and classes A(p,p);p> 0 and A(p,q);p, q > 0 introduced by M. Fujii, D. Jung, S. H. Lee, M. Y. Lee and R. Nakamoto [1]. We present a necessary and sufficient condition for p-hyponormal operator T∈B(H)to be *p-paranormal and the monotonicity of *A(p,q). We also present an alternative proof of a result of M. Fujii, et al. [1, Theorem 3.4].
文摘Let F be a number field and p be a prime. In the successive approximation theorem, we prove that, for each integer n ≥ 1, finitely many candidates for the Galois group of the nth stage of the p-class tower over F are determined by abelian type invariants of p-class groups C1pE of unramified extensions E/F with degree [E : F] = pn-1. Illustrated by the most extensive numerical results available currently, the transfer kernels (TE, F) of the p-class extensions TE, F : C1pF → C1pE from F to unramified cyclic degree-p extensions E/F are shown to be capable of narrowing down the number of contestants significantly. By determining the isomorphism type of the maximal subgroups S G of all 3-groups G with coclass cc(G) = 1, and establishing a general theorem on the connection between the p-class towers of a number field F and of an unramified abelian p-extension E/F, we are able to provide a theoretical proof of the realization of certain 3-groups S with maximal class by 3-tower groups of dihedral fields E with degree 6, which could not be realized up to now.
文摘In this paper, by initiative research on local spectral theory of total class wF(p, r, q) operators, we get some important results. Such as total class wF(p, r,q) operators is normaloid operator, the local spectral subspace of total class wF(p, r, q) operators is equal to the space EλH(Eλ the Reisz idempotent, with respect to λ1, of T), total class wF(p, r, q) operators has finite ascent, and so on.
文摘Given a fixed prime number p, the multiplet of abelian type invariants of the p-class groups of all unramified cyclic degree p extensions of a number field K is called its IPAD (index-p abeliani- zation data). These invariants have proved to be a valuable information for determining the Galois group of the second Hilbert p-class field and the p-capitulation type of K. For p=3 and a number field K with elementary p-class group of rank two, all possible IPADs are given in the complete form of several infinite sequences. Iterated IPADs of second order are used to identify the group of the maximal unramified pro-p extension of K.
基金supported by Science Foundation of Ministry of Education of China (208081)Technology and pioneering project in Henan Provice (102300410012)Education Foundation of Henan Province (2007110016, 2008B110006)
文摘In this article, we give an operator transform T (*) from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ(T ) = σ( T (*)) and σa(T )/{0} = σa( T (*))/{0}, in case T belongs to class A. Next, we obtain some relations between T and T (9).
文摘Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient M≃G/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants for the second p-class group M of K. In this paper we introduce two different kinds of generalized IPADs for obtaining more sophisticated results. The multi-layered IPAD (τ1Kτ(2)K) includes data on unramified abelian extensions L/K of degree p2 and enables sharper bounds for the order of M in the case Clpk≃(p,p,p), where current im-plementations of the p-group generation algorithm fail to produce explicit contestants for M , due to memory limitations. The iterated IPAD of second order τ(2)K contains information on non-abelian unramified extensions L/K of degree p2, or even p3, and admits the identification of the p-class tower group G for various infinite series of quadratic fields K=Q(√d) with ClpK≃(p,p) possessing a p-class field tower of exact length lpK=3 as a striking novelty.
文摘Recent examples of periodic bifurcations in descendant trees of finite p-groups with ?are used to show that the possible p-class tower groups G of certain multiquadratic fields K with p- class group of type (2,2,2) , resp. (3,3), form periodic sequences in the descendant tree of the elementary Abelian root , resp. . The particular vertex of the periodic sequence which occurs as the p-class tower group G of an assigned field K is determined uniquely by the p-class number of a quadratic, resp. cubic, auxiliary field k, associated unambiguously to K. Consequently, the hard problem of identifying the p-class tower group G is reduced to an easy computation of low degree arithmetical invariants.
文摘Let p be a prime. For any finite p-group G, the deep transfers T H,G ' : H / H ' → G ' / G " from the maximal subgroups H of index (G:H) = p in G to the derived subgroup G ' are introduced as an innovative tool for identifying G uniquely by means of the family of kernels ùd(G) =(ker(T H,G ')) (G: H) = p. For all finite 3-groups G of coclass cc(G) = 1, the family ùd(G) is determined explicitly. The results are applied to the Galois groups G =Gal(F3 (∞)/ F) of the Hilbert 3-class towers of all real quadratic fields F = Q(√d) with fundamental discriminants d > 1, 3-class group Cl3(F) □ C3 × C3, and total 3-principalization in each of their four unramified cyclic cubic extensions E/F. A systematic statistical evaluation is given for the complete range 1 d 7, and a few exceptional cases are pointed out for 1 d 8.
文摘The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.
基金Supported by the National Natural Science Foundation of China(51478308)the Scientific Research Special Fund of Marine Public Welfare Industry(201405008)the Natural Science Foundation of Tianjin(14JCYBJC23300)
文摘Zeolite P was synthesized through hydrothermal method based on a kind of Class C fly ash(FA). X-ray diffraction(XRD), scanning electron microscopy(SEM), and Brunauer–Emmett–Teller(BET) were used to analyze and characterize the synthetic sample. The kinetics and thermodynamics of copper and nickel ions removed by the zeolite samples were experimentally explored in detail. The results of kinetic treatment showed the second-order exchange second-order saturation model(SESSM) can well describe the removal process of copper ions, while the first-order empirical kinetic model(FEKM) is the best kinetic model for nickel ions. Langmuir and Freundlich isotherms were used to fit the equilibrium concentration of Cu(Ⅱ) or Ni(Ⅱ) under certain conditions. Whether for copper or nickel ion, the Langmuir model is in good agreement with the experimental equilibrium concentration.The apparent theoretical removal capacities for Cu(Ⅱ) and Ni(Ⅱ) can reach to 138.1 mg·g^(-1) and 77.0 mg·g^(-1),respectively.