The structure factors of any crystal structure can be simulated from its atomic coordinates (and temperature factors) in a SHELXL-97 run on a dummy hkl in which only the scale factor is refined. The squares of the str...The structure factors of any crystal structure can be simulated from its atomic coordinates (and temperature factors) in a SHELXL-97 run on a dummy hkl in which only the scale factor is refined. The squares of the structure factors are retrieved from the fcf, and such simulated data are used in the revision of the space groups of several incorrectly-refined crystal structures. Two cases, a P1 to P1 revision and a chemically-incorrect structure that is refined in a correct space group, are discussed.展开更多
In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedfr...In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedframework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques,which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency andoveremphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective featureextraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Liegroup domains to highlight fundamental motion patterns, coupled with employing competitive weighting forprecise target deformation field generation. Our empirical evaluations confirm TEMT’s superior performancein handling diverse PET lung datasets compared to existing image registration networks. Experimental resultsdemonstrate that TEMT achieved Dice indices of 91.40%, 85.41%, 79.78%, and 72.16% on simulated geometricphantom data, lung voxel phantom data, cardiopulmonary voxel phantom data, and clinical data, respectively. Tofacilitate further research and practical application, the TEMT framework, along with its implementation detailsand part of the simulation data, is made publicly accessible at https://github.com/yehaowei/temt.展开更多
The utilization and development of urban underground space play a crucial role in optimizing the layout of civic architecture and enhancing the urban ecological environment,which contributes toward increasing the over...The utilization and development of urban underground space play a crucial role in optimizing the layout of civic architecture and enhancing the urban ecological environment,which contributes toward increasing the overall carrying capacity and promoting sustainable development in megacities.To delve into the research progress of urban underground space,knowledge maps were created using the information visualization software VOSviewer.The literature was systematically extracted from three prominent databases,namely,Web of Science,Scopus,and China National Knowledge Infrastructure.According to the bibliometric analysis of the co-citation and core words co-occurrence,the trends and challenges of research on urban underground space were identified.As highlighted by the results obtained,it still remains highly challenging to achieve interdisciplinary collaboration in urban underground space research;the research trends of urban underground space consist of collaborative planning and whole life cycle sustainable development,multisource geological data informatization and resource evaluation,infrastructure design optimization,and intelligent construction.The knowledge map,drawn using bibliometric methods,offers a quantitative analysis of literature retrieval across various levels.It is recognized as an essential tool for exploring and identifying challenges and trends in urban underground space.展开更多
In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G (i.e., nilpotent stratified Lie group) in the generalized Morrey spaces Mp,φ(G), where Q is the homogeneous dimens...In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G (i.e., nilpotent stratified Lie group) in the generalized Morrey spaces Mp,φ(G), where Q is the homogeneous dimension of G. We find the conditions on the pair (φ1, φ2) which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 (G) to another Mq,φ2 (G), 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 (G) to the weak space Wq,φ2 (G), 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α (G) from Mp,φ^1/p(G)to Mq,φ^1/q(G) for 1 〈p〈q〈∞ and fromM1,φ(G) toWMq,φ^1/q(G)for 1〈q〈∞. In the case b ∈ BMO(G) and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair (φ1, φ2) which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 (G) to Mq,φ2(G) with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p(G) tom Mp,φ^1/p (G) for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on (φ1, φ2) and φ , which do not assume any assumption on monotonicity of (φ1, φ2) and φ in r. As applications we consider the SchrSdinger operator -△G + V on G, where the nonnegative potential V belongs to the reverse Holder class B∞(G). The MB,φ1 - Mq,φ2 estimates for the operators V^γ(-△G + V)^-β and V^γ△↓G(-△G + V)^-β are obtained.展开更多
Recently, many new features of Sobolev spaces W k,p ?RN ? were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describin...Recently, many new features of Sobolev spaces W k,p ?RN ? were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].展开更多
This paper studies some boundedness results of commutators on a class of new spaces MKp,q^αλ (G) named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups
A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene(3DOM CLPS) by hydrophilic spacer arm has been investigated.Th...A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene(3DOM CLPS) by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm(polyethylene glycol,molecular weight is 600) was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole(MBZ) group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.展开更多
Two hundred cates of nasopharyngeal carcinoma (NPC) admitted to this department from Feb. 1985 to May. 1988 were analysed according to the CT scanning and clinical findings of the primary lesions prior to radiotherapy...Two hundred cates of nasopharyngeal carcinoma (NPC) admitted to this department from Feb. 1985 to May. 1988 were analysed according to the CT scanning and clinical findings of the primary lesions prior to radiotherapy. The results showed that involvement of parapharyngeal space was very common in NPC, about 80% (160/200 cases) ; particularly unilateral or bilateral retro-styloid spaces, about 69.5% (139/200 cases). It was proposed that patients with NPC had a high Incidence of ipsilateral cervical node metastasis. Contralateral cervical node metastasis was rare. The development of cervical node metastasto in NPC has two modes: one Is direct Infiltration of the retro-stylold space by the lesion; the other Is along the nasopharyngeal lymphatic rete. The data also showed that patients with NPC who presented symptoms of Ⅸ- Ⅲ cranial nerve paralyses always had ipsilateral or bilateral retro- styloid space Infiltrations.展开更多
Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
A TAPO-11 molecular sieve with the space group lcm2 was synthesized successfully. The samples with different space group were controlled simply only by adjusting the crystallization temperature (CT) in the hydrother...A TAPO-11 molecular sieve with the space group lcm2 was synthesized successfully. The samples with different space group were controlled simply only by adjusting the crystallization temperature (CT) in the hydrothermal system. In the system of gel with a molar composition of 0.7R- xTiO2: P2O5: Al2O3: 30H2O, where x is 0.01-0.10 and the R is a mixture of di-n-propylamine and diisopropylamine as templates. When CT was between 150-160℃, the calcined sample showed the space group of Icm^2, while it showed Pna21 at CT larger than 190℃. The characterizations of UV-Vis and FT-IR confirmed that Ti was incorporated into the AEL framework successfully.展开更多
In this note,we prove that expanders cannot be coarsely embedded into group extensions of sequences of groups which are coarsely embeddable into Hardamad manifolds and certain Banach spaces due to the similar concentr...In this note,we prove that expanders cannot be coarsely embedded into group extensions of sequences of groups which are coarsely embeddable into Hardamad manifolds and certain Banach spaces due to the similar concentration theorems.展开更多
Chevkinite specimen from a rare-earth mineral deposit in Sichuan, southwest of China have been studied in detail by means of transmission electron microscope (TEM).The selected area electron diffraction (SAED)and conv...Chevkinite specimen from a rare-earth mineral deposit in Sichuan, southwest of China have been studied in detail by means of transmission electron microscope (TEM).The selected area electron diffraction (SAED)and convergent beam electron diffraction (CBED) patterns , obtained from different crystal zone axis direction , proved coincidently that the space group of chevkinite is C2/m . Fringe lattice image observation showed the mineral crystal is structurally uniform in microscale , and it is an ideal specimen for electron diffraction analysis . The mineral studied here is similar to the one from Bayan Obo , Inner Mongolia , China , in chemical composition and REE distribution . The chemical formula of the crystal is (Ce , La ,… , Ca) 4 Fe2+ (Fe, Ti, Nb) 2 O8 (Si2O7)2 From our study , we come to the conclusion that the space group of the natural chevkinite is C2/m , instead of P21/a as synthetic one . Up to now , chevkinite compositionally similar to the synthetic one , in which the complete replacements of Ce , La by Nd and Fe by Mg or Co occur , has not been discovered in nature . So we suggest that the name for synthesized chevkinite should be further discussed .展开更多
In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P(G) and HKq^α,P(G), where 1 〈 q 〈 ∞, Q(1 - 1/q) ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie ...In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P(G) and HKq^α,P(G), where 1 〈 q 〈 ∞, Q(1 - 1/q) ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie group.展开更多
This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset ...This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil's formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 (G / H, μ).展开更多
Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give...Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.展开更多
We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition a...We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.展开更多
In this paper the boundedness results for some fractional and singular integral operators on the homogeneous Morrey-Herz spaces over locally compact Vilenkin groups are shown.
The space groups of 244 crystal structures originally reported as P-1 are revised to space groups of higher symmetry. The largest number involves revisions to P2/c and C2/c.
The space group of PrCo_(12)B_6,compound has been determined using the convergent beam elec- tron diffraction method.The space group is found to be R3m.
Analysis on the space group distribution in 78 substituted phenols re-vealed its unusual high frequencies in groups with non-centrosymmetry or polar axis orhigher symmetry or Z' > 1. Based on the characteristic...Analysis on the space group distribution in 78 substituted phenols re-vealed its unusual high frequencies in groups with non-centrosymmetry or polar axis orhigher symmetry or Z' > 1. Based on the characteristics of intermolecular H-bondsformed by two OH groups,the space group distribution could be rationalized well.展开更多
文摘The structure factors of any crystal structure can be simulated from its atomic coordinates (and temperature factors) in a SHELXL-97 run on a dummy hkl in which only the scale factor is refined. The squares of the structure factors are retrieved from the fcf, and such simulated data are used in the revision of the space groups of several incorrectly-refined crystal structures. Two cases, a P1 to P1 revision and a chemically-incorrect structure that is refined in a correct space group, are discussed.
基金the National Natural Science Foundation of China(No.82160347)Yunnan Provincial Science and Technology Department(No.202102AE090031)Yunnan Key Laboratory of Smart City in Cyberspace Security(No.202105AG070010).
文摘In addressing the challenge of motion artifacts in Positron Emission Tomography (PET) lung scans, our studyintroduces the Triple Equivariant Motion Transformer (TEMT), an innovative, unsupervised, deep-learningbasedframework for efficient respiratory motion correction in PET imaging. Unlike traditional techniques,which segment PET data into bins throughout a respiratory cycle and often face issues such as inefficiency andoveremphasis on certain artifacts, TEMT employs Convolutional Neural Networks (CNNs) for effective featureextraction and motion decomposition.TEMT’s unique approach involves transforming motion sequences into Liegroup domains to highlight fundamental motion patterns, coupled with employing competitive weighting forprecise target deformation field generation. Our empirical evaluations confirm TEMT’s superior performancein handling diverse PET lung datasets compared to existing image registration networks. Experimental resultsdemonstrate that TEMT achieved Dice indices of 91.40%, 85.41%, 79.78%, and 72.16% on simulated geometricphantom data, lung voxel phantom data, cardiopulmonary voxel phantom data, and clinical data, respectively. Tofacilitate further research and practical application, the TEMT framework, along with its implementation detailsand part of the simulation data, is made publicly accessible at https://github.com/yehaowei/temt.
基金Industry-University-Research Innovation Foundation of Chinese Universities,Grant/Award Number:2020ITA03010National Natural Science Foundation of China,Grant/Award Numbers:41920104007,42227805。
文摘The utilization and development of urban underground space play a crucial role in optimizing the layout of civic architecture and enhancing the urban ecological environment,which contributes toward increasing the overall carrying capacity and promoting sustainable development in megacities.To delve into the research progress of urban underground space,knowledge maps were created using the information visualization software VOSviewer.The literature was systematically extracted from three prominent databases,namely,Web of Science,Scopus,and China National Knowledge Infrastructure.According to the bibliometric analysis of the co-citation and core words co-occurrence,the trends and challenges of research on urban underground space were identified.As highlighted by the results obtained,it still remains highly challenging to achieve interdisciplinary collaboration in urban underground space research;the research trends of urban underground space consist of collaborative planning and whole life cycle sustainable development,multisource geological data informatization and resource evaluation,infrastructure design optimization,and intelligent construction.The knowledge map,drawn using bibliometric methods,offers a quantitative analysis of literature retrieval across various levels.It is recognized as an essential tool for exploring and identifying challenges and trends in urban underground space.
基金partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0018)partially supported by the grant of Ahi Evran University Scientific Research Projects(FEN 4001.12.0019)+1 种基金by the grant of Science Development Foundation under the President of the Republic of Azerbaijan project EIF-2010-1(1)-40/06-1partially supported by the Scientific and Technological Research Council of Turkey(TUBITAK Project No:110T695)
文摘In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G (i.e., nilpotent stratified Lie group) in the generalized Morrey spaces Mp,φ(G), where Q is the homogeneous dimension of G. We find the conditions on the pair (φ1, φ2) which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 (G) to another Mq,φ2 (G), 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 (G) to the weak space Wq,φ2 (G), 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α (G) from Mp,φ^1/p(G)to Mq,φ^1/q(G) for 1 〈p〈q〈∞ and fromM1,φ(G) toWMq,φ^1/q(G)for 1〈q〈∞. In the case b ∈ BMO(G) and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair (φ1, φ2) which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 (G) to Mq,φ2(G) with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p(G) tom Mp,φ^1/p (G) for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on (φ1, φ2) and φ , which do not assume any assumption on monotonicity of (φ1, φ2) and φ in r. As applications we consider the SchrSdinger operator -△G + V on G, where the nonnegative potential V belongs to the reverse Holder class B∞(G). The MB,φ1 - Mq,φ2 estimates for the operators V^γ(-△G + V)^-β and V^γ△↓G(-△G + V)^-β are obtained.
文摘Recently, many new features of Sobolev spaces W k,p ?RN ? were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].
基金Supported by Mudanjiang Teachers College (KZ2008001)by Scientific Research Fund of Heilongjiang Provincial Education Department(No.11541378)
文摘This paper studies some boundedness results of commutators on a class of new spaces MKp,q^αλ (G) named as homogenous Morrey-Herz spaces over locally compact Vilenkin groups
基金supported by National Natural Science Funds for Young Scholar(No.50903027)the Natural Science Foundation of Hebei Province(No.E2010000058)Education Department Science Research Plan of Hebei Province(No.2007307).
文摘A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene(3DOM CLPS) by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm(polyethylene glycol,molecular weight is 600) was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole(MBZ) group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.
文摘Two hundred cates of nasopharyngeal carcinoma (NPC) admitted to this department from Feb. 1985 to May. 1988 were analysed according to the CT scanning and clinical findings of the primary lesions prior to radiotherapy. The results showed that involvement of parapharyngeal space was very common in NPC, about 80% (160/200 cases) ; particularly unilateral or bilateral retro-styloid spaces, about 69.5% (139/200 cases). It was proposed that patients with NPC had a high Incidence of ipsilateral cervical node metastasis. Contralateral cervical node metastasis was rare. The development of cervical node metastasto in NPC has two modes: one Is direct Infiltration of the retro-stylold space by the lesion; the other Is along the nasopharyngeal lymphatic rete. The data also showed that patients with NPC who presented symptoms of Ⅸ- Ⅲ cranial nerve paralyses always had ipsilateral or bilateral retro- styloid space Infiltrations.
文摘Let G be a locally compact Vilenkin gro up . We will establish the boundedness in Morrey spaces L p,λ (G) for a la rge class of sublinear operators and linear commutators.
基金This work was supported by the National Natural Science Foundation of China (No. 20473027) Science and Technology Commission of Shanghai Municipality (No. 05dz22306)Pujiang project (No. 05PJ14041).
文摘A TAPO-11 molecular sieve with the space group lcm2 was synthesized successfully. The samples with different space group were controlled simply only by adjusting the crystallization temperature (CT) in the hydrothermal system. In the system of gel with a molar composition of 0.7R- xTiO2: P2O5: Al2O3: 30H2O, where x is 0.01-0.10 and the R is a mixture of di-n-propylamine and diisopropylamine as templates. When CT was between 150-160℃, the calcined sample showed the space group of Icm^2, while it showed Pna21 at CT larger than 190℃. The characterizations of UV-Vis and FT-IR confirmed that Ti was incorporated into the AEL framework successfully.
文摘In this note,we prove that expanders cannot be coarsely embedded into group extensions of sequences of groups which are coarsely embeddable into Hardamad manifolds and certain Banach spaces due to the similar concentration theorems.
基金Financial support for this study was provided by the Scicnce Foundation of Doctorate Program 8849104-11 from the National Committce of Education
文摘Chevkinite specimen from a rare-earth mineral deposit in Sichuan, southwest of China have been studied in detail by means of transmission electron microscope (TEM).The selected area electron diffraction (SAED)and convergent beam electron diffraction (CBED) patterns , obtained from different crystal zone axis direction , proved coincidently that the space group of chevkinite is C2/m . Fringe lattice image observation showed the mineral crystal is structurally uniform in microscale , and it is an ideal specimen for electron diffraction analysis . The mineral studied here is similar to the one from Bayan Obo , Inner Mongolia , China , in chemical composition and REE distribution . The chemical formula of the crystal is (Ce , La ,… , Ca) 4 Fe2+ (Fe, Ti, Nb) 2 O8 (Si2O7)2 From our study , we come to the conclusion that the space group of the natural chevkinite is C2/m , instead of P21/a as synthetic one . Up to now , chevkinite compositionally similar to the synthetic one , in which the complete replacements of Ce , La by Nd and Fe by Mg or Co occur , has not been discovered in nature . So we suggest that the name for synthesized chevkinite should be further discussed .
基金Supported by National Science Foundation of China, No. 10261007.
文摘In this paper, the authors establish some characterizations of Herz-type Hardy spaces HKq^α,P(G) and HKq^α,P(G), where 1 〈 q 〈 ∞, Q(1 - 1/q) ≤ α 〈 ∞, 0 〈 p 〈 ∞ and G denotes a gfaded homogeneous Lie group.
文摘This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil's formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 (G / H, μ).
文摘Let G be a Heisenberg group over local field K. In the paper we give some local maximal functions which define the Hardy spaces h(P)(G) equivalently, obtain the atomic decomposition of local Hardy spaces. We also give some bounded convolution operators h(P)(G), from which we can characterize h(P)(G) by sqare functions.
文摘We consider Hardy spaces with variable exponents defined by grand maximal function on the Heisenberg group. Then we introduce some equivalent characterizations of variable Hardy spaces. By using atomic decomposition and molecular decomposition we get the boundedness of singular integral operators on variable Hardy spaces. We investigate the Littlewood-Paley characterization by virtue of the boundedness of singular integral operators.
基金The NSF(A200913) of Heilongjiang ProvinceScientific Research Fund(11541378) of Heilongjiang Provincial Education DepartmentYoung Academic Backbone Projects(G201001) of Mudanjiang Normal University
文摘In this paper the boundedness results for some fractional and singular integral operators on the homogeneous Morrey-Herz spaces over locally compact Vilenkin groups are shown.
文摘The space groups of 244 crystal structures originally reported as P-1 are revised to space groups of higher symmetry. The largest number involves revisions to P2/c and C2/c.
文摘The space group of PrCo_(12)B_6,compound has been determined using the convergent beam elec- tron diffraction method.The space group is found to be R3m.
文摘Analysis on the space group distribution in 78 substituted phenols re-vealed its unusual high frequencies in groups with non-centrosymmetry or polar axis orhigher symmetry or Z' > 1. Based on the characteristics of intermolecular H-bondsformed by two OH groups,the space group distribution could be rationalized well.