Satisfactory single crystals of deshexapeptide(B25—B30) insulin for X-ray crystal structure analysis have been grown in citrate buffer by the method of hanging-drop gas phase diffusion. The crystal belongs to the mon...Satisfactory single crystals of deshexapeptide(B25—B30) insulin for X-ray crystal structure analysis have been grown in citrate buffer by the method of hanging-drop gas phase diffusion. The crystal belongs to the monoclinic system with space group C2. The unit cell constants are α=42.6, b=37.9, c=27.2, β=125.4 and there is only one molecule of deshexapeptide insulin in an asymmetric unit.展开更多
Desheptapeptide (B24 B30) insulin (DHPI), a virtually inactive insulin analog, has been crystallized in space group P2\-12\-12\-1 with two DHPI molecules in an asymmetric unit. The orientations and positions of the mo...Desheptapeptide (B24 B30) insulin (DHPI), a virtually inactive insulin analog, has been crystallized in space group P2\-12\-12\-1 with two DHPI molecules in an asymmetric unit. The orientations and positions of the molecules were determined by molecular replacement, and a structural model was built at 0.3 nm resolution. The current model shows that the two DHPI monomers are related by a non crystallographic 2 fold axis, nearly parallel to the crystallographic c axis. This structural feature complicated the determination of the orientation of the local 2 fold axis, which was later confirmed by analysing the diffraction data of DHPI crystals.展开更多
The structure-function relationship of insulin to be understood at three-dimensional level has already been a challenging problem since the elucidation of fine crystal structures of insulin. Of course, it is a better ...The structure-function relationship of insulin to be understood at three-dimensional level has already been a challenging problem since the elucidation of fine crystal structures of insulin. Of course, it is a better experimental approach to such a problem that certain insulin-receptor complexes were prepared and their structures were展开更多
Using the crystal structure of Despentapeptide (B26-B30) insulin (DPI) as the search model, the crystal structure of DesBl-B2 Despentapeptide (B26-B30) insulin (DesBl-2 DPI) has been studied by the molecular replaceme...Using the crystal structure of Despentapeptide (B26-B30) insulin (DPI) as the search model, the crystal structure of DesBl-B2 Despentapeptide (B26-B30) insulin (DesBl-2 DPI) has been studied by the molecular replacement method. There is one DesBl-2 DPI molecule in each crystallographic asymmetric unit. The cross rotation function search and the translation function search show apparent peaks and thus determine the orientation and position of DesBl-2 DPI molecule in the cell respectively. The subsequent three-dimensional structural rebuilding and refine-ment of DesBl-2 DPI molecule confirm the results by molecular replacement method.展开更多
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the f...In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.展开更多
We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
Let L be a linear operator in L 2 (? n ) and generate an analytic semigroup {e ?tL }t?0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper ...Let L be a linear operator in L 2 (? n ) and generate an analytic semigroup {e ?tL }t?0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper type 1 and of critical lower type p o (ω) ? (n/(n+θ(L)),1] and ρ(t) = t t1/ω ?1(t ?1) for t ∈ (0,∞). We introduce the Orlicz-Hardy space H ω, L (? n ) and the BMO-type space BMO ρ, L (? n ) and establish the John-Nirenberg inequality for BMO ρ, L (? n ) functions and the duality relation between H ω, L ((? n ) and BMO ρ, L* (? n ), where L* denotes the adjoint operator of L in L 2 (? n ). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMO ρ, L* (? n ) and the molecular characterization of H ω, L (? n ); the latter is used to establish the boundedness of the generalized fractional operator L ρ ?γ from H ω, L (? n ) to H L 1 (? n ) or L q (? n ) with certain q > 1, where H L (? n ) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = t p for t ∈ (0,∞) and p ∈ (n/(n + θ(L)), 1].展开更多
Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a “dimension” n. For α ∈ (0, ∞) denote by H α p (X), H d p (X...Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a “dimension” n. For α ∈ (0, ∞) denote by H α p (X), H d p (X), and H *,p (X) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calderón reproducing formula, it is shown that all these Hardy spaces coincide with L p (X) when p ∈ (1,∞] and with each other when p ∈ (n/(n + 1), 1]. An atomic characterization for H ?,p (X) with p ∈ (n/(n + 1), 1] is also established; moreover, in the range p ∈ (n/(n + 1),1], it is proved that the space H *,p (X), the Hardy space H p (X) defined via the Littlewood-Paley function, and the atomic Hardy space of Coifman andWeiss coincide. Furthermore, it is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from H p (X) to some quasi-Banach space B if and only if T maps all (p, q)-atoms when q ∈ (p, ∞)∩[1, ∞) or continuous (p, ∞)-atoms into uniformly bounded elements of B.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Satisfactory single crystals of deshexapeptide(B25—B30) insulin for X-ray crystal structure analysis have been grown in citrate buffer by the method of hanging-drop gas phase diffusion. The crystal belongs to the monoclinic system with space group C2. The unit cell constants are α=42.6, b=37.9, c=27.2, β=125.4 and there is only one molecule of deshexapeptide insulin in an asymmetric unit.
文摘Desheptapeptide (B24 B30) insulin (DHPI), a virtually inactive insulin analog, has been crystallized in space group P2\-12\-12\-1 with two DHPI molecules in an asymmetric unit. The orientations and positions of the molecules were determined by molecular replacement, and a structural model was built at 0.3 nm resolution. The current model shows that the two DHPI monomers are related by a non crystallographic 2 fold axis, nearly parallel to the crystallographic c axis. This structural feature complicated the determination of the orientation of the local 2 fold axis, which was later confirmed by analysing the diffraction data of DHPI crystals.
文摘The structure-function relationship of insulin to be understood at three-dimensional level has already been a challenging problem since the elucidation of fine crystal structures of insulin. Of course, it is a better experimental approach to such a problem that certain insulin-receptor complexes were prepared and their structures were
基金Project supported by the Fonndation of Chinese Academy of Sciences and the National Natural Science Foundation of China
文摘Using the crystal structure of Despentapeptide (B26-B30) insulin (DPI) as the search model, the crystal structure of DesBl-B2 Despentapeptide (B26-B30) insulin (DesBl-2 DPI) has been studied by the molecular replacement method. There is one DesBl-2 DPI molecule in each crystallographic asymmetric unit. The cross rotation function search and the translation function search show apparent peaks and thus determine the orientation and position of DesBl-2 DPI molecule in the cell respectively. The subsequent three-dimensional structural rebuilding and refine-ment of DesBl-2 DPI molecule confirm the results by molecular replacement method.
基金Supported by the National Natural Science Foundation of China(11071200,11371295)
文摘In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.
基金the National Natural Science Foundation of China (Grant No. 10671049), Longjiang Scholar GrantScience Research Fund of the Education Department of Heilongjiang Province (Grant No.11531246)Harbin Normal University Academic Backbone of Youth Project
文摘We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
基金supported by National Science Foundation for Distinguished Young Scholars of China (GrantNo. 10425106)
文摘Let L be a linear operator in L 2 (? n ) and generate an analytic semigroup {e ?tL }t?0 with kernel satisfying an upper bound of Poisson type, whose decay is measured by θ(L) ∈ (0, ∞). Let ω on (0,∞) be of upper type 1 and of critical lower type p o (ω) ? (n/(n+θ(L)),1] and ρ(t) = t t1/ω ?1(t ?1) for t ∈ (0,∞). We introduce the Orlicz-Hardy space H ω, L (? n ) and the BMO-type space BMO ρ, L (? n ) and establish the John-Nirenberg inequality for BMO ρ, L (? n ) functions and the duality relation between H ω, L ((? n ) and BMO ρ, L* (? n ), where L* denotes the adjoint operator of L in L 2 (? n ). Using this duality relation, we further obtain the ρ-Carleson measure characterization of BMO ρ, L* (? n ) and the molecular characterization of H ω, L (? n ); the latter is used to establish the boundedness of the generalized fractional operator L ρ ?γ from H ω, L (? n ) to H L 1 (? n ) or L q (? n ) with certain q > 1, where H L (? n ) is the Hardy space introduced by Auscher, Duong and McIntosh. These results generalize the existing results by taking ω(t) = t p for t ∈ (0,∞) and p ∈ (n/(n + θ(L)), 1].
基金supported by the National Science Foundation of USA (Grant No. DMS 0400387)the University of Missouri Research Council (Grant No. URC-07-067)+1 种基金the National Science Foundation for Distinguished Young Scholars of China (Grant No. 10425106)the Program for New Century Excellent Talents in University of the Ministry of Education of China (Grant No. 04-0142)
文摘Let X be an RD-space, i.e., a space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property. Assume that X has a “dimension” n. For α ∈ (0, ∞) denote by H α p (X), H d p (X), and H *,p (X) the corresponding Hardy spaces on X defined by the nontangential maximal function, the dyadic maximal function and the grand maximal function, respectively. Using a new inhomogeneous Calderón reproducing formula, it is shown that all these Hardy spaces coincide with L p (X) when p ∈ (1,∞] and with each other when p ∈ (n/(n + 1), 1]. An atomic characterization for H ?,p (X) with p ∈ (n/(n + 1), 1] is also established; moreover, in the range p ∈ (n/(n + 1),1], it is proved that the space H *,p (X), the Hardy space H p (X) defined via the Littlewood-Paley function, and the atomic Hardy space of Coifman andWeiss coincide. Furthermore, it is proved that a sublinear operator T uniquely extends to a bounded sublinear operator from H p (X) to some quasi-Banach space B if and only if T maps all (p, q)-atoms when q ∈ (p, ∞)∩[1, ∞) or continuous (p, ∞)-atoms into uniformly bounded elements of B.
