Two new compounds, [Ni2（L1）（Py）6]Py·CH3OH（1） and [Ni3（LZ）2（PY）4]·2DMF（2）（H4L1=N,N＇-bisalicyl-bisthiocarbamide; H3L2=3-hydroxyl-2-naphthalene thiosemicarbazide; Py=pyridine; DMF=dimethyl fumarat...Two new compounds, [Ni2（L1）（Py）6]Py·CH3OH（1） and [Ni3（LZ）2（PY）4]·2DMF（2）（H4L1=N,N＇-bisalicyl-bisthiocarbamide; H3L2=3-hydroxyl-2-naphthalene thiosemicarbazide; Py=pyridine; DMF=dimethyl fumarate）, based upon two thiosemicarbazone ligands have been obtained and characterized by elemental analysis, Fourier transform infrared（FTIR） and X-ray diffraetion（XRD）. Compound 1 possesses a binuclear cluster, in which the bisalicylbisthi- ocarbamide acts as a hexadentate bridge. Compound 2 exhibits a linear trinuclear cluster with the triply-deprotonated ligand acting as pentadentate bridge. C--H…O, C--H…π and C--…S weak interactions further link these molecules to form interesting supramolecular networks.展开更多
Consider the Landau equation with Coulomb potential in a periodic box.We develop a new L^(2)to L^(∞)framework to construct global unique solutions near Maxwellian with small L^(∞)norm.The first step is to establish ...Consider the Landau equation with Coulomb potential in a periodic box.We develop a new L^(2)to L^(∞)framework to construct global unique solutions near Maxwellian with small L^(∞)norm.The first step is to establish global L^(2)estimates with strong velocity weight and time decay,under the assumption of L^(∞)bound,which is further controlled by such L^(2)estimates via De Giorgi’s method(Golse et al.in Ann.Sc.Norm.Super.Pisa Cl.Sci.(5)19(1),253-295(2019),Imbert and Mouhot in arXiv:1505.04608(2015)).The second step is to employ estimates in S_(p)spaces to control velocity derivatives to ensure uniqueness,which is based on Hölder estimates via De Giorgi’s method(Golse et al.in Ann.Sc.Norm.Super.Pisa Cl.Sci.(5)19(1),253-295(2019),Golse and Vas-seur in arXiv:1506.01908(2015),Imbert and Mouhot in arXiv:1505.04608(2015)).展开更多
基金Supported by the National Natural Science Foundation of China（No.21141003）, the Natural Science Foundation of Shandong Province of China（No.ZR2012BQ023 ） and the Natural Science Foundation of Liaocheng University of China（No.X09011）.
文摘Two new compounds, [Ni2（L1）（Py）6]Py·CH3OH（1） and [Ni3（LZ）2（PY）4]·2DMF（2）（H4L1=N,N＇-bisalicyl-bisthiocarbamide; H3L2=3-hydroxyl-2-naphthalene thiosemicarbazide; Py=pyridine; DMF=dimethyl fumarate）, based upon two thiosemicarbazone ligands have been obtained and characterized by elemental analysis, Fourier transform infrared（FTIR） and X-ray diffraetion（XRD）. Compound 1 possesses a binuclear cluster, in which the bisalicylbisthi- ocarbamide acts as a hexadentate bridge. Compound 2 exhibits a linear trinuclear cluster with the triply-deprotonated ligand acting as pentadentate bridge. C--H…O, C--H…π and C--…S weak interactions further link these molecules to form interesting supramolecular networks.
基金Yan Guo is supported in part by NSF grant#DMS-1810868Chinese NSF Grant#10828103as well as a Simon Fellowship.Hyung Ju Hwang was supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF-2017R1E1A1A03070105,NRF-2019R1A5A1028324).
文摘Consider the Landau equation with Coulomb potential in a periodic box.We develop a new L^(2)to L^(∞)framework to construct global unique solutions near Maxwellian with small L^(∞)norm.The first step is to establish global L^(2)estimates with strong velocity weight and time decay,under the assumption of L^(∞)bound,which is further controlled by such L^(2)estimates via De Giorgi’s method(Golse et al.in Ann.Sc.Norm.Super.Pisa Cl.Sci.(5)19(1),253-295(2019),Imbert and Mouhot in arXiv:1505.04608(2015)).The second step is to employ estimates in S_(p)spaces to control velocity derivatives to ensure uniqueness,which is based on Hölder estimates via De Giorgi’s method(Golse et al.in Ann.Sc.Norm.Super.Pisa Cl.Sci.(5)19(1),253-295(2019),Golse and Vas-seur in arXiv:1506.01908(2015),Imbert and Mouhot in arXiv:1505.04608(2015)).
