The synthesis and characterization are reported for a series of bi- and trinuclear complexes of the first transition metal ions with PBDETA, the newly syn thesized polydentate ligand. The electron transition energy in...The synthesis and characterization are reported for a series of bi- and trinuclear complexes of the first transition metal ions with PBDETA, the newly syn thesized polydentate ligand. The electron transition energy in binuclear compound is stronger than that in trinuclear. There is a weak antiferromagnetic exchange interaction in tricopper and trimanganese.展开更多
The interactions of 2,2'-bipyridyl with the lanthanide nitrates were studied and complexes of the formula Ln(NO_8)_8(bipy)_8 were isolated from water -ethanol mixed solvent.The complexes were characterized by elem...The interactions of 2,2'-bipyridyl with the lanthanide nitrates were studied and complexes of the formula Ln(NO_8)_8(bipy)_8 were isolated from water -ethanol mixed solvent.The complexes were characterized by elemental analysis, conductivity measurments,IR spectra and DAT-TG analysis.展开更多
A series of new complexes of formula Ln_2[H_2(BAA)_2en]_3nH_2 Otwhere Ln- La, Pr, Eu, Cd, Dy, Er, Yb, n-1-4) have been prepared by the reaccLon of lanthanide ions with acycllc compartmental ligand X, N'-bis(benzoy...A series of new complexes of formula Ln_2[H_2(BAA)_2en]_3nH_2 Otwhere Ln- La, Pr, Eu, Cd, Dy, Er, Yb, n-1-4) have been prepared by the reaccLon of lanthanide ions with acycllc compartmental ligand X, N'-bis(benzoylacetylacetone)ethylenediamine (H_4(BAA)_2 en) in methanol. IR and UV spectra, as well as TC DAT analysis prove that the ligand and the Lanthanide ions have coordinated. The coordination number is 12 and the complexes may be of double sandwiched structure.展开更多
Recent years,many novel complexes have been prepared by using hetero-bidentate ligands.However,complexes with such ligands as 4-vinylpyridine which has two different coordinating sites have not been reported,and only ...Recent years,many novel complexes have been prepared by using hetero-bidentate ligands.However,complexes with such ligands as 4-vinylpyridine which has two different coordinating sites have not been reported,and only a few complexes of Cu(I)have been published^(1-3).The title complex Cu_2(C_5H_4N·CH=CH_2)_3Cl was prepared and characterized by elemental analyses,ICP,IR,and electronic spectra.Its conductivity,oxidation potential and reduction potential were measured.展开更多
A new Schiff base (LK) obtained from 2, 4, -dihydroxybenzaldehyde and glycly-DL- phenylalanine reacted with Cu(II), Zn(II), Ni(II) and Co(II) to yield new complexes. The complexes were characterized by elemental an...A new Schiff base (LK) obtained from 2, 4, -dihydroxybenzaldehyde and glycly-DL- phenylalanine reacted with Cu(II), Zn(II), Ni(II) and Co(II) to yield new complexes. The complexes were characterized by elemental analyses, molar conductance, 1H NMR DTA, TG, IR and UV spectroscopy. In these complexes the ligand is coordinated to the metal through its phenolic oxygen, carboxyl oxygen, imino nitrogen and amide nitrogen. All complexes are non-electrolytes and four coordinated with 1:1(metal; ligand) stoichiometry. The probable structure of the complexes is suggested展开更多
Three new solid complexes of macrocyclic polyether ligand 2, 2'-dinitro-4, 5, 4', 5'bis-(15- crown-5)-dihenzo disulfide(L) with trivalent rare earth nitrates having composition of RE(NO_3)_3·L ·6...Three new solid complexes of macrocyclic polyether ligand 2, 2'-dinitro-4, 5, 4', 5'bis-(15- crown-5)-dihenzo disulfide(L) with trivalent rare earth nitrates having composition of RE(NO_3)_3·L ·6H_2O(RE=Ce, Pr, Nd) have been synthesized in acetonitrile. All the isolated complexes have been characterized by elementary analysis, IR and UV spectra, differential thermal and thermogravimetric analysis, X-ray powder diffraction analysis, molar conductance and measurements of solubility in some general solvents.展开更多
Complexes of La(Ⅲ),Nd(Ⅲ),Sm(Ⅲ),Eu(Ⅲ),Gd(Ⅲ),Dy(Ⅲ), Er(Ⅲ),Yb(Ⅲ)and Y(Ⅲ)with piperonal isonicotinoyl hydrazone(HPIN) have been synthesized in DMF and EtOH.The complexes have been characte- rized by elemental ana...Complexes of La(Ⅲ),Nd(Ⅲ),Sm(Ⅲ),Eu(Ⅲ),Gd(Ⅲ),Dy(Ⅲ), Er(Ⅲ),Yb(Ⅲ)and Y(Ⅲ)with piperonal isonicotinoyl hydrazone(HPIN) have been synthesized in DMF and EtOH.The complexes have been characte- rized by elemental analysis,molar conductance,i.r.,UV and^1H n.m.r. spectra,magnetic measurements,X-ray powder diffraction and DTA.展开更多
A series of nine Pd(0)complexes(L)Pd(L')[L=bis(diphenylphosphino) methane(dppm),1,2-bis(diphenylphosphino)ethane(dppe),and 1,1'-bis(diphenyl- phosphino)ferrocene(dppf),respectively;L=dibenzylideneacetone(dba),...A series of nine Pd(0)complexes(L)Pd(L')[L=bis(diphenylphosphino) methane(dppm),1,2-bis(diphenylphosphino)ethane(dppe),and 1,1'-bis(diphenyl- phosphino)ferrocene(dppf),respectively;L=dibenzylideneacetone(dba),2,3,5, 6-tetrachloro-1.4-benzoquinone(q)and 2,3-dichloro-1,4-naphthoquinone(nq)] were synthesized and characterized by means of elemental analyses,IR,UV, 1~H-NMR and^(31)P-NMR spectra.The redox wave peak potentials of the ferrocenyl group of complexes with dppf were measured by using CV method.Results showed that all the diphosphorus ligands behaved as chelating bidentate ligand and dba,q,nq were coordinated to the Pd(0)atom through their C=C moieties,not their carbonyl ones.Analytical data also showed that there were interactions between the two different ligands in each complex.展开更多
This paper presents the synthesis and structural characterization of asymmetric tripyrrane-containing macrocycle.This macrocycle could be oxidized to the methine bridged,22 π-electron aromatic macrocyclic complexes c...This paper presents the synthesis and structural characterization of asymmetric tripyrrane-containing macrocycle.This macrocycle could be oxidized to the methine bridged,22 π-electron aromatic macrocyclic complexes containing cadmium(Ⅱ),samarium (Ⅲ),europium(Ⅲ)and gadolinium(Ⅲ)by treating with corresponding metal chloride in the presence of air Their structures were characterized by spectral methods.展开更多
Six new solid complexes of macrocyclic polyether ligand 4′-bromo-5′-nitrobenzo-15-crown-5(L)with Uivalent rare earth nitrates having composition of RE(NO_3)_3·L·mCH_3CN·nH_2O(RE=L_a--Nd,m=n=0, RE=Sm,B...Six new solid complexes of macrocyclic polyether ligand 4′-bromo-5′-nitrobenzo-15-crown-5(L)with Uivalent rare earth nitrates having composition of RE(NO_3)_3·L·mCH_3CN·nH_2O(RE=L_a--Nd,m=n=0, RE=Sm,Bu,m=0.1,n=1,4)have been synthesized in acetonitrile or acetone.All the isolated complexes have been char- acterized by elementary analysis,IR and UV spectra,differential thermal and thermogravimetric analysis,X-ray powder diffraction analysis,molar conductance and measurementa of solubility in some general solventa.It shows that coordination number of the rare earth cation in the complexes of La,Ce,Pr and Nd nitrate is eleven.展开更多
Two vanadium complexes of schiff base vith rich phenolate oxygen,o-(?)-salicylideneamino- methylphenol,had been synthesized and characterized.One is a V(Ⅳ)complex with an interaction via vanadyl oxygen and the other ...Two vanadium complexes of schiff base vith rich phenolate oxygen,o-(?)-salicylideneamino- methylphenol,had been synthesized and characterized.One is a V(Ⅳ)complex with an interaction via vanadyl oxygen and the other is a novel dinuclear V(V,V)complex with an oxo bridge.The conversion between the two complexes had been discussed.展开更多
A ditopic ligand bpy-cyclam(L)and its heterometallo-binuclear complex Ru(bpy)_2(bpy-cyclam-Ni)(ClO_4)_43H_2O(3)designed for use in the catalytic photoreduction of carbon dioxide have been newly synthesized and charact...A ditopic ligand bpy-cyclam(L)and its heterometallo-binuclear complex Ru(bpy)_2(bpy-cyclam-Ni)(ClO_4)_43H_2O(3)designed for use in the catalytic photoreduction of carbon dioxide have been newly synthesized and characterized.The protonation constants of L were also determined.展开更多
The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal co...The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.展开更多
Two new lanthanide complexes with ethoxybenzene-substituted nitronyl nitroxide radical（NIT-C_8H_9O） and hexafluoroacetylacetonate（hfac） ligand,[Gd（NIT-C_8H_9O）_2（hfac）_3]·C_7H_（16）（1） and [Tb（NIT-C_8...Two new lanthanide complexes with ethoxybenzene-substituted nitronyl nitroxide radical（NIT-C_8H_9O） and hexafluoroacetylacetonate（hfac） ligand,[Gd（NIT-C_8H_9O）_2（hfac）_3]·C_7H_（16）（1） and [Tb（NIT-C_8H_9O）_2（hfac）_3]·C_7H_（16）（2）,have been successfully synthesized and characterized by IR spectroscopy,elemental analyses,thermogravimetry analyses,and single-crystal X-ray diffraction.Both 1 and 2 exhibit a mononuclear structure in which the nitronyl nitroxide radical and hfac ligand act as monodentate and bidentate chelating modes,respectively.Magnetic studies show that ferromagnetic interactions（between intramolecular Gd and radical） and antiferromagnetic interactions（between the intramolecular radicals） coexist in complex 1.No obvious frequency dependent out-of-phase signals were observed in complex 2.展开更多
Four Cu2＋ complexes of salicylidene-amino acid Schiff base with 1,10-phenanthroline （Phen） or 2,2＇- bipyridine （Bipy） were successfully intercalated in interlayer galleries of Mg/AI-NO3-1ayered double hydroxide ...Four Cu2＋ complexes of salicylidene-amino acid Schiff base with 1,10-phenanthroline （Phen） or 2,2＇- bipyridine （Bipy） were successfully intercalated in interlayer galleries of Mg/AI-NO3-1ayered double hydroxide （LDH） by the swelling-restored method. The hybrids were characterized by elemental analysis, X-ray diffraction, FT-IR spectra, UV-vis DRS, TG-DTA and SEM observation. Good protection of the complexes by LDH in neutral and weak acidic solutions was revealed by UV spectra, cyclic voltammograms and luminescence spectra.展开更多
A series of lanthanide complexes LnCl_3·L(Ln=La,Pr,Nd;L=15-C-5 or 18-C-6)have been synthesized and their molecular configuration,electronic structure and bond character have been studied by XPS and quantum chemic...A series of lanthanide complexes LnCl_3·L(Ln=La,Pr,Nd;L=15-C-5 or 18-C-6)have been synthesized and their molecular configuration,electronic structure and bond character have been studied by XPS and quantum chemical calculation.The calculated results are in good agreement with that obtained in the experiments.Three Cl atoms are on the same side of Ln in LnCl_3·15-C-5 and the crown ring on the other side.forming a complex molecule with coordination number 8.LnCl_3·15-C-5 is easily hygroscopic in air because of its unsaturated coordination,which differs sharply from the stable Ln(NO_3)_3·15-C-5 com- plex of coordination number 11.The HOMO and neighboring occupied MOs are composed of Cl 3p and O2p, and the LUMO and neighboring unoccupied MOs are composed of Ln orbitals.The level structure easily pro- duces Ln3d satellite in XPS caused by L→Ln charge transfer transition.Due to the coordination,the absolute values of the charge are decreased at Ln and O atoms,but increased at Cl atoms,which is in agreement with XPS results.展开更多
The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic de...For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.展开更多
Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some char...Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.展开更多
文摘The synthesis and characterization are reported for a series of bi- and trinuclear complexes of the first transition metal ions with PBDETA, the newly syn thesized polydentate ligand. The electron transition energy in binuclear compound is stronger than that in trinuclear. There is a weak antiferromagnetic exchange interaction in tricopper and trimanganese.
文摘The interactions of 2,2'-bipyridyl with the lanthanide nitrates were studied and complexes of the formula Ln(NO_8)_8(bipy)_8 were isolated from water -ethanol mixed solvent.The complexes were characterized by elemental analysis, conductivity measurments,IR spectra and DAT-TG analysis.
基金supported by the National Natural Science Foundation of China
文摘A series of new complexes of formula Ln_2[H_2(BAA)_2en]_3nH_2 Otwhere Ln- La, Pr, Eu, Cd, Dy, Er, Yb, n-1-4) have been prepared by the reaccLon of lanthanide ions with acycllc compartmental ligand X, N'-bis(benzoylacetylacetone)ethylenediamine (H_4(BAA)_2 en) in methanol. IR and UV spectra, as well as TC DAT analysis prove that the ligand and the Lanthanide ions have coordinated. The coordination number is 12 and the complexes may be of double sandwiched structure.
文摘Recent years,many novel complexes have been prepared by using hetero-bidentate ligands.However,complexes with such ligands as 4-vinylpyridine which has two different coordinating sites have not been reported,and only a few complexes of Cu(I)have been published^(1-3).The title complex Cu_2(C_5H_4N·CH=CH_2)_3Cl was prepared and characterized by elemental analyses,ICP,IR,and electronic spectra.Its conductivity,oxidation potential and reduction potential were measured.
文摘A new Schiff base (LK) obtained from 2, 4, -dihydroxybenzaldehyde and glycly-DL- phenylalanine reacted with Cu(II), Zn(II), Ni(II) and Co(II) to yield new complexes. The complexes were characterized by elemental analyses, molar conductance, 1H NMR DTA, TG, IR and UV spectroscopy. In these complexes the ligand is coordinated to the metal through its phenolic oxygen, carboxyl oxygen, imino nitrogen and amide nitrogen. All complexes are non-electrolytes and four coordinated with 1:1(metal; ligand) stoichiometry. The probable structure of the complexes is suggested
文摘Three new solid complexes of macrocyclic polyether ligand 2, 2'-dinitro-4, 5, 4', 5'bis-(15- crown-5)-dihenzo disulfide(L) with trivalent rare earth nitrates having composition of RE(NO_3)_3·L ·6H_2O(RE=Ce, Pr, Nd) have been synthesized in acetonitrile. All the isolated complexes have been characterized by elementary analysis, IR and UV spectra, differential thermal and thermogravimetric analysis, X-ray powder diffraction analysis, molar conductance and measurements of solubility in some general solvents.
文摘Complexes of La(Ⅲ),Nd(Ⅲ),Sm(Ⅲ),Eu(Ⅲ),Gd(Ⅲ),Dy(Ⅲ), Er(Ⅲ),Yb(Ⅲ)and Y(Ⅲ)with piperonal isonicotinoyl hydrazone(HPIN) have been synthesized in DMF and EtOH.The complexes have been characte- rized by elemental analysis,molar conductance,i.r.,UV and^1H n.m.r. spectra,magnetic measurements,X-ray powder diffraction and DTA.
文摘A series of nine Pd(0)complexes(L)Pd(L')[L=bis(diphenylphosphino) methane(dppm),1,2-bis(diphenylphosphino)ethane(dppe),and 1,1'-bis(diphenyl- phosphino)ferrocene(dppf),respectively;L=dibenzylideneacetone(dba),2,3,5, 6-tetrachloro-1.4-benzoquinone(q)and 2,3-dichloro-1,4-naphthoquinone(nq)] were synthesized and characterized by means of elemental analyses,IR,UV, 1~H-NMR and^(31)P-NMR spectra.The redox wave peak potentials of the ferrocenyl group of complexes with dppf were measured by using CV method.Results showed that all the diphosphorus ligands behaved as chelating bidentate ligand and dba,q,nq were coordinated to the Pd(0)atom through their C=C moieties,not their carbonyl ones.Analytical data also showed that there were interactions between the two different ligands in each complex.
文摘This paper presents the synthesis and structural characterization of asymmetric tripyrrane-containing macrocycle.This macrocycle could be oxidized to the methine bridged,22 π-electron aromatic macrocyclic complexes containing cadmium(Ⅱ),samarium (Ⅲ),europium(Ⅲ)and gadolinium(Ⅲ)by treating with corresponding metal chloride in the presence of air Their structures were characterized by spectral methods.
文摘Six new solid complexes of macrocyclic polyether ligand 4′-bromo-5′-nitrobenzo-15-crown-5(L)with Uivalent rare earth nitrates having composition of RE(NO_3)_3·L·mCH_3CN·nH_2O(RE=L_a--Nd,m=n=0, RE=Sm,Bu,m=0.1,n=1,4)have been synthesized in acetonitrile or acetone.All the isolated complexes have been char- acterized by elementary analysis,IR and UV spectra,differential thermal and thermogravimetric analysis,X-ray powder diffraction analysis,molar conductance and measurementa of solubility in some general solventa.It shows that coordination number of the rare earth cation in the complexes of La,Ce,Pr and Nd nitrate is eleven.
文摘Two vanadium complexes of schiff base vith rich phenolate oxygen,o-(?)-salicylideneamino- methylphenol,had been synthesized and characterized.One is a V(Ⅳ)complex with an interaction via vanadyl oxygen and the other is a novel dinuclear V(V,V)complex with an oxo bridge.The conversion between the two complexes had been discussed.
文摘A ditopic ligand bpy-cyclam(L)and its heterometallo-binuclear complex Ru(bpy)_2(bpy-cyclam-Ni)(ClO_4)_43H_2O(3)designed for use in the catalytic photoreduction of carbon dioxide have been newly synthesized and characterized.The protonation constants of L were also determined.
基金supported by National Natural Science Foundation of China(No.51674279)China Postdoctoral Science Foundation(No.2016M602227)a grant from National Science and Technology Major Project(No.2017ZX05049-006)
文摘The paper presents a novel hydraulic fracturing model for the characterization and simulation of the complex fracture network in shale gas reservoirs. We go beyond the existing method that uses planar or orthogonal conjugate fractures for representing the ＇＇complexity＇＇ of the network. Bifurcation of fractures is performed utilizing the Lindenmayer system based on fractal geometry to describe the fracture propagation pattern, density and network connectivity. Four controlling parameters are proposed to describe the details of complex fractures and stimulated reservoir volume（SRV）. The results show that due to the multilevel feature of fractal fractures, the model could provide a simple method for contributing reservoir volume calibration. The primary-and second-stage fracture networks across the overall SRV are the main contributions to the production, while the induced fracture network just contributes another 20% in the late producing period. We also conduct simulation with respect to different refracturing cases and find that increasing the complexity of the fracture network provides better performance than only enhancing the fracture conductivity.
基金supported by the special funds of Guangdong college students'scientific and technological innovation cultivation(pdjh2015a0562)the Natural Science Foundation of Guangdong Province(2015A030310407)+1 种基金the Natural Science Foundation of Zhaoqing University(201532)the Project of Provincial Key Platform of Guangdong Province(2014KTSPT040)
文摘Two new lanthanide complexes with ethoxybenzene-substituted nitronyl nitroxide radical（NIT-C_8H_9O） and hexafluoroacetylacetonate（hfac） ligand,[Gd（NIT-C_8H_9O）_2（hfac）_3]·C_7H_（16）（1） and [Tb（NIT-C_8H_9O）_2（hfac）_3]·C_7H_（16）（2）,have been successfully synthesized and characterized by IR spectroscopy,elemental analyses,thermogravimetry analyses,and single-crystal X-ray diffraction.Both 1 and 2 exhibit a mononuclear structure in which the nitronyl nitroxide radical and hfac ligand act as monodentate and bidentate chelating modes,respectively.Magnetic studies show that ferromagnetic interactions（between intramolecular Gd and radical） and antiferromagnetic interactions（between the intramolecular radicals） coexist in complex 1.No obvious frequency dependent out-of-phase signals were observed in complex 2.
基金supported by Beijing Municipal Natural Science Foundation(No.2112022)Key Laboratory of Radiopharmaceuticals of Ministry of Education(College of Chemistry, Beijing Normal University) and Analytical and Testing Center of Beijing Normal University
文摘Four Cu2＋ complexes of salicylidene-amino acid Schiff base with 1,10-phenanthroline （Phen） or 2,2＇- bipyridine （Bipy） were successfully intercalated in interlayer galleries of Mg/AI-NO3-1ayered double hydroxide （LDH） by the swelling-restored method. The hybrids were characterized by elemental analysis, X-ray diffraction, FT-IR spectra, UV-vis DRS, TG-DTA and SEM observation. Good protection of the complexes by LDH in neutral and weak acidic solutions was revealed by UV spectra, cyclic voltammograms and luminescence spectra.
文摘A series of lanthanide complexes LnCl_3·L(Ln=La,Pr,Nd;L=15-C-5 or 18-C-6)have been synthesized and their molecular configuration,electronic structure and bond character have been studied by XPS and quantum chemical calculation.The calculated results are in good agreement with that obtained in the experiments.Three Cl atoms are on the same side of Ln in LnCl_3·15-C-5 and the crown ring on the other side.forming a complex molecule with coordination number 8.LnCl_3·15-C-5 is easily hygroscopic in air because of its unsaturated coordination,which differs sharply from the stable Ln(NO_3)_3·15-C-5 com- plex of coordination number 11.The HOMO and neighboring occupied MOs are composed of Cl 3p and O2p, and the LUMO and neighboring unoccupied MOs are composed of Ln orbitals.The level structure easily pro- duces Ln3d satellite in XPS caused by L→Ln charge transfer transition.Due to the coordination,the absolute values of the charge are decreased at Ln and O atoms,but increased at Cl atoms,which is in agreement with XPS results.
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
基金Supported by the NSF of China(11171194)by the NSF of Shanxi Province(2012011001-1)
文摘For any prime p, all finite noncyclic p-groups which contain a self-centralizing cyclic normal subgroup are determined by using cohomological techniques. Some applications are given, including a character theoretic description for such groups.
基金supported by NSFC(12071484)Hunan Provincial Natural Science Foundation(2020JJ4675)Foundation of Guangdong University of Science and Technology.
文摘Let G be a finite group and Irr(G)the set of all irreducible complex characters of G.Let cd(G)be the set of all irreducible complex character degrees of G and denote byρ(G)the set of all primes which divide some character degree of G.The character-prime graphΓ(G)associated to G is a simple undirected graph whose vertex set isρ(G)and there is an edge between two distinct primes p and q if and only if the product p q divides some character degree of G.We show that the finite nonabelian simple groups A_(7),J_(1),J_(3),J_(4),L_(3)(3)and U_(3)(4)are uniquely determined by their degree-patterns and orders.
