Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate system.The method of variable separation is used to solve the timefractional heat conduction equation.The Caputo fractional derivative of the order 0 〈 α≤ 1 is used.The solution is presented in terms of the Mittag-Leffler functions.Numerical results are illustrated graphically for various values of fractional derivative.

A Co(Ⅱ) Coordinated Polymer with 2-Fold Interpenetration 3D Architecture Based on 5-(Imidazol-1-ylmethyl)isophthalate: Hydrothermal Synthesis, Crystal Structure and Properties

One cobalt coordinated polymer with 2-fold parallel interpenetration 3D architecture based on flexible 5-（imidazol-1-ylmethyl）isophthalate （L2-） as a main ligand and 4,4＇-bipyridine （bpy） as a nitrogen-containing ancillary ligand, {[CoL（bpy）0.5（H2O）3]2}n （1）, has been obtained under hydrothermal conditions and characterized by elemental analysis, powder X-ray diffraction （PXRD）, IR spectra, Uv/vis spectra, thermal gravimetric analyses （TGA） and single-crystal X-ray diffraction. It crystallizes in monoclinic, space group C2/c with a = 26.323（4）, b = 14.696（2）, c = 26.630（4） A, β= 157.747（4）°, V = 3901.2（1） A3, Z = 8, Mr= 435.27, Dc = 1.480 g/cm3, /t= 0.923 mm^-1, Rint = 0.0900, F（000） = 1792, the final R= 0.0722 and wR = 0.0946 for 3641 observed reflections （I 〉 2tr（/））. Complex 1 exhibits a two-fold interpenetration 3D framework. As a single net of the 2-fold interpenetration structure, the L2- anion of complex 1, as a bridging ligand, connects the Co（Ⅱ） ion to form two-dimensional layers （Co3L3）n which are further linked to build a three-dimensional framework by bpy ligand.

Deployment dynamics of a simplified spinning IKAROS solar sail via absolute coordinate based method

The spinning solar sail of large scale has been well developed in recent years. Such a solar sail can be considered as a rigid-flexible multibody system mainly composed of a spinning central rigid hub, a number of flexible thin tethers, sail membranes, and tip masses. A simplified interplanetary kite-craft accelerated by radiation of the Sun （IKAROS） model is established in this study by using the absolute-coordinate-based （ACB） method that combines the natural coordinate formulation （NCF） describing the central rigid hub and the absolute nodal coordinate formulation （ANCF） describing flexible parts. The initial configuration of the system in the second-stage deployment is determined through both dynamic and static analyses. The huge set of stiff equations of system dynamics is solved by using the generalized-alpha method, and thus the deployment dynamics of the system can be well understood.

A New Luminescent Cd(Ⅱ) Coordination Polymer Constructed with 2-(Carboxymethoxy) benzoic Acid

In this work, we synthesized a new Cd（Ⅱ） coordination polymer, [Cd（L）(cmb)H;O]· H;O（1）, by using mixed 2-（carboxymethoxy）benzoic acid（H2 cmb） and typical chelating N-donor ligands 2-（2-fluoro-6-fluorophenyl）-1 H-imidazo[4,5-f][1,10]phenanthroline ligand（L）. 1 crystallizes in monoclinic, space group P21/c with a = 17.6150（8）, b = 9.7811（4）, c = 18.1603（8） ?, β = 118.9150（10）o, V = 2738.9（2） ?;, Z = 4, C28 H20 CdF2 N4 O7, Mr = 674.88, Dc = 1.637 g/cm3, F（000） = 1352, μ（Mo Ka） = 0.865 mm–1, R = 0.0643 and w R = 0.1976. In 1, the cmb2– anions link neighboring Cd（Ⅱ） atoms in a bis-chelating mode, yielding a one-dimensional chain structure along the b axis. The L ligands are attached on one side of the chain through chelating the Cd（Ⅱ） atoms, and are stacked with those of an adjacent chain through π-π interactions to generate a one-dimensional double-chain structure. Furthermore, the one-dimensional double-chains are stacked by C–H???π interactions between the carbon atom of L ligand and the benzene ring of cmb2–ligand to give a layer structure. Moreover, the solid state luminescent property of 1 was also investigated at room temperature.

1D Lanthanide Coordination Polymers Based on 3-(Pyridin-4-yl)benzoic Acid: Syntheses, Structures and Luminescent Properties

ABSTRACT Four novel 1D lanthanide coordination polymers with formula [Ln（3,4-pybz）3（HzO）2. H2O]n （Ln = 1 Sm; 2 Eu; 3 Tb; 4 Dy, 3,4-Hpybz = 3-（pyridin-4-yl）benzoic acid） have been synthesized by hydrothermal reactions of lanthanide oxide and 3-（pyridine-4-yl） benzoic acid. Single-crystal X-ray diffraction shows that the four compounds are isostructural. They all crystallize in a monoelinic system, space group P1^-. They have a doubly carboxylate-bridged infinite-chain structure with alternating Ln-（carboxylate）2-Ln linkages and one chelating carboxylate group on each metal center. The Ln ion also combines to two water molecules to form an eight-coordinate square antiprismatic geometry. The pyridine nitrogen atoms of the ligand do not coordinate to the metal centers but direct the formation of a 3D network through hydrogen bonding with coordinated water molecules. The photoluminescent properties of 2 and 3 have been also studied.

Crystal Structure, Thermal Behavior and Luminescence of a New Copper Coordination Polymer Constructed with 4-(Carboxymethoxy)-benzoic Acid

A new Cu(Ⅱ) coordination polymer, [Cu(L1)(L2)](1), was synthesized under hydrothermal conditions(H_2L1 = 4-(carboxymethoxy)benzoic acid, L2 = 2-(4-fluorophenyl)-1 H-imidazo[4,5-f][1,10]phenanthroline). Crystallographic data for 1: triclinic, space group P1 with a = 9.750(5), b = 10.148(5), c = 12.869(5) ?, α = 104.904(5), β = 102.133(5), γ = 95.219(5)°, V = 1188.7(10) ?~3, Z = 2, C_(28)H_(17)FN_4O_5Cu, Mr = 572.01, D_c = 1.598 g/cm^3, F(000) = 582, μ(MoKa) = 0.977 mm^(-1), R = 0.0474 and w R = 0.1144. The TGA behaviors and luminescence of 1 have been studied in detail. The L1 dianions link neighboring Cu(Ⅱ) atoms in a bis-chelating mode, yielding a one-dimensional chain structure along the b axis. The L2 ligands are attached on one side of the chain through chelating the Cu(Ⅱ) atoms, and are stacked with those of an adjacent chain through π-π interactions, yielding a layer structure. Additionally, the N–H???O hydrogen bonds further stabilize the structure of 1.

Synthesis, Structure and Photoluminescence of a New Cd(Ⅱ) Coordination Polymer Based on 4-(Carboxymethoxy)-benzoic Acid and 1,10-Phenanthroline Derivative

A new ID coordination polymer, [Cda（L1）2（L2）2].H2O （1, H2L1 = 4-（carboxy- methoxy）benzoic acid and L2 = 2-（4-fluorophenyl）-I H-imidazo[4,5-f][1,10]phenanthroline）, has been hydrothermally synthesized and characterized by elemental analysis and single-crystal X-ray diffraction. It crystallizes in triclinic, space group P1 with a = 9.985（5）, b = 10.768（5）, c = 12.512（5） A, a = 68.959（5）, β = 80.354（5）, γ = 79.663（5）°, V= 1227.4（10） A3, Z = 1, C56H36Cd2F2N8O11, Mr = 1259.73, Dc = 1.704 g/cm3, F（000） = 630, μ（MoKa） = 0.949 mm-1, R = 0.0261 and wR = 0.0655. The L1 anions link the neighboring Cd（II） atoms to form a 1D double chain structure. The L2 ligands are alternately located on both sides of the double chains. More interestingly, the lateral L2 ligands from adjacent double chains are paired to furnish strong π-π interactions, yielding a 2D supramolecular layer. N-H...O, O-H...N and O-H...O hydrogen bonds further stabilize the structure of 1. The luminescent property of 1 was studied in solid state at room temperature.

A New Cadmium(Ⅱ) Coordination Polymer Constructed by 2-(2-Chloro-6-fluorophenyl)-1H-imidazo[4,5-f][1,10]phenanthroline and 1,2,3-Benzenecarboxylate: Synthesis, Structure and Luminescence

A new Cd（II） coordination polymer, namely, [Cd3（1,2,3-BTC）2（L）2]·2.25H2O （1, L = 2-（2-chloro-6-fluorophenyl）-1H-imidazo[4,5-A][1,10]phenanthroline and 1,2,3-BTC = 1,2,3-ben- zenetricarboxylate）, has been synthesized under hydrothermal conditions. The compound was characterized by single-crystal X-ray diffraction. It crystallizes in triclinic, space group Pī with α = 11.650（2）, b = 12.240（2）, c = 19.760（4） A, α = 72.01（3）, β = 77.11（3）, γ = 83.48（3）°, V = 2609.4（9） A3, Z = 2, C56H31Cd3Cl2F2N8O14.25, Mr = 1489.99, Dc = 1.896 g/cm3, F（000） = 1466, μ（MoKa） = 1.401 mm^-1, R = 0.0401 and wR = 0.1104. Compound 1 shows a 1D chain structure, and the neigh- boring 1D chains of 1 are joined together by π···π interactions to result in a 2D supramolecular layer. In addition, the luminescent property of 1 has been studied in the solid state at room temperature.

The Coupling Coordination Evolution Research of Economy - Ecology - Society System in Xinjiang：Based on the Interaction Perspective of Water Resources

Under the water resources perspective,coupling coordination of economy-ecology-society system in Xinjiang was taken as the research object. By building the coupling evaluation index system of the water resources-economy-ecology-society system,quantitative evaluation and analysis of the coupling coordination of the water resources-economy-ecology-society system from 2001 to 2014 were conducted. The results showed that benefit indexes of economic system and social system grew rapidly,while benefit indexes of water resources system and ecosystem fluctuated smoothly from 2001 to 2014; coupling state of the whole system was at rival stage,and coupling coordination was reluctant coordination type,and the coupling index was slightly higher than the coupling coordination index. Moreover,it showed that the more the coupling systems,the lower indices of coupling and the coupling coordination.

A New Co(Ⅱ) Coordination Polymer Based on a Flexible 1,4-Cyclohexanedicarboxylic Acid: Synthesis, Structure and Thermal Behavior

A new Co（Ⅱ） coordination polymer, [Co（1,4-chdc）（L）（H2O）]n（1）, was synthesized under hydrothermal condition（1,4-H2chdc = 1,4-cyclohexanedicarboxylic acid, L = 2-（4-fluoro-phenyl）-1 H-imidazo[4,5-f][1,10]phenanthroline）. Its crystal structure was determined by single-crystal X-ray diffraction. 1 crystallizes in triclinic, space group P1 with a = 8.790（5）, b = 10.486（5）, c = 13.305（5） ?, α = 87.391（5）, β = 82.925（5）, γ = 81.841（5）o, V = 1204.2（10） ?3, Z = 2, C27H23FN4O5Co, Mr = 561.42, Dc = 1.548 g/cm3, F（000） = 578, μ（Mo Ka） = 0.769 mm-1, R = 0.0415 and wR = 0.1043. In 1, each 1,4-chdc anion bridges two neighboring Co（Ⅱ） atoms to give a chain structure. The L ligands are attached on one side of the chain through chelating the Co（Ⅱ） atoms, and are stacked with those of an adjacent chain through π-π interactions, yielding a double-chain structure. The double-chain structures are linked into a supramolecular layer structure through N–H···O hydrogen-bonding interactions between the adjacent double-chain structures. Moreover, the thermal behavior of 1 was also studied.

Synthesis, Structure and Characterization of a New Iron Coordination Polymer:[Fe(L)(trans-1,4-chdc)]_n

A novel Fe（II） coordination polymer [Fe（L）（trans-1,4-chdc）];~ has been hydrother- mally synthesized by using 1,4-cyclohexanedicarboxylic acid （1,4-H2chdc） and 2-（2-fluoro- phenyl）-lH-imidazo[4,5-f][1,10]phenanthroline （L）. Crystallographic data： monoclinic, space group C2/c with a = 14.571（5）, b = 32.389（6）, c = 10.948（5）A, 18 = 115.186（5）°, V= 4676（3）A3, Z = 8, C27H21FFeN404, Mr = 540.33, De --- 1.535 g/cm3, F（000） = 2224, μ（MoKa） = 0.697 mmI, R = 0.0462 and wR = 0.1110. The two kinds of trans-l,4-chdc ligands link neighboring Fe（II） atoms to yield a two-dimensional layer structure. The π-π interactions between the L ligands of neighboring layers result in a three-dimensional supramolecular architecture. The IR and UV-vis spectra of the compound have been investigated in detail.

Helical Coordination Polymer with a 3-Fold Interpenetration Structure Based on 5-(Hydroxymethyl)isophthalic Acid

5-（Hydroxymethyl） isophthalic acid （H2HIA） as a novel organic ligand was prepared from 3,5-bis（methoxycarbonyl）benzoic acid by a two-step method. And then, a 3D helical coor- dination polymer with a 3-fold interpenetration structure, namely [Zn1/2（HIA）1/2（DPEE）1/2]n （1）, was hydrothermally synthesized at 160 ℃, using H2HIA ligands to assemble with DPEE ligands and Zn2＋ ions. Complex 1 crystalizes in orthorhombic system, space group Pnna, with a = 8.2118（5）, b = 17.1698（7）, c =14.9922（7） ？, V = 2113.82（18） ？3, μ = 1.194 mm-1, Z = 4 and S = 0.967. Moreover, some physical characteristics of complex 1, such as powder X-ray diffraction （PXRD）, thermogravimetry analyses （TGA） and photoluminescent properties, were also investigated.

Synthesis and Crystal Structure of a New Lead Coordination Polymer: [Pb(L)(1,4-ndc)]

The title coordination polymer, [Pb（L）（1,4-ndc）] 1 （L = 2-（4-fluorophenyl）-1Himidazo[4,5f1,10]phenanthroline, 1,4-ndc = naphthalene-1,4-dicarboxylic acid）, has been obtained by using hydrothermal synthesis and characterized by elemental analysis, IR and singlecrystal X-ray diffraction. It crystallizes in monoclinic, space group P21/c with a = 10.1043（11）, b = 14.3162（15）, c = 17.6061（18）, β = 95.3990（10）°, V = 2535.5（5）3, Z = 4, C31H17FN4O4Pb, Mr = 735.68, Dc = 1.927 g/cm3, F（000） = 1416, μ（MoKa） = 6.709 mm-1, R = 0.0201 and wR = 0.0489. The 1,4-ndc dianions link neighboring Pb（II） atoms in a bis-chelating mode, yielding a one-dimensional chain structure along the c axis. The C-H···π interactions between the carbon atom of L ligand and the benzene ring of 1,4-ndc lead the one-dimensional chains to form a two-dimensional supramolecular layer. The π-π interactions between L ligand and 1,4-ndc ligand make the two-dimensional layers generate a three-dimensional supramolecular architecture. Additionally, the N-H···O hydrogen bonds further stabilize the structure of 1.

Synthesis,Crystal Structure and Magnetic Properties of a Cobalt(Ⅱ)Coordination Polymer with4,4'-(Propane-2,2-diyl)dibenzoate and4,4'-Bis(1-imidazolyl)biphenyl

A novel coordination polymer, {[Co（CBA）（BIMB）0.5]＇H20}n （1, H2CBA = 4,4＇- （propane-2,2-diyl）dibenzoic acid, and BIMB = 4,4＇-bis（1-imidazolyl）biphenyl）, has been hydro- thermally prepared and characterized by IR spectroscopy, elemental analysis and single-crystal X-ray diffraction. The crystal is of monoclinic system, space group P2/c with a = 14.909（3）, b = 7.1963（15）, c = 24.592（5） A, β = 104.312（2）, V = 2556.5（9） A3, C26H23N2OsCo, Mr = 502.39, Dc = 1.305 g/cm3, F（000） = 1040,μ = 0.708 mm-1 and Z = 4. The final R= 0.0580 and wR = 0.1605 for 3228 observed reflections （1 〉 2a（I））. Single-crystal structure analysis shows that complex 1 exhibits a three-dimensional 2-fold interpenetrating pillared helical-layer open framework of a-Po topology based upon binuclear paddlewheel units. Moreover, its magnetic properties have also been investigated.

Synthesis, Crystal Structure and Properties of a Chiral 3D Supramolecular Coordination Polymer [Co(HL)·(DMF)]_n from 5-(Imidazol-1-ylmethyl)isophthalic Acid

A chiral supramolecular coordination polymer, [Co（HL）·（DMF）]n（1）, with helical chains from a flexible ligand 5-（imidazol-1-ylmethyl）isophthalic acid（H2L） has been obtained under hydrothermal conditions and characterized by elemental analysis, powder X-ray diffraction（PXRD）, IR, Uv/vis spectra, thermal gravimetric analyses（TGA） and also by single-crystal X-ray diffraction. It crystallizes in hexagonal, space group P6522 with a = 8.8109（3）, b = 8.8109（3）, c = 71.771（3） , γ = 120°, V = 4825.3（3） -3, Z = 6, Mr = 695.55, Dc = 1.436 g/cm-3, Rint = 0.0684, F（000） = 2166, the final R = 0.0923 and w R = 0.2697 for 3056 observed reflections（I 2σ（I））. The title coordination polymer 1 shows a chiral layered structure based on right-handed helix chains. Such layers are associated together through hydrogen-bonding interactions to form a 3D supramolecular framework.

A Novel Gd Coordination Polymer Based on 2-(Pyridin-3-yl)-1H-imidazole-4,5-dicarboxylate: Synthesis, Structure and Dielectric Properties

A new Gd coordination polymer based on 2-（pyridin-3-yl）-lH-imidazole-4,5-dicar- boxylate, formulated as {[Gd2（HPyIDC）2（H2O）5]·（bpy）·（NO3）2·3H2O}n （1, bpy = 4,4＇-bipyridine） has been synthesized under hydrothermal conditions. The compound crystallizes in triclinic, space group Pi with a = 11.451（2）, b = 11.596（2）, c = 15.7333（3） A, β = 79.47（3）°, Z = 2, V= 1948.6（7） A^3, C30H34Gd2N10O22, Dc = 2.047 g/cm^3, Mr= 1201.17, 2（MoKa） = 0.71073 A,μ = 3.477 mml, F（000） = 1176, the final R = 0.0554 and wR = 0.1181. Polymer 1 is a 2D network built up from 4-connected HPylDC2- anion and 4-connected Gd ions. Dielectric constant of complex 1 was measured at different frequencies with temperature variation.

A One-dimensional Pseudo-helical Coordination Polymer with 4,4′-(Hexafluoroisopropylidene)bis(benzoic acid)

The title complex [Zn2（hfipbb）2（2,2′-bpy）2], 1 has been hydrothermally synthesized from Zn（NO3）2·6H2O, 4,4′-（hexafluoroisopropylidene）bis（benzoic acid） and 2,2′-bipyridine. Singlecrystal X-ray analysis reveals that 1 presents a one-dimensional coordination polymer with pseudo-helical chain structure. Two Zn（Ⅱ） atoms in an unsymmetrical unit of 1 adopt distorted octahedral and square-pyramidal coordination geometries, respectively. The packing of parallel chains gives a three-dimensional supramolecular network supported by π-π stacking interactions. Crystal data： C54H32F12N4O8Zn2, Mr = 1223.58, monoclinic, space group P2 1/c, a = 27.557（6）, b = 16.751（3）, c = 11.350（2） A, β= 99.21（3）°, V= 5171.5（18） A^3, Z= 4, Dc = 1.572 g/cm^3, F（000） = 2464, μ= 1.030 mm^-1, the final R = 0.0552 and wR = 0.1070 for 6631 observed reflections （I〉 2σ（I））.

A One-dimensional Cd(Ⅱ)Coordination Polymer Constructed from 1,4-Benzene-dicarboxylic Acid and 3-(2,6-Di(pyrazin-2-yl)pyridin-4-yl)-1H-indole:Synthesis,Structure and Photoluminescence

A new coordination polymer {[Cd（C_（21）H_（14）N_6）（C_8H_4O_4）]·H_2O}_n（1） was synthesized by an elaborate design via the reaction of 3-（2,6-di（pyrazin-2-yl）pyridin-4-yl）-1H-indole（bppi）,1,4-benzene-dicarboxylic acid（H2bdc） and cadmium（Ⅱ） nitrate in CH_3OH/H_2O mixed solvents. Complex 1 crystallizes in orthorhombic,space group Ccca with a = 20.012（4）,b = 31.881（6）,c = 19.808（4） ？,V = 12638（4） ？~3,Z = 16,C_（29）H_（20）CdN_6O_5,M_r = 644.91,D_c = 1.356 g·cm^（-3）,μ = 0.735 mm^（-1）,F（000） = 5184,GOOF = 1.046,the final R = 0.0405 and wR = 0.1063 for 6870 observed reflections（I 〉 2σ（I））. The Cd（Ⅱ） centre is hepta-coordinated by three N and four O atoms from one bppi terminal ligand and two bdc2– ligands,respectively,displaying a capped trigonal prism geometry. Structure extension gives coordination polymeric chains,in which the bdc2– linkers connect Cd（Ⅱ） cations into a one-dimensional（1D） coordination polymer along the c axis,giving zigzag chains with the Cd···Cd separation of 11.178（1） ？. The adjacent bppi terminal ligands in the chains are anti-periplanar conformation. The three-dimensional（3D） structure is stabilized by π···π stacking and hydrogen-bonding interactions to form a supramolecular self-penetrating network with 1D channels. In 1,there are voids 2999.7 ？~3 with 23.7% of per unit cell volume. Thermal analysis indicates that the framework of 1 is stable until 651 K and the photoluminescence of 1 in the solid shows very weak fluorescence at 382 and 560 nm upon excitation at 310 nm.

Investigations of the electron paramagnetic resonance parameters and the tetragonal local structure for (VCl_6)^(4-) coordination complex in MCl:V^(2+) (M=Na,K,Rb) systems

By simulating the electron paramagnetic resonance （EPR） and optical spectra on the basis of the 120 × 120 complete energy matrix, this paper determines the local lattice structure parameters R1 and R2 for MCl：V2＋ （M=Na, K, Rb） systems at 77K, 195 K and RT （room temperature 295 K or 302 K）, respectively. The theoretical results indicate that there exists a compressed distortion in MCl：V2＋ systems. Meanwhile, it finds that the structure parameters R1, R2 and ｜△R｜（ = R1 - R2） increase with the rising temperature. Subsequently, from the analysis it concludes that the relation of EPR parameter D vs. △R is approximately linear. Finally, the effects of orbital reduction factor k on the g factors for the three systems have been discussed.

Aromatic Multicarboxylate Ligands Tuned One-and Three-dimensional Zn(Ⅱ) Coordination Polymers Based on 3-(1H-pyrazol-4-yl)-5-(pyridin-3-yl)-1,2,4-triazole

Two aromatic multicarboxylate ligands tuned Zn(Ⅱ) coordination polymers, namely, {[Zn0.5(H2L)(tp)0.5(H2O)]H2O}n(1) and {[Zn2(HL)(btc)(H2O)]H2O}n(2)(H2L = 3-(1 Hpyrazol-4-yl)-5-(pyridin-3-yl)-1,2,4-triazole, H2tp = terephthalic acid;H3 btc = 1,3,5-benzenetricarboxylic) have been synthesized. Their structures were characterized by single-crystal X-ray diffraction analysis, elemental analyses and infrared spectra. Compound 1 possesses a one-dimensional chain structure and is finally extended into a three-dimensional supramolecular architecture though hydrogen bonding interactions. Compound 2 shows a three-dimensional framework. Meanwhile, compounds 1 and 2 exhibit luminescent emission in the solid, and can be investigated as potential luminescent materials.