Cosine Moments and Their Application to ∑ Relationships

Recent advances In the theory of ∑ relationships lead to the Investigation of moments needed to derive the relavant joint probability densities. These together with the linear theory of relationships, make possible the calcualtion of therelationships from ∑1 to ∑2 one by one. The superior performance ofour new ∑4 and ∑r relationships, for example, with respect to the older ∑1 and ∑3 formulas strongly suggests a deeper study of the pertinent moments. In this paper a new concept, the cosine moment, is introduced which, together with a certain integral theorem, permits the derivation of the relevant joint probability densities. These lead in turn to the derivation of all ∑ relationships valid for all the space groups.     

CRYSTALLOGRAPHIC STUDIES OF SILVER CARP INSULIN

Silver carp insulin crystallizes in space group P2_12_12_1 with cell dimensions a=96.73(8), b=57.74(7), and c=53.88(9). There are six molecules in an asymmetric unit. The orientations of non-crystallographic three- and two-fold axes have been worked out by the rotation function method and the results indicate that silver carp insulin has a spatial structure and a mode of aggregation similar to that of the rhombohedral 2-Zn pig insulin, though the crystal packings are different. In the present paper, we discuss the influence of the changes in sequence of insulin upon crystallization behaviour and packing of molecules     

MOLECULAR STRUCTURE AND ABSOLUTE CONFIGURATION OF SUBEROGORGIN

In the present paper it is reported that the molecular structure and absolute configuration of poisonous suberogorgin are determined by using X-ray diffraction method. The crystal of suberogorgin belongs to orthogonal system with space group D_2~4-P2_12_12_1. The crystallographic parameters are: a=16.135, b=13.189, c=12.901, Z=8. The initial model of the crystal structure was solved by the direct method. The refinement of the strueture parameters was carried out by using the least square method and led to a final R-factor of 0.056. In accordance with the molecular structure of suberogorgin mentioned above, the solvent effect of NMR has been further discussed and the relationship between the molecular structure of suberogorgin and its toxicity has also been preliminarily investigated.     

THE CRYSTALLOGRAPHIC STRUCTURE OF THE PHOTOOXIDIZED PRODUCT OF HYPOCRELLIN A AND THE STUDY OF THE PHOTODYNAMIC ACTION MECHANISM

In attempting to study the phototherapeutic action and the photosensitized oxygenation mechanism, we have determined the crystal structure of the main oxidized product of hypocrellin A (HA). It was crystallized in monoclinic system with space group P2_1. The cell data are: a=10.030(3), b=8.877(3), c=15.764(5), β=104.50(2)°, Z=2. The crystal structure has been determined by direct method and refined to a final R of 0.055 based on the 1408 observed reflections with l>2.5σ(Ⅰ). The photooxidized product is composed of a heptacyclic aliphatic hydrocarbon connecting with two α-naphthoquinone derivatives as its skeletal molecule. No peroxidic linkage has been found. On the basis of the crystal structure determined, we have deduced part of the process of formation of the oxide, ⅰ. e. firstly, the peroxide was formed by photocycloaddition of oxygen molecule to Hypocrellin A, then thermodissociation took place to form a stable oxide.     

NUMERICAL CONSTRAINTS ON TRACE ELEMENT RATIOS DURING FRACTIONAL CRYSTALLIZATION OF IGNEOUS SYSTEM

The constraints on the variation in the ratios of pairs of trace elements during crystal fractionation are described by using a set of inequality functions. This approach to the interpretation of the variation in trace element ratios provides a more thorough basis for describing the quantitative relationships between the variation of trace element ratios during the fractional crystallization, the difference of the bulk distribution coefficients of the two elements and the degree of fractionation. The constraints imposed by the inequalities lead to certain consequences on the variation in the ratios of pairs of trace elements during crystal fractionation. For these consequences not yet recognized in literature detailed explanation will be given in the present paper.     

MOLECULAR STRUCTURE AND ABSOLUTE CONFIGURATION OF THE DITERPENE LACTONE, PRAELOLIDE

Praelolide is a new compound which was isolated out from the gorgonian, Menella praelonga (Ridley), collected from the South Sea of China at Zhanjiang, Guangdong. The molecular formula is C_(28) H_(35) O_(12)C1. The research result by X-ray diffraction method on the crystal structure is presented. The compound is orthorhombic with space group P2_12_12, cell dimensions α=16.936, b=16.709, c=10.333, and Z=4. The structure has been solved by direct method and refined to R=0.055 for 2257 unique observable reflexions by least-squares. The molecule is composed of the major conformational isomer in which the three main rings(a six-membered ring, an eight-membered ring, a six-membered ring) take separately the form of chair-chairboat-chair, a five-membered actone ring, a C1 substitution, 4 acetate groups, and a three-membered epoxide ring. The absolute configuration of the molecule has also been determined by statistics (R factor ratio =1.012) and Bijvoet pairs observation. For 30 pairs of the greatest anomalo     

RESEARCH ON TRINUCLEAR MOLYBDENUM CLUSTER COMPOUNDS——CRYSTAL AND MOLECULAR STRUCTURE OF Mo_3(μ_3—O)(μ_2—S_2)_3[S_2P(OEt)_2]_3I

The title crystals are golden yellow rhomboic plates, belonging to the monoelinic system. The space group is P_(B_1)/n with unit cell parameters a=16.570(2), b=12.370(1), c=20.007(2), β=99.97(1)°, Z=4, D_c=1.938 g.cm~(-3). The crystal structure was solved mainly by the heavy atom method and refined by the full-matrix least-squares to a final R factor of 0.047 based on 4387 unique reflections with intensities I≥2σ(I). The results show that the crystal structure consists of neutral mono-oxo-capped trinuclear molybdenum cluster molecules with an average Mo-Mo bond length of 2.626(4) and an average Mo-O bond length of 2.036(2) respectively. Each pair of Mo atoms is further bridged by an S_2~(2-) radical, in which one S atom is essentially situated on the triangular plane formed by these three Mo atoms and the other one is situated on the side of the plane opposite to the μ_3-O atom. Besides, each Mo atom is coordinated to two S atoms belonging to an [S_2P(OEt)_2]~-radical so as to complete a nearly pen     

CRYSTAL STRUCTURE OF BIS-ETHYLENEDIAMINE TRITHIOCYANATE OF COPPER(Ⅱ) AND SILVER(Ⅰ) Cu(en)_2Ag(SCN)_3

Cu(en)_2Ag(SCN)_3 crystallizes in space group P2_12_12_1 with its cell parameters, a=7.126(2), b=12.587(5), c=17.585(5). There are four formula units per unit cell(ρ_obs.=1.90g/cm~3, ρ_(calc.=1.96g/cm~3). Diffraction data are collected on a CAD4 four-circle diffractometer using Mo-Ka radiation. The structure is determiued by heavy atom method, then refined by leastsquare method to a final R=0.036. It is shown that in the crystal the coordination of Cu atoms is square pyramidal with four N atoms of en groups in the square plane and oue Natom of thiocyanate group in the apical position. The Ag atom is coordinated tetrahedrally by four S atoms of thiocyanate groups, one of which links up two AgS_4 together, thus forming the infinite AgS_4 tetrahedron chains along a axis.     

LINEAR THEORY OF Σ RELATIONSHIP

Some general formulae for relationships including those of high order are presented using a method of structure factor algebra on the basis of Hauptman-Karle's relationship theory. It is indicated that the key to solving relationship problems is the evaluation of moments. We gave the method of the linearization calculation of moments which are involved by various relationships, thus solving the problem of the dependence of each relationship on space group. It opens up an effective way for the practical application of the various relationships, especially the high order ones. A general program was compiled for the computation of using the general formula of . When applied to the crystal structure calculation of EuP_5O_(14), a better result has been obtained.     

STUDIES ON THE STRUCTURE OF FORKED CONJUGATIVE SYSTEMS——THE CRYSTAL STRUCTURE AND CONFORMATION OF 2-BENZOYLTHIOPHENE

The crystal structure and the conformational properties of the title compound have been investigated by means of X-ray single diffraction and the PCILO methods. C_(11)H_8OS belongs to the orthorhombic system, the space group is P2_12_12_1, a=11.945(4), b 10.236(7), c=7.649(4), Z=4, D_c-1.37g/cm~3. The molecule is not planar structure because of steric hindrance. The thiophene ring and the phenyl ring make dihedral angles of 21°(θ_1) and 32°(θ_2) with the carbonyl frame plane, respectively. The lowestenergy conformation obtained by PCILO calculation is in agreement with the crystallinestatc conformation. In this paper, the molecular structure, the influence of steric hindrance and the groups' abilities to conjugate upon the conformation and the variations of the potential energy of the isolated molecule in the whole conformational space are discussed.     

A MODEL OF CAPILLARY NETWORKS FOR THE EXCHANGE OF SUBSTANCES

A mathematical model of substantial exchange between three capillaries and the surrounding tissue is presented.We suppose that three capillaries, which are parallel to each other and have the same radius and circular section, are arranged in equilateral triangle.Fluid movement across the capillary walls is assumed to be governed by the generalized Starling's law.The motion of the interstitial fluid obeys Darcy's law.The calculated result obtained in this paper shows that in order to study the effect of capillary networks on the tissue space, as a whole, we have found a concept of equivalent pressure, concentration and source strength for the networks.     

ELECTRONIC ENERGY BAND STRUCTURE OF MOLECULAR CRYSTAL TTF-TCNQ——CHANGE OF ENERGY BAND STRUCTURE DURING PEIERLS PHASE TRANSITION

In this paper, the electronic energy bands of the molecular crystal TTF-TCNQ have been calculated. The results demonstrate that the positions and the widths of the energy bands of this crystal conform to the rules given by our previous paper exactly, i.e. the positions of the energy bands of crystal orbitals are determined by the energy levels of corresponding molecular orbitals of the isolated molecules, and the widths of the energy bands are determined by the interaction between the molecular orbitals belonging to different molecules in the crystal. The results also demonstrate that the dimerization which appears after Peierls phase transition has a considerable effect on band widths. The dimerization causes the band widths of TTF and TCNQ columns to become narrow sharply. According to the relationship between the mobility of charge carriers and the band width given by Frhlich and Sewell, the sharp change of electrical conductivity of TTF.TCNQ crystal during Peierls phase transition can be explained p     

THEORY OF UNIFIED REPRESENTATION OF GRAVITATIONAL FIELD

A new theory of gravitational field representation is created to unify the exterior andinterior disturbing fields of the earth by using Newton's potential operator. To do that wego this way: first, we analyze the invertibility of Newton's potential operator and come tothe conclusion that every continuous function belonging to D_g, the orthogonal complement tothe null space of this operator, is harmonic everywhere in the interior earth space; second,we formulate a new kind of boundary value problem of gravics-interior Dirichlet's prob-lem of biharmonic equation with respect to disturbing potential on the supposition that anom-alous mass density of the earth belongs to D_g; then, we simplify the disturbing field intoa quasilinear superposition of two harmonic fields by the aid of the representation theoremson biharmonics proved in this paper. In this way, we finally end up with a unified represen-tation pattern AL of disturbing potential defined throughout the whole space, where L de-notes data performed     

STUDY OF DEGRADATION MECHANISM AND PACKAGING OF ORGANIC LIGHT EMITTING DEVICES

Organic Light Emitting Devices (OLED) have attracted much attention recently, for their applications in futureFlat Panel Displays and lighting products. However, their fast degradation remained a major obstacle to theircommercialization. Here we present a brief summary of our studies on both extrinsic and intrinsic causes for the fastdegradation of OLEDs. In particular, we focus on the origin of the dark spots by "rebuilding" cathodes, which confirms thatthe growth of dark spots occurs primarily due to cathode delamination. In the meantime, we recapture the findings from thesearch for suitable OLED packaging materials, in particular polymer composites, which provide both heat dissipation andmoisture resistance, in addition to electrical insulation.     

ASSIGNMENT OF ~(13)C NMR SPECTRA OF POLYMER WITH SEMIEMPIRICAL METHOD——SURVEY OF SPECTRUM OF SECONDARY CARBON OF 1, 2-PBD

In chain molecules of 1, 2-PBD, there are two kinds of gauche arrangements, which is the cause of making the spectrum of the secondary carbon in main chain of the polymer split. In such a complex system, the gauche arrangements of the secondary carbon and the tertiary carbon occupy an important position. Hence, the contribution of the tertiary carbon to the chemical shifts of the secondary carbon has a decisive effect on the sequence structure distribution. In comparison the contribution of vinyl groups is much less. The γ values are: γ_1=-6.37～-6.41 ppm represents the effect of the tertiary carbon and γ_2=0.0～-1.56 ppm the contribution of vinyl. The mean square errors are 0.364 and 0.166×10~(-2) ppm~2, respectively in the two cases of considering the effect of vinyl and vice versa. In this paper, we discuss the effects of model chain type, chain length and temperature on the bond probability. Meanwhile, it is pointed out that there exist a few cases, which are not in accord with the usual distrib     

DETERMINATION AND REFINEMENT OF THE CRYSTAL STRUCTURE OF CHAIDAMUITE

Chaidamuite (ZnFe(SO_4)_2(OH). 4H_2O), which is a new sulphate mineral, belongs to the triclinic system, space group P1, with the cell parameters corrected by the least-squares method: a=7.309(2), b=7.202(2), c=9.691(3), α=89.64(3), β=105.89(3), γ=91.11(2)°, Z=2. The crystal structure has been determined by the Patterson method and Fourier syntheses and refined by the full-matrix least-squares method to an R factor of 0.032, using 2833 independent reflections. In the structure, a zigzag chain consists of [Fe(1)O_5(OH)] and [Fe(2)O_5(OH)] octahedra sharing the OH corners, and an octahedral-tetrahedral chain running parallel to the b axis consists of the zigzag chain of Fe octahedra and (SO_4) tetrahedra sharing four pairs of octahedral corners on either side of the zigzag chains. These chains are cross-linked by the isolated [Zn(1)O_2(H_2O)_4] and [Zn(2)O_2(H_2O)_4] octahedra into corrugated sheets parallel to the (100) plane. Adjacent sheets are hydrogenbonded through water molecules.     

THE FORMATION AND CRYSTAL STRUCTURE OF DIHYDRONITIDINE AND DISCUSSION OF ANTICANCER MECHANISM OF NITIDINE CATION

The paper reports the formation and crystal structure of dihydronitidine, expounds thereasons and conditions of easily formed oxynitidine, and discusses anticancer mechanism ofnitidine (cation). The crystallographic parameters of dihydronitidine are: space group P2_(1/n),a= 12.54(1), b = 9. 148(5), c = 14.748(8)A, β= 92. 12(6)°,Z =4. 4108 independent reflec-tions were collected within the range of 3°≤2θ≤54°, of which 2137 intensity data with I≥3σ(I) were used in the structural determination. The crystal structure has been refined byfull matrix least-square method to a final R of 0.050.     

THE CRYSTAL STRUCTURE OF Mo_203[S_2P(OC_2H_5)_2]_4

<正> Introduction. In an attempt to synthesize Mo cluster compounds from the high-valenced Mo compounds in P_2S_5/EtOH-HC1 system we have obtained a brownblack rhombohedral crystal. The composition of it Mo_2O_3[S_2P(OC_2H_5)_2]_4 has been confirmed by X-ray single crystal structure determination, which reveals that the crystal structure is different from that by Knox, J. R. & Prout, C. K. (1969).     

STATISTICS OF A NOVEL CLASS OF LIQUID CRYSTAL POLYMERS

A novel class of the liquid crystal polymers with mesogens laterally attached to flexible main chain backbones has been synthesized recently by us. While the flexible backbones tend to take configuration of maximum entropy the mesogenic side groups tend to orientate because of the anisotropie soft dispersion forces. A mean field theory is presented to describe the competition between these two trends which makes it possible for this class of polymers to show anisotropic (liquid crystal) phase within certain temperature range where the polymer main chains and the side chain mesogens will take approximately parallel arrangement, which is different from the normal side chain liquid crystal polymers. The temperature range of the liquid crystal phase, its ordering and phase transition all depend on the flexibility of the backbone, the strengthof the anisotropic forces of the side groups and the hinge elasticity. The results show that the liquid crystalisotropic phase transition is of the first order. The phase diagram, i. e. the dependence of the transition temperature on the structure of the polymers is also given.     

Software Package: An Advanced Theoretical Tool for Inhomogeneous Fluids(Atif)

In spite of the impending flattening of Moore’s law,the complexity and size of the systems we are interested in keep on increasing.This challenges the computer simulation tools due to the expensive computational cost.Fortunately,advanced theoretical methods can be considered as alternatives to accurately and efficiently capture the structural and thermodynamic properties of complex inhomogeneous fluids.In the last decades,classical density functional theory(cDFT)has proven to be a sophisticated,robust,and efficient approach for studying complex inhomogeneous fluids.In this work,we present a pedagogical introduction to a broadly accessible open-source density functional theory software package named"an advanced theoretical tool for inhomogeneous fluids"(Atif)and of the underlying theory.To demonstrate Atif,we take three cases as examples using a typical laptop computer:(i)electric double-layer of asymmetric electrolytes;(ii)adsorptions of sequencedefined semiflexible polyelectrolytes on an oppositely charged surface;and(iii)interactions between surfaces mediated by polyelectrolytes.We believe that this pedagogical introduction will lower the barrier to entry to the use of Atif by experimental as well as theoretical groups.A companion website,which provides all of the relevant sources including codes and examples,is attached.