Approximate expressions of determining the double layer energy and force of interaction between two charged colloidal spheres

The approximate expressions have been obtained to calculate the electrical double layer energy and force between two spherical colloidal particles based on the improved Derjaguin approximation. Results for identical spheres interacting under constant surface potential, constant surface charge are given. Comparison of present results with numerical results calculated by Carnie and Chan is made. The expressions are found to work quite well for the constant surface potential case, and for the constant charge case, we make correction for the expressions. The results given are satisfactory providedkh0.4.     

Scaling Function Between the Exponential-6 and the Generalized Lennard-Jones Potential Functions

The van der Waals forces for non-bonded interaction can be expressed either by the Exponential-6 or by the Lennard-Jones(m-n) potential functions, whereby m > n. Hitherto a relationship exists between the Exponential-6 and the Lennard-Jones(12-6) potential functions, with a scaling factor = 13.772 at or near the equilibrium and = 12.0 for long range interaction. This paper attempts to develop relationships between Exponential-6 and a more generalized Lennard-Jones(m-n). Analysis reveals that the relationship exists only when n = 6 and that two sets of scaling factors (as functions of index m) applies for the relationship between Exponential-6 and the Lennard-Jones(m-6), whereby m > 6.     

ELECTRON PARAMAGNETIC RESONANCE STUDIES OF SINGLE CRYSTAL SODIUM HEXAMOLYBDOCHROMATE (Ⅲ)Cr~(3+)/Na_3(AlMo_6O_(24)H_6)·8H_2O

An X-band EPR study on a Na_3(CrMo_6O_(24)H_6)·8H_2O single crystal diluted by its isomor-phic compound Na_3(AlMo_6O_(24)H_6)·8H_2O at room temperature is reported. Using the least squares-fitting method to simulate the EPR data for principal planes, the Hamiltonian parameterswere obtained. The principal values of the g tensors are g_(ZZ) = 1.904, g_(XX)= 1.973, g_(YY)=1.933. The zero field splitting tensor parameters are D = 0.275 cm~(-1), E = 0.05 cm~(-1). The fielddependence of Cr~(3+) energy levels with field at different angles from the principal axes whenthe field is along the principal planes is calculated based on these experimental parameters.The isofrequency plots of calculated field vs. angle are also shown. They agree well with theexperimental results.     

Conformation and internal mobility of 5H-dibenzo[a,d]cycloheptene derivatives in solution. Conformational analysis of highly flexible structures,part II

Summary The conformational possibilities of 5-(3-N,N-dimethylaminopropyl)-5H-dibenzo[a,d]cycloheptene (1), 5-(3-N,N-dimethylaminopropylidene)-10,11-dihydro-5H-dibenzo[a,d]cycloheptene (2), and 5-(3-N,N-dimethylaminopropyl)-10,11-dihydro-5H-dibenzo[a,d]cycloheptene (3) are analysed using empirical force field methods. Minimum energy conformations, interconversion pathways, interconversion graphs and interconversion energies are examined in view of the analysis of conformer equilibria of1,2, or3 in solution. In addition, some basic requirements of the analysis of fast interconverting conformers using the lanthanide induced shift method are discussed.

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Konformation und interne Beweglichkeit von 5H-Dibenzo[a,d]cyclohepten Derivaten in Lösung. Konformationsanalyse hochflexibler Strukturen, Teil 2

Zusammenfassung Die konformativen Möglichkeiten von 5-(3-N,N-dimethylaminopropyl)-5H-dibenzo[a,d]cyclohepten (1), 5-(3-N,N-dimethylaminopropylidene)-10,11-dihydro-5H-dibenzo[a,d]cyclohepten (2) und 5-(3-N,N-dimethylaminopropyl)-10,11-dihydro-5H-dibenzo[a,d]cyclohepten (3) wurden mit Hilfe empirischer Kraftfeldmethoden analysiert. Jene Konformationen, die einem energetischen Minimum entsprechen, sowie Interkonversionswege, Interkonversionsgraphen und Interkonversionsenergien wurden in Hinblick auf die Analyse der Konformerengleichgewichte von1,2 oder3 in Lösung untersucht. Weiters werden noch einige grundlegende Voraussetzungen für die Analyse von sich schnell ineinander umwandelnden Konformeren mittels der Lanthaniden-induzierten Verschiebungsmethode besprochen.

     

Photodissociation of Cycloketones by Ultraintense Femtosecond Laser Pulses

ThestudyofphotoionizationandphotodissociationprocessesinducedbyintensefemtosecondlaserpuIses(>lo"W/cm')withpolyatomicmoleculesbecomesofinterestbecausesomenewphenomenahavebeenobserved'-3.Sofar,mostoftheinvestigationsfocusontheexperimentalexplorationofphotoionizationprocesses'-'.Butthephotoionizationmechanismofpolyatomicmoleculesinanintensefslaserfieldisstillambiguous'.,.Incontrasttothephotoionizationprocesses,theunderstandingoffragmentationofmolecularionisevenpoorer.Corkumetal,'.,'reportedthef…     

利用AFM和SNOM对淋巴细胞膜表面超微结构及其光学性质的初步研究

利用原子力显微镜(Atomic Force Microscopy，AFM)对淋巴细胞表面形貌进行了形态学的初步研究，观察到了其膜表面其他显微技术所不能发现的超微结构．同时也运用扫描近场光学显微镜(Scanning Near field Optical Microscopy，SNOM)对淋巴细胞进行成像，观察了其对光的透射、吸收等光学性质，并对两种成像方法进行了比较．研究发现：淋巴细胞膜表面凹凸不平，分布着大量直径几十到几百纳米不等的小颗粒；淋巴细胞中央部位有自发荧光现象．结果表明，AFM和SNOM可作为进一步探讨淋巴细胞的结构与功能关系的有力工具．     

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. He also reviews the related analytic extension results, conjectures and problems. He discusses the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of q-traces and pseudo-q-traces of products of intertwining operators. He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.     

Explicit Traveling Wave Solutions and Their Dynamical Behaviors for the Coupled Higgs Field Equation

In this paper, we focus on the traveling wave solutions of the coupled Higgs field equation from the perspective of dynamical systems. Through the phase portraits, in addition to periodic wave solutions and solitary wave solutions, we also obtain explicit periodic singular wave solutions, singular wave solutions and kink wave solutions, which were not found in the previous works. The dynamical behavior of these solutions and their internal relations are revealed through asymptotic analysis. The results will help supplement the study of field equation.     

A public-key cryptosystem utilizing cyclotomic fields

While it is well-known that the RSA public-key cryptosystem can be broken if its modulusN can be factored, it is not known whether there are other ways of breaking RSA. This paper presents a public-key scheme which necessarily requires knowledge of the factorization of its modulus in order to be broken. Rabin introduced the first system whose security is equivalent to the difficulty of factoring the modulus. His scheme is based on squaring (cubing) for encryption and extracting square (cube) roots for decryption. This introduces a 14 (19) ambiguity in the decryption. Various schemes which overcome this problem have been introduced for both the quadratic and cubic case. We generalize the ideas of Williams' cubic system to larger prime exponents. The cases of higher prime order introduce a number of problems not encountered in the quadratic and cubic cases, namely the existence of fundamental units in the underlying cyclotomic field, the evaluation of higher power residue symbols, and the increased difficulty of Euclidean division in the field.     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.