# The topology of the charge distribution and the electric-field gradient at the N nucleus in imines and di-imides

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We study the discrete SchrÃ¶dinger operator H in Z[sup d] with the surface potential of the form V(x)=gÎ´(x[sub 1])tan Ï€(Î±Â·x[sub 2]+Ï‰), where for xâˆˆ Z[sup d] we write x=(x[sub 1],x[sub 2]), x[sub 1] âˆˆ Z[sup d[sub 1]], x[sub 2] âˆˆ Z[sup d[sub 2]], Î± âˆˆ R[sup...

- Symmetric-tensor eigenspectrum of the Laplacian on n-spheres. Rubin, Mark A.; Ordóñez, Carlos R. // Journal of Mathematical Physics;Jan1985, Vol. 26 Issue 1, p65
The eigenvalues and degeneracies of the covariant Laplacian acting on symmetric tensors of rank mâ‰¤2 defined on n-spheres with nâ‰¥3 are given.

- The relevance of the Laplacian of intracule and extracule density distributions for analyzing... Fradera, Xavier; Duran, Miquel; Mestres, Jodi // Journal of Chemical Physics;9/1/1997, Vol. 107 Issue 9, p3576
Examines the relevance of the Laplacian of intracule and extracule density distributions for analyzing electron-electron interactions in molecules. Findings of an analysis of the density distributions; Local minima in the topology of Laplacian maps; Conceptually different interpretation of...

- Antisymmetric tensor fields on spheres: Functional determinants and non-local counterterms. Elizalde, E.; Lygren, M.; Vassilevich, D.V. // Journal of Mathematical Physics;Jul96, Vol. 37 Issue 7, p3105
Studies the Hodge-de Rham Laplacian on spheres acting on antisymmetric tensor fields. Expressions for the spectrum; Functional determinants; Heat kernel expansion; Non-local counterterms in the quantum effective action obtained and expressed in terms of Betti numbers.

- Heat kernel coefficients of the Laplace operator on the D-dimensional ball. Bordag, M.; Elizalde, E. // Journal of Mathematical Physics;Feb96, Vol. 37 Issue 2, p895
Discusses a method for the calculation of heat kernel coefficients. Integral representations of the spectra sum, Melin transforms, non-trivial commutation of series and integrals; Application of the method to the case of heat kernel expansion of the Laplace operator.

- Heat kernel expansion for operators containing a root of the Laplace operator. Gorbar, E.V. // Journal of Mathematical Physics;Mar1997, Vol. 38 Issue 3, p1692
Suggests a method for the calculation of the DeWitt-Seely-Gilkey (DWSG) coefficients for operators containing a root of the Laplace operator. Calculation of the lowest coefficients; Problem of the calculation of the DWSG coefficients for operators.

- Wave operators for the surface Maryland model. Jaksic, Vojkan; Molchanov, Stanislav // Journal of Mathematical Physics;Jul2000, Vol. 41 Issue 7
We study scattering properties of the discrete Laplacian H on the half-space Z[sub +][sup d+1]=Z[sup d]xZ[sub +] with the boundary condition Ïˆ(n,-1)=Î» tan(Ï€Î±Â·n+Î¸)Ïˆ(n,0), where Î±âˆˆ[0,1][sup d]. We denote by H[sub 0] the Dirichlet Laplacian on Z[sub +][sup d+1]....

- Simple analysis of transient photoconductivity for determination of localized-state distributions in amorphous semiconductors using Laplace transform. Naito, Hiroyoshi; Okuda, Masahiro // Journal of Applied Physics;4/1/1995, Vol. 77 Issue 7, p3541
Focuses on a study which proposed a method for the determination of localized-state distributions in amorphous semiconductors from transient photoconductivity using Laplace transforms. Significance of spectroscopic techniques for mapping out localized-state distributions; Comparison between the...

- Circular-sector quantum-billiard and allied configurations. Liboff, Richard L. // Journal of Mathematical Physics;May94, Vol. 35 Issue 5, p2218
The circular-sector quantum-billiard problem is studied. Numerical evaluation of the zeros of first-order Bessel functions finds that there is an abrupt change in the nodal-line structure of the first excited state of the system (equivalently, second eigenstate of the Laplacian) at the critical...