Conformal invariants for determinants of laplacians on Riemann surfaces

For a Riemann surface with smooth boundaries, conformal (Weyl) invariant quantities proportional to the determinant of the scalar Laplacian operator are constructed both for Dirichlet and Neumann boundary conditions. The determinants are defined by zeta function regularization. The other quantities in the invariants are determined from metric properties of the surface. As applications explicit representations for the determinants on the flat disk and the flat annulus are derived.     

Combinatorial Laplacian and entropy of simplicial complexes associated with complex networks

Simplicial complexes represent useful and accurate models of complex networks and complex systems in general. We explore the properties of spectra of combinatorial Laplacian operator of simplicial complexes and show its relationship with connectivity properties of the Q-vector and with connectivities of cliques in the simplicial clique complex. We demonstrate the need for higher order analysis in complex networks and compare the results with ordinary graph spectra. Methods and results are obtained using social network of the Zachary karate club.     

On the area of square lattice polygons

We consider the generating function of self-avoiding square lattice polygons grouped by both area and perimeter. The generating function for polygons of arean is found to diverge atx _c =0.251834, with an exponent of zero. The mean perimeter of polygons with arean is found to be proportional ton, while the mean area of polygons with perimetern is found to be proportional ton ^1.5.     

Accurate calculation of functional determinants

A dependence of the functional determinant of the operator from the family D() satisfying the condition D()=fD()+D()f on the parameter m² of infrared regularization is found in the regularization method using a generalized function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 27–32, June, 1988.     

Heat-Kernels and functional determinants on the generalized cone

We consider zeta functions and heat-kernel expansions on the bounded, generalized cone in arbitrary dimensions using an improved calculational technique. The specific case of a global monopole is analysed in detail and some restrictions thereby placed on theA _5/2 coefficient. The computation of functional determinants is also addressed. General formulas are given and known results are incidentally, and rapidly, reproduced.     

Quasiclassical expansion of Yang-Mills heat kernels and approximate calculation of functional determinants

We find next-to-leading coefficients in the expansion of Sp exp(−tK) in powers of proper time t, where K is the differential operator for the gluon, ghost or fermion in a background Yang-Mills field. This expansion provides a possibility of estimating functional determinants in arbitrary background fields. For example, for the instanton background our very simple method gives the value of the determinants with an accuracy of a few percent, as compared to the labourious exact calculation.     

On the evaluation of tri-diagonal secular determinants

A method of solution is presented for certain high-rank tri-diagonal secular determinants whose elements along the principal diagonal occur with periodicity. Such determinants are encountered in a wide range of problems dealing with coupled vibrating systems.     

On determinants of Laplacians on Riemann surfaces

Determinants of Laplacians on tensors and spinors of arbitrary weights on compact hyperbolic Riemann surfaces are computed in terms of values of Selberg zeta functions at half integer points.Research supported in part by the U.S. Department of EnergyResearch supported in part by the National Science Foundation under Grant DMS-84-02710     

Billiards in polygons: Survey of recent results

We review the dynamics of polygonal billiards     

Extrinsic hermitian geometry of functional determinants for vector subbundles and the Drinfeld-Sokolov ghost system

In this paper, a novel method is presented for the study of the dependence of the functional determinant of the Laplace operator associated to a subbundleE of a hermitian holomorphic vector bundleE ⁰ over a Riemann surface on the hermitian structure (h, H) ofE ⁰. The generalized Weyl anomaly of the effective action is computed and found to be expressible in terms of a suitable generalization of the Liouville and Donaldson actions. The general techniques worked out are then applied to the study of a specific model, the Drinfeld-Sokolov (DS) ghost system arising inW-gravity. The expression of the generalized Weyl anomaly of the DS ghost effective action is found. It is shown that, by a specific choice of the fiber metricH _h depending on the base metrich, the effective action reduces into that of a conformal field theory. Its central charge is computed and found to agree with that obtained by the methods of hamiltonian reduction and conformal field theory. It is also shown that the dependence of the effective action onH is local. The DS holomorphic gauge group and the DS moduli space are defined and their dimensions are computed.     

Density functional theory and time-dependent density functional study a series of iridium complexes with low-efficiency roll-off properties

ABSTRACT

A series of blue phosphorescent heteroleptic cyclometalated Ir(III) complexes with mesitylphenyl-imidazole ligands for organic light-emitting devices have been theoretically studied. We want to find their electronic structures, spectroscopic properties, and application value for organic light-emitting devices. (fppz)₂Ir(acac), (fppz)₂Ir(tpip), (dfbdp)₂Ir(fppz), (F-fppz)₂Ir(acac), (F-fppz)₂Ir(tpip), and (dfbdp)₂Ir(F-fppz) are investigated with DFT and TD-DFT approaches, where, for (fppz)₂Ir(acac), (fppz denotes 2-(5-(trifluoromethyl)-4H-pyrazol-3-yl)pyridine, and acac denotes acetylacetonate); for (fppz)₂Ir(tpip), tpip denotes tetraphenylimido-diphosphinate; and, for (F-fppz)₂Ir(acac) and (F-fppz)₂Ir(tpip), F-fppz denotes 2-(5-fluoro-4H-pyrazol-3-yl)pyridine.     

A density functional study of plutonyl trifluoroacetone complexes in the gas phase and in solution

The results of a density functional study on a plutonyl compound with two trifluoroacetone ligands are presented. Several conformations of the complex have been examined, namely the structure in which the two ligands are in a cis conformation one with respect to the other, in a trans conformation one with respect to the other, and the structure in which the two ligands lie on the same plane. The calculations have been carried out at the local density approximation level of theory. The relative energies of the conformers have been determined and their geometries have been optimized in the gas phase and in an organic solution. The liquid-state environmental effects are included via a simple cavity model and by using the self-consistent reaction field method. This study shows that the trends in stability of the different conformers in the gas and liquid phases are similar and that the most stable conformer has a cis structure.     

On the donor-vacancy type complexes in germanium

Very unusual energy spectrum and defect production kinetics have been observed under ⁸⁰Co-y-irradiation and heat-treatment of high-pure germanium. The results can be explained in terms of vacancy-donor and divacancy-donor complexes. The upper limit of the vacancy migration energy in germanium has been estimated as 0.3 eV.     

Density functional study of uranyl （VI） amidoxime complexes

Uranyl (VI) amidoxime complexes are investigated using relativistic density functional theory. The equilibrium structures, bond orders, and Mulliken populations of the complexes have been systematically investigated under a generalized gradient approximation (GGA). Comparison of (acet) uranyl amidoxime complexes ([UO₂(AO)_n]^2-n, 1 ≤ n ≤ 4) with available experimental data shows an excellent agreement. In addition, the U-O(1), U-O(3), C(1)-N(2), and C(3)-N(4) bond lengths of [UO₂(CH₃AO)₄]^2- are longer than experimental data by about 0.088, 0.05, 0.1, and 0.056 Å. The angles of N(3)-O(3)-U, O(2)-N(1)-C(1), N(3)-C(3)-N(4), N(4)-C(3)-C(4), and C(4)-C(3)-N(3) are different from each other, which are due to existing interaction between oxygen in uranyl and hydrogen in amino group. This interaction is found to be intra-molecular hydrogen bond. Studies on the bond orders, Mulliken charges, and Mulliken populations demonstrate that uranyl oxo group functions as hydrogen-bond acceptors and H atoms in ligands act as hydrogen-bond donors forming hydrogen bands within the complex.