242 research outputs found
Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras
This is a continuation of our "Lecture on Kac--Moody Lie algebras of the
arithmetic type" \cite{25}.
We consider hyperbolic (i.e. signature ) integral symmetric bilinear
form (i.e. hyperbolic lattice), reflection group
, fundamental polyhedron \Cal M of and an acceptable
(corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors
orthogonal to faces of \Cal M (simple roots). One can construct the
corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth
g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by .
We show that \goth g has good behavior of imaginary roots, its denominator
formula is defined in a natural domain and has good automorphic properties if
and only if \goth g has so called {\it restricted arithmetic type}. We show
that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth
g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth
g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus,
Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a
natural class to study.
Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the
best automorphic properties for the denominator function if they have {\it a
lattice Weyl vector }. Lorentzian Kac--Moody Lie algebras of the
restricted arithmetic type with generalized lattice Weyl vector are
called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on
results and ideas. 31 pages, no figures. AMSTe
Separation of the Exchange-Correlation Potential into Exchange plus Correlation: an Optimized Effective Potential Approach
Most approximate exchange-correlation functionals used within density
functional theory are constructed as the sum of two distinct contributions for
exchange and correlation. Separating the exchange component from the entire
functional is useful since, for exchange, exact relations exist under uniform
density scaling and spin scaling. In the past, accurate exchange-correlation
potentials have been generated from essentially exact densities constructed
using information from either quantum chemistry or quantum Monte Carlo
calculations but they have not been correctly decomposed into their separate
exchange and correlation components, except for two-electron systems. exchange
and correlation components (except for two-electron systems). Using a recently
proposed method, equivalent to the solution of an optimized effective potential
problem with the corresponding orbitals replaced by the exact Kohn-Sham
orbitals, we obtain the separation according to the density functional theory
definition. We compare the results for the Ne and Be atoms with those obtained
by the previously used approximate separation scheme
Borcherds symmetries in M-theory
It is well known but rather mysterious that root spaces of the Lie
groups appear in the second integral cohomology of regular, complex, compact,
del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms)
of toroidal compactifications of M theory. Their Borel subgroups are actually
subgroups of supergroups of finite dimension over the Grassmann algebra of
differential forms on spacetime that have been shown to preserve the
self-duality equation obeyed by all bosonic form-fields of the theory. We show
here that the corresponding duality superalgebras are nothing but Borcherds
superalgebras truncated by the above choice of Grassmann coefficients. The full
Borcherds' root lattices are the second integral cohomology of the del Pezzo
surfaces. Our choice of simple roots uses the anti-canonical form and its known
orthogonal complement. Another result is the determination of del Pezzo
surfaces associated to other string and field theory models. Dimensional
reduction on corresponds to blow-up of points in general position
with respect to each other. All theories of the Magic triangle that reduce to
the sigma model in three dimensions correspond to singular del Pezzo
surfaces with (normal) singularity at a point. The case of type I and
heterotic theories if one drops their gauge sector corresponds to non-normal
(singular along a curve) del Pezzo's. We comment on previous encounters with
Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real
fermionic simple roots when they would naively aris
Testing one-body density functionals on a solvable model
There are several physically motivated density matrix functionals in the
literature, built from the knowledge of the natural orbitals and the occupation
numbers of the one-body reduced density matrix. With the help of the equivalent
phase-space formalism, we thoroughly test some of the most popular of those
functionals on a completely solvable model.Comment: Latex, 16 pages, 4 figure
Crossings, Motzkin paths and Moments
Kasraoui, Stanton and Zeng, and Kim, Stanton and Zeng introduced certain
-analogues of Laguerre and Charlier polynomials. The moments of these
orthogonal polynomials have combinatorial models in terms of crossings in
permutations and set partitions. The aim of this article is to prove simple
formulas for the moments of the -Laguerre and the -Charlier polynomials,
in the style of the Touchard-Riordan formula (which gives the moments of some
-Hermite polynomials, and also the distribution of crossings in matchings).
Our method mainly consists in the enumeration of weighted Motzkin paths, which
are naturally associated with the moments. Some steps are bijective, in
particular we describe a decomposition of paths which generalises a previous
construction of Penaud for the case of the Touchard-Riordan formula. There are
also some non-bijective steps using basic hypergeometric series, and continued
fractions or, alternatively, functional equations.Comment: 21 page
Exact Kohn-Sham exchange kernel for insulators and its long-wavelength behavior
We present an exact expression for the frequency-dependent Kohn-Sham
exact-exchange (EXX) kernel for periodic insulators, which can be employed for
the calculation of electronic response properties within time-dependent (TD)
density-functional theory. It is shown that the EXX kernel has a
long-wavelength divergence behavior of the exact full exchange-correlation
kernel and thus rectifies one serious shortcoming of the adiabatic
local-density approximation and generalized-gradient approximations kernels. A
comparison between the TDEXX and the GW-approximation-Bethe-Salpeter-equation
approach is also made.Comment: two column format 6 pages + 1 figure, to be publisehd in Physical
Review
Analytic structure factors and pair-correlation functions for the unpolarized homogeneous electron gas
We propose a simple and accurate model for the electron static structure
factors (and corresponding pair-correlation functions) of the 3D unpolarized
homogeneous electron gas. Our spin-resolved pair-correlation function is built
up with a combination of analytic constraints and fitting procedures to quantum
Monte Carlo data, and, in comparison to previous attempts (i) fulfills more
known integral and differential properties of the exact pair-correlation
function, (ii) is analytic both in real and in reciprocal space, and (iii)
accurately interpolates the newest, extensive diffusion-Monte Carlo data of
Ortiz, Harris and Ballone [Phys. Rev. Lett. 82, 5317 (1999)]. This can be of
interest for the study of electron correlations of real materials and for the
construction of new exchange and correlation energy density functionals.Comment: 14 pages, 5 figures, submitted to Phys. Rev.
Clinical diagnostic criteria of efficiency for combined etiopathogenetic therapy in patients with chronic Epstein–Barr virus infection
Treatment of chronic viral infections accompanied by permanent virus persistence in the target epitopes of the oral cavity, skin, urogenital tract is complicated by virtual lack of available drugs exerting combined systemic virulicidal and immunomodulatory effects. Here we demonstrate clinical and immunological efficacy of combined therapy in treatment of Epstein–Barr virus (EBV)-associated chronic infections. The aim of the study was to evaluate the clinical and immunological efficacy of combined etiopathogenetic therapy using the Acegram cosmetic product in patients with EBV-associated chronic infections. Materials and methods. There were enrolled 40 patients monitored before treatment as well as 20 patients followed up after combination therapy (cycle therapy consisted of oral valaciclovir (Valtrex) applied at dose of 500 μg twice a day for 10 days, glucosaminylmuramyldipeptide (Licopid) — 10 mg 2 twice a day for 10 days, topical irrigation for mucous membranes with granulocyte-macrophage colony-stimulating factor active center-derived peptide (Acegram-spray) 3 times a day for 10 days. If necessary, treatment courses were repeated 20 days after the onset. All patients were examined for the presence of EBV genomes in the oral fluid and blood using the qualitative and quantitative polymerase chain reaction (PCR) using the DNA technology test system (Russia) on a DT-Lite device prior treatment and 30, 60 days post-therapy time points. In addition, serum samples were analyzed for level of class G immunoglobulins specific to the EBV nuclear and capsid antigens by using enzyme immunoassay (test systems manufactured by CJSC Vector Best, Russia) as well as immune status (clinical methods, enu flow cytometry evaluation of the phagocytic activity of neutrophils, ELISA method). Results. Use of single or two course combination therapy in subjects with fully eradicated EBV carriage associated with reversed clinical symptoms was accompanied by recovered immune system status (T and B cells, T-helper cells, CD3+ CD25+ cells, phagocytosis parameters). A non-invasive approach proposed for controlling virus elimination in the oral fluid by using polymerase chain reaction method may serve as to objectively monitor therapeutic efficacy
Density functional theory
Density functional theory (DFT) finds increasing use in applications related to biological systems. Advancements in methodology and implementations have reached a point where predicted properties of reasonable to high quality can be obtained. Thus, DFT studies can complement experimental investigations, or even venture with some confidence into experimentally unexplored territory. In the present contribution, we provide an overview of the properties that can be calculated with DFT, such as geometries, energies, reaction mechanisms, and spectroscopic properties. A wide range of spectroscopic parameters is nowadays accessible with DFT, including quantities related to infrared and optical spectra, X-ray absorption and Mössbauer, as well as all of the magnetic properties connected with electron paramagnetic resonance spectroscopy except relaxation times. We highlight each of these fields of application with selected examples from the recent literature and comment on the capabilities and limitations of current methods
Quantum chemical calculations of X-ray emission spectroscopy
The calculation of X-ray emission spectroscopy with equation of motion coupled cluster theory (EOM-CCSD), time dependent density functional theory (TDDFT) and resolution of the identity single excitation configuration interaction with second order perturbation theory (RI-CIS(D)) is studied. These methods can be applied to calculate X-ray emission transitions by using a reference determinant with a core-hole, and they provide a convenient approach to compute the X-ray emission spectroscopy of large systems since all of the required states can be obtained within a single calculation removing the need to perform a separate calculation for each state. For all of the methods, basis sets with the inclusion of additional basis functions to describe core orbitals are necessary, particularly when studying transitions involving the 1s or- bitals of heavier nuclei. EOM-CCSD predicts accurate transition energies when compared with experiment, however, its application to larger systems is restricted by its computational cost and difficulty in converging the CCSD equations for a core-hole reference determinant, which become increasing problematic as the size of the system studied increases. While RI-CIS(D) gives accurate transition energies for small molecules containing first row nuclei, its application to larger systems is limited by the CIS states providing a poor zeroth order reference for perturbation theory which leads to very large errors in the computed transition energies for some states. TDDFT with standard exchange-correlation functionals predicts transition energies that are much larger than experiment. Optimization of a hybrid and short-range cor- rected functional to predict the X-ray emission transitions results in much closer agreement with EOM-CCSD. The most accurate exchange-correlation functional identified is a modified B3LYP hybrid functional with 66% Hartree-Fock exchange, denoted B66LYP, which predicts X-ray emission spectra for a range of molecules including fluorobenzene, nitrobenzene, ace- tone, dimethyl sulfoxide and CF3Cl in good agreement with experiment
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