Search results for "Values"
showing 10 items of 1365 documents
Hamiltonians defined by biorthogonal sets
2017
In some recent papers, the studies on biorthogonal Riesz bases has found a renewed motivation because of their connection with pseudo-hermitian Quantum Mechanics, which deals with physical systems described by Hamiltonians which are not self-adjoint but still may have real point spectra. Also, their eigenvectors may form Riesz, not necessarily orthonormal, bases for the Hilbert space in which the model is defined. Those Riesz bases allow a decomposition of the Hamiltonian, as already discussed is some previous papers. However, in many physical models, one has to deal not with o.n. bases or with Riesz bases, but just with biorthogonal sets. Here, we consider the more general concept of $\mat…
On delocalization of eigenvectors of random non-Hermitian matrices
2019
We study delocalization of null vectors and eigenvectors of random matrices with i.i.d entries. Let $A$ be an $n\times n$ random matrix with i.i.d real subgaussian entries of zero mean and unit variance. We show that with probability at least $1-e^{-\log^{2} n}$ $$ \min\limits_{I\subset[n],\,|I|= m}\|{\bf v}_I\| \geq \frac{m^{3/2}}{n^{3/2}\log^Cn}\|{\bf v}\| $$ for any real eigenvector ${\bf v}$ and any $m\in[\log^C n,n]$, where ${\bf v}_I$ denotes the restriction of ${\bf v}$ to $I$. Further, when the entries of $A$ are complex, with i.i.d real and imaginary parts, we show that with probability at least $1-e^{-\log^{2} n}$ all eigenvectors of $A$ are delocalized in the sense that $$ \min\l…
Brownian motion in trapping enclosures: Steep potential wells, bistable wells and false bistability of induced Feynman-Kac (well) potentials
2019
We investigate signatures of convergence for a sequence of diffusion processes on a line, in conservative force fields stemming from superharmonic potentials $U(x)\sim x^m$, $m=2n \geq 2$. This is paralleled by a transformation of each $m$-th diffusion generator $L = D\Delta + b(x)\nabla $, and likewise the related Fokker-Planck operator $L^*= D\Delta - \nabla [b(x)\, \cdot]$, into the affiliated Schr\"{o}dinger one $\hat{H}= - D\Delta + {\cal{V}}(x)$. Upon a proper adjustment of operator domains, the dynamics is set by semigroups $\exp(tL)$, $\exp(tL_*)$ and $\exp(-t\hat{H})$, with $t \geq 0$. The Feynman-Kac integral kernel of $\exp(-t\hat{H})$ is the major building block of the relaxatio…
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
Cytotoxic bufadienolides from the leaves of a medicinal plant Melianthus comosus collected in South Africa.
2020
Abstract From the leaves of South African medicinal plant Melianthus comosus, four previously undescribed bufadienolides, 16β-formyloxymelianthugenin (1), 2β-acetoxymelianthusigenin (2), 2β-hydroxy-3β,5β-di-O-acetylhellebrigenin (3), and 2β-acetoxy-5β-O-acetylhellebrigenin (4) were isolated together with two known bufadienolides. The structural elucidation of the compounds was based on 1D and 2D NMR spectroscopy, high-resolution mass spectrometry, and other spectroscopic methods. The relative configurations were determined by single-crystal X-ray crystallography analysis and NOESY correlations. The isolated compounds displayed strong cytotoxicity against MCF-7 breast cancer cells, sensitive…
Naphthalene Derivatives from the Roots of Pentas parvifolia and Pentas bussei
2016
The phytochemical investigation of the CH2Cl2/MeOH (1:1) extract of the roots of Pentas parvifolia led to the isolation of three new naphthalenes, parvinaphthols A (1), B (2), and C (3), two known anthraquinones, and five known naphthalene derivatives. Similar investigation of the roots of Pentas bussei afforded a new polycyclic naphthalene, busseihydroquinone E (4), a new 2,2'-binaphthralenyl-1,1'-dione, busseihydroquinone F (5), and five known naphthalenes. All purified metabolites were characterized by NMR and MS data analyses, whereas the absolute configurations of 3 and 4 were determined by single-crystal X-ray diffraction studies. The E-geometry of compound 5 was supported by DFT-base…
Valence Topological Charge-Transfer Indices for Reflecting Polarity: Correction for Heteromolecules
2005
Valence topological charge-transfer (CT) indices are applied to the calculation of dipole moments mu. The mu calculated by algebraic and vector semisums of the CT indices are defined. The model is generalized for molecules with heteroatoms and corrected for sp(3)-heteromolecules. The ability of the indices for the description of the molecular charge distribution is established by comparing them with mu of the valence-isoelectronic series of cyclopentadiene, benzene and styrene. Two CT indices, mu(vec) (vector semisum of vertex-pair mu) and mu(vec)V (valence mu(vec)) are proposed. The mu(vec) behaviour is intermediate between mu(vec) and mu(experiment). The correction is produced in the corr…
THE ROLE OF UNBOUNDED TIME-SCALES IN GENERATING LONG-RANGE MEMORY IN ADDITIVE MARKOVIAN PROCESSES
2013
Any additive stationary and continuous Markovian process described by a Fokker–Planck equation can also be described in terms of a Schrödinger equation with an appropriate quantum potential. By using such analogy, it has been proved that a power-law correlated stationary Markovian process can stem from a quantum potential that (i) shows an x-2 decay for large x values and (ii) whose eigenvalue spectrum admits a null eigenvalue and a continuum part of positive eigenvalues attached to it. In this paper we show that such two features are both necessary. Specifically, we show that a potential with tails decaying like x-μ with μ < 2 gives rise to a stationary Markovian process which is not p…
Digital generation of multivariate wind field processes
2001
Abstract A very efficient procedure for the generation of multivariate wind velocity stochastic processes by wave superposition as well as autoregressive time series is proposed in this paper. The procedure starts by decomposing the wind velocity field into a summation of fully coherent independent vector processes using the frequency dependent eigenvectors of the Power Spectral Density matrix. It is shown that the application of the method allows to show some very interesting physical properties that allow to reduce drastically the computational effort. Moreover, using a standard finite element procedure for approximating the frequency dependent eigenvectors, the generation procedure requi…
Spectrochemical Rubidium-Strontium Method for Geological Age Determination
1960
The age values of lepidolites from South Africa and from Varutrask as well as that of a microcline from Varutrask have been determined and are discussed in connection with determination according to the potassium-argon method, applied to the same materials A method is suggested which allows the spectrochemical determination of Rb and Sr with sufficient accuracy. The isotopic composition is determined by means of a Fabry-Perot etalon and hollow-cathode excitation, investigating the hyper-fine structure of the Sr line at 4078 A.