Search results for "linear"
showing 10 items of 7165 documents
Ab initio calculations of pure and Co+2-doped MgF2 crystals
2020
This research was partly supported by the Kazakhstan Science Project № AP05134367«Synthesis of nanocrystals in track templates of SiO2/Si for sensory, nano- and optoelectronic applications», as well as by Latvian Research Council project lzp-2018/1-0214. Calculations were performed on Super Cluster (LASC) in the Institute of Solid State Physics (ISSP) of the University of Latvia. Authors are indebted to S. Piskunov for stimulating discussions.
On the arithmetic and geometry of binary Hamiltonian forms
2011
Given an indefinite binary quaternionic Hermitian form $f$ with coefficients in a maximal order of a definite quaternion algebra over $\mathbb Q$, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most $s$ by $f$, as $s$ tends to $+\infty$. We compute the volumes of hyperbolic 5-manifolds constructed by quaternions using Eisenstein series. In the Appendix, V. Emery computes these volumes using Prasad's general formula. We use hyperbolic geometry in dimension 5 to describe the reduction theory of both definite and indefinite binary quaternionic Hermitian forms.
An alternative conception of PM10 concentration changes after short-term precipitation in urban environment
2018
Abstract In the article, a linear model is presented which describes a reduction of PM10 mass concentration in relation to the type of precipitation and water vapour content in the air. The model was built using covariance analysis. In studies of PM10 concentration changes, the results of 247 observations were used, which were carried out in the urban area. Concentration changes were archived during short-term (30 min) convection and large-scale rainfalls. For the determination of PM10 mass concentration, the reference method was used. To describe changes in PM10 concentration in the air after precipitation, a series of linear models were created, in which the explanatory variables were: th…
Using the Johnson-Neyman Procedure to Detect Item Bias in Personality Tests
2016
I present an alternative to a widely used item-bias analysis procedure known as the ANOVA method. The new method is based on the Johnson-Neyman procedure, which is a multiple regression-based technique with properties that can overcome the major weaknesses of the ANOVA method. I introduce the proposed procedure in a non-technical manner, provide an illustrative example, and suggest guidelines for empirical analysis that can be readily applied in personality research.
A generalization of Françoise's algorithm for calculating higher order Melnikov functions
2002
Abstract In [J. Differential Equations 146 (2) (1998) 320–335], Francoise gives an algorithm for calculating the first nonvanishing Melnikov function Ml of a small polynomial perturbation of a Hamiltonian vector field and shows that Ml is given by an Abelian integral. This is done under the condition that vanishing of an Abelian integral of any polynomial form ω on the family of cycles implies that the form is algebraically relatively exact. We study here a simple example where Francoise's condition is not verified. We generalize Francoise's algorithm to this case and we show that Ml belongs to the C [ log t,t,1/t] module above the Abelian integrals. We also establish the linear differentia…
A note on higher order Melnikov functions
2005
We present several classes of planar polynomial Hamilton systems and their polynomial perturbations leading to vanishing of the first Melnikov integral. We discuss the form of higher order Melnikov integrals. In particular, we present new examples where the second order Melnikov integral is not an Abelian integral.
Principal Poincar\'e Pontryagin Function associated to some families of Morse real polynomials
2014
It is known that the Principal Poincar\'e Pontryagin Function is generically an Abelian integral. We give a sufficient condition on monodromy to ensure that it is an Abelian integral also in non generic cases. In non generic cases it is an iterated integral. Uribe [17, 18] gives in a special case a precise description of the Principal Poincar\'e Pontryagin Function, an iterated integral of length at most 2, involving logarithmic functions with only one ramification at a point at infinity. We extend this result to some non isodromic families of real Morse polynomials.
Modelling temperature-dependent dynamics of single and mixed infections in a plant virus
2022
Multiple viral infection is an important issue in health and agriculture with strong impacts on society and the economy. Several investigations have dealt with the population dynamics of viruses with different dynamic properties, focusing on strain competition during multiple infections and the effects on viruses’ hosts. Recent interest has been on how multiple infections respond to abiotic factors such as temperature (T). This is especially important in the case of plant pathogens, whose dynamics could be affected significantly by global warming. However, few mathematical models incorporate the effect of T on parasite fitness, especially in mixed infections. Here, we investigate simple mat…
ON THE CALCULATION OF THE HEAT CAPACITY IN PATH INTEGRAL MONTE CARLO SIMULATIONS
1992
In Path Integral Monte Carlo simulations the systems partition function is mapped to an equivalent classical one at the expense of a temperature-dependent Hamiltonian with an additional imaginary time dimension. As a consequence the standard relation linking the heat capacity Cv to the energy fluctuations, <E2>−<E>2, which is useful in standard classical problems with temperature-independent Hamiltonian, becomes invalid. Instead, it gets replaced by the general relation [Formula: see text] for the intensive heat capacity estimator; β being the inverse temperature and the subscript P indicates the P-fold discretization in the imaginary time direction. This heatcapacity estimator…
Absolute measurement of quadratic nonlinearities from phase-matched second-harmonic generation in a single KTP crystal cut as a sphere
1997
We determine within an accuracy of ∼10% the absolute magnitude of the quadratic effective coefficients of types I and II phase-matched second-harmonic generation from conversion efficiency measurements in a single nonlinear crystal cut as a sphere. The agreement is good with measurements performed in thin parallelepipedal samples. The material studied is KTiOPO4, for which improved Sellmeier equations are given.