Second- and third-order bias reduction for one-parameter family models

In this paper we derive second- and third-order bias-corrected maximum likelihood estimates in general uniparametric models. We compare the corrected estimates and the usual maximum likelihood estimate in terms of their mean squared errors. We also obtain closed-form expressions for bias-corrected estimates in one-parameter exponential family models. Our results cover many important and commonly used distributions. Simulation results are also given.     

A Two-Parameter Distribution Obtained by Compounding the Generalized Exponential and Exponential Distributions

We introduce a new two-parameter lifetime distribution obtained by compounding the generalized exponential and exponential distributions. We assume that the shape parameter of the generalized exponential distribution is a random variable having the exponential distribution. The shapes of the density and hazard rate functions are derived. The model parameters are estimated by maximum likelihood, and an application of the proposed distribution is presented.

     

Parameter estimation based synchronization for an epidemic model with application to tuberculosis in Cameroon

We propose a method based on synchronization to identify the parameters and to estimate the underlying variables for an epidemic model from real data. We suggest an adaptive synchronization method based on observer approach with an effective guidance parameter to update rule design only from real data. In order, to validate the identifiability and estimation results, numerical simulations of a tuberculosis (TB) model using real data of the region of Center in Cameroon are performed to estimate the parameters and variables. This study shows that some tools of synchronization of nonlinear systems can help to deal with the parameter and state estimation problem in the field of epidemiology. We exploit the close link between mathematical modelling, structural identifiability analysis, synchronization, and parameter estimation to obtain biological insights into the system modelled.     

Synthesis of 1-substituted 1,2,3,4-tetrahydrobenz[g]isoquinoline-5,10-diones

1,2-Disubstituted 1,2,3,4-tetrahydrobenz[g]isoquinoline-5,10-diones are prepared for the first time through an activated Pictet-Spengler reaction of the corresponding imines of 2-(1,4-dimethoxynaphth-2-yl)ethylamine in the presence of an acyl chloride and AlCl(3) followed by an oxidation with silver(II) oxide in nitric acid. Depending on the reaction conditions the N-trichloroacetyl protecting group could be cleaved off, converted to an N-methoxycarbonyl group or transformed to an N-(2-oxoacetamide) moiety. The synthesized 1,2-disubstituted 1,2,3,4-tetrahydrobenz[g]isoquinoline-5,10-diones constitute a new class of quinones, which has not been reported yet.     

Thermal and optical behaviour of octa-alkoxy substituted phthalocyaninatovanadyl complexes

This paper deals with the synthesis of vanadyl phthalocyanines substituted with eight alkoxy chains in the peripheral (2, 3, 9, 10, 16, 17, 23, 24) positions. The alkoxy chain length was varied, and octa-octyloxy (C₈H₁₇O), octa-dodecyloxy (C₁₂H₂₅O) and octa-hexadecyloxy (C₁₆H₃₃O) substituted vanadyl phthalocyanine complexes were prepared. Studies by polarizing optical microscopy and small angle X-ray diffraction (XRD) revealed that all the complexes are liquid crystalline and that these metallomesogens exhibit a columnar phase. The symmetry of the 2D lattice is rectangular, with a ^c 2 ^mm space group, as determined by the indexation of the XRD reflections; hence a rectangular columnar phase (Col_r) was assigned. A double periodicity, although weak, along the axis of the columns was found, which indicates some degree of pairing or dimerization. A tentative explanation based on an antiferroelectric stacking is given. Transition enthalpies were determined by differential scanning calorimetry. The compounds start to decompose above 250°C before reaching the clearing temperatures. A significant bathochromic shift of the Q-band in the UV/Vis spectra of the vanadyl complexes compared with the metal-free ligands and other metallophthalocyanines (M=Co^II, Ni^II, Cu^II, Zn^II) was also observed.     

Mesophase behaviour and thermal stability of octa-alkoxy substituted phthalocyaninatocobalt (II) complexes

Cobalt (II) phthalocyanines substituted with eight alkoxy chains in the peripheral (2, 3, 9, 10, 16, 17, 23, 24) positions were prepared. The alkoxy chain length was varied between n-butyloxy (C₄H₉O) and n-octadecyloxy (C₁₈H₃₇O). Studies by polarizing optical microscopy and high temperature X-ray diffraction revealed that all the complexes are liquid crystalline and that they exhibit a hexagonal columnar mesophase (Col_h). Transition enthalpies were determined by differential scanning calorimetry. The clearing point could only be observed for compounds with a chain length longer than C₁₃H₂₇O. Both the melting and clearing points decrease with increasing chain length. The transition temperatures of these discotic metallomesogens are higher than those of the corresponding metal-free phthalocyanines, but are comparable with those of the corresponding copper (II) compounds. The thermal decomposition of the compounds was studied by thermogravimetry.     

Microwave, high-resolution infrared, and quantum chemical investigations of CHBrF2: ground and v4 = 1 states

A combined microwave, infrared, and computational investigation of CHBrF(2) is reported. For the vibrational ground state, measurements in the millimeter- and sub-millimeter-wave regions for CH(79)BrF(2) and CH(81)BrF(2) provided rotational and centrifugal-distortion constants up to the sextic terms as well as the hyperfine parameters (quadrupole-coupling and spin-rotation interaction constants) of the bromine nucleus. The determination of the latter was made possible by recording of spectra at sub-Doppler resolution, achieved by means of the Lamb-dip technique, and supporting the spectra analysis by high-level quantum chemical calculations at the coupled-cluster level. In this context, the importance of relativistic effects, which are of the order of 6.5% and included in the present work using second-order direct perturbation theory, needs to be emphasized for accurate predictions of the bromine quadrupole-coupling constants. The infrared measurements focused on the ν(4) fundamental band of CH(79)BrF(2). Fourier transform investigations using a synchrotron radiation source provided the necessary resolution for the observation and analysis of the rotational structure. The spectroscopic parameters of the v(4) = 1 state were found to be close to those of the vibrational ground state, indicating that the ν(4) band is essentially unaffected by perturbations.     

Direct perturbation theory in terms of energy derivatives: scalar-relativistic treatment up to sixth order

A formulation of sixth-order direct perturbation theory (DPT) to treat relativistic effects in quantum-chemical calculations is presented in the framework of derivative theory. Detailed expressions for DPT6 are given at the Hartree-Fock level in terms of the third derivative of the energy with respect to the relativistic perturbation parameter defined as λ(rel)=c(-2). They were implemented for the computation of scalar-relativistic energy corrections. The convergence of the scalar-relativistic DPT expansion is studied for energies and first-order properties such as dipole moment and electric-field gradient within the series of the hydrogen halides (HX, X = F, Cl, Br, I, and At). Comparison with spin-free Dirac-Coulomb calculations indicates that the DPT series exhibits a smooth and monotonic convergence. The rate of convergence, however, depends on the charge of the involved nuclei and significantly slows down for heavy-element compounds.