Bernstein–Frechet inequalities for the parameter of the first order autoregressive process

The autoregressive process takes an important part in predicting problems leading to decision making. In practice, we use the least squares method to estimate the parameter of the autoregressive process. In the case of the first order autoregressive process, we know that the least squares estimator converges in probability to the unknown parameter θ. In this Note, we show that the least squares estimator converges almost completely to θ and so we construct the inequalities of type Bernstein–Frechet for the coefficient of the first order autoregressive process. Using these inequalities a confidence interval is then obtained. To cite this article: A. Dahmani, M. Tari, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Properties of pectinesterase immobilized on glycophase-coated controlled-pore glass

Pectinesterase was immobilized on a porous glass support, which surface was covered with glyceryl residues. The parameters of the immobilization were characterized with respect to the coupling method used as well as the support pore size. Chemical modification level resulted an important parameter in determining the activity of the immobilized derivative. Attachment of the enzyme through thiol groups gave the best results, whereas a nominal pore size of 20 nm seemed to be the most suitable for the demethoxylating activity of the enzyme on citrus pectin. Optimum conditions for activity as well as the inhibition constant for polygalacturonic acid did not change on immobilization, as the Michaelis constant did. Fluorescence spectra revealed a partial unfolding of the enzyme tertiary structure when immobilized.     

Some definable properties of sets in non-valuational weakly o-minimal structures

Let \({\mathcal {M}}=(M,<,+,\cdot ,\ldots )\) be a non-valuational weakly o-minimal expansion of a real closed field \((M,<,+,\cdot )\). In this paper, we prove that \({\mathcal {M}}\) has a \(C^r\)-strong cell decomposition property, for each positive integer r, a best analogous result from Tanaka and Kawakami (Far East J Math Sci (FJMS) 25(3):417–431, 2007). We also show that curve selection property holds in non-valuational weakly o-minimal expansions of ordered groups. Finally, we extend the notion of definable compactness suitable for weakly o-minimal structures which was examined for definable sets (Peterzil and Steinhorn in J Lond Math Soc 295:769–786, 1999), and prove that a definable set is definably compact if and only if it is closed and bounded.     

Origin of Fluorescence Lifetimes in Human Serum Albumin. Studies on Native and Denatured Protein

Human serum albumin consists of a single polypeptide of 585 amino acid residues with 1 Trp residue. In the present work, we measured fluorescence lifetimes of the protein in both native and denatured states. The results indicate that Trp emission occurs with three lifetimes in both states. Lifetimes values and contribution to the global emission decay differ between the two states. Data are interpreted as the results of an emission occurring from three substructures of the tryptophan formed in the excited state. Two of these substructures are already present for the tryptophan free in solution. The third lifetime is the result of the interaction between the tryptophan residue and surrounding microenvironment. The populations of these substructures characterized by the pre-exponential parameters of the fluorescence lifetimes are dependent on the fluorophore microenvironment and on the global protein structure.     

Molar volume calculated at various pressures and the Pippard relations close to the melting point in benzene

The molar volume of solid and liquid benzene was calculated at various pressures (at constant temperatures), and the Pippard relations were examined close to the melting point in this organic molecule.

The molar volume calculated is in good agreement with the observed data, which decreases as the pressure increases up to about 150 MPa. The Pippard relations are also valid within this pressure range at constant temperatures studied here for the solid and liquid phases of benzene.     

Five-parameter crystallographic characteristics of the interfaces formed during ferrite to austenite transformation in a duplex stainless steel

The crystallography of interfaces in a duplex stainless steel having an equiaxed microstructure produced through the ferrite to austenite diffusive phase transformation has been studied. The five-parameter interface character distribution revealed a high anisotropy in habit planes for the austenite–ferrite and austenite–austenite interfaces for different lattice misorientations. The austenite and ferrite habit planes largely terminated on (1 1 1) and (1 1 0) planes, respectively, for the austenite–ferrite interfaces associated with Kurdjumov–Sachs (K–S) and Nishiyama–Wasserman (N–W) orientation relationships. This was mostly attributed to the crystallographic preference associated with the phase transformation. For the austenite–ferrite interfaces with orientation relationships which are neither K–S nor N–W, both austenite and ferrite habit planes had (1 1 1) orientations. Σ3 twin boundaries comprised the majority of austenite–austenite interfaces, mostly showing a pure twist character and terminating on (1 1 1) planes due to the minimum energy configuration. The second highest populated austenite–austenite boundary was Σ9, which tended to have grain boundary planes in the tilt zone due to the geometrical constraints. Furthermore, the intervariant crystallographic plane distribution associated with the K–S orientation relationship displayed a general tendency for the austenite habit planes to terminate with the (1 1 1) orientation, mainly due to the crystallographic preference associated with the phase transformation.     

Curves in the Minkowski plane and their contact with pseudo-circles

We study the caustic, evolute, Minkowski symmetry set and parallels of a smooth and regular curve in the Minkowski plane.     

Calculation of the Liquid–Solid Phase Diagram and the Thermodynamic Quantities of the Binary System of Tetradecane and Hexadecane Using the Mean Field Theory

Journal of Solution Chemistry - The T???x phase diagram of a binary system of tetradecane?+?hexadecane is calculated using the Landau phenomenological model....     

A new approach to measuring the action spectrum for singlet oxygen production by human retinal lipofuscin

The human retinal pigment epithelial (RPE) layer contains a complex mixture of components called lipofuscin; this mixture forms with age and with various genetic disorders such as Stargardt's disease. Its presence may contribute to retinal deterioration via several mechanisms including photochemical processes. In the lipofuscin mixture, both type I and II mechanisms have been identified, with the latter consisting of the generation of singlet oxygen. Several components of that mixture have been identified, most notably a bis-retinoid pyridinium compound called A2E and its derivatives. Photo-oxidative studies on the compound A2E have revealed that its dominant photochemical mechanism is via free radical or type I processes. Because singlet oxygen is an important photooxidative intermediate in tissue, its generation in the RPE may contribute to retinal maculopathies. It is therefore necessary to determine which specific component(s) in the lipofuscin mixture produce singlet oxygen upon excitation with light. This was ascertained by evaluating the action spectrum for singlet oxygen production for the whole lipofuscin mixture using time-resolved spectroscopy. Singlet oxygen was generated by excitation of the sample at different wavelengths while maintaining a constant beam energy, and was directly detected by its phosphorescence decay at 1270 nm using a Ge photodiode. The action spectrum for singlet oxygen sensitization by the organic soluble portion of lipofuscin had an absorption maximum at ca 380 nm, which is to the blue of A2E (maximum at 430 nm). Compounds with a similar absorption maximum eluted in the HPLC earlier than A2E and were detected in human lipofuscin. The concentration of this component apparently increased in concentration in human RPE lipofuscin mixture as a function of age up to 90 years old.