Generalized Kinetic Theory of Electrons and Phonons: Models, Equilibrium, Stability

In the present paper our aim is to introduce some models for the generalization of the kinetic theory of electrons and phonons (KTEP), as well as to study equilibrium solutions and their stability for the generalized KTEP (GKTEP) equations. We consider a couple of models, relevant to non standard quantum statistics, which give rise to inverse power law decays of the distribution function with respect to energy. In the case of electrons in a phonon background, equilibrium and stability are investigated by means of Lyapounov theory. Connections with thermodynamics are pointed out.Comment: 10 pages, 2 figures, (RevTeX4), to appear in Physica B (2003

Bose-Einstein Condensation in the Framework of κ\kappa-Statistics

In the present work we study the main physical properties of a gas of $\kappa$-deformed bosons described through the statistical distribution function $f_\kappa=Z^{-1}[\exp_\kappa (\beta({1/2}m v^2-\mu))-1]^{-1}$. The deformed $\kappa$-exponential $\exp_\kappa(x)$, recently proposed in Ref. [G.Kaniadakis, Physica A {\bf 296}, 405, (2001)], reduces to the standard exponential as the deformation parameter $\kappa \to 0$, so that $f_0$ reproduces the Bose-Einstein distribution. The condensation temperature $T_c^\kappa$ of this gas decreases with increasing $\kappa$ value, and approaches the $^{4}He(I)-^{4}He(II)$ transition temperature $T_{\lambda}=2.17K$, improving the result obtained in the standard case ($\kappa=0$). The heat capacity $C_V^\kappa(T)$ is a continuous function and behaves as $B_\kappa T^{3/2}$ for $TT_c^\kappa$, in contrast with the standard case $\kappa=0$, it is always increasing. Pacs: 05.30.Jp, 05.70.-a Keywords: Generalized entropy; Boson gas; Phase transition.Comment: To appear in Physica B. Two fig.p

Generalized Distribution Functions and an Alternative Approach to Generalized Planck Radiation Law

In this study, recently introduced generalized distribution functions are summarized and by using one of these distribution functions, namely generalized Planck distribution, an alternative approach to the generalized Planck law for the blackbody radiation has been tackled.Comment: 13 pages, RevTeX, 1 fi

Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.Comment: 24 pages, version accepted on Physica

Quantum gas distributions prescribed by factorization hypothesis of probability

Nonextensive quantum gas distributions are investigated on the basis of the factorization hypothesis of compound probability required by thermodynamic equilibrium. It is shown that the formalisms of Tsallis nonextensive statistical mechanics with normalized average give distribution functions for standard bosons and fermions obeying Pauli principle. The formalism with unnormalized average leads to a intermediate quantum distribution comparable to that of fractional exclusion statistics, with Fermi surface at T=0 depending on the parameter $q$.Comment: 5 pages, no figure, RevTeX, to be published in Chaos, Solitons & Fractals (2002

Many-body q-exponential distribution prescribed by factorization hypothesis

The factorization problem of $q$-exponential distribution within nonextensive statistical mechanics is discussed on the basis of Abe's general pseudoadditivity for equilibrium systems. it is argued that the factorization of compound probability into product of the probabilities of subsystems is nothing but the consequence of existence of thermodynamic equilibrium in the interacting systems having Tsallis entropy. So the factorization does not needs independent noninteracting systems and should be respected in all exact calculations concerning interacting nonextensive subsystems. This consideration makes it legitimate to use $q$-exponential distribution either for composite system or for single body in many-body systems. Some known results of ideal gases obtained with additive energy are reviewed.Comment: 13 pages, no figure, RevTe

Law and Nonlegal Norms in Government Lawyers\u27 Ethics: Discretion Meets Legitimacy

This Essay is about the role of unwritten norms in the ethical decisionmaking of government lawyers. Because the ethical obligations of lawyers, including government lawyers, are closely tied to the legal rights and obligations of clients, this analysis necessarily depends on understanding the relationship between written law and unwritten norms. As we all know, however, written law leaves gaps, ambiguities, and zones of unregulated discretion. Prosecutors in the United States, for example, have virtually unreviewable discretion to decide who to investigate and charge, what charges to bring, and whether to offer immunity in exchange for cooperation. No one has a legal entitlement not to be prosecuted, nor does anyone else—official or private citizen—have the power to compel a prosecutor to bring charges. The president possesses nearly unconstrained discretion to grant clemency to people convicted of criminal offenses. The impeachment power of Congress is constrained only by the Constitution’s requirement that the president be charged with certain enumerated offenses, including the open-ended phrase “high Crimes and Misdemeanors.” In other areas, a government official may possess the legal authority to do something but may nevertheless be criticized for exercising that authority contrary to standards that are not reducible to positive law. The question is, what standards, norms, or ethical values, if any, constrain the actions of lawyers advising government officials who exercise their power within discretionary unwritten areas of the law? In other words, is there a type of official discretion that is distinguishable from the exercise of raw power or whimsical decision-making, despite being unconstrained by positive law? If so, what is its relationship to positive law and its claim to legitimate authority

Correlation functions in the factorization approach of nonextensive quantum statistics

We study the long range behavior of a gas whose partition function depends on a parameter q and it has been claimed to be a good approximation to the partition function proposed in the formulation of nonextensive statistical mechanics. We compare our results, at large temperatures and at the critical point, with the case of Boltzmann-Gibbs thermodynamics for the case of a Bose-Einstein gas. In particular, we find that for all temperatures the long range correlations in a Bose gas decrease when the value of q departs from the standard value q=1.Comment: revtex file, 10 pages, two eps style figures, packaged as a single tar.gz fil

Scalar curvature of systems with fractal distribution functions

Starting with the relative entropy for two close statistical states we define the metric and calculate the scalar curvature $R$ for systems with classical, boson and fermion fractal distribution functions with moment order parameter $q$. In particular, we find that for $q\neq 1$ the scalar curvature is closer to zero implying that the fractal bosonic and fermionic systems are more stable than the standard ones.Comment: 9 pages, 2 figures, some typos were corrected, the Conclusions section was expande

Anticholinesterase and Anti-inflammatory Activities of Essential Oils of Naturally Grown Daucus L. Species in Turkey

Objective:This present study was conducted to determine the interspecific chemical variability and evaluate the biological effects of the essential oils of Daucus L. species growing naturally in Turkey. The species were D. carota, D. broteri, D. guttatus, D. littoralis, D. involucratus and D. conchitae (endemic).Methods:The essential oils were obtained from fruit samples by distillation method and were analyzed both by GC-FID and GC-MS. The anti-inflammatory and anticholinesterase effects of the essential oils were investigated. The anti-inflammatory effect was evaluated by in vitro LOX enzyme inhibition activity. The anticholinesterase effect was tested on AChE and BChE enzymes.Results:The components, ratios, and yields of D. carota essential oils differed depending on the locations where the samples were collected. The main components were detected as carotol (1-74.6%), β-bisabolen (0.9-62.4%), 11αH-himachal-4-en-1β-ol (0.3-49.4%), trans-methylisoeugenol (1-45.7%). The main volatile compounds were found in D. broteri, D. guttatus, D. involucratus, D. littoralis, D. conchitae as β-sinensal (30.4%), methyleugenol (30.5%), methyleugenol (40.9%), α-humulene (29.4%), methyleugenol (29.6%) respectively. The essential oils didn’t exhibit anti-inflammatory activity. Two essential oil samples of D. carota showed high anticholinesterase effects compared to the standard. The AChE IC50 was calculated as 6.04±0.30 μg/mL, 2.15±0.10 μg/mL (Galantamine IC50 1.13±0.02 μg/mL) and BChE IC50 11.32±0.20 μg/mL, 31.03±0.02 μg/mL (Galantamine IC50 12.15±0.36 μg/mL). These essential oils contained high levels of 11αH-himachal-4-en-1β-ol (25.04%, 49.42%).Conclusion:Because of their anticholinesterase potential, some D. carote essential oils can be evaluated in the preparation of pharmaceutical or nutraceutical products as a complementary therapy for Alzheimer’s disease by standardizing their components