Exact and approximate results of non-extensive quantum statistics

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson system which we compare with other approximate scheme (i.e. factorization approach), and with the recently obtained exact result. To do this, we investigate the predictions on Bose-Einstein condensation and the blackbody radiation. We find that both approximation techniques give results similar to (up to ${\cal O}(q-1)$) the exact ones, making them a useful tool for computations. Because of the simplicity of the factorization approach formulae, it appears that this is the easiest way to handle with physical systems which might exhibit slight deviations from extensivity.Comment: 15 pages, prl revtex style, 4 ps figures. New -shortened- version accepted for publication in Eur. Phys. J.

Generalized quantal distribution functions within factorization approach: Some general results for bosons and fermions

The generalized quantal distribution functions are investigated concerning systems of non-interacting bosons and fermions. The formulae for the number of particles and energy are presented and applications to the Chandrasekhar limit of white dwarfs stars and to the Bose-Einstein condensation are commented.Comment: 10 pages, prl revtex style, 2 ps figure

Aging in coherent noise models and natural time

Event correlation between aftershocks in the coherent noise model is studied by making use of natural time, which has recently been introduced in complex time-series analysis. It is found that the aging phenomenon and the associated scaling property discovered in the observed seismic data are well reproduced by the model. It is also found that the scaling function is given by the $q$-exponential function appearing in nonextensive statistical mechanics, showing power-law decay of event correlation in natural time.Comment: 4 pages and 5 figure

Chaos edges of zz-logistic maps: Connection between the relaxation and sensitivity entropic indices

Chaos thresholds of the $z$-logistic maps $x_{t+1}=1-a|x_t|^z$ $(z>1; t=0,1,2,...)$ are numerically analysed at accumulation points of cycles 2, 3 and 5. We verify that the nonextensive $q$-generalization of a Pesin-like identity is preserved through averaging over the entire phase space. More precisely, we computationally verify $\lim_{t \to\infty}< S_{q_{sen}^{av}} >(t)/t= \lim_{t \to\infty}(t)/t \equiv \lambda_{q_{sen}^{av}}^{av}$, where the entropy $S_{q} \equiv (1- \sum_i p_i^q)/ (q-1)$ ($S_1=-\sum_ip_i \ln p_i$), the sensitivity to the initial conditions $\xi \equiv \lim_{\Delta x(0) \to 0} \Delta x(t)/\Delta x(0)$, and $\ln_q x \equiv (x^{1-q}-1)/ (1-q)$ ($\ln_1 x=\ln x$). The entropic index $q_{sen}^{av}0$ depend on both $z$ and the cycle. We also study the relaxation that occurs if we start with an ensemble of initial conditions homogeneously occupying the entire phase space. The associated Lebesgue measure asymptotically decreases as $1/t^{1/(q_{rel}-1)}$ ($q_{rel}>1$). These results led to (i) the first illustration of the connection (conjectured by one of us) between sensitivity and relaxation entropic indices, namely $q_{rel}-1 \simeq A (1-q_{sen}^{av})^\alpha$, where the positive numbers $(A,\alpha)$ depend on the cycle; (ii) an unexpected and new scaling, namely $q_{sen}^{av}(cycle n)=2.5 q_{sen}^{av}(cycle 2)+ \epsilon$ ($\epsilon=-0.03$ for $n=3$, and $\epsilon = 0.03$ for $n=5$).Comment: 5 pages, 5 figure

Rhizomucor miehei Lipase-Immobilized Sodium Alginate Membrane Preparation and Usage in a Pervaporation Biocatalytic Membrane Reactor

In this study, Rhizomucor miehei lipase-coated alginate membrane was prepared and put in a biocatalytic membrane reactor to produce ethyl lactate from ethyl alcohol and lactic acid. Effects of the amount of coated lipase, reaction temperature and initial molar ratio on lactic acid conversion were investigated to evaluate the performance of the system. In order to compare the performance of the membrane reactor, the reaction was also carried out in a classical batch reactor by using lipase-immobilized membrane as a catalyst. The highest lactic acid conversion achieved was 0.63 in the membrane reactor at 50 °C, while the lactic acid conversion was 0.37 in the batch reactor under the same operating conditions. After six reaction runs, approximately 90 % of the lipase’s catalytic activity was preserved in the membrane reactor

R&D and productivity in OECD firms and industries: A hierarchical meta-regression analysis

The relationship between R&D investment and firm/industry productivity has been investigated widely following seminal contributions by Zvi Griliches and others from late 1970s onwards. We aim to provide a systematic synthesis of the evidence, using 1253 estimates from 65 primary studies that adopt the so-called primal approach. In line with prior reviews, we report that the average elasticity and rate-of-return estimates are positive. In contrast to prior reviews, however, we report that: (i) the estimates are smaller and more heterogeneous than what has been reported before; (ii) residual heterogeneity remains high among firm-level estimates even after controlling for moderating factors; (iii) firm-level rates of return and within-industry social returns to R&D are small and do not differ significantly despite theoretical predictions of higher social returns; and (iv) the informational content of both elasticity and rate-of-return estimates needs to be interpreted cautiously. We conclude by highlighting the implications of these findings for future research and evidence-based policy

Effects of Wastewater Treatment Plant on Water Column and Sediment Quality in Izmir Bay (Eastearn Aegean Sea)

WOS: 00038516170001

Analysis of return distributions in the coherent noise model

The return distributions of the coherent noise model are studied for the system size independent case. It is shown that, in this case, these distributions are in the shape of q-Gaussians, which are the standard distributions obtained in nonextensive statistical mechanics. Moreover, an exact relation connecting the exponent $\tau$ of avalanche size distribution and the q value of appropriate q-Gaussian has been obtained as q=(tau+2)/tau. Making use of this relation one can easily determine the q parameter values of the appropriate q-Gaussians a priori from one of the well-known exponents of the system. Since the coherent noise model has the advantage of producing different tau values by varying a model parameter \sigma, clear numerical evidences on the validity of the proposed relation have been achieved for different cases. Finally, the effect of the system size has also been analysed and an analytical expression has been proposed, which is corroborated by the numerical results.Comment: 14 pages, 3 fig

Developing experiment based science teaching skills : a lifelong learning opportunity for teachers in a rural area of Turkey

Modular Mobile Education: Science Experiments (MOBILIM) is an innovative pilot project for the vocational training of science teachers in rural regions of central Turkey supported by the European Commission in the frames of the Leonardo da Vinci programme. In this project, a mobile science laboratory (MSL) was established in order to cope with the great disparities in opportunities between science teaching in urban and rural areas. Teacher training both in what concerns practical competencies and subject knowledge is one of the main reasons for these disparities in the standards of science teaching. Teacher training via MOBILIM is based on hands-on and demonstration practical activities. At the end of the MSL based phase a two-day conference was organized to provide an opportunity for discussion with and among teachers and also to make it possible to exchange ideas and experiences with European partners of the project. Results indicate that in order to improve teachers’ practice in the classroom, experimental vocational education via mobile laboratories is advisable and allow good results. The majority of the teachers were pleased with the participation in both the training phase and the subsequent project conference. All of the teachers involved want to become a better and more active teaching force. There is a high expectation to carry on with similar courses in the future