Precision cosmology as a test for statistics

We compute the shift in the epoch of matter-radiation equality due to the possible existence of a different statistical (non-extensive) background. The shift is mainly caused by a different neutrino-photon temperature ratio. We then consider the prospects to use future large galaxy surveys and cosmic microwave background measurements to constrain the degree of non-extensivity of the universe.Comment: to appear in Physica

Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis thermostatistics. The generalized partition functions, internal energies, free energies and temperature factor (or Debye-Waller factor) are calculated. It has also been observed that the temperature factor is dependent on the non-extensive parameter q which behaves like a scale parameter in the harmonic oscillator model. As $q\to 1$, we also show that these approximations agree with the result of Gaussian network model.Comment: 8 pages, 2 figure

Landau Diamagnetism in Noncommutative Space and the Nonextensive Thermodynamics of Tsallis

We consider the behavior of electrons in an external uniform magnetic field B where the space coordinates perpendicular to B are taken as noncommuting. This results in a generalization of standard thermodynamics. Calculating the susceptibility, we find that the usual Landau diamagnetism is modified. We also compute the susceptibility according to the nonextensive statistics of Tsallis for (1-q)<<1, in terms of the factorization approach. Two methods agree under certain conditions.Comment: Clarifications and new references. Version to appear in Phys.Lett.

Extension of Nikiforov-Uvarov Method for the Solution of Heun Equation

We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere and hyperbolic double-well potential are investigated by this method

Farklı Olgunluk Dönemlerinde Hasat Edilen Yonca Bitkisinden Hazırlanan Silajlarda Laktik Asit Bakterisi ve Enzim Karışım İnokulant İlavesinin Silaj Fermantasyon Özellikleri ve Yem Değeri Üzerindeki Etkileri

This study was carried out to determine the effects of lactic acid bacteria+ enzyme (LAB+E)inoculants on the fermentation characteristics and feed values of silages prepared from alfalfaharvested at three maturity stages. Alfalfa was harvested at the early, middle and late floweringstages. Sil-All (Alltech, UK) were used as LAB+E inoculants. Inoculants were applied to thesilages at the rates of 1×105, 5×105and 1×106cfu/g levels in 1 liter capacity plastic bags. Thebags were stored at 20±2°C under the laboratory conditions. Three bags from each group weresampled for chemical and microbiological analyses on the 45th day after ensiling. The resultsshowed that LAB+E inoculants reduced pH values and ammonia-nitrogen content, whereasincreased lactic acid contents and lactobacillus count of alfalfa silages. High doses LAB+Einoculant decreased neutral detergent fiber and acid detergent fiber content, increased in vitroorganic matter digestibility and metabolic energy of alfalfa silages. It has been demonstratedthat the most effective application dose of LAB+E inoculant to improve fermentation and feedvalue of alfalfa silage was 1×106cfu/g, but 1x105and 5×105cfu/g level can also be consideredas effective doseBu çalışma, üç ayrı vejetasyon döneminde hasat edilen yonca bitkisine farklı düzeylerde laktik asit bakteri+enzim (LAB+E) inokulantı ilavesinin silaj fermantasyon özellikleri ve yem değeri üzerindeki etkilerinin saptanması amacıyla yürütülmüştür. Yonca bitkisi çiçeklenme başlangıcı, çiçeklenme ortası ve çiçeklenme sonu döneminde hasat edilmiştir. Laktik asit bakteri+enzim karışımı inokulant kaynağı olarak Sil-All (Alltech, UK) kullanılmıştır. İnokulant, yonca hasıllarına 1×105 , 5×105 ve 1×106 kob/g düzeyinde katılmıştır. Kontrol ve katkı maddeleri ile muamele edilen yonca 1 litre hacimli polietilen torbalarda silolanmıştır. Torbalar laboratuvar koşullarında 20±2°C sıcaklıkta depolanmışlardır. Silolamadan sonraki 45. günde her gruptan 3'er torba açılarak silajlarda kimyasal ve mikrobiyolojik analizler yapılmıştır. Sonuç olarak, LAB+E inokulantı silajların pH ve amonyak azotu içeriklerini azaltırken; laktik asit, asetik asit içerikleri ve lactobacilli sayısını artırmıştır. Yüksek dozda LAB+E ilavesi silajların nötr deterjanda çözünmeyen lif ve asit deterjanda çözünmeyen lif içeriğini azaltmış, in vitro organik madde sindirilebilirliğini ve metabolik enerji değerlerini artırmıştır. Yoncanın LAB+E inokulantı ilave edilerek silolanmasının fermantasyon özellikleri ve yem değerini iyileştirdiği, en etkili dozun 1×106 kob g/kg olmakla birlikte, 1×105 kob g/kg ve 5×105 kob/g dozlarında da uygulanabileceği belirlenmişti

q-thermostatistics and the analytical treatment of the ideal Fermi gas

We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and low-temperature regimes, and the approximate results pertaining to the case q \sim 1 (the conventional Fermi-Dirac statistics corresponds to q=1). We compare our findings with previous Tsallis' literature.Comment: v2: comparison with conventional results and validity of approximations clarified, typos corrected; accepted for publication in Physica

Quantal distribution functions in non-extensive statistics and an early universe test revisited

Within the context of non-extensive thermostatistics, we use the factorization approximation to study a recently proposed early universe test. A very restrictive bound upon the non-extensive parameter is presented: $|q-1| < 4.01 \times 10^{-3}$.Comment: 4 pages, prl revtex style, no figures. To appear in Physica A, 199

BCS Model in Tsallis' Statistical Framework

We show that there is an effect of nonextensivity acting upon the BCS model for superconductors in the ground state that motivates its study in the Tsallis' statistical framework. We show that the weak-coupling limit superconductors are well described by $q \sim 1$, where q is a real parameter which characterizes the degree of nonextensivity of the Tsallis' entropy. Nevertheless, small deviations with respect to q = 1 provide better agreement when compared with experimental results. To illustrate this point, making use of an approximated Fermi function, we show that measurements of the specific heat, ultrasonic attenuation and tunneling experiments for tin (Sn) are better described with q = 0.99.Comment: 13 pages, amssym