From fractional exclusion statistics back to Bose and Fermi distributions

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this Letter I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.     

Assessing the subsequent effect of nitrogen released from tobacco-waste on maize crop using a 15N isotope technique

The investigation of the residual effect of nitrogen (N) released from tobacco-waste (TW) using isotope techniques will provide valuable data for sustainable organic farming. For this aim, a pot experiment was conducted using the ¹⁵N isotope technique. The experiment was based on a completely randomised design with four replications and was conducted on a calcareous ustochrepts soil. TW at levels of 0, 10, 20, 30 and 40 t ha^?1 and N fertiliser as (NH₄)₂SO₄ at levels of 0, 20, 40, 60 and 80 kg N ha^?1 were used for the Bezostaja-1 wheat variety. Concerning mineral N fertilisation with 20 and 80 kg N ha^?1, additional treatments with ¹⁵N-labelled (NH₄)₂SO₂ (10 at.% exc.) have been applied. Following harvesting wheat plants, the Pioneer 3377 maize variety was used to see the residual effect of TW. After harvesting, dry matter yields were recorded and total N concentrations were determined. ¹⁵N determinations and calculations were also made for ¹⁵N treatments separately. TW had a significant residual effect on the growth of corn plant under the pot condition. Increasing rates of TW significantly increased the dry matter yield of corn plant following wheat from 3.31 t ha^?1 (at control) to 7.89 t ha^?1 (at the TW treatment of 40 t ha^?1). The ¹⁵N values derived from the ¹⁵N fertiliser decreased with increasing TW application. The average values of N derived from N fertiliser (Ndff) varied from 2.14 to 3.09% at the rates of 20 and 80 kg N ha^?1, respectively. However, N derived from TW (Ndftw) significantly increased from 16.93 to 24.59% (at 20 kg N ha^?1), and it also increased from 23.06 to 28.15% (at 80 kg N ha^?1) with increasing TW applications from 20 to 40 t ha^?1, respectively.     

Generalized Bosbach states: part I

States have been introduced on commutative and non-commutative algebras of fuzzy logics as functions defined on these algebras with values in [0,1]. Starting from the observation that in the definition of Bosbach states there intervenes the standard MV-algebra structure of [0,1], in this paper we introduce Bosbach states defined on residuated lattices with values in residuated lattices. We are led to two types of generalized Bosbach states, with distinct behaviours. Properties of generalized states are useful for the development of an algebraic theory of probabilistic models for non-commutative fuzzy logics.     

Optical Fiber Excitation of Fano Resonances in a Silicon Microsphere

In this article, Fano lineshape whispering gallery modes were observed in the light scattering spectrum of a silicon microsphere in near-infrared telecommunication wavelengths. A simple model is presented to explain the transition from Lorentzian lineshape to the Fano lineshape resonances with the coupled-mode theory of multiple whispering gallery modes. Polar mode spacing of 0.23 nm is observed in the spectra, which correlates well with the calculated value. The quality factor of the Lorentzian and Fano resonances are on the order of 10⁵. By using an appropriate interface design for the microsphere coupling geometries, Fano lineshape optical resonances herald novel device applications for silicon volumetric lightwave circuits.     

On Dedekind Modules

In this article the authors give the relation between a finitely-generated torsionfree Dedekind module M over a domain R and prime submodules of the 𝒪(M)-module M and the ring 𝒪(M). They also prove that M is a finitely-generated torsionfree Dedekind module over a domain R if and only if every semi-maximal submodule of R-module M is invertible.     

Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings

Recently, O’Hara, Pillay and Xu (Nonlinear Anal. 54, 1417–1426, 2003) considered an iterative approach to finding a nearest common fixed point of infinitely many nonexpansive mappings in a Hilbert space. Very recently, Takahashi and Takahashi (J. Math. Anal. Appl. 331, 506–515, 2007) introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, motivated by these authors’ iterative schemes, we introduce a new iterative approach to finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space. The main result of this work is a strong convergence theorem which improves and extends results from the above mentioned papers.     

Comparing Singlet Oxygen Generation of Schiff Base Substituted Novel Silicon Phthalocyanines by Sonophotochemical and Photochemical Applications

Although the sonophotodynamic method has an effective therapeutic outcome for anticancer treatment compared with the photodynamic method, there are not enough related studies in the literature and this study aims to contribute to the development of sonophotodynamic studies. For this purpose, the Schiff base substituted silicon phthalocyanines were designed and synthesized as effective sensitizer candidates and the photophysicochemical and sonophotochemical features of the phthalocyanines were examined to increase singlet oxygen efficiency. The calculated Φ_Δ values indicate that the contribution of substituent groups improved the production of singlet oxygen compared with silicon (IV) phthalocyanine dichloride (SiPcCI₂) and also the sonophotochemical applications increased the singlet oxygen yields. The Φ_Δ values (Φ_Δ = 0.76 for axially bis-{4-[(E)-(pyridin-3-ylimino)methyl]phenol} substituted silicon (IV) phthalocyanine ( 2a ), 0.68 for axially bis-4-[(E)-{[(pyridin-3-yl)methyl]imino}methyl]phenol substituted silicon (IV) phthalocyanine ( 2b ) in photochemical study) reached to Φ_Δ = 0.98 for 2a , 0.94 for 2b in sonophotochemical study. This article will enrich the literature on increasing singlet oxygen yield.     

Swelling of <Emphasis Type="Italic">N</Emphasis>-vinylcaprolactam-dodecyl methacrylate gel in {heptane + toluene} mixtures

A copolymer gel has been synthesized from N-vinylcaprolactam and dodecyl methacrylate in ethanol using the free radical cross-linking polymerization method. Characterizations of the gel were performed by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and thermal gravimetric analysis (TGA) techniques. Swelling behavior of the gel was investigated in heptane, toluene, and their binary mixtures with different compositions. Swelling value in toluene is higher than that in heptane and swelling value increases with the increasing initial content of toluene in the binary mixture with heptane. The swelling values are correlated by the first- and second-order differential equations, and the best model correlating the experimental results is a second-order one. Diffusion coefficients have also been calculated for heptane and toluene at each concentration by power-law and first-order equations. While the diffusion mechanism of the gel in heptane is a Fickian one, the gel swelled in toluene exhibits a non-Fickian character. Diffusion mechanisms of the gels in binary mixtures are much more complicated. Because of the higher swelling degree in toluene compared to that in heptane, selectivity of the gel in different {heptane + toluene} mixtures with selectivity close to 1 has also been taken into consideration.