Inferences on the common mean of several normal populations under heteroscedasticity

In this paper, we consider the problem of making inferences on the common mean of several normal populations when sample sizes and population variances are possibly unequal. We are mainly concerned with testing hypothesis and constructing confidence interval for the common normal mean. Several researchers have considered this problem and many methods have been proposed based on the asymptotic or approximation results, generalized inferences, and exact pivotal methods. In addition, Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) proposed a parametric bootstrap (PB) approach for this problem based on the maximum likelihood estimators. We also propose a PB approach for making inferences on the common normal mean under heteroscedasticity. The advantages of our method are: (i) it is much simpler than the PB test proposed by Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) since our test statistic is not based on the maximum likelihood estimators which do not have explicit forms, (ii) inverting the acceptance region of test yields a genuine confidence interval in contrast to some exact methods such as the Fisher’s method, (iii) it works well in terms of controlling the Type I error rate for small sample sizes and the large number of populations in contrast to Chang and Pal (Comput Stat Data Anal 53:321–333, 2008) method, (iv) finally, it has higher power than recommended methods such as the Fisher’s exact method.     

Flatness,plateau limit and limit length of single-plateau functions

In this paper we consider iteration of single-plateau functions, an important class of continuous functions with infinitely many forts, and investigate changes of number and length of plateaux under iteration.We use the indices flatness, plateau limit and limit length to formulate those changes. Furthermore, we compute the flatness, plateau limit and limit length for all the nine types of single-plateau functions.     

ZL-amenability and characters for the restricted direct products of finite groups

Let G   be a restricted direct product of finite groups _{Gi}i∈I${\{G_i\}}_{i\in I}$, and let Z?¹(G)${\mathrm{Z}?}^1(G)$ denote the centre of its group algebra. We show that Z?¹(G)${\mathrm{Z}?}^1(G)$ is amenable if and only if _Gi$G_i$ is abelian for all but finitely many i  , and characterize the maximal ideals of Z?¹(G)${\mathrm{Z}?}^1(G)$ which have bounded approximate identities. We also study when an algebra character of Z?¹(G)${\mathrm{Z}?}^1(G)$ belongs to _c0$c_0$ or ?^p${?}^p$ and provide a variety of examples.     

X-ray diffraction and Mössbauer spectroscopy of high energy ball-milled α-Fe2O3/TiO2 composite powders

α–Fe₂O₃/TiO₂ Composite powders have been prepared by high energy ball-milling for different times. The composites were studied using Mössbauer Spectroscopy (MS) and X-ray diffraction (XRD). The patterns of XRD show broadening in the diffraction peaks, indicating a decrease in the particle size of the composites with milling time. Also, the XRD patterns show an evolving new structural phase correlated with an evolving Titanium ferrite species with milling time. Mössbauer Spectroscopy shows the evolving titanium ferrite species characterized by a quadrupole doublet at the expense of the α–Fe₂O₃ represented by the magnetic sextet. The doublet corresponding to the Ti-ferrite phase dominates the Mössbauer spectra at long milling time (greater than 100 h of milling).     

Pressure anisotropy effects on nonlinear electrostatic excitations in magnetized electron-positron-ion plasmas

The propagation of linear and nonlinear electrostatic waves is investigated in a magnetized anisotropic electron-positron-ion (e-p-i) plasma with superthermal electrons and positrons. A two-dimensional plasma geometry is assumed. The ions are assumed to be warm and anisotropic due to an external magnetic field. The anisotropic ion pressure is defined using the double adiabatic Chew-Golberger-Low (CGL) theory. In the linear regime, two normal modes are predicted, whose characteristics are investigated parametrically, focusing on the effect of superthermality of electrons and positrons, ion pressure anisotropy, positron concentration and magnetic field strength. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential (disturbance) via a reductive perturbation method. The parametric role of superthermality, positron content, ion pressure anisotropy and magnetic field strength on the characteristics of solitary wave structures is investigated. Following Allen and Rowlands [J. Plasma Phys. 53, 63 (1995)], we have shown that the pulse soliton solution of the ZK equation is unstable to oblique perturbations, and have analytically traced the dependence of the instability growth rate on superthermality and ion pressure anisotropy.     

Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

A New Emissive Chalcone-Based Chemosensor Armed by Coumarin and Naphthol with Fluorescence “Turn-on” Properties for Selective Detection of F<Superscript>−</Superscript> Ions

A new chalcone-based probe containing coumarin and naphthol at both ends has been synthesized via aldol condensation. The uniqueness of the newly derived probe can be ascribed to the presence of naphthol and coumarin units acting as binding site and signaling element, respectively. The fluorogenic behaviors toward various anions were investigated. The probe was characterized by various spectroscopic techniques and the in-depth study led to show excellent selectivity and sensitivity for fluoride ions. The hydrogen bonding thus formed with fluoride anion provides remarkable fluorometric responses. The interactions of the probe with fluoride ions were determined by fluorescence, FT-IR and NMR spectroscopic techniques. The exploratory studies by fluorescent spectral changes augur well for the naked-eye sensing applications.     

Entanglement of a two-level atom and its spontaneous emission near the edge of a photonic band gap

The entanglement of a two-level atom and its radiation field near the edge of a photonic band gap is studied by using the quantum entropy. Unlike the free space case, there is a steady-state entanglement between the atom and its spontaneous emission field even when the atomic transition frequency lies outside the band gap. Moreover, the degree of entanglement, which is due to the formation of atom–photon bound dressed state, depends on the detuning of the atomic transition frequency from the photonic band edge and can be controlled by a controllable photonic band gap crystal.