A Significance Test for Simultaneous Quanta1 and Quantitative Responses

A significance test is designed for a situation where a discrete variate r, representing the number of successes in a sample of size n, is observed together with a continuous variate , representing the arithmetic mean of a measure concerning only the r successes (or the n – r failures). The aim is to test the null-hypothesis H ₀ : ω = ω₀, μ = μ₀ against an alternative (say) H ₁ : ω<ω₀ and/or μ<μ₀, where ω is the proportion of successes of the whole population, estimated by r/n, and μ is the mean, estimated by , of the above mentioned measure concerning the r successes alone. The parameters ω₀, μ₀. are either given or unknown parameters associated with a second sample to be compared with the first.

Although the two variates r and are usually not independent, the above problems can be solved by combination of probabilities. Moreover, it is shown that, quite generally, Fisher's method of combining probabilities of continuous variates and its generalization for discrete variates can be extended to variates that are not stochastically independent.     

Testing the Mean and Standard Deviation of a Normal Distribution Using Quantiles

Assuming a normally distributed population and a large sample size, three tests of hypotheses are presented using sample quantiles. First, we test whether μ = μ₁ and σ = σ₁ or μ = μ₂ and σ = σ₂, using one optimum quantile. Then test statistics and acceptance regions are given for testing the mean and standard deviation independently. The efficiency of each test is given relative to the best test using all the sample values.     

Robust feedback control of singularly perturbed uncertain dynamical systems

A class of uncertain singularly perturbed control systems described by ordinary differential equations is considered. The uncertainties are characterized determimstically; the singular perturbation is characterized by a real non-negative system parameter μ For μ = 0, the system order is lower than that for μ > 0. Based mainly on information available on the uncertain reduced-order system. (μ=0), controllers are proposed which ensure that the behaviour of the feedback controlled reduced-order system is close to that of global uniform asymptotic stability about zero. Subject to the same controllers, the full-order system (μ >0) has the same qualitative behaviour, provided μ<μ*, where μ* >0 can be

computed from, the available information     

Control Charts for Binary Correlated Variables

To monitor the nonconforming fraction of a production process, usually np or p control charts are used for this purpose. However, in many practical situations, the binary variables are correlated but not easily perceived by practitioners. The aim of this article is to present the maximum likelihood and method of moment estimators of the correlation parameter ρ of an overdispersed binomial distribution. Inferential procedure is also introduced to test the null hypothesis H₀: ρ = 0 x H₁: ρ > 0. A Shewhart‐type control chart np_ρ and an Exponentiated Weighted Moving Average (EWMA)‐type control chart (EWMA np_ρ) are proposed to evaluate the nonconforming fraction when the binary variables are correlated. The traditional np chart is a particular case of the np_ρ control chart when ρ = 0. The misuse of control limits of np control in case of correlated binary variables will result a large number of false alarms. To have the same performance (in terms of average run length) of the traditional np control chart, the np_ρ control chart needs at least to double the sample size. Numerical example illustrates the proposal. Copyright © 2012 John Wiley & Sons, Ltd.     

Magnetoresistivity study on Cr added Bi-2212 superconductor ceramics with experimental and theoretical approaches

This study investigates the change of the superconducting and physical properties of Cr added Bi-2212 superconductor ceramics prepared by the conventional solid-state reaction method with the aid of magnetoresistivity measurements performed in a range from 0 to 7 T. The zero resistivity transition temperatures (T_c), irreversibility fields (μ₀H_irr), upper critical fields (μ₀H_c2), penetration depths (λ) and coherence lengths (ξ) are estimated from the magnetoresistivity curves. Furthermore, activation energy (U₀) values of the ceramics produced are found using thermally activated flux creep model. The results show that the T_c value decreases from 80.7 K (52.6 K) to 70.4 K (13.4 K) for the pure sample (the sample doped with 1wt% Cr) with the increasement in the applied magnetic field. Likewise, the U₀ values reduce dramatically with increasing applied magnetic field. In fact, the U₀ of 302 K is the smallest at 7 T applied field for the sample doped with 1wt% Cr. Additionally, the μ₀H_irr and μ₀H_c2 values decrease with the increase of the Cr addition. At absolute zero temperature (T = 0 K), the extrapolation of the μ₀H_irr(T) and μ₀H_c2(T) curves is used to obtain the μ₀H_irr(0) and μ₀H_c2(0) values of the samples. The inner (latter) is found to be about 85.87 T (191.21 T) T and 13.88 T (86.89 T) for the pure sample and the sample doped with 1wt% Cr, respectively. On the other hand, the ξ and λ values inferred from μ₀H_irr(0) and μ₀H_c2(0) are obtained to increase from 13.13 to 19.48 ? and 19.60 to 48.73 ?, respectively as the Cr addition level increases in the Bi-2212 bulk superconductor, presenting that the Cr doping suppresses the physical and superconducting properties of the samples as a result of the pair-breaking mechanism.     

Surface tension and peculiarity of the vortex state in magnetic superconductors

The behavior of ferromagnetic superconductors (FS) with large GL parameter in a magnetic field is studied as a function of temperature. Both the exchange and the electromagnetic mechanisms of interaction between superconducting electrons and localized magnetic moments (LM) are taken into account. It is shown that various exotic states can be realized by lowering the temperature, for instance: (1)H _c2>H _c>_c1, _ns>0; (2)H _c>H _c2>H _c1, _ns>0, etc., depending on temperature and x. Here, _ns is the surface tension for the planar geometry of the FS. At the same time, the barrier fieldH _s for the penetration of a vortex line inside a semiinfinite specimen of a real FS is practically the same as in a nonmagnetic superconductor.On leave of absence from Institute of Physics, Belgrade, Yugoslavia.     

A molecular dynamics-aided fracture mechanics parameter and its application to a tensile problem

To evaluate fracture by a single parameter like J integral in molecular dynamics (MD) calculation, we propose a parameter derived by extending integral to atomic model, being referred to as H-sum. To examine the path independence of H, we first apply H to a simple tensile problem of two dimensional model of -iron by using molecular dynamics method. As a result, we confirm that H has the path independence within an accuracy of 8.5%. In addition, the validity of the proposed parameter is clarified by analyzing a problem of microscopic crack initiation and propagation process. H increases with increasing tensile stress and reaches a critical value when a crack initiates, and subsequently decreases with the crack growth. Calculating K _IC from this critical H, we compare K _IC with deCelis' and the Mullins' results calculated directly from MD calculation, and get good agreement.     

On the Likelihood Ratio Test for Compound Distributions for Homogeneity of Mixing Proportions

We consider the problem of comparing two multivariate compound distributions each with component densities f ₁, (x) and f ₂(x) and with mixing proportions p _x and (1 – p_x) for the first compound distribution and p_y and (1 – p_y ) for the second. The likelihood ratio test of the hypothesis H ₀: p_x = p_y is presented by using the EM algorithm to derive the maximum likelihood estimates. This test is applied to some actual data under the assumption that the underlying component densities are normal. The result is contrasted with results obtained using some existing univariate methods of testing H₀.     

Scaling Behavior and Estimation of Activation Energy of Polycrystalline RuSr2GdCu2O8 Superconductor from AC Susceptibility Measurements

In this study, the measured curves of AC susceptibility (ACS) components, (T) and (T), of polycrystalline RuSr₂GdCu₂O₈ (Ru-1212) superconductor were scaled onto a single curve using the peak temperature of its imaginary part (T _p) as the scaling parameter for various AC field amplitudes from 0.5 to 24 G. The dependence of the AC magnetic field amplitude on T _p is scaled as: H _ac (1–T _p/T _c)^2.25. Similarly, the current density J _c, extracted from the AC field amplitude is also scaled as: J _c (1 – T _p/T _c)^2.25. The dependencies of T _p on frequency and AC field amplitude are also investigated and the time parameter t ₀ of the order of 10^–8 s is estimated from the dependence of T _p on frequency. The dependencies of activation energy on temperature, T, and the field amplitude, H _ac, are obtained from the Arrhenius-like semilog plot of frequency () and T _p. Such dependencies on temperature and field amplitude can be described by a scaling law of the form: U(H _ac,T) = U ₀[1 – T/T _p]H _ac ^–0.17.     

The Power Function,of the Exact Test for the 2 × 3 Contingency Table

In continuation of the authors' tables of significance tests (1963), the power function of this exact test for the 2 × 3 contingency table using the Freeman & Halton principle is derived and evaluated numerically in the form of contours of constant power for the cases: A = 5(5) 15, where A is the total number in each of the three groups observed according to the numbers of ‘Successes’ (= a _i ) in each. Comparisons are also made with the exact significance points of the competing X ² and (?2 log λ) tests under the null hypothesis H ₀ and also alternatives to H ₀.     

Effect of annealing temperature on magnetoresistivity, activation energy, irreversibility and upper critical field of the Cu-diffused MgB2 bulk superconductors

This study manifests the change of the pinning mechanism, superconducting and physical properties of Cu-diffused MgB₂ superconductors prepared at different annealing temperature from 650 to 850 °C by means of the magnetoresistivity measurements conducted at several applied magnetic fields in a range of 0–7 T as a function of temperature from 15 to 50 K. The onset (T _c ^onset ) and offset (T _c ^offset ) critical temperatures, activation energies (U₀), irreversibility fields (μ₀H_irr), upper critical fields (μ₀H_c2), residual resistivity ratios (R_R), cross-sectional area fractions (A_F), penetration depths (λ), coherence lengths (ξ) and electronic mean free path ( $ \ell $ ) of the samples are evaluated from the magnetoresistivity curves. Thermally activated flux creep (TAFC) model is used for the determination of the U₀ values; likewise, the μ₀H_irr and μ₀H_c2 values are obtained by resistivity criteria of 10 and 90 % normal-state resistivity, respectively. At absolute zero temperature (T = 0 K), the extrapolation of the μ₀H_irr(T) and μ₀H_c2(T) curves is used to find the μ₀H_irr(0) and μ₀H_c2(0) values of the samples. Moreover, the ξ values are deduced from the μ₀H_c2(0) values when the λ values are calculated from the Ginzburg–Landau parameter ( $ \kappa $ ). It is found that the superconducting and physical properties of the samples improve with the increment of the diffusion-annealing temperature; however, the presence of the magnetic field leading to the decrease of the flux pinning in the samples causes the reduction of these properties. Namely, the T _c ^onset and T _c ^offset values are found to increase from 38.4 to 39.3 K and 36.9 and 38.3 K with the enhancement in the diffusion-annealing temperature at zero filed. Similarly, the U₀ values increase significantly with the increase of the annealing temperature. In fact, the U₀ of 9,162 K belonging to the sample annealed at 850 °C is determined to be the maximum activation energy value. On the other hand, the minimum T _c ^onset of 30.9 K, T _c ^offset of 27.6 K and U₀ of 1,365 K at 7 T applied magnetic field are obtained for the pure sample, indicating that the sample annealed at 850 °C obtains much stronger flux pinning, better crystallinity and connectivity between grains compared to the other samples prepared. Based on these results, the superconducting and physical properties of the MgB₂ superconductors produced in this work are observed to enhance with the increase of the diffusion-annealing temperature as a result of the improvement of pinning abilities, crystallinity and connectivity between grains. The magnetic field and temperature dependence of the activation energy are also discussed.     

First- and second-order superconducting phase transitions of tin whiskers in a magnetic field

Using a sensitive inductance technique, first- and second-order phase transitions in tin (type I) whiskers have been observed in both parallel and perpendicular magnetic fields. ForT much less thanT _c the samples exhibit considerable superheating and supercooling from which values of the Ginzburg-Landau parameter are calculated. However, these values are not as low as those obtained for single spheres (diameters 10–30 µ), probably due to mean free path and size effects. Close to the transition temperature it is observed that the hysteresis vanishes indicating the onset of a second-order phase transition. Good qualitative agreement between these results and theoretical predictions based on the Ginzburg-Landau theory are obtained. Size effects on the ratioH _C3/H _C2 H _SC /H _C2 are clearly illustrated.     

Metamagnetic-like transition in CeRu2Si2?

Extensive magnetization and magnetoresistivity experiments on CeRu₂Si₂ are described, with special emphasis on the metamagnetic-like transition that occurs atH*=80 kOe. By contrast to the low-field susceptibility, the differential susceptibility atH* almost diverges atT0. It is suggested that high magnetic fields (H>H*) restore a situation where the interactions between particles have collapsed. Comparison is made with other well-known examples: TiBe₂, UPt₃, TmSe, and³He.     

Upper Critical Field Hc2 on c Axis of Ag/Bi-2223 Polycrystal Tape

The upper critical field H _c2, based on Ginzburg–Landau theory at medial magnetic fields, can be calculated from the relationship of the magnetization intensity M(H) versus magnetic field H if M is linear with ln₀ H. For Ag/Bi-2223 tapes, the measured M(H) was found to be linear with ln₀ H. In this case, the values of H _c2(T) may in principle be determined. To do this, we will meet another problem in that the obliquity of crystal planes is not equal for different grains in tapes, and values of grain-oblique angle will appear in the calculated H _c2. Obviously, for Ag/Bi-2223 tapes is an uncertain parameter and hard to determine. To avoid the effects of , we only study the H _c2 in the c axis direction and the projections of H onto the c axis is taken as the actual applied fields. Thus, the effects of grain-oblique angle may be counteracted when measuring critical current density J, if the external magnetic fields are applied to the tape along both the parallel to and perpendicular to the c axes directions (on the narrow surfaces of the tape). On medial fields (H = 0 – 3 T), the upper critical fields H _c2(T) on c axis for the Ag/Bi-2223 tape are obtained and fitted as ₀ H _c2(T) = 830 e ^–0.07T . The average slope d[₀ H _c2(T)]/dT – 8T/K is found to be as large as that of Bi-2212. On extrapolating the relation to T = 0 K, the value of ₀ H _c2(0) 800T. The coherence length _ab is determined from H _c2(c), and _ab (0) = 0.63 nm at T = 0 K.     

Hc2 of MgCNi3 Determined from the Specific Heat and Resistivity Measurements

H _c2 of MgCNi₃ has been determined from the specific heat C and resistivity measurements in the same sample. The results from are nearly identical with those determined from the anomaly in C. Furthermore, utilizing the relation (H) H and the value of d/dH, the obtained value of H _c2 is the same as that by the WHH model, if the spin paramagnetic effect and the spin–orbit interaction are taken into account. The results of this comparison have strong implications on the order parameter of MgCNi₃.     

Microstructure,phase stability and properties of CoCr0.5CuxFeyMoNi compositionally complex alloys

Liquid-phase separation occurred in CoCrCu_xFeMoNi (x?≥?0.5) alloys when the mixing entropies are positive in our previous work. So in this work, CoCr_0.5Cu_xFe_yMoNi alloys are designed to investigate the microstructure, component phases and properties. FCC and BCC were detected in CoCr_0.5Cu_xFe_yMoNi alloys, accompanied with a topologically close-packed μ phase. A parameter, V_R, was defined, where V_R is the ratio of the volume fraction of BCC plus μ phases and that of FCC phase. The maximum strength and the ductility were obtained at the minimum V_R of the alloys, whereas the hardness increased with the increasing V_R. It can be presumed that the strange balance between strength, ductility and hardness is an indirect result of the degree of brittle failure.     

Anisotropic Superconducting Properties of MgB2 and Related Compounds

Anisotropic superconducting properties of inter-metallic compounds MgB₂, Y₂PdGe₃, and CaAlSi with AlB₂ structure are studied by detailed angular dependent transport measurements. MgB₂ and CaAlSi shows appreciable anisotropy of the upper critical field, H _c2, with mass anisotropy parameter =3 and 2, respectively, while Y₂PdGe₃ is almost isotropic. In-plane anisotropy of H _c2 in these hexagonal superconductors is very small, consistent with the prediction based on GL theory.