An admissible minimax estimator of a bounded scale-parameter in a subclass of the exponential family under scale-invariant squared-error loss

A subclass of the scale-parameter exponential family is considered and for the rth power of the scale parameter, which is lower bounded, an admissible minimax estimator under scale-invariant squared-error loss is presented. Also, an admissible minimax estimator of a lower-bounded parameter in the family of transformed chi-square distributions is given. These estimators are the pointwise limits of a sequence of Bayes estimators. Some examples are given.     

From the Boltzmann equation to the Stokes‐Fourier system in a bounded domain

We prove that the renormalized solutions of the Boltzmann equation considered in a bounded domain with different types of (kinetic) boundary conditions converge to the Stokes‐Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and D. Levermore [9] to the case of a bounded domain. © 2003 Wiley Periodicals, Inc.     

The phase diagram of the lyotropic nematic mesophase in the TTAB/NaBr/water system

The phase diagram of the nematic mesophase present in the tetradecyltrimethylammonium bromide/sodium bromide/water ternary system was determined. A calamitic nematic mesophase (N_C) was observed which extends to very high concentrations of electrolyte. The order parameters of the surfactant head group in the mesophases were studied by the NMR quadrupolar splitting of the deuterated surfactant. On increasing the temperature of nematic mesophases with low electrolyte concentrations, a phase separation occurs with the formation of a more highly ordered hexagonal phase and an isotropic phase. Diffusion measurements of the isotropic micellar solution by the NMR PFG method were used to estimate hydrodynamic radii at low surfactant concentrations and to study micelle diffusion as the concentration of the surfactant was increased to the liquid crystalline region. At higher surfactant concentrations, the diffusion coefficient reached a limiting value. The calamitic nematic mesophase in this surfactant/electrolyte/water system appears to be formed by long wormlike micelles.     

Ergodic theory of amenable semigroup actions

In this paper, among other things, we state and prove the mean ergodic theorem for amenable semigroup algebras.     

Label-Free Impedance Biosensors: Opportunities and Challenges

Impedance biosensors are a class of electrical biosensors that show promise for point-of-care and other applications due to low cost, ease of miniaturization, and label-free operation. Unlabeled DNA and protein targets can be detected by monitoring changes in surface impedance when a target molecule binds to an immobilized probe. The affinity capture step leads to challenges shared by all label-free affinity biosensors; these challenges are discussed along with others unique to impedance readout. Various possible mechanisms for impedance change upon target binding are discussed. We critically summarize accomplishments of past label-free impedance biosensors and identify areas for future research.     

A portable positron accumulator for antihydrogen formation

A pulsed source of positrons has been developed which may be useful for antihydrogen ( ) formation because it is portable when compared to accelerator-based sources. This positron accumulator uses a Penning-style trap to collect moderated positrons from a radioactive source. The positron pulses may be emitted with repetition rates in the range of 50–1000 Hz, which is appropriate for production schemes involving laser-induced recombination. Bunching techniques may be used to vary the width of the positron pulses over the range 30–120 ns (FWHM) to match the width of the antiproton and/or laser pulses. The efficiency of the accumulator increases from ∼ 10% at 100 Hz to ∼ 50% at 1000 Hz. 250 Hz the efficiency is ∼ 25% and the accumulator has delivered up to 8 e⁺/pulse per mCi of positron activity. This translates into ∼ 1.2 × 10⁵ e⁺/pulse for a 100 Ci⁵⁸Co source.     

Solubility Optimization of Loxoprofen as a Nonsteroidal Anti-Inflammatory Drug: Statistical Modeling and Optimization

Industrial-based application of supercritical CO₂ (SCCO₂) has emerged as a promising technology in numerous scientific fields due to offering brilliant advantages, such as simplicity of application, eco-friendliness, and high performance. Loxoprofen sodium (chemical formula C₁₅H₁₈O₃) is known as an efficient nonsteroidal anti-inflammatory drug (NSAID), which has been long propounded as an effective alleviator for various painful disorders like musculoskeletal conditions. Although experimental research plays an important role in obtaining drug solubility in SCCO₂, the emergence of operational disadvantages such as high cost and long-time process duration has motivated the researchers to develop mathematical models based on artificial intelligence (AI) to predict this important parameter. Three distinct models have been used on the data in this work, all of which were based on decision trees: K-nearest neighbors (KNN), NU support vector machine (NU-SVR), and Gaussian process regression (GPR). The data set has two input characteristics, P (pressure) and T (temperature), and a single output, Y = solubility. After implementing and fine-tuning to the hyperparameters of these ensemble models, their performance has been evaluated using a variety of measures. The R-squared scores of all three models are greater than 0.9, however, the RMSE error rates are 1.879 × 10⁻⁴, 7.814 × 10⁻⁵, and 1.664 × 10⁻⁴ for the KNN, NU-SVR, and GPR models, respectively. MAE metrics of 1.116 × 10⁻⁴, 6.197 × 10⁻⁵, and 8.777 × 10⁻⁵errors were also discovered for the KNN, NU-SVR, and GPR models, respectively. A study was also carried out to determine the best quantity of solubility, which can be referred to as the (x₁ = 40.0, x₂ = 338.0, Y = 1.27 × 10⁻³) vector.