Stochastic Order and Generalized Weighted Mean Invariance

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.     

The Quantum Regularization of Singular Black-Hole Solutions in Covariant Quantum Gravity

An excruciating issue that arises in mathematical, theoretical and astro-physics concerns the possibility of regularizing classical singular black hole solutions of general relativity by means of quantum theory. The problem is posed here in the context of a manifestly covariant approach to quantum gravity. Provided a non-vanishing quantum cosmological constant is present, here it is proved how a regular background space-time metric tensor can be obtained starting from a singular one. This is obtained by constructing suitable scale-transformed and conformal solutions for the metric tensor in which the conformal scale form factor is determined uniquely by the quantum Hamilton equations underlying the quantum gravitational field dynamics.     

Multiple scattering and modeling of laser in fog

When a laser is transmitted in fog, and the water droplets will scatter and absorb the laser, which affects the intensity of the laser transmission and the accuracy of radar detection. Therefore, it is of great significance to study the laser transmission in the fog. At present, the main method of calculating the scattering and attenuation characteristics of fog is based on the radiation transmission theory, which is realized by a large number of numerical calculations or physical simulation methods, which takes time and cannot meet the requirements for obtaining the fast and accurate results. Therefore, in this paper established are a new laser forward attenuation model and backward attenuation model in low visibility fog. It is found that in low visibility environments, the results calculated by the Monte Carlo method are more accurate than those from most of the existing forward attenuation models. For the cases of 0.86-μm, 1.06-μm, 1.315-μm, 10.6-μm typical lasers incident on different fogs with different visibilities, a backscatter model is established, the error between the fitting result and the calculation result is analyzed, the backward attenuation fitting parameters of the new model are tested, and a more accurate fitting result is obtained.     

Numerical simulation of the soliton solutions for a complex modified Korteweg—de Vries equation by a finite difference method

In this paper,a Crank-Nicolson-type finite difference method is proposed for computing the soliton solutions of a complex modifed Korteweg de Vries(MKdV)equation(which is equivalent to the Sasa-Satsuma equation)with the vanishing boundary condition.It is proved that such a numerical scheme has the second order accuracy both in space and time,and conserves the mass in the discrete level.Meanwhile,the resuling scheme is shown to be unconditionally stable via the von Nuemann analysis.In addition,an iterative method and the Thomas algorithm are used together to enhance the computational efficiency.In numerical experiments,this method is used to simulate the single-soliton propagation and two-soliton collisions in the complex MKdV equation.The numerical accuracy,mass conservation and linear stability are tested to assess the scheme's performance.     

BMP-6 Loaded Polyelectrolyte Complex Nanoparticles Inducing Osteogenic Differentiation and Apoptosis of Malignant Plasma Cells for Local Treatment of Multiple Myeloma

In the malignant plasma cell disease multiple myeloma (MM), bone lesions and resulting fractures caused by MM cell (MMC) accumulation represent a major cause of morbidity and mortality. Despite recent advantages in systemic treatment, residual MMCs remain, especially in bone lesions. Therefore an interfacial delivery system for local treatment of MM and induced bone disease based on polyelectrolyte complex nanoparticles (PEC NP) loaded with bone morphogenetic protein 6 (BMP-6) inducing de-novo bone formation and MMC apoptosis is presented herein. BMP-6 loaded PEC NP are fabricated by defined mixing bio-related cationic and anionic polysaccharides and BMP-6 according to molar ratio of BMP-6/PEC-NP of 1/3. BMP-6/PEC NP bound to a model substrate releases 10% BMP-6 sustainably within two weeks as accessed by infrared spectroscopy. BMP-6 loaded PEC NP adheres to cell membranes of MMCs and MSCs and activated phosphorylation of Smad 1/5. Osteogenic differentiation (ALP-concentration) is enhanced in MSCs (p < 0.05). All patient samples (10/10) of MMCs show significant induction of apoptosis (median 84%, p < 0.05). Finally, BMP-6/PEC NP are successfully integrated in a commercial hyaluronic acid based hydrogel material revealing MMC death as principal proof for the local treatment of MM induced bone lesions.     

Surface analysis of ripple pattern on PS and PEN induced with ring‐shaped mask due to KrF laser treatment

The approach for ripple nanopattern construction on surface of two polymer substrates [polyethylene naphthalate (PEN) and polystyrene (PS)] exposed by a KrF pulse excimer UV laser through a contact lithographic mask with circular slit was proposed in this paper. Thin layer of gold was deposited on samples after the laser treatment. Changes in the morphology of the surface of both the shielded and exposed areas of the substrates, as well as the dimensions of the laser‐induced periodic surface structures, were determined (by atomic force microscopy, laser confocal microscopy and scanning electron microscopy), compared with observations and measurements made on samples treated directly (without a contact mask) under the same conditions. The morphology of the interface between the treated and untreated regions was also closely studied. Surface chemistry of treated samples was studied in detail by X‐ray Photoelectron Spectroscopy. The detailed study of surface chemistry of modified PEN and PS revealed a significant increase of oxygen concentration for laser treated PS and increase of carboxyl groups in case of PEN. The potential application of this research can be found in biotechnology, micro technology and several other fields. Copyright © 2016 John Wiley & Sons, Ltd.     

Determination of Immunosuppressive Pharmaceuticals in Whole Blood Following Kidney Transplantation by High-performance Liquid Chromatography–Tandem Mass Spectrometry

Cyclosporine, tacrolimus, sirolimus, and everolimus are commonly used immunosuppressants following organ transplantation. Their monitoring is used to determine the optimal dose for therapeutic effectiveness and minimize toxicity. High-performance liquid chromatographic–tandem mass spectrometry with positive electrospray ionization and multiple reaction monitoring mode was validated for the determination of cyclosporine A, tacrolimus, sirolimus, and everolimus in whole blood. A C18 analytical column was employed with a gradient elution of pH 4.0 aqueous 10?mmol/L ammonium acetate and acetonitrile. For the pretreatment of whole blood, simple protein precipitation was used with methanol:zinc sulfate. The calibration curves were linear from 20.0 to 1000?ng/mL for cyclosporine A, 1.0 to 50?ng/mL for tacrolimus and sirolimus, and 1.0 to 30?ng/mL for everolimus. The intra-assay precision and inter-assay precision were less than 15%. The method provides reliable and reproducible results according to the linearity, precision, accuracy, recovery, and matrix effects. The method has been introduced to routine clinical practice in Slovakia for the determination of immunosuppressants in patients after kidney transplantation.     

Effect of liquid oils on the properties of multiple emulsions containing liquid crystals

Recently, many cosmetic researchers have been focused on multiple emulsions due to better performance. Limited application of multiple emulsions has been attributed to their instability, which can be resolved by the presence of liquid crystals. Multiple emulsions containing liquid crystals are affected by various formulation parameters, such as liquid oils. In this paper, the influence of liquid oils on the formation mechanism was studied. Besides, stability, small-angle x-ray scattering (SAXS) spectra analysis, and rheological analysis of the emulsions were investigated as well. The results showed that when the gap of the polarity between inner oils and external liquid oils is greater, the multiple structures were more easily formed. Multiple emulsions containing liquid crystals were superior in stability to multiple emulsions prepared in the same way with liquid oils that did not form liquid crystals. SAXS indicated that the liquid crystal orientation was lamellar. Rheological analysis indicated that the different structure emulsions showed shear-thinning behavior. The presence of liquid crystal decreased the viscosity and resulted in pseudoplastic enhancement. Both the storage modulus (G′) and the loss modulus (G″) of multiple emulsions were slightly higher than those of O/W-type emulsions, implying the existence of multiple structures.     

Application of the fractional factorial design in multiple W/O/W emulsions

In presented research, multiple W/O/W emulsions were developed by using experimental design method. A 24-1 fractional factorial design was performed by varying the following input parameters: primary polymeric emulsifier (PEG 30-dipolyhydroxystearate) concentration (0.8% and 2.4%), secondary polymeric emulsifier (Poloxamer 407) concentration (0.8% and 1.2%), electrolyte magnesium sulfate heptahydrate (0.08% and 0.4%) and electrolyte sodium chloride (0.08% and 0.4%). Multiple emulsions were prepared by a two-step emulsification process. Obtained emulsions were characterized with rheological measurements, conductivity and centrifugation tests. Factorial analysis revealed that the concentration of the primary emulsifier was the predominant factor influencing the phase separation, conductivity and maximal apparent viscosity. Additionally, electrolyte magnesium sulfate heptahydrate was more efficient in stabilizing these systems, compared to sodium chloride. The applied fractional factorial design method enabled determination of the optimal concentrations of the primary and secondary emulsifier, as well as the concentration of electrolytes, in order to obtain W/O/W emulsions with desired maximal apparent viscosities, low values of conductivity and without phase separation after centrifugation.     

Control of a Nonlinear System Using the Saturation Phenomenon

In this paper, a theoretical investigation of nonlinear vibrations of a 2 degrees of freedom system when subjected to saturation is studied. The method has been especially applied to a system that consists of a DC motor with a nonlinear controller and a harmonic forcing voltage. Approximate solutions are sought using the method of multiple scales. It is shown that the closed-loop system exhibits different response regimes. The nature and stability of these regimes are studied and the stability boundaries are obtained. The effects of the initial conditions on the response of the system have also been investigated. Furthermore, the second-order solution is presented and the corresponding results are compared with those of the first-order solution. It is shown that by increasing the amplitude of the excitation voltage, the higher-order term in the solution becomes significant and causes a drift in the response. In order to verify the obtained theoretical results, they are compared with the corresponding numerical results. Good agreement between the two sets of results is observed.