Narrow Results

This paper is concerned with existence and concentration phenomena of semiclassical solutions of the following nonlinear Dirac equation

The concentration dependence of atomic short range order (SRO) has been studied in Ni_100-xHf_x and Re_100-xTi_x alloys (where x = 2, 5, 10, 15, 20 at.%) using the framework of transition metal model pseudopotential (TMMP). The ordering energies and Warren–Cowley SRO parameters were calculated for the Ni-Hf and Re-Ti alloys. It was found that this model predicted the correct sign of SRO for Ni_100-xHf_x system but failed in the case of Re_100-xTi_x alloys.

Due to its geometry simplicity, the forces of thin liquid film are widely investigated and equivalently employed to explore the phys–chemical properties and mechanical stability of many other surfaces or colloid ensembles. The surface tension of bulk liquid (${\sigma }_{\infty }$) and film tension ($\gamma$) are the most important parameters. Considering the insufficiency of detailed interpretation of film tension under micro-scale circumstances, a method for film tension was proposed based on numerical modeling. Assuming surface tension at different slab thicknesses being identical to the surface tension of film, the surface tension and disjoining pressure were subsequently used to evaluate the film tension based on the derivation of film thermodynamics, and a decreasing tendency was discovered for low temperature regions. The influence of saline concentration on nano-films was also investigated, and the comparison of film tensions suggested that higher concentration yielded larger film tension, with stronger decreasing intensity as a function of film thickness. Meanwhile, at thick film range (15–20 nm), film tension of higher concentration film continued to decrease as thickness increase, however it arrived to constant value for that of lower concentration. Finally, it was found that the film tension was almost independent on the film curvature, but varied with the thickness. The approach is applicable to symmetric emulsion films containing surfactants and bi-layer lipid films.

In recent years, the safety of traditional Chinese medicine has gradually attracted consumers’ attention. Therefore, the qualitative and quantitative detection of traditional Chinese medicine has become a hot research topic in recent years. In this paper, we chose prepared Rehmannia root as the research object. By using the fluorescence polarization spectrum and the least-square method, a method for predicting the concentration of traditional Chinese medicine solutions was established. First, we scanned the fluorescence polarization spectra of the prepared Rehmannia root solution to obtain the inner anisotropy and anisotropy of each sample. Then, the least-square method was used to obtain the functional relationship between concentration and anisotropy. Finally, the functional relation was applied to predict the concentration of the prepared Rehmannia root solution. The correlation coefficients of the predicted concentration were 0.9944 and 0.9928, with an average recovery rate of 100.94% and 99.58%, respectively. The results show that fluorescence polarization spectroscopy combined with the least-squares method can quickly and accurately detect the concentration of Rehmannia glutinosa root solution. This provides a new method for the content detection of traditional Chinese medicine components.

We proposed a physical scheme to concentrate unknown non-maximally entangled atomic states via cavity quantum electrodynamics (QED) techniques. In this scheme, the unique advantage is that the effects of the cavity decay and thermal field have been eliminated by using a classical driving field. The discussion indicates that it can be realized by current technologies.

We propose a scheme for concentrating an arbitrary two-particle non-maximally entangled state into a maximally entangled state assisted with three cavities. The scheme involves two interaction–detection cycles and resonant interaction between atom and cavity mode. With the help of the atom trapped in the cavity, the concentration of a two-particle non-maximally entangled state trapped in separate cavities can be realized with a certain probability according to the results of photon detectors. The important feature of our scheme is that we can realize the concentration of an arbitrary two-atom non-maximally entangled state and we do not perform Bell-state measurements.

We present a protocol for concentrating an arbitrary four-photon entangled state into a maximally entangled state assisted with singled photons. The concentration protocol uses the linear optics and the cross-Kerr nonlinearity based on the post selection principle. Four parties called Alice, Bob, Charlie and Dan in different distant locations can obtain the cluster state from an arbitrary entangled four-photon state with a certain probability. Quantum non-demolition (QND) measurements are available in this protocol. Moreover, this scheme can be steady with a higher success possibility.

It is known that redox reaction can take place among the solutions of potassium ferrocyanide (K₄[Fe(CN)₆]), glucose (C₆H${}_{12}$O₆) and glucose oxidase (Glucose Oxidase, GOD). In this work, the method of electrochemical biosensor detection based on screen printed electrode was used to observe the redox reaction among these solutions. The relationship between redox reaction and parameters was studied by examining the effects of concentration and scanning speed of three solutions.

A new method for colorimetric detection of solution concentration is presented. A paper-based microfluidic device was designed and made using printed circuit board technology. Detection zone patterns were designed and transferred to a printed circuit board by hollowing technology. The printed circuit board with patterns was stuck onto a copper sheet. The hollowed zone was filled with solid paraffin and then covered with a piece of filter paper. The paraffin wax was melted by heating the copper sheet and permeated into the filter paper. Solution to be detected was pipetted on the paper-based device with detective zones. The images of the detective zones were obtained using a microscope with charge-coupled device, which is used for calculating RGBI model to further obtain the solution concentration. Litmus was demonstrated in sample experiments. Results showed that maximum error of measured value of solution concentration to its true value is less than 2% using the presented method.

In order to satisfy the requirements of high quality and optimal material manufacturing process, it is important to control the environment of the manufacturing process. Depending on these processes, it is possible to improve the quality of the product by adjusting various gases. With the advent of the tunable laser absorption spectroscopy (TDLAS) technique, the temperature and concentration of the gases can be measured simultaneously. Among them, computed tomography-tunable diode laser absorption spectroscopy (CT-TDLAS) is the most important technique for measuring the distributions of temperature and concentration across the two-dimensional planes. This study suggests a three-dimensional measurement to consider the irregular flow of supplying gases. The simultaneous multiplicative algebraic reconstruction technique (SMART) algorithm was used among the CT algorithms. Phantom datasets have been generated by using Gaussian distribution method. It can show expected temperature and concentration distributions. The (HITRAN) database in which the thermo-dynamical properties and the light spectra of H₂O are listed were used for the numerical test. The relative average temperature error ratio in the results obtained by the SMART algorithm was about 3.2% for temperature. The maximum error was 86.8 K.

To use supplying gases and energy resources efficiently, accurate measurement of irregular gas is necessary. The TDLAS (Tunable laser absorption spectroscopy) technique can be used to control and monitor the supplying gas conditions and combustion of industrial processes. Recently, CT-TDLAS (Computed tomography-tunable diode laser absorption spectroscopy) has been developed to measure the temperature and concentration field of gases. In this study, the 2-dimensional temperature distribution of the Propane-Air premixed flame in several mixing conditions of fuel has been measured by the constructed CT-TDLAS system. 2-Dimensional temperature distributions are measured by 16 path cells. Further, the third-order polynomial regression analysis was applied to resolve the absorption spectra from the incident and transmitted light for a particular gas. The SMART (simultaneous multiplicative algebraic reconstruction technique) algorithm has been adopted for reconstructing the absorption coefficients on the detecting area. As a result of comparing the temperature for the 2-dimensional detecting area using the thermocouple and CT-TDLAS technique, it has been verified that the relative error for the temperatures measured by the thermocouples and calculated by the CT-TDLAS was up to 8%.

Study of heat and mass transfers is carried out for MHD Oldroyd-B fluid (OBF) over an infinite vertical plate having time-dependent velocity and with ramped wall temperature and constant concentration. It is proven in many already published articles that the heat and mass transfers do not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately, thus, a different concept of differentiation is needed to capture such process. Very recently, a new class of differential operators were introduced and have been recognized to be efficient in capturing processes following the power-law, the decay law and the crossover behaviors. For the study of heat and mass transfers, we applied the newly introduced differential operators to model such flow and compare the results with integer-order derivative. Laplace transform and inversion algorithms are used for all the cases to find analytical solutions and to predict the influences of different parameters. The obtained analytical solutions were plotted for different values of fractional orders $\alpha$ and $\beta$, $\lambda$, ${\lambda }_r$, $M$, $G_r$ and $Pr$ on the velocity field. In comparison, Atangana–Baleanu (ABC) fractional derivatives are found to be the best to explain the memory effects than the classical, Caputo (C) and Caputo–Fabrizio (CF) fractional derivatives. Some calculated values for Nusselt number and Sherwood number are presented in tables. Moreover, from the present solutions, the already published results were found as limiting cases.

Inequality, asymmetry, and the median-mean ratio are related but different concepts, although they have been frequently treated as equivalent in the literature. In this paper, we find important connections between these three concepts under particular conditions. We show that the Atkinson family and the generalized entropy class of inequality indices are simple functions of the medianmean ratio when a distribution is symmetrizable by a power transformation. In such a case, the coefficient of asymmetry can be interpreted as the aversion inequality parameter of a social planner, and a social evaluation function à la Kolm-Atkinson is shown to be equivalent to median income. A social evaluation function that depends only on mean income and inequality of opportunity is found as a by-product. In addition, the Hannah-Kay family of concentration indices (of which the Herfindahl-Hirschman is a special case) is also obtained as a function of the median-mean ratio. We illustrate these results empirically using the CPS dataset for the U.S. (1992—2007) and the EU-SILC dataset for the European Union (2005–2007).

Porous silicon layers have been prepared from n-type silicon wafers of (100) orientation. SEM, XRD, FTIR, and PL have been used to characterize the morphological and optical properties of porous silicon. The influence of varying HF concentration in the anodizing solution, on structural and optical properties of porous silicon has been investigated. It is observed that pore size increases with HF:ethanol concentration ratio and attain maximum for 1:2 ratio and then decreases.

Different organometallic nanostructures on highly oriented pyrolytic graphite (HOPG) have been synthesized by different metal ions coordinating with 1,4-Dibromo-2,5-diiodobenzene (C₆H₂Br₂I₂). Scanning tunneling microscopy (STM) images directly demonstrated the transformation of the nanostructure from self-assembled nanostructures formed by C₆H₂Br₂I₂ through halogen bond into organometallic network, formed by the dehalogenated C₆H₂Br₂I₂ molecules covalent bonded with metal ions. Moreover, by varying the concentrations of C₆H₂Br₂I₂ molecules or valence states of metal ions, organometallic structures with different shapes and sizes have been fabricated, which illustrates that the concentrations and valence states of the metal ions play important roles in the organometallic nanostructures.

Rhodamine B (RhB) is most often used as the reference in the two-photon induced fluorescence (TPIF) method to measure the two-photon absorption (TPA) cross-section. In this work, we investigate the influences of dimer formation, energy transfer and self-absorption on the two-photon fluorescence process. Those three effects will result in a large measurement error of the TPA cross-section. We thus provide a concentration gradient correction method by considering the above three processes to eliminate the measurement error.

By using Bernstein functions, existence and concentration properties are studied for invariant measures of the infinitesimal generators associated to a large class of stochastic generalized porous media equations. In particular, results derived in Ref. 4 are extended to equations with non-constant and stronger noises. Analogous results are also proved for invariant probability measures for strong solutions.

Demographic transition has already become a major issue in the recent decades. Lower fertility rate and higher expected life length result in population aging. Most developed countries face social problems due to demographic transitions, especially in the economic and financial field. To take a closer look at this phenomenon, this paper screened 99 stocks provided by Taiwan Stock Exchange (TSE) to explore the impact of population aging on the stock market in Taiwan. Population aging indirectly takes up a larger portion of elder investors in the stock market, compared to the past. This paper employed risk and return variables to analyze the investors’ behaviors in Taiwan stock market. We divided our samples into whole industry, financial industry, technology industry, and traditional industry groups to find the impact of investors aging among different industries. The results showed that there is no significant evidence to prove that the elder investors pursue lower risk stocks in Taiwan stock market, which is inconsistent with the results of the past research. On the other hand, the findings from the whole industry, technology industry, and traditional industry groups are different from the past research results, showing that Taiwan’s elderly investors prefer stocks with higher return in those industries.

Using a careful analysis of the Morse indices of the solutions obtained by using the Mountain Pass Theorem applied to the associated Euler–Lagrange functional acting both in the full space and in its subspace of radially symmetric functions, we prove the existence of non-radially symmetric solutions of a problem of Ambrosetti–Prodi type in a ball.

Let $N\ge 2$, $a>0$ and $0<b\le N$. Our aim is to clarify the influence of the constraint $S_{a,b}:=\{u\in W^{1,N}({ℝ}^N)|\parallel \nabla u{\parallel }_N^a+\parallel u{\parallel }_N^b=1\}$ on concentration phenomena of (spherically symmetric and non-increasing) maximizing sequences for the Trudinger–Moser supremum