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Erbium doped borate glass is widely used in luminescent materials, the luminescence dynamics of erbium doped borate glass is of great significance for optimizing and improving the luminous efficiency. The 2% molar ratio erbium doped borate glass was synthesized by the traditional melt quenching method, and annealed at 260 °C below the borate glass transition temperature. The thermal performance parameters of borate glass undoped and doped with Er3+ were measured by differential scanning calorimetry with 10 °C/min. The transient emission spectrum and decay kinetics curves were measured for the luminescence mechanism of erbium doped borate. Er3+ ions have different lifetime when emitted at 556 nm with different excitation wavelengths, the excited state trap may exist in erbium doped borate glass.

In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in derivinga prioriestimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.

The rare earth materials have attracted intensive attention due to their strong luminescent characteristic. However, the split fine Stark levels are difficult to be determined. Here we report a room-temperature detection for Stark levels of YNbO

In this paper, we study unique, globally defined uniformly bounded weak solutions for a class of semilinear reaction-diffusion-advection systems. The coefficients of the differential operators and the initial data are only required to be measurable and uniformly bounded. The nonlinearities are quasi-positive and satisfy a commonly called mass control or dissipation of mass property. Moreover, we assume the intermediate sum condition of a certain order. The key feature of this work is the surprising discovery that quasi-positive systems that satisfy an intermediate sum condition automatically give rise to a new class of $L^p$-energy type functionals that allow us to obtain requisite uniform a priori bounds. Our methods are sufficiently robust to extend to different boundary conditions, or to certain quasi-linear systems. We also show that in case of mass dissipation, the solution is bounded in sup-norm uniformly in time. We illustrate the applicability of results by showing global existence and large time behavior of models arising from a spatio-temporal spread of infectious disease., 36 pages. Accepted in SIAM Journal on Mathematical Analysis. The section of applications is significantly shortened where the last two examples are removed. Some typos are corrected

The rare earth materials have attracted intensive attention due to their strong luminescent characteristic. However, the split fine Stark levels are difficult to be determined. Here we report a room-temperature detection for Stark levels of YNbO4: Er3+ using established laser-induced spectroscopy system with dye laser of superhigh resolution of wavelength at 0.005 nm. From excitation spectra, six split Stark levels of 4G11/2 (Er3+) were directly detected. Moreover, nonradiative relaxations of 4G9/2→4G11/2 and 4G11/2→2H11/2/ 4S3/2 have been observed with weighed lifetimes of 0.70 μs and 6.15 μs, and characteristic green emission of Er3+ (@555 nm) yields lifetime of 31.78 μs.

In this paper we study a model which describes the pattern formation of vegetation spots and strips in a semi-arid or arid landscape. The mathematical model consists of a nonlinear cross-diffusion system with evaporation and absorption sources. Global existence and uniqueness in classical sense for the system are established. Some asymptotic behaviors of the solution are derived for a linearized system. It is shown that the solution of the linearized system is asymptotically stable near the steady-state solution. Moreover, we show that the Turing phenomenon occurs for the linearized cross-diffusion system and the cross-diffusion destabilizes the ecosystem.

In this paper we study a corporate bond-pricing model with credit rating migration and a stochastic interest rate. The volatility of bond price in the model strongly depends on potential credit rating migration and stochastic change of the interest rate. This new model improves the previous existing models in which the interest rate is considered to be a constant. The existence, uniqueness and regularity of the solution for the model are established. Moreover, some properties including the smoothness of the free boundary are obtained. Furthermore, some numerical computations are presented to illustrate the theoretical results.

In this paper we study an optimization problem arising from a sterilization process for packaged foods by using a microwave heating method. The goal of the optimal control is to find the optimal frequency function such that the temperature profile at the final stage has a relative uniform distribution in the food product. The underlying state variables are electric, magnetic fields and temperature which satisfy the coupled nonlinear Maxwell’s system and a nonlinear heat equation. The control variable for the system is chosen to be the electric frequency function. We show that there exists an optimal frequency which minimizes the cost functional. Moreover, an optimality condition is also derived.

In this paper, we consider a new corporate bond-pricing model with credit-rating migration risks and a stochastic interest rate. In the new model, the criterion for rating change is based on a predetermined ratio of the corporation&rsquo, s total asset and debt. Moreover, the rating changes are allowed to happen a finite number of times during the life-span of the bond. The volatility of a corporate bond price may have a jump when a credit rating for the bond is changed. Moreover, the volatility of the bond is also assumed to depend on the interest rate. This new model improves the previous existing bond models in which the rating change is only allowed to occur once with an interest-dependent volatility or multi-ratings with constant interest rate. By using a Feynman-Kac formula, we obtain a free boundary problem. Global existence and uniqueness are established when the interest rate follows a Vasicek&rsquo, s stochastic process. Calibration of the model parameters and some numerical calculations are shown.

In this paper, we study an American option-pricing model with an uncertain volatility. Some properties for the option price are derived. Particularly, a global spread for the option price is proved when the volatility depends on the underlying security and time. This result confirms the observed fact from the real financial data in option markets. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we study the regularity of a weak solution for a coupled system derived from a microwave-heating model. The main feature of this model is that electric conductivity in the electromagnetic field is assumed to be temperature dependent. It is shown that the weak solution of the coupled system possesses some regularity under certain conditions. In particular, it is shown that the temperature is Hölder continuous, even if electric conductivity has a jump discontinuity with respect to the temperature change. The main idea in the proof is based on an estimate for a linear degenerate system in Campanato space. As an application, the regularity result for the coupled system is used to derive the necessary condition for an optimal control problem arising in microwave heating processes.

In this paper, we study an optimization problem for a microwave/induction heating process. The cost function is defined such that the temperature profile at the final stage has a relative uniform distribution in the field. The control variable is the applied electric field on the boundary. We show that there exists an optimal electric field which minimizes the cost function. Moreover, a necessary condition for a special case is also derived.

In this paper we study global properties of the optimal excising boundary for the American option-pricing model. It is shown that a global comparison principle with respect to time-dependent volatility holds. Moreover, we proved a global regularity for the free boundary.

Photodissociation of p-aminobenzoic acid at 266 nm was investigated by probing the nascent OH photoproduct employing the laser-induced fluorescence technique. It was found that the nascent OH radical was vibrationally cold and its rotational state distribution conformed to be a Boltzmann behavior, characterized by a rotational temperature of 1040 110 K. The rotational energy of OH was determined to be 8.78 0.84 kJ/mol. Between the two spin-orbit states of OH, 23/2 and 21/2, the former was found to be preferentially populated. The distribution of the (A) state for the -doublet was dominant. Finally, a probable mechanism for the formation of OH produced from the photodissociation of p-aminobenzoic acid is discussed.

Photodissociation dynamics of benzenesulfonic acid at 266 nm was studied by probing the nascent OH photoproduct using the single-photon laser-induced fluorescence technique. Measurements on the nascent OH fragment revealed that it was produced vibrationally cold and its rotational state distribution was Boltzmann-like, characterized by a rotational temperature of 840 +/- 70 K. The ratios of 2 Pi(3/2) to 2 Pi(1/2) states of the OH fragment were found to be more than unity and the population of the Pi(+) state for the Lambda-doublet was dominant. Based on both experimental and theoretical results, a probable mechanism for the formation of OH fragment produced from the photodissociation of BSA is proposed. (C) 2008 Elsevier B. V. All rights reserved.

Photodissociation of gaseous 2-nitrophenol at 266 and 355 nm was investigated by probing the nascent OH products with the laser-induced-fluorescence (LIF) technique. Rotational state distributions of the OH photofragments were measured and characterized by Boltzmann temperatures of 900 ± 40 K and 1070 ± 80 K at 266 and 355 nm, respectively. The OH photoproducts were found to be vibrationally cold at both photolysis wavelengths. Preferential populations of the OH F 1 (Π 3/2 ) spin–orbit state and Π + Λ-doublet state were observed at both photolysis wavelengths. We have proposed a mechanism for OH production involving the photoisomerization to form aci-nitro isomers, which then dissociate into OH fragments.

In this paper we study a degenerate parabolic system U t − Δ ( | U | m − 1 U ) = 0 , where U ( x , t ) = ( u 1 , u 2 , … , u l ) is a vector function and m > 1 . The system can be derived from a time-dependent p -curl system which describes Bean's critical-state model in the superconductivity theory. It is shown that the degenerate system has a unique global solution. Moreover, it is shown that the weak solution is continuous and the modulus of continuity depends only on known data.

Photodissociation dynamics of benzoic acid monomer (BAM) at different ultraviolet excitation wavelengths (280-295 nm) has been investigated. The nascent OH product state distributions were measured using the laser-induced fluorescence (LIF) technique. The rotational state distributions, the Lambda-doublet-state ratio, and spin-orbit state distributions of the OH fragment were also measured at 280-294 nm. The OH fragments are vibrationally cold, and their rotational state distributions are peaked at J'' = 3.5 at each photolysis wavelength. No LIF signal of OH fragments was observed at 295 nm. The photodissociation threshold is determined to be 102.5-103.9 kcal/mol for OH channel. The dissociative state and mechanism have been discussed for OH produced from the photodissociation of BAM.

Measurements of the nascent NO fragments from the photodissociation of gaseous n -butyl nitrite at 266 nm were performed using the one-photon excited laser induced fluorescence technique. The rotational state distributions of the photofragment NO are found to be well characterized by a Gaussian distribution, which indicates that the photolysis process in the S 2 state is a direct and fast dissociation. The measured relative population of NO v ″ = 0:1:2:3 is 0.65:0.19:0.11:0.05, respectively. Preferential populations of the NO Π + Λ-doublet state and F 1 ( 2 Π 1/2 ) spin-orbit state are observed. The TD-DFT calculations of n -butyl nitrite are in good agreement with the experimental results.

Superheating is a phenomenon in which the temperature in a solid phase is higher than the melting temperature. This phenomenon is common when a microwave or an induction heating method is used during a melting process. The classical interface conditions (Stefan conditions) have to be modified in order to model this phenomenon. In this paper we study a melting process for highly conductive materials by using an induction heating method with possible superheating in the process. To derive the mathematical model, we recall Maxwell’s equations for an electric field E(x, t) and a magnetic field H(x, t) in R3 ([11, 16])

The photodissociation dynamics of benzoic acid monomer at 266 nm is investigated by probing the nascent OH photoproduct using the laser-induced-fluorescence (LIF) technique. The nascent OH radical is distributed in the ground vibrational state and the rotational temperature is 620 ± 30 K. The F 1 ( 2 Π 3/2 ) and F 2 ( 2 Π 1/2 ) spin-orbit states of OH photofragment are unstatistically populated, and Λ-doublet levels are not equally populated. The present study associated with the available dynamics information predicts that OH radical is mainly produced from benzoic acid monomer on the T 2 energy surface.

Measurements of the nascent OH product from photodissociation of gaseous nitromethane and nitroethane at 266 nm were performed using the single-photon laser induced fluorescence technique. The OH fragment is found to be vibrationally cold for both systems. The rotational state distribution of nitromethane are Boltzmann, with rotational temperature of T-rot=2045 +/- 150 and 1923 +/- 150 K for both (2)Pi(3/2) and (2)Pi(1/2) states, respectively. For nitroethane, the rotational state distribution shows none Boltzmann and cannot be well characterized by a rotational temperature, which indicates the different mechanisms in producing OH radicals from photodissociation of nitromethane and nitroethane. The rotational energy is calculated as 14.36 +/- 0.8 and 4.98 +/- 0.8 kJ/mol for nitromethane and nitroethane, respectively. A preferential population of the low spin-orbit component ((2)Pi(3/2)) is observed for both nitromethane and nitroethane. The dominant population of Pi(+) state in two Lambda-doublet states is also observed for both nitromethane and nitroethane, which indicates that the unpaired pi lobe of the OH fragment is parallel to the plane of rotation.

In this paper we study a phase-change problem arising from induction heating. The mathematical model consists of time-harmonic Maxwell’s system in a quasi-stationary field coupled with nonlinear heat conduction. The enthalpy form is used to characterize the phase-change in the material. It is shown that the problem has a global solution. Moreover, it is shown that the solution is unique and regular in one-space dimension even with an unbounded resistivity.

We report laser-induced fluorescence spectra of the B ˜ 2 A ′ - X ˜ 2 A ′ transition of the formyl radical, HCO, produced by photolysis of jet-cooled formaldehyde. Two spectral regions were studied: from 38 615 to 38 712 cm −1 , which corresponds to the overlapping 0 0 0 and 3 1 1 transitions, and from 37 535 to 37 640 cm −1 , corresponding to the overlapping, and 3 1 0 and 3 2 1 transitions. Over 170 transitions in the 3 1 1 band and 80 transitions in the 3 2 1 band were assigned and fit using a non-linear least squares routine to provide rotational, centrifugal distortion and spin–rotation constants in the HCO X ˜ 2 A ′ ( 0 , 0 , 2 ) and B ˜ 2 A ′ ( 0 , 0 , 1 ) states.

Even in small molecules, the influence of electronic state on rotational and vibrational product energies is not well understood. Here, we use experiments and theory to address this issue in photodissociation of formaldehyde, H 2 CO, to the radical products H + HCO. These products result from dissociation from the singlet ground electronic state or the first excited triplet state ( T 1 ) of H 2 CO. Fluorescence spectra reveal a sudden decrease in the HCO rotational energy with increasing photolysis energy accompanied by substantial HCO vibrational excitation. Calculations of the rotational distribution using an ab initio potential energy surface for the T 1 state are in very good agreement with experiment and strongly support dominance of the T 1 state in the dynamics at the higher photolysis energies.

This paper deals with Maxwell's equations with a thermal effect, where the electric conductivity strongly depends on the temperature. It is shown that the coupled system has a global weak solution and the temperature is Holder continuous if the conductivity decays suitably as temperature increases. Moreover, uniqueness of the solution is proved, which gives a positive answer for a open question from the previous research. The main idea for the global existence is based on deriving various energy estimates for the solution of the coupled system. Copyright © 2006 John Wiley & Sons, Ltd.

In this paper we study a free boundary problem modeling a phase-change process by using microwave heating. The mathematical model consists of Maxwell's equations coupled with nonlinear heat conduction with a phase-change. The enthalpy form is used to characterize the phase-change process in the model. It is shown that the problem has a global solution.

In this paper we first study the regularity of weak solution for time-harmonic Maxwell's equations in a bounded anisotropic medium Ω . It is shown that the weak solution to the linear degenerate system, ∇ ×(γ(x) ∇ × E )+ξ(x) E = J (x), x∈Ω⊂R 3 , is Holder continuous under the minimum regularity assumptions on the complex coefficients γ(x) and ξ(x). We then study a coupled system modeling a microwave heating process. The dynamic interaction between electric and temperature fields is governed by Maxwell's equations coupled with an equation of heat conduction. The electric permittivity, electric conductivity and magnetic permeability are assumed to be dependent of temperature. It is shown that under certain conditions the coupled system has a weak solution. Moreover, regularity of weak solution is studied. Finally, existence of a global classical solution is established for a special case where the electric wave is assumed to be propagating in one direction.

Ethyl isocyanate-solvated magnesium cation complexes Mg+(OCNC2H5)n were produced in a laser-ablation supersonic expansion nozzle source. Photoinduced reactions in the complexes of Mg+(OCNC2H5)n (n ...

The photodissociation dynamics of methyl nitrite (CH3ONO) was studied using 266 nm laser photolysis, and NO photofragments X 2∏ ν″=0,1,2,3) were probed by single photon laser-induced fluorescence spectroscopy. The ground vibrational state of the NO was found to be most populated, and the rotational distributions of each vibrational level were quite hot. The alignment A0(2) between the electronic transition dipole moment involved in the absorption of the parent molecule and the rotational angular momentum J of the photofragment NO (v″=0) was measured. Polarization experiments showed that the rotational angular momentum of NO was aligned perpendicularly to the transition moment of the parent molecule. The negative A0(2) values and a preferential population of the ∏− doublet state revealed that the dissociation process has some characteristics of in-plane dissociation.

The density function theory was used to calculate the potential energy surface for the decomposition of CF3OF. The geometries, vibrational frequencies and energies of all stationary points were obtained. The calculated harmonic frequencies agreed well with the experimental ones. Three decomposition channels of CF3OF were studied. The calculated reaction enthalpy (29.85 kcal/mol) of the elimination reaction CF3OF --> CF2O + F-2 was in good agreement with the experimental value (27.7 kcal/mol). The O-F bond of CF3OF is broken easily by comparing the energies, while the decomposition channel to yield the CF30 and F radicals is the main reaction path. (C) 2002 Published by Elsevier Science B.V.

In this paper we study a degenerate evolution system $\mathbf H_t +\nabla \times [|\nabla \times \mathbf H|^{p-2}\nabla \times \mathbf H]=\mathbf F$ in a bounded domain as well as its limit as $p\to \infty$ subject to appropriate initial and boundary conditions. This system governs the evolution of the magnetic field $\mathbf H$ in a conductive medium under the influence of a system force $\mathbf F$. The system is an approximation of Bean's critical-state model for type-II superconductors. The existence, uniqueness and regularity of solutions to the system are established. Moreover, it is shown that the limit of $\mathbf H(x, t)$ as $p\to \infty$ is a solution to the Bean model.

In this paper we prove a fundamental estimate for the weak solution of a degenerate elliptic system: $\nabla\times [\rho(x)\nabla\times H]=F$, $\nabla\cdot H=0$ in a bounded domain in $R^3$, where $\rho(x)$ is only assumed to be in $L^{\infty}$ with a positive lower bound. This system is the steady-state of Maxwell’s system for the evolution of a magnetic field $H$ under the influence of an external force $F$, where $\rho(x)$ represents the resistivity of the conductive material. By using Campanato type of techniques, we show that the weak solution to the system is Holder continuous, which is optimal under the assumption. This result solves the regularity problem for the system under the minimum assumption on the coefficient. Some applications arising in inductive heating are presented.

The structure and frequencies of c12b24n24 have been calculated by means of an ab initio method. by comparing the average bond energies with c-60, the calculated results predict that the cage c12b24n24 is a stable molecule. the calculated results indicate that the cage molecule c12b24n24 has a relative large homo-lumo energy gap and a low rigidity the structures and stability of six possible isomers of c2b4n4 are used to suggest a possible transformation path from the pentagon cb2n2 to the c12b24n24 materials. (c) 2001 john wiley & sons, inc.

In this paper we study Maxwell’s system coupled with a heat equation in one space dimension. The system models a microwave heating process. The feature of the model is that the electric conductivity $\sigma(u)$ strongly depends on the temperature. It is shown that the system has a global solution for $\sigma(u)=1+u^k$ with any $k\ge 1$. The long time behavior of the solution is also investigated.