Stability of a quadratic Jensen type functional equation in the spaces of generalized functions

Making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic Jensen type functional equation

     

Solving Non-Isospectral mKdV Equation and Sine-Gordon Equation Hierarchies with Self-Consistent Sources via Inverse Scattering Transform

N-soliton solutions of the hierarchy of non-isospectral mKdV equation with self-consistent sources and the hierarchy of non-isospectral sine-Gordon equation with self-consistent sources are obtained via the inverse scattering transform.     

结合小波分析法与导数光声光谱技术测量弱光谱信号的实验研究

结合导数光声光谱技术与小波分析方法,精确测量了光声光谱中的弱光谱信号.首先利用自己设计的仪器装置实现光声光谱的一阶导数,在此基础上,根据导数光声光谱的数据选择合理的分析小波,将光声光谱信号分解为不同频率信号的叠加,被分解的信号满足线性性质且原信号的峰值信息保持不变,由频率的差异可区分出光声信号和噪声信号,从而提取出光声光谱中的弱光谱信号.结合物理方法与软件方法的分析结果,准确地测量了氙灯的输出光声光谱中3个不明显的弱峰值,位置分别为699.7nm、753.4nm和776.5nm.该方法可以更准确地提取出光声光谱的峰值信息,有效地提高了光声光谱的测量精度,为光声光谱分析法在生物医学及化学分析中的应用提供了一种更精确的分析方法.     

High sensitivity CW-cavity ring down spectroscopy of CO2 near 1.35 μm (II): New observations and line intensities modeling

In a previous contribution [Kassi S, Song KF, Campargue A. High sensitivity CW-cavity ring down spectroscopy of ¹²CO₂ near 1.35 μm (I): line positions. JQSRT 110 (2009) 1801-1814], the line positions analysis of the high sensitivity absorption spectrum of carbon dioxide has been reported in the 7123-7793 cm⁻¹ region. In this second contribution, the spectral region investigated by CW-cavity ring down spectroscopy has been extended up to 7917 cm⁻¹. It added about 400 lines to our previous list of about 2500 transitions. These additional lines include transitions belonging to six newly observed ¹²C¹⁶O₂ bands for which we provide the spectroscopic parameters. Over the whole 7123-7917 cm⁻¹ region, the accurate intensities of about 2900 lines belonging to four isotopologues (¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O and ¹⁶O¹²C¹⁷O) were retrieved with an average accuracy of 3%. Intensity values range between 1.2×10⁻²⁹ and 4.1×10⁻²⁵ cm/mol. Compared to the present version of the carbon dioxide spectroscopic databank recently adopted for the HITRAN database, important deviations were evidenced for some weak bands of the main isotopologue. The CW-CRDS intensity data relative to a total of 46 ¹²C¹⁶O₂ bands together with selected intensity information available in the literature for nine bands have been fitted simultaneously using the effective operators approach. The ΔP=11 set of the ¹²C¹⁶O₂ effective dipole moment parameters has been refined leading to a much better agreement with the measured intensity values. In addition, the ΔP=10 effective dipole moment parameters of the ¹⁶O¹²C¹⁸O minor isotopologue were determined for the first time. The obtained results will help to improve the carbon dioxide spectroscopic databank (CDSD).     

Image encryption based on double random amplitude coding in random Hartley transform domain

We propose an image encryption scheme based on double random amplitude coding technique by using random Hartley transform, which is defined according to the random Fourier transform. The significant feature of this algorithm is that the encrypted image is real and convenient for storage as well as transfer of the encrypted information. Moreover, the algorithm has enhanced security and the correct information of original image can be well protected under bare decryption, blind decryption and brute force attacks. Numerical simulation results are also presented in support of the proposed scheme.     

Studies on adsorption energy distributions computation from adsorption isotherms by the ansatz method

Since the well-known adsorption integral equation (AIE) is an ill-posed problem, calculation of relevant energetic properties from gas and liquid adsorption isotherms on porous solids still remains a challenging field of research. There are two approaches for solving the AIE: (1) the numerical regularization method and (2) the fitting of the experimental adsorption data by functions possessing an analytical solution. Up to now the latter approach has been treated without consideration of the ill-posedness. The inclusion of ill-posedness in the approach leads to its specification which we call the ansatz method. By showing that a certain class of ansatz functions cannot be used for describing the total isotherms, we were urged to consider more general solutions being connected with the Stieltjes integrals. After applying a general inversion formula we can restrict the theoretically possible total isotherms and outline a feasible general ansatz.     

Similarity analytical solutions for the Schrӧdinger equation with the Riesz fractional derivative in quantum mechanics

The present article deals with the similarity method to tackle the fractional Schrӧdinger equation where the derivative is defined in the Riesz sense. Moreover, the procedure of reducing a fractional partial differential equation (FPDE) into an ordinary differential equation (ODE) has been efficiently displayed by means of suitable scaled transform to the proposed fractional equation. Furthermore, the ODEs are treated effectively via the Fourier transform. The graphical solutions are also depicted for different fractional derivatives α .     

Resolvent estimates in homogenisation of periodic problems of fractional elasticity

We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier–Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces.     

Radial symmetry for systems of fractional Laplacian

In this paper, we consider systems of fractional Laplacian equations in Rnwith nonlinear terms satisfying some quite general structural conditions. These systems were categorized critical and subcritical cases. We show that there is no positive solution in the subcritical cases, and we classify all positive solutions ui in the critical cases by using a direct method of moving planes introduced in Chen-Li-Li [11] and some new maximum principles in Li-Wu-Xu [27].