Local Stability for an Inverse Coefficient Problem of a Fractional Diffusion Equation

Time-fractional diffusion equations are of great interest and importance on describing the power law decay for diffusion in porous media. In this paper, to identify the diffusion rate, i.e., the heterogeneity of medium, the authors consider an inverse coefficient problem utilizing finite measurements and obtain a local HSlder type conditional stability based upon two Carleman estimates for the corresponding differential equations of integer orders.

Study on Oxygen Isotope Fractionation in RE Oxide Minerals

The oxygen isotope fractionation equations are calculated for major rare earth oxide minerals by using an increment model. The effects of the variation of RE composition, the isomorphic replacement of Ti 4+ , Nb 5+ , Ta 5+ , and Th 4+ and the metamictization on the oxygen isotope fractionation in minerals are also discussed. The rare earth oxides are not applicable for geothermometry due to their changeable oxygen isotope fractionation coefficients.

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM (Ⅱ):DOUBLE■-l

The wavefunctions of L-S coupling fermion system, which are classified by group chain U(4ι1 + 4ι2 + 4) Us(2)×(U L(2ι+ 2ι2 + 2) O(2ι1 + 2ι2 + 2) O(2ι+1) ×O(2ι2 + 1) O1 (3)×O2 (3) O(3)), are constructed through introducing generalized pairs coupled by fermions with different ι. With the help of the fractional parentage coefficients of single-ιfermion system, the author obtains the corresponding fractional parentage coefficients of double-ιfermion system.

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM(Ⅰ): SINGLE-l

In this paper. it is discussed how to constrnct wavefunctions of L-S couplingfermion system, which are classified by group chain A recurrent formula of fractional parentage coefficients with fixedseniority is also given.

Cluster-Cluster Potentials for the Carbon Nucleus

Two types of potentials are given in the present paper. The two potentials have Gaussian radial dependences. Such shapes of radial functions are suitable for using in the unitary scheme model. The first potential is given in the form of an attractive force and the second is given in the form of a superposition of repulsive and attractive forces. The two potentials are used to calculate the binding energy of the carbon nucleus 12C. For this purpose, we expand the ground-state wave function of carbon in a series of the bases of the unitary scheme model and apply the variational method. To calculate the necessary matrix elements required to obtain the binding energy of carbon, we factorized the unitary scheme model bases in the form of products of two wave functions: the first function represents the set of the A-4 nucleons and the second function represents the set of the last four nucleons by using the well-known four-body fractional parentage coefficients. Good results are obtained for the binding energy of 12C by using the two potentials.

Fractional differential approach to detecting textural features of digital image and its fractional differential filter implementation

This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.

Boundary Control of Coupled Non-Constant Parameter Systems of Time Fractional PDEs with Different-Type Boundary Conditions

This paper addresses a boundary state feedback control problem for a coupled system of time fractional partial differential equations(PDEs)with non-constant(space-dependent)coefficients and different-type boundary conditions(BCs).The BCs could be heterogeneous-type or mixed-type.Specifically,this coupled system has different BCs at the uncontrolled side for heterogeneous-type and the same BCs at the uncontrolled side for mixed-type.The main contribution is to extend PDE backstepping to the boundary control problem of time fractional PDEs with space-dependent parameters and different-type BCs.With the backstepping transformation and the fractional Lyapunov method,the Mittag-Leffler stability of the closed-loop system is obtained.A numerical scheme is proposed to simulate the fractional case when kernel equations have not an explicit solution.

Mapping groundwater dependent ecosystem potential in a semi-arid environment using aremote sensing-based multiple-lines-of-evidence approach

Groundwater dependent ecosystems(GDEs)are vulnerable to groundwater regime changes.However,their protection is often hampered by challenges in their identification.Within is presented a remote sensing-based GDE potential mapping approach based on the persistency of relevant vegetation parameters during prolonged dry periods as an indicator of potential‘consistency’of water supply(e.g.groundwater).The study uses a novel approach to characterising persistency for selected vegetation parameters based on a normalised difference measure and an adaptation of the coefficient of variation statistic.Aggregation of parameters was facilitated through the analytic hierarchy process providing a structured weighting approach to minimise parameter bias.The approach is demonstrated in the semi-arid Flinders Ranges of South Australia where new groundwater resources are being sought to support local domestic and industry needs.Variations in GDE potential were mapped to better target areas where exploration of groundwater should be avoided.Mapping results indicated a high-level of agreement of 77%with an independent springs dataset,along with an 87%agreement with areas coinciding with known phreatophyte species and depths to groundwater.The index-based mapping approach has potential applicability across landscapes,as it normalises for variations in vegetation cover,minimises technical overheads,and employs continental-wide remote sensing data-products.