A hybrid radial basis functions collocation technique to numerically solve fractional advection–diffusion models

In this work, we propose a hybrid radial basis functions (RBFs) collocation technique for the numerical solution of fractional advection–diffusion models. In the formulation of hybrid RBFs (HRBFs), there exist shape parameter (c* ) and weight parameter (ϵ) that control numerical accuracy and stability. For these parameters, an adaptive algorithm is developed and validated. The proposed HRBFs method is tested for numerical solutions of some fractional Black–Sholes and diffusion models. Numerical simulations performed for several benchmark problems verified the proposed method accuracy and efficiency. The quantitative analysis is made in terms of L_∞, L₂, L_rms , and L_rel error norms as well as number of nodes N over space domain and time-step δt. Numerical convergence in space and time is also studied for the proposed method. The unconditional stability of the proposed HRBFs scheme is obtained using the von Neumann methodology. It is observed that the HRBFs method circumvented the ill-conditioning problem greatly, a major issue in the Kansa method.     

New type of fixed point result of F-contraction with applications

The purpose of this paper is to prove theorem which generalize the corresponding results of Rhoades [B. E. Rhoades, Two New Fixed Point Theorems, Gen. Math. Notes, 2015, 27(2), 123--132]. This paper is to introduce the notion of dynamic process for generalized $F-$contraction mappings and to obtain coincidence and common fixed point results for such process. It is worth mentioning that our results do not rely on the commonly used range inclusion condition. We provide some examples to support our results. As an application of our results, we obtain the existence and uniqueness of solutions of dynamic programming and integral equations. Our results provide extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.     

Anomalous Fermi-surface dependent pairing in a self-doped high-Tc superconductor

We report the discovery of a self-doped multilayer high Tc superconductor Ba2Ca3Cu4O8F2 (F0234) which contains distinctly different superconducting gap magnitudes along its two Fermi-surface sheets. While formal valence counting would imply this material to be an undoped insulator, it is a self-doped superconductor with a Tc of 60 K, possessing simultaneously both electron- and hole-doped Fermi-surface sheets. Intriguingly, the Fermi-surface sheet characterized by the much larger gap is the electron-doped one, which has a shape disfavoring two electronic features considered to be important for the pairing mechanism: the van Hove singularity and the antiferromagnetic (pi/a, pi/a) scattering.     

Energy Conditions and Conservation Laws in LRS Bianchi Type I Spacetimes via Noether Symmetries

In this paper, we have completely classified the locally rotationally symmetric (LRS) Bianchi type I spacetimes via Noether symmetries (NS). The usual Lagrangian corresponding to LRS Bianchi type I metric is used to find the set of determining equations. To achieve a complete classification, these determining equations are generally integrated to find the components of NS vector field and the metric coefficients. During this procedure, several cases arise which give different Noether algebras of dimension 5,..., 9, 11, and 17. A comparison is established between the obtained NS and the Killing and homothetic vectors. Corresponding to all NS generators, the conservation laws are stated by using Noether's theorem. The metrics which we have obtained as a result of our classification are shown to be anisotropic or perfect fluids which satisfy certain energy conditions.     

A Privacy Scheme for Digital Images Based on Quantum Particles

International Journal of Theoretical Physics - Quantum processing inspired every field of science and technology. Quantum digital content privacy schemes usually employs photons to communicate a...     

Plasmon versus shake-up satellites in XPS spectroscopy of adsorbed species

Shake-up satellites found in photoemission spectroscopy from core levels of adsorbed atoms are considered using a simple diatomic molecule model. Time scales and the competition between surface plamons and shake-up for the satellite strength are considered.     

Optimization of linearity by use of a glass plate in carousel interferometers

Carousel interferometers are compact swinging interferometers, but their popularity is limited because of significant nonlinearity in rotational measurements. Introducing a glass plate in a rotating interferometer and optimizing its thickness has improved the linearity drastically. Computer simulations show reductions in nonlinearity of several orders of magnitude.     

SOME GENERALIZATIONS OF KY FAN＇S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map onmetrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derivedfor the map studied. Our work generalizes severl results in approximation theory.     

Two new diterpenoids from Ballota limbata

Two new clerodane-type diterpenoids trivially named as ballotenic acid (1) and ballodiolic acid (2) have been isolated from Ballota limbata along with three the known compounds; beta-amyrin, oleanolic acid, and beta-sitosterol. The structure elucidation of the new compounds was based primarily on two-dimensional (2D)-NMR techniques including correlation spectroscopy (COSY), heteronuclear multiple quantum coherence (HMQC), heteronuclear multiple bond correlation (HMBC), and nuclear Overhauser effect (NOE) experiments. Compounds 1 and 2 displayed inhibitory potential against lipoxygenase enzyme in a concentration-dependent fashion with IC(50) values of 99.6 microM and 38.3 microM, respectively.     

Ball lens coupled fiber-optic probe for depth-resolved spectroscopy of epithelial tissue

A ball lens coupled fiber-optic probe design is described for depth-resolved measurements of the fluorescence and reflectance properties of epithelial tissue. A reflectance target, fluorescence targets, and a two-layer tissue phantom consisting of fluorescent microspheres suspended in collagen are used to characterize the performance of the probe. Localization of the signal to within 300 microm of the probe tip is observed by use of reflectance and fluorescence targets in air. Differential enhancement of the fluorescence signal from the top layer of the two-layer tissue phantom is observed.