On multi-term fractional differential equations with multi-point boundary conditions

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We also demonstrate the application of the obtained results with the aid of examples. The paper concludes with the study of multi-term fractional integro-differential equations supplemented with multi-point boundary conditions. Our results are new and contribute significantly to the existing literature on the topic.     

Artifact-free black-blood cine cardiac imaging in a single breath-hold

Fast imaging using the STimulated Echo Acquisition Mode (STEAM) sequence can produce cine images of the heart with black-blood contrast. Nevertheless, correction of deformation-related artifacts is required in order to maintain myocardial signal throughout the cardiac cycle. Recent work by our group has eliminated this artifact by combining two STEAM sequences acquired with two different demodulation gradients. Unfortunately, these two STEAM sequences were acquired on two separate breath-holds; thus, scan time doubled. In this work, we present a technique to reduce the total scan time by one half, without sacrificing image quality. The technique is based on interleaving two demodulations within one acquisition in order to obtain quality cine images of the heart in a single breath-hold. The technique was tested on animal models and human subjects, and the impact of interleaved acquisition on image quality was studied using quantitative and qualitative measures.     

Comparison of reactivity on step and terrace sites of Pd (3 3 2) surface for the dissociative adsorption of hydrogen: A quantum chemical molecular dynamics study

The notion of “active sites” is fundamental to heterogeneous catalysis. However, the exact nature of the active sites, and hence the mechanism by which they act, are still largely a matter of speculation. In this study, we have presented a systematic quantum chemical molecular dynamics (QCMD) calculations for the interaction of hydrogen on different step and terrace sites of the Pd (3 3 2) surface. Finally the dissociative adsorption of hydrogen on step and terrace as well as the influence of surface hydrogen vacancy for the dissociative adsorption of hydrogen has been investigated through QCMD. This is a state-of-the-art method for calculating the interaction of atoms and molecules with metal surfaces. It is found that fully hydrogen covered (saturated) step sites can dissociate hydrogen moderately and that a monovacancy surface is suitable for significant dissociative adsorption of hydrogen. However in terrace site of the surface we have found that dissociation of hydrogen takes place only on Pd sites where the metal atom is not bound to any pre-adsorbed hydrogen atoms. Furthermore, from the molecular dynamics and electronic structure calculations, we identify a number of consequences for the interpretation and modeling of diffusion experiments demonstrating the coverage and directional dependence of atomic hydrogen diffusion on stepped palladium surface.     

Effect of laser irradiation on the electrical properties of dysprosium doped LiCo-Ferrite

The effect of laser irradiation on the electrical properties of Li_0.5+z Co _z Dy _x Fe_2.5?2z?x O₄ ferrite (0.0 ≤ x ≤ 0.2, z = 0.1) has been studied in the temperature range 300 K ≤ T ≤ 750 K at frequencies of 10 kHz?5 MHz, using a LIMO-IR laser diode, at a wavelength of 808 nm. It was found that laser irradiation increases the polarization, the resistivity and the paramagnetic region. As the result of electronic rearrangement and lattice defects, small polorons and clusters were created. The doping of LiCo-Ferrite by Dy³⁺ increases both the AC and DC resistance of the investigated material. The variation of the AC and DC resistance with the Dy-content (x) obeys the following correlations R _ac/100 = 50x ²+4x+0.005 and R _dc/1000 = 31x ²+0.099x+0.09, respectively. A peculiar behaviour was obtained for the sample with Dy-content x = 0.075, as the resistance notably decreases. The applicable result is that laser irradiation increases the resistance of LiCo-ferrite by about 17% while its doping by dysprosium at x = 0.15 increases the resistance by about 23%. Its value is nearly stable for the temperature range from 340 to 480 K.     

Preparation and thermoelectric power of SnBi4Se7

Polycrystalline samples of Bi₂Se₃ and a stoichiometric ternary compound in the quasi-binary system SnSe–Bi₂Se₃ have been prepared and characterized by X-ray powder diffraction analysis. At room temperature the carrier concentration values are n?=?1.1?×?10¹⁹?cm^?3 for Bi₂Se₃ and n?=?0.53?×?10¹⁹?cm^?3 for SnBi₄Se₇. The thermoelectric power has been measured over the temperature range 90–420?K. The thermoelectric power of Bi₂Se₃ is higher than that for SnBi₄Se₇, which shows that the Sn impurity has an acceptor character. Therefore, doping Bi₂Se₃ with tin atoms does not improve thermoelectric properties of this material, due to decrease the value of the power factor σS ². Transport properties of the studied polycrystalline samples are characterized by a mixed transport mechanism of free carriers. It is necessary to add more than one Sn atom to the Bi₂Se₃ compound in order to suppress the electron concentration by one electron. Such behaviour of the dopant is explained by the formation of various structural defects. Besides the dominant substitutional defect, Sn_Bi, tin atoms also form uncharged defects, corresponding to seven-layer lamellae of the composition Se–Bi–Se–Sn–Se–Bi–Se which corresponds to the structure of the SnBi₂Se₄.     

Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

Search for the scalar top quark in pp collisions at square root[s] = 1.8 TeV

We have performed a search for scalar top quark (stop) pair production in the inclusive electron-muon-missing transverse energy final state, using a sample of pp events corresponding to 108.3 pb(-1) of data collected with the D0 detector at Fermilab. The search is done in the framework of the minimal supersymmetric standard model assuming that the sneutrino is the lightest supersymmetric particle. For the dominant decays of the lightest stop, t-->b chi+1 and t-->blnu, no evidence for signal is found. We derive cross-section limits as a function of stop ( t ), chargino ( chi+1), and sneutrino ( nu) masses.     

Finite temperature infinitesimally deformed classical and quantum gravity

Deformed classical mechanics and gravity is discussed. Infinitesimally deformed quantum field theory is reviewed. Infinitesimally deformed Bose-Einstein distribution is derived. Infinitesimally deformed thermofield dynamics is constructed and applied to a scalar field and string theories.On leave of absence from: Mathematics Department, Faculty of Science, Mansoura University, Mansoura, Egypt