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.     

A New Emissive Chalcone-Based Chemosensor Armed by Coumarin and Naphthol with Fluorescence “Turn-on” Properties for Selective Detection of F<Superscript>−</Superscript> Ions

A new chalcone-based probe containing coumarin and naphthol at both ends has been synthesized via aldol condensation. The uniqueness of the newly derived probe can be ascribed to the presence of naphthol and coumarin units acting as binding site and signaling element, respectively. The fluorogenic behaviors toward various anions were investigated. The probe was characterized by various spectroscopic techniques and the in-depth study led to show excellent selectivity and sensitivity for fluoride ions. The hydrogen bonding thus formed with fluoride anion provides remarkable fluorometric responses. The interactions of the probe with fluoride ions were determined by fluorescence, FT-IR and NMR spectroscopic techniques. The exploratory studies by fluorescent spectral changes augur well for the naked-eye sensing applications.     

Interferences in Photodetachment of a Negative Molecular Ion

The photodetachment of a negative molecular ion is studied theoretically using a two-center model. The detached electron wave function is obtained as a superposition of two coherent waves originating from each center. The photo-detached electron flux is evaluated on a screen placed at a large distance from the negative molecular ion. The electron flux on the screen displays strong interferences, the peak positions are related to the distance between the two centers in the negative molecular ion. We a/so obtained a simple analytical formula for the total photodetachment cross section. It approaches one and two times of the cross section for the one-center system in the high and lowphoton energy limits respectively.     

Phase Transitions in the Early Universe with Negatively Induced Supergravity Cosmological Constant

We consider that the observable cosmological constant is the sum of the vacuum （Avac） and the induced term （Aind - 3m^2/4） with m being the ultra-llght masses （≈ Hubble parameter） implemented in the theory from supergravities arguments and non-minimal coupling. In the absence of a scalar buildup of matter fields, we study its effects on spontaneous symmetry breaking with a Higgs potential and show how the presence of the ultra-light masses yields some important consequences for the early universe and new constraints on the Higgs and electroweak gauge bosons masses.     

Effect of substitution of K ions on the structural and electrical properties of nanocrystalline MgAl2O4 spinel oxide

Potassium substituted nanosized magnesium aluminates having a nominal composition Mg_1−xK_xAl₂O₄ where x=0.0, 0.25, 0.5, 0.75, 1.0 have been synthesized by the chemical co-precipitation method. The samples have been characterized by means of X-ray diffraction (XRD), scanning electron microscope (SEM), and dc electrical resistivity measurements. The XRD results reveal that the samples are spinel single phase cubic close packed crystalline materials. The calculated crystallite size ranges between 6 and 8 nm. The behaviour of the lattice constant seems to deviate from the Vegard's law. While X-ray density clearly increases, the bulk density and consequently, the percentage porosity do not exhibit a significant change on increasing the K⁺ content. The SEM micrographs suggest homogeneous distribution of the nanocrystallites in the samples. The dc electrical resistivity exhibits a typical semiconducting behaviour. Substitution of a Mg²⁺ ion by a K⁺ ion provides an extra hole to the system, which forms small polaron. Thermally activated hopping of these small polarons is believed to be the conduction mechanism in the Mg_1−xK_xAl₂O₄. The activation energy of hopping of small polarons has been calculated and found K⁺ ions content dependent.     

Role of ion energy flux on the structural and morphological properties of silicon oxy-nitride composite films deposited by plasma focus device

ABSTRACT

Crystalline silicon oxy-nitride (SiON) composite films are deposited on Si substrate for multiple (5, 15, 25 and 50) focus shots (FS) by plasma focus device. The X-rays diffraction patterns reveal the development of various diffraction peaks related to Si, Si₃N₄, and SiO₂ phases which confirms the formation of SiON composite film. The intensity of Si₃N₄ (1 0 2) plane is linearly increased with the increase of FS. The Si₃N₄ (1 0 2) phase does not nucleate for 5 FS. Raman analysis confirms the formation of β–Si–N phase. Raman and Fourier transform infrared spectroscopy analysis reveals that the strength of chemical bonds like Si–N, Si–O formed during the deposition process of SiON composite films is associated with the bonds intensity which in turn depends on the number of FS. The field emission scanning electron microscopic analysis reveals that the surface morphology like size, shape and distribution of micro/nano-dimensional particles, film compactness and the formation of micro-rods, micro-teethes and micro-tubes of SiON composite films is entirely associated with the rise in substrate surface transient temperature which in turn depends on the increasing number of FS. The EDX spectrum confirms the presence of Si (22.5?±?4.7 at. %), N (13.4?±?4.5 at. %) and O (54.7?±?11.3 at. %) in the SiON composite film. The thickness of SiON composite film deposited for 50 FS is found to ～15.47?µm.     

Assessment of health risk associated with natural gamma dose rate levels and isodose mapping of Jordan

ABSTRACT

As a pioneering study in Jordan, an extensive measurement for external gamma dose rate (GDR) was conducted. A portable gamma radiation detector was used to perform these measurements at 1?m above the soil surface. A geographical positioning system Garmin was used to record a total of 823 measured points. The GDRs’ measurement ranged from 35 to 470?nGy?h^?1 giving a mean value of 90?nGy?h^?1, which was found to be one and half times higher than the world average of 59?nGy?h^?1. The lowest mean GDR 72?nGy?h^?1 was found in the Albalqa governate, while the highest mean GDR 131?nGy?h^?1 was found to be for the Alkarak governate. The mean annual effective dose was found to be 0.551?mSv, which is higher than the world average value of 0.48?mSv. This is a pivotal study evaluating the risks associated with GDR levels in Jordan that were the relative excess lifetime cancer risk, the mean collective effective dose, the mean weighted GDR and the mean lifetime dose that are 2.24?×?10^?3, 5538manSv?y^?1, 0.531?mSv and 39?mSv, respectively. The cosmic rays mean GDR was determined to be 20?nGy?h^?1. This study focuses on constructing GDRs’ baseline data in Jordan, which will be used to determine the possible change in the natural radiation due to other human activities in the future. ArcGIS software was employed to generate an isodose map to characterise exposure rates caused by GDR in Jordan.