Pairwise soft separation axioms in soft bitopological spaces

A. Kandil,O. A. E. Tantawy,S. A. El-Sheikh,Shawqi A. Hazza 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.13 No.5

The motivation of the current paper is to define and study some soft separation axioms in soft bitopological spaces in terms of pairwise softness namely, pairwise soft $T^{*}_{0}$, pairwise soft $T^{*}_{1}$, pairwise soft $T^{*}_{2}$, and pairwise soft $R^{*}_{1}$. Characterizations and properties of these soft separation axioms have been obtained. Moreover, we study the implications of these types of soft separation axioms in soft and crisp cases. Finally, we show that these properties are hereditary.

$\G$-Proximity Spaces

A. Kandil,S. A. El-Sheikh,E. Said 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.6

In this paper, we introduce a new approach of proximity structure based on the grill notion. For $\G=P( X) \backslash \{ \phi \}$, we have the Efremovi\v{c} proximity structure and for the other types of $\G$, we have many types of proximity structures. Some results on these spaces have been obtained. Some of these results are : every $\G$-normal $T_{1}$space is $\G$-proximizable space (Theorem 3.8). Also, for such space, we show that it has a unique compatible $\G$-proximity under the condition that $X$ is compact relative to $\tau^{*}$ (Theorem 4.10). Finally, for a surjective map $f$ : $X\longrightarrow (Y,$ $\delta_{f(\G)})$ ($\G$ is a grill on $X$), we establish the largest $\G$-proximity $\delta_{\G}$ on $X$ for which the map $f$ is a $\G$-proximally continuous (Theorem 4.16).

$\tilde{I}$-proximity spaces based on soft sets

A. Kandil,S. A. El-Sheikh,E. Said 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.1

In this paper, we present a new structure of basic proximity of soft sets based on the notion of soft ideal. For $\tilde{I}=\{\tilde{\Phi}\},$ we have the basic proximity of soft sets and for other types of $\tilde{I}$ we obtain many types of basic proximity structure of soft sets. Also we redefine this structure by using soft ideals. Some results of these spaces are: if $(X,E,\tau )$ is $\tilde{I}$% -soft normal space and $(X,E,\tau ^{\ast })$ is $R_{0}^{^{\prime }}$-space, then there exists $\tilde{I}$-Lodato proximity of soft sets $\delta _{\tilde{I}}$ such that $\tau ^{\ast }=\tau _{\delta _{\tilde{I}}}$. Also the soft topology generated by $\tilde{I}$-basic proximity of soft sets is finer than the soft topology generated by $R_{0}^{^{\prime }}$-$\check{C}$ech closure operator of soft sets. Finally, for a bijective soft map $% f:(X,E_{1})\rightarrow (Y,E_{2},\delta _{f(\tilde{I})}),$ we construct the largest $\tilde{I}$-Lodato proximity of soft sets $\delta _{\tilde{I}}$ on $(X,E_{1})$ such that $f$ is $\tilde{I}$-proximally soft continuous mapping.

Controlling the Optical and Magnetic Properties of Nanostructured Cuprous Oxide Synthesized from Waste Electric Cables

S. M. Abdelbasir,S. M. El-Sheikh,M.M. Rashad,D.A. Rayan 대한금속·재료학회 2018 ELECTRONIC MATERIALS LETTERS Vol.14 No.4

Cuprous oxide Cu2Onanopowders were purposefully synthesised from waste electric cables (WECs) via a simple precipitationroute at room temperature using lactose as a reducing agent. In this regard, dimethyl sulfoxide (DMSO) was first appliedas an organic solvent for the dissolution of the cable insulating materials. Several parameters were investigated during dissolutionof WECs such as dissolution temperature, time and solid/liquid ratio to determine the dissolution percentage of theinsulating materials in DMSO. The morphology and the optical properties of the formed Cu2Oparticles were investigatedusing X-ray diffraction (XRD), field emission-scanning electron microscopy (FE-SEM), Fourier-transform infrared spectroscopyand UV–visible–near IR spectrophotometer. XRD data confirmed the presence of single crystalline phase of Cu2Onanoparticles. FE-SEM and TEM images revealed spherical, cubic and octahedral shapes with the various particle sizesranged from 16 to 57 nm depending on the synthesis conditions. A possible mechanism explaining the Cu2Onanostructuresformation was proposed. The band gap energies of the Cu2Onanostructures were estimated and the values were locatedbetween 1.5 and 2.08 eV. Photoluminescence spectroscopy analysis clearly showed a noticeably blue-shifted emission forthe synthesized samples compared to spectrum of the bulk. Eventually, magnetic properties of the synthesized nanoparticleshave been measured by vibrating sample magnetometer and the attained results implied that the synthesized particles areweakly ferromagnetic in nature at normal temperature.

ON STABILITY AND BIFURCATION OF PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS

EL-SHEIKH, M. M. A.,EL-MAHROUF, S. A. A. 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

Fuzzy soft hyperconnected spaces

A. Kandil,O. Tantawy,S. A. El-Sheikh,Sawsan S. S. El-Sayed 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.13 No.6

The purpose of this paper is to introduce concepts of fuzzy soft D-space, fuzzy soft extremally disconnected spaces and fuzzy soft hyperconnected spaces. The relationship between these concepts is investigated. The properties of fuzzy soft hyperconnected spaces are studied.

On stability and bifurcation of periodic solutions of delay differential equations

M. M. A. El-Sheikh,S. A. A. El-Mahrouf 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.19 No.1-2

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

Marker-assisted selection for scab resistance and columnar growth habit in inter-varietal population of apple (Malus × domestica)

Rasool Aatifa,Bhat K. M.,Mir M. A.,Sundouri A. S.,ALshamrani Salha Mesfer,Aloufi Abeer S.,El Moneim Diaa Abd,Mansoor Sheikh,정용석 한국식물생명공학회 2024 Plant biotechnology reports Vol.18 No.1

In recent years, there has been significant progress in enhancing the genetic foundation underlying important agricultural traits such as resistance to scab and the development of a columnar growth habit. V. inaequalis is a hemibiotrophic fungus widely distributed in temperate regions where apples are grown on commercial scale. The present investigation was undertaken to identify Vf gene and Co gene, which, respectively, confer resistance against apple scab disease and columnar phenotype in apple cultivar ‘Rosalie’ and introgression of both the genes in commercially important cultivar ‘Fuji’. Polymorphism sur- vey was carried out between the two parents using 22 simple sequence repeat (SSR) and sequence-characterized amplified region (SCAR) markers. The observations revealed that almost 50% hybrids fall in resistant category and 50% in susceptible category. The results of marker-assisted screening confirmed 38 F1s carrying resistance gene for scab while the remain- ing 32 F1 plants were found to be lacking the gene. The 38 genotypically scab-resistant hybrids were selected for further characterization as columnar and non-columnar plants. Based on the selection criteria, 21 individuals were categorized as columnar and the remaining 17 were categorized as non-columnar. The phenotypic screening was followed by screening of F1 s using molecular markers for Co gene. The amplification of Co-specific markers yielded columnar-specific fragments in the population and fitted the expected 1:1 Mendelian ratio. 18 scab-resistant F1 hybrids were found to carry Co gene and the remaining 20 did not possess the gene for columnar growth habit. Gene-specific primers identified in the present study can be directly used for screening large apple germplasm in a short period of time for developing resistant varieties against apple scab as well as varieties with columnar growth habit. Hybrids with verified scab resistance and columnar growth can be swiftly utilized as scab-resistant columnar cultivars.