Abstract. One of the fibrewise micro-topological space is one in which the topology is decided through a group of fibre bundles, in comparison to the usual case in normal, fibrewise topological space. The micro-topological spaces draw power from their ability to be used in descriptions of a wide range of mathematical objects. These can be used to describe the topology of a manifold or even the topology of a group. Apart from easy manipulation, the fibrewise micro-topological spaces yield various mathematical applications, but the one being mentioned here is the possibility for geometric investigation of space or group structure. In this essay, we shall explain what fibrewise micro-topological spaces are, indicate why they are useful in mathematics, and explore some of the uses of this concept. In this paper, an elaboration of what they are, what they involve, and what they mean will be taken. This is a recent development in mathematics: the study of objects having a "fiber" over another object. This study focuses on constructing and investigating novel ideas from fibrewise micro-topological spaces over ℬ, specifically fibrewise micro-topological spaces over ℬ. Additionally, we present the concepts of fibrewise micro-closed and micro-open spaces over ℬ, along with various propositions related to these notions.
Abstract
Experimental work from Magnetic Abrasive Finishing (MAF) tests was carried out design parameters (amplitude, and number of cycle which are formed the shape of electromagnetic pole), and technological parameters (current, cutting speed, working gap, and finishing time) all have an influence on the mechanical properties of the surface layer in MAF process. This research has made to study the effect of design and technological parameters on the surface roughness (Ra), micro hardness (Hv) and material removal (MR) in working zone. A set of experimental tests has been planned using response surface methodology according to Taguchi matrix (36) with three levels and six factors
... Show MorePorosity plays an essential role in petroleum engineering. It controls fluid storage in aquifers, connectivity of the pore structure control fluid flow through reservoir formations. To quantify the relationships between porosity, storage, transport and rock properties, however, the pore structure must be measured and quantitatively described. Porosity estimation of digital image utilizing image processing essential for the reservoir rock analysis since the sample 2D porosity briefly described. The regular procedure utilizes the binarization process, which uses the pixel value threshold to convert the color and grayscale images to binary images. The idea is to accommodate the blue regions entirely with pores and transform it to white in r
... Show MoreIt is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.
We study one example of hyperbolic problems it's Initial-boundary string problem with two ends. In fact we look for the solution in weak sense in some sobolev spaces. Also we use energy technic with Galerkin's method to study some properties for our problem as existence and uniqueness
In this paper we introduce new class of open sets called weak N-open sets and we study the relation between N-open sets , weak N-open sets and some other open sets. We prove several results about them.
Background: Dental erosion is a common oral condition which results due to consumption of high caloric and low pH acidic food such as carbonated drinks and fruit juices. It is expected that these food types can cause irreversible damage to dental hard tissues and early deterioration of the dental restorations. So, this study aimed to evaluate and compare the erosive potential effects of orange fruit juice and Miranda orange drink on the microhardness of an orthodontic composite material. Materials and methods: Thirty discs with a thickness of 2 mm and a diameter of 10 mm were prepared from orthodontic bonding composite. The prepared discs were equally divided into three groups (n=10). Microhardness analysis was carried out both prior to
... Show MoreAn optoelectronic flow-through detector for active ingredients determination in pharmaceutical formulations is explained. Two consecutive compact photodetector’s devices operating according to light-emitting diodes-solar cells concept where the LEDs acting as a light source and solar cells for measuring the attenuated light of the incident light at 180˚ have been developed. The turbidimetric detector, fabricated of ten light-emitting diodes and five solar cells only, integrated with a glass flow cell has been easily adapted in flow injection analysis manifold system. For active ingredients determination, the developed detector was successfully utilized for the development and validation of an analytical method for warfarin determination
... Show MoreExpressions for the molecular topological features of silicon carbide compounds are essential for quantitative structure-property and structure-activity interactions. Chemical Graph Theory is a subfield of computational chemistry that investigates topological indices of molecular networks that correlate well with the chemical characteristics of chemical compounds. In the modern age, topological indices are extremely important in the study of graph theory. Topological indices are critical tools for understanding the core topology of chemical structures while examining chemical substances. In this article, compute the first and second k-Banhatti index, modified first and second k-Banhatti index, first and second k-hyper Banhatti index, fir
... Show MoreNumerous integral and local electron density’s topological parameters of significant metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp* Ir) (Cp Ru)2 (μ3-H) (μ-H)3]1 (Cp = η5 -C5Me5), (Cp* = η5 -C5Me4Et) were calculated and interpreted by using the quantum theory of atoms in molecules (QTAIM). The properties of bond critical points such as the delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇2ρ(r), the local energy density
... Show MoreIn this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.