A co-area formula with applications to monotone rearrangement and to regularity

1990 ◽  
Vol 109 (3) ◽  
pp. 213-238 ◽  
Author(s):  
Jean Michel Rakotoson ◽  
Roger Temam
Keyword(s):  
Area Formula ◽  
Monotone Rearrangement

Irreducible first Brillouin zone for two-dimensional magnonic crystals with asymmetric complex lattices

2021 ◽  
pp. 2150170
Author(s):  
Hui Yang ◽  
Guo-Hong Yun ◽  
Yong-Jun Cao
Keyword(s):  
Brillouin Zone ◽  
Unit Cell ◽  
Square Lattice ◽  
Two Dimensional ◽  
Area Formula ◽  
Irreducible Part ◽  
Full Band ◽  
Magnonic Crystals ◽  
Magnonic Crystal ◽  
Complex Basis

Two-dimensional (2D) magnonic crystal (MC) with an asymmetric complex basis is proposed in this paper, and its band structures are calculated in the whole area of the first Brillouin zone (BZ). This kind of MCs is composed of two different atoms in the unit cell, and the symmetry of the unit cell is broken due to changes in the position of the second atom, so the irreducible part of the BZ is no longer the small area [Formula: see text] for square lattice, and it must be expanded to the whole first BZ. Only by investigating the whole first BZ, can we get the true full band-gap for this kind of MCs.

High-resolution stratigraphic characterization of natural fracture attributes in the Woodford Shale, Arbuckle Wilderness and US-77D Outcrops, Murray County, Oklahoma

2018 ◽  
Vol 6 (1) ◽  
pp. SC29-SC41 ◽  
Author(s):  
Sayantan Ghosh ◽  
John N. Hooker ◽  
Caleb P. Bontempi ◽  
Roger M. Slatt
Keyword(s):  
Natural Fracture ◽  
Fracture Aperture ◽  
Aperture Size ◽  
Fracture Density ◽  
Area Formula ◽  
Woodford Shale ◽  
Fracture Spacing ◽  
Spacing Ratio ◽  
Fracture Intensity ◽  
Bed Thickness

Natural fracture aperture-size, spacing, and stratigraphic variation in fracture density are factors determining the fluid-flow capacity of low-permeability formations. In this study, several facies were identified in a Woodford Shale complete section. The section was divided into four broad stratigraphic zones based on interbedding of similar facies. Average thicknesses and percentages of brittle and ductile beds in each stratigraphic foot were recorded. Also, five fracture sets were identified. These sets were split into two groups based on their trace exposures. Fracture linear intensity (number of fractures normalized to the scanline length [[Formula: see text]]) values were quantified for brittle and ductile beds. Individual fracture intensity-bed thickness linear equations were derived. These equations, along with the average bed thickness and percentage of brittle and ductile lithologies in each stratigraphic foot, were used to construct a fracture areal density (number of fracture traces normalized to the trace exposure area [[Formula: see text]]) profile. Finally, the fracture opening-displacement size variations, clustering tendencies, and fracture saturation were quantified. Fracture intensity-bed thickness equations predict approximately 1.5–3 times more fractures in the brittle beds compared with ductile beds at any given bed thickness. Parts of zone 2 and almost entire zone 3, located in the upper and middle Woodford, respectively, have high fracture densities and are situated within relatively organic-rich (high-GR) intervals. These intervals may be suitable horizontal well landing targets. All observed fracture cement exhibit a lack of crack-seal texture. Characteristic aperture-size distributions exist, with most apertures in the 0.05–1 mm (0.00016–0.0032 ft) range. In the chert beds, fracture cement is primarily bitumen or silica or both. Fractures in dolomite beds primarily have calcite cement. The average fracture spacing indices (i.e., bed thickness-fracture spacing ratio) in brittle and ductile beds were determined to be 2 and 1.2, respectively. Uniform fracture spacing was observed along all scanlines in the studied beds.

scholarly journals STUDENTS’ COGNITIVE PROCESSES IN SOLVING PROBLEM RELATED TO THE CONCEPT OF AREA CONSERVATION

2019 ◽  
Vol 10 (1) ◽  
pp. 21-36 ◽  
Author(s):  
Rooselyna Ekawati ◽  
Ahmad Wachidul Kohar ◽  
Elly Matul Imah ◽  
Siti Maghfirotun Amin ◽  
Shofan Fiangga
Keyword(s):  
Problem Solving ◽  
Cognitive Processes ◽  
Cognitive Process ◽  
Low Achievers ◽  
High Achievers ◽  
Seventh Graders ◽  
Test Results ◽  
Area Formula ◽  
High Achiever ◽  
Cyclic Processes

This study aimed to determine the cognitive process employed in problem-solving related to the concept of area conservation for seventh graders. Two students with different mathematical ability were chosen to be the subjects of this research. Each of them was the representative of high achievers and low achievers based on a set of area conservation test. Results indicate that both samples performed more cyclic processes on formulating solution planning, regulating solution part and detecting and correcting error during the problem-solving. However, it was found that the high achiever student performed some processes than those of low achiever. Also, while the high achiever student did not predict any outcomes of his formulated strategies, the low achiever did not carry out the thought process after detecting errors of the initial solution gained. About the concept of area conservation, the finding also reveals that within the samples’ cognitive processes, the use of area formula come first before students decided to look for another strategy such as doing ‘cut-rotate-paste’ for the curved planes, which do not have any direct formula. The possible causes of the results were discussed to derive some recommendation for future studies.

Synthesis of Novel g-C3N4/NH2-MIL-88B(Fe) Composite Photocatalysis for Efficient Ciprofloxacin Degradation Under Simulated Sunlight Irradiation

NANO ◽  
2021 ◽  
pp. 2150063
Author(s):  
Jungang Yi ◽  
Kun Wu ◽  
Huadong Wu ◽  
Jia Guo ◽  
Linfeng Zhang ◽  
...  
Keyword(s):  
Photoelectron Spectroscopy ◽  
Adsorption Property ◽  
Catalytic Performance ◽  
Step Method ◽  
Area Formula ◽  
Aquatic Life ◽  
X Ray ◽  
Transmission Electron ◽  
Uniform Dispersion ◽  
Composite Photocatalysts

The presence of the antibiotics in the wastewater has posed a huge risk to aquatic life and human health. It is a great significance to develop an effective technology to treat the antibiotics-containing wastewater. In this study, a series of g-C3N4/NH2-MIL-88B(Fe) composite photocatalysts are synthesized through a simple one-step method. The structure and optical properties of prepared photocatalysts are detected by X-ray diffraction (XRD), field emission scanning electron microscope (FESEM), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), UV–Vis absorption spectra (UV–Vis DRS), photoluminescence (PL) spectroscopy and transient photocurrent techniques, respectively. FESEM and TEM show that MOF is uniformly dispersed in petaloid g-C3N4. The uniform dispersion of Fe-MOFs in the heterojunction composites increases the specific surface area ([Formula: see text] of g-C3N4, which results in a great adsorption property for the nanocomposite. The capture experiment shows that [Formula: see text]O[Formula: see text] and h[Formula: see text] are the main active substances in ciprofloxacin (CIP) degradation. These prepared composite photocatalysts exhibit excellent CIP photodegradation activity under visibly light irradiation with an apparent rate constant of 0.0127[Formula: see text]min[Formula: see text] (3.74 times as the rate of single component). The remarkable catalytic performance can be ascribed to the fact that the g-C3N4/NH2-MIL-88B(Fe) heterojunction inhibits the recombination of photoinduced electron–hole pairs and improved the visible light absorption.

The Surveyor's Area Formula

1986 ◽  
Vol 17 (4) ◽  
pp. 326 ◽  
Author(s):  
Bart Braden
Keyword(s):  
Area Formula

Quadrilaterals with area formula

2012 ◽  
Vol 96 (536) ◽  
pp. 345-347
Author(s):  
Nick Lord
Keyword(s):  
Area Formula

Areas of Polygons on Isometric Dot Paper: Pick's Formula Revised

1983 ◽  
Vol 30 (8) ◽  
pp. 38-40
Author(s):  
Bonnie H. Litwiller ◽  
David R. Duncan
Keyword(s):  
Area Formula

Many students and teachers are familiar with Pick's area formula for square dot paper. Can Pick's formula be applied to simple closed polygons drawn on isometric dot paper? The answer to this question is the focus of this article.

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