scholarly journals Geometric model of microscopic raphide crystals in plant cells

Botanica ◽  
2021 ◽  
pp. 62-68
Author(s):  
Ali Özdemir
Keyword(s):  
Minimal Surface ◽  
Simple Structure ◽  
Geometric Model ◽  
Mineral Acid ◽  
Surface Feature ◽  
Convex Polyhedra ◽  
Mathematical Formulas ◽  
Different Shapes ◽  
Space Occupation ◽  
Phosphate Carbonate

In the present study, we showed that the microscopic structures of some plant crystals have the geometric model and mathematical formulas. Plant crystals are the storage of many mineral acid salts in many plants, such as chloride, phosphate, carbonate, silicate anhydrides and sulfates, formed due to metabolism. The crystals formed take different shapes. The shaping of plant crystals is not a simple structure. They are created in specific shapes and sizes by this biomineralisation process. Seventy-five per cent of flowering plants make one or more kinds of crystals. One of these is called a raphide crystal. Our study determined that the microscopic structures of some raphide crystals show the elongated triangular bipyramid that is a mathematics definition. In geometry, the elongated triangular bipyramid is one of the Johnson solids (J14), convex polyhedra, whose faces are regular polygons. At the same time, it was determined that the crystals show a minimal surface feature. The feature takes an essential place in geometry. The minimal surface feature provides the advantages of resistance and minimal space occupation to the crystals

scholarly journals Yagya Kunds of one-hast (24 angul) with different shapes have equal volume

2021 ◽  
Vol 3 (2) ◽  
pp. 01-08
Author(s):  
Ekta Chandel ◽  
Vivek Vijay
Keyword(s):  
Surface Area ◽  
Complex Structures ◽  
Mathematical Formula ◽  
Ancient India ◽  
Circular Shape ◽  
Different Types ◽  
Mathematical Formulas ◽  
Different Shapes ◽  
The Difference

Yagya kund construction is the outcome of great research of ancient India. Indian scripture has given very sophisticated Vedic mathematical formulations for construction of Yagya kund. There are different types of shapes described for Yagya kund; Circular & Lotus, Semi-circular, Vulvar, Trigonal, Square, Pentagonal, Hexagonal, Heptagonal, Octagonal. Irrespective of shapes,all these Yagya kunds have same surface area. Based on the fact given in the literature, 1000 offerings (ahutis) require construction of BhuHastatmakaKund (1 hand or 24 angul long). In addition, height of the all one-hand long kunds are same. Hence, the present research tests the hypothesis that the volume should be same for all different shaped kunds. In the present study, the volume of 1 hast Yagya kund (24 angul) for all these shapes is calculated using the dimensions given in the scripture using available simple available mathematical formulas. Volume of all these kunds is compared with circular shape kund. The difference in the volume of different shapes is foundbelow 0.3% in all the kunds except for vulvar, pentagonal and octagonal shapes which is observed to be 7.48%, 1.76% and 2.83% respectively. The difference isdueto inappropriate mathematical formula for these complex structures having different angles in the slants and multiple sides of the bases.

Nature of fine materials compaction when roll briquetting in cells of different shapes

2021 ◽  
pp. 39-44
Author(s):  
N. A. Babaylov ◽  
Yu. N. Loginov ◽  
L. I. Polyanskiy
Keyword(s):  
Cell Shape ◽  
Geometric Model ◽  
Cell Types ◽  
Technological Parameters ◽  
Technological Gap ◽  
Different Types ◽  
A Cell ◽  
Different Shapes ◽  
The Russian Federation ◽  
The Government

In the work, the influence of the technological parameters for roll briquetting on the compaction coefficient and distribution of briquetting pressure along the curly generatrix of the cell cut on the roll of the briquetting press is investigated. The influence of the cell shape on the pressing roll and the size of the gap between the rolls was studied. The paper considers various forms of cells on rolls (or roll bandages) of four different types of the shapes. The purpose of the work is to describe the conditions manifestation of the so-called re-pressing of the briquette back part, leading to the appearance of cracks and destruction of the briquette according to the “dovetail” type. This phenomenon leads to a decrease in yield on the briquetting press and the formation of the return of material that must be involved in the processing of waste. A geometric model of material compaction in the cells of the briquetting press for four different shapes is constructed: pillow-shaped and three conical types. When creating the model, assumptions are made that are commonly used in the formulation of powder rolling problems. The conditions of the problem are fulfilled in a flat setting. In the model, a briquette of arbitrary shape is conventionally divided into several infinitely small volumes. The briquette formation begins in the capture section by densification of the selected volume element, the thickness of which remains unchanged until the end of the briquetting process. Plots of the compaction coefficients distribution along the direction of roll briquetting for the material for the considered cell types are constructed. The obtained data show that for the entire range of gaps between the rollers, the calculated compressibility of the briquetted material in a conical cell is higher than in a cell with a pillow-shaped shape. It was determined that the compaction coefficient in the front of the briquette is noticeably lower. To determine the plot of briquetting pressure along the generatrix of the cell, the method of standards was used, in which the dependence of the compaction coefficient on the briquetting pressure is preliminarily constructed. Then, the compaction coefficient is converted according to the compression curve for the material under study into compression forces. It is shown that to reduce the effect of re-pressing, it is necessary to increase the technological gap between the rollers of the briquetting press. The work was performed under the theme № 0391-2016-0001 (AAAA-A18-118020790140-5) and with the partial financial support of the Resolution № 211 of the Government of the Russian Federation, contract № 02.A03.21.0006.

Structural phenomena in the growth of carbon nanotubes

1993 ◽  
Vol 51 ◽  
pp. 750-751
Author(s):  
Jun Jiao
Keyword(s):  
Carbon Nanotubes ◽  
Growth Mechanism ◽  
Carbonaceous Material ◽  
Cluster Growth ◽  
Structural Elements ◽  
Rich Variety ◽  
Different Shapes ◽  
Point To Point

HREM studies of the carbonaceous material deposited on the cathode of a Huffman-Krätschmer arc reactor have shown a rich variety of multiple-walled nano-clusters of different shapes and forms. The preparation of the samples, as well as the variety of cluster shapes, including triangular, rhombohedral and pentagonal projections, are described elsewhere.The close registry imposed on the nanotubes, focuses attention on the cluster growth mechanism. The strict parallelism in the graphitic separation of the tube walls is maintained through changes of form and size, often leading to 180° turns, and accommodating neighboring clusters and defects. Iijima et. al. have proposed a growth scheme in terms of pentagonal and heptagonal defects and their combinations in a hexagonal graphitic matrix, the first bending the surface inward, and the second outward. We report here HREM observations that support Iijima’s suggestions, and add some new features that refine the interpretation of the growth mechanism. The structural elements of our observations are briefly summarized in the following four micrographs, taken in a Hitachi H-8100 TEM operating at an accelerating voltage of 200 kV and with a point-to-point resolution of 0.20 nm.

The Application of Laboratory Formulas to Clinical Voice Management

1995 ◽  
Vol 4 (2) ◽  
pp. 62-69 ◽  
Author(s):  
Katherine Verdolini ◽  
Ingo R. Titze
Keyword(s):  
Fundamental Frequency ◽  
Voice Disorders ◽  
Clinical Interventions ◽  
Case Examples ◽  
Interactive Nature ◽  
Mathematical Formulas

In this paper, we discuss the application of mathematical formulas to guide the development of clinical interventions in voice disorders. Discussion of case examples includes fundamental frequency and intensity deviations, pitch and loudness abnormalities, laryngeal hyperand hypoadduction, and phonatory effort. The paper illustrates the interactive nature of theoretical and applied work in vocology

A Comparison of Simple Structure Rotation Criteria in Temporal Exploratory Factor Analysis for Event-Related Potential Data

Methodology ◽  
2019 ◽  
Vol 15 (Supplement 1) ◽  
pp. 43-60 ◽  
Author(s):  
Florian Scharf ◽  
Steffen Nestler
Keyword(s):  
Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Simple Structure ◽  
Ground Truth ◽  
Event Related Potential ◽  
Suitable Alternative ◽  
Factor Rotation ◽  
Rotation Methods ◽  
Simple Structure Rotation ◽  
Temporal Overlap

Abstract. It is challenging to apply exploratory factor analysis (EFA) to event-related potential (ERP) data because such data are characterized by substantial temporal overlap (i.e., large cross-loadings) between the factors, and, because researchers are typically interested in the results of subsequent analyses (e.g., experimental condition effects on the level of the factor scores). In this context, relatively small deviations in the estimated factor solution from the unknown ground truth may result in substantially biased estimates of condition effects (rotation bias). Thus, in order to apply EFA to ERP data researchers need rotation methods that are able to both recover perfect simple structure where it exists and to tolerate substantial cross-loadings between the factors where appropriate. We had two aims in the present paper. First, to extend previous research, we wanted to better understand the behavior of the rotation bias for typical ERP data. To this end, we compared the performance of a variety of factor rotation methods under conditions of varying amounts of temporal overlap between the factors. Second, we wanted to investigate whether the recently proposed component loss rotation is better able to decrease the bias than traditional simple structure rotation. The results showed that no single rotation method was generally superior across all conditions. Component loss rotation showed the best all-round performance across the investigated conditions. We conclude that Component loss rotation is a suitable alternative to simple structure rotation. We discuss this result in the light of recently proposed sparse factor analysis approaches.

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

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