Regular Bodies Research Articles

The emergence of symmetries in classical physics

Abstract Since antiquity symmetry has proved to be a central guiding idea of research with which the microcosm and macrocosm are to be explained. Euclidean mathematics established a unified theory of proportions of the world in which the spherical symmetries of the macrocosm and the regular (“Platonic”) bodies of the microcosm were distinguished. In the Pythagorean tradition symmetrical proportions were understood as an expression of the beauty and harmony of the cosmos until the Renaissance.

Form and Matter of Regular Geometrical Bodies in Luca Pacioli’s Summa (1494) and Compendium de divina proportione (1498)

Abstract Luca Pacioli (ca. 1447–1517) is widely considered a central figure in the Italian Renaissance, particularly in the history of practical mathematics. The perspectival representations of geometrical bodies that Leonardo da Vinci drew for Pacioli’s Compendium de divina proportione are, in turn, often singled out to illustrate the relationships between the visual arts and mathematics in the late fifteenth century. Yet despite increasing scholarly attention, the philosophical framework of Pacioli’s works deserves to be further explored. This paper discusses how Pacioli ably developed his arguments on regular geometrical bodies by relying on a predominantly Aristotelian philosophical framework. In this way, Pacioli established correlations among the quantitative, material, and formal properties of regular geometrical bodies, concluding with the visualisation of their (geometrically defined) form at the level of the intellect.

History of Parliamentary System of Government in Pakistan 1947 to 2002

The British Parliamentary System in India has straightforwardly added to the development of parliament in Pakistan. The regular authoritative bodies picked the individuals from the Constituent Assembly. It might be said that the historical backdrop of a democratic organization in Pakistan is a background marked by overturning ubiquity based establishments and a past filled with making new assumptions with every misfortune. Pakistan keeps on making progress toward accomplishing an irrefutable and solid structure in view of well-known request. Vote based change to democratization included a verifiable cycle. This paper's system was subjective in nature. All through most of the parliamentary structure, obviously organization in administrative issues was continuously being deterred. With the heaviness of Martial Law, the administrative framework was at last unhindered. When contrasted with parliamentary, the authority structure has reliably outperformed it in Pakistan's situation on the grounds that to its more evolved economy. To evaluate the History of Parliamentary System of Government in Pakistan from 1947 to 2002. The fundamental motivation behind this paper is to incorporate the historical backdrop of parliamentary arrangement of Pakistan from its introduction to the world to year 2002. Also, in addition which job the parliament has played in the majority rule government of Pakistan in this time span. This paper likewise centers around the progressions in the financial dependability of Pakistan because of Parliamentary vote based system. This study draws together writing on the total history of the parliament and the parliamentary vote based system alongside its impact on the financial security of the Pakistan. The information was assembled from the information tanks, sites and the exploration work of early individuals. A certain solicitation in such a situation can notice plans in the improvement of political events and choose if these models have a typical subject of all time. The fundamental and assistant sources were used for getting information and social event data to complete the investigation and show up at the last revelations and recommendations.

The Parliamentary System of Government in Pakistan and Progression in Financial Dependability of Pakistan (1947 - 2002)

The British Parliamentary System in India has straightforwardly added to the development of parliament in Pakistan. The regular authoritative bodies picked the individuals from the Constituent Assembly. In the following study the evaluation of the History of Parliamentary System of Government in Pakistan from 1947 to 2002 was analyzed. It might be said that the historical backdrop of a democratic organization in Pakistan was a background marked by overturning ubiquity based establishments and a past filled with making new assumptions with every misfortune. The fundamental motivation behind this paper was to incorporate the historical backdrop of parliamentary arrangement of Pakistan from its introduction to the world to year 2002. The following study likewise centers around the progressions in the financial dependability of Pakistan because of Parliamentary vote based system. This study draws together writing on the total history of the parliament and the parliamentary vote based system alongside its impact on the financial security of the Pakistan. The information was assembled by using qualitative analysis. Pakistan keeps on making progress toward accomplishing an irrefutable and solid structure in view of well-known request. Vote based change to democratization included a verifiable cycle. This paper's system was subjective in nature. All through most of the parliamentary structure as organization in administrative issues was continuously being deterred. With the heaviness of Martial Law, the administrative framework was at last unhindered. When contrasted with parliamentary, the authority structure has reliably outperformed it in Pakistan's situation on the grounds that to its more evolved economy.

The role of thermal effusivity on the incipient growth of the surface temperature in a semi-infinite region absorbing heat flux at the surface

Heat conduction theory stipulates that two thermo-physical properties of materials: the thermal conductivity “k” and the thermal diffusivity “ ” influence the temperature evolution in regular and irregular bodies as a response to various cooling/heating conditions. The traditional statement involving the two thermo-physical properties is examined at length in the present study for the case of a semi-infinite region. The primary objective of the present study is to investigate the influence of the less known thermo-physical property called the thermal effusivity “e” on the incipient surface temperature raise in a semi-infinite body affected by uniform surface heat flux. The secondary objective of the study is to identify a key figure-of-merit named the dimensionless threshold time that separates the incipient temperature elevation in a semi-infinite region from the incipient temperature elevation in a large wall of finite thickness under the same uniform surface heat flux. The outcome of the methodical analysis suggests that the accurate estimate for the dimensionless threshold time in the semi-infinite region should be 0.10.

Inclusion of unsteady heat conduction in regular bodies subject to uniform surface heat flux in a heat transfer course

The present study is concerned with the analysis of unsteady heat conduction in regular bodies (large plane wall, long cylinder, and sphere) with constant initial temperature, prescribed surface heat flux and thermal properties of the solid that are invariant with temperature. Surprisingly, this important topic is absent in textbooks on heat transfer. The exact evaluation of the dimensionless surface temperatures varying with the dimensionless time in the regular bodies over the entire dimensionless time domain [Formula: see text] is carried out with a symbolic algebra code. Thereafter, regression analysis is applied to the data gathered for the dimensionless surface temperatures varying with the dimensionless time of the regular bodies inside the dimensionless “small time” time sub-domains [Formula: see text]. The dimensionless threshold time [Formula: see text] is a decisive parameter that establishes the borderline between the “small time” sub-domain [Formula: see text] and the “large time” sub-domain [Formula: see text] comprising the entire dimensionless time domain [Formula: see text]. Based on regression analysis, compact asymptotes are constructed for the dimensionless surface temperatures varying with the dimensionless time inside the dimensionless “small time” sub-domain [Formula: see text]. At the end, agreements with the dimensionless exact, analytical surface temperature distributions (the baseline solutions) valid for the dimensionless time sub-domain [Formula: see text]. are considered of excellent quality.

A computational package to compute the electrical resistivity tomography response for regular bodies immersed in a homogeneous half-space

A 3D forward algorithm is presented to model electrical resistivity tomography (ERT) measurements with the capability to use different electrode array configurations. We have implemented the algorithm as an open-source package with the assumption that the medium can be modeled as a homogeneous half-space with immersed bodies of different resistivities with regular geometry. This algorithm incorporates a novel numerical approximation by using the volume integral method, with the hypothesis of weak scattering, where the secondary currents generated in the bodies due to the main field are not considered. The algorithm also includes a new method called cubature to calculate volume integrals and the ERT response. In addition, the code has a module to display the results as color resistivity profiles. This method avoids the limitation of the complex geometry of the medium or even of the immersed bodies. The method is useful for planning a field survey, exploring the use of a specific electrode array, or implementing new arrays. The package, called the volume integral model of the electric response, is computationally efficient and can be easily ported to any operating system that supports MATLAB.

Aircraft Accident Provisions in Islamic Jurisprudence

Aircraft accidents have become a serious problem that is difficult to solve despite all efforts made by governments, regular bodies and others to solve the problem. However, the danger is constantly increasing as it causes the loss of hundreds of thousands of lives. It affects millions of people around the world. Transportation in all its forms by land, sea and air, public or private, is one of the main pillars for the development and growth of people and societies. Therefore, accidents that occur by means of transportation in all their forms must be avoided, which is a cause for concern and threatens the safety and health of transportation. The right to life is one of the fundamental human rights that no one has the right to violate. Preserving human life and soul is one of the purposes of the Sharia. Islamic Sharia considers assaulting and killing an innocent person a major crime and a great sin, making the amount of punishment necessary for the perpetrators of premeditated murder. This research deals with the subject of the provisions of aircraft accidents in light of Islamic jurisprudence. In this research, an analytical and descriptive approach was used. Researching this issue is necessary because most traffic accidents result in material or non-material damages. And the need to know the legal provisions of those who commit these incidents directly or indirectly. As a guarantee of physical and physical damage, the nature of this guarantee and who is responsible for it or to whom it goes. In this research, I seek to explain the concept of aircraft accidents, the causes of aircraft accidents that are different, and the provisions of aircraft accidents whose ruling differs due to the intent of the perpetrator. If it is an unreliable accident, it is not guaranteed, and if it is an unreliable accident due to the failure of the commander, it is guaranteed. And if it is approved, it is considered premeditated murder, and retaliation is required for it. At the end of the article, I explained the ruling on hijacking planes, that it is the same as the crime of spearing. Its rulings explained its punishment in the light of Islamic jurisprudence.

Response and Application of Full-Space Numerical Simulation Based on Finite Element Method for Transient Electromagnetic Advanced Detection of Mine Water

The issue of water hazards has led to the restriction of safe and efficient coal mine production in China. The transient electromagnetic method (TEM) is one of the most effective means of detecting the hidden dangers of water hazards in coal mines. However, the current understanding of the whole-space transient electromagnetic response of mine water is only on the general law due to the late start of the forward research. Therefore, this paper established multiple sets of simulation models in the whole area in order to study the rules and factors of transient electromagnetic responses. Subsequently, these laws are used to explain the detection data of TEM in the field. According to the simulation results, the electric properties, distance, and size had the greatest influence on the transient electromagnetic response of regular anomalous geological bodies, while the electromagnetic field projection area also had an impact on irregular ones. Furthermore, field application demonstrated that the response law and TEM’s affecting factors are acceptable for directing the detection of transient electromagnetic in coal mines. This research can advance the TEM’s data processing and interpretation technology and offer a theoretical basis for detailed investigation.

Description and characteristics of chert nodules in Appollonia Formation, Al Hmmeda road-cut, Al Jabal Al Akhdar, NE Libya

Physical, petrographic and bulk elements analysis of Chert Nodules in Appollonia Formation, Al Hmmeda road-cut were conducted and showed that the origin of these chert by replacement. The suspected siliceous organic matters are of low crystallized silica and were dissolved under the influence of increasing temperature and pH. Most of the chert was localized in the limestone and dolomitic limestone of Appollonia Formation (nodular zone) by percolation of silica-rich solution along microfractures and porous/permeability zones. This local porosity and permeability variations, mostly produced mixing of the diffused digenetic fluids. This process produces the nodular form of the cherts in the Appollonia mudstone facies in the nodular zone, while less marked permeability variations could have produced more regular tabular bodies of chert, which were not observed at least in the studied section. The absence of chert nodules in some adjacent rocks and even at higher elevation in the Appollonia stratigraphic section (nonnodular zone), might reflect effective exhaustion of the silica supply, fewer microfractures condition and perhaps dilution by the marine water of highly reduced silica-rich solution.

Homothetic packings of centrally symmetric convex bodies

A centrally symmetric convex body is a convex compact set with non-empty interior that is symmetric about the origin. Of particular interest are those that are both smooth and strictly convex—known here as regular symmetric bodies—since they retain many of the useful properties of the d-dimensional Euclidean ball. We prove that for any given regular symmetric body C, a homothetic packing of copies of C with randomly chosen radii will have a (2, 2)-sparse planar contact graph. We further prove that there exists a comeagre set of centrally symmetric convex bodies C where any (2, 2)-sparse planar graph can be realised as the contact graph of a stress-free homothetic packing of C.

An Improved 3D Box-Counting Dimension Computing Technology for Estimating the Complexity of 3D Models

The box-counting dimension, which can effectively reflect the complexity and self-similarity of models, is an important method for calculating the fractal dimension of models. To improve the precision of the box-counting dimension algorithm, in this study, we propose an improved 3D box-counting dimension algorithm for models composed of triangular meshes. Through linear coding and optimization of intersection detection between triangles and octree cells, we can accurately calculate the box dimension of models with less memory expense. Through the results of measuring regular geometric bodies and spatial Voronoi bodies, it can be seen that the method has good performance, and the ability of filling space of fractal bodies can be calculated accurately. In the circumstance of 3D box-counting dimension algorithm cannot work well for comparing curvature changes of non-fractal surfaces, the weighted box-counting dimension algorithm can be used to quantitatively analyze the complexity of surface curvature.

Compact Algebraic Asymptotes for Small and Large Time Surface Temperatures for Regular Solid Bodies Heated With Uniform Heat Flux: Scrutiny of New Critical Fourier Numbers

Abstract The alternate infinite series at “small time” have been used to analyze the time variation of surface temperatures (ϕs) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for ϕs in a plate, cylinder, and sphere in the “small time” sub-domain extending from 0 to the critical dimensionless time or critical Fourier number. For the “large time” sub-domain, the exact solution is approximated in two ways: with the “one-term” series and with the simple asymptotes corresponding to extreme “large time” conditions. Maximum relative errors of 1.23%, 6.24%, and 0.96% in ϕs for the plate, cylinder, and sphere are τcr obtained, respectively, with the “small time”—“large time” approximation using a traditional approach to fix the τcr value. An alternative approach to set the τcr is proposed to minimize the maximum relative error of the approximated solutions so that values of 1.19%, 3.93%, and 0.16% are then obtained for the plate, cylinder, and sphere, respectively, with the “small time”—“large time” approximation. For the “small time”—“one-term” approximation maximum relative errors of 0.024%, 1.33%, and 0.004% for the plate, cylinder, and sphere are obtained, respectively, with this approach.

Peculiarities of Electrosynthesis of Polyaniline Coating on Activated Graphite Foil

It has been demonstrated that, due to the heterogeneity of the surface of anodized graphite foil (AGF), the adsorption of the aniline monomer (An) occurs on active oxygen-containing sites. The latter results in its oxidation, dimerization, and oligomerization and growth of rodlike polyaniline (PAni) structures. Further electrosynthesis (ES) of PAni has produced a two-phase coating including the above-mentioned rodlike structures and regular polyaniline bodies of a granular structure. Cycling of electrodes with such coating in the expanded area of anode potentials (up to 0.8–0.9 V) leads to the formation of a homogeneous coating. The electrodes processed in this way have appeared to be highly stable at storing and conducting a large number of charge–discharge cycles.

Um estudo sobre o capítulo XXV da "De Divina Proportione" (1509) de Luca Pacioli (1447-1517)

O presente estudo trata-se de um recorte da pesquisa de mestrado em andamento e tem por objetivo apresentar a definição de corpos regulares adotada pelo frade italiano Luca Pacioli (1447-1517) em seu tratado intitulado De Divina Proportione, publicado em 1509, listando alguns casos considerados possíveis e impossíveis perante as condições descritas pelo autor. Na intenção de colaborar no ensino de Geometria Espacial sobre os corpos regulares, este estudo traz alguns detalhes acerca da definição utilizada pelo frade, elencando características relevantes e exemplos de situações trazidos no tratado. Percebendo, através desse estudo, que o ensino sobre corpos regulares através das propriedades citadas por Luca Pacioli pode contribuir na compreensão de conceitos sobre essa temática, idealiza-se como passos seguintes a realização de ações que contribuam na formação de professores de matemática e, consequentemente, de seus alunos da Educação Básica.

Improved pore network models to simulate single-phase flow in porous media by coupling with lattice Boltzmann method

In this paper, different pore network models to simulate single-phase flow in porous media are built and their accuracy is evaluated. In addition to the conventional pore network model (CPNM) which consists of regular pore bodies and throat bonds, three improved pore network models (IPNMs) are developed allowing to better describing the real pore and throat geometry. The first improved pore network model (IPNM1) replaces the regular throat bond with a throat bond showing the real throat cross section. The second improvement (IPNM2) uses a series of sub-throat bonds with varying cross sections to better describe the real throat geometry, which is firstly proposed in this paper. The third model (IPNM3) extracts the real pore-throat-pore geometry without simplification. The conductance of fluid flow through these more realistic throat bonds is calculated by the lattice Boltzmann method (LBM). The accuracy and computational efficiency of the different pore network models are evaluated taking the LBM simulation over the whole porous medium as reference solution. The global permeability and detailed pressure distributions in the pores for the different pore network models are validated. The results show that the accuracy of the pore network model increases from CPNM to IPNM3, but at the expense of increasing computational cost. This study suggests that IPNM3 can replace a whole-domain LBM simulation with similar accuracy but much lower computational cost. As a first-order approximation the newly proposed IPNM2 is suggested as good compromise between accuracy and computational cost.

Interdisciplinary Secondary-School Workshop

The paper describes a teaching unit of four hours with talented students aged 15-18. The workshop was designed as a problem-based sequence of tasks and was intended to deal with judging dice whether they are regular or loaded. We first introduced the students to the physics of free rotations of rigid bodies to develop the physics background of rolling dice. The highlight of this part was to recognise that cubes made from homogeneous material are the optimal form for six-sided objects leading to equal probabilities of the single faces. Experiments with all five regular bodies would lead to similar results; nevertheless, in our experiments we focused on regular cubes. This reinsures that the participants have their own experience with the context. Then, we studied rolling dice from the probabilistic point of view and – step-by-step – by extending tasks and simulations, we introduced the idea of the chi-squared test interactively with the students. The physics and the statistics part of the paper are largely independent and can be also be read separately. The success of the statistics part is best described by the fact that the students recognised that in some cases of loaded dice, it is easier to detect that property and in other cases one would need many data to make a decision with small error probabilities. A physical examination of the dice under inspection can lead to a quick and correct decision. Yet, such a physical check may fail for some reason. However, a statistical test will always lead to reasonable decision, but may require a large database. Furthermore, especially for smaller datasets, balancing the risk of different types of errors remains a key issue, which is a characteristic feature of statistical testing.
 Subject Classification: F90, K90, M50, R30

The Effect of Light on Plastid Differentiation, Chlorophyll Biosynthesis, and Essential Oil Composition in Rosemary (Rosmarinus officinalis) Leaves and Cotyledons.

It is unclear whether light affects the structure and activity of exogenous secretory tissues like glandular hairs. Therefore, transmission electron microscopy was first used to study plastid differentiation in glandular hairs and leaves of light-grown rosemary (Rosmarinus officinalis “Arp”) plants kept for 2 weeks under ambient light conditions. During our detailed analyses, among others, we found leucoplasts with tubuloreticular membrane structures resembling prolamellar bodies in stalk cell plastids of peltate glandular hairs. To study the effect of darkness on plastid differentiation, we then dark-forced adult, light-grown rosemary plants for 2 weeks and observed occasionally the development of new shoots with elongated internodes and pale leaves on them. Absorption and fluorescence spectroscopic analyses of the chlorophyllous pigment contents, the native arrangement of the pigment-protein complexes and photosynthetic activity confirmed that the first and second pairs of leaf primordia of dark-forced shoots were partially etiolated (contained low amounts of protochlorophyll/ide and residual chlorophylls, had etio-chloroplasts with prolamellar bodies and low grana, and impaired photosynthesis). Darkness did not influence plastid structure in fifth leaves or secretory tissues (except for head cells of peltate glandular hairs in which rarely tubuloreticular membranes appeared). The mesophyll cells of cotyledons of 2-week-old dark-germinated rosemary seedlings contained etioplasts with highly regular prolamellar bodies similar to those in mesophyll etio-chloroplasts of leaves and clearly differing from tubuloreticular membranes of secretory cells. Analyses of the essential oil composition obtained after solid phase microextraction and gas chromatography-mass spectroscopy showed that in addition to light, the age of the studied organ (i.e., first leaf primordia and leaf tip vs. fifth, fully developed green leaves) and the type of the organ (cotyledon vs. leaves) also strongly influenced the essential oil composition. Therefore, light conditions and developmental stage are both important factors to be considered in case of potential therapeutic, culinary or aromatic uses of rosemary leaves and their essential oils.

Semi–analytical, piecewise temperature–time distributions in solid bodies of regular shape affected by uniform surface heat flux employing the Method Of Lines (MOL) and the eigenvalue method

The central objective of the present study is to generate an approximate, semi–analytical piecewise solution of the one-dimensional, unsteady heat conduction equation in regular solid bodies (large wall, long cylinder and sphere) with uniform heat flux at the exposed surfaces. The main obstacle in these heat conduction problems lies in the boundary condition of uniform heat flux that is non-homogeneous, and of course is not conducive to the direct utilization of the method of separation of variables. To circumvent this restrictive obstacle, the traditional solution procedure relies on the principle of superposition of solutions composed of three degraded sub-solutions: one sub-solution in terms of the space coordinate and time, another sub-solution in terms of the space coordinate and another sub-solution in terms of time. In the present study, we exploit a radical different approach applying the Method Of Lines (MOL) forthwith to the one-dimensional, unsteady, heat conduction equation with prescribed uniform heat flux. Essentially, MOL discretizes the spatial partial derivatives in the one-dimensional, unsteady, heat conduction equation, while leaving the time partial derivative continuous. Correspondingly, the MOL transformation gives way to an adjoint system of linear, ordinary differential equations of first order in time, which is solved analytically (not numerically) with the potent eigenvalue method in the platform of a symbolic algebra code. The outcome of the two-part computational procedure provides a sequence of semi-analytical piecewise temperature distributions at the pre-selected lines in the large wall, long cylinder and sphere, which are expressed in terms of linear combinations of exponential functions of time comprising the required set of eigenvalues and eigenvectors. At the end, it was determined that the semi-analytical piecewise surface, center and mean temperature-time distributions based on seven lines exhibit excellent quality in the entire time domain.

Global mapping of asteroids by frozen orbits: The case of 216 kleopatra

In this paper, the global mapping of an irregular asteroid is studied referring to the ground track properties of a frozen orbit (at constant eccentricity and argument of pericentre on average). In fact, when the size of the asteroid is in the order of hundreds of kilometres or more, an appropriate design of the ground track becomes an important element to optimise the coverage and guarantee regular cycles of observation. To this end, the methodology used to design the ground track in missions for the observation of regular bodies, like planets, is extended to the case of irregular bodies, such as asteroids. Moreover, to manage the irregular shape of the asteroid, the classical spherical coordinates (geographical longitude and latitude) are replaced by cylindrical coordinates, whereas the regions that are not reached by the ground track are modelled by using appropriate tetrahedra, useful to plan the coverage. In this context, the case of asteroid 216 Kleopatra has been investigated.