Geometric Progression Research Articles

Abstract- Poster

BACKGROUND (Current Scenario):Evidently, SARS-II due to COVID-19 is a problem increasing at a geometric progression affecting human civilization at large. Unfortunately there is no cure hence we are left to mercy of preventive and social medicine measures. These models of preventive and social medicine measures are dependent on available information.OBJECTIVE (Research Question):To assess the level of awareness about prevention of transmission of COVID-19 illness in community.Methodology:Cases were chosen by purposive sampling as per criteria. After screening and rating, assessment of the level of awareness about prevention of transmission of COVID-19 illness was done by structured questionnaire. The samples shall be collected from community around Burdwan Medical College and Hospital.Result: 1.Demographic characteristics(n=110) showed predominance of female subjects, mainly residing in urban area with majority educated upto higher secondary.2. Source of information was news paper, followed by news app and television.3. Majority were worried and had a close person who was affected by COVID.4.Absence of information was evident as in a scale with maximum score of 23 mean score was 15 and median 12.5.Conclusion:The accelerating rate of new case load of COVID-19 point to a gap in knowledge, attitude and practices. Hence, a deficit in knowledge is evident. Enhancement of public awareness of COVID appropriate behavior is needed for prevention of pandemic. Introduction:Death due to cardiovascular disease is one of the leading causes of mortality in persons with severe mental disorder. There is dearth of information on cardiovascular risk profile of persons with SMD.This study is done to examine the documentation of cardiovascular disease (CVD) risk profile among patients who had cardiac event during inpatient admission in a tertiary care centre.Methods:An audit of electronic medical records for documentation of CVD risk factors of smoking, alcohol use, obesity, elevated glucose levels, elevated blood pressure was done.Results:18 among 1260 in patients with Severe mental disorders had cardiac event during 2-year study period. Nearly half of them were smokers and had alcohol use disorder. Majority of them have diabetes and hypertension. There was no documentation of history of hyperlipidemia or family history of cardiometabolic risk factors in the medical records. Out of 18 who had cardiac event, 13 had elevated FBS, 10 had elevated BP, 10 had BMI>25, 9 had high HBA1C, 17 had deranged lipid profile when evaluated during hospital stay. Though some of the patients were on treatment for diabetes, hypertension and dyslipidemia, these parameters were deranged in most of them suggesting either poor compliance to medications or inadequate management.Conclusion:This study has shown that there are inadequacies in cardiovascular risk assessment and documentation in persons with severe mental disorders. Although the sample may not be representative of persons with severe mental disorders, major disparities in risk factor evaluation were found- particularly in hospitalised patients.

Biology and morphometric studies of beet armyworm, Spodoptera exigua (Hub.)

The study is mainly focused on the morphology of different stages i.e., egg, larvae, pupa and adult. The head capsule measurements (widest head width) were taken by use of Stereozoom binocular microscope. The beet armyworm undergoes 5 instars with a maximum and minimum head width of 0.26 ± 0.01 and 1.70 ± 0.05 mm respectively. The head capsule width of larval instars showed successive increase in a different ratio at each moult and did not follow regular geometrical progression (Dyar's law). Colour polymorphism was clearly observed in the fifth instar of S. exigua recording about 34 morphs with a range of colours i.e., green, black, pink and yellow being dominant with combination of colours and cannibalism also reported in the late instar stages. The total developmental period lasted for 32.38 ± 5.13 days.

Using Grandi's Series for Complex Analysis of Infinite Geometric Progression

Using Grandi's Series for Complex Analysis of Infinite Geometric Progression

Evaluation of Measurement Uncertainty from Pour Plate Method in Bacterial Enumeration in Water

The evaluation of measurement uncertainty (MU) is an important method for quantitative determinations derived by microbial cultivation, thus it could further improve the result accuracy. In this study, we aimed to evaluate the MU in total bacteria counts (TBC) in water. Experiments were carried out using Pour Plate Method. The bottom-up approach was used to access the MU of TBC and different mathematical models were set up based on microbial growth principles and test process. Two geometric and five non-geometric progression factors derived from fishbone diagram were selected in these models, especially considering the influence of the bacteria binary fission. The results showed that the calculated value of expanded uncertainty was between 82 and 120CFU/mL when the test result was 100CFU/mL with the 95% confidence level. The geometric progression factor had a greater impact on MU evaluation with almost 80% of contribution, whilst non-geometric progression factor dedicated 60%. Experimental procedures such as sample repeatability, reproducibility and inoculation time should be drawn more attention, thus the accuracy of results could be improved. These innovative models not only reasonable and reliable, but also easy to use. The achievements of this study illustrated that the MU evaluation method could also be applied for analyzing other microbial indicators in water.

АНАЛИЗ КРАЕВОЙ ЗАДАЧИ ДЛЯ УРАВНЕНИЯ ПУАССОНА

The mixed boundary value problem for the Poisson equation is considered in a bounded flat domain. The continuation of this problem through the boundary with the Dirichlet condition to a rectangular domain is carried out. Consideration of the continued problem in the operator form is proposed. To solve the continued problem, a method of iterative extensions is formulated in an operator form. The extended problem in operator form is considered on a finitedimensional subspace. To solve the previous problem, an iterative extension method is formulated in operator form on a finite-dimensional subspace. The continued problem is presented in matrix form. To solve the continued problem in matrix form, the method of iterative extensions in matrix form is formulated. It is shown that in the proposed versions of the method of iterative extensions, the relative errors converge in a rate that is stronger than the energy norm of the extended problem with the rate of geometric progression. The iterative parameters in these methods are selected using the minimum residual method. Conditions are indicated that are sufficient for the convergence of the applied iterative processes. An algorithm is written that implements the method of iterative extensions in matrix form. In this algorithm, the iterative parameters are automatically selected and the stopping criterion is indicated when the estimate of the required accuracy is reached. Examples of application of the method of iterative extensions for solving problems on a computer are given.

Computation for the Summation of Integers and Geometric Progression of Powers of Two

Computation for the Summation of Integers and Geometric Progression of Powers of Two

Вложение гомотета в выпуклый компакт: алгоритм и его сходимость

The problem of covering of a given convex compact set by a homothetic image of another convex compact set with a given homothety center is considered, the coefficient of homothety is calculated. The problem has an old history and is closely related to questions about the Chebyshev center, problems about translates, and other problems of computational geometry. Polyhedral approximation methods and other approximation methods do not work in a space of already moderate dimension (more than 5 on a PC). We propose an approach based on the application of the gradient projection method, which is much less sensitive to dimension than the approximation methods. We select classes of sets for which we can prove the linear convergence rate of the gradient method, i. e. convergence with the rate of a geometric progression with a positive ratio strictly less than 1. These sets must be strongly convex and have, in a certain sense, smoothness of the boundary.

Comparison behaviors of some scintillators for radiation shielding


 
 
 In this research, the photon interaction of NaI:Tl, LiI:Tl and CsI:Tl scintillators have been comparative studied. The photon interaction effectiveness of scintillators was investigated by determine mass attenuation coefficient (m) and half value layer (HVL) at photon energy ranging 1 keV – 100 GeV using WinXCom computer software program. Build–up factors were computed by Geometric Progression (G–P) fitting formula at energy ranging 15 keV – 15 MeV up to 40 mfp penetration depth. The result shown that, CsI:Tl scintillator was excellent at interacting with photons. This study indicated that CsI:Tl can be developed for radiation detectors and sensors.
 
 

Effects of WO3 on Radiation Shielding Properties of WO3–TeO2 Binary Tellurite Glass System

In this research, a series of (100–x)TeO2–xWO3 glass systems (where x = 0, 10, 20, 30, 40 and 50 mol%) have been simulated in terms of radiation shielding behaviors. The simulation of mass attenuation coefficients (μm), effective atomic numbers (Zeff) and effective electron densities (Nel) were calculated by WinXCom software program at energies ranging from 1 keV–100 GeV. The method of geometric progression (G–P) fitting has been used to calculate at wide energies ranging from 15 keV–15 MeV and up to 40 penetration depths (mfp) for buildup factors: exposure and energy absorption buildup factors (EBF and EABF). The simulated data reports that WO3 partial replacement of TeO2 in glass system (100–x)TeO2–xWO3 which increases behavior of radiation attenuation and 50TeO2–50WO3 showed the best shielding properties and potential to use as a transparent shielding material.

The Use of Logical Implication as an Indicator of Understanding the Concept of Number Sequences

This paper aims to characterise an indicator of the development of the number sequence scheme among students at the level of Compulsory Secondary Education (14-16 years old students). To do so, we use a scheme development proposed by the APOS theory to characterise students’ use of relations between mathematical elements when solving a mathematical task. We use a qualitative methodology and the data collection instruments are a written questionnaire and a semi-structured interview. In this work we show the questionnaire task that provides analytical expressions and ask students to determine which of them numbers sequences are. We find that students’ use of logical implication when solving tasks related to number sequences is an indicator of the development of the scheme. This indicator helps to locate the transition mechanisms between the levels of development of the number sequence scheme. Moreover, our research shows that arithmetic and geometric progressions play a key role as an indicator of the development of the number sequence scheme.

Security-driven distributed platforms for intellectual property resource provision - a case study of TSITE IP

In the information age, with the vigorous development of big data and artificial intelligence, intellectual property protection is an essential part of the current scientific and technological development. Intellectual property related data grows in a geometric progression, so the demand for IP data storage space is also increasing day by day. With the rise of cloud computing technology, intellectual property data distributed platforms based on cloud storage have also been produced one after another. Because the biggest feature of cloud storage is that storage is a service, it puts forward higher requirements for the intellectual property service industry. Firstly, it introduces the domestic intellectual property cloud platform services from the perspectives of government support, state-owned enterprises and private enterprises; Secondly, four typical distributed platforms provided by commercial resources are selected to introduce their operation modes, focusing on the problems faced by domestic intellectual property service modes; Secondly, it compares and discusses the current situation of domestic intellectual property distributed platforms; Then, aiming at the current domestic intellectual property service mode, taking tsite as an example, this paper puts forward the design and construction strategy of intellectual property protection, intellectual property operation service distributed platform and operation service mode under the background of information age.

Metric Discrepancy Results for Subsequences of Geometric Progressions

Metric Discrepancy Results for Subsequences of Geometric Progressions

Автоматизированная генерация каскадных моделей турбулентности методами компьютерной алгебры

Описана разработанная методика генерации уравнений каскадных моделей турбулентности с помощью систем компьютерной алгебры. Методика позволяет варьировать размер масштабной нелокальности модели, вид квадратичных законов сохранения и спектральных законов, знаменатель геометрической прогрессии масштабов. Ее использование позволяет быстро и безошибочно генерировать целые классы моделей. Может использоваться для разработки каскадных моделей гидродинамических, магнитогидродинамических и конвективных турбулентных систем. There is a great variety of shell turbulence models. Such models reproduce certain characteristics of turbulence. A model that could reproduce all turbulence regimes does not exist at the moment. Information about a particular model is contained in a set of persistent quantities, which are some quadratic forms of turbulent fields. These quadratic forms should be formal analogs of the exact conserved quantities. It is important to note that the main idea of Shell models presupposes a refusal to describe the geometric structure of movements. At the same time, it is well known that turbulent processes in spaces of two and three dimensions behave differently. Therefore, the provision of certain combinations of conserved quantities allows indirect introducing into the shell model the information about the dimension of the physical space in which the turbulent process develops. Purpose. The aim of this work was to create software tools that would quickly generate classes of models that satisfy one or another set of conservation laws. The choice of a specific model within these classes can then be specified using additional physical considerations, for example, the existence of a given probability distribution for the interaction of certain shells. Methods. The developed technique for generating equations of shell turbulence models is carried out using symbolic computation systems (computer algebra systems - CAS). Note that symbolic packages are used not for studying ready-made shell models, but for the automated generation of the equations of these models themselves. The technique allows varying the value of the scale nonlocality of the model, the form of the quadratic conservation laws and spectral laws, the denominator of the geometric progression of scales. It allows quickly and accurately generating the entire set of classes of the models. It can be used to develop shell models of hydrodynamic, magnetohydrodynamic and convective turbulent systems. Findings. It seems that the proposed technique will be useful for studying the properties of turbulence in the framework of cascade models

Gamma radiation shielding properties of recycled polyvinyl chloride composites reinforced with micro/nano-structured PbO and CuO particles

In this work, the γ-ray shielding characteristics of fabricated recycled polyvinyl chloride (rPVC) loaded with micro and nano fillers of PbO and CuO composites were investigated. The PbO/rPVC and CuO/rPVC composites were prepared by changing the percentage of injected materials (PbO and CuO) between 10% and 40% with additions by 10%. Gamma-ray attenuation properties, such as mass attenuation coefficients, linear attenuation coefficients and half-value layer for PbO and CuO-supported polymers were obtained in the energy range between 59.5 and 1408.0 keV using narrow beam transmission geometry. These experiments were carried out by using a HPGe detector and five standard radioactive sources [241Am, 133Ba, 137Cs, 60Co and 152Eu]. Moreover, equivalent atomic numbers and the exposure buildup factor (EBF) values for incident photon energy in the range from 0.015 MeV to 15 MeV were also calculated by Geometric Progression (G-P) method. The experimental results revealed that, the measured values of the linear attenuation coefficients of the PbO/rPVC and CuO/rPVC composites showed their dependence on the type and the concentration of the filler (either PbO or CuO) and also on the incident gamma ray energy. Increasing the filler weight fractions wt.% in the rPVC matrix, increases the linear attenuation coefficients of the composite and the improvement is more significant in case of PbO compared to CuO of the same filler wt.% at the same energy. The results also demonstrated an enhancement in the radiation protection behavior of rPVC composites due to the addition of PbO and CuO fillers as nano-sized particles.

A novel inverse methodology for the extraction of bulk elasto-plastic tensile properties of metals using spherical instrumented indentation

This paper presents an inverse methodology relying on finite element simulation based optimization to extract material constitutive parameters from a single spherical indentation, which are used to estimate its bulk true stress–true strain curve. Methods of this type usually assume that the tensile curve of the studied material can be modelled by a power-law involving, for example, Young’s modulus, yield stress and a hardening coefficient. Since the tensile behaviour of some materials cannot be adequately fitted by such models, our approach rather relies on an optimization procedure which extracts a group of six points on the true stress–true strain curve, distributed as per a geometric progression in the strain space, as well as the elastic modulus. A direct search black-box optimization algorithm is used and is shown to be capable of eluding local minima. A surrogate step is introduced in the methodology, which is a simplified version of the inverse problem, to find a suitable starting point. The performance of the method is first investigated in a numerical study in which the estimated true stress–true strain curves lie within a maximum error of 5.7% from the corresponding target tensile curves, for four materials with different hardening behaviours. The maximum errors on the extracted elastic modulus and yield stress are 0.5% and 11.1%, respectively. A study of the convergence behaviour of the proposed method demonstrates an expected significant increase in computational times as compared to when using a hardening model. Finally, an experimental application of the method to two materials with a plastic plateau leads to true stress–true strain curves estimations with average differences of 3.9% and 0.9% with the macroscopic experimental tensile curve, respectively. The method is thus found to be accurate even in the presence of modelling and experimental errors.

Gamma radiation shielding performance of CuxAg(1-x)-alloys: Experimental, theoretical and simulation results

Different types of photon shielding parameters such as total mass attenuation coefficient (μ/ρ), linear attenuation coefficients (μ), half value layers (HVL), mean free paths (MFP), effective atomic numbers (ZEff), energy absorption build-up factors (EABF), exposure build-up factors (EBF) and kerma relative to air were investigated for the fabricated Cu–Ag based alloys. The considered parameters were measured through gamma spectrometer equipped with HPGe detector in order to obtain the experimental attenuation coefficients and other related parameters at various photon energy in the energy range 59.5–1332.5 keV. The measured μ/ρ values were confirmed with WinXCOM database results. FLUKA and GEANT4 simulation codes were used to examine the compatibility of the experimental and WinXCOM database results with these simulation codes. The exposure buildup factors of the alloy samples were estimated with help of Geometric Progression fitting formula over photon energy 0.015–15 MeV up to 40 mfp penetration depth. The results revealed that the exhibited effectiveness of Cu0.2Ag0.8 alloys against high energetic photon radiations had a good performance than that of alternative absorbers such conventional concretes, glasses and some alloys. The results of the present survey can be quite useful for possible applications of such materials, especially in nuclear laboratory and reactor core design for preference of effective photon shielding materials.

Ground view factor computation model for bifacial photovoltaic collector field: uniform and non-uniform surfaces

The photovoltaic collectors in a field are subject to three types of solar radiation: direct, diffuse, and reflected irradiance. The reflected irradiance received by solar photovoltaic (PV) depends on the view factor from solar PV to the ground. This view factor component is dominant for bifacial PV due to additional reflected irradiance gain, which can be achieved from the module’s rear side.This paper proposes and verifies a finite element method based view factor computation model, which can handle both uniform and non-uniform ground surfaces. The unique contribution of this work is that it introduces a geometric progression based finite element mesh generation process that forms the quasi-uniform grid. The generated grid values are fitted into the computation model to calculate the view factor from bifacial photovoltaics to the ground, known as the ground view factor (GVF). The proposed computation model can achieve an accuracy of 99%. To keep accuracy at this level, the smallest element size of the coarse mesh should be within 0.1%–0.4% of surface width or length. Moreover, the geometric progression ratio of the fine and coarse mesh should be in the range of 1.001–1.002 and 1.01–1.04, respectively. The model is analysed under six different PV field variables: multiple reflective ground surfaces, the height of PV, tilted ground surface, PV position in the ground, length and width of the ground, and PV string length. For the different string sizes considered here, the view factor model’s computation time varies from 180 s to 257 min for the iteration size of 7.67 billion to 765 billion. The view factor computation model will contribute to analyse reflected irradiance at the rear side of bifacial PV, which is essential to predict the energy generation accurately. The proposed model is also beneficial for urban planning and addressing heat gain of the building-integrated PV system and energy usage.

Zagrożenia cyberbezpieczeństwa sektora ropy naftowej, gazu ziemnego i energii elektrycznej w kontekście ewolucji technologicznej

<p>The announcement of the state of global COVID-19 pandemic, in addition to the negative health, economic and social phenomena, has triggered a massive phenomenon of transferring most aspects of human life to cyberspace. The last decade has shown a geometric progression of the growth of cybersecurity incidents worldwide, including the energy sector. This paper is a conceptual work, while the basic research problem refers to the determination of the level and area of cybersecurity regulation of the energy sector in the supranational, EU and national systems. The fundamental thesis is to confirm the initial assumption of insufficient degree of legal protection of the network, both in the systems of international and internal law. The main purpose is to demonstrate critical legal solutions that will result in the future in critical and serious incidents in the energy supply chain, as well as energy logistics. The originality of the study is associated with the attempt to compile separate legal systems, the subject of regulation of which is cybersecurity of the energy sector. The cognitive value for practice is associated with the indication of a unified conceptual grid and the indication of the main regulations of the issue.</p>

Analysis of physical and mechanical traits and nuclear radiation transmission aspects of Gallium(III) trioxide constituting Bi2O3-B2O3 glasses

For five Ga2O3-Bi2O3-B2O3 composition glasses for improved Bi2O3 content at 25 to 65 mol% (10% continuously each time) at a fixed 10 mol% Ga2O3 amount, distinct physical and mechanical aspects and nuclear radiation attenuation factors were investigated. Increased Λ (optical basicity) values with a gradual Bi2O3 addition indicate studied samples’ improving basic character. Applying BC (bond compression) model key mechanical traits such as Ybc (Young’s modulus), Kbc (bulk modulus), S (shear modulus), L (longitudinal modulus), and σ (Poisson’s ratio) are evaluated where in all glasses 10Ga2O3-65Bi2O3-25B2O3 (mol%) sample exhibits superior elastic moduli. Enhanced Bi2O3 causes for compactness of the gallium borate network as ǹc (average cross-link density) improves from 2.3 to 3.4 indicating increased rigidity of glasses. Later, PHITS, FLUKA, and MCNPX codes are wielded to derive μ/ρ (mass attenuation coefficient) of all selected samples for photons having energy ranging from 15 KeV to 15 MeV. Simulated μ/ρ quantities exactitude is tested via Phy-X/PSD and WinXCOM programs’ μ/ρ results and identified a fairly good harmony among them. With photon energy, MFP (mean free path), TVL (tenth-value layer), and HVL (half-value layer) values variations show a similar tendency and against the trend which noticed for μ/ρ and μ (linear attenuation coefficient) values. 10Ga2O3-65Bi2O3-25B2O3 (mol%) sample’s MFP and HVL are correlated with five commercial γ-ray glass shields’ respective values at 1.25 MeV, 0.662 MeV (137Cs), and 0.2 MeV energies. Further, Zeq (equivalent atomic number) and using G–P (geometric progression) fitting approach for ten individual PDs (penetration depths) within 1–40 mfp range at 15 – 15 × 103 KeV energy region BUFs (buildup factors) were estimated. Attained RPE (radiation protection efficiency) findings attest all chosen Ga2O3-Bi2O3-B2O3 glasses’ competent absorption capacity for lower energy photons. Next, α-particles and protons MSPs (mass stopping powers), i.e. ΨA and ΨP and PRs (projected ranges), i.e. ΦA and ΦP by utilizing SRIM code as well as for electrons MSPs (ΨE) and CSDA (continuous slowing‐down approximation) ranges by ESTAR database have been calculated within 15–15 × 103 KeV KE (kinetic energy) range. Also, ΣR (fast neutron removal cross-section) and for 0.253 × 10–4 KeV energy neutrons σT (total cross-section) and SP (shielding percentage) values were approximated. With Bi2O3 addition, realized ΣR is changed at 0.1161–0.1213 cm−1 extent. For thermal neutrons absorption, 10Ga2O3-25Bi2O3-65B2O3 (mol%) glass shows larger σT (=17.534 cm−1) and at any considered thickness higher SP whereas 10Ga2O3-65Bi2O3-25B2O3 (mol%) (lead-free) glass has better attenuating features for photons affirming the incorporated Bi2O3 favorable effect.

Scientific and Practical Approaches to Improving Noise Muffler Designs of Piston Internal Combustion Engines Based on Theory of Numbers

A methodological method based on the use of the theory of preferred numbers has been proposed in order to improve the most important parameters of the working bodies of noise mufflers. As a result of many years of scientific research, the authors have established a previously unknown theoretical relationship between the main series of preferred numbers, golden ratio and Fibonacci series numbers. A new direction in the development of number theory has been considered in the paper, its classification has been compiled, including the geometric theory of numbers, preferred numbers, containing a new basic series of preferred numbers using the Fibonacci sequence. New formulas have been obtained to determine the denominators of geometric progressions for the series of preferred numbers and the area of a circle. Determining the area of a circle using the new formula allows to get more accurate values. A new formula for determining the circumference of a circle has also been derived. The designs of perforated partitions have been developed, in which the laws of the new basic series of preferred numbers are used. Determining the area of a circle using the new formula allows you to get more accurate values. A new formula for determining the circumference of a circle is also obtained. The designs of perforated partitions have been developed, in which the regularities of the new basic series of preferred numbers have been used. A calculated substantiation of the main geometric and structural dimensions of noise mufflers is given using a mathematical model of a perforated golden partition and new basic series of preferred numbers, which allow to obtain a noise muffler design that has the lowest possible aerodynamic resistance with the maximum possible reduction in the noise level of exhaust gases from internal combustion engines. An innovative model of a noise muffler for reciprocating internal combustion engines with improved hydraulic and acoustic characteristics based on the theory of numbers is proposed in the paper. The theory of preferred numbers applies to any technical device.