Geometric Progression Research Articles

TeO2–B2O3–ZnO–La2O3 glasses: γ-ray and neutron attenuation characteristics analysis by WinXCOM program, MCNP5, Geant4, and Penelope simulation codes

γ-ray, fast and thermal neutrons shielding features for five Pb-free {[(TeO2)0.70(B2O3)0.30]0.7 (ZnO)0.30}(1-x)(La2O3)x (x = 0.01, 0.02, 0.03, 0.04, and 0.05 mol%) glasses have been inspected in this work. For all samples, within the photon energy range of 0.015–15 MeV, linear attenuation coefficients (μ) and mass attenuation coefficients (μ/ρ) were estimated using WinXCOM program (theoretical approach), and obtained μ/ρ values are in fine agreement with computed μ/ρ results of respective MCNP5, Geant4, and Penelope codes. By utilizing μ/ρ values of WinXCOM, γ-ray attenuation parameters like effective atomic number (Zeff), effective electron density (Neff), half-value layer (HVL), and mean free path (MFP) were assessed within 0.015–15 MeV photon energy range, for all samples. Additionally, exposure buildup factors (EBFs) and energy absorption buildup factors (EABFs) were calculated for all samples by applying a five parameter geometric progression (G‒P) fitting method as a function of various penetration depths (1, 5, 10, 15, 20, 25, 30, 35, and 40 mfp) within 0.015–15 MeV photon energy range. The derived radiation protection efficiency (RPE) results indicate all samples' effective attenuation competence for lower energy γ-rays. Among all glasses, 46.55TeO2-19.95B2O3-28.5ZnO–5La2O3 (mol%) sample, by having relatively bigger μ/ρ and Zeff, minimal HVL and MFP, and lowest EBF and EABF, endorse its' excellent γ-ray shielding effectiveness. Further, neutron shielding parameters such as macroscopic removal cross-section for fast neutrons (ΣR), coherent and incoherent scattering cross-sections (σcs & σics), absorption cross-section (σA), and total cross-section (σT) for thermal neutrons were explored. By using the Geant4 code, ‘σT’ values have been deduced within 10−4‒10−8 MeV neutron energy range. The 46.55TeO2-19.95B2O3-28.5ZnO–5La2O3 (mol%) glass owns relatively larger ΣR (0.1474 cm−1) for fast neutrons attenuation and ‘σT’ (10.1444 cm−1 at 0.0253 eV neutron energy, 15.9824 cm−1 → 0.551 cm−1 from 1 × 10−8 MeV →1 × 10−4 MeV neutron energy) for thermal neutrons absorption, respectively, revealing its' superior neutrons shielding ability.

White and some colored marbles as alternative radiation shielding materials for applications

ABSTRACT In this paper, the radiation shielding parameters such as linear attenuation coefficients (LAC, µ), mass attenuation coefficients (MAC, µ/ρ), effective atomic numbers (Zeff), effective electron densities (Neff), half value of layers (HVL), mean free paths (MFP) and buildup factors (exposure (EBF) and energy absorption (EABF)) were investigated for cream (M1), pink (M2), white (M3), maroon (M4) and green (M5) marbles. Attenuation coefficients were measured in the energy region 31.18–661.66 keV photon energies. The values of Zeff and Neff were then calculated using these coefficients with logarithmic interpolation method, and HVLs and MFPs were calculated using the values of LAC of marble samples at the same photon energies. The experimental results were compared with the theoretical values obtained from WinXCom program, and good agreements were observed between the experimental and theoretical results. HVLs and MFPs of all marble samples were compared with those of some concretes, glasses and commercial radiation shielding glasses (SCHOTT Co.). The studied marbles were better radiation shielding materials than standard shielding concretes due to lower HVL and MFP values lower than the ordinary concrete. Finally, EBFs and EABFs of the marbles were calculated in the energy region 0.015–1 MeV up to penetration depths of 40 mfps by Geometric Progression method (G-P), and the results were discussed in terms of photon energies and chemical compositions of the marbles.

The impact of Gd2O3 on nuclear safety proficiencies of TeO2–ZnO–Nb2O5 glasses: A GEANT4 Monte Carlo study

This work was carried out to specify the effect of Gd2O3 on the gamma and neutron radiation shielding capacities of tellurite rich glasses with 75TeO2+15ZnO+(10-x)Nb2O5+xGd2O3 (TZNG), where (x = 0, 1, 1.5, 2 and 2.5 mol%) nominal composition. The mass attenuation coefficients (μ/ρ) of the studied glasses were acquired with GEANT4 Monte Carlo codes and the results were found to match the theoretical Phy-X values. Next, the variables of Effective atomic number (Zeff), Half Value Layer (HVL) and Mean Free Path (MFP) were calculated employing μ/ρ values. According to the corollaries, the increment of Gd2O3 insertion to the tellurite based glasses was enhanced the μρ and Zeff values for total photon, electron, proton and alpha interactions whereas it was dropped the HVL and MFP values. It is also observed that the total stopping powers of the glasses for electron interaction were declined. The geometric progression (GP) approximation was employed to determine the exposure buildup factor (EBF) for the proposed glasses. The EBFs showed the lowest values for TZNG-E glass with 2.5% mole Gd2O3 addition. Finally, the fast neutron reduction capacity of the TZNG glasses was surveyed by calculating the effective removal cross-sections (ΣR) of the glasses. It is determined that the ΣR values increased with enhancing Gd2O3 content since the addition of Gd2O3 increased the glass density. Consequently, the TZNG-E glass with the highest Gd2O3 additive is the more skillful nominee for gamma-ray and neutron security applications among the investigated glasses.

Investigation of some nuclear engineering materials in terms of gamma ray buildup factors at experimental energies used in nuclear physics experiments

ABSTRACT In shielding studies, the gamma ray buildup factor is referred to an attenuation correction when the narrow beam transmission geometry conditions are not met. This is the case if there is a beam divergence and a considerably thick material is used as shield. In the present work, a linear logarithmic interpolation based on five parameter geometric progression (G-P) fitting method was used to calculate energy absorption (EABF) and exposure buildup factors (EBF) at discrete energies for some standard nuclear engineering materials (SNEM) such as concrete, Pb glass, brass, bronze and stainless steel, and for some recently developed shielding alloys and glasses. Calculations were made at different penetration depths (1–20 mfp) using photons emitted from the standard radioactive sources such as 133Ba (0.356 MeV), 137Cs (0.662 MeV), 60Co (1.173, 1.332 MeV) and 22Na (0.511, 1.275 MeV). Results have been compared with MCNP6.1 Monte Carlo simulation code wherever possible and a reasonable agreement (Relative difference around 10% up to 10 mfp except for Pb glass) has been achieved. Results also showed that the gamma ray buildup correction is necessarily required since buildup factors are greater than unity even at lowest penetration depth, i.e. 1 mfp. The reported data on EABF and EBF for the energy values of radioactive sources may be of practical use in shielding calculations and estimations.

Relationship between melting-conditions and gamma shielding performance of fluoro-sulfo-phosphate (FPS) glass systems: A comparative investigation

To assess the relationship between gamma ray shielding performance and glass-melting conditions, an extensive investigation was performed on different types of fluoro-sulfo-phosphate (FPS) glasses. Four different FPS glasses melted in Al and Pt crucibles were modeled in MCNPX (version 2.6.0) general purpose Monte Carlo code. For this aim, a gamma-ray transmission setup has been modeled with essential simulation equipment. The mass attenuation coefficients for each glass sample in different melting-condition were determined. The obtained mass attenuation coefficients were utilized for determination of Half Value Layers (HVL) and mean free paths (mfp). Next, energy absorption buildup factors (EABF) and exposure buildup factors (EBF) of investigated FPS glasses were determined by using geometric-progression (G-P) fitting method. To evaluate the effect of glass-melting conditions on fast neutrons, effective removal cross sections of FPS glasses were calculated. Finally, an extensive comparison between the superior samples of FPS glasses melted in Al and Pt crucibles were performed. The results showed that GPT-4 sample melted in Pt crucible has relatively higher radiation shielding properties than GAL-2 sample which melted in Al crucible. In addition to material additive, the results showed that even glass-melting conditions has a significant impact on radiation shielding properties of glass material. It can be concluded that, in addition to the most effective material additives into glass structures to improve radiation shielding performances, providing them in the most favorable melting-conditions can provide a versatile improvement.

Investigation of the gamma ray shielding properties for polyvinyl chloride reinforced with chalcocite and hematite minerals.

Polyvinyl chloride (PVC) is the most widely produced synthetic plastic polymer in the world: it has a variety of applications due to its low cost, elasticity, light weight, good mechanical characteristics and corrosion resistance. In order to protect living beings from harmful radiation such as gamma rays, novel low-cost chalcocite and hematite-based PVCs were fabricated for shielding purposes. The mass attenuation coefficient μm for various fabricated hematite and chalcocite-based PVCs was calculated using MCNP-5 code. The results were compared with the values calculated theoretically using XCOM software between 0.015 and 15 MeV. Moreover, the simulated μm parameter for chalcocite/PVC and hematite/PVC was used to calculate other shielding factors, such as the half value layer (HVL), the mean free path (MFP) effective atomic number Zeff, the geometric-progress (G-P) fitting parameters and the exposure buildup factor (EBF). The simulated data of μm for all composites is comparable to that obtained from a theoretical calculation. The results showed that the addition of hematite and chalcocite enhance the μm of PVC polymers. We also found that the μm of chalcocite/PVC is higher than that of hematite/PVC due to the copper content in the former.

Novel harmonic elimination strategy based on Multi-Objective Grey Wolf Optimizer to ameliorate voltage quality of odd-nary multi-level structure

In this paper, a novel Asymmetrical Multi-Level Inverter (AMLI) is suggested to solve the voltage quality problem. The suggested AMLI has been constructed based on series connection of sub-AMLIs to create a high-step quasi-sinusoidal voltage with considering few semiconductor switches. The ladder capacitors of sub-AMLI have been clamped to the H-bridge structure via several bi-directional switches. Based on an innovative geometric progression for DC power supplies of AMLI, it can operate as so-called odd-nary AMLI. It has effectually created a quasi-sinusoidal with high steps i.e., low Total Harmonic Distortion (THD) with respect to low number of switches. The performance of suggested AMLI has been thoroughly compared with other inventive asymmetrical and symmetrical multilevel inverters. Following that, scission-style harmonic elimination based on Pulse Width Modulation (PWM) is introduced to enhance voltage quality of AMLI. Three prominent criterions related to voltage quality i.e., desired fundamental component, elimination of third harmonic and reduction of THD have been assigned as objective functions of optimization problem. Considering the multi-objective nature of the optimization problem, non-dominated sorting Multi-Objective Grey Wolf Optimizer (MOGWO) has been implemented to solve the optimization problem, and then compared with Non-dominated Sorting Genetic Algorithm II (NSGA-II). To sum up, the relevant analytical studies along with both the simulation and experimental results have transparently validated the performance of suggested AMLI. Also, the voltage quality problem using MOGWO-based scission-style harmonic elimination strategy has been well approved.

The reliability of the Titius–Bode relation and its implications for the search for exoplanets

Abstract The major semiaxes of the planets in our solar system obey a simple geometric progression known as the Titius–Bode (TB) relation, whose physical origin remains disputed. It has been shown that the exoplanetary systems follow a similar (but not identical) progression of the form $a_n= a_0$ e$^{bn}$, where $a_0$ and b are constants to be determined for each system. Since its formulation, the TB relation has proved to be highly predictive in our solar system. Using data from 27 exoplanetary systems with five or more planets and applying a proposed method, we conclude that reliable TB-like fits can be obtained for systems with at least four planets and that the precision of the TB relation is $78\%$. By means of a statistical test we show that the periods of planets in real exoplanetary systems are not consistent with a random distribution. Rather, they show signs that their configuration is shaped by their mutual interactions.

CONSTRUCTION METHOD OF “CELL-CUBE” SPATIO-TEMPORAL DATA MODEL FOR BIG DATA

Abstract. In recent years, with high accuracy, high frequency, considerable coverage of remote sensing images, map tiles, video surveillance, web crawlers, social networking platforms and other types of spatiotemporal data have exploded in geometric progression. Human society has come into the era of big data in time and space. In view of the characteristics of multi-attribute, multi-dimensional, multisource and heterogeneous spatiotemporal big data, how to make use of the emerging information technology means, combined with the geographic information data analysis means, the rapid mining and utilization of spatiotemporal big data has become a key problem to be solved. Built on the background of spatiotemporal big data and the process of geospatial cognition, this paper proposes a "cell-cube" spatiotemporal object data model. This paper constructs a model system of geo-spatiotemporal big data from the aspects of data organization, data storage and data partition, and abstracts the geo-space into an infinite number of geo-cells, and the adjacent geo-cells gather around the core cells to form geographical clusters, and the geographical clusters with similar attributes are clustered into geographical blocks. At the level of data organization, the spatial and temporal characteristics of structured data and unstructured data are considered as organizational dimensions, and a multi-factor extended cube data model is proposed. In the aspect of data storage, the organization model is further abstracted into the cell-cube structure of distributed data warehouse, and then the spatiotemporal data is stored uniformly. At the level of data segmentation, the mathematical table and space calculation method of multi-feature extended cube are proposed, and the geographical cell data division model based on connection is established. It solves the organization and management problem of spatiotemporal big data, provides a more complete data organization framework and solution for the application of geo-spatiotemporal big data, and promotes the development of deep mining of spatiotemporal extensive data in GIS. And to achieve space-time big data in the geographical space microscopic and the macroscopic unification cognition.

Design and Implementation of a Digital Dual Orthogonal Outputs Chaotic Oscillator

Discrete time dynamical chaotic systems obey a set of recurrence equations involving one or more variables. Many chaotic maps have been proposed. None that simultaneously provides two sine–cosine outputs has stationary mean and standard deviation, or is quite robust with respect to the data format used in the hardware implementation. Here, we propose a chaotic oscillator based on a complex phasor whose angular argument evolves according to a geometric progression that is independent of the instantaneous amplitude. In order to maintain the oscillations, the phasor magnitude is normalized at each iteration using an approximation factor. The statistical characteristics of this oscillator are stationary in the short term, and do not depend on the initial conditions. The mean and standard deviation of the two orthogonal sequences quickly approach 0 and 1 / 2 , respectively. The resulting distribution is similar to that of a digital sine with a constant angular step. We also present an FPGA architecture and its implementation results. This oscillator can be used in modulation schemes, such as the chaotic shift keying one or for data and image encryption. Finally, we show an original application that exploits the orthogonality of the two chaotic signals for the simultaneous encryption of two digital images.

Improvement of radiation shielding properties of some tellurovanadate based glasses

In this research, various valuable features having discriminating characteristics, namely the mass attenuation coefficient (μm), effective atomic number (Zeff), energy absorption buildup factor (EABF), neutron removal cross-section (ΣR), mass stopping power (MSP) and projected range values were studied in the energy range of 0.015–15 MeV for vanado-telluride glass network had heavy or transition metal oxides. μm for the different glass series were calculated using Monte Carlo code. Besides, the EABFs were also calculated using geometric progression fitting technique. The proton and alpha MSP as well as projected range values were computed using SRIM code. Moreover, the generated μm by MCNPX for the different glass series was compared to the outputs of XMuDat and XCOM. The analysis indicated that the glass sample VTBi6 had good magnitudes of μm and the lowest values of half value layer, i.e. the sample had the superior radiation shielding properties among the explored glasses.

Novel vanadyl lead-phosphate glasses: P2O5–PbO–ZnO[sbnd]Na2O–V2O5: Synthesis, optical, physical and gamma photon attenuation properties

A novel glass of Vanadyl lead-phosphate with the chemical formula P2O5–(40-x) PbO–ZnONa2O–xV2O5 where x = 0, 0.2, 0.4, 0.8, 1.5, and 2 wt% have been synthesized using melt-quenching method. The amorphous nature of the prepared glasses was examined via XRD spectra. UV–vis spectra were recorded in the range of 190–1100 nm wavelength. The optical energy band gaps and refractive index via Tauc's model, absorbance spectrum fitting (ASF), and the first derivation of the absorption spectrum fitting (DASF) have been determined for all glasses. Gamma-photons shielding capability of the fabricated glasses have been evaluated using MCNP-5 code. Furthermore, different shielding factors were calculated. The geometric progress fitting parameters, exposure and energy absorption buildup factors were also computed using newly created program Phys-X/PSD. The results show that energy gaps for all glasses were close together, but the index of refraction was high. In addition, the shielding properties of the fabricated glasses decreases with increase the vanadium pentoxide content in the fabricated samples. The glasses without vanadium pentoxide had the best shielding capacity among the synthesized vanadyl lead-phosphate glasses. The buildup factors were observed to decrease with increase the vanadium pentoxide. Comparison of the synthesized glasses with standard references material and previously synthesized glasses showed that the Vanadyl lead phosphate glasses can be used as a radiation shielding material.

Structural, mechanical and radiation shielding properties of newly developed tungsten lithium borate glasses: An experimental study

The melt quench technique was used to fabricate the (25-x)Li2O-75B2O3-xWO3 (x = 1, 3, 5 and 7.5 mol%). The mass attenuation coefficients (μm) of the studied glasses were obtained by using the Gamma (γ) rays spectrometer (CANBERRA photo multiplier tube base model 802) which includes a detector (3 × 3 in.) NaI(Tl) crystal and the multichannel analyzer. The measured values have been compared with XCOM program at selected photon energies. Geometric progression (G–P) fitting method has been used to calculate the exposure build-up factor (EBF) and energy absorption build-up factor (EABF) in the energy range of 0.015–15 MeV. Moreover, EBF and EABF values have been applied to compute the specific fraction of absorbed energy (Sfae) and relative dose distribution (Rdd). The pulse-echo technique has been used to measure the elastic moduli for glass samples. The TBL4 glass sample shows the highest μm, effective atomic number (Zeff) and Young moduli values and lowest half value layer (HVL), mean free path (MFP), EBF, EABF, Sfae and Rdd values. The results of this investigations revealed that the fabricated TBL4 glass sample could be potentially utilized as an efficient and desirable kind of glass material as gamma shield to reduce the deleterious effects of radiation.

On quadratic progression sequences on smooth plane curves

We study the arithmetic (geometric) progressions in the x-coordinates of quadratic points on smooth planar curves defined over a number field k. Unless the curve is hyperelliptic, we prove that these progressions must be finite. We, moreover, show that the arithmetic gonality of the curve determines the infinitude of these progressions in the set of k‾-points with field of definition of degree at most n, n≥3.

MELAWAN TEORI OTENTISITAS HADITS

In the scientific tradition, the study of Islam in the orientalisme is not stagnant, but has experienced development. This article focuses on the arguments of Nabia Abbot's argument and theory in refuting Goldziher's theory of the study of hadith. The author calls it a counter discourse. At least this article found three outlines of Nabia Abbot's rebuttal to Goldziher: (a) the theory of authenticity, Goldziher said the hadith was not an authentic report but a form of doctrinal reflection during the first two centuries after the prophet Muhammad. Abbot denies he views this view as wrong because it ignores historical evidence. For Abbot the hadith had appeared early in the century, as evidenced by the oral hadith of Muawwiyah (d. 60/680), Marwan (d. 65/684) and Abd Malik bin Marwan (d. 86/705). (b) Isnad's theory. Goldziher mentioned that the growth of the hadith in the third century Hijriyah was due to the history of history and the fabrication of the hadith. Nabia Abbott has argued with the argument that the number of hadiths is due to the growth of the hadith path in the geometric progression, not forgery. (c) Hadith Writing Theory, Goldziher said that the early hadith did not have a written reference, only oral, so the hadith in the form of thoughts could not be verified. Abbot denied, he said, that the beginning had been carried out in the narration and the modification of the hadith. Besides there are a number of books of hadith as in the text of Hammâm b. Munabbih (40-131 / 132 H).

Modelling the COVID-19 Epidemic As a Geometric Progression – Application to Nigeria, United Kingdom & Other Select Countries

This article applies a geometric progression (GP) in modelling the spread of COVID-19 using data from Nigeria as a case study and explores application of a Gt

A single-vendor single-buyer supply chain model with price and green sensitive demand under batch shipment policy and planned backorder

This paper considers a two-level supply chain which consists of a single-vendor and a single-buyer. The vendor produces a single product in lot and transfers the whole lot to the buyer in a combination of equal and unequal sized batches. All unequal sized batches are in a geometric progression with a fixed common ratio. Consumer's demand is sensitive to the retail price and greening improvement level of the product. At the buyer, planned shortages are allowed and are completely backlogged. Assuming that the buyer has higher decision power than the vendor, we develop non-coordinated decentralised model and coordinated model with cost sharing contract, and the integrated centralised model. The numerical results show that the cost sharing contract gives an impressive improvement in the profits of both the vendor and the buyer over their profits in the non-coordinated system. A sensitivity analysis is performed to explore how the changes in the key model-parameters effect the optimal profits of the vendor and the buyer and the whole supply chain.

An Overview of Challenges of Unemployment in South Sudan, Theoretical and Empirical Review

The problem of unemployment in South Sudan is a national issue that should be handled with care. The rate of unemployment in South Sudan since 2011 has been growing in a geometric progression. Its source could be traced to the diversification of South Sudan economy into oil sector, agriculture, construction etc. that provides less employment opportunity to its labor force. The main aim of this article is to illustrate the major challenges of unemployed people in South Sudan and around the world in general, through various studies conducted in the country and around the globe. The performance and problems of government functioning varies regionally based on the implication of system by state governments and the central, hence this article would give a holistic picture of major problems in creating employment opportunity in the country. The assessment of previous studies represents, corruption, less efficiency in the day to day functioning of the public, private and bi-lateral bodies in formulating and implementing policies to regulate in reducing unemployment in the country.

ОПРЕДЕЛЕНИЕ ГЛУБИНЫ БЕЗНАПОРНОГО ПОТОКА ПРИ НЕРАВНОМЕРНОМ РЕЖИМЕ ТЕЧЕНИЯ В ПРИЗМАТИЧЕСКИХ РУСЛАХ

The aim of the work is to analyze the existing method of calculating the spillway from the depth of the free flow under uneven mode in prismatic channels with a slowly changing movement and to develop a method of calculations that allows applying it to any flows in a prismatic channel without using any special tables. The existing methods for calculating flow parameters are based on the use of the Chesy formula to determine the flow consumption with a slowly changing water movement. At the same time, there is a V.I. Charnomsky’s method of direct calculation of the flow parameters from the energy equation without limiting the value of the channel slope. The disadvantage of this method is a possibility to solve the energy equation by the method of sequential approximation since the flow energy equation includes two variables, the flow depth and the distance between the sections. To eliminate this difficulty, it is proposed to determine the distance between the depths that make up the geometric progression on the considered part of the channel which allows calculating parameters of the free fl ow surface for any channel slopes and hydraulic flow modes without to special tables.

The role of primary care in the Brazilian healthcare system: limits and possibilities for fighting COVID-19.

On March 12, 2020, the World Health Organization (WHO) declared the disease caused by the novel coronavirus (SARS-CoV-2) a pandemic. The infection (COVID-19) is more transmissible and has a higher case-fatality rate than influenza, estimated at some 14 times greater. The high infection rate, with each case infecting 2 to 3 other individuals on average, leads to the epidemic’s expansion in geometric progression. In Brazil, where community transmission throughout the country was declared on March 20, more than 147,000 cases and 10,000 deaths from COVID-19 had been confirmed as of May 9, 2020. COVID-19 treatment aims to meet the patients’ needs in different phases of the infection and throughout the spectrum of severity, in a line of care that ranges from monitoring mild cases in isolation at home, with instructions on management of symptoms and the identification of early warning signs, to admission in intensive care units (ICUs) and post-discharge rehabilitation. Mitigation of risks of infection to health professionals and other patients should guide the choice of the best strategies for organizing the health care system to meet these needs.