Geometric Progression Research Articles

Assessment of gamma-rays and fast neutron beam attenuation features of Er2O3-doped B2O3–ZnO–Bi2O3 glasses using XCOM and simulation codes (MCNP5 and Geant4)

The authors aim to study the gamma-rays and neutron beam shielding capabilities of zinc bismuth borate glasses doped with erbium ions. Mass attenuation coefficient (MAC) (μ/ρ) values were computed employing XCOM and two different simulation codes, MCNP5 and Geant4, within 0.015–15 MeV photon energy, which showed good agreement within the derived values. The effective atomic number (Zeff), electron density (Ne), half-value layer (HVL) and mean free path (MFP) values were derived using MAC values. To account on the scattering effects of photons from the samples, exposure buildup factor (EBF) were determined, applying geometric progression (G-P) method, within 0.015–15 MeV photon energy and penetration depth of 1–40 mfp (intervals: 1, 5, 10, 15, and 40 mfp). The high MAC, Zeff values and low HVL, MFP values of 16.93B2O3‒22.57ZnO‒60Bi2O3‒0.5Er2O3 (mol%) glass optimized its shielding effects against gamma-rays. The macroscopic effective removal cross-section for fast neutron (ΣR) values lie within the range of 0.1142–0.1232 cm−1 for the selected Er2O3-doped samples. The studied parameters of the experimented glasses revealed their dominant radiation shielding features compared to commercial shielding glasses, concretes, and alloys.

Metric discrepancy results for geometric progressions perturbed by irrational rotations

For $$\theta \in (-\infty , -1)\cup (1, \infty )$$ and for almost every x, it is known that the sequence $$\{\theta ^k x\}$$ is uniformly distributed modulo 1. The speed of convergence sensitively depends on the algebraic nature of $${\theta}$$. In this paper we prove that such dependence vanishes if we perturb the sequence by adding the irrational rotation $$\{\kappa\gamma\}$$. The speed becomes identical with that of the sequence of uniformly distributed independent random variables.

Gamma ray shielding effectiveness of the Portland cement pastes doped with brass-copper: An experimental study

This work focused to survey the radiation shielding properties of cement paste samples doped without and with Cu 10% and brass 5, 10, 15, 20% wt. Molar volume of the cement samples was determined by the densities obtained with the Archimedes principle. Transmission measurements of the samples were achieved using an Ultra Ge detector at 81, 276, 302, 356, 383 keV photon energies emitted from the Ba-133 radioactive point source. The essential parameters; mass attenuation coefficient (μ/ρ), half value layer (HVL) and effective atomic number (Zeff), for the cement samples were obtained experimentally and classed with the theoretical outcomes computed by using WinXCOM program. Zeff and effective electron density (Nel) were also assessed for cement samples in the energy range 1 keV-100 GeV by utilizing theoretical results. Additionally, a five parameter geometric progression (G-P) fitting approximation was used to estimate EBF at 0.015-15 MeV photon energies and penetration depths (up to 40 mfp). The results indicate that, smallest HVL and Nel and largest μ/ρ values belong to 20% brass doped sample. The highest Zeff values were found for brass 20% containing sample, as un-doped Portland cement possesses the lowest values of Zeff. The smallest EBF values are observed for high proportion of brass doped cement samples. It is concluded from the results that the cement paste samples containing brass have remarkable and comparable shielding competence.

The effect of different concentrations of nanometals (Fe and Cu) on the activity of antioxidant protection of Solánum tuberósum L

At present, rapid development of nanotechnology requires assessment of their effects on plants, interaction with plant cells and concentration dependence. The degree of toxicity of nanocompounds affecting plants depends on physical properties of nanoparticles (dimension, shape, catalytic activity, concentration). The research objects were Tarasov potato tubers treated in Fe° (90-110 Nm) and Cu° (50-110 Nm) NPs at four concentrations with a geometric progression (0,0125; 0,025; 0.05 and 0.1 M). The aim of the research is to study the effect of iron and copper metals on the activity of Solánumtuberósum L. antioxidant protection of plants. The Fe0 NPs caused oxidative stress and decreased the content of MD (1.3 - 26.7%) and phenolic compounds with a simultaneous increase in peroxidase. After exposure to Cu0 nanoparticles, there was a redox imbalance in the roots and sprouts which manifested itself as a decrease in CAT (7.4-36.7%) and FS (19.1 - 34.0%) activity with a sharp increase in the content of MD and an increase in peroxidase activity.

Effect of iron, copper and molybdenum nanoparticles on morphometric parameters of Solanum tuberosum L. plants

Over the past decade, nanotechnology caused the need for rigorous research on ultrafine nanomaterials which enhance productivity and quality of agricultural products. However, most studies are controversial; it is difficult to compare doses of nanoparticles and types of plants. In the experiment, nanoparticles of Fe (90–110 nm), Cu (50–110 nm) and Mo (100–120 nm) at four concentrations with a geometric progression were used to treat potato tubers. Germination energy was determined according to GOST 12038-84; the content of photosynthetic pigments was determined according to the method by N. D. Smashevsky (2011), phytotoxicity was determined according to the method by Kazev K. (2013). Thus, the data indicate that treatment of Solánum tuberósum L. tubers with iron nanoparticles stimulated the growth of the length of sprouts (55.1% and 21.4%), roots (34.4% and 12.5%) and chlorophyll a (57 - 98%) at a concentration of 0.0125 … 0.025 M. At the same time, copper and molybdenum nanoparticles are ineffective by the significance of their effects on plants.

The effect of nanoparticles of iron, copper and molybdenum on the morphometric parameters of plants Solanum tuberosum L

Over the past decade, nanotechnology has led to the need for rigorous research on ultrafine nanomaterials, which increase productivity and quality of agricultural products. However, most studies are extremely controversial regarding the effect of nanomaterials on the seed germination rate, the growth of the roots and the aerial parts of plants, or it is difficult to compare both in doses and dimensions of nanoparticles, and in types of plants. In the experiment, nanoparticles of Fe (90-110 nm), Cu (50-110 nm) and Mo (100-120 nm) in 4 concentrations with a geometric progression were used. Germination energy and germination were determined according to GOST 12038-84, the content of photosynthetic pigments according to the method of N. D. Smashevsky (2011), phytotoxicity according to the method of Kazeev K. (2003). Thus, the data obtained indicate that the treatment of Solánum tuberósum L. tubers with iron nanoparticles stimulated the growth of sprout length (55.1% and 21.4%), roots (34.4% and 12.5%) and the content of chlorophyll a (57 - 98%) relative to the control at a concentration of 0.0125 … 0.025 M. At the same time, the nanoparticles of copper and molybdenum by the significance of their effects on plants turned out to be ineffective.

EFFECTIVENESS OF CLASSIFICATION METHOD AND COLOR SYMBOL SCHEME ON CHOROPLETH MAP OF POPULATION DENSITY IN SPECIAL REGION OF YOGYAKARTA

Abstract. The need for presenting information in maps is increasingly high in various scientific fields. All scientific fields need to present effective data for decision making. Good decision making based on maps requires good understanding but not all scientific fields are familiar with using maps. Supporting factors for easy maps to understand are classification method and color symbol scheme. The purpose of this study was to select and test the classification method and the most effective color symbol scheme for mapping population density in the Special Region of Yogyakarta. The classification methods used in this study are constant interval, arithmetic progression, geometric progression, quantile, standard deviation and dispersal graph. The effectiveness test method for the most effective classification method is the proportion assessment. The color symbol scheme used in this study is a sequential color scheme, diverging color schemes, Corel Draw color schemes and color symbol schemes provided in ArcMap 10.3 software. The effectiveness test method for the most effective color symbol scheme is conventional eye tracking. The results showed that according to the proportion test the most effective classification method was the arithmetic interval classification method with results of 0.26. The most effective color symbol scheme in accordance with the effectiveness test using the conventional eye tracking method shows that the most effective color symbol scheme is a diverging color scheme. The important aspects to consider are average answering duration of 8.15 seconds, the accuracy of the answer is 98.9%, and easiness level of symbolization readings is 341. This research can be one of the references on the most effective classification method and reference regarding the selection of the most effective color symbol scheme on Choropleth Map of Population Density in Special Region of Yogyakarta, so that further research can continue the analysis of appropriate classification methods for demographic data. The method discussed in this study is also expected to be applicable to other data.

Standardization of Reading Charts: A Review of Recent Developments.

This review gives an overview of the current status of standardization by statistical evaluation of reading charts. First begun only 20 years ago, the statistical evaluation of reading charts now reflects an increasing clinical and scientific interest in standardized, comparable, and reproducible reading charts.For clinical or research purposes in human subjects, standardization of psychophysical tests and their test items by statistical evaluation is mandatory because it provides experimental control. Initial attempts at reading chart standardization were made by characterizing the test items, either in terms of a selection of unrelated words or in terms of sentences representing a constant number of characters, including spaces. As initiated by the RADNER Reading Charts, standardization of reading charts (and test items) by statistical evaluation has gained increasing clinical and scientific interest in the last two decades and has later also been applied to some of the other modern reading charts. A literature search was performed with respect to reading charts that (a) have been produced in accordance with the recommendations of the International Council of Ophthalmology (geometrical print size progression), (b) have been statistically analyzed, and/or (c) use clearly characterized test items (conceptually and statistically). These reading charts are as follows: the Bailey-Lovie Word Reading Charts, the Colenbrander Cards, the RADNER Reading Charts, the MNREAD Acuity Charts, the Smith-Kettlewell Reading Test (SKread Test), the C-Read Charts, and the Balsam Alabdulkader-Leat (BAL) Chart. The test items of these charts have been characterized either empirically or by statistical analysis and selection. The extent of the statistical evaluation of the reading charts varies. Despite their different methodological approaches, these reading charts represent an advancement that has made possible the useful comparison and reproducible evaluation of near visual performance.

Nuclear radiation shielding and mechanical properties of colemanite mineral doped concretes

ABSTRACTThe present research focused on the investigation of photon and fast neutron shielding parameters of colemanite mineral doped and undoped concretes. The fabricated concretes have been exposed to gamma rays at 59.5 and 81 keV energies and the measurements have been carried out with NaI(Tl) detector. The parameters of effective atomic number (Zeff) and electron density (Nel) have been determined experimentally and theoretically. The exposure buildup factor (EBF) and energy absorption buildup factor (EBF) have been computed utilizing the Geometric progression (G–P) fitting method. In addition to the photon shielding parameters, the macroscopic effective removal cross-section calculations for fast neutron (ΣR) were performed. As a result, it was observed that the concretes doped with colemanite mineral are not very effective in gamma radiation shielding. On the contrary, it was observed that concretes with colemanite were more effective in shielding fast neutrons and the fast neutron removal cross-section values increased with increasing colemanite concentration in the concrete. Additionally, compressive strength values (MPa) of concretes were tested using ALFA TESTING (B001-PC) 200 tons capacity device.

Estimation of energy absorption buildup factors of some human tissues at energies relevant to brachytherapy and external beam radiotherapy

Purpose: Estimation of energy absorption buildup factors (EABFs) of some human tissues for photon energies commonly used in brachytherapy (BT) and external beam radiotherapy (EBRT).Methods: A five parameter geometric progression (G-P) fitting approximation was used to estimate EABF at different energies and penetration depths (up to 20 mfp). MCNP6.1 was used to obtain EABF for comparison.Results: For radiation sources with lower mean energies (MEs), adipose tissue, which has lowest Zeq, has highest EABF values while bone, which has highest Zeq, has lowest EABF values. EABF reaches to a maximum value (EABFmax∼550) for Ir-192 BT source, which has a mean energy of 0.35 MeV. The radiation sources (MEs from 300 keV to a few MeV) were found to have higher values of EABF. At higher energies, e.g. 5 MeV, the annihilation photons contribute EABF at higher penetration depths, e.g. 20 mfp. In general, both MCNP and GP fitted EABF values along with available experimental data were found to agree well.Conclusions: EABFs of various human tissues have been investigated at radiation source energies relevant to BT and EBRT extensively. The presented data on EABF for the human tissues should be useful for accurate dose estimation at BT and EBRT.

Layout optimization for non-equidistant thrust system of tunneling machine based on geometric progression under mixed ground.

For the difference of rock and soil strength on the tunneling face, curved tunneling, and the top-heavy structure of the main machine forming the complex geological structure, the adoption of uniform thrust system arising from large unbalanced load easily causes cracks and dislocations in the rear segments. Therefore, non-equidistant driving system would be adopted in this composite foundation. This article presents a geometric progression method for layout design of non-uniform thrust system. Based on the force transmission laws of the thrust system, the geometric progression increasing difference model of arranging non-uniform driving system has been proposed. Then, the characteristics of the design method have been discussed in detail. Finally, the model has been applied to a diameter of 9.49 m of tunneling machine with a thrust system of 14 pairs of jacks which has been successfully used in curved tunnel construction in Germany. By adopting the coefficient of variation representing the force transmission performance derived from all thrusts for jacks, it indicates that the performance of the optimized thrust system is better than the original one. The results would provide a theoretical basis for the design of a non-equidistant thrust system with better force transmission performance under working geological conditions.

Radiation shielding investigations for selected tellurite-based glasses belonging to the TNW system

In this paper, we have investigated the properties of tellurite-based glass system in the form (100 -x -y)TeO2–xNbO2.5-yWO3, x = 5, 10, 15, 20, 25 mol% and y = 5 mol% for gamma and neutron shielding applications and to achieve that, mass attenuation coefficients (μm) for the selected glasses have been investigated using Geant4 toolkit and XCOM program, respectively, in the energy range between 1 keV and 10 MeV. A good agreement was observed between μm values simulated by Geant4 and those evaluated by XCOM. The obtained μm values were then utilized to derive effective atomic numbers (Zeff), mean free path (MFP), and half value layer (HVL) for the selected glasses. In addition, we used Geometric Progression method (G-P) to evaluate exposure buildup factor (EBF) values in the range of 0.015 MeV–15 MeV up to penetration depths of 40 mfp (mean free path). Among these glasses, the glass coded as TN05W05 is a superior shielding material against gamma-rays as compared with different traditional concretes, commercial glass, and HMO glasses. In addation, the fast neutron removal cross sections were calculated for the glasses involved. It is found that the present glasses offer an excellent ability for protecting against fast neutrons. Present investigation on shielding properties of the selected tellurite-based glasses would be useful for radiation protection application.

A B-spline approach to [formula omitted]-Eulerian polynomials

We present q-analogues of exponential Euler polynomials and Euler–Frobenius polynomials from B-splines with knots both at q-integers and in geometric progression. We also investigate the relations between q-Eulerian numbers, q-Eulerian polynomials, q-Euler–Frobenius polynomials and B-splines. We derive q-Euler–Frobenius polynomials using q-analogue of exponential splines. It is shown that B-splines with knots at q-integers and B-splines with knots in geometric progression have same values on their knot points. We also construct a q-analogue of Worpitzky identity.

Sparse subsets of the natural numbers and Euler’s totient function

In this article, we investigate sparse subsets of the natural numbers and study the sparseness of some sets associated to the Euler’s totient function $$\phi $$ via the property of ‘Banach density’. These sets related to the totient function are defined as follows: $$V:=\phi ({\mathbb {N}})$$ and $$N_i:=\{N_i(m):m\in V \}$$ for $$i = 1, 2, 3,$$ where $$N_1(m)=\max \{x\in {\mathbb {N}}:\phi (x)\le m\}$$ , $$N_2(m)=\max (\phi ^{-1}(m))$$ and $$N_3(m)=\min (\phi ^{-1}(m))$$ for $$ m\in V$$ . Masser and Shiu (Pacific J. Math. 121(2) (1986) 407–426) called the elements of $$N_1$$ as ‘sparsely totient numbers’ and constructed an infinite family of these numbers. Here we construct several infinite families of numbers in $$N_2\setminus N_1$$ and an infinite family of composite numbers in $$N_3$$ . We also study (i) the ratio $$\frac{N_2(m)}{N_3(m)}$$ which is linked to the Carmichael’s conjecture, namely, $$|\phi ^{-1}(m)|\ge 2$$ for all $$m\in V$$ , and (ii) arithmetic and geometric progressions in $$N_2$$ and $$N_3$$ . Finally, using the above sets associated to the totient function, we generate an infinite class of subsets of $${\mathbb {N}}$$ , each with asymptotic density zero and containing arbitrarily long arithmetic progressions.

Gamma ray buildup factors for conventional shielding materials and buildup factors computed for tungsten with a thickness beyond 40 mean free paths

In this study, gamma ray buildup factors were investigated for conventional shielding materials such as lead, iron, concrete, and tungsten based on standard formulations in order to understand the variations between different formulations. The exposure buildup factors for 1 MeV gamma rays in lead, iron, and concrete for thicknesses beyond 40 mean free paths were computed using the modified geometric progression fitting formula and compared with previously reported data. For the first time, the exposure buildup factors were computed for tungsten at gamma ray energies from 15 keV to 15 MeV and for a penetration depth beyond 40 mean free paths.

Evaluation the gamma, charged particle and fast neutron shielding performances of some important AISI-coded stainless steels: Part II

This is the second part of a two-part study on the investigation of radiation shielding performances of some important AISI-coded stainless steels (AISI-302, 304, 321 and 430). Part 1 addressed experimental evaluation by means of measured photon-material interaction parameters. In this second part, we focused on the calculation and discussion of other interaction parameters, which are a guide to choice optimum shielding materials in the nuclear processes for the present AISI-coded stainless steels. The present stainless steels have superior mechanical properties, high temperature and corrosion resistances and these properties can make them favorite materials for nuclear applications. For this reason, firstly, the incoherent scattering/total attenuation ratio (Rinc/total) and equivalent atomic number (Zeq) were calculated in the energy region of 0.015–15 MeV. Secondly, the exposure build-up factor (EBF) and energy absorption build-up factor (EABF) were determined to select steels by using Geometric Progression (G-P) fitting method, which have five parameters (a, b, c, d and XK coefficients), up to penetration depth of 40 MFP at energy 0.015–15 MeV. Thirdly, the mass stopping powers (MSPs; dE/ρdx ; MeVcm2/g) and ranges (Re, Rp and Rα; μm) for electron, proton and alpha particle interactions were calculated at energy 10 keV-20 MeV. Finally, the fast neutron removal cross-sections (FNRCSs; ∑R; cm−1) were calculated. To be able to make comparison and a satisfying assessment about radiation shielding capabilities of present AISI-coded steels, all parameters were also computed for ordinary (OC), steel-scrap (SS) and steel-magnetite (SM) concretes (Fe-based steel concretes) that are most commonly used as a shielding material in many nuclear applications. The shielding capabilities of the present stainless steels against both gamma and the fast neutron and charged particle radiation were evaluated in the light of the calculated parameters. As a result of the mutual evaluation of the results obtained for the shielding concretes and the examined stainless steels, it was found that present stainless steels had excellent shielding properties compared to shielding concretes in terms of both photon radiation and particle radiation.

A novel comprehensive utilization of vanadium slag/epoxy resin/antimony trioxide ternary composite as gamma ray shielding material by MCNP 6.2 and BXCOM

New research on composite materials was proposed for both gamma ray shielding and fireproofing. When compared to concrete, composite materials show up higher shielding properties in the 0.015 MeV–15 MeV incident energy range. The composite was prepared with vanadium slag, epoxy resin and antimony-trioxide. Different ratios of ternary composite were investigated in order to determine the optimum ratio for shielding and anti-flame properties. Photon atomic parameters with shielding were determined by BXCOM and MCNP 6.2. BXCOM program determines the buildup factors (both EBF and EABF) in the 0.015–15 MeV energy range for up to 40 mean free path (mfp) penetration depth. It uses geometric progression (G-P) fitting method. The effective electron number (Neff) and the effective atomic number (Zeff) were also obtained with the BXCOM software. Furthermore, parameters such as the mass attenuation coefficients (μρ), half-value layer (HVL) and tenth-value layer (TVL) were determined by MCNP 6.2 in order to confirm and compare with WinXCOM results. Obtained results may be concluded to have preferable shielding properties for the composite as an alternative to concrete. Antimony-trioxide (x=0.03), was found to exhibit the minimum EBF and EABF values, and is a convenient radiation shielding material. The Epoxy resin-vanadium slag and antimony-trioxide ternary glassy composite indicates better radiation shielding properties than concrete, but weaker than lead.

EFFECT OF SUBATMOSPHERIC NEGATIVE PRESSURE ON BIASED pH CHANGES IN PURULENT NECROTIC DEFECTS IN DIABETIC FOOT SYNDROME

The number of patients with diabetes mellitus worldwide is increasing with geometric progression, and thus there is an increase in the percentage of related complications. Diabetic foot syndrome is one of the most serious chronic complications that often results in early disability, long stretches of hospitalization, mounting expenses, and an amputated limb. At present, vacuum therapy in the treatment of purulent necrotic lesions of diabetic foot syndrome is being successfully used in medical practice. The aim of our study was to search and verify for indirect methods of express control of the vacuum therapy efficacy. Based on applying our patented local treatment technique, which includes the negative pressure wound therapy, we determined the pH dynamic changes and the monitored the microbiological climate of wounds. According to the results obtained, the high efficacy of the proposed technique has been found out and statistically confirmed. Starting from the 4th day of applying this technique, the main group demonstrated induced, significantly accelerated pH changes in the wounds that create the conditions for early growth of granulation tissue; the reduction of microbial load in the wound indirectly enhances these processes that were found out twice as slow in the comparison group. Therefore, the contact pH monitoring of wound is quite helpful for checking the therapy efficacy as well as for predicting the course of wound healing. Our study has confirmed its effectiveness in pH changing that positively affects the course of wound healing. Applying negative pressure wound therapy as an integral component of combined treatment of purulent necrotic lesions of diabetic foot syndrome allows medical practitioners to accelerate pH changes to reach their optimum values and considerably promotes the beginning of the second phase of wound healing. The study has also proven the enhanced elimination of bacterial agents from the wound by using this technique that also promotes the early activation of the phase 2 and significantly reduces the percentage of suppurative complications in the future.

Digital Control of a Buck Converter Based on Input-Output Linearization. An Interpretation Using Discrete-Time Sliding Control Theory

This paper presents the analysis and design of a PWM nonlinear digital control of a buck converter based on input-output linearization. The control employs a discrete-time bilinear model of the power converter for continuous conduction mode operation (CCM) to create an internal current control loop wherein the inductor current error with respect to its reference decreases to zero in geometric progression. This internal loop is as a constant frequency discrete-time sliding mode control loop with a parameter that allows adjusting how fast the error is driven to zero. Subsequently, an outer voltage loop designed by linear techniques provides the reference of the inner current loop to regulate the converter output voltage. The two-loop control offers a fast transient response and a high regulation degree of the output voltage in front of reference changes and disturbances in the input voltage and output load. The experimental results are in good agreement with both theoretical predictions and PSIM simulations.

The construction and validation of a geometric reasoning test item to support the development of learning progression

This article presents preliminary analysis of a test item in a large-scale study design to promote the development of geometric reasoning progression. Two sets of data were analysed to validate the item designed to assess secondary school students’ knowledge of a rectangle. The first data set involved 155 Year 4–10 students from seven trial schools across social strata. The second data set involved 585 Year 7–10 students from eleven project schools situated in lower socio-economic areas. The aim was to audit Australian students’ knowledge of hierarchy of shapes and document the process of validating a test item. The findings indicated that an iterative process of design, test and redesign, incorporating Sfard’s mathematical discourse framework and a multi-stage Rasch analysis, is vital in validating the results. A distinct change in students’ reasoning about rectangle is observed and this is not due to age. Moreover, Rasch analysis identified eight distinct thinking zones to assist in mapping out a learning progression for developing geometric reasoning.