Geometric Progression Research Articles

Highly Productive Laser Annealing Manufacturing Method Using Continuous Blue WBC (Wavelength Beam Combining) Technique.

Blue laser annealing can be used to obtain a high-mobility thin-film transistor (TFT) through a laser annealing (i.e., LTPS: low-temperature Poly-Si) process. However, the laser annealing process's low productivity (as well as high cost) is an issue because the high output power of blue lasers still needs to be addressed. Therefore, productivity can be improved if blue laser energy is efficiently supplied during the laser annealing process using a continuous wave laser instead of a conventional pulsed excimer laser. We developed a blue laser light source (440 ± 10 nm) using the wavelength beam combining (WBC) method, which can achieve a laser power density of 73.7 kW/cm2. In this semiconductor laser, when the power was increased s by 2.9 times, the laser scanning speed was increased by 5.0 times, achieving twice the productivity of conventional lasers. After laser annealing, the size of the crystal grains varied between 2 and 15 μm, resulting in a crystallization rate of 100% by Raman scattering rsult and low resistivity of 0.04 Ωcm. This increase in production capacity is not an arithmetic increase with increased power but a geometric production progression.

Chlorophyll films for radiation dosimetry: a feasibility study

Abstract Novel Chlorophyll-PVA composite films have been prepared and tested for the dosimetry of therapeutic radiation. The radiation response has been quantified using UV–vis spectroscopy. FTIR and XRD spectroscopies have been used to characterize the physical properties and irradiation response of the films. The films have shown response towards the therapeutic x-rays beams of 6 MV nominal energy in the tested dose range of 0.25 Gy to 32 Gy in discrete dose levels occurring in the geometric progression series of 2. The dosimeter has been found to exhibit sensitivity at a low dose of 0.25 Gy. The dose response curve of the dosimeter exhibits an exponential relationship of the absorbance and absorbed dose. A region of saturated absorbance has been observed beyond 4 Gy. The peak intensities of the FTIR spectra have been found to decrease with increasing doses as compared to the unirradiated samples, because of the changes in the bond polarities and molecular geometries. The XRD spectra indicates a change in the molecular orientation resulting in a decrease in peak intensity with increasing dose. This study indicates the feasibility of chl-PVA films in the dosimetry of therapeutic radiation. This film dosimeter can be processed locally with minimum resources and standardized against a known standard before clinical use. The chlorophyll molecules need careful handling owing to their sensitivity to light and temperature.

Development of Vertical Radar Reflectivity Profiles Based on Lightning Density Using the Geostationary Lightning Mapper Dataset in the Subtropical Region of Brazil

The study aims to develop vertical radar reflectivity profiles based on lightning density data from the Geostationary Lightning Mapper (GLM) on the GOES-16 satellite in the subtropical region of Brazil. The primary objective is to improve the assimilation of lightning data in numerical weather prediction models. The methodology involves the analysis of polarimetric radar data from Chapecó-SC and Jaraguari-MS, spanning from January 2019 to December 2023, and their correlation with lightning data from the GLM. Radar reflectivity profiles were created for different lightning density classes, categorized into six classes based on geometric progression. Results show a significant relationship between lightning activity and radar reflectivity, with distinct profiles for convective and stratiform events. These findings demonstrate the potential of using GLM data to enhance short-term weather forecasting, particularly for severe weather events. The study concludes that the integration of GLM data into weather models can lead to more accurate predictions of intense precipitation events, contributing to better preparedness and response strategies.

Benefits of Information Technology to the Development of Nigeria

The sustainability and development of businesses and organization solely rely on the geometric progression of the impact of information technology (IT); aside the significant impact on individual lives, many organizations globally have experienced increase in productivity, reduce costs, improvement on the quality of goods and services, enhance communication systems and promote good transportation systems. Every sector has direct impact of the information technology, and the level of development currently is directly proportional to the degree of the impact. In today`s world information technology has become pivotal element in the economic growth; many solutions to everyday challenges could not have been possible without the impact of information technology. Medical and surgical processes of restoring good health to many patients today would not exist, the possibility of travelling globally without difficulties, enhancing communications that has no limitation by location, and many more that makes lives meaningful and dreams achievable are made possible by the influence of information technology. This article will describe the influence of Information Technology in enhancing the growth and development of Nigeria in relation to various sectors such as; education, health, manufacturing industries, real estate, energy, utilities, to mention a few, which will promote business and global image

Temporal geometric mapping defines morphoelastic growth model of Type B aortic dissection evolution

The human aorta undergoes complex morphologic changes that mirror the evolution of disease. Finite element analysis (FEA) enables the prediction of aortic pathologic states, but the absence of a biomechanical understanding hinders the applicability of this computational tool. We incorporate geometric information from computed tomography angiography (CTA) imaging scans into FEA to predict a trajectory of future geometries for four aortic disease patients. Through defining a geometric correspondence between two patient scans separated in time, a patient-specific FEA model can recreate the deformation of the aorta between the two time points, showing that pathologic growth drives morphologic heterogeneity. FEA-derived trajectories in a shape-size geometric feature space, which plots the variance of the shape index versus the inverse square root of aortic surface area (δS vs. AT−1), quantitatively demonstrate an increase in δS. This represents a deviation from physiologic shape changes and parallels the true geometric progression of aortic disease patients.

Recurrent Relationships as an Important Class of Mathematical Equations in Chemistry

The unique potential and different areas of applications of recurrent (synonymous: recursive) relationships in chemistry and chromatography are considered. Recurrent relations can be used in two forms: as functions of integer arguments, y(x+ 1) = ay(x) + b, and as functions of equidistant argument values, A(x+ Δx) = aA(x)+ b, Δx= const. The first form applies to all physicochemical properties of homologs in organic chemistry, because the number of carbon (and other) atoms in a molecule can be integer only. The second one applies to chemical variables depending on temperature, pressure, concentrations, etc., when the chemists should provide equal “steps” of their variations. Recurrent relations combine the properties of arithmetic and geometric progressions, which accounts for their unique approximation abilities. This was illustrated by approximating the number of isomers of alkanes, the boiling points of homologs (nonlinear dependencies), the melting points of homologs (alternation effects), the temperature dependence of the solubility of inorganic salts in water, and by revealing the anomalies of gas chromatographic retention indices and retention times in reversed-phase high performance liquid chromatography.

The extremals of the Kahn-Saks inequality

A classical result of Kahn and Saks states that given any partially ordered set with two distinguished elements, the number of linear extensions in which the ranks of the distinguished elements differ by k is log-concave as a function of k. The log-concave sequences that can arise in this manner prove to exhibit a much richer structure, however, than is evident from log-concavity alone. The main result of this paper is a complete characterization of the extremals of the Kahn-Saks inequality: we obtain a detailed combinatorial understanding of where and what kind of geometric progressions can appear in these log-concave sequences. This settles a partial conjecture of Chan-Pak-Panova, while the analysis uncovers new extremals that were not previously conjectured. The proof relies on a much more general geometric mechanism—a hard Lefschetz theorem for nef classes that was obtained in the setting of convex polytopes by Shenfeld and Van Handel—which forms a model for the investigation of such structures in other combinatorial problems.

Math Calculation and Financial Literacy: The Incidence of Geometric Progressions in the Calculation of Financial Interest

Math Calculation and Financial Literacy: The Incidence of Geometric Progressions in the Calculation of Financial Interest

Approximation of classes of Poisson integrals by rectangular Fejér means

The article is devoted to the problem of approximation of classes of periodic functions by rectangular linear means of Fourier series. Asymptotic equalities are found for upper bounds of deviations in the uniform metric of rectangular Fejér means on classes of periodic functions of several variables generated by sequences that tend to zero at the rate of geometric progression. In one-dimensional cases, these classes consist of Poisson integrals, namely functions that can be regularly extended in the fixed strip of a complex plane.

Gamma-ray shielding features of Co1-xCuxFe2O4 ferrite: A combined experimental, theoretical and simulation investigation

This study describes a rapid synthesis of Co1-xCuxFe2O4 nanoparticles using sol–gel auto-ignition and the produced materials were examined using different techniques such as XRD (X-Ray Diffraction), UV–Vis (Ultraviolet–visible), (FTIR Fourier Transform Infrared Spectroscopy), FE-SEM (Field emission scanning electron microscopy), and EDS (Energy-dispersive X-ray spectroscopy) to explore their structural, optical, and functional group morphological properties, and elemental analysis. Additionally, utilizing several gamma-ray sources and a NaI (Tl) scintillation detector, we studied the gamma-ray shielding characteristics for the prepared materials. Experimental results were validated by the results of XCOM program and the Geant4 simulations. For four chosen ferrites, the gamma ray energy absorption build-up factor is investigated at 0.01–15 MeV incident photon energy and penetration depths of 1–40 mean free path, mfp, using the geometric progression fitting technique. Ferrite samples can be employed as radiation attenuators across a range of nuclear domains, as per the findings of this study. In comparison to the other spinel ferrites, the Co1-xCuxFe2O4 (x = 0.75) ferrite demonstrated superior shielding capabilities. Important details regarding the physio-chemical properties of spinel ferrites and their ability to shield against gamma radiation are provided in the present study.

Predominance of Yb3+ and Ce3+ on the AlTaBaBO: Yb and BaTiSbBPO: Ce glasses for effective photoluminescence and radiation shielding properties towards w-LED and γ-ray shielding applications

Alumino tantalum barium borate - 65B2O3 +10Al2O3 +5SrCO3 +5BaCO3 +14Li2CO3 +4Ta2O5 +1Yb2O3 (AlTaBaBO: Yb) and barium antimony borophosphate - 35P2O5 +35B2O3 +10TiO2 +5 KF +10Li2CO3 +4SbO3 +1CeO3 (BaTiSbBPO: Ce) glasses were prepared using melt – quenching technique. The structural property of as-prepared glass materials is investigated by powder X–ray diffraction to identify the amorphous nature of the materials. FTIR and FT-Raman spectroscopic analyses examined various functional groups of glasses. The linear optical behaviours were characterized using UV–visible spectroscopy, and besides the different linear optical parameters such as refractive index and optical bandgap, optical conductivity was estimated. Excitation and emission spectra of the harvested glasses were characterized using a Photoluminescence spectrophotometer. Rare earth – R.E (Yb3+ and Ce3+) doped both glasses have greater emission efficiency due to their 2F7/2 → 2F5/2 (951 nm) and 5d1 → 2F5/2, 2F7/2 (550 and 663 nm) electronic transitions, which shows that the as-prepared glass materials have their potential applications. Colour chromaticity (CIE) diagrams of the cultivated glasses were examined with colour co – ordinations x = 0.3054, y = 0.2881 for AlTaBaBO: Yb and x = 0.3874, y = 0.3436 for BaTiSbBPO: Ce and the obtained outcomes confirmed w-LED device fabrication. Moreover, the various γ– ray shielding parameters were analyzed theoretically using Phy-X software. The five (a, b, c, d, and Xk) parameters of the Geometric Progression (G-P) fitting scheme were used to determine the energy-related energy buildup factor (EBF) as well as energy absorption buildup factor (EABF) of glasses in terms of infiltration deepness up to 40 mfp. At lower photon energy, the AlTaBaBO: Yb and BaTiSbBPO: Ce glasses have the highest μ/ρ values of 4.47 × 105 cm2/g and 3.864 × 103 cm2/g, respectively. For AlTaBaBO: Yb and BaTiSbBPO: Ce glasses, the calculated mean free path (MFP) values at 15 MeV photon energy are 0.143 cm and 12.18 cm, respectively. The result of all findings reveals that the synthesised glasses are viable materials for the futuristic utilization of w-LED and neutron radiation shielding applications.

Population Pressure and Changing Land Use Land Cover in Morigaon District, Assam, India - A Geospatial Analysis

Objective: This study intends to prioritize the underlying mechanisms underpinning the spatial-temporal variations in Land Use and Land Cover (LULC) change in the Morigaon district, located in the middle part of Brahmaputra valley of Assam, India covering an area of 1498 km2.At the same time, this study focuses on the impact of population pressure on changing LULC in the study area. Methods: This research adopted geospatial approach for analysing land use land cover change in the study area. Satellite images from the years 1992 to 2022 have been utilized to identify the land transformation. The analysis of the land transformation has taken into account the five main LULC classifications of agriculture, forest, water bodies, built-up lands, and sand deposits. It has been discovered that the LULC classes identified in this study, which comprise both natural and anthropogenic elements, have a very strong link with the population growth in the Morigaon district. To show the relationship between population expansion and LULC indicators Pearson correlation method is used. Findings: Water bodies, forests and agriculture have significantly decreased by 0.13%, 4.66% and 1.64% respectively due to substantial anthropogenic activity during the past 30 years. In contrast, sand deposits and built-up lands increased by 3.13% and 3.30%. To show the relationship between population expansion and LULC indicators Pearson correlation method is used. Very significant relationships have been found between population and built-up lands with rho value 0.95. The relationship between population with agriculture, forest, water bodies and sand deposits have been seen with rho value -0.51, -0.89, -0.64 and 0.97 respectively. The loss of the geographic extent of natural classes like water bodies, forests, signifies that the geometrical progression in the human population has greatly amplified anthropogenic activities. Novelty: The novelty lies in adopting geospatial techniques that would certainly enhance land resource conservation. Environmental concerns have been increasing due to significant land surface change, which is predominantly the result of human-induced activities. In the studied area, socioeconomic, demographic, and proximity factors have a significant impact on the LULC change processes. The findings can be utilized to forecast potential LULC scenarios and offer direction for land management strategy. Keywords: LULC, Satellite Images, Anthropogenic, Pearson Correlation, Proximity Factor

Novel chattering free binomial hyperbolic sliding mode controller for asymmetric cascaded E-type bonded T-type multilevel inverter-based dynamic voltage restorer to meliorate FRT capability of DFIG-based wind turbine

The endurance capability of Doubly Fed Induction Generator (DFIG)-based wind turbine to network against different disturbances is an important criterion to meet the recent grid codes requirements. This generator has to provide the required energy under the perturbation conditions which is principally specified by Fault Ride-Through (FRT) capability. It refers to safe and continuous operation of DFIG without interruption which has been performed by Dynamic Voltage Restorer (DVR) using fast and accurate compensation of the voltage fluctuations. This paper aims to introduce an innovative quasi-sinusoidal voltage synthesizer for DVR to enhance the power quality and power delivery. Hence, a new Asymmetric Cascaded E-type Bonded T-type Multilevel Inverter (ACEBTMI) with binary geometric progression form of DC sources is proposed to provide high-step staircase sinusoidal voltage containing low semiconductor switches. Then, accurate triggering signals for the suggested ACEBTMI corresponding to the voltage fluctuations have been provided by new Chattering Free Binomial Hyperbolic Sliding Mode Controller (CFBHSMC). To validate compensation capability of the proposed DVR, ACEBTMI part has been compared with some traditional and familiar multilevel inverters, and also CFBHSMC part has been compared with SMC, FLC and PID controllers. In precise, the simulation results have definitely confirmed the accurate tracking and robust control performance of CFBHSMC to support ACEBTMI-based DVR which enables DFIG to ride-through different voltage perturbations.

Triangles with arithmetic, geometric and harmonic progressions

This article explores the fascinating world of triangles with angle and side sequences in arithmetic, geometric and harmonic progressions. The properties and relationships between these progressions and the corresponding triangle parameters are investigated. The main focus is on proving a series of theorems that provide insights into the conditions under which triangles exhibit these progressions. The proofs are presented with meticulous attention to detail, offering a deep understanding of the results. The presented findings contribute to the field of mathematical education by providing rich material for classroom activities and discussions.

A Patient-Specific Morphoelastic Growth Model of Aortic Dissection Evolution.

The human aorta undergoes complex morphologic changes that indicate the evolution of disease. Finite element analysis enables the prediction of aortic pathologic states, but the absence of a biomechanical understanding hinders the applicability of this computational tool. We incorporate geometric information from computed tomography angiography (CTA) imaging scans into finite element analysis (FEA) to predict a trajectory of future geometries for four aortic disease patients. Through defining a geometric correspondence between two patient scans separated in time, a patient-specific FEA model can recreate the deformation of the aorta between the two time points, showing pathologic growth drives morphologic heterogeneity. A shape-size geometric feature space plotting the variance of the shape index versus the inverse square root of aortic surface area (δ𝒮 vs. ) quantitatively demonstrates the simulated breakdown in aortic shape. An increase in δ𝒮 closely parallels the true geometric progression of aortic disease patients.

The Shadow of the Future: A Framework for Reform in Higher Education

The vast majority of professions practiced a century ago no longer exist, having been supplanted by robotics and other technological advancements. The Global Technology Network posits that the acceleration of technological unemployment is likely to emerge as one of the most challenging societal issues of the twenty-first century. While 'creative destruction', wherein obsolete job roles are replaced by new ones, will play a significant role, our latest technologies possess the potential to eliminate more jobs than they generate. Given the geometric progression of technological advancements, robotics, artificial intelligence, 3D printing, and other disruptive innovations are poised to significantly impact conventional professions in the labor market imminently. Billions of individuals worldwide are currently employed in industries likely to be affected, and billions more entering the workforce will require employment. Higher Education (HE) is confronted with dual challenges in this process: on one hand, it needs to align its entire knowledge production chain with these dynamic requirements to ensure its outputs remain relevant; on the other hand, it must undergo self-transformation to maintain its significance in the production of both technical and non-technical knowledge. This research endeavors to pinpoint Albania's position within these global trends and explores how HE in Albania can adapt without undergoing a catastrophic shock. We advocate for a fundamental overhaul of the higher education system, focusing on transforming the relationship between the state and higher education institutions. Starting from the premise that the socialist experiment with the university system has failed, we propose the outline of a potential reform that reimagines the role of stakeholders. The efficient utilization of new technologies could facilitate this transformation. Received: 25 December 2023 / Accepted: 25 February 2024 / Published: 23 April 2024

Exploring the Human History: Cybernetic Modeling, Systemic Perspectives, and Applications in Archaeological Eras

Since the 1970s, cybernetic modeling of evolutionary processes has progressed, particularly with the development of the informatics-cybernetic model (ICM). This model conceptualizes humanity as a self-regulating hierarchical network system, continuously tracking energy-based target crite-ria through search optimization algorithms. The outcomes are recorded in the system memory of corresponding hierarchical subsystems. Within the ICM framework, the spatio-temporal charac-teristics of global evolution exhibit modifications reminiscent of the Zhirmunsky-Kuzmin number series, a geometric progression they identified in the exploration of critical levels in biosystem development. The study also showcases applications of mathematical-cybernetic modeling results in understanding historical processes examined by archaeologists and historians.

Rising challenges of head and neck cancer in Nigeria: The burden, trends, issues and prospects

Head and neck cancers exert a rising toll on healthcare in developing countries, Nigeria inclusive. The population has been growing in geometric progression, so is the number of people living with head and neck cancers in the country, yet few efforts have been targeted at improving existing resources and manpower dedicated to providing quality care for head and neck cancer patients. This review presents up-to-date assessment of the burden of head and neck cancers and challenges of managing patients with the disease in Nigeria, based on current literature and published peer reviewed studies in Medline, Embase, PubMed, and Cochrane Database of systematic reviews for articles in English language.

On Disjunctive Rado Numbers for Some Sets of Equations

Given a set of linear equations $S$ with positive integral parameters $a_1,\ldots,a_k$, $k \ge 2$, the disjunctive Rado number for the set $S$ is the least positive integer $R=R_d(S)$, if it exists, such that every $2$-coloring $\chi$ of the integers in $[1, R]$ admits a monochromatic solution to at least one equation in $S$. We give conditions for the existence of $R_d(S)$, and also give general upper and lower bounds on $R_d(S)$, when $S$ is a set of additive equations $\{y=x+a_1,\ldots,y=x+a_k\}$. We also determine $R_d(S)$ when $\max a_i$ is large enough, or when $a_1,\ldots,a_k$ form an arithmetic or geometric progression. We also give conditions for the existence of $R_d(S)$ when $S$ is a set of multiplicative equations $\{y=a_1 x,\ldots,y=a_k x\}$. Further, we give a general search-based algorithm to determine $R_d(S)$ when $S$ is a system of equations in two variables, given an upper bound on $R_d(S)$ and an algorithm to determine solutions to $S$. This algorithm runs in time $O(ka_k \log a_k)$ for the case of additive equations, which is exponentially better than the brute-force algorithm for the problem.

Analysis of Shielded Harmonic and Biharmonic Systems by the Iterative Extension Method

To describe stationary physical systems, well-known boundary problems for shielded Poisson and Sophie Germain equations are used. The obtained shielded harmonic and biharmonic systems are approximated using the finite element method and fictitiously continued. The resulting problems are solved using the developed method of iterative extensions. To expedite the convergence of this method, the relationships between physical quantities on the extension of systems and additional parameters of the iterative method are employed. The formulations of sufficient convergence conditions for the iterative process utilize interdisciplinary connections with functional analysis, applying discrete analogs of the principles of function extensions while preserving norm and class. In the algorithmic implementation of the iterative extensions method, automation is applied to control the selection of the optimal iterative parameter value during information processing. In accordance with the fictitious domain methodology, solvable problems from domains with a complex geometry are reduced to problems in a rectangle in the two-dimensional case and in a rectangular parallelepiped in the three-dimensional case. But now, in the problems being solved, the minimization of the error of the iterative processes is carried out with a norm stronger than the energy norm. Then, all relative errors are estimated from above in the used norms by terms of infinitely decreasing geometric progressions. A generalization of the developed methodology to boundary value problems for polyharmonic equations is possible.