Lorentzian Curve Research Articles

An Image Processing-Based Correlation Method for Improving the Characteristics of Brillouin Frequency Shift Extraction in Distributed Fiber Optic Sensors

This paper demonstrates how the processing of Brillouin gain spectra (BGS) by two-dimensional correlation methods improves the accuracy of Brillouin frequency shift (BFS) extraction in distributed fiber optic sensor systems based on the BOTDA/BOTDR (Brillouin optical time domain analysis/reflectometry) principles. First, the spectra corresponding to different spatial coordinates of the fiber sensor are resampled. Subsequently, the resampled spectra are aligned by the position of the maximum by shifting in frequency relative to each other. The spectra aligned by the position of the maximum are then averaged, which effectively increases the signal-to-noise ratio (SNR). Finally, the Lorentzian curve fitting (LCF) method is applied to the spectrum with improved characteristics, including a reduced scanning step and an increased SNR. Simulations and experiments have demonstrated that the method is particularly efficacious when the signal-to-noise ratio does not exceed 8 dB and the frequency scanning step is coarser than 4 MHz. This is particularly relevant when designing high-speed sensors, as well as when using non-standard laser sources, such as a self-scanning frequency laser, for distributed fiber-optic sensing.

Timelike Constant Axis Ruled Surface Family in Minkowski 3-Space

A timelike (TL) constant axis ruled surface in E13 (Minkowski 3-space), as determined by its ruling, forms a constant dual angle with its Disteli-axis (striction axis or curvature axis). In this article, we employ the symmetry through point geometry of Lorentzian dual curves and the line geometry of TL ruled surfaces. This produces the capability to expound a set of curvature functions that specify the local configurations of TL ruled surfaces. Then, we gain some new constant axis ruled surfaces in Lorentzian line space and their geometrical illustrations. Further, we also earn several organizations among a TL constant axis ruled surface and its striction curve.

Analysis of spatial distribution characteristics of A-level tourist attractions in Yunnan Province based on GIS

Based on GIS geographic information technology, this paper analyses and researches the spatial distribution characteristics of tourist attractions in Yunnan Province based on the data of Class A tourist attractions in Yunnan Province in 2022, using the nearest-neighbour index, kernel density analysis, geographic concentration index, imbalance index and Lorenz curve method. The results show that: (1) The spatial distribution type of A-grade tourist scenic spots in Yunnan Province is agglomeration, and the balance is low and the concentration degree is high, and the Lorentz curve shows a significant upward trend. From the perspective of the geographical area of Yunnan Province, the number of A-level tourist attractions in Kunming, Dalizhou, Puer, Qujing and Lijiang exceeds 50% of the province, showing obvious imbalance. (2) The spatial distribution of tourist attractions in Yunnan Province is obviously different, and the overall distribution characteristics of more northwest, less eastern edge, and more central area are mainly concentrated in central Yunnan and western Yunnan, while eastern Yunnan and northeast Yunnan are less distributed.

Tele-connecting renewable energy availability from production to consumption via multi-national supply chains

Renewable energy transition is recognized as an irreplaceable strategy under low-carbon transition, which has gradually drawn due attention worldwide. Through combining the gravity center and the Lorentz curve, this study conducts a comparative assessment to depict gravity center trajectories across countries/regions and renewable energy inequality within income groups, providing a new perspective to clarify renewable energy transition worldwide. From the results, renewable energy availability experienced a rapid growth over time, and the gravity center of renewable energy availability shifted slightly towards the northeast. Through tele-connecting renewable energy availability via multi-national supply chains, renewable energy exchanges greatly expanded between 2000 and 2019, with Canada-USA, China-USA, Paraguay-Argentina, Mexico-USA, China-India, and China-Japan identified as intensive trade partners. In consideration of inequality levels, an obvious decrease in Gini coefficients could be witnessed, however, the Gini coefficients of renewable energy inequalities worldwide remained high. When compared, the upper-middle-income countries had the lowest Gini coefficients and gradually surpassed high-income countries as the most equitable group. By unveiling the trajectory and inequality of renewable energy availability from both production- and consumption-based perspectives, some rational and feasible strategies would be practical in consideration of economic growth and regional disparity to promote sustainable and equitable renewable energy transition worldwide.

The inequality of household carbon footprint in China: A city-level analysis

Climate change mitigation and carbon inequality reduction are of great significance to the sustainable development. Most of the existing studies on China's household carbon footprint inequality are at provincial level and lack in-depth analysis of cross-dimension of consumption categories. We calculated the carbon footprints in 309 city-level areas in China based on the multi-regional input-output table, and further explored the inequality of household carbon footprints from perspective of cross-dimension with Gini coefficient and Lorentz curve based on the China Family Panel Studies dataset. We found that although the carbon footprint inequality of different areas, income groups and family size were relatively high on the whole, the level of that in different consumption categories showed significant different characters. For instance, affluent demographics possess the requisite financial capacity to acquire luxury apparel, whereas economically disadvantaged cohorts predominantly procure garments at standard price points. This dynamic may engender heightened carbon disparity within the realm of clothing, with a proclivity for greater imbalances observed in high-income strata as opposed to their low-income counterparts. Specific measures for guiding residents to rationally consume luxury food and allocate educational resources, and advocate low-carbon travel to eliminate household carbon footprint inequality in China are proposed.

Measurement of Rubidium Vapor Density Based on Spin‐Exchange Rate

AbstractAn efficient method is proposed for quantifying rubidium vapor density by analyzing the spin‐exchange rate between alkali metals. This method effectively addresses two primary challenges in measuring alkali vapor density. First, it overcomes the limitation of absorption spectroscopy to measure vapor density under optically thick conditions, typically restricted to temperature higher than 420K, equivalent to alkali vapor density exceeding . Second, it mitigates the risk of disrupting shielding functionality due to the application of a strong magnetic field, often in the range of several tens of Gauss or higher, when employing the Faraday rotation for vapor‐density measurement. The spin‐exchange rate between atoms, inherently related to the vapor density, is evident in the electron‐paramagnetic‐resonance spectrum of spin‐polarized , thereby providing a possibility for measuring alkali vapor density. To eliminate overlap between two Lorentzian curves resulting from two decomposed components of an oscillating field, a small rotating magnetic field with identical amplitude and frequency but a 90‐degree phase shift along both the x and y axes is applied. This method is successfully employed to measure vapor density in the temperature range of 373–433 K, with the measured outcomes closely matching the saturation vapor curve.

Equity and efficiency of health resource allocation in township health centers in Sichuan Province, China.

To analyze the equity and efficiency of health resource allocation in township health centers in Sichuan Province, and to provide a scientific basis for promoting the development of township health centers in Sichuan Province, China. The Lorenz curve, Gini coefficient and health resource density index were used to analyze the equity of health resource allocation in township health centers in Sichuan Province from 2017 to 2021, and data envelopment analysis(DEA) was used to analyze the efficiency of health resource allocation in township health centers in Sichuan Province from 2017 to 2021. The Gini coefficient of health resources of township health centers in Sichuan Province is below 0.2 by population in addition to the number of beds in 2020-2021 and practicing (assistant) physicians in 2021, and the Gini coefficient of health resources of township health centers in Sichuan Province is above 0.6 by geography. The Lorentz curve of health resources of township health centers in Sichuan Province is closer to the equity line by population allocation and further from the equity line by geographical allocation. The average level of township health centers in Sichuan Province is used as the standard to calculate the health resource density standard index(W) of each region, the Ws of Panzhihua, Ganzi, Aba and Liangshan are less than 1, and the Ws of Ziyang, Neijiang, Deyang and Meishan are greater than 1. The overall efficiency of township health centers in Sichuan Province in 2017 and 2021 is 1, and the DEA is relatively effective. The overall efficiency of township health centers in Sichuan Province in 2018 and 2019 is not 1, and the DEA is relatively ineffective. The overall efficiency of all health resources in Mianyang and Ziyang is 1, and the DEA is relatively effective. The overall efficiency of all health resources in Suining, Neijiang, Yibin, Aba and Ganzi is not 1, and the DEA is relatively ineffective. The equity of health resource allocation by population is better than that by geography in township health centers in Sichuan Province. Combining population and geographical factors, the health resource allocation of Panzhihua, Ganzi, Aba and Liangshan is lower than the average level of Sichuan Province. The efficiency of health resource allocation in township health centers in Sichuan Province is low.

China Educational Resources Analysis Based on GINI Coefficients

This article is based on the Gini coefficient to analyze the current educational status in China, and the Gini coefficient is calculated by the educational resources in different provinces. To diversify the sample, the work includes four different educational parameters: number of graduate students, number of institutions of higher learning, and number of high schools and middle schools. Based on the Chinese identity data from 2013 to 2021, this work calculates a line plot of the Gini coefficient, applying the correlation between the Lorentz curve and dynamic conditions. Concerning the different levels of education developments in China, it can draw the following conclusions: the Gini coefficient on the number of postgraduate students and institutions of higher learning is decreasing year by year, and the Gini coefficient on the number of high schools and middle schools appear an opposite trend. Regarding China’s basic national conditions, the research results show that postgraduate and institutions of higher learning education resources are more equal. Still, the trend for middle and high school is on the contrary.

Is there a common pattern of dental specialties in the world? Orthodontics, the constant element

BackgroundThere is a lack of studies comparing the status of dental specialties worldwide. Therefore, this study aimed to analyze the differences and similarities between the number and types of dental specialties in 31 countries, including every continent, in the world.Materials and methodsAvailable official documents and webpages from regulatory bodies, official colleges and councils, and dental institutions were collected from 31 countries and analyzed to obtain reliable data on dental specialties. Differences were analyzed using the Lorentz curve and Gini test. Additionally, a cluster analysis was performed to obtain groups of countries with similar patterns in the number and types of dental specialties.ResultsA total of 32 different specialties were officially recognized among all the analyzed countries. Orthodontics and oral surgery (100% and 93.1%, respectively) were the two most frequently officially recognized dental specialties worldwide. The total global degree of inequality in the 31 analyzed countries was 42.4%. The Anglo-Saxon countries showed the greatest similarity, approximately 15-fold higher than the European countries. Cluster analysis differentiated six main groups of countries according to the number and types of dental specialties. European countries formed one of the two largest clusters, and the other cluster was of Anglo-Saxon, Asian, African, and several Eastern European countries with a high number of specialties.ConclusionsOfficially recognized dental specialties in the different continents and countries show an asymmetric organization. The number, names, and skills of officially recognized dental specialties exhibited significant differences, showing inequalities in their organization. The Anglo-Saxon pattern of dental specialties showed greater equality than the European pattern. Orthodontics was the only constant element among the different patterns.

Сравнительный анализ методов измерения неравенства

The purpose of this article is to substantiate the danger of large income inequality in society and to consider the main coefficients of measuring inequality in the world. According to international reports, there has been an increase in global inequality since the pandemic. Today, more than half of the world’s income is concentrated in the hands of 10% of the population. There is not a single shit that does not face this problem. The increase in inequality undermines the possibility of economic growth both in an individual country and at the global level. Of the three methods proposed by the UN to measure inequality, two are considered in the article – the Gini and Palma coefficients. The Gini Index evaluates the distribution of income by groups of people. Depending on what is taken as a unit of account (annual income or wealth), the value of the Gini index may vary. As a rule, when choosing wealth, the value of Gini is greater. The Gini coefficient can also be calculated using the formula or the Lorentz curve. Next, the Palma index is considered, it allows you to circumvent such limitations of the Gini index as ignoring the shadow economy and the general standard of living in the country. To do this, the middle class is excluded from the Palm index. The article proves that both calculation options lead to almost the same result. The author evaluates the global level of inequality by both coefficients and conducts a comparative analysis of the results obtained. The coincidence of the results at the level of inequality in the regional context has been established. The leaders are European countries, the situation is worst in Africa, Latin America and North America. However, at the country level, there are significant discrepancies between the Gini and Palma indices.

Health Expenditure Among the Outpatient of Type 2 Diabetes in Selected Hospital of Kathmandu District: A Cross‐Sectional Study

Background: Out‐of‐pocket (OOP) expenditure is the dominant financing mechanism in low‐ and middle‐income countries. In these countries, the prevalence of diabetes has been rising more rapidly leading to various microvascular complications thus increasing the risk of dying prematurely.Methods: A cross‐sectional hospital‐based study was carried out to compare the OOP expenditure of diabetic patients treating in public and private hospitals. A total of 154 diabetic patients, that is, 77 in each type of hospital were selected for face‐to‐face interviews using structured questionnaires. Lorentz curve and concentration curve were prepared using the income and expenditure of the patients.Results: Among 154 patients, 97.4% of patients paid OOP for the treatment of diabetes. The mean direct cost per month was NPR 7312.17 (about 55 USD) in public and NPR 10,125.31 (around 76 USD) in private hospitals. Direct medical cost had a higher share in total direct cost, that is, 60.5% in public and 69.3% in private hospitals.Conclusion: Direct medical cost was higher in private hospital compared to public hospital. All the income groups paid a similar amount of money for the treatment, placing a higher economic burden on poor patients, as there was no financial protection mechanism fully covering their health expenditure.

Spacelike Ac-Slant Curves with Non-Null Principal Normal in Minkowski 3-Space

In this paper, we define a spacelike ac-slant curve whose scalar product of its acceleration vector and a unit non-null fixed direction is a constant in Minkowski 3-space. Furthermore, we give a characterization depending on the curvatures of the spacelike ac-slant curve. After that, we get the relationship between a spacelike ac-slant curve and several distinct types of curves, such as spacelike Lorentzian spherical curves, spacelike helices, spacelike slant helices, and spacelike Salkowski curves, enhancing our understanding of its geometric properties in Minkowski 3-space. Finally, we used Mathematica, a symbolic computation software, to support the notions of an ac-slant curve with attractive images.

Analysis on the allocation equality in occupational health technology service resource in Gansu Province

Objective: To investigate and analyze the allocation equality of occupational health technology service resource of Gansu disease control and prevention institutions, providing reference basis for optimizing the allocation of occupational health technology service resources. Methods: Combined with the survey data in September 2021, Gansu Province was divided into five economic regions by geographical location and economic characteristics. Taking the service number of enterprises and workers as the analysis dimensions, the allocation level of occupational health technology service resources in different regions was compared. The allocation equality was analyzed through Lorentz curve, Gini coefficient and Theil index. Results: There were 301 occupational health technicians and 1914 sampling and testing equipments of Gansu Provincial disease control and prevention institutions in 2021. All of the technicians and equipments were used for serving 1952 enterprises and 465800 workers. The curvature of Lorentz curves and Gini coefficient which measured by the service number of enterprises and workers were: occupational health technicians>radioactive factor sampling and testing equipment >physical factor sampling and testing equipment >chemical factor sampling and testing equipment, and chemical factor sampling and testing equipment>physical factor sampling and testing equipment >radioactive factor sampling and testing equipment >occupational health technicians, respectively. Theil index of occupational health technology service resources suggested that differences in regions were the main unfair reason effected the allocation of occupational health technicians and radioactive factor sampling and testing equipment, while the differences between regions were the main unfair reason effected the allocation of chemical and physical factor sampling and testing equipment. Conclusion: The allocation equality in occupational health technology service resources of Gansu Provincial disease control and prevention institutions was not enough, and the differences in regions and between regions should be considered. This study suggests that it is necessary to introduce more occupational health technicians. The allocation of occupational health technology service resources should match with the number of local enterprises and the types of potential hazard factors of enterprises as far as possible.

Brillouin frequency shift extraction by bidirectional integration of Brillouin gain spectrum

A novel Brillouin frequency shift (BFS) extraction approach based on bidirectional integration is proposed and investigated for mitigating the fluctuations in Brillouin optical time domain reflectometer (BOTDR) system. The proposed method involves calculating the BFS through the forward and backward integrations of the original Brillouin gain spectrum (BGS) data. The findings from both simulations and experiments demonstrate that bidirectional integration achieves superior BFS accuracy compared to Lorentzian curve fitting. To further evaluate its performance, the root mean square error of BFS is measured under the different signal-to-noise ratios (SNRs) and frequency steps and the results show that bidirectional integration has higher tolerance for low SNR. Specifically, bidirectional integration achieves a BFS accuracy of 0.853 MHz under SNR of 5.22 dB and significantly reduces the measurement time by 85.86 %. Additionally, the introduced coefficient k characterizes the influence on the BGS compression, with bidirectional integration exhibiting a narrower full width at half maximum of BGS (52.74 MHz) compared to Lorentzian curve fitting (67.45 MHz).

Further development and application of a method for assessing radionuclide surface activity distribution and source location based on measurements of ambient dose equivalent rate

A method has been developed for solving the Fredholm equation in the barrier geometry for reconstructing the surface activity density (SAD) from the results of measuring the ambient dose equivalent rate (ADER). Inclusion of the barrier geometry means that the method takes into account the shielding effect of buildings and structures on the contaminated site. The method was based on the representation of the industrial site, buildings and radiation fields in the form of a raster and the use of the visibility matrix (VM) of raster cells to describe the barrier geometry. The developed method was applied to a hypothetical industrial site with a size of 200 × 200 conventional units for four types of SAD distribution over the surface of the industrial site: ‘fragmentation’, ‘diffuse’, ‘uniform’ and ‘random’. The method of Lorentz curves was applied to estimate the compactness of the distributions of SAD and the ADER for the considered radiation sources. It was shown that the difference between the Lorentz curve for SAD and ADER means that the determination of the spatial distribution of SAD over the industrial site by solving the integral equation is essentially useful for determining the location of radiation source locations on the industrial site. The accuracy of SAD reconstruction depends on the following parameters: resolution (fragmentation) of the raster, the height of the radiation detector above the scanned surface, and the angular aperture of the radiation detector. The measurement of ADER is simpler and quicker than the direct measurement of SAD and its distribution. This represents a significant advantage if SAD distribution needs to be determined in areas with high radiation dose-rate during limited time. The developed method is useful for supporting radiation monitoring and optimizing the remediation of nuclear legacies, as well as during the recovery phase after a major accident.

A Study on a Spacelike Line Trajectory in Lorentzian Locomotions

In this study, we establish a novel Lorentzian interpretation of the Euler–Savary (E−S) and Disteli (Dis) formulae. Subsequently, we proceed to establish a theoretical structure for a Lorentzian torsion line congruence which is the spatial symmetry of the Lorentzian circling-point dual curve, in accordance with the principles of the kinematic theory of spherical locomotions. Further, a timelike (Tlike) torsion line congruence is defined and its spatial equivalence is examined. The findings contribute to an enhanced comprehension of the interplay between axodes and Lorentzian spatial movements, which has possible significance in various disciplines, such as the fields of robotics and mechanical engineering.

The Socio-spatial stratagems of human capital development in the Southern Federal Districts of Russia

Purpose:is to substantiate promising strategies for sustainable development of human capital in the current conditions of the demographic crisis on the basis of scientific generalization of key social and spatial aspects of the formation, use and accumulation of human capital.Methods:the application of expert-rating methods based on the Lorentz curve and the Gini index to determine the reasons for the disparities in personal income is done in addition to the use of conventional and specific approaches.Results: the research examines the existing situation of human capital and defines strategic means of promoting its growth. The findings of the analysis of trends in human development parameters, which are one of the factors ensuring macroeconomic growth and competitiveness in the South Federal Districts of Russia and should be based on various socio-spatial development strategies, are presented. A self-sufficient socio-spatial-economic system and human capital, which provide competitive advantages, are the foundations of sustainable economic development. The key factors influencing the state of human capital and the trends of its integral indicators show low rates of socio-spatial development.Conclusions and Relevance:the research findings revealed certain negative tendencies in human capital indicators, which point to the necessity for rethinking and additional inventive adjustments to the system of social and spatial management. The work-out of mechanisms for the regulation of imbalances in its development, reversing trends in the narrowing of the labour market, developing socio-spatial programs for institutional support and regulation of labour migration, and spatial human development are among the strategies for human capital that are proposed as the top priorities

A Refinement of Backward Correlation Technique for Precise Brillouin Frequency Shift Extraction

A new method for extracting the Brillouin frequency shift (BFS) from the Brillouin gain spectrum (BGS), the modified backward correlation method (MBWC), is presented. The possibilities of using MBWC, and MBWC in combination with the Lorentzian curve fitting (LCF) based on Levenberg–Marquardt (LM) method, are studied. The effectiveness of the new method, and its combination with LM, has been demonstrated for processing spectra with a low signal-to-noise ratio (SNR). The experiments, which were in good agreement with the performed simulation, showed that at SNR = 0 dB, the combined (MBWC + LM) method provided the BFS extraction error of less than 4 MHz, while the state-of-the-art LM algorithm extracted it with the error greater than 4.5 MHz. The advantage of correlation methods becomes more significant with the decreasing SNR: at SNR = −2 dB, the LM’s error is 14.3 MHz, and that of the combined one is 8.1 MHz.

Microstructure and Raman spectroscopy analysis of LiNiZn ferrite ceramics sintered by spark plasma method

In this study, the effects of different parameters (sintering temperature and holding time) of spark plasma sintering (SPS) on the microstructure and magnetic properties of LiNiZn ferrite ceramics were systematically investigated, and the samples sintered by SPS (SPS samples) were compared with the samples sintered by traditional sintering (TS samples). X-ray diffraction analysis confirmed that all the samples were ferrites with spinel structure. The microstructure of the samples was analyzed by scanning electron microscopy. Compared with TS samples, SPS samples exhibited finer and more uniform grains and denser structure. At the sintering temperature of 1000 °C, SPS samples exhibited higher saturation magnetization (Ms, 79.7 emu⋅g−1) and lower ferromagnetic resonance linewidth (ΔH, 231 Oe) than TS samples (Ms: 69.3 emu⋅g−1, ΔH: 298 Oe). The phase structure and cation distribution of the samples were analyzed by Raman spectroscopy. Herein, it was speculated that the instantaneous high temperature generated by spark plasma redistributed the cations in the crystal, and the distribution mode was stabilized by rapid cooling. Based on the change of magnetic moment of ferrite molecules caused by cation distribution, a method of judging the specific Ms by fitting analysis of Lorentz curve of A1g Raman signal of ferrite ceramics was proposed. The SPS samples showed more compact and uniform microstructure and more reasonable cation distribution than TS samples, and these characteristics were mainly responsible for the remarkable improvement of magnetic properties. The results indicate that SPS method can effectively alleviate the contradiction between Ms and ΔH, and provide an alternative pathway to prepare high-performance soft magnetic ferrite.

COVID-19 Pandemic Severity Criterion Based on the Number of Deaths and the Uneven Distribution of These

The aim of this article is to define a criterion related to the number of Coronavirus disease 2019 (COVID-19) deaths in different countries to compare them themselves in two aspects. First, the higher the number of deaths, the worse it is for society; second, if the inequality of deaths is greater between regions of a country, the worse the assessment of pandemic management should be. On a global scale, this unevenness is evident because it is not controlled by anything. In particular countries, it should be the result of efficient and honest management of the spread of the epidemic. The authors assume in the proposed algorithm that the number of deaths in individual organizational units of the state (regions, states, provinces, etc.) is known in the existing administrative division. By considering the population numbers in these units, the Lorentz curve is prepared, and the Gini coefficient is calculated for the entire world and for individual countries such as USA, India, Brazil, Poland, and the Balkan and Eastern European countries with the highest number of deaths per million inhabitants in the world. Moreover, an attempt was made to present the universal mortality rate in a given country in the form of a bicriterion combining the Gini index and the number of deaths per million inhabitants achieved. We obtained definitely different values of this criterion for the countries under consideration. The method is universal and allows calculating the criterion for any country or group of countries.