Search results for: vertex PI index

Authors: Lizhou Chen, Abdelhamid Belgaid, Assem Elsayed, Xiaoming Yang

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Compression index is essential in foundation settlement calculation. The traditional method for determining compression index is consolidation test which is expensive and time consuming. Many researchers have used regression methods to develop empirical equations for predicting compression index from soil properties. Based on a large number of compression index data collected from consolidation tests, the accuracy of some popularly empirical equations were assessed. It was found that primary compression index is significantly overestimated in some equations while it is underestimated in others. The sensitivity analyses of soil parameters including water content, liquid limit and void ratio were performed. The results indicate that the compression index obtained from void ratio is most accurate. The ANOVA (analysis of variance) demonstrates that the equations with multiple soil parameters cannot provide better predictions than the equations with single soil parameter. In other words, it is not necessary to develop the relationships between compression index and multiple soil parameters. Meanwhile, it was noted that secondary compression index is approximately 0.7-5.0% of primary compression index with an average of 2.0%. In the end, the proposed prediction equations using power regression technique were provided that can provide more accurate predictions than those from existing equations.

Keywords: compression index, clay, settlement, consolidation, secondary compression index, soil parameter

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Authors: Ji-Yuan Lin, Yu-Ming Liou, Yi-Ting Chen, Chen-Syuan Lin

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Soil water index obtained by tank model is now commonly used in soil and sand disaster alarm system in Japan. Comparing with the rainfall trigging index in Taiwan, the tank model is easy to predict the slope water content on large-scale landslide. Therefore, this study aims to estimate the threshold value of large-scale landslide using the soil water index Sixteen typhoons and heavy rainfall events, were selected to establish the, to relationship between landslide event and soil water index. Finally, the proposed threshold values for landslides on country road No.89 are suggested in this study. The study results show that 95% landslide cases occurred in soil water index more than 125mm, and 30% of the more serious slope failure occurred in the soil water index is greater than 250mm. Beside, this study speculates when soil water index more than 250mm and the difference value between second tank and third tank less than -25mm, it leads to large-scale landslide more probably.

Keywords: soil water index, tank model, landslide, threshold values

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Authors: Kaveh Shahi, Helmi Z. M. Shafri, Ebrahim Taherzadeh

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In remote sensing, shadow causes problems in many applications such as change detection and classification. It is caused by objects which are elevated, thus can directly affect the accuracy of information. For these reasons, it is very important to detect shadows particularly in urban high spatial resolution imagery which created a significant problem. This paper focuses on automatic shadow detection based on a new spectral index for multispectral imagery known as Shadow Detection Index (SDI). The new spectral index was tested on different areas of World-View 2 images and the results demonstrated that the new spectral index has a massive potential to extract shadows effectively and automatically.

Keywords: spectral index, shadow detection, remote sensing images, World-View 2

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Authors: Shaikah Alsubayae, Gianluigi Casse, Carlos Chavez, Jon Taylor, Alan Taylor, Mohammad Alsulimane

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Achieving precise radiotherapy through carbon therapy necessitates the accurate monitoring of radiation dose distribution within the patient's body. This process is pivotal for targeted tumor treatment, minimizing harm to healthy tissues, and enhancing overall treatment effectiveness while reducing the risk of side effects. In our investigation, we adopted a methodological approach to monitor secondary proton doses in carbon therapy using Monte Carlo (MC) simulations. Initially, Geant4 simulations were employed to extract the initial positions of secondary particles generated during interactions between carbon ions and water, including protons, gamma rays, alpha particles, neutrons, and tritons. Subsequently, we explored the relationship between the carbon ion beam and these secondary particles. Interaction vertex imaging (IVI) proves valuable for monitoring dose distribution during carbon therapy, providing information about secondary particle locations and abundances, particularly protons. The IVI method relies on charged particles produced during ion fragmentation to gather range information by reconstructing particle trajectories back to their point of origin, known as the vertex. In the context of carbon ion therapy, our simulation results indicated a strong correlation between some secondary particles and the range of carbon ions. However, challenges arose due to the unique elongated geometry of the target, hindering the straightforward transmission of forward-generated protons. Consequently, the limited protons that did emerge predominantly originated from points close to the target entrance. Fragment (protons) trajectories were approximated as straight lines, and a beam back-projection algorithm, utilizing interaction positions recorded in Si detectors, was developed to reconstruct vertices. The analysis revealed a correlation between the reconstructed and actual positions.

Keywords: radiotherapy, carbon therapy, monitor secondary proton doses, interaction vertex imaging

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Authors: Samson Davoyan, Ashot Davoyan, Ani Khachatryan

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The indexes (Global Competitiveness Index, Economic Freedom Index, Human Development Index, etc.) developed by different international and non-government organizations in time and space express the quantitative and qualitative features of different fields of various reforms implemented in different countries. The main objective of our research is to develop new methodology that we will use to create integral index based on many indexes and that will include many areas of reforms. To achieve our aim we have used econometric methods (regression model for panel data method). The basis of our methodology is the development of the new integral index based on quantitative assessment of the change of two main parameters: the score of the countries by different indexes and the change of the ranks of countries for following two periods of time. As a result of the usage of methods for analyzes we have defined the indexes that are used to create the new integral index and the scales for each of them. Analyzing quantitatively and qualitatively analysis through the integral index for more than 100 countries for 2009-2014, we have defined comparative efficiency that helps to conclude in which directions countries have implemented reforms more effectively compared to others and in which direction reforms have implemented less efficiently.

Keywords: development, rank, reforms, comparative, index, economic, corruption, social, program

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Authors: Febrina Natalia, Noriyuki Tanaka, Mitsuru Osaki

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Sustainability Index for REDD-plus implementation was constructed to evaluate the sustainability of different communities in 5 villages (Taruna Jaya, Tumbang Nusa, Marang, Terantang, and Seragam Jaya) in Central Kalimantan, Indonesia based on the main objectives of REDD-plus project (reducing emission from deforestation and forest degradation, increasing carbon stock, preserving biodiversity and sustaining forest management). This index was separately composed of 3 different components; (1) ecology, (2) economy, and (3) society. The index of sustainability was determined into four categories; 3,3-4,0 (excellent), 2,5-3,2 (good), 1,8-2,4 (fair), and 1,0-1,7 (poor). Overall, this technique aims to assist all stakeholders and local government in particular in providing information of villages’ sustainability index before implementing REDD-plus project that the assistance and benefits given to villages will be beneficial, effective and efficient.

Keywords: central kalimantan, Indonesia, REDD-plus, sustainability index

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Authors: A. Belay, B. Kebede

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The concentration- and temperature-dependent refractive indices of solutions extracted from defective and non-defective coffee beans have been investigated using a He–Ne laser. The refractive index has a linear relationship with the presumed concentration of the coffee solutions in the range of 0.5–3%. Higher and lower values of refractive index were obtained for immature and non-defective coffee beans, respectively. The Refractive index of bean extracts can be successfully used to separate defective from non-defective beans.

Keywords: coffee extract, refractive index, temperature dependence

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Authors: Abdul Jalil M. Khalaf, Esraa M. Kadhim

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The Hosoya polynomial of a graph G is a graphical invariant polynomial that its first derivative at x= 1 is equal to the Wiener index and second derivative at x=1 is equal to the Hyper-Wiener index. In this paper we study the Hosoya polynomial of zero-divisor graphs.

Keywords: Hosoya polynomial, wiener index, Hyper-Wiener index, zero-divisor graphs

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Authors: Yuan-Lin Chen

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This paper presents an approaching forward collision probability index (AFCPI) for alerting and assisting driver in keeping safety distance to avoid the forward collision accident in highway driving. The time to collision (TTC) and time headway (TH) are used to evaluate the TTC forward collision probability index (TFCPI) and the TH forward collision probability index (HFCPI), respectively. The Mamdani fuzzy inference algorithm is presented combining TFCPI and HFCPI to calculate the approaching collision probability index of the vehicle. The AFCPI is easier to understand for the driver who did not even have any professional knowledge in vehicle professional field. At the same time, the driver’s behavior is taken into account for suiting each driver. For the approaching index, the value 0 is indicating the 0% probability of forward collision, and the values 0.5 and 1 are indicating the 50% and 100% probabilities of forward collision, respectively. The AFCPI is useful and easy-to-understand for alerting driver to avoid the forward collision accidents when driving in highway.

Keywords: approaching index, forward collision probability, time to collision, time headway

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Authors: Ti-An Tsai, Chun-Chih Wang, Hung-Wen Wang, I-Ling Chang, Lien-Wen Chen

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In this study, we demonstrate a high-resolution refractive index sensor based on a magnetic photonic crystal (MPC) composed of a triangular lattice array of air holes embedded in Si matrix. A microcavity is created by changing the radius of an air hole in the middle of the photonic crystal. The cavity filled with gyrotropic materials can serve as a refractive index sensor. The shift of the resonant frequency of the sensor is obtained numerically using finite difference time domain method under different ambient conditions having refractive index from n = 1.0 to n = 1.1. The numerical results show that a tiny change in refractive index of Δn = 0.0001 is distinguishable. In addition, the spectral response of the MPC sensor is studied while an external magnetic field is present. The results show that the MPC sensor exhibits a dramatic improvement in resolution.

Keywords: magnetic photonic crystal, refractive index sensor, sensitivity, high-resolution

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Authors: D. Mohammadzadeh S., J. Bolouri Bazaz

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This paper presents a new prediction model for compression index of fine-grained soils using multi-gene genetic programming (MGGP) technique. The proposed model relates the soil compression index to its liquid limit, plastic limit and void ratio. Several laboratory test results for fine-grained were used to develop the models. Various criteria were considered to check the validity of the model. The parametric and sensitivity analyses were performed and discussed. The MGGP method was found to be very effective for predicting the soil compression index. A comparative study was further performed to prove the superiority of the MGGP model to the existing soft computing and traditional empirical equations.

Keywords: new prediction model, compression index soil, multi-gene genetic programming, MGGP

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Authors: Hamed Movahedizadeh, Annuar Md Nassir, Mehdi Karimimalayer, Navid Samimi Sedeh, Ehsan Bagherpour

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The aim of this paper is to evaluate Tehran’s Stock Exchange (TSE) performance regarding with impact of four macroeconomic factors including world crude Oil Price (OP), World Gold Price (GP), Consumer Price Index (CPI) and total Supplied Oil by Iran (SO) from January 2006 to December 2012 that Iran faced with economic and oil sanctions. Iran's exports of crude oil and lease condensate reduced to roughly 1.5 million barrels per day (bbl/d) in 2012, compared to 2.5 million bbl/d in 2011 due to hard sanctions. Monthly data are collected and subjected to a battery of tests through ordinary least square by EViews7. This study found that gold price and oil price are positively correlated with stock returns while total oil supplied and consumer price index have negative relationship with stock index, however, consumer price index tends to become insignificant in stock index. While gold price and consumer price index have short run relationship with TSE index at 10% of significance level this amount for oil price is significant at 5% and there is no significant short run relationship between supplied oil and Tehran stock returns. Moreover, this study found that all macroeconomic factors have long-run relationship with Tehran Stock Exchange Index.

Keywords: consumer price index, gold price, macroeconomic, oil price, sanction, stock market, supplied oil

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Authors: Omid Azimaraghi, Noushin Khazaei

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Background: Fluid therapy is an important aspect of the perioperative period and a major challenge for anesthesiologists. To authors best knowledge, there is a lack of strong guidance and evidence regarding the optimal approach to fluid therapy. Therefore a variety of medical devices have been introduced to help physicians. In this study, we aimed to evaluate the effectiveness of pleth variability index in guiding fluid therapy in different patient positions. Materials and Methods: Inclusion criteria consisted of patients aged 18-50 years old and classified as American Society of Anesthesiologists physical status I and II, who were candidates for elective thyroidectomy surgery. In total, 36 patients meeting the inclusion criteria were enrolled in the study. After induction of anesthesia and start of mechanical ventilation Pleth variability index was measured in the supine position, then patients were placed in Trendelenburg and reverse Trendelenburg position (30 degrees, 5 minutes); Pleth Variability Index has measured again in the mentioned positions. Results: Mean PVI (Pleth Variability Index) in the supine position was 14.3 ± 3.7 in comparison to 21.5 ± 4.3 in the reverse Trendelenburg position. The mean PVI in Trendelenburg position was 9.1 ± 2.0 in Trendelenburg position (p < 0.05). Conclusion: In conclusion, we found that Pleth Variability Index varies with patient position and this should be taken into account when using this index during fluid therapy.

Keywords: fluid therapy, Pleth Variability Index, position, surgery

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Authors: Gong Zhang, Hong Cai, Bin Dong, Jifang Tao, Aiqun Liu, Dim-Lee Kwong, Yuandong Gu

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An on-chip refractive index sensor with high sensitivity and large measurement range is demonstrated in this paper. The sensing structures are based on Mach-Zehnder interferometer configuration, built on the SOI substrate. The wavelength sensitivity of the sensor is estimated to be 3129 nm/RIU. Meanwhile, according to the interference pattern period changes, the measured period sensitivities are 2.9 nm/RIU (TE mode) and 4.21 nm/RIU (TM mode), respectively. As such, the wavelength shift and the period shift can be used for fine index change detection and larger index change detection, respectively. Therefore, the sensor design provides an approach for large index change measurement with high sensitivity.

Keywords: Mach-Zehnder interferometer, nanotechnology, refractive index sensing, sensors

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Authors: Sapan Bhatnagar, Danish Akhtar, Salman Ahmed, Asif Ekbal, Gufran Beig

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Particulates are the solid and liquid droplets present in the atmosphere, they have serious negative effects on human health and environment. PM10 and PM2.5 are so small that they can penetrate deep into our lungs through the respiratory system. Determination of the amount of particulates present in the atmosphere per cubic meter is necessary to monitor, regulate and model atmospheric particulate levels. Air Quality Index is an index tells us how clean or polluted our air is, and what associated health effects might be a concern for us. The AQI focuses on health affects you may experience within a few hours or days after breathing polluted air. The quality rating for each pollutant was calculated. The geometric mean of these quality ratings gives the Air Quality Index. The existing concentrations of pollutants were compared with ambient air quality standards.

Keywords: air quality index, particulate, respirable dust sampler, dust sampler

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Authors: Salako Rotimi, Oshungade Stephen, Ojewoye Opeyemi

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The maintenance of price stability is one of the macroeconomic challenges facing Nigeria as a nation. This paper attempts to build a co-integration multivariate time series model for inflation movement in Nigeria using data extracted from the abstract of statistics of the Central Bank of Nigeria (CBN) from 2008 to 2017. The Johansen cointegration test suggests at least one co-integration vector describing the long run relationship between Consumer Price Index (CPI), Food Price Index (FPI) and Non-Food Price Index (NFPI). All three series show increasing pattern, which indicates a sign of non-stationary in each of the series. Furthermore, model predictability was established with root-mean-square-error, mean absolute error, mean average percentage error, and Theil’s unbiased statistics for n-step forecasting. The result depicts that the long run coefficient of a consumer price index (CPI) has a positive long-run relationship with the food price index (FPI) and non-food price index (NFPI).

Keywords: economic, inflation, model, series

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Authors: Smriti Bhatnagar

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This study aims to find if the Transit-oriented planning and development approach benefit the quality of air in neighborhoods of New Delhi. Two methodologies, namely the land use regression analysis and the Transit-oriented development index analysis, are being used to explore this relationship. Land Use Regression Analysis makes use of urban form characteristics as obtained for 33 neighborhoods in Delhi. These comprise road lengths, land use areas, population and household densities, number of amenities and distance between amenities. Regressions are run to establish the relationship between urban form variables and air quality parameters (dependent variables). For the Transit-oriented development index analysis, the Transit-oriented Development index is developed as a composite index comprising 29 urban form indicators. This index is developed by assigning weights to each of the 29 urban form data points. Regressions are run to establish the relationship between the Transit-oriented development index and air quality parameters. The thesis finds that elements of Transit-oriented development if incorporated in planning approach, have a positive effect on air quality. Roads suited for non-motorized transport, well connected civic amenities in neighbourhoods, for instance, have a directly proportional relationship with air quality. Transit-oriented development index, however, is not found to have a consistent relationship with air quality parameters. The reason could this, however, be in the way that the index has been constructed.

Keywords: air quality, land use regression, mixed-use planning, transit-oriented development index, New Delhi

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Authors: Changju Lee, Seungmo Ku, Sondo Kim, Woojin Chang

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How to detecting financial bubble? Addressing this simple question has been the focus of a vast amount of empirical research spanning almost half a century. However, financial bubble is hard to observe and varying over the time; there needs to be more research on this area. In this paper, we used abnormal difference between common stocks price and those preferred stocks price to explain financial bubble. First, we proposed the ‘W-index’ which indicates spread between common stocks and those preferred stocks in stock market. Second, to prove that this ‘W-index’ is valid for measuring financial bubble, we showed that there is an inverse relationship between this ‘W-index’ and S&P500 rate of return. Specifically, our hypothesis is that when ‘W-index’ is comparably higher than other periods, financial bubbles are added up in stock market and vice versa; according to our hypothesis, if investors made long term investments when ‘W-index’ is high, they would have negative rate of return; however, if investors made long term investments when ‘W-index’ is low, they would have positive rate of return. By comparing correlation values and adjusted R-squared values of between W-index and S&P500 return, VIX index and S&P500 return, and TED index and S&P500 return, we showed only W-index has significant relationship between S&P500 rate of return. In addition, we figured out how long investors should hold their investment position regard the effect of financial bubble. Using this W-index, investors could measure financial bubble in the market and invest with low risk.

Keywords: financial bubble detection, future return, forecasting, pairs trading, preferred stocks

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Authors: Amir Bahrami

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In the fields of chemical graph theory, molecular topology, and mathematical chemistry, a topological index or a descriptor index also known as a connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. Topological indices are used for example in the development of quantitative structure-activity relationships (QSARs) in which the biological activity or other properties of molecules are correlated with their chemical structure. In this paper some descriptor index (descriptor index) of single-walled carbon nanotubes, is determined.

Keywords: chemical graph theory, molecular topology, molecular descriptor, single-walled carbon nanotubes

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Authors: Shamil Mardi Al Islam, Zaima Ahmed

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The aim of this article is to explore whether certain macroeconomic variables such as industrial index, inflation, broad money, exchange rate and deposit rate as a proxy for interest rate are interlinked with Dhaka stock price index (DSEX index) precisely after the introduction of new index by Dhaka Stock Exchange (DSE) since January 2013. Bangladesh stock market has experienced rapid growth since its inception. It might not be a very well-developed capital market as compared to its neighboring counterparts but has been a strong avenue for investment and resource mobilization. The data set considered consists of monthly observations, for a period of four years from January 2013 to June 2018. Findings from cointegration analysis suggest that DSEX and macroeconomic variables have a significant long-run relationship. VAR decomposition based on VAR estimated indicates that money supply explains a significant portion of variation of stock index whereas, inflation is found to have the least impact. Impact of industrial index is found to have a low impact compared to the exchange rate and deposit rate. Policies should there aim to increase industrial production in order to enhance stock market performance. Further reasonable money supply should be ensured by authorities to stimulate stock market performance.

Keywords: deposit rate, DSEX, industrial index, VAR

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Authors: Hamid Rostami Jaz, Kamran Ameri Siahooei

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Up to now different methods have been used to forecast the index returns and the index rate. Artificial intelligence and artificial neural networks have been one of the methods of index returns forecasting. This study attempts to carry out a comparative study on the performance of different Radial Base Neural Network and Feed-Forward Perceptron Neural Network to forecast investment returns on the index. To achieve this goal, the return on investment in Tehran Stock Exchange index is evaluated and the performance of Radial Base Neural Network and Feed-Forward Perceptron Neural Network are compared. Neural networks performance test is applied based on the least square error in two approaches of in-sample and out-of-sample. The research results show the superiority of the radial base neural network in the in-sample approach and the superiority of perceptron neural network in the out-of-sample approach.

Keywords: exchange index, forecasting, perceptron neural network, Tehran stock exchange

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Authors: İsmail İnce

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The aim of this study is to determine index and mechanical properties of pyroclastic rock in a practical way by means of electrical resistivity method. For this purpose, electrical resistivity, uniaxial compressive strength, point load strength, P-wave velocity, density and porosity values of 10 different pyroclastic rocks were measured in the laboratory. A simple regression analysis was made among the index-mechanical properties of the samples compatible with electrical resistivity values. A strong exponentially relation was found between index-mechanical properties and electrical resistivity values. The electrical resistivity method can be used to assess the engineering properties of the rock from which it is difficult to obtain regular shaped samples as a non-destructive method.

Keywords: electrical resistivity, index-mechanical properties, pyroclastic rocks, regression analysis

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Authors: Yingjie Zhang, Ming Li, Ying Zhang, Jing Zhang, Zuolei Hu

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In the actual start-up process of DC motors, the DC drive system often faces a conflict between energy consumption and acceleration performance. To resolve the conflict, this paper proposes a comprehensive performance index that energy consumption index is added on the basis of classical control performance index in the DC motor starting process. Taking the comprehensive performance index as the cost function, particle swarm optimization algorithm is designed to optimize the comprehensive performance. Then it conducts simulations on the optimization of the comprehensive performance of the DC motor on condition that the weight coefficient of the energy consumption index should be properly designed. The simulation results show that as the weight of energy consumption increased, the energy efficiency was significantly improved at the expense of a slight sacrifice of fastness indicators with the comprehensive performance index method. The energy efficiency was increased from 63.18% to 68.48% and the response time reduced from 0.2875s to 0.1736s simultaneously compared with traditional proportion integrals differential controller in energy saving.

Keywords: comprehensive performance index, energy consumption, acceleration performance, particle swarm optimal control

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Authors: Zhanfeng Ma, Zhiping Xiong, Hu Yin, Zhengwei She, Aditya P. Gurajada, Tianlun Chen, Ying Li

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Many RDBMS vendors use B-tree index to achieve high performance for point queries and range queries, and some of them also employ hash index to further enhance the performance as hash table is more efficient for point queries. However, there are extra overheads to maintain a separate hash index, for example, hash mapping for all data records must always be maintained, which results in more memory space consumption; locking, logging and other mechanisms are needed to guarantee ACID, which affects the concurrency and scalability of the system. To relieve the overheads, Hash Cached B-tree (HCB) index is proposed in this paper, which consists of a standard disk-based B-tree index and an additional in-memory lock-free hash table. Initially, only the B-tree index is constructed for all data records, the hash table is built on the fly based on runtime workload, only data records accessed by point queries are indexed using hash table, this helps reduce the memory footprint. Changes to hash table are done using compare-and-swap (CAS) without performing locking and logging, this helps improve the concurrency and avoid contention. The hash table is also optimized to be cache conscious. HCB index is implemented in SAP ASE database, compared with the standard B-tree index, early experiments and customer adoptions show significant performance improvement. This paper provides an overview of the design of HCB index and reports the experimental results.

Keywords: B-tree, compare-and-swap, lock-free hash table, point queries, range queries, SAP ASE database

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Authors: Enikő Bene

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Our sowing date experiment took place in the Demonstration Garden of Institution of Plant Sciences, Agricultural Center of University of Debrecen, in 2012-2014. The thesis contains data of test year 2014. Our purpose, besides several other examinations, was to observe how sowing date influences leaf area index and activity of photosynthesis of maize hybrids, and how those factors affect fruiting. In the experiment we monitored the change of the leaf area index and the photosynthesis of hybrids with four different growing seasons. The results obtained confirm that not only the environmental and agricultural factors in the growing season have effect on the yield, but also other factors like the leaf area index and the photosynthesis are determinative parameters, and all those factors together, modifying effects of each other, develop average yields

Keywords: sowing date, hybrid, leaf area index, photosynthetic capacity

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Authors: Dongjoo Kim, Chang-Sik Son, Won-Seok Kang

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Adequate sleep affects various parts of one’s overall physical and mental life. As one of the methods in determining the appropriate amount of sleep, this research presents a heart rate based sleep quality index. In order to evaluate sleep quality using the heart rate, sleep data from 280 subjects taken over one month are used. Their sleep data are categorized by a three-part heart rate range. After categorizing, some features are extracted, and the statistical significances are verified for these features. The results show that some features of this sleep quality index model have statistical significance. Thus, this heart rate based sleep quality index may be a useful discriminator of sleep.

Keywords: sleep, sleep quality, heart rate, statistical analysis

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Authors: Mario Zgela

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Application of Benford’s Law is very rarely covered in the field of stock market analysis, especially in percentage change of stock market indices. Deutscher Aktien IndeX (DAX) is very important stock market index of Frankfurt Deutsche Börse which serves as underlying basis for large number of financial instruments. It is calculated for selected 30 German blue chips stocks. In this paper, Benford's Law first digit test is applied on 10 year DAX daily percentage changes in order to check compliance. Deviations of 10 year DAX percentage changes set as well as distortions of certain subsets from Benford's Law distribution are detected. It is possible that deviations are the outcome of speculations; and psychological influence should not be eliminated.

Keywords: Benford's Law, DAX, index percentage changes, stock market

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Authors: Claudeline D. Cellan

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Development is multifaceted, and efforts to hasten growth in all these facets have been gaining traction in recent years. Thus, producing a composite index that is reflective of these multidimensional impacts captures the interests of policymakers. The problem lies in going through a mixture of theoretical, methodological and empirical decisions and complexities which, when done carelessly, can lead to inconsistent and unreliable results. This study looks into index computation from a different and less complex perspective. Borrowing the idea of archetypes or ‘pure types’, archetypal analysis looks for points in the convex hull of the multivariate data set that captures as much information in the data as possible. The archetypes or 'pure types' are estimated such that they are convex combinations of all the observations, which in turn are convex combinations of the archetypes. This ensures that the archetypes are realistically observable, therefore achievable. In the sense of composite indices, we look for the best among these archetypes and use this as a benchmark for index computation. Its straightforward and simplistic approach does away with aggregation and substitutability problems which are commonly encountered in index computation. As an example of the application of archetypal analysis in index construction, the country data for the Human Development Index (HDI 2017) of the United Nations Development Programme (UNDP) is used. The goal of this exercise is not to replicate the result of the UNDP-computed HDI, but to illustrate the usability of archetypal analysis in index construction. Here best is defined in the context of life, education and gross national income sub-indices. Results show that the HDI from the archetypal analysis has a linear relationship with the UNDP-computed HDI.

Keywords: archetypes, composite index, convex combination, development

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Authors: Shokofeh Ebrtahimi

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Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G.Chemical graph theory is the topology branch of mathematical chemistry which applies graph theory to mathematical modelling of chemical phenomena.[1] The pioneers of the chemical graph theory are Alexandru Balaban, Ante Graovac, Ivan Gutman, Haruo Hosoya, Milan Randić and Nenad TrinajstićLet G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new program for computing the detour index of molecular graphs of nanotubes by heptagons is determineded. Some Conjectures about detour index of Molecular graphs of nanotubes is included.

Keywords: chemical graph, detour matrix, Detour index, carbon nanotube

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Authors: Helen Frialde-Dupale

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Critical thinking Index (CTI) of 150 third year college students from five State Colleges and Universities (SUCs) in Region I were determined. Only students with Grade Point Average (GPA) of at least 2.0 from four general classification of degree courses, namely: Education, Arts and Sciences, Engineering and Agriculture were included. Specific problem No.1 dealt with the profile variables, namely: age, sex, degree course, monthly family income, number of siblings, high school graduated from, grade point average, personality type, highest educational attainment of parents, and occupation of parents. Problem No. 2 determined the critical thinking index among the respondents. Problem No. 3 investigated whether or not there are significant differences in the critical thinking index among the respondents across the profile variables. While problem No.4 determined whether or not there are significant relationship between the critical thinking index and selected profile variables, namely: age, monthly family income, number of siblings, and grade point average of the respondents. Finally, on problem No. 5, the critical thinking instrument which obtained the lowest rates, were used as basis for outlining an intervention program for enhancing critical thinking index (CTI) of students. The following null hypotheses were tested at 0.05 level of significance: there are no significant differences in the critical thinking index of the third college students across the profile variables; there are no significant relationships between the critical thinking index of the respondents and selected variables, namely: age, monthly family income, number of siblings, and grade point average.

Keywords: attitude as critical thinker, critical thinking applied, critical thinking index, self-perception as critical thinker

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