Search results for: uncertainty and error visualisation

Authors: Huan Lin, Liwen Pang

Abstract:

In order to reduce the ambiguity and uncertainty of product form bionic design, a product form bionic design method based on eye tracking is proposed. The eye-tracking experiment is designed to calculate the average time ranking of the specific parts of the bionic shape that the subjects are looking at. Key bionic shape is explored through the experiment and then applied to a desk lamp bionic design. During the design case, FAHP (Fuzzy Analytic Hierachy Process) and SD (Semantic Differential) method are firstly used to identify consumer emotional perception model toward desk lamp before product design. Through investigating different desk lamp design elements and consumer views, the form design factors on the desk lamp product are reflected and all design schemes are sequenced after caculation. Desk lamp form bionic design method is combined the key bionic shape extracted from eye-tracking experiment and priority of desk lamp design schemes. This study provides an objective and rational method to product form bionic design.

Keywords: Bionic design; Form; Eye tracking; FAHP; Desk lamp

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Authors: Jan-Tore H. Horn, Jørgen Juncher Jensen

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Uncertainties related to fatigue damage estimation of non-linear systems are highly dependent on the tail behaviour and extreme values of the stress range distribution. By using a combination of the First Order Reliability Method (FORM) and Monte Carlo simulations (MCS), the accuracy of the fatigue estimations may be improved for the same computational efforts. The method is applied to a bottom-fixed, monopile-supported large offshore wind turbine, which is a non-linear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending on the sea-state dependent response characteristics, and the effect of a bi-linear S-N curve is discussed. Finally, analyses are performed on several environmental conditions to investigate the long-term applicability of this multistep method. Wave loads are calculated using state-of-the-art theory, while wind loads are applied with a simplified model based on rotor thrust coefficients.

Keywords: fatigue damage, FORM, monopile, Monte Carlo, simulation, wind turbine

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Authors: Zhongzhi Hu, Jie Shen, Jiqiang Wang

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A high precision aeroengine model is needed when developing the engine control system. Compared with other main components, the axial compressor is the most challenging component to simulate. In this paper, a compressor map optimizing tool based on the introduction of a modifiable β function is developed for FWorks (FADEC Works). Three parameters (d density, f fitting coefficient, k₀ slope of the line β=0) are introduced to the β function to make it modifiable. The comparison of the traditional β function and the modifiable β function is carried out for a certain type of compressor. The interpolation errors show that both methods meet the modeling requirements, while the modifiable β function can predict compressor performance more accurately for some areas of the compressor map where the users are interested in.

Keywords: beta function, compressor map, interpolation error, map optimization tool

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Authors: Marwin M. Dela Cruz

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Aviation as a transport sector is supportive of the seventeen (17) Sustainable Goals espoused by the United Nations. Air Transport Action Group (ATAG) states that over 18.1 million indirect jobs globally were sustained through the purchase of goods and services by companies in the aviation industry. This supply chain activity contributed approximately $816.4 billion to global GDP. This was achieved through numerous actions to lessen economic uncertainty and challenges. Its impact is not just a by-product of economic activity but of the facilities it generates. As the aviation industry is unifying its efforts, education and training should also come with it. The need for aviation education and training and a well-crafted regulatory policy initiated by lawmakers can provide a better aviation education. The Philippine State College of Aeronautics (PhilSCA), being the only government Higher Education Institution (HEI) in the Philippines, is given a very distinct congressional mandate to offer aviation-related courses to afford those in the aviation industry the opportunity to pursue studies. Having this, the industry has become the precursor and venue of present-day communities. In addition, it becomes an essential measure of a better life.

Keywords: Philippine state college of aeronautics, aviation industry, sustainable goals, aviation education

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Authors: J. T. Manhire

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A tax authority wants to take actions it knows will foster the greatest degree of voluntary taxpayer compliance to reduce the “tax gap.” This paper suggests that even if a tax authority could attain a state of complete knowledge, there are constraints on whether and to what extent such actions would result in reducing the macro-level tax gap. These limits are not merely a consequence of finite agency resources. They are inherent in the system itself. To show that this is one possible interpretation of the tax gap data, the paper formulates known results in a different way by analyzing tax compliance as a population with a single covariate. This leads to a standard use of the logistic map to analyze the dynamics of non-compliance growth or decay over a sequence of periods. This formulation gives the same results as the tax gap studies performed over the past fifty years in the U.S. given the published margins of error. Limitations and recommendations for future work are discussed, along with some implications for tax policy.

Keywords: income tax, logistic map, tax compliance, tax law

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Authors: Nilamadhab Mohanty

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It is essential to use message formats that make communication understandable and correct. It is because; the information format can influence consumer decision on the purchase of a product. This study combines information from qualitative inquiry, media trend analysis, eye tracking experiment, and questionnaire data to examine the impact of specific message format and consumer perceived risk on attention to the information and risk retention. We investigated the influence of message framing (goal framing, attribute framing, and mix framing) on consumer memory, study time, and decisional uncertainty while deciding on the purchase of drugs. Furthermore, we explored the impact of consumer perceived risk (associated with the use of the drug, i.e., RISK-AB and perceived risk associated with the non-use of the drug, i.e., RISK-EB) on message format preference. The study used eye-tracking methods to understand the differences in message processing. Findings of the study suggest that the message format influences information processing, and participants' risk perception impacts message format preference. Eye tracking can be used to understand the format differences and design effective advertisements.

Keywords: message framing, consumer perceived risk, advertising, eye tracking

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Authors: Sardar Ameer Akram Khan, Shahzad Amin Sheikh

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Blind equalization is an important technique amongst equalization family. Multimodulus algorithms based on blind equalization removes the undesirable effects of ISI and cater ups the phase issues, saving the cost of rotator at the receiver end. In this paper a new algorithm combination of recursive least square and Multimodulus algorithm named as RLSMMA is proposed by providing few assumption, fast convergence and minimum Mean Square Error (MSE) is achieved. The excellence of this technique is shown in the simulations presenting MSE plots and the resulting filter results.

Keywords: blind equalizations, constant modulus algorithm, multi-modulus algorithm, recursive least square algorithm, quadrature amplitude modulation (QAM)

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Authors: Bharti Singh, Shri K. Singh

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Child malnutrition is a multifaceted issue that transcends geographical boundaries. Malnutrition not only stunts physical growth but also leads to a spectrum of morbidities and child mortality. It is one of the leading causes of death (~50 %) among children under age five. Despite economic progress and advancements in healthcare, child malnutrition remains a formidable challenge for India. The objective is to investigate the impact of women's empowerment on child nutrition outcomes in India from 2006 to 2021. A composite index of women's empowerment was constructed using Confirmatory Factor Analysis (CFA), a rigorous technique that validates the measurement model by assessing how well-observed variables represent latent constructs. This approach ensures the reliability and validity of the empowerment index. Secondly, kernel density plots were utilised to visualise the distribution of key nutritional indicators, such as stunting, wasting, and overweight. These plots offer insights into the shape and spread of data distributions, aiding in understanding the prevalence and severity of malnutrition. Thirdly, linear polynomial graphs were employed to analyse how nutritional parameters evolved with the child's age. This technique enables the visualisation of trends and patterns over time, allowing for a deeper understanding of nutritional dynamics during different stages of childhood. Lastly, multilevel analysis was conducted to identify vulnerable levels, including State-level, PSU-level, and household-level factors impacting undernutrition. This approach accounts for hierarchical data structures and allows for the examination of factors at multiple levels, providing a comprehensive understanding of the determinants of child malnutrition. Overall, the utilisation of these statistical methodologies enhances the transparency and replicability of the study by providing clear and robust analytical frameworks for data analysis and interpretation. Our study reveals that NFHS-4 and NFHS-5 exhibit an equal density of severely stunted cases. NFHS-5 indicates a limited decline in wasting among children aged five, while the density of severely wasted children remains consistent across NFHS-3, 4, and 5. In 2019-21, women with higher empowerment had a lower risk of their children being undernourished (Regression coefficient= -0.10***; Confidence Interval [-0.18, -0.04]). Gender dynamics also play a significant role, with male children exhibiting a higher susceptibility to undernourishment. Multilevel analysis suggests household-level vulnerability (intra-class correlation=0.21), highlighting the need to address child undernutrition at the household level.

Keywords: child nutrition, India, NFHS, women’s empowerment

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Authors: Qusai Alshahwan

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The arbitrator’s duties of independence and impartiality play a significant role in delivering arbitral awards which legitimate the fundamental of arbitration concepts. For this reason, the international and national arbitration rules require arbitrators to be independent and impartial to solve the arbitration disputes fairly between the parties. However, solving the disputes fairly also requires arbitrators to disclose any existing conflicts of interest with the parties to avoid misunderstanding and late challenges. In contrary with the international and national arbitration rules, the English Arbitration Act 1996 does not include independence as a separate ground for arbitrator’s removal, and importantly the English Arbitration Act 1996 is deliberately silent to the arbitrator duty of disclosure. The absence of arbitrator duty of disclosure is an issue had generated uncertainty and concerns for the arbitration community under the English jurisdiction, particularly when the English courts rejected the IBA guidelines of arbitrator conflict of interest such as in case of Halliburton v Chubb for example. This article is highlighting on the legal consequences of the absence of arbitrator duty of disclosure under the English Arbitration Act 1996 and the arbitrator's contractual obligations.

Keywords: arbitration, impartiality, independence, duty of disclosure, English Arbitration Act 1996

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Authors: Abdulsalam Mas’ud

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Though Nigerian Biofuel Policy and Incentive was introduced in 2007, however, little if any is known about the impact of such policy for biodiesel development in Nigeria. It can be argued that lack of raw materials is one of the important factors that hinder the proper implementation of the policy. In line with this argument, this study aims to explore the determinants of smallholder farmers’ intention to adopt Jatropha as raw materials for biodiesel development in northern Nigeria, with Jigawa State as area of study. The determinants proposed for investigation covers personal factors, physical factors, institutional factors, economic factors, risk and uncertainty factors as well as social factors. The validation of the proposed model will have the implication of guiding policymakers towards enhancement of farmers’ participation in the Jatropha project for biodiesel raw materials production. The eventual byproducts of the proposed model validation and implementation will be employment generation, poverty reduction, combating dessert encroachment, economic diversification to renewable energy sources and electricity generation.

Keywords: adoption, biodiesel, factors, jatropha

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Authors: Navdeep Singh Randhawa

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Wireless communication system has been proved as the best for any communication. However, there are some undesirable threats of a wireless communication channel on the information transmitted through it, such as attenuation, distortions, delays and phase shifts of the signals arriving at the receiver end which are caused by its band limited and dispersive nature. One of the threat is ISI (Inter Symbol Interference), which has been found as a great obstacle in high speed communication. Thus, there is a need to provide perfect and accurate technique to remove this effect to have an error free communication. Thus, different equalization techniques have been proposed in literature. This paper presents the equalization techniques followed by the concept of adaptive filter equalizer, its algorithms (LMS and RLS) and applications of adaptive equalization technique.

Keywords: channel equalization, adaptive equalizer, least mean square, recursive least square

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Authors: Satyanarayana Engu, Ahmed Mohd, V. Murugan

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We study the large time asymptotics of solutions to the Cauchy problem for a forced Burgers equation (FBE) with the initial data, which is continuous and summable on R. For which, we first derive explicit solutions of FBE assuming a different class of initial data in terms of Hermite polynomials. Later, by violating this assumption we prove the existence of a solution to the considered Cauchy problem. Finally, we give an asymptotic approximate solution and establish that the error will be of order O(t^(-1/2)) with respect to L^p -norm, where 1≤p≤∞, for large time.

Keywords: Burgers equation, Cole-Hopf transformation, Hermite polynomials, large time asymptotics

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Authors: Gaoguang Yang, Shan Fu

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Human-machine interface (HMI) intermediate system information to human operators to facilitate human ability to manage and control the system. Well-designed HMI would enhance human ability. An evaluation must be performed to confirm that the designed HMI would enhance but not degrade human ability. However, the prevalent HMI evaluation techniques have difficulties in more thoroughly and accurately evaluating the suitability and fitness of a given HMI for the wide variety of uncertainty contained in both the existing HMI evaluation techniques and the large number of task scenarios. The first limitation should be attributed to the subjective and qualitative analysis characteristics of these evaluation methods, and the second one should be attributed to the cost balance. This study aims to explore the connection between objective HMI characters and ergonomic safety and step forward toward solving these limitations with objective, characterized HMI parameters. A simulation experiment was performed with the time needed for human operators to recognize the HMI information as characterized HMI parameter, and the result showed a strong correlation between the parameter and ergonomic safety level.

Keywords: Human-Machine Interface (HMI), evaluation, objective, characterization, simulation

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Authors: Majid Pourahmadi

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The performance of time-reversal MUSIC algorithm will be dramatically degrades in presence of strong noise and multiple scattering (i.e. when scatterers are close to each other). This is due to error in determining the number of scatterers. The present paper provides a new approach to alleviate such a problem using an information theoretic criterion referred as minimum description length (MDL). The merits of the novel approach are confirmed by the numerical examples. The results indicate the time-reversal MUSIC yields accurate estimate of the target locations with considerable noise and multiple scattering in the received signals.

Keywords: microwave imaging, time reversal, MUSIC algorithm, minimum description length (MDL)

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Authors: Hong-Ming Chen

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This work considers the resolution of the Hull and White interest rate model with the jump process. A deterministic process is adopted to model the random behavior of interest rate variation as deterministic perturbations, which is depending on the time t. The Brownian motion and jumps uncertainty are denoted as the integral functions piecewise constant function w(t) and point function θ(t). It shows that the interest rate function and the yield function of the Hull and White interest rate model with jump process can be obtained by solving a nonlinear semi-infinite programming problem. A relaxed cutting plane algorithm is then proposed for solving the resulting optimization problem. The method is calibrated for the U.S. treasury securities at 3-month data and is used to analyze several effects on interest rate prices, including interest rate variability, and the negative correlation between stock returns and interest rates. The numerical results illustrate that our approach essentially generates the yield functions with minimal fitting errors and small oscillation.

Keywords: optimization, interest rate model, jump process, deterministic

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Pınar Yardımcı

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This paper tries to answer to the questions whether or not trade openness cause economic growth and trade policy changes is good for Turkey as a developing country in global economy before and after 1980. We employ Johansen cointegration and Granger causality tests with error correction modelling based on vector autoregressive. Using WDI data from the pre-1980 and the post-1980, we find that trade openness and economic growth are cointegrated in the second term only. Also the results suggest a lack of long-run causality between our two variables. These findings may imply that trade policy of Turkey should concentrate more on extra complementary economic reforms.

Keywords: globalization, trade policy, economic growth, openness, cointegration, Turkey

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Authors: Wilson Enríquez, Daniel Cardenas

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This article proposes a filter bank format combined with the mathematical tool called polyphase decomposition and the discrete Fourier transform (DFT) with the purpose of improving the performance of the fifth-generation communication systems (5G). We started with a review of the literature and the study of the filter bank theory and its combination with DFT in order to improve the performance of wireless communications since it reduces the computational complexity of these communication systems. With the proposed technique, several experiments were carried out in order to evaluate the structures in 5G systems. Finally, the results are presented in graphical form in terms of bit error rate against the ratio bit energy/noise power spectral density (BER vs. Eb / No).

Keywords: multi-carrier system (5G), filter bank, polyphase decomposition, FIR equalizer

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Authors: Yashar Ibragimov, Nino Berishvili

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Technological, economic and other innovation-related advances of the 21st century have influenced the old, traditional business models. Presently, organizational change has become an integral part of corporate strategy for the majority of businesses. Such shifts have resulted in both new challenges and opportunities. The expansion of the use of information and communication technologies has driven fundamental shifts towards digital change. Organizations are being forced to revise processes, goals and overall mission in order to stay competitive in the marketplace. However, the implementation of digital transformation brings uncertainty, causes stress and raises concerns about future jobs. The study employs systematic literature review to fill the gap in understanding relationship between employee motivation and commitment during the transformation. A conceptual model proposes the antecedents (OCB and Leader Member Exchange) of employee motivation and investigates its impact on employee commitment to change. The utilized model elucidates how to maintain employee motivation and commitment in the context of organizational transformation and sets the ground for future research.

Keywords: employee motivation, change commitment, change management, leader member exchange, organizational citizenship behavior

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Authors: Garry A. Einicke, Langford B. White

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This paper describes an optimum filter and smoother for recovering a Markov process message from noisy measurements. The developments follow from an equivalence between a state space model and a hidden Markov chain. The ensuing filter and smoother employ transition probability matrices and approximate probability distribution vectors. The properties of the optimum solutions are retained, namely, the estimates are unbiased and minimize the variance of the output estimation error, provided that the assumed parameter set are correct. Methods for estimating unknown parameters from noisy measurements are discussed. Signal recovery examples are described in which performance benefits are demonstrated at an increased calculation cost.

Keywords: optimal filtering, smoothing, Markov chains

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Authors: Xin Jie Li

Abstract:

Due to population agglomeration, huge scale, and complex activities, megacities have become risk centers. To resist the risks brought by development uncertainty, the construction of resilient cities has become a common strategic choice for megacities. As a key link in promoting the modernization of the national governance system and governance capacity, optimizing the layout of national land space that focuses on ecology, production, and life and improving the rationality of spatial resource allocation are conducive to fundamentally promoting the resilience construction of megacities. Therefore, based on the perspective of territorial space governance, this article explores the potential risks faced by the territorial space of megacities and proposes possible paths for the resilience construction of megacities from four aspects: promoting the construction of a resilience system throughout the entire life cycle, constructing a disaster prevention and control system with ecological resilience, creating an industrial spatial pattern with production resilience, and enhancing community resilience to anchor the front line of risk response in megacities.

Keywords: mega cities, potential risks, resilient city construction, territorial and spatial governance

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Authors: Ibrahim Özbek, Erdoğan Mehmet Özkan

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In this study, we generalize (k,n) threshold secret sharing scheme on the study Ozbek and Siap to the codes over the ring Fq+ αFq. In this way, it is mentioned that the method obtained in that article can also be used on codes over rings, and new advantages to be obtained. The method of securely sharing the key in cryptography, which Shamir first systematized and Massey carried over to codes, became usable for all error-correcting codes. The firewall of this scheme is based on the hardness of the syndrome decoding problem. Also, an open study area is left for those working for other rings and code classes. All codes that correct errors with this method have been the working area of this method.

Keywords: secret sharing scheme, linear codes, algebra, finite rings

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Authors: Min-ju Kwon, Chae-won Kim, Jeong-yun Seo, Hee-guk Chae, Yong-seo Koo

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In this paper, we presented the LDO (low-dropout) regulator which enhanced the PSRR by applying the constant current source generation technique through the BGR (Band Gap Reference) to form the noise sensing circuit. The current source through the BGR has a constant current value even if the applied voltage varies. Then, the noise sensing circuit, which is composed of the current source through the BGR, operated between the error amplifier and the pass transistor gate of the LDO regulator. As a result, the LDO regulator has a PSRR of -68.2 dB at 1k Hz, -45.85 dB at 1 MHz and -45 dB at 10 MHz. the other performance of the proposed LDO was maintained at the same level of the conventional LDO regulator.

Keywords: LDO regulator, noise sensing circuit, current reference, pass transistor

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Authors: Zylfi Shehu, Rozeta Shatku

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The aim of this study is the identification of the goods and the consequences it brings up the mountain climbing to the youth, how mountain climbing influences in physical activity and the health of young people. Taken to study 37 young people aged 18-30 years, 25 males and 12 females. The selection was made at random and voluntary. Subjects were not professionals but amateurs climbing in the mountain. They were informed and instructed for the test to be carried out. The ascent was made in January 2016 in the Mount of Gjallica in Kukës, Albania, the height of the mountain is 2489 m above sea level. Backpack for each subject weighing 32 kg. Time of ascent, attitude and descent was 6 days. In 22 males, 2 of them did not afford the ascent on the first day and went back. Of the 12 women, 5 of them withdrew on the first day. During the descent on day six, 20 males 7 of them had minor injuries, three with serious injuries. While a total of 7 women, 4 of them had minor injuries and one with serious injuries. Most of the men and women who deal with physical activity throughout life faced the light and were not injured, and the rest that were not dealt with physical activity were more injured. Lack of experience and knowledge was one of the causes of injuries. The subjects had anxiety all the time, uncertainty and fear of avalanches of snow and difficult terrain.

Keywords: climbing, physical activity, young people

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Authors: Tovondahiniriko Fanjirindratovo, Olga Ramiarinjanahary, Paulisimone Rasoavonjy

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The sunshine duration, which is the sum of all the moments when the solar beam radiation is up to a minimal value, is an important parameter for climatology, tourism, agriculture and solar energy. Its measure is usually given by a pyrheliometer installed on a two-axis solar tracker. Due to the high cost of this device and the availability of global radiation on a horizontal surface, on the other hand, several studies have been done to make a correlation between global radiation and sunshine duration. Most of these studies are fitted for the northern hemisphere using a pyrheliometric database. The aim of the present work is to list and assess all the existing methods and apply them to Reunion Island, a tropical region in the southern hemisphere. Using a database of ten years, global, diffuse and beam radiation for a horizontal surface are employed in order to evaluate the uncertainty of existing algorithms for a tropical region. The methodology is based on indirect comparison because the solar beam radiation is not measured but calculated by the beam radiation on a horizontal surface and the sun elevation angle.

Keywords: Carpentras method, data fitting, global radiation, sunshine duration, Slob and Monna algorithm, step algorithm

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Authors: Mohammad Mahdi Kioumarsi

Abstract:

In this paper, using the response surface method (RSM), tornado diagram method and non-linear finite element analysis, the effect of four parameters on residual bending capacity of a corroded RC beam was investigated. The parameters considered are amount of localised cross section reduction, ratio of pit distance on adjacent bars to rebar distance, concrete compressive strength, and rebar tensile strength. The focus is on the influence on the bending ultimate limit state. Based on the obtained results, the effects of the ratio of pit distance to rebar distance (Lp⁄Lr) and the ratio of the localised cross section reduction to the original area of the rebar (Apit⁄A0) were found significant. The interference of localised corrosion on adjacent reinforcement bars reduces the bending capacity of under-reinforced concrete beam. Using the sensitivity analysis could lead to recognize uncertainty parameters, which have the most influences on the performance of the structure.

Keywords: localised corrosion, concrete beam, sensitivity analyses, ultimate capacity

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Authors: Rimac Smiljanic Ana, Pepur Sandra, Bulog Ivana

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Financial decision-making in the household is not simple, and it demands that the decision-maker has proper knowledge and skills. Usually, high uncertainty, risk, and stress surround household financial decision-making since it is extremely important and critical for household wealth accumulation and for the well-being of all household members. Generally, skilful people tend to have higher confidence in certain tasks they perform, and they achieve better results. Therefore, in the household context, the possession of certain skills by the ones who make financial decisions for the household is of particular importance. This paper addresses financial literacy as an important skill for household decision-making. Apart from financial literacy, the paper also considers other factors, such as employment, education, and age, as significant for household financial decision-making. The analysis is based on quantitative individual-level survey data. The data collection was conducted during January and February 2021 in Croatia through an online survey. To reach a wide variety of participants, the snowball sampling method was used. The result revealed interesting and somewhat puzzling results. Our results point to the importance of financial literacy skills for household decision-making.

Keywords: skill, financial literacy, decision-making, household financijal decision making

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Authors: Lei Ren, Michael Hartnett, Stephen Nash

Abstract:

The abundant measured surface current from HF radar system in coastal area is assimilated into model to improve the modeling forecasting ability. A simple sequential data assimilation scheme, Direct Insertion (DI), is applied to update model forecast states. The influence of Direct Insertion data assimilation over time is analyzed at one reference point. Vector maps of surface current from models are compared with HF radar measurements. Root-Mean-Squared-Error (RMSE) between modeling results and HF radar measurements is calculated during the last four days with no data assimilation.

Keywords: data assimilation, CODAR, HF radar, surface current, direct insertion

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Authors: Nishant Shrivastava, D. K. Sehgal

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In Finite Element Technique nodal stresses are calculated through displacement as nodes. In this process, the displacement calculated at nodes is sufficiently good enough but stresses calculated at nodes are not sufficiently accurate. Therefore, the accuracy in the stress computation in FEM models based on the displacement technique is obviously matter of concern for computational time in shape optimization of engineering problems. In the present work same is focused to find out unique points within the element as well as the boundary of the element so, that good accuracy in stress computation can be achieved. Generally, major optimal stress points are located in domain of the element some points have been also located at boundary of the element where stresses are fairly accurate as compared to nodal values. Then, it is subsequently concluded that there is an existence of unique points within the element, where stresses have higher accuracy than other points in the elements. Therefore, it is main aim is to evolve a generalized procedure for the determination of the optimal stress location inside the element as well as at the boundaries of the element and verify the same with results from numerical experimentation. The results of quadratic 9 noded serendipity elements are presented and the location of distinct optimal stress points is determined inside the element, as well as at the boundaries. The theoretical results indicate various optimal stress locations are in local coordinates at origin and at a distance of 0.577 in both directions from origin. Also, at the boundaries optimal stress locations are at the midpoints of the element boundary and the locations are at a distance of 0.577 from the origin in both directions. The above findings were verified through experimentation and findings were authenticated. For numerical experimentation five engineering problems were identified and the numerical results of 9-noded element were compared to those obtained by using the same order of 25-noded quadratic Lagrangian elements, which are considered as standard. Then root mean square errors are plotted with respect to various locations within the elements as well as the boundaries and conclusions were drawn. After numerical verification it is noted that in a 9-noded element, origin and locations at a distance of 0.577 from origin in both directions are the best sampling points for the stresses. It was also noted that stresses calculated within line at boundary enclosed by 0.577 midpoints are also very good and the error found is very less. When sampling points move away from these points, then it causes line zone error to increase rapidly. Thus, it is established that there are unique points at boundary of element where stresses are accurate, which can be utilized in solving various engineering problems and are also useful in shape optimizations.

Keywords: finite elements, Lagrangian, optimal stress location, serendipity

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Authors: Ahteshamul Haq, Srikant Gupta, Murshid Kamal, Irfan Ali

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This case study designs and builds a multi-objective production planning model for a hardware firm with certain & uncertain data. During the time of interaction with the manager of the firm, they indicate some of the parameters may be vague. This vagueness in the formulated model is handled by the concept of fuzzy set theory. Triangular & Trapezoidal fuzzy numbers are used to represent the uncertainty in the collected data. The fuzzy nature is de-fuzzified into the crisp form using well-known defuzzification method via graded mean integration representation method. The proposed model attempts to maximize the production of the firm, profit related to the manufactured items & minimize the carrying inventory costs in both certain & uncertain environment. The recommended optimal plan is determined via fuzzy programming approach, and the formulated models are solved by using optimizing software LINGO 16.0 for getting the optimal production plan. The proposed model yields an efficient compromise solution with the overall satisfaction of decision maker.

Keywords: production planning problem, multi-objective optimization, fuzzy programming, fuzzy sets

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