Search results for: change point estimation

Authors: Jianqin Qu

Abstract:

This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: Covariant point, point matching, dimension free, rigid registration.

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Authors: Tanuj Kanchan, Anadi Gupta, Kewal Krishan

Abstract:

Human skull is shown to exhibit numerous sexually dimorphic traits. Estimation of sex is a challenging task especially when a part of skull is brought for medicolegal investigation. The present research was planned to evaluate the sexing potential of the dimensions of foramen magnum in forensic identification by craniometric analysis. Length and breadth of the foramen magnum was measured using Vernier calipers and the area of foramen magnum was calculated. The length, breadth, and area of foramen magnum were found to be larger in males than females. Sexual dimorphism index was calculated to estimate the sexing potential of each variable. The study observations are suggestive of the limited utility of the craniometric analysis of foramen magnum during the examination of skull and its parts in estimation of sex.

Keywords: Forensic Anthropology, Skeletal remains, Identification, Sex estimation, Foramen magnum.

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Authors: N. P. Waweru, D. B. O. Konditi, P. K. Langat

Abstract:

Direction of Arrival estimation refers to defining a mathematical function called a pseudospectrum that gives an indication of the angle a signal is impinging on the antenna array. This estimation is an efficient method of improving the quality of service in a communication system by focusing the reception and transmission only in the estimated direction thereby increasing fidelity with a provision to suppress interferers. This improvement is largely dependent on the performance of the algorithm employed in the estimation. Many DOA algorithms exists amongst which are MUSIC, Root-MUSIC and ESPRIT. In this paper, performance of these three algorithms is analyzed in terms of complexity, accuracy as assessed and characterized by the CRLB and memory requirements in various environments and array sizes. It is found that the three algorithms are high resolution and dependent on the operating environment and the array size. 

Keywords: Direction of Arrival, Autocorrelation matrix, Eigenvalue decomposition, MUSIC, ESPRIT, CRLB.

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Authors: Nicholas D. Assimakis

Abstract:

In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: Discrete time, linear estimation, Kalman filter, Kalman filter gain.

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Authors: Siriwan Saksiriruthai

Abstract:

This paper develops models to analyze the relationship between leisure time and wage change. Using Thailand-s Time Use Survey and Labor Force Survey data, the estimation of wage changes in response to leisure time change indicates that media receiving, personal care and social participation and volunteer activities are the ones that significantly raise hourly wages. Thus, the finding suggests the stimulation in time use for media access to enhance knowledge and productivity, personal care for attractiveness and healthiness in order to raise productivity, and social activities to develop connections for possible future opportunities including wage increase. These activities should be promoted for productive leisure time and for welfare improvement.

Keywords: Leisure, wage, time use, Thailand.

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Authors: Hossein Pazhoumand-Dar, Amir Mohsen Toliyat Abolhassani, Ehsan Saeedi

Abstract:

Speed estimation is one of the important and practical tasks in machine vision, Robotic and Mechatronic. the availability of high quality and inexpensive video cameras, and the increasing need for automated video analysis has generated a great deal of interest in machine vision algorithms. Numerous approaches for speed estimation have been proposed. So classification and survey of the proposed methods can be very useful. The goal of this paper is first to review and verify these methods. Then we will propose a novel algorithm to estimate the speed of moving object by using fuzzy concept. There is a direct relation between motion blur parameters and object speed. In our new approach we will use Radon transform to find direction of blurred image, and Fuzzy sets to estimate motion blur length. The most benefit of this algorithm is its robustness and precision in noisy images. Our method was tested on many images with different range of SNR and is satisfiable.

Keywords: Blur Analysis, Fuzzy sets, Speed estimation.

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Authors: Won-Jae Shin, Young-Hwan You

Abstract:

Cyclic delay diversity (CDD) is a simple technique to intentionally increase frequency selectivity of channels for orthogonal frequency division multiplexing (OFDM).This paper proposes a residual carrier frequency offset (RFO) estimation scheme for OFDMbased broadcasting system using CDD. In order to improve the RFO estimation, this paper addresses a decision scheme of the amount of cyclic delay and pilot pattern used to estimate the RFO. By computer simulation, the proposed estimator is shown to benefit form propoerly chosen delay parameter and perform robustly.

Keywords: OFDM, cyclic delay diversity, FM system, synchronization

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Authors: C. Agrawal, R. Kumar, A. Gupta, B. Chatterjee

Abstract:

An experimental investigation has been carried out to study the cooling of a hot horizontal Stainless Steel surface of 3 mm thickness, which has 800±10 C initial temperature. A round water jet of 22 ± 1 oC temperature was injected over the hot surface through straight tube type nozzles of 2.5- 4.8 mm diameter and 250 mm length. The experiments were performed for the jet exit to target surface spacing of 4 times of jet diameter and jet Reynolds number of 5000 -24000. The effect of change in jet Reynolds number on the surface quenching has been investigated form the stagnation point to 16 mm spatial location.  

Keywords: Hot-Surface, Jet Impingement, Quenching, Stagnation Point.

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Authors: Xiaowei Zhang, Min Xu, Saeid Habibi, Fengjun Yan, Ryan Ahmed

Abstract:

Recently, Electric Vehicles (EVs) have received extensive consideration since they offer a more sustainable and greener transportation alternative compared to fossil-fuel propelled vehicles. Lithium-Ion (Li-ion) batteries are increasingly being deployed in EVs because of their high energy density, high cell-level voltage, and low rate of self-discharge. Since Li-ion batteries represent the most expensive component in the EV powertrain, accurate monitoring and control strategies must be executed to ensure their prolonged lifespan. The Battery Management System (BMS) has to accurately estimate parameters such as the battery State-of-Charge (SOC), State-of-Health (SOH), and Remaining Useful Life (RUL). In order for the BMS to estimate these parameters, an accurate and control-oriented battery model has to work collaboratively with a robust state and parameter estimation strategy. Since battery physical parameters, such as the internal resistance and diffusion coefficient change depending on the battery state-of-life (SOL), the BMS has to be adaptive to accommodate for this change. In this paper, an extensive battery aging study has been conducted over 12-months period on 5.4 Ah, 3.7 V Lithium polymer cells. Instead of using fixed charging/discharging aging cycles at fixed C-rate, a set of real-world driving scenarios have been used to age the cells. The test has been interrupted every 5% capacity degradation by a set of reference performance tests to assess the battery degradation and track model parameters. As battery ages, the combined model parameters are optimized and tracked in an offline mode over the entire batteries lifespan. Based on the optimized model, a state and parameter estimation strategy based on the Extended Kalman Filter (EKF) and the relatively new Smooth Variable Structure Filter (SVSF) have been applied to estimate the SOC at various states of life.

Keywords: Lithium-Ion batteries, genetic algorithm optimization, battery aging test, and parameter identification.

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Authors: Sang Hyun Kim

Abstract:

In this paper, a fast motion compensation algorithm is proposed that improves coding efficiency for video sequences with brightness variations. We also propose a cross entropy measure between histograms of two frames to detect brightness variations. The framewise brightness variation parameters, a multiplier and an offset field for image intensity, are estimated and compensated. Simulation results show that the proposed method yields a higher peak signal to noise ratio (PSNR) compared with the conventional method, with a greatly reduced computational load, when the video scene contains illumination changes.

Keywords: Motion estimation, Fast motion compensation, Brightness variation compensation, Brightness change detection, Cross entropy.

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Authors: Gabriel Jinga, Madalina Dumitru

Abstract:

The objective of this paper is to present the process of change in management accounting in Romania, a former communist country from Eastern Europe. In order to explain this process, we used the contingency and institutional theories. We focused on the following directions: the presentation of the scientific context and motivation of this research and the case study. We presented the state of the art in the process of change in the management accounting from the international and national perspective. We also described the evolution of management accounting in Romania in the context of economic and political changes. An important moment was the fall of communism in 1989. This represents a starting point for a new economic environment and for new management accounting. Accordingly, we developed a case study which presented this evolution. The conclusion of our research was that the changes in the management accounting system of the company analysed occurred in the same time with the institutionalisation of some elements (e.g. degree of competition, training and competencies in management accounting). The management accounting system was modelled by the contingencies specific to this company (e.g. environment, industry, strategy).

Keywords: Management accounting, change, Romania, contingency and institutional theory.

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Authors: Young-Jae Kim, Young-Hwan You

Abstract:

This paper presents a integer frequency offset (IFO) estimation scheme for the 3GPP long term evolution (LTE) downlink system. Firstly, the conventional joint detection method for IFO and sector cell index (CID) information is introduced. Secondly, an IFO estimation without explicit sector CID information is proposed, which can operate jointly with the proposed IFO estimation and reduce the time delay in comparison with the conventional joint method. Also, the proposed method is computationally efficient and has almost similar performance in comparison with the conventional method over the Pedestrian and Vehicular channel models.

Keywords: LTE, OFDMA, primary synchronization signal (PSS), IFO, CID

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Authors: Nermin Sökmen

Abstract:

An effort estimation model is needed for softwareintensive projects that consist of hardware, embedded software or some combination of the two, as well as high level software solutions. This paper first focuses on functional decomposition techniques to measure functional complexity of a computer system and investigates its impact on system development effort. Later, it examines effects of technical difficulty and design team capability factors in order to construct the best effort estimation model. With using traditional regression analysis technique, the study develops a system development effort estimation model which takes functional complexity, technical difficulty and design team capability factors as input parameters. Finally, the assumptions of the model are tested.

Keywords: Functional complexity, functional decomposition, development effort, technical difficulty, design team capability, regression analysis.

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Authors: Changhyuk Jang, Keechul Jung

Abstract:

Human pose estimation can be executed using Active Shape Models. The existing techniques for applying to human-body research using Active Shape Models, such as human detection, primarily take the form of silhouette of human body. This technique is not able to estimate accurately for human pose to concern two arms and legs, as the silhouette of human body represents the shape as out of round. To solve this problem, we applied the human body model as stick-figure, “skeleton". The skeleton model of human body can give consideration to various shapes of human pose. To obtain effective estimation result, we applied background subtraction and deformed matching algorithm of primary Active Shape Models in the fitting process. The images which were used to make the model were 600 human bodies, and the model has 17 landmark points which indicate body junction and key features of human pose. The maximum iteration for the fitting process was 30 times and the execution time was less than .03 sec.

Keywords: Active shape models, skeleton, pose estimation.

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Authors: Kalu Ram Meena, Aditi Kar Gangopadhyay, Satrajit Mandal

Abstract:

Two normal populations with different means and same variance are considered, where the variance is known. The population with the smaller sample mean is selected. Various estimators are constructed for the mean of the selected normal population. Finally, they are compared with respect to the bias and MSE risks by the mehod of Monte-Carlo simulation and their performances are analysed with the help of graphs.

Keywords: Estimation after selection, Brewster-Zidek technique.

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Authors: Yang Jiang, Zhuchao Yu, Zhu Wang, Xueying Hong

Abstract:

Reference point effects of top managers exerts an influence on managerial decision-making behaviors. We introduces the main idea of developing the decision behavior testing system designed for top manager in team task circumstance. According to the theory of the reference point effect, study of testing experiments in the reference point effect is carried out. Under managerial decision-making simulation environment, a platform is designed for testing reference point effect. The system uses the outcome of the value of the reference point to report the characteristics of the decision behavior of top managers.

Keywords: reference point effect, decision-making behavior, top manager, managerial decision-making simulation environment.

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Authors: Thomas K. Wanner

Abstract:

This paper examines the link between gender equality and climate change policies in Australia. It critically analyses the extent to which gender mainstreaming and gender dimensions have been taken into account in the national policy processes for climate change in Australia. The paper argues that climate change adaptation and mitigation policies in Australia neglect gender dimensions. This endangers the advances made in gender equality and works against socially equitable and effective climate change strategies.

Keywords: Climate change, gender equality, gendermainstreaming, sustainable development.

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Authors: Zamri Noranai, Dayang Siti Zainab Abang Bujang, Rosli Asmawi, Hamidon Salleh, Mohammad Zainal Md Yusof

Abstract:

Air conditioning is mainly to be used as human comfort medium. It has been use more often in country in which the daily temperatures are high. In scientific, air conditioning is defined as a process of controlling the moisture, cooling, heating and cleaning air. Without proper estimation of cooling load, big amount of waste energy been used because of unsuitable of air conditioning system are not considering to overcoming heat gains from surrounding. This is due to the size of the room is too big and the air conditioning has to use more energy to cool the room and the air conditioning is too small for the room. The studies are basically to develop a program to calculate cooling load. Through this study it is easy to calculate cooling load estimation. Furthermore it-s help to compare the cooling load estimation by hourly and yearly. Base on the last study that been done, the developed software are not user-friendly. For individual without proper knowledge of calculating cooling load estimation might be problem. Easy excess and user-friendly should be the main objective to design something. This program will allow cooling load able be estimate by any users rather than estimation by using rule of thumb. Several of limitation of case study is judged to sure it-s meeting to Malaysia building specification. Finally validation is done by comparison manual calculation and by developed program.

Keywords: Building, Energy and Coaling Load

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Authors: Chen-Yu Wang, Tsung-Chien Chen, Ming-Hui Lee, Jen-Feng Huang

Abstract:

In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to three kinds of samples (Copper, Iron and Steel/AISI 304) with the same 3mm thickness. The temperature measurements are then regarded as the inputs into the FWIEM to estimate the heat flux. The experiment results show that the proposed algorithm can estimate the unknown time-varying heat flux on-line.

Keywords: Fuzzy Weighted Input Estimation Method, IHCP andHeat Flux.

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Authors: Amit Kumar Gautam, Sudipta Majumdar

Abstract:

This paper presents parameter estimation of a single-phase rectifier using extended Kalman filter (EKF). The state space model has been obtained using Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL). The capacitor voltage and diode current of the circuit have been estimated using EKF. Simulation results validate the better accuracy of the proposed method as compared to the least mean square method (LMS). Further, EKF has the advantage that it can be used for nonlinear systems.

Keywords: Extended Kalman filter, parameter estimation, single phase rectifier, state space modelling.

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Authors: M. Tridi, N. Nacereddine, N. Oucief

Abstract:

This paper describes a novel method for automatic estimation of the contours of weld defect in radiography images. Generally, the contour detection is the first operation which we apply in the visual recognition system. Our approach can be described as a region based maximum likelihood formulation of parametric deformable contours. This formulation provides robustness against the poor image quality, and allows simultaneous estimation of the contour parameters together with other parameters of the model. Implementation is performed by a deterministic iterative algorithm with minimal user intervention. Results testify for the very good performance of the approach especially in synthetic weld defect images.

Keywords: Contour, gaussian, likelihood, rayleigh.

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Authors: T. Arsan

Abstract:

Video streaming over lossy IP networks is very important issues, due to the heterogeneous structure of networks. Infrastructure of the Internet exhibits variable bandwidths, delays, congestions and time-varying packet losses. Because of variable attributes of the Internet, video streaming applications should not only have a good end-to-end transport performance but also have a robust rate control, furthermore multipath rate allocation mechanism. So for providing the video streaming service quality, some other components such as Bandwidth Estimation and Adaptive Rate Controller should be taken into consideration. This paper gives an overview of video streaming concept and bandwidth estimation tools and then introduces special architectures for bandwidth adaptive video streaming. A bandwidth estimation algorithm – pathChirp, Optimized Rate Controllers and Multipath Rate Allocation Algorithm are considered as all-in-one solution for video streaming problem. This solution is directed and optimized by a decision center which is designed for obtaining the maximum quality at the receiving side.

Keywords: Adaptive Video Streaming, Bandwidth Estimation, QoS, Software Architecture.

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Authors: Parit Kanjanavirojkul, Kiatwarakorn Keeratishananond, Prapun Suksompong

Abstract:

We study the performance of compressed beamforming weights feedback technique in generalized triangular decomposition (GTD) based MIMO system. GTD is a beamforming technique that enjoys QoS flexibility. The technique, however, will perform at its optimum only when the full knowledge of channel state information (CSI) is available at the transmitter. This would be impossible in the real system, where there are channel estimation error and limited feedback. We suggest a way to implement the quantized beamforming weights feedback, which can significantly reduce the feedback data, on GTD-based MIMO system and investigate the performance of the system. Interestingly, we found that compressed beamforming weights feedback does not degrade the BER performance of the system at low input power, while the channel estimation error and quantization do. For comparison, GTD is more sensitive to compression and quantization, while SVD is more sensitive to the channel estimation error. We also explore the performance of GTDbased MU-MIMO system, and find that the BER performance starts to degrade largely at around -20 dB channel estimation error.

Keywords: MIMO, MU-MIMO, GTD, Imperfect CSI.

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Authors: C.Ramesh, V.Vaidehi

Abstract:

Ultra-wide band (UWB) communication is one of the most promising technologies for high data rate wireless networks for short range applications. This paper proposes a blind channel estimation method namely IMM (Interactive Multiple Model) Based Kalman algorithm for UWB OFDM systems. IMM based Kalman filter is proposed to estimate frequency selective time varying channel. In the proposed method, two Kalman filters are concurrently estimate the channel parameters. The first Kalman filter namely Static Model Filter (SMF) gives accurate result when the user is static while the second Kalman filter namely the Dynamic Model Filter (DMF) gives accurate result when the receiver is in moving state. The static transition matrix in SMF is assumed as an Identity matrix where as in DMF, it is computed using Yule-Walker equations. The resultant filter estimate is computed as a weighted sum of individual filter estimates. The proposed method is compared with other existing channel estimation methods.

Keywords: Channel estimation, Kalman filter, UWB, Channel model, AR model

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Authors: A. Thabet, M. Boutayeb, M. N. Abdelkrim

Abstract:

This paper investigates a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation (DAE) models using the extended Kalman filter. The method involves the use of a transformation from a DAE to ordinary differential equation (ODE). A relevant dynamic power system model using decoupled techniques will be proposed. The estimation technique consists of a state estimator based on the EKF technique as well as the local stability analysis. High performances are illustrated through a simulation study applied on IEEE 13 buses test system.

Keywords: Power system, Dynamic decoupled model, Extended Kalman Filter, Convergence analysis, Time computing.

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Authors: Nandini N., Srikanta Murthy K., G. Hemantha Kumar

Abstract:

This paper includes two novel techniques for skew estimation of binary document images. These algorithms are based on connected component analysis and Hough transform. Both these methods focus on reducing the amount of input data provided to Hough transform. In the first method, referred as word centroid approach, the centroids of selected words are used for skew detection. In the second method, referred as dilate & thin approach, the selected characters are blocked and dilated to get word blocks and later thinning is applied. The final image fed to Hough transform has the thinned coordinates of word blocks in the image. The methods have been successful in reducing the computational complexity of Hough transform based skew estimation algorithms. Promising experimental results are also provided to prove the effectiveness of the proposed methods.

Keywords: Dilation, Document processing, Hough transform, Optical Character Recognition, Skew estimation, and Thinning.

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Authors: Damien Gondre, Hatem Ben Maad, Abdelkrim Trabelsi, Frédéric Kuznik, Joseph Virgone

Abstract:

The use of a radiant cooling solution would enable to lower cooling needs which is of great interest when the demand is initially high (hot climate). But, radiant systems are not naturally compatibles with humid climates since a low-temperature surface leads to condensation risks as soon as the surface temperature is close to or lower than the dew point temperature. A radiant cooling system combined to a dehumidification system would enable to remove humidity for the space, thereby lowering the dew point temperature. The humidity removal needs to be especially effective near the cooled surface. This requirement could be fulfilled by a system using a single desiccant fluid for the removal of both excessive heat and moisture. This task aims at providing an estimation of the specification requirements of such system in terms of cooling power and dehumidification rate required to fulfill comfort issues and to prevent any condensation risk on the cool panel surface. The present paper develops a preliminary study on the specification requirements, performances and behavior of a combined dehumidifier/cooling ceiling panel for different operating conditions. This study has been carried using the TRNSYS software which allows nodal calculations of thermal systems. It consists of the dynamic modeling of heat and vapor balances of a 5m x 3m x 2.7m office space. In a first design estimation, this room is equipped with an ideal heating, cooling, humidification and dehumidification system so that the room temperature is always maintained in between 21^◦C and 25^◦C with a relative humidity in between 40% and 60%. The room is also equipped with a ventilation system that includes a heat recovery heat exchanger and another heat exchanger connected to a heat sink. Main results show that the system should be designed to meet a cooling power of 42W.m⁻² and a desiccant rate of 45 g_H2O.h⁻¹. In a second time, a parametric study of comfort issues and system performances has been achieved on a more realistic system (that includes a chilled ceiling) under different operating conditions. It enables an estimation of an acceptable range of operating conditions. This preliminary study is intended to provide useful information for the system design.

Keywords: Dehumidification, nodal calculation, radiant cooling panel, system sizing.

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Authors: M. Moosavi, H. Khatibzadeh

Abstract:

In this article, we study demiclosed and strongly quasi-nonexpansive of a sequence generated by the proximal point algorithm for a finite family of quasi-nonexpansive mappings in Hadamard spaces. Δ-convergence of iterations for the sequence of strongly quasi-nonexpansive mappings as well as the strong convergence of the Halpern type regularization of them to a common fixed point of sequence are also established. Our results generalize and improve several previously known results of the existing literature.

Keywords: Fixed point, Hadamard space, proximal point algorithm, quasi-nonexpansive sequence of mappings, resolvent.

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Authors: M. Y. Misro, A. Ramli, J. M. Ali

Abstract:

Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use different approach to find the best approximation for the curve so that it will resembles highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first, the Bezier curve estimates the real shape of the curve which can be verified visually. Even though, fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed are acceptable. We verified our result with the manual calculation of the curvature from the map.

Keywords: Speed estimation, path constraints, reference trajectory, Bezier curve.

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Authors: Jelena Zagorska, Inga Ciprovica

Abstract:

The freezing point of milk is in important indicator of the milk quality. The freezing point of milk is determined primarily to prove milk adulteration with water and to determine the amount of water in it. Chemical composition and properties of milk, thermal treatment and presence of any substance can influence freezing point of product. There are different substances, which can be added to milk with main purpose to prolong shelf-life of raw milk. There are detergent, preservatives, formaldehyde, hydrogen peroxide, antibiotics, sodium carbonate, and hydrogen peroxide. Therefore the aim of the present study was to determine freezing point of milk, skimmed milk, pasteurized milk and milk with different substances (formaldehyde, antibiotics, sodium carbonate, hydrogen peroxide, disinfectant, and detergent) in different concentrations. The thermal treatment and different undesirable substances presence in milk have significant influence on freezing point of it.

Keywords: Antibiotics, freezing point, milk, pH, thermal treatment.

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