Search results for: Functional point

Authors: M. Pepe, S. Ackermann, L. Fregonese, C. Achille

Abstract:

3D models obtained with advanced survey techniques such as close-range photogrammetry and laser scanner are nowadays particularly appreciated in Cultural Heritage and Archaeology fields. In order to produce high quality models representing archaeological evidences and anthropological artifacts, the appearance of the model (i.e. color) beyond the geometric accuracy, is not a negligible aspect. The integration of the close-range photogrammetry survey techniques with the laser scanner is still a topic of study and research. By combining point cloud data sets of the same object generated with both technologies, or with the same technology but registered in different moment and/or natural light condition, could construct a final point cloud with accentuated color dissimilarities. In this paper, a methodology to uniform the different data sets, to improve the chromatic quality and to highlight further details by balancing the point color will be presented.

Keywords: Color models, cultural heritage, laser scanner, photogrammetry, point cloud color.

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Authors: Werner Reichenfelser, Harald Hackl, Josef Hufgard, Karin Gstaltner, Margit Gfoehler

Abstract:

Training with Functional Electrical Stimulation (FES) has both physiological and psychological benefits for spinal cord injured subjects. Commonly used methods for quantification of spasticity have shown controversial reliability. In this study we propose a method for quick determination of spasticity in spinal cord injured subjects on a cycling and measurement system. 23 patients did training sessions on an instrumented mobile FES cycle three times a week over two months as part of their clinical rehabilitation program. Spasticity (MAS) and the legs resistance to the pedaling motion were assessed before and after the FES training and measurements were done on the subjects ability to pedal with our without motor assistance. Measurements with test persons with incomplete spastic paraplegia have shown that spasticity is decreased after a 30 min cycling training with functional electrical stimulation (FES).

Keywords: Spasticity, paraplegia, spinal cord injury, functional electrical stimulation.

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Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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Authors: Amjad Abdullah, Amjad Yahya, Bushra Aljohani, Amani S. Alghamdi

Abstract:

Change point detection is an important part of data analysis. The presence of a change point refers to a significant change in the behavior of a time series. In this article, we examine the detection of multiple change points of parameters of the exponential Lomax distribution, which is broad and flexible compared with other distributions while fitting data. We used the Schwarz information criterion and binary segmentation to detect multiple change points in publicly available data on the average temperature in the ozone layer. The change points were successfully located.

Keywords: Binary segmentation, change point, exponential Lomax distribution, information criterion.

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Authors: Xiaoli Shen, Yuehui Chen

Abstract:

Interactions among proteins are the basis of various life events. So, it is important to recognize and research protein interaction sites. A control set that contains 149 protein molecules were used here. Then 10 features were extracted and 4 sample sets that contained 9 sliding windows were made according to features. These 4 sample sets were calculated by Radial Basis Functional neutral networks which were optimized by Particle Swarm Optimization respectively. Then 4 groups of results were obtained. Finally, these 4 groups of results were integrated by decision fusion (DF) and Genetic Algorithm based Selected Ensemble (GASEN). A better accuracy was got by DF and GASEN. So, the integrated methods were proved to be effective.

Keywords: protein interaction sites, features, sliding windows, radial basis functional neutral networks, genetic algorithm basedselected ensemble.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

Abstract:

In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Alemayehu Geremew Negash

Abstract:

In this paper, we prove some common fixed point theorems for co-cyclic weak contractions in compact metric spaces.

Keywords: Cyclic weak contraction, Co-cyclic weak contraction, Co-cyclic representation, Common fixed point.

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Authors: M. Uysal, M. Yilmaz, I. Tiryakioğlu

Abstract:

Digital Terrain Model (DTM) is a digital numerical representation of the Earth's surface. DTMs have been applied to a diverse field of tasks, such as urban planning, military, glacier mapping, disaster management. In the expression of the Earth' surface as a mathematical model, an infinite number of point measurements are needed. Because of the impossibility of this case, the points at regular intervals are measured to characterize the Earth's surface and DTM of the Earth is generated. Hitherto, the classical measurement techniques and photogrammetry method have widespread use in the construction of DTM. At present, RADAR, LiDAR, and stereo satellite images are also used for the construction of DTM. In recent years, especially because of its superiorities, Airborne Light Detection and Ranging (LiDAR) has an increased use in DTM applications. A 3D point cloud is created with LiDAR technology by obtaining numerous point data. However recently, by the development in image mapping methods, the use of unmanned aerial vehicles (UAV) for photogrammetric data acquisition has increased DTM generation from image-based point cloud. The accuracy of the DTM depends on various factors such as data collection method, the distribution of elevation points, the point density, properties of the surface and interpolation methods. In this study, the random data reduction method is compared for DTMs generated from image based point cloud data. The original image based point cloud data set (100%) is reduced to a series of subsets by using random algorithm, representing the 75, 50, 25 and 5% of the original image based point cloud data set. Over the ANS campus of Afyon Kocatepe University as the test area, DTM constructed from the original image based point cloud data set is compared with DTMs interpolated from reduced data sets by Kriging interpolation method. The results show that the random data reduction method can be used to reduce the image based point cloud datasets to 50% density level while still maintaining the quality of DTM.

Keywords: DTM, unmanned aerial vehicle, UAV, random, Kriging.

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Authors: Sanghyeok Oh, Keechul Jung

Abstract:

Although lots of research work has been done for human pose recognition, the view-point of cameras is still critical problem of overall recognition system. In this paper, view-point insensitive human pose recognition is proposed. The aims of the proposed system are view-point insensitivity and real-time processing. Recognition system consists of feature extraction module, neural network and real-time feed forward calculation. First, histogram-based method is used to extract feature from silhouette image and it is suitable for represent the shape of human pose. To reduce the dimension of feature vector, Principle Component Analysis(PCA) is used. Second, real-time processing is implemented by using Compute Unified Device Architecture(CUDA) and this architecture improves the speed of feed-forward calculation of neural network. We demonstrate the effectiveness of our approach with experiments on real environment.

Keywords: computer vision, neural network, pose recognition, view-point insensitive, PCA, CUDA.

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Authors: Cemil Tunc

Abstract:

In this paper, we study the instability of the zero solution to a nonlinear differential equation with variable delay. By using the Lyapunov functional approach, some sufficient conditions for instability of the zero solution are obtained.

Keywords: Instability, Lyapunov-Krasovskii functional, delay differential equation, fifth order.

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Authors: Hitoshi Takata, Tomohiro Hachino, Masaki Horai, Kazuo Komatsu

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In this paper, we are concerned with the design and its simulation studies of a modified extremum seeking control for nonlinear systems. A standard extremum seeking control has a simple structure, but it takes a long time to reach an optimal operating point. We consider a modification of the standard extremum seeking control which is aimed to reach the optimal operating point more speedily than the standard one. In the modification, PD acceleration term is added before an integrator making a principal control, so that it enables the objects to be regulated to the optimal point smoothly. This proposed method is applied to Monod and Williams-Otto models to investigate its effectiveness. Numerical simulation results show that this modified method can improve the time response to the optimal operating point more speedily than the standard one.

Keywords: Extremum seeking control, Monod model, Williams- Otto model, PD acceleration term, Optimal operating point.

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Authors: Chien-Chih Chen, Ya-Hsin Hsueh, Zong-Cian He

Abstract:

With getting older in the whole population, the prevalence of stroke and its residual disability is getting higher and higher recently in Taiwan. The functional electrical stimulation cycling system (FESCS) is useful for hemiplegic patients. Because that the muscle of stroke patients is under hybrid activation. The raw electromyography (EMG) represents the residual muscle force of stroke subject whereas the peak-to-peak of stimulus EMG indicates the force enhancement benefiting from ES. It seems that EMG signals could be used for a parameter of feedback control mechanism. So, we design the feedback control protocol of FESCS, it includes physiological signal recorder, FPGA biomedical module, DAC and electrical stimulation circuit. Using the intensity of real-time EMG signal obtained from patients, as a feedback control method for the output voltage of FES-cycling system.

Keywords: Functional Electrical Stimulation cycling system EMG, control protocol.

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Authors: Padmakumar S., Vivek Agarwal, Kallol Roy

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With the advent of inexpensive 32 bit floating point digital signal processor-s availability in market, many computationally intensive algorithms such as Kalman filter becomes feasible to implement in real time. Dynamic simulation of a self excited DC motor using second order state variable model and implementation of Kalman Filter in a floating point DSP TMS320C6713 is presented in this paper with an objective to introduce and implement such an algorithm, for beginners. A fractional hp DC motor is simulated in both Matlab® and DSP and the results are included. A step by step approach for simulation of DC motor in Matlab® and “C" routines in CC Studio® is also given. CC studio® project file details and environmental setting requirements are addressed. This tutorial can be used with 6713 DSK, which is based on floating point DSP and CC Studio either in hardware mode or in simulation mode.

Keywords: DC motor, DSP, Dynamic simulation, Kalman Filter

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Authors: R. Usubamatov

Abstract:

The velocity of a moving point in a general path is the vector quantity, which has both magnitude and direction. The magnitude or the direction of the velocity vector can change over time as a result of acceleration that the time rate of velocity changes. Acceleration analysis is important because inertial forces and inertial torques are proportional to rectilinear and angular accelerations accordingly. The loads must be determined in advance to ensure that a machine is adequately designed to handle these dynamic loads. For planar motion, the vector direction of acceleration is commonly separated into two elements: tangential and centripetal or radial components of a point on a rotating body. All textbooks in physics, kinematics and dynamics of machinery consider the magnitude of a radial acceleration at condition when a point rotates with a constant angular velocity and it means without acceleration. The magnitude of the tangential acceleration considered on a basis of acceleration for a rotating point. Such condition of presentation of magnitudes for two components of acceleration logically and mathematically is not correct and may cause further confusion in calculation. This paper presents new analytical expressions of the radial and absolute accelerations of a rotating point with acceleration and covers the gap in theoretical study of acceleration analysis.

Keywords: acceleration analysis, kinematics of mechanisms.

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Authors: M. Volpini, D. Alves, A. Horta, M. Borges, P. Reis

Abstract:

The gait pattern in people that present motor limitations foment the demand for auxiliary locomotion devices. These artifacts for movement assistance vary according to its shape, size and functional features, following the clinical applications desired. Among the ortheses of lower limbs, the ankle-foot orthesis aims to improve the ability to walk in people with different neuromuscular limitations, although they do not always answer patients' expectations for their aesthetic and functional characteristics. The purpose of this study is to explore the possibility of using new design in additive manufacturer to reproduce the shape and functional features of a ankle-foot orthesis in an efficient and modern way. Therefore, this work presents a study about the performance of the mechanical forces through the analysis of finite elements in an ankle-foot orthesis. It will be demonstrated a study of distribution of the stress on the orthopedic device in orthostatism and during the movement in the course of patient's walk.

Keywords: Additive manufacture, new designs, orthoses, finite elements.

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Authors: N. Drir, L. Barazane, M. Loudini

Abstract:

It is well known that photovoltaic (PV) cells are an attractive source of energy. Abundant and ubiquitous, this source is one of the important renewable energy sources that have been increasing worldwide year by year. However, in the V-P characteristic curve of GPV, there is a maximum point called the maximum power point (MPP) which depends closely on the variation of atmospheric conditions and the rotation of the earth. In fact, such characteristics outputs are nonlinear and change with variations of temperature and irradiation, so we need a controller named maximum power point tracker MPPT to extract the maximum power at the terminals of photovoltaic generator. In this context, the authors propose here to study the modeling of a photovoltaic system and to find an appropriate method for optimizing the operation of the PV generator using two intelligent controllers respectively to track this point. The first one is based on artificial neural networks and the second on fuzzy logic. After the conception and the integration of each controller in the global process, the performances are examined and compared through a series of simulation. These two controller have prove by their results good tracking of the MPPT compare with the other method which are proposed up to now.

Keywords: Maximum power point tracking, neural networks, photovoltaic, P&O.

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Authors: Sanghyeok Oh, Yunli Lee, Kwangjin Hong, Kirak Kim, Keechul Jung

Abstract:

This paper proposes view-point insensitive human pose recognition system using neural network. Recognition system consists of silhouette image capturing module, data driven database, and neural network. The advantages of our system are first, it is possible to capture multiple view-point silhouette images of 3D human model automatically. This automatic capture module is helpful to reduce time consuming task of database construction. Second, we develop huge feature database to offer view-point insensitivity at pose recognition. Third, we use neural network to recognize human pose from multiple-view because every pose from each model have similar feature patterns, even though each model has different appearance and view-point. To construct database, we need to create 3D human model using 3D manipulate tools. Contour shape is used to convert silhouette image to feature vector of 12 degree. This extraction task is processed semi-automatically, which benefits in that capturing images and converting to silhouette images from the real capturing environment is needless. We demonstrate the effectiveness of our approach with experiments on virtual environment.

Keywords: Computer vision, neural network, pose recognition, view-point insensitive.

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Authors: Phool Singh, Ashok Jangid, N.S. Tomer, Deepa Sinha

Abstract:

The aim of this paper is to study the oblique stagnation point flow on vertical plate with uniform surface heat flux in presence of magnetic field. Using Stream function, partial differential equations corresponding to the momentum and energy equations are converted into non-linear ordinary differential equations. Numerical solutions of these equations are obtained using Runge-Kutta Fehlberg method with the help of shooting technique. In the present work the effects of striking angle, magnetic field parameter, Grashoff number, the Prandtl number on velocity and heat transfer characteristics have been discussed. Effect of above mentioned parameter on the position of stagnation point are also studied.

Keywords: Heat flux, Oblique stagnation point, Mixedconvection, Magneto hydrodynamics

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Authors: Nisarg A. Patel, Hiren B. Patel

Abstract:

Quantum cryptography is described as a point-to-point secure key generation technology that has emerged in recent times in providing absolute security. Researchers have started studying new innovative approaches to exploit the security of Quantum Key Distribution (QKD) for a large-scale communication system. A number of approaches and models for utilization of QKD for secure communication have been developed. The uncertainty principle in quantum mechanics created a new paradigm for QKD. One of the approaches for use of QKD involved network fashioned security. The main goal was point-to-point Quantum network that exploited QKD technology for end-to-end network security via high speed QKD. Other approaches and models equipped with QKD in network fashion are introduced in the literature as. A different approach that this paper deals with is using QKD in existing protocols, which are widely used on the Internet to enhance security with main objective of unconditional security. Our work is towards the analysis of the QKD in Mobile ad-hoc network (MANET).

Keywords: QKD, cryptography, quantum cryptography, network performance.

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Authors: Paul W. Murray

Abstract:

This research explorers the relationship between leadership style and continuous improvement (CI) teams. CI teams have several features that are not always found in other types of teams, including multi-functional members, short time period for performance, positive and actionable results, and exposure to senior leadership. There is no one best style of leadership for these teams. Instead, it is important to select the best leadership style for the situation. The leader must have the flexibility to change styles and the skill to use the chosen style effectively in order to ensure the team’s success.

Keywords: Leadership style, Lean Manufacturing, Teams, Cross-functional.

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Authors: Lv Yuhua

Abstract:

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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Authors: Yuan-Jye Tseng, Jia-Shu Li

Abstract:

To design a product with the given product requirement and design objective, there can be alternative ways to propose the detailed design specifications of the product. In the design modeling stage, alternative design cases with detailed specifications can be modeled to fulfill the product requirement and design objective. Therefore, in the design evaluation stage, it is required to perform an evaluation of the alternative design cases for deciding the final design. The purpose of this research is to develop a product evaluation model for evaluating the alternative design cases by integrated evaluating the criteria of functional design, Kansei design, and design for supply chain. The criteria in the functional design group include primary function, expansion function, improved function, and new function. The criteria in the Kansei group include geometric shape, dimension, surface finish, and layout. The criteria in the design for supply chain group include material, manufacturing process, assembly, and supply chain operation. From the point of view of value and cost, the criteria in the functional design group and Kansei design group represent the design value of the product. The criteria in the design for supply chain group represent the supply chain and manufacturing cost of the product. It is required to evaluate the design value and the supply chain cost to determine the final design. For the purpose of evaluating the criteria in the three criteria groups, a fuzzy analytic network process (FANP) method is presented to evaluate a weighted index by calculating the total relational values among the three groups. A method using the technique for order preference by similarity to ideal solution (TOPSIS) is used to compare and rank the design alternative cases according to the weighted index using the total relational values of the criteria. The final decision of a design case can be determined by using the ordered ranking. For example, the design case with the top ranking can be selected as the final design case. Based on the criteria in the evaluation, the design objective can be achieved with a combined and weighted effect of the design value and manufacturing cost. An example product is demonstrated and illustrated in the presentation. It shows that the design evaluation model is useful for integrated evaluation of functional design, Kansei design, and design for supply chain to determine the best design case and achieve the design objective.

Keywords: Design evaluation, functional design, Kansei design, supply chain, design value, manufacturing cost, fuzzy analytic network process, technique for order preference by similarity to ideal solution.

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Authors: Mikel Alonso López

Abstract:

In the first decade of the twenty-first century, advanced imaging techniques began to be applied for neuroscience research. The Functional Magnetic Resonance Imaging (fMRI) is one of the most important and most used research techniques for the investigation of emotions, because of its ease to observe the brain areas that oxygenate when performing certain tasks. In this research, we make a review about the main research carried out on the influence of the emotions in the decision-making process that is exposed by using the fMRI.

Keywords: Decision making, emotions, fMRI.

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Authors: S. Karthika, K. Velayutham, P. Rathika, D. Devaraj

Abstract:

The electric power supplied by a photovoltaic power generation systems depends on the solar irradiation and temperature. The PV system can supply the maximum power to the load at a particular operating point which is generally called as maximum power point (MPP), at which the entire PV system operates with maximum efficiency and produces its maximum power. Hence, a Maximum power point tracking (MPPT) methods are used to maximize the PV array output power by tracking continuously the maximum power point. The proposed MPPT controller is designed for 10kW solar PV system installed at Cape Institute of Technology. This paper presents the fuzzy logic based MPPT algorithm. However, instead of one type of membership function, different structures of fuzzy membership functions are used in the FLC design. The proposed controller is combined with the system and the results are obtained for each membership functions in Matlab/Simulink environment. Simulation results are decided that which membership function is more suitable for this system.

Keywords: MPPT, DC-DC Converter, Fuzzy logic controller, Photovoltaic (PV) system.

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Authors: Jun-ya Nagase, Toshiyuki Satoh, Norihiko Saga, Koichi Suzumori

Abstract:

In recent years, Japanese society has been aging, engendering a labor shortage of young workers. Robots are therefore expected to perform tasks such as rehabilitation, nursing elderly people, and day-to-day work support for elderly people. The pneumatic balloon actuator is a rubber artificial muscle developed for use in a robot hand in such environments. This actuator has a long stroke and a high power-to-weight ratio compared with the present pneumatic artificial muscle. Moreover, the dynamic characteristics of this actuator resemble those of human muscle. This study evaluated characteristics of force control of balloon actuator using a predictive functional control (PFC) system with disturbance observer. The predictive functional control is a model-based predictive control (MPC) scheme that predicts the future outputs of the actual plants over the prediction horizon and computes the control effort over the control horizon at every sampling instance. For this study, a 1-link finger system using a pneumatic balloon actuator is developed. Then experiments of PFC control with disturbance observer are performed. These experiments demonstrate the feasibility of its control of a pneumatic balloon actuator for a robot hand.

Keywords: Disturbance observer, Pneumatic balloon, Predictive functional control, Rubber artificial muscle.

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Authors: Amar Al-Obaidi, Verena Kräusel, Dirk Landgrebe

Abstract:

Induction assisted single point incremental forming (IASPIF) is a flexible method and can be simply utilized to form a high strength alloys. Due to the interaction between the mechanical and thermal properties during IASPIF an evaluation for the process is necessary to be performed analytically. Therefore, a numerical simulation was carried out in this paper. The numerical analysis was operated at both room and elevated temperatures then compared with experimental results. Fully coupled dynamic temperature displacement explicit analysis was used to simulated the hot single point incremental forming. The numerical analysis was indicating that during hot single point incremental forming were a combination between complicated compression, tension and shear stresses. As a result, the equivalent plastic strain was increased excessively by rising both the formed part depth and the heating temperature during forming. Whereas, the forming forces were decreased from 5 kN at room temperature to 0.95 kN at elevated temperature. The simulation shows that the maximum true strain was occurred in the stretching zone which was the same as in experiment.

Keywords: Induction heating, single point incremental forming, FE modeling, advanced high strength steel.

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Authors: Magda S. Taipina, Maria L. Garbelotti, Mariana G.B. Cadioli

Abstract:

Banana is one of the most consumed fruits in the tropics and subtropics. Brazil accounts for about 9% of the world banana production. However, the production losses are as high as 30 to 40% and even much higher in some developing countries. The green banana flour is a complex carbohydrate source, including a high total starch (73.4%), resistant starch (17.5%) with functional properties. Gamma irradiation is considered to be an alternative method for food preservation. It has been performed due to the need of extending the shelf - life of foods, whilst maintaining their safety and avoiding one of the main concerns: the nutrient loss. In this work data about on the effects of ionizing radiation on the physicochemical analysis (carbohydrate, proteins, lipids, alimentary fiber, moistures and ashes) of Brazilian functional products (biscuits and bread) of the green banana pulp are presented. The caloric value was calculated. No significant difference was observed between the samples of irradiated and non – irradiated green banana biscuits with the following determinations: carbohydrates, proteins, alimentary fiber and ashes. Only a small significant difference was found in lipids (macronutrients). The results of physical chemical analysis of the irradiated and non- irradiated green banana bread non- irradiated showed no significant difference with the following determinations: carbohydrates, lipids (macronutrients), moisture, ashes and caloric value. A small difference was found in proteins (macronutrients). Irradiation of functional products (biscuits and bread) with doses of 1 and 3kGy maintained their original macronutrients content, showing good radioresistance.

Keywords: Irradiation, Functional Food, Nutritional value.

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Authors: Debesh R. Roy

Abstract:

The fundamental issue in understanding the origin and growth mechanism of nanomaterials, from a fundamental unit is a big challenging problem to the scientists. Recently, an immense attention is generated to the researchers for prediction of exceptionally stable atomic cluster units as the building units for future smart materials. The present study is a systematic investigation on the stability and electronic properties of a series of bimetallic (semiconductor-alkaline earth) clusters, viz., BxMg3 (x=1-5) is performed, in search for exceptional and/ or unusual stable motifs. A very popular hybrid exchange-correlation functional, B3LYP along with a higher basis set, viz., 6-31+G[d,p] is employed for this purpose under the density functional formalism. The magic stability among the concerned clusters is explained using the jellium model. It is evident from the present study that the magic stability of B4Mg3 cluster arises due to the jellium shell closure.

Keywords: Atomic Clusters, Density Functional Theory, Jellium Model, Magic Clusters, Smart Nanomaterials.

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Authors: Serap Akcan, Ali Kokangul

Abstract:

We consider a single-echelon, single-item inventory system where both demand and lead-time are stochastic. Continuous review policy is used to control the inventory system. The objective is to calculate the reorder point level under stochastic parameters. A case study is presented in Neonatal Intensive Care Unit.

Keywords: Inventory control system, reorder point level, stochastic demand, stochastic lead time

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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