Search results for: Non sinusoidal and unbalanced voltage conditions.

Authors: V. Bezlepkin, M. Karaseva, A. Frolov, E. Kharchenko, L. Lebedev

Abstract:

The main features of NPP-2006/MIR-1200 design are described. Estimation of individual doses for population under normal operation and accident conditions is performed for Leningradskaya NPP – 2 as an example. The radiation effect on population and environment doesn-t exceed the established normative limit and is as low as reasonably achievable. NPP- 2006/MIR-1200 design meets all Russian and international requirements for power units under construction.

Keywords: Accident release, beyond design basis accident (BDBA), nuclear power plant (NPP), radiation safety.

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Authors: Chenxi Yang, Zhouhong Li

Abstract:

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.

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Authors: Xiaoyan Dou, Yongkun Li

Abstract:

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

Keywords: Almost periodic solution, food-limited population, feedback control, permanence.

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Authors: Kateřina Sekulová, Michal Šimon

Abstract:

Ergonomics is a useful tool for creating a healthy and safe workplace. The long-term action of harmful conditions on the health of workers is the emergence of occupational disease, and the firm-s increased compensation costs associated with these diseases, but is also the loss of time needed for educating and including new workers in the work process. The article deals with the link of ergonomics to occupational diseases, factors which influence these diseases. In the conclusion, a model is described to help reduce the risk of selected occupational diseases using ergonomic principles and knowledge.

Keywords: ergonomics, occupational diseases, optimization, workplace health

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Authors: Padmanabhan Balasubramanian, C. Hari Narayanan

Abstract:

This paper discusses a new, systematic approach to the synthesis of a NP-hard class of non-regenerative Boolean networks, described by FON[FOFF]={mi}[{Mi}], where for every mj[Mj]∈{mi}[{Mi}], there exists another mk[Mk]∈{mi}[{Mi}], such that their Hamming distance HD(mj, mk)=HD(Mj, Mk)=O(n), (where 'n' represents the number of distinct primary inputs). The method automatically ensures exact minimization for certain important selfdual functions with 2n-1 points in its one-set. The elements meant for grouping are determined from a newly proposed weighted incidence matrix. Then the binary value corresponding to the candidate pair is correlated with the proposed binary value matrix to enable direct synthesis. We recommend algebraic factorization operations as a post processing step to enable reduction in literal count. The algorithm can be implemented in any high level language and achieves best cost optimization for the problem dealt with, irrespective of the number of inputs. For other cases, the method is iterated to subsequently reduce it to a problem of O(n-1), O(n-2),.... and then solved. In addition, it leads to optimal results for problems exhibiting higher degree of adjacency, with a different interpretation of the heuristic, and the results are comparable with other methods. In terms of literal cost, at the technology independent stage, the circuits synthesized using our algorithm enabled net savings over AOI (AND-OR-Invert) logic, AND-EXOR logic (EXOR Sum-of- Products or ESOP forms) and AND-OR-EXOR logic by 45.57%, 41.78% and 41.78% respectively for the various problems. Circuit level simulations were performed for a wide variety of case studies at 3.3V and 2.5V supply to validate the performance of the proposed method and the quality of the resulting synthesized circuits at two different voltage corners. Power estimation was carried out for a 0.35micron TSMC CMOS process technology. In comparison with AOI logic, the proposed method enabled mean savings in power by 42.46%. With respect to AND-EXOR logic, the proposed method yielded power savings to the tune of 31.88%, while in comparison with AND-OR-EXOR level networks; average power savings of 33.23% was obtained.

Keywords: AOI logic, ESOP, AND-OR-EXOR, Incidencematrix, Hamming distance.

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Authors: Long Jye Sheu, Wei Ching Chen, Yen Chu Chen, Wei Tai Weng

Abstract:

In this paper, a two-channel secure communication using fractional chaotic systems is presented. Conditions for chaos synchronization have been investigated theoretically by using Laplace transform. To illustrate the effectiveness of the proposed scheme, a numerical example is presented. The keys, key space, key selection rules and sensitivity to keys are discussed in detail. Results show that the original plaintexts have been well masked in the ciphertexts yet recovered faithfully and efficiently by the present schemes.

Keywords: fractional chaotic systems, synchronization, securecommunication.

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Authors: Alessandro A. Zizzari, Francesca Calabrese, Giovanni Indiveri, Andrea Coraddu, Diego Villa

Abstract:

The aim of this paper is to present a comparative study on two different methods for the evaluation of the equilibrium point of a ship, core issue for designing an On Board Stability System (OBSS) module that, starting from geometry information of a ship hull, described by a discrete model in a standard format, and the distribution of all weights onboard calculates the ship floating conditions (in draught, heel and trim).

Keywords: Algorithms, Computer applications, Equilibrium, Marine applications, Stability System.

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Authors: B. Demirel, T.T. Onay, O. Yenigün

Abstract:

The potential, opportunities and drawbacks of biogas technology use in Turkey are evaluated in this paper. Turkey is dependent on foreign sources of energy. Therefore, use of biogas technology would provide a safe way of waste disposal and recovery of renewable energy, particularly from a sustainable domestic source, which is less unlikely to be influenced by international price or political fluctuations. Use of biogas technology would especially meet the cooking, heating and electricity demand in rural areas and protect the environment, additionally creating new job opportunities and improving social-economical conditions.

Keywords: anaerobic digestion, agricultural biogas plant, biogas, biomass, methane, waste

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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: K. Karuppasamy

Abstract:

In this paper, analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill-poor soil system overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behaviour of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedal iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil–foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include magnitude of applied load, velocity of load, damping, ultimate resistance of poor soil and granular fill layer. Range of values of parameters has been considered as per Indian Railway conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil–foundation system.

Keywords: Infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load, nonlinear behavior of poor soil.

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Authors: Guangbin Wang, Fuping Tan

Abstract:

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.

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Authors: Sizhong Zhou, Hongxia Liu

Abstract:

Let G be a graph of order n, and let k  2 and m  0 be two integers. Let h : E(G)  [0, 1] be a function. If e∋x h(e) = k holds for each x  V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e  E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e  E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G)  k + m + m k+1 , n  4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)}  n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.

Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.

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Authors: Pavlo Selyshchev

Abstract:

The theoretical approach is developed to describe the change of drops in the atmosphere of own steam and buffer gas under irradiation. It is shown that the irradiation influences on size of stable droplet and on the conditions under which the droplet exists. Under irradiation the change of drop becomes more complex: the not monotone and periodical change of size of drop becomes possible. All possible solutions are represented by means of phase portrait. It is found all qualitatively different phase portraits as function of critical parameters: rate generation of clusters and substance density.

Keywords: Irradiation, steam, plasma, cluster formation, liquid droplets, evolution.

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Authors: Meng-Cong Zheng

Abstract:

When the public space is in an emergency, how to quickly establish spatial cognition and emergency shelter in the closed underground space is the urgent task. This study takes Taipei Station as the research base and aims to apply the use of Internet of things (IoT) application for underground evacuation mobility design. The first experiment identified passengers' evacuation behaviors and spatial cognition in underground spaces by wayfinding tasks and thinking aloud, then defined the design conditions of User Interface (UI) and proposed the UI design.  The second experiment evaluated the UI design based on passengers' evacuation behaviors by wayfinding tasks and think aloud again as same as the first experiment. The first experiment found that the design conditions that the subjects were most concerned about were "map" and hoping to learn the relative position of themselves with other landmarks by the map and watch the overall route. "Position" needs to be accurately labeled to determine the location in underground space. Each step of the escape instructions should be presented clearly in "navigation bar." The "message bar" should be informed of the next or final target exit. In the second experiment with the UI design, we found that the "spatial map" distinguishing between walking and non-walking areas with shades of color is useful. The addition of 2.5D maps of the UI design increased the user's perception of space. Amending the color of the corner diagram in the "escape route" also reduces the confusion between the symbol and other diagrams. The larger volume of toilets and elevators can be a judgment of users' relative location in "Hardware facilities." Fire extinguisher icon should be highlighted. "Fire point tips" of the UI design indicated fire with a graphical fireball can convey precise information to the escaped person. "Fire point tips" of the UI design indicated fire with a graphical fireball can convey precise information to the escaped person. However, "Compass and return to present location" are less used in underground space.

Keywords: Evacuation behaviors, IoT application, map UI design, underground station.

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Authors: Shuguo Yang, Xiaoyan Yang

Abstract:

It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result shows that queuing theory is applied in the study of intersection traffic flow and it can provide references for the other similar designs.

Keywords: Intersection, Queuing theory, Statistical experiment, System metrics.

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Authors: Amir Shafeeq, Ayyaz Muhammad, Noman Hassan, Rofice Dickson

Abstract:

Different vegetable oil based biodiesel (FAMES) were prepared by alkaline transesterification using refined oils as well as waste frying oil (WFO). Methanol and sodium hydroxide are used as catalyst under similar reaction conditions. To ensure the quality of biodiesel produced, a series of different ASTM Standard tests were carried out. In this context, various testwere done including viscosity, carbon residue, specific gravity, corrosion test, flash point, cloud point and pour point. Results revealed that characteristics of biodiesel depend on the feedstock and it is far better than petroleum diesel.

Keywords: Biodiesel, Edible oils, Separation.

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Authors: Adam Czornik, Aleksander Nawrat

Abstract:

This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.

Keywords: Exponential stability, time-varying linear systems, periodic systems.

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Authors: N. Chanchay, S. Sirisansaneeyakul, C. Chaiyasut, N. Poosaran

Abstract:

This study aims to screen out and to optimize the major nutrients for maximum carotenoid production and antioxidation characteristics by Rhodotorula rubra. It was found that supplementary of 10 g/l glucose as carbon source, 1 g/l ammonium sulfate as nitrogen source and 1 g/l yeast extract as growth factor in the medium provided the better yield of carotenoid content of 30.39 μg/g cell dry weight the amount of antioxidation of Rhodotorula rubra by DPPH, ABTS and MDA method were 1.463%, 34.21% and 34.09 μmol/l, respectively.

Keywords: Carotenoid, Rhodotorula rubra, Antioxidation, DPPH, ABTS

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Authors: R. Sekula

Abstract:

Epoxy composites are broadly used as an electrical insulation for the high voltage applications since only such materials can fulfill particular mechanical, thermal, and dielectric requirements. However, properties of the final product are strongly dependent on proper manufacturing process with minimized material failures, as too large shrinkage, voids and cracks. Therefore, application of proper materials (epoxy, hardener, and filler) and process parameters (mold temperature, filling time, filling velocity, initial temperature of internal parts, gelation time), as well as design and geometric parameters are essential features for final quality of the produced components. In this paper, an approach for three-dimensional modeling of all molding stages, namely filling, curing and post-curing is presented. The reactive molding simulation tool is based on a commercial CFD package, and include dedicated models describing viscosity and reaction kinetics that have been successfully implemented to simulate the reactive nature of the system with exothermic effect. Also a dedicated simulation procedure for stress and shrinkage calculations, as well as simulation results are presented in the paper. Second part of the paper is dedicated to recent developments on formulations of functional composites for electrical insulation applications, focusing on thermally conductive materials. Concepts based on filler modifications for epoxy electrical composites have been presented, including the results of the obtained properties. Finally, having in mind tough environmental regulations, in addition to current process and design aspects, an approach for product re-design has been presented focusing on replacement of epoxy material with the thermoplastic one. Such “design-for-recycling” method is one of new directions associated with development of new material and processing concepts of electrical products and brings a lot of additional research challenges. For that, one of the successful products has been presented to illustrate the presented methodology.

Keywords: Curing, epoxy insulation, numerical simulations, recycling.

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Authors: Emad Hazbkhah. Abdolreza Zahiri, Hossein Ghorbanizade Kharazi

Abstract:

Reducing river sediments through path correction and preservation of river walls leads to considerable reduction of sedimentation at the pumping stations. Path correction and preservation of walls is not limited to one particular method but, depending on various conditions, a combination of several methods can be employed. In this article, we try to review and evaluate methods for preservation of river banks in order to reduce sediments.

Keywords: Erosion , River Banks , Sediments

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Authors: M. R. Yadav, A. K. Sharma, B. S. Thakur

Abstract:

The purpose of this paper is to present a best proximity point theorems through rational expression for a combination of contraction condition, Kannan and Chatterjea nonlinear cyclic contraction in what we call MT-K and MT-C rational cyclic contraction. Some best proximity point theorems for a mapping satisfy these conditions have been established in metric spaces. We also give some examples to support our work.

Keywords: Cyclic contraction, rational cyclic contraction, best proximity point and complete metric space.

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Authors: Amir. AL-Haddad, Hisham. Ettouney, Samiya. Saqer

Abstract:

The main objectives of this paper are to measure pollutants concentrations in the oil refinery area in Kuwait over three periods during one year, obtain recent emission inventory for the three refineries of Kuwait, use AERMOD and the emission inventory to predict pollutants concentrations and distribution, compare model predictions against measured data, and perform numerical experiments to determine conditions at which emission rates and the resulting pollutant dispersion is below maximum allowable limits.

Keywords: Emissions, ISCST3 model, Modeling, Pollutants, Refinery

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Authors: L. Parisi

Abstract:

A method which allows a diabetic quadriplegic patient that has had four limb amputations (above the knee and elbow) to self-administer injections of insulin has been designed. The aim of this research project is to improve a quadriplegic patient’s selfmanagement, affected by diabetes, by designing a suitable device for self-administering insulin. The quadriplegic patient affected by diabetes has to be able to selfadminister insulin safely and independently to guarantee stable healthy conditions. The device also should be designed to adapt to a number of different varying personal characteristics such as height and body weight.

Keywords: Robotics, diabetes, quadriplegia, self-management.

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Authors: Fakharuddin Ibrahim, Jamaludin Md. Ali, Ahmad Ramli

Abstract:

In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G¹ continuity. The conditions considered are known as the G¹ Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

Keywords: Continuity, data interpolation, Hermite condition, rational Ball curve.

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Authors: Asadollah Aghajani, Yaghoub Jalilian

Abstract:

Using the concept of measure of noncompactness, we present some results concerning the existence, uniform local attractivity and global attractivity of solutions for a functional integral equation. Our results improve and extend some previous known results and based on weaker conditions. Some examples which show that our results are applicable when the previous results are inapplicable are also included.

Keywords: Functional integral equation, fixed-point, measure of noncompactness, attractive solution, asymptotic stability.

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Authors: Meng Hu, Lili Wang

Abstract:

By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of antiperiodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.

Keywords: Anti-periodic solution, coincidence degree, CGSICNNs, impulse, time scales.

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Authors: Ekin Kıpçak, Mesut Akgün

Abstract:

Recently, a growing interest has emerged on the development of new and efficient energy sources, due to the inevitable extinction of the nonrenewable energy reserves. One of these alternative sources which have a great potential and sustainability to meet up the energy demand is biomass energy. This significant energy source can be utilized with various energy conversion technologies, one of which is biomass gasification in supercritical water.

Water, being the most important solvent in nature, has very important characteristics as a reaction solvent under supercritical circumstances. At temperatures above its critical point (374.8^oC and 22.1MPa), water becomes more acidic and its diffusivity increases. Working with water at high temperatures increases the thermal reaction rate, which in consequence leads to a better dissolving of the organic matters and a fast reaction with oxygen. Hence, supercritical water offers a control mechanism depending on solubility, excellent transport properties based on its high diffusion ability and new reaction possibilities for hydrolysis or oxidation.

In this study the gasification of a real biomass, namely olive mill wastewater (OMW), in supercritical water conditions is investigated with the use of Ru/Al₂O₃ catalyst. OMW is a by-product obtained during olive oil production, which has a complex nature characterized by a high content of organic compounds and polyphenols. These properties impose OMW a significant pollution potential, but at the same time, the high content of organics makes OMW a desirable biomass candidate for energy production.

The catalytic gasification experiments were made with five different reaction temperatures (400, 450, 500, 550 and 600°C) and five reaction times (30, 60, 90, 120 and 150s), under a constant pressure of 25MPa. Through these experiments, the effects of reaction temperature and time on the gasification yield, gaseous product composition and OMW treatment efficiency were investigated.

Keywords: Catalyst, Gasification, Olive mill wastewater, Ru/Al2O3, Supercritical water.

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Authors: M. Rodionov, Z. Dedovets

Abstract:

This article discusses ways to implement a differentiated approach to developing academic motivation for mathematical studies which relies on defining the primary structural characteristics of motivation. The following characteristics are considered: features of realization of cognitive activity, meaningmaking characteristics, level of generalization and consistency of knowledge acquired by personal experience. The assessment of the present level of individual student understanding of each component of academic motivation is the basis for defining the relevant educational strategy for its further development.

Keywords: Learning activity, mathematics, motivation, student.

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Authors: Masoud Fathi Kazerouni, Jens Schlemper, Klaus-Dieter Kuhnert

Abstract:

Green planet is one of the Earth’s names which is known as a terrestrial planet and also can be named the fifth largest planet of the solar system as another scientific interpretation. Plants do not have a constant and steady distribution all around the world, and even plant species’ variations are not the same in one specific region. Presence of plants is not only limited to one field like botany; they exist in different fields such as literature and mythology and they hold useful and inestimable historical records. No one can imagine the world without oxygen which is produced mostly by plants. Their influences become more manifest since no other live species can exist on earth without plants as they form the basic food staples too. Regulation of water cycle and oxygen production are the other roles of plants. The roles affect environment and climate. Plants are the main components of agricultural activities. Many countries benefit from these activities. Therefore, plants have impacts on political and economic situations and future of countries. Due to importance of plants and their roles, study of plants is essential in various fields. Consideration of their different applications leads to focus on details of them too. Automatic recognition of plants is a novel field to contribute other researches and future of studies. Moreover, plants can survive their life in different places and regions by means of adaptations. Therefore, adaptations are their special factors to help them in hard life situations. Weather condition is one of the parameters which affect plants life and their existence in one area. Recognition of plants in different weather conditions is a new window of research in the field. Only natural images are usable to consider weather conditions as new factors. Thus, it will be a generalized and useful system. In order to have a general system, distance from the camera to plants is considered as another factor. The other considered factor is change of light intensity in environment as it changes during the day. Adding these factors leads to a huge challenge to invent an accurate and secure system. Development of an efficient plant recognition system is essential and effective. One important component of plant is leaf which can be used to implement automatic systems for plant recognition without any human interface and interaction. Due to the nature of used images, characteristic investigation of plants is done. Leaves of plants are the first characteristics to select as trusty parts. Four different plant species are specified for the goal to classify them with an accurate system. The current paper is devoted to principal directions of the proposed methods and implemented system, image dataset, and results. The procedure of algorithm and classification is explained in details. First steps, feature detection and description of visual information, are outperformed by using Scale invariant feature transform (SIFT), HARRIS-SIFT, and FAST-SIFT methods. The accuracy of the implemented methods is computed. In addition to comparison, robustness and efficiency of results in different conditions are investigated and explained.

Keywords: SIFT combination, feature extraction, feature detection, natural images, natural plant recognition, HARRIS-SIFT, FAST-SIFT.

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Authors: Hong Li, Shou-Ming Zhong, Hou-Biao Li

Abstract:

In this paper, we mainly study the stability of linear and interval linear fractional systems with time delay. By applying the characteristic equations, a necessary and sufficient stability condition is obtained firstly, and then some sufficient conditions are deserved. In addition, according to the equivalent relationship of fractional order systems with order 0 < α ≤ 1 and with order 1 ≤ β < 2, one may get more relevant theorems. Finally, two examples are provided to demonstrate the effectiveness of our results.

Keywords: Fractional order systems, Time delay, Characteristic equation.

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