Search results for: Hardy-Sobolev type inequalities

Authors: M. H. M. Rashid

Abstract:

Given H a Hilbert space and B(H) the algebra of bounded linear operator in H, let δAB denote the generalized derivation defined by A and B. The main objective of this article is to study Weyl type theorems for generalized derivation for (A,B) satisfying a couple of Fuglede.

Keywords: Fuglede Property, Weyl’s theorem, generalized derivation, Aluthge Transformation.

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Authors: Bhupendra C. S. Chauhan, P. S. Bisht, O. P. S. Negi

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According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient, divergence and curl in seven dimension. It is shown that the identity n(n - 1)(n - 3)(n - 7) = 0 is satisfied only for 0, 1, 3 and 7 dimensional vectors. We have tried to write all the vector inequalities and formulas in terms of seven dimensions and it is shown that same formulas loose their meaning in seven dimensions due to non-associativity of octonions. The vector formulas are retained only if we put certain restrictions on octonions and split octonions.

Keywords: Octonions, Vector Space and seven dimensions

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Authors: F. P., Chew, M. H., Teong, Z. Ishak

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School homework has been synonymous with students- life in Chinese national type primary schools in Malaysia. Although many reports in the press claimed that students were burdened with too much of it, homework continues to be a common practice in national type schools that is believed to contribute to academic achievement. This study is conducted to identify the relationship between the burden of school homework and academic achievement among pupils in Chinese National Type Primary School in the state of Perak, Malaysia. A total of 284 students (142 from urban and 142 from rural) respectively were chosen as participants in this study. Variables of gender and location (urban/rural areas) has shown significant difference in student academic achievement. Female Chinese student from rural areas showed a higher mean score than males from urban area. Therefore, the Chinese language teachers should give appropriate and relevant homework to primary school students to achieve good academic performance.

Keywords: homework, academic achievement, Chinese National Type Primary Schools

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Authors: Said Ali Al-Hadhrami

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Ranked set sampling (RSS) was first suggested to increase the efficiency of the population mean. It has been shown that this method is highly beneficial to the estimation based on simple random sampling (SRS). There has been considerable development and many modifications were done on this method. When a concomitant variable is available, ratio estimation based on ranked set sampling was proposed. This ratio estimator is more efficient than that based on SRS. In this paper some ratio type estimators of the population mean based on RSS are suggested. These estimators are found to be more efficient than the estimators of similar form using simple random sample.

Keywords: Bias, Efficiency, Ranked Set Sampling, Ratio Type Estimator

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Authors: Renata Carneiro, Jody Russon, Allena Moncrief, Erica Wilkins

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Views on therapists- attraction have influenced the ethical and professional development of the mental health fields. Because the majority of therapist attraction literature (63.6%) has been conducted from a psychoanalytic standpoint, approaches to attraction from feminist perspectives have not been adequately developed. Considering the lack of a feminist voice regarding attraction, this article attempts to offer a feminist perspective on this issue. The purpose of this article is to offer a feminist perspective on the phenomenon of attraction in order to raise awareness about the importance of power inequalities, intersectionalities, contextual variables and the need for action in the field.

Keywords: attraction, feminism, power inequality, silence

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Authors: Dongdong Zhang, Deran Zhang

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In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

Keywords: Risk model, ruin probability, Markov jump process, integral equation.

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Authors: Tomoaki Hashimoto

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Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research field. Although probabilistic constraints are generally intractable in optimization problems, several methods haven been proposed to deal with probabilistic constraints. In most methods, probabilistic constraints are transformed to deterministic constraints that are tractable in optimization problems. This paper examines a method for transforming probabilistic constraints into deterministic constraints for a class of probabilistic constrained optimal control problems.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: Matthias Dehmer1 Jürgen Kilian

Abstract:

Problems on algebraical polynomials appear in many fields of mathematics and computer science. Especially the task of determining the roots of polynomials has been frequently investigated.Nonetheless, the task of locating the zeros of complex polynomials is still challenging. In this paper we deal with the location of zeros of univariate complex polynomials. We prove some novel upper bounds for the moduli of the zeros of complex polynomials. That means, we provide disks in the complex plane where all zeros of a complex polynomial are situated. Such bounds are extremely useful for obtaining a priori assertations regarding the location of zeros of polynomials. Based on the proven bounds and a test set of polynomials, we present an experimental study to examine which bound is optimal.

Keywords: complex polynomials, zeros, inequalities

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Authors: P. Prema, B. Ramadoss

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Testing is an activity that is required both in the development and maintenance of the software development life cycle in which Integration Testing is an important activity. Integration testing is based on the specification and functionality of the software and thus could be called black-box testing technique. The purpose of integration testing is testing integration between software components. In function or system testing, the concern is with overall behavior and whether the software meets its functional specifications or performance characteristics or how well the software and hardware work together. This explains the importance and necessity of IT for which the emphasis is on interactions between modules and their interfaces. Software errors should be discovered early during IT to reduce the costs of correction. This paper introduces a new type of integration error, presenting an overview of Integration Testing techniques with comparison of each technique and also identifying which technique detects what type of error.

Keywords: Integration Error, Integration Error Types, Integration Testing Techniques, Software Testing

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Authors: Magdy B. Eteiba, Essam A. Alzahab, Yomna O. Shaker

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In this paper, a thermal model of cast- resin dry type transformer is proposed. The proposed thermal model is solved by finite element technique to get the temperature at any location of the transformer. The basic modes of heat transfer such as conduction; convection and radiation are used to get the steady state temperature distribution of the transformer. The predicted temperatures are compared with experimental results reported in this paper and it is found a good agreement between them. The effects of various parameters such as width of air duct, ambient temperature and emissivity of the outer surface were also studied.

Keywords: Convection, dry type transformer, finite-elementtechnique, thermal model.

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Authors: Kaihong Zhao, Jiuqing Liu

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In this letter, we considers a delayed predatory-prey system with Holling type II functional response. Under some sufficient conditions, the existence of multiple positive periodic solutions is obtained by using Mawhin’s continuation theorem of coincidence degree theory. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Predatory-prey system, Coincidence degree, Holling type II functional response.

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Authors: Mohamed A. Hammad, Dzul Azri Mohamed Noor, Syed Azhar Syed Sulaiman, Ahmed A. Khamis, Abeer Kharshid, Nor Azizah Aziz

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The effect of statins dose intensity (SDI) on glycemic control in patients with existing diabetes is unclear. Also, there are many contradictory findings were reported in the literature; thus, it is limiting the possibility to draw conclusions. This project was designed to compare the effect of SDI on glycated hemoglobin (HbA1c%) control in outpatients with Type 2 diabetes in the endocrine clinic at Hospital Pulau Pinang, Malaysia, between July 2015 and August 2016. A prospective cohort study was conducted, where records of 345 patients with Type 2 diabetes (Moderate-SDI group 289 patients and high-SDI cohort 56 patients) were reviewed to identify demographics and laboratory tests. The target of glycemic control (HbA1c < 7% for patient < 65 years, and < 8% for patient ≥ 65 years) was estimated, and the results were presented as descriptive statistics. From 289 moderate-SDI cohorts with a mean age of 57.3 ± 12.4 years, only 86 (29.8%) cases were shown to have controlled glycemia, while there were 203 (70.2%) cases with uncontrolled glycemia with confidence interval (CI) of 95% (6.2–10.8). On the other hand, the high-SDI group of 56 patients with Type 2 diabetes with a mean age 57.7±12.4 years is distributed among 11 (19.6%) patients with controlled diabetes, and 45 (80.4%) of them had uncontrolled glycemia, CI: 95% (7.1–11.9). The study has demonstrated that the relative risk (RR) of uncontrolled glycemia in patients with Type 2 diabetes that used high-SDI is 1.15, and the excessive relative risk (ERR) is 15%. The absolute risk (AR) is 10.2%, and the number needed to harm (NNH) is 10. Outpatients with Type 2 diabetes who use high-SDI of statin have a higher risk of uncontrolled glycemia than outpatients who had been treated with a moderate-SDI.

Keywords: Cohort study, diabetes control, dose intensity, HbA1c, Malaysia, statin, Type 2 diabetes mellitus, uncontrolled glycemia.

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Authors: M.J. Park, K.H. Kim, O.M. Kwon

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This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.

Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.

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Authors: Design of 3-Step Skew BLAC Motor for Better Performance in Electric Power Steering System

Abstract:

In Electric Power Steering (EPS), spoke type Brushless AC (BLAC) motors offer distinct advantages over other electric motor types in terms torque smoothness, reliability and efficiency. This paper deals with the shape optimization of spoke type BLAC motor, in order to reduce cogging torque. This paper examines 3 steps skewing rotor angle, optimizing rotor core edge and rotor overlap length for reducing cogging torque in spoke type BLAC motor. The methods were applied to existing machine designs and their performance was calculated using finite- element analysis (FEA). Prototypes of the machine designs were constructed and experimental results obtained. It is shown that the FEA predicted the cogging torque to be nearly reduce using those methods.

Keywords: EPS, 3-Step skewing, spoke type BLAC, cogging torque, FEA, optimization.

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Authors: F. R. Sultanov Ch. Daulbayev, B. Bakbolat, Z. A. Mansurov, A. A. Zhurintaeva, R. I. Gadilshina, A. B. Dugali

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Both hydrophilic-oleophobic and hydrophobic-oleophilic membranes were obtained by coating of the substrate of membranes, presented by stainless steel meshes with various dimensions of their openings, with a composition that forms the special type of their surface wettability via spray-coating method. The surface morphology of resulting membranes was studied using SEM, the type of their wettability was identified by measuring the contact angle between the surface of membrane and a drop of studied liquid (water or organic liquid) and efficiency of continuous separation of water and organic liquid was studied on self-assembled setup.

Keywords: Membrane, stainless steel mesh, oleophobicity, hydrophobicity, separation, water, organic liquids.

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Authors: Mukhtar H. Hassan, Muhammed A. Basher, Elhadi E. Saad, Almahdi M. Almahdi

Abstract:

The aim of this study was to demonstrate the possible effect of some variables such as age, gender, blood sugar level, and duration of diabetes on the serum level of zinc in diabetic individuals from Murzuk area. Serum zinc (Zn), Fasting blood sugar (FBS), hemoglobin HbA1c (HbA1c) were evaluated in 46 type I diabetic subjects (group 1), 48 type II diabetic subjects (group 2) and 43 healthy individuals (control) of both genders aged (30-81) years. Data showed that both diabetic groups have significantly higher (P<0.05) serum levels of Zn, FBS and HbA1c compared with controls. No significant (p>0.05) differences in serum Zn levels were observed between Males and Females. Serum Zn levels were non-significantly decreased with increasing age. In type II diabetic subjects, serum Zn levels were non-significantly decreased with increasing duration of disease whereas those in type I were non-significantly increased.

Keywords: Blood sugar, diabetes, HbA1c, zinc.

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Authors: Yusof. Mohd Kamir, Mat Deris. Mohd Sufian, Abidin. Ahmad Faisal Amri

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The purpose of this paper is to show efficiency and capability LZWµ in data compression. The LZWµ technique is enhancement from existing LZW technique. The modification the existing LZW is needed to produce LZWµ technique. LZW read one by one character at one time. Differ with LZWµ technique, where the LZWµ read three characters at one time. This paper focuses on data compression and tested efficiency and capability LZWµ by different data format such as doc type, pdf type and text type. Several experiments have been done by different types of data format. The results shows LZWµ technique is better compared to existing LZW technique in term of file size.

Keywords: Data Compression, Huffman Encoding, LZW, LZWµ, RLL, Size.

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Authors: Kianoosh Samimi, Farhad Estakhr, Mahdi Mahdikhani, Faramaz Moodi

Abstract:

Due to their fluidity and simplicity of use, self-compacting concretes (SCCs) have undeniable advantages. In recent years, the role of metakaolin as a one of pozzolanic materials in concrete has been considered by researchers. It can modify various properties of concrete, due to high pozzolanic reactions and also makes a denser microstructure. The objective of this paper is to examine the influence of three type of Portland cement and metakaolin on fresh state, compressive strength and sulfuric acid attacks in self- consolidating concrete at early age up to 90 days of curing in lime water. Six concrete mixtures were prepared with three types of different cement as Portland cement type II, Portland Slag Cement (PSC), Pozzolanic Portland Cement (PPC) and 15% substitution of metakaolin by every cement. The results show that the metakaolin admixture increases the viscosity and the demand amount of superplasticizer. According to the compressive strength results, the highest value of compressive strength was achieved for PSC and without any metakaolin at age of 90 days. Conversely, the lowest level of compressive strength at all ages of conservation was obtained for PPC and containing 15% metakaolin. According to this study, the total substitution of PSC and PPC by Portland cement type II is beneficial to the increasing in the chemical resistance of the SCC with respect to the sulfuric acid attack. On the other hand, this increase is more noticeable by the use of 15% of metakaolin. Therefore, it can be concluded that metakaolin has a positive effect on the chemical resistance of SCC containing of Portland cement type II, PSC, and PPC.

Keywords: SCC, metakaolin, cement type, durability, compressive strength, sulfuric acid attacks.

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Authors: Hiroyuki Nishida, Taku Nonomura, Takashi Abe

Abstract:

Wall-surface jet induced by the dielectric barrier discharge (DBD) has been proposed as an actuator for active flow control in aerodynamic applications. Discharge plasma evolution of the DBD plasma actuator was simulated based on a simple fluid model, in which the electron, one type of positive ion and negative ion were taken into account. Two-dimensional simulation was conducted, and the results are in agreement with the insights obtained from experimental studies. The simulation results indicate that the discharge mode changes depending on applied voltage slope; when the applied voltage is positive-going with high applied voltage slope, the corona-type discharge mode turns into the streamer-type discharge mode and the threshold voltage slope is around 300 kV/ms in this simulation. The characteristics of the electrohydrodynamic (EHD) force, which is the source of the wall-surface jet, also change depending on the discharge mode; the tentative peak value of the EHD force during the positive-going voltage phase is saturated by the periodical formation of the streamer-type discharge.

Keywords: Dielectric barrier discharge, Plasma actuator, Fluid simulation.

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Authors: Delly C. Lestari, Linosefa, Ardiana Kusumaningrum, Andi Yasmon, Anis Karuniawati

Abstract:

The objective of this study is to determine the prevalence of methicillin-resistant Staphylococcus aureus (MRSA) harboring mecA genes from screening isolates among intensive care unit (ICU) patients. All MRSA screening isolates from ICU’s patients of Cipto Mangunkusumo Hospital during 2011 and 2014 were included in this study. Identification and susceptibility test was performed using Vitek2 system (Biomereux®). PCR was conducted to characterize the SCCmec of S. aureus harboring the mecA gene on each isolate. Patient’s history of illness was traced through medical record. 24 isolates from 327 screening isolates were MRSA positive (7.3%). From PCR, we found 17 (70.8%) isolates carrying SCCmec type I, 3 (12.5%) isolates carrying SCCmec type III, and 2 (8.3%) isolates carrying SCCmec type IV. In conclusion, SCCmec type I is the most prevalent MRSA colonization among ICU patients in Cipto Mangunkusumo Hospital.

Keywords: MRSA, mecA genes, ICU, colonization.

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Authors: Kyoung-jae Kim, Hyunchul Ahn, Sangwon Jeong

Abstract:

This study proposes a novel recommender system to provide the advertisements of context-aware services. Our proposed model is designed to apply a modified collaborative filtering (CF) algorithm with regard to the several dimensions for the personalization of mobile devices – location, time and the user-s needs type. In particular, we employ a classification rule to understand user-s needs type using a decision tree algorithm. In addition, we collect primary data from the mobile phone users and apply them to the proposed model to validate its effectiveness. Experimental results show that the proposed system makes more accurate and satisfactory advertisements than comparative systems.

Keywords: Location-based advertisement, Recommender system, Collaborative filtering, User needs type, Mobile user.

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Authors: A. Thabet, G. B. H. Frej, M. Boutayeb

Abstract:

This paper presents a design of dynamic feedback control based on observer for a class of large scale Lipschitz nonlinear systems. The use of Differential Mean Value Theorem (DMVT) is to introduce a general condition on the nonlinear functions. To ensure asymptotic stability, sufficient conditions are expressed in terms of linear matrix inequalities (LMIs). High performances are shown through real time implementation with ARDUINO Duemilanove board to the one-link flexible joint robot.

Keywords: Feedback stabilization, DMVT, Lipschitz nonlinear systems, nonlinear observer, real time implementation.

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Authors: Omid A. Zargar

Abstract:

In this project three type of tools, straight cylindrical, taper cylindrical and triangular tool all made of High speed steel (Wc-Co) used for the friction stir welding (FSW) aluminum alloy H20–H20 and the mechanical properties of the welded joint tested by tensile test and vicker hardness test. Besides, mentioned mechanical properties compared with each other to make conclusion. The result helped design of welding parameter optimization for different types of friction stir process like rotational speed, depth of welding, travel speed, type of material, type of joint, work piece dimension, joint dimension, tool material and tool geometry. Previous investigations in different types of materials work pieces; joint type, machining parameter and preheating temperature take placed. In this investigation 3 mentioned tool types that are popular in FSW tested and the results completed other aspects of the process. Hope this paper can open a new horizon in experimental investigation of mechanical properties for friction stir welded joint with other different type of tools like oval shape probe, paddle shape probe, three flat sided probe, and three sided re-entrant probe and other materials and alloys like titanium or steel in near future.

Keywords: Friction stir welding (FSW), tool, CNC milling machine, aluminum alloy H20, Vickers hardness test, tensile test, straight cylindrical tool, taper cylindrical tool, triangular tool.

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Authors: Arunrungrusmi S, Chaokamnerd W , Tanitteerapan T , Mungkung N., Yuji T.

Abstract:

This research aimed to develop plasma system used in air conditioners. This developed plasma system could be installed in the air conditioners - all split type. The quality of air could be improved to be equal to present plasma system. Development processes were as follows: 1) to study the plasma system used in the air conditioners, 2) to design a plasma generator, 3) to develop the plasma generator, and 4) to test its performance in many types of the air conditioners. This plasma system was developed by AC high voltage – 14 kv with a frequency of 50 kHz. Carbon was a conductor to generate arc in air purifier system. The research was tested by installing the plasma generator in the air conditioners - wall type. Whereas, there were 3 types of installations: air flow out, air flow in, and room center. The result of the plasma generator installed in the air conditioners, split type, revealed that the air flow out installation provided the highest average of o-zone at 223 mg/h. This type of installation provided the highest efficiency of air quality improvement. Moreover, the air flow in installation and the room center installation provided the average of the o-zone at 163 mg/h and 64 mg/h, respectively.

Keywords: Air Conditioner, Plasma generator, High voltage, Optimization, Installation position.

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Authors: Zixin Liu

Abstract:

The problem of robust stability and robust stabilization for a class of discrete-time uncertain systems with time delay is investigated. Based on Tchebychev inequality, by constructing a new augmented Lyapunov function, some improved sufficient conditions ensuring exponential stability and stabilization are established. These conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. Compared with some previous results derived in the literature, the new obtained criteria have less conservatism. Two numerical examples are provided to demonstrate the improvement and effectiveness of the proposed method.

Keywords: Robust stabilization, robust stability, discrete-time system, time delay.

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Authors: V. Rodas, L. Almache

Abstract:

The interaction effects between the existing soil and the substructure of a 5-story building with an underground one, were evaluated in such a way that the structural-geotechnical concepts were validated through the method of impedance factors with a program based on the method of the finite elements. The continuous wall-type foundation had a constant thickness and followed inclined and orthogonal directions, while the ground had homogeneous and medium-type characteristics. The soil considered was type C according to the Ecuadorian Construction Standard (NEC) and the corresponding foundation comprised a depth of 4.00 meters and a basement wall thickness of 40 centimeters. This project is part of a mid-rise building in the city of Azogues (Ecuador). The hypotheses raised responded to the objectives in such a way that the model implemented with springs had a variation with respect to the embedded base, obtaining conservative results.

Keywords: interaction, soil, substructure, springs, effects, modeling, embedment

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Authors: N. Hernández Huertas, F. Rojas Mora

Abstract:

Sounding rockets are aerospace vehicles that were developed in the mid-20th century, and since then numerous investigations have been executed with the aim of innovate in this type of technology. However, the costs associated to the production of this type of technology are usually quite high, and therefore the challenge that exists today is to be able to reduce them. In this way, the main objective of this document is to present the design process of a Colombian aerospace mission capable to reach the thermosphere using low-cost “Candy” type solid fuel engines. This mission is the latest development of the Uniandes Aerospace Project (PUA for its Spanish acronym), which is an undergraduate and postgraduate research group at Universidad de los Andes (Bogotá, Colombia), dedicated to incurring in this type of technology. In this way, the investigations that have been carried out on Candy-type solid fuel, which is a compound of potassium nitrate and sorbitol, have allowed the production of engines powerful enough to reach space, and which represents a unique technological advance in Latin America and an important development in experimental rocketry. In this way, following the engineering iterative design methodology was possible to design a 2-stage sounding rocket with 1 solid fuel engine in each one, which was then simulated in RockSim V9.0 software and reached an apogee of approximately 150 km above sea level. Similarly, a speed equal to 5 Mach was obtained, which after performing a finite element analysis, it was shown that the rocket is strong enough to be able to withstand such speeds. Under these premises, it was demonstrated that it is possible to build a high-power aerospace mission at low cost, using Candy-type solid fuel engines. For this reason, the feasibility of carrying out similar missions clearly depends on the ability to replicate the engines in the best way, since as mentioned above, the design of the rocket is adequate to reach supersonic speeds and reach space. Consequently, with a team of at least 3 members, the mission can be obtained in less than 3 months. Therefore, when publishing this project, it is intended to be a reference for future research in this field and benefit the industry.

Keywords: Aerospace missions, candy type solid propellant engines, design of solid rockets, experimental rocketry, low costs missions.

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Authors: Nurhakimah Ab. Rahman, Lazim Abdullah

Abstract:

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

Keywords: Dual fuzzy polynomial equations, Interval type-2, Ranking method, Value.

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Authors: Petter Eklund, Jonathan Sjölund, Sandra Eriksson, Mats Leijon

Abstract:

The spoke type rotor can be used to obtain magnetic flux concentration in permanent magnet machines. This allows the air gap magnetic flux density to exceed the remanent flux density of the permanent magnets but gives problems with leakage fluxes in the magnetic circuit. The end leakage flux of one spoke type permanent magnet rotor design is studied through measurements and finite element simulations. The measurements are performed in the end regions of a 12 kW prototype generator for a vertical axis wind turbine. The simulations are made using three dimensional finite elements to calculate the magnetic field distribution in the end regions of the machine. Also two dimensional finite element simulations are performed and the impact of the two dimensional approximation is studied. It is found that the magnetic leakage flux in the end regions of the machine is equal to about 20% of the flux in the permanent magnets. The overestimation of the performance by the two dimensional approximation is quantified and a curve-fitted expression for its behavior is suggested.

Keywords: End effects, end leakage flux, permanent magnet machine, spoke type rotor.

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Authors: Jing Li, Guang Zhou

Abstract:

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.

Keywords: Hadamard product, Fan product; nonnegative matrix, M-matrix, Spectral radius, Minimum eigenvalue, 1-path cover.

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