Search results for: positive periodic solutions

Authors: Zi-Gui Huang, Shen-Hsien Hu

Abstract:

This study proposes a fabrication of phononic-crystal acoustic wave device. A graphene-like atomic structure was adopted as the main research subject, and a graphene-like structure was designed using piezoelectric material zinc oxide and its periodic boundary conditions were defined using the finite element method. The effects of a hexagonal honeycomb structure were investigated regarding the band gap phenomenon. The use of micro-electromechanical systems process technology to make the film etched micron graphics, designed to produce four kinds of different piezoelectric structure (plat, periodic, single defect and double defects). Frequency response signals and phase change were also measured in this paper.

Keywords: MEMS, phononic crystal, piezoelectric material, Zinc oxide

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Authors: Maesoomeh Khorshidi Mehr, Mohammad Sajadian, Shadi Alipour

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The purpose of the present study was to compare the effects of eight weeks of continuous and periodic aerobic exercises on serum levels of CRP in overweight woman. 36 woman aged between 20 and 35 years from the city of Ahwaz were randomly selected as the sample of the study. This sample was further divided into three groups (n= 12) of continuous aerobic exercise, periodic aerobic exercise, and control. Subjects of the groups of continuous and periodic aerobic exercise participated in 8 weeks of specialized exercises while the control group subjects did not take part in any regular physical activity program. Blood samples were collected from subjects in 24 hours prior to and 48 hours past to the intervention period. Afterwards, the serum level of CRP was measured for each blood sample. Results showed that BMI and serum level of CRP both significantly reduced as a result of aerobic exercises. However, no statistically significant difference was recorded between the extent of effects of the former and latter aerobic exercise types. Eight weeks of aerobic exercise will probably result in reduced inflammation and cardiovascular diseases risk in overweight women. The reason for lack of difference between effects of continuous and periodic aerobic exercise may lie in the similarity of average intensity and length of physical administered activities.

Keywords: heart diseases, aerobic exercise, inflammation, CRP, overweight

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Authors: Rajib Mia, Badam Singh Kushvah

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The present research was motivated by the recent discovery of the binary star systems. In this paper, we use the restricted three-body problem in the binary stellar systems, considering photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. The stability and periodic orbits of collinear points and the stability and trajectories of the triangular points are studied in stellar binary systems Kepler-34, Kepler-35, Kepler-413 and Kepler-16 systems. A detailed comparison is made among periodic orbits and trajectories.

Keywords: exoplanetary systems, lagrangian points, periodic orbit, restricted three body problem, stability

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Authors: Magdy G. Asaad

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Solitons are among the most beneficial solutions for science and technology for their applicability in physical applications including plasma, energy transport along protein molecules, wave transport along poly-acetylene molecules, ocean waves, constructing optical communication systems, transmission of information through optical fibers and Josephson junctions. In this talk, we will apply the bilinear technique to generate a class of soliton solutions to the (3+1)-dimensional nonlinear soliton equation of Jimbo-Miwa type. Examples of the resulting soliton solutions are computed and a few solutions are plotted.

Keywords: Pfaffian solutions, N-soliton solutions, soliton equations, Jimbo-Miwa

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Saeed Poormoaied, Zumbul Atan

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Emergency shipments provide a powerful mechanism to alleviate the risk of imminent stock-outs and can result in substantial benefits in an inventory system. Customer satisfaction and high service level are immediate consequences of utilizing emergency shipments. In this paper, we consider a single-echelon periodic review inventory system consisting of a single local warehouse, being replenished from a central warehouse with ample capacity in an infinite horizon setting. Since the structure of the optimal policy appears to be complicated, we analyze this problem under an order-up-to-S inventory control policy framework, the (S, T) policy, with the emergency shipment consideration. In each period of the periodic review policy, there is a single opportunity at any point of time for the emergency shipment so that in case of stock-outs, an emergency shipment is requested. The goal is to determine the timing and amount of the emergency shipment during a period (emergency shipment policy) as well as the base stock periodic review policy parameters (replenishment policy). We show that how taking advantage of having an emergency shipment during periods improves the performance of the classical (S, T) policy, especially when fixed and unit emergency shipment costs are small. Investigating the structure of the objective function, we develop an exact algorithm for finding the optimal solution. We also provide a heuristic and an approximation algorithm for the periodic review inventory system problem. The experimental analyses indicate that the heuristic algorithm is computationally more efficient than the approximation algorithm, but in terms of the solution efficiency, the approximation algorithm performs very well. We achieve up to 13% cost savings in the (S, T) policy if we apply the proposed emergency shipment policy. Moreover, our computational results reveal that the approximated solution is often within 0.21% of the globally optimal solution.

Keywords: emergency shipment, inventory, periodic review policy, approximation algorithm.

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Authors: Shoji Katagiri

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This paper is to clarify the relationship between ICT and income inequality. To do so, we develop the general equilibrium model with ICT investment, obtain the equilibrium solutions, and then simulate the model with these solutions for some OECD countries. As a result, generally, during the corresponding periods we confirm that the relationship between ICT investment and income inequality is positive. In this mode, the increment of the ratio of ICT investment to the aggregated investment in stock enhances the capital’s share of income, and finally leads to income inequality such as the increase of the share of the top decile income. Although we confirm the positive relationship between ICT investment and income inequality, the upward trend for that relationship depends on the values of parameters for the making use of the simulations and these parameters are not deterministic in the magnitudes on the calculated results for the simulations.

Keywords: ICT, inequality, capital accumulation, technology

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Authors: Avan Al-Saffar, Eun-Jin Kim

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Both the logistic growth model and the gompertz growth model are used to describe growth processes. Both models driven by perturbations in different cases are investigated using information theory as a useful measure of sustainability and the variability. Specifically, we study the effect of different oscillatory modulations in the system's parameters on the evolution of the system and Probability Density Function (PDF). We show the maintenance of the initial conditions for a long time. We offer Fisher information analysis in positive and/or negative feedback and explain its implications for the sustainability of population dynamics. We also display a finite amplitude solution due to the purely fluctuating growth rate whereas the periodic fluctuations in negative feedback can lead to break down the system's self-regulation with an exponentially growing solution. In the cases tested, the gompertz and logistic systems show similar behaviour in terms of information and sustainability although they develop differently in time.

Keywords: dynamical systems, fisher information, probability density function (pdf), sustainability

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Authors: Sung Duk Kim, Kwan U. Kim, Jin Sim, Ryong Jin Jang

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The phenomenon of seasonal variations in the Earth’s rotation velocity was discovered in the 1930s when a crystal clock was developed and analyzed in a quantitative way for the first time between 1955 and 1968 when observation data of the seasonal variations was analyzed by an atomic clock. According to the previous investigation, atmospheric circulation is supposed to be a factor affecting the seasonal variations in the Earth’s rotation velocity in many cases, but the problem has not been solved yet. In order to solve the problem, it is necessary to apply dynamics to consider the Earth’s spatial motion, rotation and change of shape of the Earth (movement of materials in and out of the Earth and change of the Earth’s figure) at the same time and in interrelation to the accuracy of post-Newtonian approximation regarding the Earth body as a system of mass points because the stability of the Earth’s rotation angular velocity is in the range of 10⁻⁸~10⁻⁹. For the purpose, the equation was derived, which can consider the 3 kinds of motion above mentioned at the same time by taking the effect of the resultant of external force on the Earth’s rotation into account in a relativistic way to the accuracy of post-Newtonian approximation. Therefore, the equation has been solved to obtain the theoretical values of periodic change in the Earth’s rotation velocity and they have been compared with the astronomical observation data, so to reveal the cause for the periodic change in the Earth’s rotation velocity.

Keywords: Earth rotation, moment function, periodic change, seasonal variation, relativistic change

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Authors: Matthaios Katsanikas

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We study the structure of the invariant manifolds of complex unstable periodic orbits of a family of periodic orbits, in a 3D autonomous Hamiltonian system of galactic type, after a transition of this family from stability to complex instability (Hamiltonian Hopf bifurcation). We consider the case of a supercritical Hamiltonian Hopf bifurcation. The invariant manifolds of complex unstable periodic orbits have two kinds of structures. The first kind is represented by a disk confined structure on the 4D space of section. The second kind is represented by a complicated central tube structure that is associated with an extended network of tube structures, strips and flat structures of sheet type on the 4D space of section.

Keywords: dynamical systems, galactic dynamics, chaos, phase space

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Authors: Chao-Qing Dai

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Two families of exact travelling solutions for the discrete sine-Gordon equation are constructed based on the variable-coefficient Jacobian elliptic function method and different transformations. When the modulus of Jacobian elliptic function solutions tends to 1, soliton solutions can be obtained. Some soliton solutions degenerate into the known solutions in literatures. Moreover, dynamical properties of exact solutions are investigated. Our analysis and results may have potential values for certain applications in modern nonlinear science and textile engineering.

Keywords: exact solutions, variable-coefficient Jacobian elliptic function method, discrete sine-Gordon equation, dynamical behaviors

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Authors: G. De Matteis, L. Martina, V. Turco

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The work is focused on determining and comparing special nonlinear static configurations in cholesteric liquid crystals (CLCs), confined between two parallel plates and in the presence of an external static electric/magnetic field. The solutions are stabilised by topological and non-topological conservation laws since they are described in terms of integrable or partially integrable nonlinear boundary value problems. In cholesteric liquid crystals which are subject to geometric frustration; anchoring conditions at boundaries, i.e., homeotropic conditions, are incompatible with the cholesteric twist. This aspect turns out to be essential in the admissible classes of solutions, allowing also for disclination type singularities. Within the framework of Frank-Oseen theory, we study the static configurations for CLCs. First, we find numerical solutions for isolated axisymmetric states in confined CLCs with weak homeotropic anchoring at the boundaries. These solutions describe 3-dimensional modulations, namely spherulites or cholesteric bubbles, actually observed in these systems, of standard baby skyrmions. Relations with well-known nonlinear integrable systems are found and are used to explore the asymptotic behavior of the solutions. Then we turn our attention to extended periodic static configurations called Helicoids or cholesteric fingers, described by an elliptic sine-Gordon model with appropriate boundary conditions, showing how their period and energies are determined by both the thickness of the cell and the intensity of the external electric/magnetic field. We explicitly show that helicoids with π or 2π of rotations of the molecular director are different in many aspects and are not simply algebraically related. The behaviour of the solutions, their energy and the properties of the associated disclinations are discussed in detail, both analytically and numerically.

Keywords: cholesteric liquid crystals, geometric frustration, helicoids, skyrmions

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Authors: Edamana Krishnan, Khalil Al-Ghafri

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In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: Muhammad A. Alsubaie, Mubarak K. H. Alhajri, Tarek S. Altowaim

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A repetitive controller designed to accommodate periodic disturbances via state feedback is discussed. Periodic disturbances can be represented by a time delay model in a positive feedback loop acting on system output. A direct use of the small gain theorem solves the periodic disturbances problem via 1) isolating the delay model, 2) finding the overall system representation around the delay model and 3) designing a feedback controller that assures overall system stability and tracking error convergence. This paper addresses uncertainty conditions for the repetitive controller designed in state feedback in either past error feedforward or current error feedback using singular values. The uncertainty investigation is based on the overall system found and the stability condition associated with it; depending on the scheme used, to set an upper/lower limit weighting parameter. This creates a region that should not be exceeded in selecting the weighting parameter which in turns assures performance improvement against system uncertainty. Repetitive control problem can be described in lifted form. This allows the usage of singular values principle in setting the range for the weighting parameter selection. The Simulation results obtained show a tracking error convergence against dynamic system perturbation if the weighting parameter chosen is within the range obtained. Simulation results also show the advantage of weighting parameter usage compared to the case where it is omitted.

Keywords: model mismatch, repetitive control, singular values, state feedback

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Authors: H. Ait Abderrahmane, M. Fayed, H. D. Ng, G. H. Vatistas

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The present paper expands details and confirms the transition mechanism between two subsequent polygonal patterns of the hollow-core vortex. Using power spectral analysis, we confirm in this work that the transition from any N-gon to (N+1)-gon pattern observed within a hollow-core vortex of shallow rotating flows occurs in two steps. The regime was quasi-periodic before the frequencies lock (synchronization). The ratios of locking frequencies were found to be equal to (N-1)/N.

Keywords: patterns, swirling, quasi-periodic, synchronization

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Authors: Yongyi Chen, Li Qin, Peng Jia, Yongqiang Ning, Yun Liu, Lijun Wang

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The distributed feedback (DFB) lasers are indispensable in optical phase array (OPA) used for light detection and ranging (LIDAR) techniques, laser communication systems and integrated optics, thanks to their stable single longitudinal mode and narrow linewidth properties. Traditional index-coupled (IC) DFB lasers with uniform gratings have an inherent problem of lasing two degenerated modes. Phase shifts are usually required to eliminate the mode degeneration, making the grating structure complex and expensive. High-quality antireflection (AR) coatings on both lasing facets are also essential owing to the random facet phases introduced by the chip cleavage process, which means half of the lasing energy is wasted. Gain-coupled DFB (GC-DFB) lasers based on the periodic gain (or loss) are announced to have single longitudinal mode as well as capable of the unsymmetrical coating to increase lasing power and efficiency thanks to facet immunity. However, expensive and time-consuming technologies such as epitaxial regrowth and nanoscale grating processing are still required just as IC-DFB lasers, preventing them from practical applications and commercial markets. In this research, we propose a low-cost, single-mode regrowth-free GC-DFB laser based on periodic surface p-contacts. The gain coupling effect is achieved simply by periodic current distribution in the quantum well caused by periodic surface p-contacts, introducing very little index-coupling effect that can be omitted. It is prepared by i-line lithography, without nanoscale grating fabrication or secondary epitaxy. Due to easy fabrication techniques, it provides a method to fabricate practical low cost GC-DFB lasers for widespread practical applications.

Keywords: DFB laser, gain-coupled, low cost, periodic p-contacts

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Nadia Theuma

Abstract:

Climate change is a reality that has started to leave an impact on the physical environment as well as on the built environment, in particular built heritage. This paper explores the argument that climate change is also a trigger which can lead to identifying a number of creative solutions that can transform built heritage into sustainable buildings. Using the Maltese Islands, and in particular the city of Valletta which is also a World Heritage Site, this paper illustrates some of the innovative solutions that are being developed to make heritage buildings more sustainable and in doing so, mitigating the negative impacts of climate change. The paper looks in detail at the most notable initiatives being developed, their implementation and application, which at times is not easy considering the restrictions within protected built heritage areas and the positive impacts that they will have on visitor experience and overall sustainability of the Maltese tourism product. The paper will conclude by outlining how these solutions can be adapted to buildings with similar climatic conditions.

Keywords: built heritage, creative solutions, climate change, Maltese Islands

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Authors: Anuraj Singh

Abstract:

The complex dynamics is explored in a prey predator system with multiple delays. The predator dynamics is governed by Leslie-Gower scheme. The existence of periodic solutions via Hopf bifurcation with respect to delay parameters is established. To substantiate analytical findings, numerical simulations are performed. The system shows rich dynamic behavior including chaos and limit cycles.

Keywords: chaos, Hopf bifurcation, stability, time delay

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Authors: Sina Modares Ahmadi, Mohamad Reza Ghazavi, Mandana Sheikhzad

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Squeeze film damper systems (SFD) are often used in machines with high rotational speed to reduce non-periodic behavior by creating external damping. These types of systems are frequently used in aircraft gas turbine engines. There are some structural parameters which are of great importance in designing these kinds of systems, such as oil film thickness, C, and outer race mass, mo. Moreover, there is a crucial parameter associated with manufacturing process, under the title of waviness. Geometric imperfections are often called waviness if its wavelength is much longer than Hertzian contact width which is a considerable source of vibration in ball bearings. In this paper, a system of a flexible rotor and two ball bearings with floating ring squeeze film dampers and consideration of waviness has been modeled and solved by a numerical integration method, namely Runge-Kutta method to investigate the dynamic response of the system. The results show that by increasing the number of wave lobes, which is due to inappropriate manufacturing, non- periodic and chaotic behavior increases. This result reveals the importance of manufacturing accuracy. Moreover, as long as C< 1.5×10-4 m, by increasing the oil film thickness, unwanted vibrations and non-periodic behavior of the system have been reduced, On the other hand, when C>1.5×10-4 m, increasing the outer oil film thickness results in the increasing chaotic and non-periodic responses. This result shows that although the presence of oil film results in reduction the non-periodic and chaotic behaviors, but the oil film has an optimal thickness. In addition, with increasing mo, the disc displacement amplitude increases. This result reveals the importance of utilizing light materials in manufacturing the squeeze film dampers.

Keywords: squeeze-film damper, waviness, ball bearing, bifurcation

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Authors: C. H. Chang, R. Z. Qiu, C. W. Tsao, Y. H. Cheng, C. H. Chen, W. J. Hsueh

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Characteristics of photoluminescence (PL) in a resonant quasi-periodic double-period quantum wells (DPQW) are demonstrated. The maximum PL intensity in the DPQW is remarkably greater than that in a traditional periodic QW (PQW) under the Bragg or anti-Bragg conditions. The optimal PL spectrum in the DPQW has an asymmetrical form instead of the symmetrical form in the PQW. Moreover, there are two large values of PL intensity in the DPQW, which also differs from the PQW.

Keywords: Photoluminescence, quantum wells, quasiperiodic structure

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Authors: Meziane Belkacem

Abstract:

We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Pilar Rey del Castillo

Abstract:

This document describes the building of an average indicator of the general sentiments about the future exposed in the newspapers in Spain. The raw data are collected through the scraping of the Digital Periodical and Newspaper Library website. Basic tools of natural language processing are later applied to the collected information to evaluate the sentiment strength of each word in the texts using a polarized dictionary. The last step consists of summarizing these sentiments to produce daily indices. The results are a first insight into the applicability of these techniques to produce periodic sentiment indicators.

Keywords: natural language processing, periodic indicator, sentiment analysis, web scraping

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Authors: Muhammad A. Alsubaie

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An iterative learning control framework designed in state feedback structure suffers a lack in investigating load disturbance considerations. The presented work discusses the controller previously designed, highlights the disturbance problem, finds new conditions using singular value principle to assure safe operation conditions with error convergence and reference tracking under the influence of load disturbance. It is known that periodic disturbances can be represented by a delay model in a positive feedback loop acting on the system input. This model can be manipulated by isolating the delay model and finding a controller for the overall system around the delay model to remedy the periodic disturbances using the small signal theorem. The overall system is the base for control design and load disturbance investigation. The major finding of this work is the load disturbance condition found which clearly sets safe operation condition under the influence of load disturbances such that the error tends to nearly zero as the system keeps operating trial after trial.

Keywords: iterative learning control, singular values, state feedback, load disturbance

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Authors: Pawel Martynowicz

Abstract:

Vibrations are a crucial problem for slender structures such as towers, masts, chimneys, wind turbines, bridges, high buildings, etc., that is why most of them are equipped with vibration attenuation or fatigue reduction solutions. In this work, a slender structure (i.e., wind turbine tower-nacelle model) equipped with nonlinear, semiactive tuned vibration absorber(s) is analyzed. For this study purposes, magnetorheological (MR) dampers are used as semiactive actuators. Several optimal-based approaches to structural vibration attenuation are investigated against the standard ‘ground-hook’ law and passive tuned vibration absorber(s) implementations. The common approach to optimal control of nonlinear systems is offline computation of the optimal solution, however, so determined open loop control suffers from lack of robustness to uncertainties (e.g., unmodelled dynamics, perturbations of external forces or initial conditions), and thus perturbation control techniques are often used. However, proper linearization may be an issue for highly nonlinear systems with implicit relations between state, co-state, and control. The main contribution of the author is the development as well as numerical and experimental verification of the Pontriagin maximum-principle-based vibration control concepts that produce directly actuator control input (not the demanded force), thus force tracking algorithm that results in control inaccuracy is entirely omitted. These concepts, including one-step optimal control, quasi-optimal control, and optimal-based modified ‘ground-hook’ law, can be directly implemented in online and real-time feedback control for periodic (or semi-periodic) disturbances with invariant or time-varying parameters, as well as for non-periodic, transient or random disturbances, what is a limitation for some other known solutions. No offline calculation, excitations/disturbances assumption or vibration frequency determination is necessary, moreover, all of the nonlinear actuator (MR damper) force constraints, i.e., no active forces, lower and upper saturation limits, hysteresis-type dynamics, etc., are embedded in the control technique, thus the solution is optimal or suboptimal for the assumed actuator, respecting its limitations. Depending on the selected method variant, a moderate or decisive reduction in the computational load is possible compared to other methods of nonlinear optimal control, while assuring the quality and robustness of the vibration reduction system, as well as considering multi-pronged operational aspects, such as possible minimization of the amplitude of the deflection and acceleration of the vibrating structure, its potential and/or kinetic energy, required actuator force, control input (e.g. electric current in the MR damper coil) and/or stroke amplitude. The developed solutions are characterized by high vibration reduction efficiency – the obtained maximum values of the dynamic amplification factor are close to 2.0, while for the best of the passive systems, these values exceed 3.5.

Keywords: magnetorheological damper, nonlinear tuned vibration absorber, optimal control, real-time structural vibration attenuation, wind turbines

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Authors: Aziza Altaibayeva, Ertan Güdekli, Ratbay Myrzakulov

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In this letter, we explore exact solutions for the Horava-Lifshitz gravity. We use of an extension of this theory with first order dynamical lapse function. The equations of motion have been derived in a fully consistent scenario. We assume that there are some spherically symmetric families of exact solutions of this extended theory of gravity. We obtain exact solutions and investigate the singularity structures of these solutions. Specially, an exact solution with the regular horizon is found.

Keywords: quantum gravity, Horava-Lifshitz gravity, black hole, spherically symmetric space times

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Authors: Takashi Mitsuishi

Abstract:

Fuzzy logic has gained acceptance in the recent years in the fields of social sciences and humanities such as psychology and linguistics because it can manage the fuzziness of words and human subjectivity in a logical manner. However, the major field of application of the fuzzy logic is control engineering as it is a part of the set theory and mathematical logic. Mamdani method, which is the most popular technique for approximate reasoning in the field of fuzzy control, is one of the ways to numerically represent the control afforded by human language and sensitivity and has been applied in various practical control plants. Fuzzy logic has been gradually developing as an artificial intelligence in different applications such as neural networks, expert systems, and operations research. The objects of inference vary for different application fields. Some of these include time, angle, color, symptom and medical condition whose fuzzy membership function is a periodic function. In the defuzzification stage, the domain of the membership function should be unique to obtain uniqueness its defuzzified value. However, if the domain of the periodic membership function is determined as unique, an unintuitive defuzzified value may be obtained as the inference result using the center of gravity method. Therefore, the authors propose a method of circular-polar-coordinates transformation and defuzzification of the periodic membership functions in this study. The transformation to circular polar coordinates simplifies the domain of the periodic membership function. Defuzzified value in circular polar coordinates is an argument. Furthermore, it is required that the argument is calculated from a closed plane figure which is a periodic membership function on the circular polar coordinates. If the closed plane figure is continuous with the continuity of the membership function, a significant amount of computation is required. Therefore, to simplify the practice example and significantly reduce the computational complexity, we have discretized the continuous interval and the membership function in this study. In this study, the following three methods are proposed to decide the argument from the discrete polygon which the continuous plane figure is transformed into. The first method provides an argument of a straight line passing through the origin and through the coordinate of the arithmetic mean of each coordinate of the polygon (physical center of gravity). The second one provides an argument of a straight line passing through the origin and the coordinate of the geometric center of gravity of the polygon. The third one provides an argument of a straight line passing through the origin bisecting the perimeter of the polygon (or the closed continuous plane figure).

Keywords: defuzzification, fuzzy membership function, periodic function, polar coordinates transformation

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Authors: Zhenjie Liu

Abstract:

This paper investigates the existence and uniqueness of solutions for singular higher order boundary value problems on time scales by using mixed monotone method. The theorems obtained are very general. For the different time scale, the problem may be the corresponding continuous or discrete boundary value problem.

Keywords: mixed monotone operator, boundary value problem, time scale, green's function, positive solution, singularity

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Authors: Wu Qinglong, Zhou Qicai, Xiong Xiaolei, Zhang Richeng

Abstract:

In order to achieve the layout and size optimization of the web members of tower crane boom, a truss topology and cross section size optimization method based on continuum is proposed considering three typical working conditions. Firstly, the optimization model is established by replacing web members with web plates. And the web plates are divided into several sub-domains so that periodic soft kill option (SKO) method can be carried out for topology optimization of the slender boom. After getting the optimized topology of web plates, the optimized layout of web members is formed through extracting the principal stress distribution. Finally, using the web member radius as design variable, the boom compliance as objective and the material volume of the boom as constraint, the cross section size optimization mathematical model is established. The size optimization criterion is deduced from the mathematical model by Lagrange multiplier method and Kuhn-Tucker condition. By comparing the original boom with the optimal boom, it is identified that this optimization method can effectively lighten the boom and improve its performance.

Keywords: tower crane boom, topology optimization, size optimization, periodic, SKO, optimization criterion

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Authors: D. G. Piliposyan

Abstract:

Propagation of electro-elastic waves in a piezoelectric waveguide with finite stacks and a defect layer is studied using a modified transfer matrix method. The dispersion equation for a periodic structure consisting of unit cells made up from two piezoelectric materials with metallized interfaces is obtained. An analytical expression, for the transmission coefficient for a waveguide with finite stacks and a defect layer, that is found can be used to accurately detect and control the position of the passband within a stopband. The result can be instrumental in constructing a tunable waveguide made of layers of different or identical piezoelectric crystals and separated by metallized interfaces.

Keywords: piezoelectric layered structure, periodic phononic crystal, bandgap, bloch waves

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