Search results for: Ceramic Fixed Partial Dentures

Authors: Fengxia Zheng

Abstract:

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

Keywords: Fractional differential equation, boundary value problem, positive solution, existence and uniqueness, fixed point theorem, mixed monotone operator.

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Authors: Ji–Wook Mauk, Yu–Suk Kim, Hyung–Joon Kim

Abstract:

This study carried out comparative seismic performance of reinforced concrete frames infilled by masonry walls with different heights. Partial and fully infilled reinforced concrete frames were modeled for the research objectives and the analysis model for a bare reinforced concrete frame was also established for comparison. Non–linear static analyses for the studied frames were performed to investigate their structural behavior under extreme seismic loads and to find out their collapse mechanism. It was observed from analysis results that the strengths of the partial infilled reinforced concrete frames are increased and their ductilities are reduced, as infilled masonry walls are higher. Especially, reinforced concrete frames with higher partial infilled masonry walls would experience shear failures. Non–linear dynamic analyses using 10 earthquake records show that the bare and fully infilled reinforced concrete frame present stable collapse mechanism while the reinforced concrete frames with partially infilled masonry walls collapse in more brittle manner due to short-column effects.

Keywords: Fully infilled RC frame, partially infilled RC frame, masonry wall, short–column effects.

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Authors: Ali F. Al-Baz, Mohsen M. Al-Husaini, James M. Bishop

Abstract:

Intertidal fixed stake net trap (Hadrah) is one of the oldest fishing gears used throughout the Arabian Gulf countries since the 1800s and also one of most the efficient methods of capturing fish from the intertidal area. This study describes the hadrah fishery in Kuwait.

From October 2001 to December 2002, more than 37,372 specimens representing 95 species (89 fish, 2 mollusks and 4 crustaceans) were measured from hadrah, located in three different areas along Kuwait's coast. In Kuwait Bay, catch rates averaged 62 kg/sir-day (from 14 kg/sir-day in February to 160 kg/sir-day in October 2002). Commercial species accounted for 41% of the catches. Catches from Failakah Island averaged 96 kg/sir-day from June to September, with 61% of the catch being commercial species. In the southern area, catches averaged only 32 kg/sir-day and only 34% were commercially important.

Forty percent of the hadrah catches were juveniles, which shows that Kuwait’s shallow intertidal waters, particularly in Kuwait Bay, served as prime nursery habitat,. To maintain ecosystem biodiversity and recruitment success of the fishes, we recommended that all hadrah should be removed from Kuwait Bay. In the future, removal of hadrah from other locations should be considered.

Keywords: Catch and effort, Hadrah, Intertidal Fixed stake net, Kuwait, Species composition.

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Authors: Shanar Askar, Shahzad Memon, LachhmanDas, MSKalhoro

Abstract:

Wimax (Worldwide Interoperability for Microwave Access) is a promising technology which can offer high speed data, voice and video service to the customer end, which is presently, dominated by the cable and digital subscriber line (DSL) technologies. The performance assessment of Wimax systems is dealt with. The biggest advantage of Broadband wireless application (BWA) over its wired competitors is its increased capacity and ease of deployment. The aims of this paper are to model and simulate the fixed OFDM IEEE 802.16d physical layer under variant combinations of digital modulation (BPSK, QPSK, and 16-QAM) over diverse combination of fading channels (AWGN, SUIs). Stanford University Interim (SUI) Channel serial was proposed to simulate the fixed broadband wireless access channel environments where IEEE 802.16d is to be deployed. It has six channel models that are grouped into three categories according to three typical different outdoor Terrains, in order to give a comprehensive effect of fading channels on the overall performance of the system.

Keywords: WIMAX, OFDM, Additive White Gaussian Noise, Fading Channel, SUI, Doppler Effect.

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Authors: Muhammad Imran, Iqra Basit, Mobushir Riaz Khan, Sajid Rasheed Ahmad

Abstract:

The present study investigates the space-time impact of climate change on the rice crop calendar in tropical Gujranwala, Pakistan. The climate change impact was quantified through the climatic variables, whereas the existing calendar of the rice crop was compared with the phonological stages of the crop, depicted through the time series of the Normalized Difference Vegetation Index (NDVI) derived from Landsat data for the decade 2005-2015. Local maxima were applied on the time series of NDVI to compute the rice phonological stages. Panel models with fixed and cross-section fixed effects were used to establish the relation between the climatic parameters and the time-series of NDVI across villages and across rice growing periods. Results show that the climatic parameters have significant impact on the rice crop calendar. Moreover, the fixed effect model is a significant improvement over cross-sectional fixed effect models (R-squared equal to 0.673 vs. 0.0338). We conclude that high inter-annual variability of climatic variables cause high variability of NDVI, and thus, a shift in the rice crop calendar. Moreover, inter-annual (temporal) variability of the rice crop calendar is high compared to the inter-village (spatial) variability. We suggest the local rice farmers to adapt this change in the rice crop calendar.

Keywords: Landsat NDVI, panel models, temperature, rainfall.

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Authors: F. N. Budiman, Y. Khan, A. A. Khan, A. Beroual, N. H. Malik, A. A. Al-Arainy

Abstract:

It is well known that metallic particles reduce the reliability of Gas-Insulated Substation (GIS) equipments by initiating partial discharge (PDs) that can lead to breakdown and complete failure of GIS. This paper investigates the characteristics of PDs caused by metallic particle adhering to the solid spacer. The PD detection and measurement were carried out by using IEC 60270 method with particles of different sizes and at different positions on the spacer surface. The results show that a particle of certain size at certain position possesses a unique PD characteristic as compared to those caused by particles of different sizes and/or at different positions. Therefore PD characteristics may be useful for the particle size and position identification.

Keywords: Particle, partial discharge, GIS, spacer.

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Authors: S. Karabulut, A. Güllü, A. Güldas, R. Gürbüz

Abstract:

This study investigates the effects of the lead angle and chip thickness variation on surface roughness during the machining of compacted graphite iron using ceramic cutting tools under dry cutting conditions. Analytical models were developed for predicting the surface roughness values of the specimens after the face milling process. Experimental data was collected and imported to the artificial neural network model. A multilayer perceptron model was used with the back propagation algorithm employing the input parameters of lead angle, cutting speed and feed rate in connection with chip thickness. Furthermore, analysis of variance was employed to determine the effects of the cutting parameters on surface roughness. Artificial neural network and regression analysis were used to predict surface roughness. The values thus predicted were compared with the collected experimental data, and the corresponding percentage error was computed. Analysis results revealed that the lead angle is the dominant factor affecting surface roughness. Experimental results indicated an improvement in the surface roughness value with decreasing lead angle value from 88° to 45°.

Keywords: CGI, milling, surface roughness, ANN, regression, modeling, analysis.

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Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: Yung-Tan Lee, Ren-Yi Huang, Ju-Chin Chen, Jyh-Yi Shih, Meng-Lung Lin, Hsiao-Ling Yu, Yen-Tsui Hu, Chih-Cheng Chen

Abstract:

Cenozoic basalts found in Jiangsu province of eastern China include tholeiites and alkali basalts. The present paper analyzed the major, trace elements, rare earth elements of these Cenozoic basalts and combined with Sr-Nd isotopic compositions proposed by Chen et al. (1990)[1] in the literatures to discuss the petrogenesis of these basalts and the geochemical characteristics of the source mantle. Based on major, trace elements and fractional crystallization model established by Brooks and Nielsen (1982)[2] we suggest that the basaltic magma has experienced olivine + clinopyroxene fractionation during its evolution. The chemical compositions of basaltic rocks from Jiangsu province indicate that these basalts may belong to the same magmatic system. Spidergrams reveal that Cenozoic basalts from Jiangsu province have geochemical characteristics similar to those of ocean island basalts(OIB). The slight positive Nb and Ti anomalies found in basaltic rocks of this study suggest the presence of Ti-bearing minerals in the mantle source and these Ti-bearing minerals had contributed to basaltic magma during partial melting, indicating a metasomatic event might have occurred before the partial melting. Based on the Sr vs. Nd isotopic ratio plots, we suggest that Jiangsu basalts may be derived from partial melting of mantle source which may represent two-end members mixing of DMM and EM-I. Some Jiangsu basaltic magma may be derived from partial melting of EM-I heated by the upwelling asthenospheric mantle or asthenospheric diapirism.

Keywords: Geochemistry, Jiangsu Province, Cenozoic basalts, Fractional crystallization.

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Authors: Nwakaego C. Onyenokporo

Abstract:

Cement is the most extensively used construction material due to its strength and versatility of use. However, the production of Portland cement has become unsustainable because of high energy usage, reduction of natural non-renewable resources and emissions of greenhouse gases. Production of cement contributes to anthropogenic greenhouse gases emissions annually. The growing concerns for the environment resulting from this constant and excessive use of cement has therefore raised the need for more green materials and technology. The use of supplementary cementitious materials (SCMs) is considered as one of the many alternatives suited to address this issue and serve as a sustainable partial replacement for cement in construction. This paper will examine the reuse of these waste materials to partially replace Portland cement. It provides a critical review of literature analysing various supplementary cementitious materials which are applicable in the building industry as either partial replacement for cement or aggregates. These materials have been grouped based on source into industrial wastes, domestic/general wastes, and agricultural wastes. The reuse of these waste materials could potentially reduce the negative effects of cement production and reduce landfills which constitute an environmental nuisance. This paper seeks to inform building industry professionals and researchers in the field on the applicability of these waste materials in construction.

Keywords: cement, greenhouse gases, landfills, sustainable, waste materials

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Authors: Nwakaego C. Onyenokporo

Abstract:

Cement is the most extensively used construction material due to its strength and versatility of use. However, the production of Portland cement has become unsustainable because of high energy usage, reduction of natural non-renewable resources and emissions of greenhouse gases. Production of cement contributes to anthropogenic greenhouse gases emissions annually. The growing concerns for the environment resulting from this constant and excessive use of cement has therefore raised the need for more green materials and technology. The use of supplementary cementitious materials (SCMs) is considered as one of the many alternatives suited to address this issue and serve as a sustainable partial replacement for cement in construction. This paper will examine the reuse of these waste materials to partially replace Portland cement. It provides a critical review of literature analysing various supplementary cementitious materials which are applicable in the building industry as either partial replacement for cement or aggregates. These materials have been grouped based on source into industrial wastes, domestic/general wastes, and agricultural wastes. The reuse of these waste materials could potentially reduce the negative effects of cement production and reduce landfills which constitute an environmental nuisance. This paper seeks to inform building industry professionals and researchers in the field on the applicability of these waste materials in construction.

Keywords: Cement, greenhouse gases, landfills, sustainable, waste materials.

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Authors: Gholamreza Zahedi, M. Tarin, M. Biglari

Abstract:

This work investigated the steady state and dynamic simulation of a fixed bed industrial naphtha reforming reactors. The performance of the reactor was investigated using a heterogeneous model. For process simulation, the differential equations are solved using the 4th order Runge-Kutta method .The models were validated against measured process data of an existing naphtha reforming plant. The results of simulation in terms of components yields and temperature of the outlet were in good agreement with empirical data. The simple model displays a useful tool for dynamic simulation, optimization and control of naphtha reforming.

Keywords: Dynamic simulation, fixed bed reactor, modeling, reforming

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Authors: Ali Safdari-Vaighani

Abstract:

Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: Radial basis function, basket option, jump diffusion, RBF-PUM.

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Authors: Fengxia Zheng, Chuanyun Gu

Abstract:

By using a fixed point theorem of a sum operator, the existence and uniqueness of positive solution for a class of boundary value problem of nonlinear fractional differential equation is studied. An iterative scheme is constructed to approximate it. Finally, an example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator.

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Authors: Ali Shojaei-Fard

Abstract:

In this paper we consider quantum motion integrals depended on the algebraic reconstruction of BPHZ method for perturbative renormalization in two different procedures. Then based on Bogoliubov character and Baker-Campbell-Hausdorff (BCH) formula, we show that how motion integral condition on components of Birkhoff factorization of a Feynman rules character on Connes- Kreimer Hopf algebra of rooted trees can determine a family of fixed point equations.

Keywords: Birkhoff Factorization, Connes-Kreimer Hopf Algebra of Rooted Trees, Integral Renormalization, Lax Pair Equation, Rota- Baxter Algebras.

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Authors: Nikol Žižková

Abstract:

The aim of this study was to observe the behavior of polymer-modified cement mortars with regard to the use of a pozzolanic admixture. Polymer-modified mortars (PMMs) containing various types of waste glass (waste packing glass and fluorescent tube glass) were produced always with 20% of cement substituted with a pozzolanic-active material. Ethylene/vinyl acetate copolymer (EVA) was used for polymeric modification. The findings confirm the possibility of using the waste glass examined herein as a partial substitute for cement in the production of PMM, which contributes to the preservation of non-renewable raw material resources and to the efficiency of waste glass material reuse.

Keywords: Recycled waste glass, polymer-modified mortars, pozzolanic admixture.

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Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: Meng Hu, Lili Wang

Abstract:

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form:  Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

Keywords: Fractional differential equation, Integral boundary condition, Schauder fixed point theorem, Banach contraction principle.

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Authors: Savvas Varitis, Panagiotis Kavouras, George Vourlias, Eleni Pavlidou, Theodoros Karakostas, Philomela Komninou

Abstract:

A chromium-loaded ash originating from incineration of tannery sludge under anoxic conditions was mixed with low grade soda-lime glass powder coming from commercial glass bottles. The relative weight proportions of ash over glass powder tested were 30/70, 40/60 and 50/50. The solid mixtures, formed in green state compacts, were sintered at the temperature range of 800o C up to 1200o C. The resulting products were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive X-ray spectrometry (EDXS) and micro-indentation. The above methods were employed to characterize the various phases, microstructure and hardness of the produced materials. Thermal treatment at 800o C and 1000o C produced opaque ceramic products composed of a variety of chromium-containing and chromium-free crystalline phases. Thermal treatment at 1200o C gave rise to composite products, where only chromium-containing crystalline phases were detected. Hardness results suggest that specific products are serious candidates for structural applications.

Keywords: Chromium-rich tannery residues, glass-ceramic materials, mechanical properties, microstructure

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Authors: Faghihnia Torshizi Mostafa, Saitoh Masato

Abstract:

An efficient method is developed for the response of a group of vertical, cylindrical fixed-head, finite length piles embedded in a homogeneous elastic stratum, subjected to harmonic force atop the pile group cap. Pile to pile interaction is represented through simplified beam-on-dynamic-Winkler-foundation (BDWF) with realistic frequency-dependent springs and dashpots. Pile group effect is considered through interaction factors. New closed-form expressions for interaction factors and curvature ratios atop the pile are extended by considering different boundary conditions at the tip of the piles (fixed, hinged). In order to investigate the fundamental characteristics of inertial bending strains in pile groups, inertial bending strains at the head of each pile are expressed in terms of slenderness ratio. The results of parametric study give valuable insight in understanding the behavior of fixed head pile groups in fundamental natural frequency of soil stratum.

Keywords: Winkler-foundation, fundamental frequency of soil stratum, normalized inertial bending strain, harmonic excitation.

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Authors: M. Hemam, M. Djezzar, T. Djouad

Abstract:

We are interested in the problem of building an ontology in a heterogeneous organization, by taking into account different viewpoints and different terminologies of communities in the organization. Such ontology, that we call multi-viewpoint ontology, confers to the same universe of discourse, several partial descriptions, where each one is relative to a particular viewpoint. In addition, these partial descriptions share at global level, ontological elements constituent a consensus between the various viewpoints. In order to provide response elements to this problem we define a multi-viewpoints knowledge model based on viewpoint and ontology notions. The multi-viewpoints knowledge model is used to formalize the multi-viewpoints ontology in description logics language.

Keywords: Description logic, knowledge engineering, ontology, viewpoint.

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Authors: Hong-fang Ma, Cong-yi He, Hai-tao Zhang, Wei-yong Ying, Ding-ye Fang

Abstract:

A Ni-based catalyst supported by γ-Al₂O₃ was prepared by impregnation method, and the catalyst was used in a low CO and CO₂ concentration methanation system. The effect of temperature, pressure and space velocity on the methanation reaction was investigated in an experimental fixed-bed reactor. The methanation reaction was operated at the conditions of 190-240°C, 3000-24000ml•g^-1•h^-1 and 1.5-3.5MPa. The results show that temperature and space velocity play important role on the reaction. With the increase of reaction temperature the CO and CO₂ conversion increase and the selectivity of CH₄ increase. And with the increase of the space velocity the conversion of CO and CO₂ and the selectivity of CH₄ decrease sharply.

Keywords: Coke oven gas, methanation, catalyst, fixed-bed.

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Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

Abstract:

This paper proposes a solution to the motion planning and control problem of a point-mass robot which is required to move safely to a designated target in a priori known workspace cluttered with fixed elliptical obstacles of arbitrary position and sizes. A tailored and unique algorithm for target convergence and obstacle avoidance is proposed that will work for any number of fixed obstacles. The control laws proposed in this paper also ensures that the equilibrium point of the given system is asymptotically stable. Computer simulations with the proposed technique and applications to a planar (RP) manipulator will be presented.

Keywords: Point-mass Robot, Asymptotic stability, Motionplanning, Planar Robot Arm.

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Authors: Mohd Agos Salim Nasir, Ahmad Izani Md. Ismail

Abstract:

Several numerical schemes utilizing central difference approximations have been developed to solve the Goursat problem. However, in a recent years compact discretization methods which leads to high-order finite difference schemes have been used since it is capable of achieving better accuracy as well as preserving certain features of the equation e.g. linearity. The basic idea of the new scheme is to find the compact approximations to the derivative terms by differentiating centrally the governing equations. Our primary interest is to study the performance of the new scheme when applied to two Goursat partial differential equations against the traditional finite difference scheme.

Keywords: Goursat problem, partial differential equation, finite difference scheme, compact finite difference

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Authors: Chuanyun Gu, Shouming Zhong

Abstract:

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

Keywords: Fractional differential equation, Boundary value problem, Positive solution, Existence and uniqueness, Fixed point theorem of a sum operator

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Authors: Thomas Kampke

Abstract:

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.

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Authors: Yongzhi Liao

Abstract:

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.

Keywords: positive almost periodic solution, Lotka-Volterra, neural networks, Banach fixed point theorem, harvesting

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Authors: H. D. Ibrahim, H. C. Chinwenyi, A. H. Usman

Abstract:

Valuing derivatives (options, futures, swaps, forwards, etc.) is one uneasy task in financial mathematics. The two ways this problem can be effectively resolved in finance is by the use of two methods (Martingales and Partial Differential Equations (PDEs)) to obtain their respective options price valuation formulas. This research paper examined two different stochastic financial models which are Constant Elasticity of Variance (CEV) model and Black-Karasinski term structure model. Assuming their respective option price valuation formulas, we proved the analogous of the Martingales and PDEs options price valuation formulas for the two different Stochastic Differential Equation (SDE) models. This was accomplished by using the applications of Girsanov theorem for defining an Equivalent Martingale Measure (EMM) and the Feynman-Kac theorem. The results obtained show the systematic proof for analogous of the two (Martingales and PDEs) options price valuation formulas beginning with the Martingales option price formula and arriving back at the Black-Scholes parabolic PDEs and vice versa.

Keywords: Option price valuation, Martingales, Partial Differential Equations, PDEs, Equivalent Martingale Measure, Girsanov Theorem, Feyman-Kac Theorem, European Put Option.

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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Authors: S. J. Shahidzadeh Tabatabaei, A. M. Fattahi

Abstract:

Modal analysis of a FGM plate containing the ceramic phase of Al₂O₃ and metal phase of stainless steel 304 was performed using ABAQUS, with the assumptions that the material has an elastic mechanical behavior and its Young modulus and density are varying in thickness direction. For this purpose, a subroutine was written in FOTRAN and linked with ABAQUS. First, a simulation was performed in accordance to other researcher’s model, and then after comparing the obtained results, the accuracy of the present study was verified. The obtained results for natural frequency and mode shapes indicate good performance of user-written subroutine as well as FEM model used in present study. After verification of obtained results, the effect of clamping condition and the material type (i.e. the parameter n) was investigated. In this respect, finite element analysis was carried out in fully clamped condition for different values of n. The results indicate that the natural frequency decreases with increase of n, since with increase of n, the amount of ceramic phase in FGM plate decreases, while the amount of metal phase increases, leading to decrease of the plate stiffness and hence, natural frequency, as the Young modulus of Al₂O₃ is equal to 380 GPa and the Young modulus of stainless steel 304 is equal to 207 GPa.

Keywords: FGM plates, Modal analysis, Natural frequency, Finite element method.

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