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In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials.

To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter.

Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes.

In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

The purpose of this study aims to analyze the dynamic behavior of the relationship between atmospheric carbon emissions and the Organisation for Economic Co-operation and Development (OECD) industrial production index (IPI) in the short and long term by applying multifractal techniques.

Multifractal de-trended cross-correlation technique is used for this analysis based on the relevant literature. In addition, it is the most widely used approach to estimate multifractality because it generates robust empirical results against non-stationarities in the time series.

It is revealed that industrial production causes long and short term environmental costs. The OECD IPI and atmospheric carbon emissions were found to have a strong correlation between the time domain. However, this relationship does not mostly take into account the frequency-based correlations with the tail effects caused by shocks that are effective on the economy. In this study, the long-term dependence of the relationship between the OECD IPI and atmospheric carbon emissions differs from the correlation obtained by linear methods, as the analysis is based on the frequency. The major finding is that the Hurst coefficient is in the range 0.40-0.75 indicating.

In this study, the local singular behavior of the time-series is analyzed to test for the multifractality characteristics of the series. In this context, the scaling exponents and the singularity spectrum are obtained to determine the origins of this multifractality. The multifractal time series are defined as the set of points with a given singularity exponent a where this exponent a is illustrated as a fractal with fractal dimension f(α). Therefore, the multifractality term indicates the existence of fluctuations, which are non-uniform and more importantly, their relative frequencies are also scale-dependent.

The results provide information based on the fluctuation in IPI, which determines the main conjuncture of the economy. An optimal strategy for shaping the consequences of climate change resulting from industrial production activities will not only need to be quite comprehensive and global in scale but also policies will need to be applicable to the national and local conditions of the given nation and adaptable to the needs of the country.

The results provide information for the analysis of the environmental cost of climate change depending on the magnitude of the impact on the total supply. In addition to environmental problems, climate change leads to economic problems, and hence, policy instruments are introduced to fight against the adverse effects of it.

This study may be of practical and technical importance in regional climate change forecasting, extreme carbon emission regulations and industrial production resource management in the world economy. Hence, the major contribution of this study is to introduce an approach to sustainability for the analysis of the environmental cost of growth in the supply side economy.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

This paper aims to test purchasing power parity (PPP) hypothesis for Greece, Italy, Ireland, Portugal and Spain, which are known as the GIIPS countries.

The authors conduct a comprehensive analysis by using unit root approaches without and with structural breaks and non-linearity.

The PPP is valid for the GIIPS countries. Considering structural breaks in non-linear framework plays a crucial role.

There is no empirical study testing PPP hypothesis by focusing on the GIIPS countries. This study further takes into account for structural breaks and non-linearity in the real exchange rates of these countries.

This paper conducts an empirical analysis for the estimations of volume-weighted price of the Korean stock market and provides the implications of the estimation errors regarding the characteristics of the market and the corresponding securities. We employ fast Fourier transformation strategy and traditional simple average strategy and compare the performances of the two methods using five minute interval intra-day data of KOSPI50 stocks. Estimations errors of the two methods from Ex Post real VWAP are computed and the relationships between the errors and other market variables are examined. We find that larger market value leads to smaller error whereas average trading in dollar has negative relationship with the estimation error. We also look at the behavior of institutional traders and the order execution mechanism to explain our statistical findings.

This study aims to examine the hysteresis hypothesis in unemployment using monthly data from 13 countries in transition.

Stationarity in the unemployment rate of selected transition economies was analyzed using four different group unit root tests, namely, linear, structural breaks, non-linear and structural breaks and non-linear.

The empirical results show that the unemployment hysteresis hypothesis is valid for the majority of transition economies, including Bulgaria, Croatia, the Czech Republic, Estonia, Hungary, the Kyrgyz Republic, Latvia, Lithuania, Poland, Romania and Slovenia. However, the results strongly reject the null hypothesis of unemployment hysteresis for the Kazakhstan and the Slovak Republics.

This study revealed that, for countries in transition, advanced unit root tests exhibit greater validity when compared to standard tests

We study an efficient numerical method for pricing European options when the dynamics of the underlying asset are described by Levy processes. In this case. we can write a characteristic function solution for a specific Levy option model and then take its inversion numerically. Specifically we use Variance Gamma process as an example of Levy option model and consider various characteristic function representation forms of European option price such as Carr and Madan (1999), Bakshi and Madan (2000). and Lewis (2001). Fast Fourier Transform method is applied to solve the numerical inversion problem with parameters for the KOSPI 200 options data. After analysing the problems in the FFT method, we propose alternative numerical inversion method, Gaussian Quadrature. This paper reports that Gaussian Quadrature numerical inversion method with the representation form of Bakshi & Madan (2000) is more efficient and accurate than other alternatives considered in this paper.

The purpose of the study is to obtain and analyze vibro-acoustic characteristics.

A unified analysis model for the rotary composite laminated plate and conical–cylindrical double cavities coupled system is established. The related parameters of the unified model are determined by isoparametric transformation. The modified Fourier series are applied to construct the admissible displacement function and the sound pressure tolerance function of the coupled systems. The energy functional of the structure domain and acoustic field domain is established, respectively, and the structure–acoustic coupling potential energy is introduced to obtain the energy functional. Rayleigh–Ritz method was used to solve the energy functional.

The displacement and sound pressure response of the coupled systems are acquired by introducing the internal point sound source excitation, and the influence of relevant parameters of the coupled systems is researched. Through research, it is found that the impedance wall can reduce the amplitude of the sound pressure response and suppress the resonance of the coupled systems. Besides, the composite laminated plate has a good noise reduction effect.

This study can provide the theoretical guidance for vibration and noise reduction.

The purpose of this paper is to examine a solution strategy for coupled nonlinear magnetic-thermal problems and apply it to the heating process of a thin moving steel sheet. Performing efficient numerical simulations of induction heating processes becomes ever more important because of faster production development cycles, where the quasi steady-state solution of the problem plays a pivotal role.

To avoid time-consuming transient simulations, the eddy current problem is transformed into frequency domain and a harmonic balancing scheme is used to take into account the nonlinear BH-curve. The thermal problem is solved in steady-state domain, which is carried out by including a convective term to model the stationary heat transport due to the sheet velocity.

The presented solution strategy is compared to a classical nonlinear transient reference solution of the eddy current problem and shows good convergence, even for a small number of considered harmonics.

Numerical simulations of induction heating processes are necessary to fully understand certain phenomena, e.g. local overheating of areas in thin structures. With the presented approach it is possible to perform large 3D simulations without excessive computational resources by exploiting certain properties of the multiharmonic solution of the eddy current problem. Together with the use of nonconforming interfaces, the overall computational complexity of the problem can be decreased significantly.

This study aims to investigate the effect of vibration on ceramic tools under dry cutting conditions and find the optimum cutting condition for the hardened steel machining process in a computer numerical control (CNC) lathe machine.

In this research, an integrated fuzzy TOPSIS-based Taguchi L9 optimization model has been applied for the multi-objective optimization (MOO) of the hard-turning responses. Additionally, the effect of vibration on the ceramic tool wear was investigated using Analysis of Variance (ANOVA) and Fast Fourier Transform (FFT).

The optimum cutting conditions for the multi-objective responses were obtained at 98 m/min cutting speed, 0.1 mm/rev feed rate and 0.2 mm depth of cut. According to the ANOVA of the input cutting parameters with respect to response variables, feed rate has the most significant impact (53.79%) on the control of response variables. From the vibration analysis, the feed rate, with a contribution of 34.74%, was shown to be the most significant process parameter influencing excessive vibration and consequent tool wear.

The MOO of response parameters at the optimum cutting parameter settings can significantly improve productivity in the dry turning of hardened steel and control over the input process parameters during machining.

Most studies on optimizing responses in dry hard-turning performed in CNC lathe machines are based on single-objective optimization. Additionally, the effect of vibration on the ceramic tool during MOO of hard-turning has not been studied yet.