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"ABSTRAKA complete system of Maxwell equations is splitting into independent subsystems by means of a special dynamic projecting technique. The technique relies upon a direct link between field components that determine correspondent subspaces. The explicit form of links and corresponding subspace evolution equations are obtained inconditions of certain symmetry, it is illustrated by examples of spherical and quasi one dimensional waves. "

"Dalam disertasi ini telah dilakukan penelitian tentang keterlibatan volume pada harga penutupan dihari transaksi. Hal ini dilakukan dalam upaya untuk mendapatkan indikator harga saham yang lebih baik. Hukum distribusi dan probabilitas statistik Maxwel-Boltzmann digunakan untuk menganalisis harga saham beserta perubahan persentasi harga pada pasar modal Bursa Efek Indonesia. Besaran volume dan harga digunakan sebagai variabelvariabelnya. Banyak trader tidak menghiraukan akan nilai besaran volume ini, namun sebenarnya disanalah banyak terkandung sejumlah informasi penting. Oleh karena analisis ini dapat digunakan untuk memprediksi harga dinamik saham di Bursa Efek Indonesia, baik dalam keadaan harga saham bulish atau bearish, naik maupun turun, juga persentasi perubahan harganya, maka diperoleh 1. Bahwa perbandingan antara indikator Statistik MaxwellBoltzmann terhadap indikator Stokastik Osilator George Lane dan lain-lainnya, diperoleh Maxwell-Boltzmann 69 benar, Stockastic Ocscillator 40.55 benar, 10 Simple dan 10 Exponential Moving Average 10 SMA- 10 EMA 43.55 yang benar, Relative Strengt Indexs RSI 46,67 , R William 45 benar, MACD 40,33 dan OBV 41,44 . 2. Pada sisi lain, dengan menggunakan rumus probabilitas Maxwell-Boltzmann, untuk memperkirakan perubahan harga, diperoleh minimum perubahan harga 0 to 3.59 persen deviasi minimum , and deviasi maksimumnya berada diantara 0 to 4,67 persen.

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In this disertaion, we rsquo;ve investigated the involvement of closing volumes on closing prices as additional variables in order to achieve the better trend lines indicator. The MaxwellBoltzmann distribution physical statistic law and its probabilistic formula were utilized to analyze the dynamic trend lines and deviation percentage of price changes, where prices and volumes were used as variables indeed. Many traders ignore volumes; however, there is a huge number of information in it, particularly in volume of closing prices. This Maxwell-Boltzmann distribution law could be manipulated to predict shares dynamic trend lines in Indonesian Stock Exchange Idx market. Since these analysis could be utilized to predict the dynamic trend lines on bullish or bearish market, and percentage of price changes, than; 1. We are going to have the comparison of the dynamic trend line changes uptrend or down trend by utilizing MaxwellBoltzmann distribution law, and compare them to the George Lane stochastic oscillator formula. The result of the comparison percentage was Maxwell-Boltzmann for 69 right, Stochastic Oscillator 40.55 , 10 Simple and 10 Exponential Moving Average 10 SMA- 10 EMA for 43.55 , Relative Strength Index rsquo;s RSI 46,67 , R William for 45 right, MACD 40.33 right and OBV 41.44 2. On the other hand, the development of the MB probability formula, in term for predicting percentage of price changes, data rsquo;s given that minimum price changes around 0 to 3.59 percent minimum deviation , and maximum deviation around 0 to 4,67 percent in Indonesian Stock Exchanges Idx market."

"ABSTRAKIn this paper a new way of derivation of an evolution equation for short pulses in a dielectric waveguide including one model of a metamaterial waveguide is shown. This derivation model relies upon projecting to an orthogonal basis. In our case such orthogonal basis for cylindrical waveguides is chosen as Bessel functions. "

"ABSTRAKWe consider a generalization of the projection operator method for the case of the Cauchy problem in 1D space for systems of evolution differential equations of first order with variable coefficients. It is supposed that the dependence of coefficients on the only variable𝑥is weak, that is described by the introduction of a small parameter. Such problem corresponds, for example, to the case of wave propagation in a weakly inhomogeneous medium. As an example, we specify the problem to adiabatic acoustics in waveguides with a variable cross section. Projection operators are constructed for the Cauchy problem to fix unidirectional modes. The method of successive approximations perturbation theory is developed and based on the pseudodifferential operators theory. The application of projection operators adapted for the case under consideration allows deriving approximate evolution equations corresponding to the separated directed waves."

"Self-adjoint extensions in quantum mechanics begins by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes of the naïve treatment. The necessary mathematical background is then built by developing the theory of self-adjoint extensions. Through examination of various quantum-mechanical systems, the authors show how quantization problems associated with the correct definition of observables and their spectral analysis can be treated consistently for comparatively simple quantum-mechanical systems. Systems that are examined include free particles on an interval, particles in a number of potential fields including delta-like potentials, the one-dimensional Calogero problem, the Aharonov–Bohm problem, and the relativistic Coulomb problem."