Solubility Property of Baganuur Coal: Performance Assessment by FTIR Spectroscopic Analysis

In the present work, the extraction of Mongolian Baganuur coal in solvents as pyridine and ionic liquid with 1-butyl-3-methyl-imidazolium chloride ([Bmim]Cl) anion was first applied. The as recieved coal, its extracts and insoluble residues were then characterized using the Fourier transform infrared (FTIR) spectroscopy. The obtained FTIR spectra have revealed many new features in the field of coal study. An appearance or sharpening of the particular bands after the chemical treatment allow a determination of inactive or weak fundamental vibrations precisely. Some emphasis are as follows, substantial quantitative change, the integrated area decrease of water molecule band at 3260 cm−1 comparing to as received sample and ionic liquid treated extract, can be seen for the extract spectrum in the pyridine treatment. Pyridine react to coal structure particularly in long-wave frequency zone means very susceptible to the oxygen containing functional group. Upon interaction between acidic group of the coal and the basic solvent as pyridine, the inter-fragment hydrogen and ester bonding in the coal structure is breaking, thus increasing the solubility of the individual fragments via producing new components. Towards forming H bond in the short wave zone Cl− anion shows a strong effect on the coal molec-ular structure. A stabilization of hydrogen bonds show well fluidization and a strong intermolecular interaction of the process via its powerful spectral intensity that is followed many new bands and con-siderable strengthening of band spectral integral area in this frequency region. In long-wave vibrational region there are appearances of many new bands, shift in frequency and depletion of the as recieved coal bands. [Bmim]Cl treatment exhibits the highest effect of the disruption on the carboxylic acids dimer.

Fractional spectral integral methods for valuing cryptocurrency asset flow fractional differential equations.

Since its inception in 2009, the cryptocurrency market has grown considerably. Several authors have proposed models to explain the price movements of assets in this new emerging market. However, only few researches have been done using the dynamical approach. This paper proposes a robust time fractional spectral method for studying a three dimensional fractional differential equation that models cryptocurrency asset flow obtained by utilizing the concept of liquidity price. The method relies on fractional spectral integration matrix operator approach. Numerical simulations are conducted to show efficiency of the numerical method on the fractional cryptocurrency model compared to existing methods.

Fractional spectral integral methods for valuing cryptocurrency asset flow fractional differential equations.

Since its inception in 2009, the cryptocurrency market has grown considerably. Several authors have proposed models to explain the price movements of assets in this new emerging market. However, only few researches have been done using the dynamical approach. This paper proposes a robust time fractional spectral method for studying a three dimensional fractional differential equation that models cryptocurrency asset flow obtained by utilizing the concept of liquidity price. The method relies on fractional spectral integration matrix operator approach. Numerical simulations are conducted to show efficiency of the numerical method on the fractional cryptocurrency model compared to existing methods.

Regge amplitudes in generalized fishnet and chiral fishnet theories

We extend the analysis of [1] to study the Regge trajectories of the Mellin amplitudes of the 0- and 1-magnon correlators of the generalized Fishnet theory in d dimensions and one type of correlators of chiral fishnet theory in 4 dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our d dimensional results reduce to previously known results in d = 4 for 0-magnon and 1-magnon. As a non-trivial check, we show that the results for 1-magnon correlator in d = 8, when evaluated using the exact techniques in [1, 2] are in perfect agreement with our d dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator $$ \left\langle \mathrm{Tr}\left[{\phi}_1\left({x}_1\right){\phi}_1\left({x}_2\right)\right]\mathrm{Tr}\left[{\phi}_1^{\dagger}\left({x}_3\right){\phi}_1^{\dagger}\left({x}_4\right)\right]\right\rangle $$ Tr ϕ 1 x 1 ϕ 1 x 2 Tr ϕ 1 † x 3 ϕ 1 † x 4 using the techniques developed in this paper. Since this correlator has two couplings κ and ω, we have obtained closed-form results in the limit κ → 0, ω → 0 with κ/ω held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement.

On the Calculation of 2D Green's Functions Via Sommerfeld Integrals and the Spatial Singularity Method

<p>We provide a low-level review of the computation of Sommerfeld integration theory using the singularity expansion method (SEM) to analytically estimate the short-wavelength components of the 2-dimensional Green's function. The SEM is employed to replace the infinite tail of the spectral integral by a closed-form evaluation. The various steps in the SEM substitution and the calculations are elaborately presented and discussed with emphasis on giving the missing details often not included in the published literature.<b></b></p>