Adomian decomposition method and Padé approximants for solving the Blaszak--Marciniak lattice

The Adomian decomposition method （ADM） and Pade approximants are combined to solve the well-known Blaszak-Marciniak lattice, which has rich mathematical structures and many important applications in physics and mathematics. In some cases, the truncated series solution of ADM is adequate only in a small region when the exact solution is not reached. To overcome the drawback, the Pade approximants, which have the advantage in turning the polynomials approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. By using the ADM-Pade technique, the soliton solutions of the Blaszak-Marciniak lattice are constructed with better accuracy and better convergence than by using the ADM alone. Numerical and figurative illustrations show that it is a promising tool for solving nonlinear problems.     

Efficient beam-propagation method based on Padé approximants in the propagation direction

We propose a novel beam-propagation method (BPM) based on the higher-order Padé approximants in both the transverse and the longitudinal directions. Extending the Padé approximation to the propagation direction and adopting the multistep method increase the programming effort by only a small amount. Compared with the conventional BPM's, this method is more accurate and efficient. The accuracy and the propagation step size are well predicted by a phase analysis.     

First-principles study of elastic and slip properties of non-canonical β-based Al–Cu–Fe approximants

Ab initio calculations were carried out to compare the mechanical properties of β-based non-canonical Al–Cu–Fe approximants of quasicrystals with cubic (β), monoclinic (η) and orthorhombic (ξ1, ξ2) structures, which all demonstrate high strengthening. The aim was to elucidate the competitive effects of the η- and ξ-ordering and iron content on deformation behaviour of these phases. We found that the Young’s modulus, polycrystalline shear modulus, mechanical stability and shear elastic modulus G(n,m) for different slip planes decrease for β-Al₅₀Cu_1-xFe_x with lowering iron content, but they grow from β-Al₅₀Cu_31.25Fe_18.75 to the ordered η-Al₅₀Cu₄₅Fe₅, and ξ2-Al_45.5Cu₅₀Fe_4.5 that indicates a growing resistance to plastic deformation due to ordering and agrees well with our experimental finding. The preferable slip systems were predicted based on the calculated generalised stacking fault (GSF) energies in β-(Cu,Fe)Al and η-(Cu,Fe)Al with similar Fe concentration. The GSF energies confirmed also that the strengthening observed in η-phase is related to ordering rather than the Fe effect in consistence with a stronger covalent bonding in η-phase.     

Investigation of the Spectral Line Intensities of the ν9 Band of the Trans-Conformer of Ethylene

Russian Physics Journal - The intensities of 740 vibrational-rotational lines of the ν9 fundamental band in the IR spectrum of the trans-C2H2D2 molecule are first analyzed. The...     

On the interpretation of the results of the experimental test of the Askar’yan effect

The effect of the environment on the results of measuring the radio radiation spectrum is considered in the experimental simulation of the cascade shower by a high-energy γ-ray beam in a dense medium. The calculation shows that the character of the measured energy spectrum depends on the location of the receiving antenna with respect to the shower axis.     

Description of the evolution of the state of “josephson atoms” in the context of the informational interpretation of quantum mechanics

The evolution of a quantum system is informationally interpreted and used to describe decay in the coherent states of Josephson atoms, including qubits based on two- and three-junction superconducting quantum interferometers. The reduced Lindblad equation is employed to examine the measurement procedure of the Josephson qubit state and the influence of a measuring device on its coherent-state decay.     

A comparison of the reproducibility of the parameters of the ¹³C-aminopyrine breath test for the assessment of hepatic function

This study determined the within-subject and between-subject variability of different ways of expressing the results of the (13)C-aminopyrine breath test ((13)C-ABT) and the effect of shortening the test duration. The (13)C-ABT was conducted on three separate occasions in 10 healthy volunteers and on a single occasion in 22 patients with established liver cirrhosis. The within-subject variability of cumulative percentage dose recovered (cPDR), using measured CO(2) production rate (VCO(2)), in the reference group over three trials was 15% over 120 min. Higher within-subject variability in cPDR would have been evident if the test was terminated at either 30 or 60 min. Substitution of predicted VCO(2) to calculate cPDR yielded comparable values at all time points. Significant differences between cirrhotics and reference group were evident after just 10 min using PDR/h, cPDR or enrichment (all P<0.05). The ABT demonstrates clinically acceptable reproducibility. Shortening of the duration may make the test more acceptable clinically, but it is associated with increasing imprecision.     

Calculation of the phase diagram of the TiZr alloy and investigation of the tendency toward separation of the ω phase

The electronic, structural, and thermodynamic properties of the TiZr equiatomic alloy have been calculated in terms of the electron density functional theory and Debye-Grüneisen model. The calculated lattice parameters a and c/a agree well with experimental data for the α, ω, and β phases. It has been shown that the ω phase is stable at atmospheric pressure and low temperatures, and it remains energetically more favorable up to T = 600 K. In the temperature range 600 K < T < 900 K, the α phase becomes stable, and above 900 K, the β phase of the TiZr alloy is stable. The phase diagram constructed in this study agrees qualitatively with the available experimental data. A tendency toward separation of the TiZr equiatomic alloy in the ω phase has been analyzed. It has been demonstrated that, in the ground state, the TiZr equiatomic alloy in the ω phase exhibits a tendency toward ordering rather than toward phase separation.     

Some tree-like Julia sets and Padé approximants

The Julia set B for T(z)=(z–)², the equilibrium electrostatic measure on B, the associated orthogonal polynomials, P _n, and the Padé approximants to the moment-generating function for are considered. When 02, the locations of the zeros and poles for the Padé approximant sequence (z), n=0, 1, 2, ..., are described precisely as vertices of trees of analytic arcs associated with B. For infinitely-many values of B is the closure of these trees. P ₂ ⁿ is shown to be a Chebychev polynomial on B for positive, attaining its maximum modulus at 2 ⁿ⁺¹ points of B if 2.Supported by NSF Grant MCS-8104862Supported by NSF Grant MCS-80002731     

Evaluation of the Intensities of Spectral Lines under the Influence of Interferences and the Determination of Global Maxima of the Mass–Spectrum Peaks

We describe the technique by which the intensity of spectral lines can be evaluated and the global maxima of the mass–spectrum peaks under the influence of pulse interferences can be defined using an experimental setup based on a commercial MX–7304A mass spectrometer, IBM personal computer (PC), and a digital extremum regulator that allows one to ignore local extrema and bring about automatic search for a global maximum of the mass–spectrum peak and its tracking with an accuracy of 0.0012% at a speed of response of 50 kHz, elevated speeds of the scanning of masses 500 amu/sec, and stability of regulation.     

Analysis of the Structure of Thin Films of Zn‐Porphyrins by the Kinetics of the Fluorescence Anisotropy

The structure of thin films of Zntetraoctylphenylporphyrin (ZnTOPP) obtained by the spinning method is investigated. The kinetics of the decay of the fluorescence anisotropy of the films is analyzed in the form of a sum of exponents and by simulating the orientation of ZnTOPP complexes on the substrate (quartz) surface with allowance for the processes of the electron excitation energy transfer. The ZnTOPP films have a lamellar structure where individual layers form ordered domains. Within a domain, linear nonintersecting stacks of molecules are formed. In each stack the planes of the molecules are collinear, oriented perpendicularly to the surface of the substrate base, and form an angle of 45° with the directing axis of a stack.     

Analysis of the Structure of the Bands in the IR Spectrum of β-D Glucose by the Regularized Method of Deconvolution

Deconvolution of the IR absorption spectrum of -D glucose in the spectral range 1500–450 cm^–1 has been carried out. The results of the deconvolution were compared with the IR and Raman spectra recorded at room and low temperatures and with the data obtained by theoretical calculations for the frequencies of the normal vibrations of the -D glucose molecule in the crystalline state. It is shown that deconvolution of the IR spectra recorded at room temperature makes it possible to separate the bands observed experimentally only at a very low temperature of the sample and a number of components that were not resolved earlier. The number of bands separated on deconvolution of the IR spectra of -D glucose in the spectral range 1500–450 cm^–1 is more than twice the number of visible absorption maxima in the usual spectrum. The results of deconvolution of the IR spectrum of -D glucose are in good agreement with the data of theoretical calculations for the frequencies of the normal vibrations of the -D glucose molecule in the crystalline state. The existence of the factor-group (Davydov) splitting of a number of frequencies of the nondegenerate fundamental vibrations of molecules in a crystal cell has been revealed in the IR spectrum of -D glucose. It was concluded that the model of an isolated molecule is insufficient for detailed theoretical interpretation of the vibrational spectra of carbohydrates.     

Measurement of the integrated luminosity of the Phase 2 data of the Belle Ⅱ experiment

From April to July 2018,a data sample at the peak energy of the T(4 S) resonance was collected with the Belle Ⅱ detector at the SuperKEKB electron-positron collider.This is the first data sample of the Belle Ⅱ experiment.Using Bhabha and digamma events,we measure the integrated luminosity of the data sample to be(496.3±0.3±3.0) pb~(-1),where the first uncertainty is statistical and the second is systematic.This work provides a basis for future luminosity measurements at Belle Ⅱ.     

The Structure of the Algebra of Observables in the Intermediate Situation of the ∈-Model

We look at the action of the spin-1/2 operatorsof quantum mechanics on the state of an entity in aphysical way, and use this as a guideline to define theoperators of the intermediate situations of a general spin-1/2 measurement model called the-model. Then we test the possible linearity ofthe operators so constructed.     

Optimization of the Loading Process of the QUIC Magnetic Trap for the Experiment of Bose-Einstein Condensation

The magnetic quadrupole-Ioffe configuration (QUIC) trap in our Bose-Einstein condensation experiment is introduced. The magnetic trap loading process after laser cooling is ana/ysed and the optimization of the loading process is studied experimentally, Calculation of the magnetic field explains the loss of the atoms during the loading process of the QUIC trap. The number of atoms loaded in the QUIC trap is increased by 40% after optimization in comparison with the normal loading process.     

The Effect of the Relative Motion of Atoms on the Frequency of the Emitted Light and the Reinterpretation of the Ives-Stilwell Experiment

We examine the process of the emission of light from an atom that is in a relative translational motion with respect to the medium at rest in which the electromagnetic excitations propagate. The effect of Lorentz contraction of the of electron orbits on the emitted frequency is incorporated in the Rydberg formula, as well as the emitter’s Doppler effect is acknowledged. The result is that the frequency of the emitted light is modified by a factor that is identical with what is called the ‘relativistic Doppler effect’. The new emission formula is applied for reinterpretation of the Ives-Stilwell experiment and shown that within the second order of approximation with respect to the speeds of the atom and the ‘absolute speed’ (Earth’s speed relative to the medium), the absolute motion does not affect the interference. The expression for the modification of the frequency involves both a first and a second-order term with respect to the speed of the atoms in the cathode tube. The latter turns out to be quantitatively the same as if the time would have changed its rate in the frame moving with the atoms. Thus, a new interpretation of the results of this famous experiment is provided without stipulating time dilation.     

Development of the Model of the Generalized Quintom Dark Energy

We consider a generalized quintom （GQ） dark energy model for changing the equal weight of the negative-kinetic scalar field （phantom） and the normal scalar field （quintessence） in quintom dark energy. Though the phantomdominated scaling solution is a stable late-time attractor, the early evolution of GQ is different from that of the quintom model and the adjustability of the dark energy state equation in the model is improved.     

Measurement of the strong-interaction shift and broadening of the ground state of the pp̄ atom

The K_α X-rays from pp̄ atoms formed in H₂ gas at normal temperature and pressure are unambiguously identified by coincidences with L X-rays populating the 2P level. Background due to inner bremsstrahlung is suppressed by selecting events annihilating into neutral final states only. The K_α line is observed with a significance of more than 25 standard deviations at an energy of 8.67 (15) keV. From fits to the K_α line we obtain a strong-interaction shift and width of the 1S level, averaged over the unresolved spin singlet and triplet contributions, of ΔE + iΓ/2 = [−0.70(15) + i0.80(20)] keV.     

Measurement of the leptonic branching ratios of the τ lepton

The leptonic branching ratios of the tau lepton have been determined from data collected by the OPAL detector in 1991 and 1992. From a sample of 27196 e⁺e^–+– candidates we find 7322 and 7941 candidates. Using efficiency and background estimates determined from a study of Monte Carlo events and control samples of data, the branching ratios =(18.14±0.20±0.28)% and =(17.48±0.18±0.23)% have been obtained. These new results have been combined with the published results for the 1990 OPAL data to yield the following branching ratios for data taken between 1990 and 1992: