On invexity-type nonlinear programming problems

In this paper, we propose a new class of nonlinear programing, called SFJ-invex programming. The optimality characterization shows that a problem is SFJ-invex if and only if a Fritz John point together with its multiplier, is a Fritz John saddle point of the problem. Under any constraint qualification assumption, a problem is SFJ-invex if and only if a Kuhn-Tucker point together with its multiplier is a Kuhn-Tucker saddle point of the problem. Furthermore, a generalization of the SFJ-invex, class is developed; the applications to (h, )-convex programming, particularly geometric programming, and to generalized fractional programming provide a relaxation in constraint qualification for differentiable problems to get saddle-point type optimality criteria.The author wishes to thank the referee for helpful comments.     

Randomly transitional phenomena in the system governed by Duffing's equation

This paper deals with turbulent or chaotic phenomena which occur in the system governed by Duffing's equation, a special type of two-dimensional periodic system. By using analog and digital computers, experiments are carried out with special reference to the change of attractors and of average power spectra of the random processes under the variation of the system parameters. On the basis of the experimental results, an outline of the random process is made clear. The results obtained in this paper will be applied to various physical problems and will also serve as material for the development of a proper mathematics of this phenomenon.     

Investigation of proton channeling using nuclear-reaction resonances

To investigate orientation effects, an approach based on the measurements of γ-ray yields following the excitation of “narrow" isolated resonances in the reactions occurring on the nuclei of interstitial impurity atoms, that occupy certain positions in a crystal, has been proposed. The carbon atoms were shown to be located in octahedral interstitial sites of the Re-0.4 at. % ¹³C monocrystalline solution. The proton flux distribution in the (0001) channel was investigated via the 1.7476 MeV resonance of the ¹³C(p,γ)¹⁴N reaction. Some particular qualities of the reaction yield were found to be dependent upon the proton energy. The method of measurement of the electronic stopping power of channeled particles has been deduced. The γ-ray yield of the resonance reactions induced by the channeled protons was shown to be dependent on the amplitude of the thermal vibrations of carbon atoms.     

The optical properties of HgS under high pressures

The DOS (density of states) and the optical properties of HgS under high pressure are studied with the first-principle computations. The change of the imaginary part, ε₂(ω), of the dielectric function shows that HgS tends to metallization with increasing pressure, and this well agrees with the band gap calculations and the conductivities measurement results in the previous work. Under the pressures below 15 GPa, ε₂(ω) is relatively anisotropic and tends to be more anisotropic with increasing pressure; while under the pressures above 15 GPa, the anisotropy decreases and finally becomes almost absolutely isotropic after the phase transition. The behavior of ε₂(ω) is strongly related to the structure change in the cinnabar to rocksalt phase transition process under high pressure.     

Ab initio calculations of elastic constants and thermodynamic properties of Li2O for high temperatures and pressures

The elastic constants and thermodynamic properties of Li₂O for high temperatures and pressures are calculated by the ab initio unrestricted Hartree-Fock (HF) linear combination of atomic orbital (LCAO) periodic approach. The lattice constant, elastic constants, Debye temperature, and thermal expansion coefficient obtained are in good agreement with the available experimental data and other theoretical results. It is found that at zero pressure the elastic constants C₁₁, C₁₂ and C₄₄, bulk modulus B and Debye temperature Θ_D decrease monotonically over the wide range of temperatures from 0 to 1100 K. When the temperature , C₁₂ approaches zero, consistently with the transition temperature 1200 K. However, with increasing pressure, they all increase monotonically and the anisotropy will weaken.     

A novel BEDT-TTF-based purely organic magnetic conductor, α - (BEDT - TTF)2(TEMPO - N(CH3)COCH2SO3) ⋅ 3H2O

A new BEDT-TTF-based salt with an organic free radical TEMPO has been prepared. The salt consists of alternate layers of conducting and magnetic sheets, between which are short S(BEDT-TTF) …O(TEMPO) contacts. The magnetic susceptibility is well modelled by the combination of a 2D Heisenberg and a Curie-Weiss model with and .     

Renormalization group dependence of the QCD coupling

The general relation between the standard expansion coefficients and the beta function for the QCD coupling is exactly derived in a mathematically strict way. It is accordingly found that an infinite number of logarithmic terms are lost in the standard expansion with a finite order, and these lost terms can be given in a closed form. Numerical calculations, by a new matching-invariant coupling with the corresponding beta function to four-loop level, show that the new expansion converges much faster.     

Analytical characterization of spectral anomalies in polychromatic apertured beams

The power spectrum of polychromatic apertured spherical waves changes strongly in the vicinity of phase singularities. A spectral shift effect is observed and, in some cases, a spectral switch occurs together with a broadening of the power spectrum. Low-order moments of the power spectrum are evaluated in points of the focal volume with spectral anomalies. First-order analytical expressions are proposed for the evaluation of the relative spectral shift and the relative spectral broadening in the transverse focal plane and along the optical axis. The influence of the fractional bandwidth and the selected singularity order is considered.     

Comparison of polarization-mode dispersion tolerances in polarization-multiplexing systems with different modulation formats

The polarization-mode dispersion (PMD) tolerance of 10 Gb/s polarization-multiplexing (PM) system is investigated. Using the importance sampling (IS) method, the outage probabilities of the PM systems with three modulation formats, including on-off keying (OOK), differential phase-shift keying (DPSK) and differential quadrature phase-shift keying (DQPSK), are quantified. When the amplified spontaneous emission (ASE) noise is assumed to be dominant, we evaluate the optical power penalties caused by the PMD effect at bit error rate (BER) of 10⁻¹². The performance of compensated PM systems with variable optical delay line is also described. The simulation results indicate that the OOK signal with higher duty cycle (DC) performs better in the PM systems with PMD compensation. It is found that the higher-order PMD impairs seriously the performance of the PM system, and phase-keying formats are more sensitive to the PMD than the OOK.     

Non-Markovian thermalisation of a two-level atom

We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima-Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.