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A new x-ray-spectrum-analysis program, which is capable of fitting with response functions including a tail function, an escape peak and sub-lines, has been developed. In this code, the tail function is expressed by combination of two or three Gaussian functions. A tail function, an escape and sub- or satellite-lines are regarded as functions belonging to the main peak and are included in it. A small shift of peak position depending on measuring conditions can be easily corrected in the program. As a result of fitting to practical spectra with the response function thus prepared, it becomes possible to draw a smooth background over a wide x-ray-energy range and to analyze a whole spectrum simultaneously. Thus, accuracy and reproducibility of a spectrum analysis are much improved. By means of this code, correct values of peak yield of Co-Kα, which overlaps with the tail of Fe-Kβ and is quite difficult to be accurately separated by fitting with Gaussians, have been obtained. Furthermore, accuracy of peak separation of a small peak, which overlaps with the escape peak belonging to a huge peak, has been improved. Accuracy of quantitative analysis for high-Z elements by means of Kβ yields has also been improved by using the response function including sub-lines, and it became possible to accurately separate small Kα lines from Kβ lines of the other elements.

For more detailed understanding of the line shape of X-ray peaks observed with Si(Li) detectors, a new Monte Carlo code was developed and tested in the range of incident X-ray energy less than 5 keV. In our simulation the individual elastic and inelastic processes in the solid and the charge collection probabilities in the different region of detectors are taken into account. The results of our model calculations are compared with experimental data. In general, good agreement is found between the experimental and calculated line shapes. This fact demonstrates the validity of the present model.

The Coulomb sum rule (CSR) and structure factor are calculated for inelastic electron scattering from nuclear matter at zero and finite temperature in the nonrelativistic limit. The effect of short-range correlation (SRC) is presented by using lowest order constrained variational (LOCV) method and the Argonne Av₁₈ and Δ-Reid soft-core potentials. The effects of different potentials as well as temperature are investigated. It is found that the nonrelativistic version of Bjorken scaling approximately sets in at the momentum transfer of about 1.1 to 1.2 GeV/c and the increase of temperature makes it to decrease. While different potentials do not significantly change CSR, the SRC improves the Coulomb sum rule and we get reasonably close results to both experimental data and others theoretical predictions.

Building on an analogy with conformal invariance, local scale transformations consistent with dynamical scaling are constructed. Two types of local scale invariance are found which act as dynamical space–time symmetries of certain nonlocal free field theories. The scaling form of two-point functions is completely fixed by the requirement of local scale invariance. These predictions are confirmed through tests in the 3D ANNNI model at its Lifshitz point and in ageing phenomena of simple ferromagnets, here studied through the kinetic Ising model with Glauber dynamics.

A condition for ergodicity is derived, applicable to a Hermitian many body model in both the classical and quantum domains. Using this ergodic condition, the validity of the ergodic hypothesis is examined in certain solvable 1d magnetic models. A simple but general picture has emerged which shows why the hypothesis can be valid and why it can also fail.

In this paper, we investigate the dynamical evolution and the decoherence of a single flux qubit due to its coupling with the external environment bath. We consider two typical baths: boson bath and spin bath. It is shown that, at low but finite temperature, if the two typical baths have smooth and continuous spectrum, the dynamics of the system is in general non-Markovian though of finite memory time. Most important of all, affected by the external environment bath, the flux qubit exhibits resonance of the coherence of the qubit. Comparing with the spin bath, the boson bath's destruction of the coherence is more serious.

In this paper, we calculate a self-contained theoretical analysis of the dynamical response of the electron system in the fractional dimensional space within the random phase approximation. We find the static response function in several integer and non-integer dimensions. The plasma frequencies except in the quasi-one-dimensional system are damped into particle–hole excitation. In the long-wavelength limit the plasma frequency is finite at zero wave vector in three-dimensional system while these vanish at the same wave vector in the lower-dimensional systems.

In this paper, the one- and two-parameter bifurcations of a discrete-time prey–predator model with a mixed functional response are investigated by computing their critical normal form coefficients. The flip, Neimark–Sacker and strong resonance bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. The complex dynamical behavior of the model up to the 16th iteration is investigated.

The ambiguities proposed by Benhar et al., about the the different implementation of the impulse approximation for calculating the response function of many-fermion systems, are investigated theoretically in the frame work of simple harmonic oscillator shell model for the double closed shell nuclei, e.g. ⁴He, ¹⁶O and ⁴⁰Ca nuclei. For each nucleus as a finite system, we evaluate the response function by using its definition in terms of the one-body spectral function and the one-body momentum distribution. It is demonstrated analytically, that there exists a sizable shift between the two schemes for each nucleus, which increases as we switch to the heavier nuclei. So one can conclude that for the nuclei with atomic number less than 4, such as ²H, ³H or ³He, it is good approximation to ignore this discrepancy. This conclusion is important for theoretical explanation of the ongoing deep inelastic scattering (DIS) experiments of ³H or ³H in the Jefferson Laboratory. However present calculation confirms the work of Modarres and Younesizadeh (2010), in which they have shown that, the above shift can be removed by imposing the impulse approximation in the same footing in the many-fermion wave-function.

In this work, we study the differential scattering cross-section (DSCS) in the first-order Born approximation. It is not difficult to show that the DSCS can be simplified in terms of the system response function. Also, the system response function has this property to be written in terms of the spectral function and the momentum distribution function in the impulse approximation (IA) scheme. Therefore, the DSCS in the IA scheme can be formulated in terms of the spectral function and the momentum distribution function. On the other hand, the DSCS for an electron off the ${}^4\mathrm{\text{He}}$ and ${}^{16}\mathrm{\text{O}}$ nuclei is calculated in the harmonic oscillator shell model. The obtained results are compared with the experimental data, too. The most important result derived from this study is that the calculated DSCS in terms of the spectral function has a high agreement with the experimental data at the low-energy transfer, while the obtained DSCS in terms of the momentum distribution function does not. Therefore, we conclude that the response of a many-fermion system to a probe particle in IA must be written in terms of the spectral function for getting accurate theoretical results in the field of collision. This is another important result of our study.

The fuzzy systems based on the universal triple I method are investigated, and then their response functions are analyzed. First, the conclusions show that 100 fuzzy systems via the universal triple I method are approximately interpolation functions, which can be used in practical systems, and that 90 ones are approximately fitted functions, which may be usable. Second, as its special cases, the Compositional Rule of Inference (CRI) method and the triple I method are discussed, with the results that 19 fuzzy systems via the CRI method and 2 ones via the triple I method are practicable. Therefore, the universal triple I method has larger effective choosing space, which can obtain more usable fuzzy systems than the others. Lastly, it is found that the first implication and second implication, respectively, embody the function of rule base and reasoning mechanism, further demonstrating the reasonability of the universal triple I method.

A condition for ergodicity is derived, applicable to a Hermitian many body model in both the classical and quantum domains. Using this ergodic condition, the validity of the ergodic hypothesis is examined in certain solvable 1d magnetic models. A simple but general picture has emerged which shows why the hypothesis can be valid and why it can also fail.

We compute, from first principles, the dielectric function and electron energy loss spectrum (EELS) of an oxidized Si(100)(2×2) surface. The surface local field effect is found to be important for the calculation of EELS in a reflection geometry. Theoretical problems that arise when local fields are included within the periodic supercell approach are discussed in detail.