Photoionization Study of the 2s^(2)2p^(2)(^(1)D)ns(^(2)D),2s^(2)2p^(2)(^(1)D)nd(^(2)P),2s^(2)2p^(2)(^(1)D)nd(^(2)S),2s^(2)2p^(2)(^(1)S)nd^(2)D,and 2s^(2)2p^(3)(^(3)P)np(^(2)D)Rydberg Series of O+Ions via the Modified Atomic Orbital Theory

We report in this paper energy positions of the 2P˚_2s^(2)2p^(2)(^(1)D)nd 2P,2P˚_2s^(2)2p^(2)(^(1)D)nd 2S,2P˚_2s^(2)2p^(2)(^(1)D)ns^(2)D,2P˚_2s^(2)2p^(2)(^(1)S)nd ^(2)D,and 2P˚_2s^(2)2p^(3)(^(3)P)np ^(2)D Rydberg series in the photoionization spectra originating from 2P˚metastable state of O+ions.Calculations are performed up to n=30 using the Modified Orbital Atomic Theory(MAOT).The present results are compared to the experimental data of Aguilar which are the only available values.The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies.

OLD AND RECENT RESULTS IN THE ANALYTIC THEORY OF DIRICHLET SERIES:A SURVEY

This survey is dedicated to the memory of Professor Jiarong Yu,who recently passed away.It is concerned by a topic of which he was fond,an interest shared by myself:the analytic theory of Dirichlet series.

Modified atomic orbital theory applied to the calculation of high-lying ₂(K,T)_n^±1,3P°rydberg series of he-like ions

The 2(1,0)n-1P°, 2(1,0)n +3P°, 2(0,1)n+1P°, and 2(0,1)n-3P° intershell Rydberg series of the helium-like ions are investigated in the framework of the modified Atomic Orbital Theory (MAOT). High-lying energy resonances of He and excitation energy of the he- lium-like Li+ up to n = 10 are tabulated. In addition, total energy positions for low-lying states (n1,3P° autoionizing states of two-electron systems.

General Theory of Antithetic Time Series

A generalized antithetic time series theory for exponentially derived antithetic random variables is developed. The correlation function between a generalized gamma distributed random variable and its pth exponent is derived. We prove that the correlation approaches minus one as the exponent approaches zero from the left and the shape parameter approaches infinity.

Cognitive Translation of Paintings of Lijiang Painting School Under the Guidance of Rewriting Theory

It is an important task to communicate Chinese culture with other countries in the more conflicting global world.Lijiang Painting School plays a very important part in Chinese art,and it greatly influences the painters of various periods in China.In this context,some representative paintings of Lijiang Painting School in different periods were collected in this paper as the research objects.The rewriting theory was applied in the study because Chinese readers and English readers have different cultural backgrounds and diverse thinking.Based on the rewriting theory,these representative paintings were translated and the explained in English.In the study,it is found that as an intersemiotic translation,the translation of the representative paintings of Lijiang Painting School should be focused on those target readers who can’t comprehend directly from the paintings.In addition,the artistic integrity should be considered first before details in paintings.Therefore,the overall perception of target readers gaining from the translations should be paid more attention to rather than metaphrase.The translation under the guidance of rewriting theory will be helpful for the target readers to understand the connotation of source culture with some cultural images of target readers.

Analysis on the Homogeneities between Traditional Chinese Music and Painting Arts from Qichang Dong＇s ＂Theory of Southern and Northern Schools＂

Qichang Dong was a famous calligraphy and painting artist in ancient China. The theory of southern and northern schools proposed by him was a conclusion to traditional Chinese landscape painting art, and played an incomparable function in the traditional Chinese painting history in comparison with other painting theories. In the painting history, there were the theory of ＂pre-Dong＂ and the theory of ＂post-Dong＂ . In this paper, by starting from Qichang Dong＇ s ＂theory of southern and northern schoots＂ , the homogeneities between traditional Chinese music and painting arts are analyzed from the principle of spirit and the principle of technology, so that the homogeneities between traditional Chinese music and painting arts are explored in aesthetic concept and actual art creation.

Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings

Based on the evolution of geological dynamics and spatial chaos theory, we proposed the advanced prediction an advanced prediction method of a gas desorption index of drill cuttings to predict coal and gas outbursts. We investigated and verified the prediction method by a spatial series data of a gas desorption index of drill cuttings obtained from the 113112 coal roadway at the Shitai Mine. Our experimental results show that the spatial distribution of the gas desorption index of drill cuttings has some chaotic charac- teristics, which implies that the risk of coal and gas outbursts can be predicted by spatial chaos theory. We also found that a proper amount of sample data needs to be chosen in order to ensure the accuracy and practical maneuverability of prediction. The relative prediction error is small when the prediction pace is chosen carefully. In our experiments, it turned out that the optimum number of sample points is 80 and the optimum prediction pace 30. The corresponding advanced prediction pace basically meets the requirements of engineering applications.

Accuracy estimation of site coordinates derived from GNSS-observations by non-classical error theory of measurements

The velocities of tectonic plates derived from GNSS time series are regularly used as input data for geophysical models. However, as shown by numerous researches, the coordinates time series contain residual errors of a systematic nature, which can significantly affect the reliability of the obtained velocity estimates. This research shows that using non-classical error theory of measurement(NETM)for processing GNSS time series allows detecting the presence of weak, not removed from GNSS processing, sources of systematic errors. Based on the coordinate time series of selected permanent GNSS stations in Europe, we checked the empirical distributions of errors by the NETM on G. Jeffries’ recommendations and on the principles of the theory of hypothesis tests according to Pearson’s criterion. It is established that the obtained coordinates time series of GNSS-stations only partially confirm the hypothesis of their conformity to the normal Gaussian distribution law, and this may be the main reason for their unrepresentative classification. In the future, it is necessary to identify and take into account the causes of residual errors that distort the real distribution of the results of the GNSS time series.

Photoionization Study of Cl II, Ar II and Kr II Ions Using the Modified Atomic Orbital Theory

Resonance energies of the Cl II-[3s23p3(2D5/2)]nd and [3s23p3(2P3/2)]nd, Ar II-3s23p4(1D2)ns, nd and of the Kr II [4s24p4(1D2)]ns, nd and 4s24p4(3P2,3P1)]ns, 4s24p4(3D2)]ns, nd and 4s24p4(3D2, 1S0)]ns, nd Rydberg series are reported. Natural widths of the Ar II-[3s23p4(1D2)]ns, nd series are also reported. Calculations are done in the framework of the Modified Atomic Orbital Theory (MAOT). Excellent agreements are obtained with available theoretical and experimental data. High lying accurate resonance energies up to n = 40 are tabulated. The possibility to use the MAOT formalism report rapidly with an excellent accuracy the position of the excitation resonances as well as their width within simple analytical formulae is demonstrated.

Modified Atomic Orbital Theory of the O+ Ion Originating from 2D0 and 4S0 Metastable States

We report in this paper energy positions of the 2D0_2s22p2(1D)nd(2F);2D0_2s22p2(1D)nd(2D);2D0_2s22p2(1D)nd(2P);2D0_2s22p2(1D)ns(2D);2D0_2s22p3(3D)np(2P);2D0_2s22p3(3D0)np(2F), and 4S0_2s22p3(5S0)np(4P) Rydberg series in the photoionization spectra originating from 2D0 and 4S0 metastable states of O+ ion. Calculations are performed up to n = 20 using the Modified Orbital Atomic Theory (MAOT) [1]. The present results are compared to the experimental data of Aguilar et al. [2] which are the only available values. The accurate data presented in this work may be a useful guideline for future experimental and other theoretical studies.

Mean-field and high temperature series expansion calculations of some magnetic properties of Ising and XY antiferromagnetic thin-films

In this work, the magnetic properties of Ising and XY antiferromagnetic thin-films are investigated each as a function of Neel temperature and thickness for layers （n = 2, 3, 4, 5, 6, and bulk （∞） by means of a mean-field and high temperature series expansion （HTSE） combined with Pade approximant calculations. The scaling law of magnetic susceptibility and magnetization is used to determine the critical exponent γ, veff （mean）, ratio of the critical exponents γ/v, and magnetic properties of Ising and XY antiferromagnetic thin-films for different thickness layers n = 2, 3, 4, 5, 6, and bulk （∞）.

Arrhythmia Detection by Using Chaos Theory with Machine Learning Algorithms

Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.

Theoretical analysis of ionic autoionization spectra of lanthanum via an intermediate state [Xe]5d6d 1P1

In the framework of multi-channel quantum defect theory, eigenquantum defects μα and the transformation matrices Uiα of La＋ are calculated from first principles by relativistic multi-channel theory, while the dipole matrix elements DCr are obtained by fitting with experimental data. Then the ionic autoionization spectra of lanthanum via the intermediate state [Xe]5d6d 1p1 in the energy region of 90213-91905 cm-1 axe obtained. Experimental peaks are classified and assigned by comparing with the corresponding calculated spectra. More specifically, four ionic autoionization Rydberg series converging to La2＋ 5d5/2 2D5/2 and several states converging to higher lying states of La2＋ are found and assigned.

Domain of Euler Mean in the Space of Absolutely p-Summable Double Sequences with 0

In this study, as the domain of four dimensional Euler mean E(r,s) of orders r,sin the space L_p for 0 < p < 1, we examine the double sequence space ε_p^(r,s) and some properties of four dimensional Euler mean. We determine the α-and β(bp)-duals of the space εp r,s, and characterize the classes(ε_p^(r,s):M_u),(ε_p^(r,s):C_(bp)) and(ε_p^(r,s):L_q) of four dimensional matrix transformations, where 1 ≤q < ∞. Finally, we shortly emphasize on the Euler spaces of single and double sequences, and note some further suggestions.

Numerical Procedures for Calculating the Probabilities of Recurrent Runs

Run count statistics serve a central role in tests of non-randomness of stochastic processes of interest to a wide range of disciplines within the physical sciences, social sciences, business and finance, and other endeavors involving intrinsic uncertainty. To carry out such tests, it is often necessary to calculate two kinds of run count probabilities: 1) the probability that a certain number of trials results in a specified multiple occurrence of an event, or 2) the probability that a specified number of occurrences of an event take place within a fixed number of trials. The use of appropriate generating functions provides a systematic procedure for obtaining the distribution functions of these probabilities. This paper examines relationships among the generating functions applicable to recurrent runs and discusses methods, employing symbolic mathematical software, for implementing numerical extraction of probabilities. In addition, the asymptotic form of the cumulative distribution function is derived, which allows accurate runs statistics to be obtained for sequences of trials so large that computation times for extraction of this information from the generating functions could be impractically long.

Chaos in Time Series of Sakarya River Daily Flow Rate

In this study, possible low dimensional chaotic behavior of Sakarya river flow rates is investigated via nonlinear time series techniques. To reveal the chaotic dynamics, the maximal positive Lyapunov exponent is calculated from the reconstructed phase space, which is obtained using the phase space reconstruction method. The method reconstructs a phase space from the scalar time series, which depicts the real system’s invariants Positive values, because the Lyapunov exponent values calculated using the appropriate software program indicate possibility of chaotic behavior. Analyzed data involve the monthly average flow rates of eleven main branches of Sakarya River through the years 1960-2000.

Grey Relation between Nonlinear Characteristic and Dynamic Uncertainty of Rolling Bearing Friction Torque

The rolling bearing friction torque which is characterized by its uncertainty and nonlinearity affects heavily the dynamic performance of a system such as missiles, spacecrafts and radars, etc. It is difficult to use the classical statistical theory to evaluate the dynamic evaluation of the rolling bearing friction torque for the lack of prior information about both probability distribution and trends. For this reason, based on the information poor system theory and combined with the correlation dimension in chaos theory, the concepts about the mean of the dynamic fluctuant range （MDFR） and the grey relation are proposed to resolve the problem about evaluating the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque. Friction torque experiments are done for three types of the rolling bearings marked with HKTA, HKTB and HKTC separately; meantime, the correlation dimension and MDFR are calculated to describe the nonlinear characteristic and the dynamic uncertainty of the friction torque, respectively. And the experiments reveal that there is a certain grey relation between the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque, viz. MDFR will become the nonlinear increasing trend with the correlation dimension increasing. Under the condition of fewer characteristic data and the lack of prior information about both probability distribution and trends, the unitive evaluation for the nonlinear characteristic and the dynamic uncertainty of the rolling bearing friction torque is realized with the grey confidence level of 87.7%-96.3%.

Determination of safe mud window considering time-dependent variations of temperature and pore pressure:Analytical and numerical approaches

Wellbore stability is a key to have a successful drilling operation.Induced stresses are the main factors affecting wellbore instability and associated problems in drilling operations.These stresses are significantly impacted by pore pressure variation and thermal stresses in the field.In order to address wellbore instability problems,it is important to investigate the mechanisms of rockefluid interaction with respect to thermal and mechanical aspects.In order to understand the induced stresses,different mathematical models have been developed.In this study,the field equations governing the problem have been derived based on the thermo-poroelastic theory and solved analytically in Laplace domain.The results are transferred to time domain using Fourier inverse method.Finite difference method is also utilized to validate the results.Pore pressure and temperature distributions around the wellbore have been focused and simulated.Next,induced radial and tangential stresses for different cases of cooling and heating of formation are compared.In addition,the differences between thermo-poroelastic and poroelastic models in situation of permeable and impermeable wellbores are described.It is observed that cooling and pore pressure distribution reinforce the induced radial stress.Whereas cooling can be a tool to control and reduce tangential stress induced due to invasion of drilling fluid.In the next step,safe mud window is obtained using Mohr-Coulomb,Mogi-Coulomb,and modified Lade failure criteria for different inclinations.Temperature and pore pressure distributions do not change the minimum allowable wellbore pressure significantly.However,upper limit of mud window is sensitive to induced stresses and it seems vital to consider changes in temperature and pore pressure to avoid any failures.The widest and narrowest mud windows are proposed by modified Lade and Mohr-Coulomb failure criteria,respectively.