A stochastic Model for Predicting Irrigation Water Requirements (IWR)

The main objective of this paper is to develop a stochastic time series model with trend, periodic and irregular components using a ten years IWR decade data for three different types of cotton crops cultivated in Gezira Scheme, SUDAN. The model was applied to cotton Brackat and then used to Shmbat & Akala cotton. In the analysis of IWR time series the correlogram technique was used to detect the periodicity which then smoothed by Fourier series method. The series is then tested for stationary and the dependent part of irregular component is found to be well expressed by the first order autoregressive model for all the crops. The developed model superimposes a periodic-deterministic process and an irregular componen

Principal component and multiple correspondence analysis for handling mixed variables in the smoothed location model

The issue of classifying objects into groups when the measured variables are mixtures of continuous and binary variables has attracted the attention of statisticians. Among the discriminant methods in classification, Smoothed Location Model (SLM) is used to handle data that contains both continuous and binary variables simultaneously. However, this model is infeasible if the data is having a large number of binary variables. The presence of huge binary variables will create numerous multinomial cells that will later cause the occurrence of large number of empty cells. Past studies have shown that the occurrence of many empty cells affected the performance of the constructed smoothed location model. In order to overcome the problem of many empty cells due to large number of measured variables (mainly binary), this study proposes four new SLMs by combining the existing SLM with Principal Component Analysis (PCA) and four types of Multiple Correspondence Analysis (MCA). PCA is used to handle large continuous variables whereas MCA is used to deal with huge binary variables. The performance of the four proposed models, SLM+PCA+Indicator MCA, SLM+PCA+Burt MCA, SLM+PCA+Joint Correspondence Analysis (JCA), and SLM+PCA+Adjusted MCA are compared based on the misclassification rate. Results of a simulation study show that SLM+PCA+JCA model performs the best in all tested conditions since it successfully extracted the smallest amount of binary components and executed with the shortest computational time. Investigations on a real data set of full breast cancer also showed that this model produces the lowest misclassification rate. The next lowest misclassification rate is obtained by SLM+PCA+Adjusted MCA followed by SLM+PCA+Burt MCA and SLM+PCA+Indicator MCA models. Although SLM+PCA+Indicator MCA model gives the poorest performance but it is still better than a few existing classification methods. Overall, the developed smoothed location models can be considered as alternative methods for classification tasks in handling large number of mixed variables, mainly the binary

The phase relation between sunspot numbers and soft X-ray flares

To better understand long-term flare activity, we present a statistical study on soft X-ray flares from May 1976 to May 2008. It is found that the smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of 13, 8, and 8 months in cycle 21 respectively with respect to the smoothed monthly sunspot numbers. There is no time lag between the sunspot numbers and M-class flares in cycle 22. However, there is a one-month time lag for C-class flares and a one-month time lead for X-class flares with regard to sunspot numbers in cycle 22. For cycle 23, the smoothed monthly peak fluxes of C-class, M-class, and X-class flares have a very noticeable time lag of one month, 5 months, and 21 months respectively with respect to sunspot numbers. If we take the three types of flares together, the smoothed monthly peak fluxes of soft X-ray flares have a time lag of 9 months in cycle 21, no time lag in cycle 22 and a characteristic time lag of 5 months in cycle 23 with respect to the smoothed monthly sunspot numbers. Furthermore, the correlation coefficients of the smoothed monthly peak fluxes of M-class and X-class flares and the smoothed monthly sunspot numbers are higher in cycle 22 than those in cycles 21 and 23. The correlation coefficients between the three kinds of soft X-ray flares in cycle 22 are higher than those in cycles 21 and 23. These findings may be instructive in predicting C-class, M-class, and X-class flares regarding sunspot numbers in the next cycle and the physical processes of energy storage and dissipation in the corona.Comment: 8 pages, 3 figures, Accepted for publication in Astrophysics & Space Scienc

Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations

This paper presents buckling and free vibration analysis of composite plate/shell structures of various shapes, modulus ratios, span-to-thickness ratios, boundary conditions and lay-up sequences via a novel smoothed quadrilateral flat element. The element is developed by incorporating a strain smoothing technique into a flat shell approach. As a result, the evaluation of membrane, bending and geometric stiffness matrices are based on integration along the boundary of smoothing elements, which leads to accurate numerical solutions even with badly-shaped elements. Numerical examples and comparison with other existing solutions show that the present element is efficient, accurate and free of locking

Excited-state quantum phase transitions in systems with two degrees of freedom: III. Interacting boson systems

The series of articles [Ann. Phys. 345, 73 (2014) and 356, 57 (2015)] devoted to excited-state quantum phase transitions (ESQPTs) in systems with $f=2$ degrees of freedom is continued by studying the interacting boson model of nuclear collective dynamics as an example of a truly many-body system. The intrinsic Hamiltonian formalism with angular momentum fixed to $L=0$ is used to produce a generic first-order ground-state quantum phase transition with an adjustable energy barrier between the competing equilibrium configurations. The associated ESQPTs are shown to result from various classical stationary points of the model Hamiltonian, whose analysis is more complex than in previous cases because of (i) a non-trivial decomposition to kinetic and potential energy terms and (ii) the boundedness of the associated classical phase space. Finite-size effects resulting from a partial separability of both degrees of freedom are analyzed. The features studied here are inherent in a great majority of interacting boson systems.Comment: 14 pages, 6 figure