A novel explicit three-sub-step time integration method for wave propagation problems

A novel explicit three-sub-step time integration method is proposed. From linear analysis, it is designed to have at least second-order accuracy, tunable stability interval, tunable algorithmic dissipation and no overshooting behaviour. A distinctive feature is that the size of its stability interval can be adjusted to control the properties of the method. With the largest stability interval, the new method has better amplitude accuracy and smaller dispersion error for wave propagation problems, compared with some existing second-order explicit methods, and as the stability interval narrows, it shows improved period accuracy and stronger algorithmic dissipation. By selecting an appropriate stability interval, the proposed method can achieve properties better than or close to existing second-order methods, and by increasing or reducing the stability interval, it can be used with higher efficiency or stronger dissipation. The new method is applied to solve some illustrative wave propagation examples, and its numerical performance is compared with those of several widely used explicit methods.

Orthonormal piecewise Bernoulli functions: Application for optimal control problems generated using fractional integro-differential equations

In this study, the orthonormal piecewise Bernoulli functions are generated as a new kind of basis functions. An explicit matrix related to fractional integration of these functions is obtained. An efficient direct method is developed to solve a novel set of optimal control problems defined using a fractional integro-differential equation. The presented technique is based on the expressed basis functions and their fractional integral matrix together with the Gauss–Legendre integration method and the Lagrange multipliers algorithm. This approach converts the original problem into a mathematical programming one. Three examples are investigated numerically to verify the capability and reliability of the approach.

Path Integral Estimates of the Quantum Fluctuations of the Relative Soliton-Soliton Velocity in a Gross-Pitaevskii Breather

In this paper, the quantum fluctuations of the relative velocity of constituent solitons in a Gross-Pitaevskii breather are studied. The breather is confined in a weak harmonic trap. These fluctuations are monitored, indirectly, using a two-body correlation function measured at a quarter of the harmonic period after the breather creation. The results of an ab initio quantum Monte Carlo calculation, based on the Feynman-Kac path integration method, are compared with the analytical predictions using the recently suggested approach within the Bogoliubov approximation, and a good agreement is obtained.

A variational inequality arising from optimal surrender of variable annuity with lookback benefit

We introduce a variable annuity (VA) contract with a surrender option and lookback benefit, that is, the benefit of the VA contract is linked to the maximum process of the policyholder’s account value. In contrast to the constant guarantee model provided in Bernard et al. (Insur. Math. Econ. 55:116–128, 2014), it is optimal for the policyholder of the VA contract with lookback benefit to surrender the VA contract when the policyholder’s account value is below or equal to the optimal surrender boundary. Thus, from the perspective of the insurer to construct a portfolio of VA contracts, utilizing the VA contracts with lookback benefit along with VA contracts with constant guarantee provides the diversification of early surrenders. The valuation of this contract can be described as a two-dimensional parabolic variational inequality. By converting this into the one-dimensional problem, we obtain the integral equations for the value function and the free boundary. The recursive integration method is applied to obtain the numerical solutions. We also provide comparative statics of the optimal surrender boundaries with respect to various parameters.

Detection of Economy-Related Turkish Tweets Based on Machine Learning Approaches

Conducting NLP for Turkish is a lot harder than other Latin-based languages such as English. In this study, by using text mining techniques, a pre-processing frame is conducted in which TF-IDF values are calculated in accordance with a linguistic approach on 7,731 tweets shared by 13 famous economists in Turkey, retrieved from Twitter. Then, the classification results are compared with four common machine learning methods (SVM, Naive Bayes, LR, and integration LR with SVM). The features represented by the TF-IDF are experimented in different N-grams. The findings show the success of a text classification problem is relative with the feature representation methods, and the performance superiority of SVM is better compared to other ML methods with unigram feature representation. The best results are obtained via the integration method of SVM with LR with the Acc of 82.9%. These results show that these methodologies are satisfying for the Turkish language.

Seismic Performance of RC Column Using Fiber Hinge Concept with Time Integration Method

Recent seismic events showed the importance of understanding the structural performance of RC column that can be predicted numerically. The accuracy of column performance depends on type of the analysis and representation of seismic effect. Therefore, in this paper a nonlinear time history analysis has been performed to assess the seismic performance of bridge column using fiber hinge concept with time integration method using sap2000 software. A long bridge RC column is utilized and subjected to seismic excitation. The column has been divided into different size and numbers of fiber to assess the accuracy of the analysis and time consuming to analyze each case of fiber hinges. In addition, this paper used three-time integration methods, Newmark, Hilber-Hughes-Taylor, and Chung & Hulbert to predict the most suitable method to be used in column seismic analysis. The time history displacement and base shear in addition to moment rotation of the column are the most important factors to evaluate the column seismic performance. The analysis results demonstrated that the most suitable time integration method is Hilber-Hughes-Taylor for such type of the analysis since it gives more stable base shear result than other two methods. Furthermore, the results indicated that the accuracy of seismic performance increased by number of fibers incremental. Moreover, the number of steel fibers should be equal to the number of bars with same area and location. The unconfined and confined concrete should be divided into small areas to get accurate prediction of column seismic performance.