We present the equations of condition up to sixth order for Runge-Kutta (RK) methods, when integrating scalar autonomous problems. Two RK pairs of orders 5(4) are derived. The first at a cost of only five stages per step, while the other having an extremely small principal truncation error. Numerical tests show the superiority of the new pairs over traditional ones.

The effect of chemical reactions on the blast initiation of detonation in gaseous media has been investigated in this paper. Analytical method is based on the numerical solution of onedimensional reactive Euler equations. So far, analyses on the blast initiation of detonation have modeled the combustion process as a one-step chemical reaction, which follows the Arrhenius rate law. Previous stud...

Conventional treatments for osteoarthritis (OA), the most common form of arthritis, are associated with unpleasant adverse effects and often ineffective. Acupuncture and traditional Chinese medicine (TCM) have been used for thousands of years to treat pain and other dysfunctions. However, the scientific evidence on the efficacy of acupuncture and TCM is equivocal, and adapting the Western biome...

Numerical experiments were carried out using the Tel-Aviv University 2-D cloud model to investigate the effects of increased concentrations of Cloud Condensation Nuclei (CCN), giant CCN (GCCN) and Ice Nuclei (IN) on the development of precipitation and cloud structure in mixedphase sub-tropical convective clouds. In order to differentiate between the contribution of the aerosols and the meteoro...

Automatic speech recognition (ASR) is one of the most demanding tasks in natural language processing owing to its complexity. Recently, deep learning approaches have been deployed for this task and proven outperform traditional machine such as Artificial Neural Network (ANN). In particular, deep-learning methods long short-term memory (LSTM) achieved improved ASR performance. However, method li...

The paper provides a literature review of the STEPNC compliant research around the world. The first part of this paper focuses on projects based on STEP compliance followed by research and development in this area based on machining operations. Review the literature relating to relevant STEP standards and application in the area of turning centers. This research will review the various research...

We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of functions of split-biquaternionic variables. c ©2016 all rights reserved.

Chaining can reduce the number of iterations required for symbolic state-space generation and model-checking, especially in Petri nets and similar asynchronous systems, but requires considerable insight and is limited to a static ordering of the events in the high-level model. We introduce a two-step approach that is instead fine-grained and dynamically applied to the decision diagrams nodes. T...