One–Step Hybrid Block Scheme for the Numerical Approximation for Solution of Third Order Initial Value Problems

In this research, we have proposed the simulation of linear block algorithm for modeling third order highly stiff problem without reduction to a system of first order ordinary differential equation, to address the weaknesses in reduction method. The method is derived using the linear block method through interpolation and collocation. The basic properties of the block method were recovered and was found to be consistent, convergent and zero-stability. The new block method is been applied to model third order initial value problems of ordinary differential equations without reducing the equations to their equivalent systems of first order ordinary differential equations. The result obtained on the process on some sampled modeled third order linear problems give better approximation than the existing methods which we compared our result with.

Parallel impelementation of RC6 algorithm

Data security is very important in the field of Computer Science. In this paper the encryption algorithm called RC6 will be analyzed and its standard and parallel implementation will be done. First the field of Cryptology is discussed in general terms, then the classification of encryption algorithms according to operation and techniques is explained. RC6 is a symmetric block algorithm derived from the RC5 algorithm. RC6 operates on 128-bit blocks and accepts 128, 192, 256-bit keys until 2040 bytes. In the Advanced Encryption Standard (AES) competition, RC6 managed to rank among the five finalists. The structure of the RC6 algorithm will be analyzed also the encryption and decryption methods. The comparison between standard and parallel implementation will be made.

DERIVATION AND IMPLEMENTATION OF A THREE-STEP HYBRID BLOCK ALGORITHM (TSHBA) FOR DIRECT SOLUTION OF LINEAR AND NONLINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

The development and application of an implicit hybrid block method for the direct solution of second order ordinary differential equations with given initial conditions is shown in this research. The derivation of the three-step scheme was done through collocation and interpolation of power series approximation to give a continuous linear multistep method. The evaluation of the continuous method at the grid and off grid points formed the discrete block method. The basic properties of the method such as order, error constant, zero stability, consistency and convergence were properly examined. The new block method produced more accurate results when compared with similar works carried out by existing authors on the solution of linear and non-linear second order ordinary differential equations

Looking through the photoionisation wake: Vela X−1 at φorb ≈ 0.75 with Chandra/HETG

Context. The supergiant X-ray binary Vela X−1 represents one of the best astrophysical sources to investigate the wind environment of an O/B star irradiated by an accreting neutron star. Previous studies and hydrodynamic simulations of the system have revealed a clumpy environment and the presence of two wakes: an accretion wake surrounding the compact object and a photoionisation wake trailing it along the orbit. Aims. Our goal is to conduct, for the first time, high-resolution spectroscopy on Chandra/HETGS data at the orbital phase φorb ≈ 0.75, when the line of sight is crossing the photoionisation wake. We aim to conduct plasma diagnostics, inferring the structure and the geometry of the wind. Methods. We performed a blind search employing a Bayesian block algorithm to find discrete spectral features and identify them thanks to the most recent laboratory results or through atomic databases. Plasma properties were inferred both with empirical techniques and with photoionisation models within CLOUDY and SPEX. Results. We detect and identify five narrow radiative recombination continua (Mg XI-XII, Ne IX-X, O VIII) and several emission lines from Fe, S, Si, Mg, Ne, Al, and Na, including four He-like triplets (S XV, Si XIII, Mg XI, and Ne IX). Photoionisation models reproduce the overall spectrum well, except for the near-neutral fluorescence lines of Fe, S, and Si. Conclusions. We conclude that the plasma is mainly photoionised, but more than one component is most likely present, which is consistent with a multi-phase plasma scenario, where denser and colder clumps of matter are embedded in the hot, photoionised wind of the companion star. Simulations with the future X-ray satellites Athena and XRISM show that a few hundred seconds of exposure is sufficient to disentangle the lines of the Fe Kα doublet and the He-like Fe XXV, improving, in general, the determination of the plasma parameters.

Approximating non linear higher order ODEs by a three point block algorithm

Differential equations are commonly used to model various types of real life applications. The complexity of these models may often hinder the ability to acquire an analytical solution. To overcome this drawback, numerical methods were introduced to approximate the solutions. Initially when developing a numerical algorithm, researchers focused on the key aspect which is accuracy of the method. As numerical methods becomes more and more robust, accuracy alone is not sufficient hence begins the pursuit of efficiency which warrants the need for reducing computational cost. The current research proposes a numerical algorithm for solving initial value higher order ordinary differential equations (ODEs). The proposed algorithm is derived as a three point block multistep method, developed in an Adams type formulae (3PBCS) and will be used to solve various types of ODEs and systems of ODEs. Type of ODEs that are selected varies from linear to nonlinear, artificial and real life problems. Results will illustrate the accuracy and efficiency of the proposed three point block method. Order, stability and convergence of the method are also presented in the study.

Privacy-Preserving Vehicle Assignment in the Parking Space Sharing System

Nowadays, the availability of parking spaces is far behind the quick rising number of cars. Rather than building more lots, a better way is to share private-owned parking spaces. However, this faces the challenge that users are not willing to expose their privacy to the public. To solve this problem, we propose a new architecture for parking space sharing, integrating homomorphic cryptography into the design of a secure protocol for parking space searching and booking. The proposed privacy-preserving matching scheme (PPMS) is constructed in an untrusted third-party service system including two independent entities, namely, a server and an intermediary platform. Via the participant comparison protocol (PCP), a driver can choose from the matching result and be navigated to the parking space near his destination, without knowing any information of the provider and vice versa. In the meanwhile, in order to further improve the efficiency of matching, we also propose a block algorithm based on the longitude and latitude (BABLL), which utilizes a novel partitioning scheme. The feasibility of the architecture is validated through the detailed theoretical analysis and extensive performance evaluations, including the assessment of the resilience to attacks.