Algebraic Structures of Bernoulli Numbers and Polynomials

In a field of Laurent series, we construct a subring which has a module structure over a Weyl algebra. Identities of Bernoulli numbers and polynomials are obtained from these algebraic structures.Comment: This article was submitted to J. Number Theory on 2008. The referee(s) agreed to review the article did not write reports and not even response to the editor. The paper was rejected by J. Number Theory on 2012, since `it is impossible for us (editors) to get this paper refereed'. The author will no longer seek publication for this article in journals. Comments on the article are welcome

Development of a Saltwater Intrusion Software Using Visual Basic

Coastal aquifers play important roles for sources of water. With growing concern on groundwater resources both in term of quantity and quality, proper assessments and computation tools are becoming more important. Groundwater regional scale phenomena usually cannot be studied accurately using laboratory scale physical models; therefore mathematical tools of analysis must be applied. The advance of the computer technology should be used to solve the complicated mathematical task in solving arithmetic operations. The purpose of this study was to develop a user-friendly steady state model for simulation of saltwater intrusion into coastal aquifers. The model made use of the mathematical formulation developed by Ganfoud (1997). Two equations were derived, one for water flow, and the other for solute transport that were coupled through Darcy's velocity and concentration. In the numerical model formulation, two-dimensional Galerkin finite element approach was applied for deriving the elemental matrix equation through quadrilateral elements. The system of linear equations was solved using successive substitution employing the Gaussian elimination techniques. The whole formulation was set up by using the Visual Basic programming and Surfer graphic program (developed by Golden Software) to analyze the results. The results of intrusion were shown graphically under steady state conditions. The program has been proven to be user- friendly than other programming languages. For model verification, a hypothetical unconfined model and a physical model were used to compare the model's results with previous studies. These models applied the constant and velocity-dependent dispersion coefficient. The comparison showed a good agreement in numerical term between the proposed model and the previous ones. However, the Visual Basic program is not as powerful as the FORTRAN engineering programming and caused minor discrepancies when compared to the previous study

Inverse Relations and Schauder Bases

AbstractThe concept of inter-changes of Schauder bases is used to interpret inverse relations for sequences. For a given power series, the interplay between different representations by Schauder bases can result in combinatorial identities, new or known. Local cohomology residues and local duality are used for computations. The viewpoint of Riordan arrays is examined using Schauder bases

Speed Efficient Hardware Implementation Of Advanced Encryption Standard (Aes)

Cryptography plays a vital role in data security against the attacks from the third party. In this thesis, the focus is to leverage existing, commonly used cryptography algorithm which is the Advanced Encryption Standard (AES) and improve its speed performance. The motivation is to make encryption process as short as possible to aid in increasing a system's ability to process large amount of data. FPGA is chosen as the platform due to it does not have software overhead and is meant to be customized for real time applications. Most of the researches are done on the area of optimizing hardware resources to implement AES on FPGA. The methods of optimization include on the fly computations and looping architecture, where all these of methods reduce the speed. This thesis presents a high throughput design of the 128-bit AES algorithm using loop unrolling, pipelined architecture and LUT approach which is able to work in parallel to allow accurate synchronization in order to fulfill the real time application needs. The system design is coded using Verilog HDL in ModelSim and the hardware design is analyzed through Altera Cyclone II in Quartus II. The maximum throughput of 32 Gbits/s operating at 250 MHz for the encryption process can be achieved. Also, one full cycle of a 128-bit AES encryption only needs 41 clock cycles in order to get the encrypted data. The comparison with the related works is done and eventually achieved higher throughput than the related works by 3.47% and 22% respectively. The two objectives set in this thesis are achieved

An Explicit Construction of Residual Complexes

AbstractLet φ: Y→X be a morphism of finite type between locally Noetherian schemes whose fibers have bounded dimensions. Given concretely a residual complex on X, we construct canonically a concrete residual complex on cY