Classical Algebraic Methods Research Articles

Coding theory for h(x)-Fibonacci polynomials

The amount of information transmitted over the internet network has dramatically increased with the prevailing of internet use. As a result of this increase, the algorithms used in data encryption methods have gained importance. In this paper, h(x)-Fibonacci coding/decoding method for h(x)-Fibonacci polynomials is introduced. The proposed method is fast because it is based on basic matrix operations, and it is suitable for cryptographic applications because it uses the ASCII character encoding system. For this reason, it differs from the classical algebraic methods in literature. Furthermore, the fact that h(x) is a polynomial improves the security of cryptography.

Techniques of Integration: An Alternative Tool for Solving Problems of Financial Transactions Concerning Simple Interest

Money has time value. The value of Tk today is more worthy than the value of Tk 1 tomorrow as today’s money can be invested to earn positive returns in future. This economic principle recognizes that the value of money is affected with the passage of time. Problems of financial transactions concerning simple interest are usually solved by algebraic formula. This paper attempts to solve such problems using techniques of integration and makes a comparison with the results obtained by the classical algebraic method and finds no error. The proposed techniques could be implemented in the practical field as it provides error-free result.

An Improved Algebraic Method for Transit Signal Priority Scheme and Its Impact on Traffic Emission

Transit signal priority has a positive effect on improving traffic congestion and reducing transit delay and also has an influence on traffic emission. In this paper, an optimal transit signal priority scheme based on an improved algebraic method was developed and its impact on vehicle emission was evaluated as well. The improved algebraic method was proposed on the basis of classical algebraic method and has improvements in three aspects. First, the calculation rules of split loss are more reasonable. Second, the delay caused by transit stations and queued vehicles can be considered. Third, measures for finding optimal ideal intersection interval are improved. By establishing a microscopic traffic emission simulation platform based on microscopic traffic simulation model VISSIM and the comprehensive modal emission model (CMEM), the traffic emissions can be evaluated. Then, an optimal transit signal priority scheme based on the traffic data collected in Changzhou city was developed and its impact on emission was simulated in the VISSIM-CMEM platform. Comparative analysis results showed that proposed scheme can outperform original scheme in the aspects of reducing emission and passenger delay and an average reduction of 25.0% on transit emission and relative decrease in overall traffic emission can be achieved.

Improvement of Classical Algebraic Method of Signal Timing for Arterial Road Coordinate Control

AbstractFollowing the design principle of maximum green wave bandwidth and making use of the time-space diagram for arterial road coordinate control, many problems existed in classical algebraic method such as the determination of value range of ideal intersection distance, the calculation of green wave bandwidth, the selection of optimal intersection distance and the value of signal offsets were deeply analyzed through some practical examples. On the basis of detailed analysis, the value range of ideal intersection distance was determined by the allowable value range of common signal cycle, a new calculation method for green wave bandwidth was presented, and a new selection rule of optimal intersection distance was established. The examples effectively demonstrate that the improved classical algebraic method can make arterial road coordinate control system get green wave bandwidth as wide as possible and obtain optimal common signal cycle and green wave bandwidth more practically and accurately.

Construction of the integral closure of an affine domain in a finite field extension of its quotient field

The construction of the normalization of an affine domain over a field is a classical problem solved since sixteen's by Stolzenberg (1968) and Seidenberg (1970–1975) thanks to classical algebraic methods and more recently by Vasconcelos (1991–1998) and de Jong (1998) thanks to homological methods. The aim of this paper is to explain how to use such a construction to obtain effectively the integral closure of such a domain in any finite extension of its quotient field, thanks to Dieudonné characterization of such an integral closure. As application of our construction, we explain how to obtain an effective decomposition of a quasi-finite and dominant morphism from a normal affine irreducible variety to an affine irreducible variety as a product of an open immersion and a finite morphism, conformly to the classical Grothendieck's version of Zariski's main theorem.

Some remarks on generalized elliptic-type integrals

Two limit relationship for a family of generalized elliptic-type integrals are derived here by means of a classical algebraic method which is based upon the convergence theorems of recurrence sequences and some recursive for hypergeometric functions.

A Novel Approach To The Design Of Multiple-probe High-power Microwave Automatic Impedance Measuring Schemes

Starting with a modified look at the phasor diagram of a multiple-probe system on a lossless waveguide, one can attain a geometrical method for designing various direct-reading microwave impedance-measuring schemes using fixed probes. This geometrical method will bypass a significant amount of algebraic complexity as encountered in classical algebraic methods. Hence it allows one to visualize the physical picture more clearly and guides one to modify the design more effectively to meet higher performance demands. This article reports a trend of design developments derived from this new point of view. It starts with the analysis of a two-probe system for measuring an unknown impedance /bar z/. This is followed by modifications on the design guided by the new geometrical technique. Finally, two practical designs are derived for measuring an unknown microwave impedance automaticaly. One is to be used under fixed-frequency, swept-power conditions, and the other, under swept-frequency, swept-power conditions. These systems require only inexpensive low-frequency signal processors (either analog or digital) and fixed multiple probes. The output can be either analog with polar display or digital with accurate readouts. To the author's knowledge these designs have not been derived in the past using multiple probes. A critical review on all multiple-probe systems reported in the literature is also discussed with their comparison to the present system.