East West Math

HILBERT FUNCTION AND MULTIPLICITY OF IDEALIZTIONS

Tran Nguyen An — 2025-01-17

Let (R, m) be a Noetherian local ring and M a finitely generated Rmodule. We study the relations of the Hilbert function, the multiplicity of an m-primary ideal of R and these of m × M-primary ideal of the idealization. Some applications to the Cohen-Macaulayness of idealization are given.

DETERMINATION OF THE FIFTH SINGER ALGEBRAIC TRANSFER IN SOME DEGREES

Nguyễn Sum — 2025-01-17

Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] over the prime field F2 with two elements and the degree of each variable xi being 1, and let GLk be the general linear group over F2 which acts on Pk as the usual manner. The algebra Pk is considered as a module over the mod-2 Steenrod algebra A. In 1989, Singer [19] defined the k-th homological algebraic transfer, which is a homomorphism

ϕk : TorA k,k+d(F2, F2) → (F2 ⊗A Pk)GLk d

from the homological group of the Steenrod algebra TorA k,k+d(F2, F2) to the subspace (F2 ⊗A Pk)GLk d of F2⊗APk consisting of all the GLkinvariant classes of degree d.

In this paper, by using the results of the Peterson hit problem we present the proof of the fact that the Singer algebraic transfer of rank five is an isomorphism in the internal degrees d = 20 and d = 30. Our result refutes the proof for the case of d = 20 in Phúc [15].

A SIMPLE STRATEGY TO INVEST IN THE VIETNAMESE STOCKS FOR A MODEST PROFIT

Quoc-Bao Nguyen — 2025-01-17

Any small investor faces the eternal dilemma - Whether to park his/her hard earned money in the bank fixed deposits which may earn low interest but has no risk, or invest in the stock market which may provide a better return but comes with some risk of losing that money. Further, the small investors may lack resources to afford expensive and powerful analytical tools to get an edge in the market. So we have asked a simple question: With the publicly available market information, can a small investor devise a simple strategy to beat the bank fixed deposit rates?

This work presents a simple strategy where we observe an individual stock’s volatility through the "spread" over each unit of time (defined as the interval of (min, max) per unit of time). This spread is a random variable having its own probability distribution, but we make no parametric assumption for this probability distribution.

A stock’s inter percentile range length (IPRL) is then suitably and nonparametrically calculated based on a training sample of a number of n units of time preceding an intended transaction at a given unit time interval. For our study we have used one hour as our unit of time, and it is assumed that a stock’s behavior in one time unit is independent of the others. Also, only one transaction is to be done per unit of time for an individual stock.

We have studied the overall performance of a portfolio of 26 Vietnamese stocks chosen from the list of Top VN 100 Stocks, and we have used the hourly data over N = 1245 hours spanning over all the 249 business days for the year 2023. For an individual stock, a bandwidth is created using the IPRL; if the price falls below the lower margin then stocks are bought, and they are sold if the price crosses the upper threshold. Results of our simulation study show our portfolio profit margin of 9.6% in one year, with an estimated standard error (SE) of 1.84%. This is better than the one-year fixed deposit interest rates in the reputed Vietnamese banks which stood approximately at 5% APY (annual percentage yield) by the end of 2023.

‘SECOND DEGREE ENGLISH-MAJOR’ AT SAI GON UNIVERSITY: AN ANALYSIS OF RECENT STUDENTS’ PERFORMANCE

Yen-Anh Thi Pham — 2025-01-17

This study aims to analyze the self-assessment data of students participating in the ‘Second-Degree English-Major’ (SDEM) program at Sai Gon University (SGU). Using data from a recent survey conducted in October 2023 with a graduating batch of 55 students, this study examines students’ perceptions of their improvements in listening, reading, writing, and speaking skills. Data from 37 students (though for some skills it was 38 as well as 39) with complete information were analyzed using the logistic regression model as well as the bootstrap method (to assess the variations in the estimates of the model parameters) to determine whether the level of improvement depended on their background factors (such as - gender, age and the type of job held). The results show no significant impact of background factors on the students’ self-assessment, suggesting that improvements were evenly distributed across different student groups (identified by the background factors). The subjective nature of the self-assessment data is recognized as a potential source of bias which needs to be addressed in future studies.

A STATISTICAL ANALYSIS OF BANGKOK TRAFFIC ACCIDENT DATA

Kanokwan Channgam — 2025-01-17

A nonlinear regression model has been used to explain the adjusted monthly number of road accidents per 100,000 people (referred as "Adjusted Road Accident Rate") occurred within Bangkok, Thailand, from 2010 to 2016 in term of seven other variables. The extensive analysis is quite interesting, as it indicated that the main and overwhelming factor that contributed to accident rate is the total number of vehicles in the city. In addition, three other variables, namely - mean temperature, the total amount of rainfall and the number of holidays, also contributed to the accident rate, albeit mildly. The implications of this study is quite profound in the sense that if the city planners and policy makers want to reduce the accident rate then total number of vehicles need to be reduced, perhaps through investing more resources into public transportation and/or increasing vahicular fees which may discourage more vehicles on the streets. Other major cities in Southeast Asia, such as Kolkata, Dhaka, Ho Chi Minh City, etc. having similar characteristics as Bangkok can draw lessons from this study.

TEMPERATURE OF PERFECT FLUID BLACK HOLES IN VARIOUS COORDINATES AND ENTROPY COMPOSITION OF BLACK HOLE SYSTEMS

Kunlapat Sansuk — 2025-01-17

The laws of thermodynamics describe the temperature and the entropy of perfect fluid black holes. The temperature can be calculated from the thermal radiation or Hawking radiation using surface gravity, while the entropy is related to the determined temperature. In this paper, we explain in detail the temperature and the entropy of black holes. Finally, we calculate the entropy composition of the perfect fluid black hole systems that have three black holes in the same coordinates. We are interested in two of these coordinates, the Schwarzschild coordinates and the isotropic coordinates, and will also analyze the two types of entropy compositions.