1. ### Note on the Relation Between Cesaro Averages for Discrete Weighted Shift Operator and the Behavior of the Resolvent

Ali A. Shukur

Department of functional analysis, Belarusian State University, St.Nisovizimosti 4, 22003, Minsk, Belarus.

Abstract: The behavior of the limit of the Cesaro averages was studied in different ergodic theorems. In this note we study these averages for discrete weighted shift operators. The relation between the coefficients of the mentioned operators, the behavior of the Cesaro averages and the behavior of the resolvent is given.

Keywords: Cesaro averages, power-bounded operator, Kriess resolvent condition, Ritt resolvent condition, weighted shift operator.

2. ### Using Simulation by Excel and R in the Teaching of Probability and Statistics for Non-Math Major Students

Bui Anh Kiet1, Jean-baptiste Lagrange2

1. Cantho University.
2. LDAR, Université Paris-Diderot, France.

Abstract: In Vietnam, the teaching of probability gives an important place to a «classical» approach based on the formula of Laplace, and inferential statistics is seen as an application. Moreover, the teaching does not include the use of software, generic or dedicated to statistics. This leads to difficulties that have special meaning for students of other disciplines as mathematics, to be prepared for an understanding of random phenomena and a statistical approach in real life. This article aims to assess the possibility of introducing “viable” innovations in teaching probability and statistics at the university level in Vietnam, and the improvements that these innovations bring to the understanding of the students.

Keywords: frequentist approach, probability and statistics, R, spreadsheet, models.

3. ### Fuzzy Almost p-Continuous and Almost p*-Continuous Functions

Anjana Bhattacharyya

Department of Mathematics, Victoria Institution (College), 78 B, A.P.C. Road, Kolkata – 700009, India.

Abstract: This paper deals with two different types of fuzzy continuous functions, viz., fuzzy almost p-continuous and fuzzy almost p*-continuous functions. It is shown that fuzzy almost p*-continuous function is fuzzy almost p-continuous but the converse is true under certain condition only. Again it is proved that the composition of two fuzzy almost p*-continuous functions is also so but this is not true for fuzzy almost p-continuous function. In the last section a new type of fuzzy regularity is introduced under which fuzzy almost p-continuous function is fuzzy almost p*-continuous.

Keywords: Fuzzy almost p-continuous function, fuzzy almost p*-continuous function, fuzzy p*-open q-nbd, p*-closure of a fuzzy set, fuzzy p*-open nbd, fuzzy p*-regular space.