ABSTRACT. The relationship between the discharger and the water quality of the receptor streams was described by a mathematical equation, for the first time introduced in the early 20th century, known as the Streeter – Phelps equation. There have been many follow-up studies to develop this work; however, most of these stopped in the case of steady-state flows and discharges. The expansion through the unsteady case is unnoticed. In this study, the Steeter-Phelps equation is considered in its most general form, accounting for the temporal variation of both the flow and the discharger over time. This study inherits the previous studies but considers for the case of an unstead discharger, especially when the pollutant concentration in the wastewater exceeds the allowable standard. The mathematical model Streeter – Phelps is applied in the case of insteady of the waste discharger is applied. The results show that the error with other products like MIKE is in the range of less than 10%. This result allows the application of the Streeter - Phelps model to the pollution control problem.

ABSTRACT. We present the dynamics of fast two-beam collisions in linear bulk optical media with weak cubic loss. We first generalize the perturbation theory developed for studying two-pulse collisions in spatial dimension 1 to spatial dimension 2. We then use the generalized two-dimensional perturbation theory to calculate the collision-induced amplitude shift in a fast two-beam collision with cubic loss. Furthermore, we show that in the important case of a separable initial condition for both beams, the longitudinal part in the expression for the amplitude shift is universal, while the transverse part is not universal. The theoretical predictions are confirmed by extensive numerical simulations with the weakly perturbed linear propagation model.

ABSTRACT. We study the dynamics of flat-top solitary waves of the cubic-quintic nonlinear Schr\"odinger equation in the presence of randomness. We show that the probability density function of the solitary wave’s amplitude exhibits loglognormal divergence near the maximum possible amplitude. The methodology is based on Ito’s calculations and Monte Carlo simulations. We relate the super-exponential approach of the probability density function of the amplitude to its maximum possible value and extend this statistical behavior to other related solitary wave models.

ABSTRACT. The decision-making process is a human activity in which the human being, as the decision-maker, can hardly escape the influence of multiple circumstances and sources. Fuzzy systems are found to be useful in dealing with the uncertainties and vague concepts. Sometimes decisions are to be made whenever there is insufficient or ambiguous information. In such situations fuzzy systems can be helpful to make good decisions. If a fuzzy measure is available on a referential, it is interesting to have tools able to summarize all the pieces of information provided by a function in a single value; this value would be computed by aggregation functions, in terms of the underlying fuzzy measure. Such tools are the fuzzy integrals. In addition, business administration and education management always raise issues that making choice in precarious context by prioritizing and ordering different task, solutions and resources. This paper aims at clarifying fuzzy integral class based on fuzzy measure and introducing the applications these type of integral for real situations in administration and management

ABSTRACT. In this talk, we present some recent results on exponential stability in mean square of linear and nonlinear stochastic difference systems with time-varying delays. A discussion and some examples are provided to illustrate the obtained results.

ABSTRACT. In the current work, this article studies a time-fractional diffusion equation with a Hyper-Bessel operator. The time-fractional derivative is understood in the sense of a regularized hyper-Bessel operator. First, we represent some stability results on the parameters of the Mittag-Leffler functions. Then, in our primary results, we concentrate on analyzing the continuity of the solution of the initial problem that corresponds to the fractional-order. One of the issues encountered when we do this work is estimating all constants independently of fractional orders. Our main idea is to merge Mittag-Leffler function theories, the Banach fixed point theorem, and Sobolev embeddings to achieve a good result.

ABSTRACT. We present some results on stability and robust stability of linear and nonlinear integro-differential systems with finite and infinite delays. Some examples and applications are provided to illustrate the obtained results.

ABSTRACT. This study proposes a new method to classify image data for two groups, and effectively apply it in identifying people infected with Covid-19 based on their lung image. First, based on the Grey Level Co-occurrence Matrix (GLCM), we extract each image into a two-dimensional interval. Next, a method to find the prior probabilities based on the fuzzy relationship between the classified element with the groups is established. Finally, combining the above improvements, we propose a new principle that is like the Bayesian method for classification. An image is classified into a group if it has the greatest value for prior probability, and the smallest value for the overlap distance between the representative interval for the image and the groups. Applying the set of lung X-ray images to distinguish people infected with Covid-19, the proposed algorithm has given the outstanding result in comparing with many well-known methods. The result also shows that this research can be applied in practice and the potential of the proposed algorithm in a real application in different fields...

ABSTRACT. This talk investigates the stability of solutions to nonlinear optimal control problems. We first consider the boundedness property of solutions of the state equations and the compactness of feasible sets of the such problems. Then, under suitable assumptions, sufficient conditions for the Painlev\'e-Kuratowski convergence of the solution sets for reference problems are established.

ABSTRACT. This article proposes an expansion of initial doain combined to backward to boundary implicit approach to traditional finite difference schema for front tracking of one dimensional moving boundary classical Stefan problem. Numerical results are compared to analytical solution as well as to approximated solution by traditional implicit schema.

ABSTRACT. The Covid-19 pandemic, which lasted over two years, had a global impact on educational activities. In this article, we examined the results of some Math courses taken by students at HCM University of Technology during the semesters 201, 202, and 211. These semesters were chosen to correspond to different Covid-19 pandemics in Vietnam. The analysis was conducted using both descriptive and inferential methods. Pie charts, histograms, t-tests, and chi-square tests, in particular, have been used to compare scores from different semesters or exams. Lecturers of the Division of Applied Mathematics made significant contributions to the use of technology in teaching methods with the goal of increasing teaching effectiveness during those periods, the most notable of which was the use of MyOpenMath. We conducted a survey of 450 students who had used MyOpenMath in their studies over the period of three semesters. The majority of them had a positive experience with MyOpenMath in their studies, as evidenced by more than 70% of satisfied and strongly satisfied responses. Approximately 75% of them also recommend that MyOpenMath be used in future semesters. Motivated by those pilot results, we propose further experiments, such as using MyOpenMath in some Math subjects and project-based teaching in Probability and Statistics courses. Those experiments will be carefully carried out using control groups and experiential groups. The findings will give a formal decision of widely use of those teaching methods.

ABSTRACT. In this talk, we propose a method for finding approximately the width of cracks from their 2D binary images. We apply the connected orthogonally convex hull structure to determine the upper bounds of the width of cracks and reduce possible errors in the image processing step. We also introduce an improvement of the O-Graham algorithm to find connected orthogonal convex hulls to speed up the computation time.

ABSTRACT. It is well known that the algorithms with using a proximal operator can be not convergent for monotone variational inequality problems in the general case. Malitsky (Optim. Methods Softw. 33 (1) 140{164, 2018) proposed a proximal extrapolated gradient algorithm ensuring convergence for the problems, where the constraints are a finite-dimensional vector space. Based on this proximal extrapolated gradient techniques, we propose a new subgradient proximal iteration method for solving monotone multivalued variational inequality problems with the closed convex constraint. At each iteration, two strongly convex subprograms are required to solve separately by using proximal operators. Then, the algorithm is convergent for monotone and Lipschitz continuous cost mapping. We also use the proposed algorithm to solve a jointly constrained Cournot-Nash equilibirum model. Some numerical experiment and comparison results for convex nonlinear programming confirm efficiency of the proposed modification.

ABSTRACT. In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational e!ciency of the given algorithm and comparison with other known algorithms.

ABSTRACT. In this talk we consider set optimization problems involving set relations. Using the well-known KKM-Fan Lemma and relaxed convexity assumptions, we study existence conditions for these problems. Moreover, we introduce parametric nonlinear scalarization functions for sets and study their properties. By utilizing the concerning functions, we investigate relationships between set optimization problems and equilibrium problems. Finally, sufficient conditions for the H\"older continuity of solution maps to such problems via equilibrium problems are established.

ABSTRACT. In this paper, we propose a new hybrid iterative process for approximating common elements of solution set of a generalized mixed variational-like inequality problem and fixed point set of a Bergman quasi-asymptotically nonexpansive mapping. After that, under some suitable conditions, we establish and prove a strong convergence result for the proposed iteration in reflexive Banach spaces. In addition, we give some examples to illustrate the obtained results.

ABSTRACT. In this talk, we consider set optimization problems with variable ordering structures. First, we introduce a variable set less order relation and investigate its properties. Next, we propose the concepts of solutions to reference problems based on this relation. Finally, under suitable assumptions, the upper and lower convergences of the sequence of solutions are established. Our results are new or improve the existing ones in the literature.

ABSTRACT. Robust optimization (RO) is a popular methodology to solve mathematical optimization problems with uncertain data. For the problem RO, the solutions that are immune to all perturbations of the data in a so-called uncertainty set are found. Adjustable robust optimization (ARO), on the other hand, is a branch of RO where some of the decision variables can be adjusted after the uncertain data (or some of its portion) reveals itself. This work deal with the optimality conditions and duality for a class of convex adjustable robust optimization problems.

ABSTRACT. In this paper, new second-order set-valued directional derivatives are proposed for C$^1$ functions, whose derivative is locally calm (stable), in normed spaces. Its existence, main calculus, as well as Taylor's expansions are studied. We then employ them to investigate optimality conditions for optimization problems with geometric and functional constraints. The results also improve the corresponding ones for problems involving C$^{1,1}$ functions. Examples that analyze and illustrate our results are given.

ABSTRACT. This talk deals with a form of Gerstewitz’s nonlinear scalarization functional concerning the set-less relation introduced by Kuroiwa. We first give some of its properties. Then, it is employed to define a directional derivative and a subgradient for cone-convex set-valued maps, which are the extensions of the corresponding ones for convex functions. Some of the usual calculus rules for these concepts are provided and employed to derive some necessary and sufficient optimality conditions for set optimization problems subject to geometric constraints. Examples are provided for analyzing and illustrating the obtained results.

ABSTRACT. Consider images of aircraft's that are vertical in 2D. We propose a novel aircraft type recognition algorithm based on the aircraft's orthogonal convex hull features and Random Forest classification. The aircraft's external contours while removing background and then the planar orthogonal convex hulls of the external contours are determined. Based on the orthogonal convex hulls, we combine the characteristics unique to the aircraft object, to introduce some characters. Finally, we use the Random Forest method to perform the classification. Some experiment results are given.

ABSTRACT. Computer vision has been widely applied to the pothole detection task and significantly promote the accuracy. The first image processing technique by Koch et al. in 2011 was the foundation of the ongoing development of pothole detection algorithms. In this research, we propose a modification to this method which helps to segment and obtain each pothole's width more accurately. We replace the ellipses in the pipeline by convex and orthogonally convex hulls and compute all their widths, where the width of a pothole with respect of a given set is the supremum of the widths at all points of the set. In our experiments, this pulls the width value of the potholes closer to the ground truth and has shown a noticeable improvement in some detection metrics.

ABSTRACT. A set-valued optimization problem with variable preferences is considered. Relations between local and global solutions, optimality conditions, and Wolfe and Mond-Weir duality properties are studied. Both minimal and nondominated solutions are discussed with general variable preferences. The results are proved for three mains types of solutions in vector optimization: weak, Pareto, and strong solutions. New variants of generalized derivatives and convexity are proposed and used in all the results.

ABSTRACT. Let Lie(n,2) be the class of all n-dimensional real solvable Lie algebras having 2-dimensional derived ideals. In 2020 the authors et al. gave a classification of all non 2-step nilpotent Lie algebras of Lie(n,2). In this talk we study representations of these Lie algebras as well as their corresponding connected and simply connected Lie groups. That is, for each algebra, we give an upper bound of the minimal degree of a faithful representation. Then, we give a geometrical description of coadjoint orbits of corresponding groups. Moreover, we show that the characteristic property of the family of maximal dimensional coadjoint orbits of a MD-group is still true for the Lie groups considered here. Namely, we prove that, for each considered group, the family of the maximal dimensional coadjoint orbits forms a measurable foliation in the sense of Connes.

ABSTRACT. We consider all connected and simply connected Lie groups which are corresponding to Lie algebras of dimension 7 such that the nilradical of them is 5-dimensional nilpotent Lie algebra introduced by Dixmier. First, we give a geometric description of the maximal-dimensional orbits in the coadjoint representation of all considered Lie groups. Next, we prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. Finally, the topological classification of all these foliations is also provided.

ABSTRACT. We consider exponential, connected and simply connected Lie groups which are corresponding to seven-dimensional Lie algebras such that their nilradical is a five-dimensional nilpotent Lie algebra $\mathfrak{g}_1 \oplus \mathfrak{g}_4$ given in \cite{dix}. In particular, we give a description of the geometry of the generic orbits in the coadjoint representation of some considered Lie groups. We prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes \cite{con}.

ABSTRACT. The research subject is p-separability of semigroups where P is any ordinary predicate, given on semigroups, in particular, the Green relations separability, monogenic subsemigroup separability and division separability are considered. The study also deals with the problem of finding minimum p-separability for some classes of semigroups.

ABSTRACT. Numerous problems in applied mathematics can be transformed and described by the differential inclusion x'∈f(t,x)-N_Q (x) involving N_Q (x), which is a normal cone for a closed convex set Q∈R^n at x∈Q. We study the Cauchy problem for this inclusion. Since the variations of x leading to changing N_Q (x), the solution of the analyzed inclusion becomes extremely complicated. We consider an ordinary differential equation containing a control parameter K. If K is sufficiently large, then the indicated equation gives a solution approximating the solution of the original inclusion. We also prove the theorem on approximating of these solutions with arbitrary small errors (the errors can be controlled by increasing the parameter K).

ABSTRACT. In this paper, we consider some matrix equations that involve the weighted geometric mean. Based on the properties of the Thompson metric, we prove that these nonlinear matrix equations always have a unique positive definite solution and that the fixed-point iteration method can be efficiently employed to compute it. In addition, the approximations of the positive definite solution and perturbation analysis are investigated. Numerical experiments are given to confirm the theoretical analysis.

ABSTRACT. Let $\Omega \subset \mathbb{C}^n$ be a bounded, strongly pseudo-convex domain with minimally smooth boundary. An Integral formula are used to prove the $L^p$ continuity of Bergman projection. It gives us a tool to study the $\bar\partial$- Neumann problem on domains of finite type.

ABSTRACT. The Bergman kernel is a fundamental object in the theory of analytic functions. Recently it has found many applications and connection to other areas in mathematics such as potential theory and complex geometry. In this talk I will give a survey of recent results on estimates of the Bergman kernel. Several applications will also be discussed.

ABSTRACT. In this work, we study a class of partial differential equations driven by an operator so called double phase on a bounded domain. The presence of a critical nonlinear term makes those equations become harder. We establish a result on the concentration-compactness principle to overcome the difficulty. Then we apply it to get some results on the existence of solutions for the mentioned problem. This talk is based on a work supervised by Dr.Ho Ngoc Ky, University of Economics HCMC.

ABSTRACT. In this paper, we present DC (difference of convex functions) auxiliary principle methods for solving lexicographic equilibrium problems. Under the strongly monotone and Lipchitz-type assumptions of the cost bifunction, we study the convergence of the sequence generated by the proposed algorithms to a unique solution of the considered lexicographic equilibrium problem. Moreover, we also study the asymptotic behavior of the algorithm for solving the considered problem under the presence of computational errors. Finally, we give some numerical experiments to illustrate the behaviour of the proposed algorithms and provide their comparison with some known algorithms.

ABSTRACT. We consider a bilevel equilibrium problems in real Hilbert spaces over the intersection of the fixed point set of demicontractive mappings. An inexact simultaneous projection method for solving the problem is introduced and its strong convergence is established under mild and standard conditions. Primary numerical experiments in finite an infinite dimensional spaces with comparisons to related results, illustrate the algorithm performances and emphasize its computational and convergence advantages.