ON NECESSARY CONDITIONS FOR EFFICIENCY IN DIRECTIONALLY DIFFERENTIABLE OPTIMIZATION PROBLEMS

This paper deals with multiobjective programming problems with in- equality, equality and set constraints involving Dini or Hadamard differentiable func- tions. A theorem of the alternative of Tucker type is established, and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Theorem of the alternative, Kuhn-Tucker necessary conditions, direc- tionally differentiable functions.

On alternative theorems and necessary conditions for efficiency

In this paper, we establish theorems of the alternative for a system described by inequalities, equalities and an inclusion, which are generalizations of Tucker's classical theorem of the alternative, and develop Kuhn-Tucker necessary conditions for efficiency to mathematical programs in normed spaces involving inequality, equality and set constraints with positive Lagrange multipliers of all the components of objective functions.Theorem of the alternative, Kuhn-Tucker necessary condition, constraint qualification.

On constraint qualifications with generalized convexity and optimality conditions

This paper deals with a multiobjective programming problem involving both equality constraints in infinite dimensional spaces. It is shown that some constraint qualifications together with a condition of interior points are sufficient conditions for the invexity of constraint maps with respect to the same scale map. Under a new constraint qualification which involves an invexity condition and a generalized Slater condition a Kuhn-Tucker necessary condition is established.Invexity, scale, constraint qualification, nearly S-convelike mapping.

On necessary conditions for efficiency in directionally differentiable optimization problems

This paper deals with multiobjective programming problems with inequality, equality and set constraints involving Dini or Hadamard differentiable functions. A theorem of the alternative of Tucker type is established and from which Kuhn-Tucker necessary conditions for local Pareto minima with positive Lagrange multipliers associated with all the components of objective functions are derived.Directionally differentiable functions, Kunh-Tucker necessary conditions, Lagrange multipliers, theorem of the alternative.

Contextual factors affecting the development of digital library education in Vietnam

In Vietnam the need for digital library education (DLE) has increased significantly in the last two decades. Educating staff to establish and manage digital libraries has become a critical issue. However, there are no DLE programmes offered by library and information management (LIM) education providers in Vietnam and we do not know why this is the case. The aim of this study is to investigate and understand the factors affecting the development of DLE for LIM practitioners in Vietnam. The interpretive study employed a qualitative approach and its findings are based on the analysis of data gathered in 17 individual interviews and 11 focus groups with key stakeholders, as well as from documentary evidence. The stakeholders involved in this study include LIM practitioners, LIM managers, LIM lecturers, library school deans, government policy makers, academic library directors, professional association chairpersons and LIM students. To guide the data gathering and analysis, an initial conceptual model of factors affecting DLE was developed from three sources: Fullan’s Educational Change theory, Nowlen’s Performance Model in continuing education for practitioners, and Rogers’s Diffusion of Innovations theory. The study found seven major factors were affecting the development of DLE in Vietnam: the government, the information technology infrastructure, the prevailing social and cultural values, the efforts of change agents, the attitudes of key stakeholders, the characteristics of DLE design, and the nexus of the educational needs of library staff and the libraries in which they were working. Of these the government factor was the most influential. These factors were inter-related and affected DLE development at different levels. The initial conceptual model was revised based on the study's findings. The revised model provides a contribution to educational change theories relevant to the identification and understanding of factors affecting professional educational programmes in universities in developing countries. The study’s findings are also of value to governments, libraries, library schools and library associations for developing relevant policies and new curricula for DLE, and for establishing new professional development programmes in DLE for library staff

CHARACTERISTICS OF 7th GRADERS IN THAI NGUYEN CITY (VIETNAM) FROM THE PERSPECTIVE OF DIFFERENTIAL LEARNERS IN PHYSICAL EDUCATION ACTIVITIES

Differentiated-oriented physical education (PE) helps learners to participate in learning activities with content and form suitable to their individual characteristics. Capturing the individual characteristics of learners is of great significance in the process of physical education. Through document research, interviews, pedagogical observations and examination, the research assesses the characteristics of 7th graders in Thai Nguyen City from the perspective of differential learners in Physical Education. This is an important basis for organizing physical education activities in the direction of differentiation for 7th graders in Thai Nguyen City.  Article visualizations

CDIO-based teaching at universities: A case study for students majoring in electrical and electronic engineering technology, Vietnam

In the 1980s of the twentieth century, universities in developed countries began to realize the growing gap between the capabilities of new graduate engineers and the actual requirements of engineering branches. The strong progress of technology requires engineers to have the intellectual abilities and necessary job-specific skills to master that progress. This paper focuses on Conceive, Design, Implement and Operate (CDIO) approach-based teaching for students majoring in electrical and electronic engineering technology at engineering universities in Vietnam to demonstrate the feasibility of the teaching model. The experimental method of synthesizing qualitative and quantitative results for 90 students in control and experimental classes was used. The experimental and control classes both had 45 students. SPSS software version 22 was used to gather data and evaluate the learning results of the two experimental and control groups. According to the findings of the T-test analysis of the independent variables for the two groups, the experimental class performed better in academics and had students in the experimental group who were more satisfied with their post-test scores. This result contributes to confirm that the use of the CDIO-based teaching model in Vietnam is effective for students majoring in electrical and electronic engineering technology