36,423 research outputs found

    A cross-intersection theorem for subsets of a set

    Full text link
    Two families A\mathcal{A} and B\mathcal{B} of sets are said to be cross-intersecting if each member of A\mathcal{A} intersects each member of B\mathcal{B}. For any two integers nn and kk with 0kn0 \leq k \leq n, let ([n]k){[n] \choose \leq k} denote the family of all subsets of {1,,n}\{1, \dots, n\} of size at most kk. We show that if A([m]r)\mathcal{A} \subseteq {[m] \choose \leq r}, B([n]s)\mathcal{B} \subseteq {[n] \choose \leq s}, and A\mathcal{A} and B\mathcal{B} are cross-intersecting, then ABi=0r(m1i1)j=0s(n1j1),|\mathcal{A}||\mathcal{B}| \leq \sum_{i=0}^r {m-1 \choose i-1} \sum_{j=0}^s {n-1 \choose j-1}, and equality holds if A={A([m]r) ⁣:1A}\mathcal{A} = \{A \in {[m] \choose \leq r} \colon 1 \in A\} and B={B([n]s) ⁣:1B}\mathcal{B} = \{B \in {[n] \choose \leq s} \colon 1 \in B\}. Also, we generalise this to any number of such cross-intersecting families.Comment: 12 pages, submitted. arXiv admin note: text overlap with arXiv:1212.695

    Factors determining career choice

    Get PDF
    The answers that people provide to these questions: why do people work? why do they decide on the fields which they choose? and what factors affect their decision? are very important to career planning and subsequent satisfaction during the adult years. After all, work affects most persons between the ages of 16 and 61, and the decisions adolescents make about their work, occupations, and careers will significantly affect their future social relationships and leisure-time activities. It is evident then that work is a major part of human experience. Many young people appear to sense that it is through work that they must ultimately validate their adult status and acquire a measure of power and self- determination. Work is so central to most of people's daily existence that their entire outlook is affected by it. In essence, a vocational decision implies a lifestyle decision. For choice of career is not an event which can be located at one point in time. It is a process which stretches back into childhood where basic personality characteristics begin to be formed {Stephens, 1970; Gothard, 1985 ). In making a choice, the individual will seek a career which s/he sees as desirable, as one in which s/he will have the best chance of realising the various needs, hopes and expectations which at the moment of choice s/he believes to be important.peer-reviewe

    Conducting critique : reconsidering Foucault’s engagement with the question of the subject

    Get PDF
    A common criticism of Michel Foucault’s works is that his writings on power relations over-emphasized the effects that technologies of power have upon the subjection of humans, rendering any attempt of resistance futile and reducing the subject to a mere passive effect of power. This criticism treats Foucault’s consideration of ethics in his later works as a break from his earlier views. In this paper, by reading Foucault’s books alongside his lectures and interviews, two ways will be proposed through which the question of the subject can be productively raised and located throughout Foucault’s works, even within his concerns with power relations. The first way is through the relation between assujettisement and critique, and the second way is through the notions of government and conduct.peer-reviewe

    Media education in church schools in Malta

    Get PDF
    During a discussion I had with a class of 15 year old girls about the use they make of t.v. I found that in spite of the fact that they were preparing for the G.C.E. examination they watch approximately an average of 2.5 hours a day. (This is a bit lower than the national average which according to a study made by GALLUP LTD. in 1984 is 2.64 hours daily.) This amounts to 38 days a year. We tried to compare this with the time students spend at school. They have 175 school days a year with 5 hours every day which gives a total of 36 days a year. Both the school administrators and the students were greatly surprised with the result. This little incident helped me a lot in my meetings with different heads of schools while discussing with them the need of introducing media education in their schools.peer-reviewe

    Developing a theme in social studies : an alternative approach

    Get PDF
    The Council of Europe in its documents on the place of History in Secondary schools, states that 'the teacher who stands in front of the class with a chalk is almost soundly condemned as the teacher who uses the stick'. The statement, directed to teachers who still insist on boring their students by chalking and talking, leaves no room for interpretation. It is direct and clear, emphasizing that: beyond the world of soar throats and chalky air there is a wealth of resources that can inject interest and curiosity, make possible variation of teaching methods, provide stimuli for the fantasy world of students, acquaint students with research techniques, make it easier for students to pursue self-instruction, show the relation of previously isolated facts, relate abstract generalisations with realistic details and, above all, add clarity and precision to the way the lesson is presented.peer-reviewe
    corecore