with 1 < n1 | … | nr be a finite abelian group, d*(G) = n1 +…+nr −r, and let d(G) denote the maximal length of a zerosum free sequence over G. Then d(G) ≥ d*(G), and the standing conjecture is that equality holds for G = Cnr. We show that equality does not hold for C2 ⊕ C2nr, where n ≥ 3 is odd and r ≥ 4. This gives new information on the structure of extremal zero-sum free sequences over C2nr.
Summary For a finite abelian group G, we investigate the invariant s(G) (resp. the invariant s0(G)) which is defined as the smallest integer l ? N such that every sequence S in G of length |S| = l has a subsequence T with sum zero and length |T|= exp(G) (resp. length |T|=0 mod exp(G)).
The paper gives a brief account of von Neumann's contribution to the foundation of game theory: definition of abstract games, the minimax theorem for two-person zero-sum games and the stable set solution for cooperative games with side payments. The presentation is self-contained, uses very little mathematical formalism and caters to the nonspecialist. Basic concepts and their implications are in focus. It is also indicated how von Neumann's groundbreaking work initiated further research, and a few unsolved problems are also mentioned.
Tanulmányunkban feltártuk a sportolási szokások és a tanulmányi eredményesség egy
fontos mutatójának, a tanulmányok melletti kitartás (perzisztencia) közötti
összefüggéseket magyarországi és romániai (partiumi) felsőoktatási intézmények
hallgatóinak körében (N = 2619). Megvizsgáltuk a sportolási
szokások és intézményi formák szerint elkülönülő hallgatói csoportok közötti
különbségeket a perzisztencia egyes állításaiban és összemutatójában. A kutatás
elméleti hátteréhez a fejlődési modell, a zero-sum és a hallgatói integrációs
modell elméleteket használtuk fel. Eredményeink szerint a fejlődés modell
elmélet a leggyakrabban sportolók kiemelkedő eredményeiben látszik érvényesülni,
de fontos kiemelni, hogy a legnagyobb szerepe az alkalmi, társak kedvéért
sportoló hallgatók közé tartozásnak van. Az egyetemi sportklubban sportolók a
legkevésbé elszántak a tanulmányaik befejezését illetően, miközben a nem
sportkörtagok érték el a legmagasabb pontszámokat.
This paper focuses on the principle of proportionality as a unique technique used in arguing judicial decisions dealing with fundamental rights disputes. I will contest that the principle of proportionality offers fixed steps of examination and makes the thought process of the court transparent. With this approach, conflicts of fundamental rights cannot be handled as zero-sum games, but as disputes in which it is possible to find a fair balance. Furthermore, the principle of proportionality offers a plausible method of controlling the quality of judicial decisions. The function of the principle of proportionality can be identified from different perspectives. Its formal function is to promote a valid and proper judgment. However, after closer examination one can argue that the formal function of the method is to support (a) the justifiability of the decision, (b) the correctness of the legal interpretation, and (c) the transparency of the arguments used. Besides, there are convincing arguments that the principle of proportionality has also an important substantive function in (a) offering more effective protection for human rights, (b) deepening the values of the rule of law, and (c) strengthening the democratic character of the decision-making process by the verifiability of the judicial argumentation.
The paper is concerned with the problem of financing of complex research programs. One of tasks to be solved consists in assigning research teams, willing to participate in a given program, to research projects being its elements, under conditions of constrained budget. It is assumed that the strategy of every research team head is to maximize the average time-discounted income per person. In the previous paper of the authors a special negotiation procedure has been proposed to solve this problem. This paper presents some possible extensions and modifications of the procedure. At each stage of this procedure the heads of research teams involved have to make decisions on the assignment of their workers to particular projects. The proposed system of interactions among the research teams heads provides a possibility of reaching the consensus in the matter of this assignment. Simultaneously, it makes possible to solve the problem of research funds allocation. Such a system is considered as a multiperson game of Nash type with the non-zero sum of the players payments.
flow of knowledge and skilled labour towards the geographical agglomeration of activities. In reality, competitiveness does not mean zero-sum competition between nations ( WEF 2019 ). The WEF concept is a system for assessing and ranking the