We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and minimal trees for the difference of remoteness and radius proving thus that the corresponding conjectures posed in [4] hold for trees.

Abstract This paper presents an approach to the development of condition-based maintenance of aircraft to improve aircraft maintenance in the limits and conditions of small countries and in accordance with global technological achievements. For the aircraft that were under a limited lifespan maintenance concept, a new condition-based maintenance model is developed. This model applies a technical diagnostic method that brought us to decreasing numbers of failures in the ageing period of those technical systems and at the same time decreases the time when it is out of use and lowers maintenance expenses. An analysis based on this model showed its applicability, preservation of operational readiness, and potential for decreasing the cost of aircraft maintenance.

Power system is a complex, dynamic system, composed of a large number of interrelated elements. Its primary mission is to provide a safe and reliable production, transmission and distribution of electrical energy to final consumers, extending over a large geographic area. It comprises of a large number of individual elements which jointly constitute a unique and highly complex dynamic system. Some elements are merely the system's components while others affect the whole system (Machowski, 1997). Securing necessary level of safety is of great importance for economic and reliable operation of modern electric power systems.

Objective. To describe the intrahepatic bile duct transposition (anatomical variation occurring in intrahepatic ducts) and to determine the frequency of this variation. Material and Methods. The researches were performed randomly on 100 livers of adults, both sexes. Main research methods were anatomical macrodissection. As a criterion for determination of variations in some parts of bile tree, we used the classification of Segmentatio hepatis according to Couinaud (1957) according to Terminologia Anatomica, Thieme Stuugart: Federative Committee on Anatomical Terminology, 1988. Results. Intrahepatic transposition of bile ducts was found in two cases (2%), out of total examined cases (100): right-left transposition (right segmental bile duct, originating from the segment VIII, joins the left liver duct-ductus hepaticus sinister) and left-right intrahepatic transposition (left segmental bile duct originating from the segment IV ends in right liver duct-ductus hepaticus dexter). Conclusion. Safety and success in liver transplantation to great extent depends on knowledge of anatomy and some common embryological anomalies in bile tree. Variations in bile tree were found in 24–43% of cases, out of which 1–22% are the variations of intrahepatic bile ducts. Therefore, good knowledge on ductal anatomy enables good planning, safe performance of therapeutic and operative procedures, and decreases the risk of intraoperative and postoperative complications.

We list scalar leptoquarks that mediate proton decay via renormalizable couplings to the Standard Model fermions. We employ a general basis of baryon number violating operators to parameterize contributions of each leptoquark towards proton decay. This then sets the stage for investigation of bounds on the leptoquark couplings to fermions with respect to the most current Super Kamiokande results on proton stability. We quantify if, and when, it is necessary to have leptoquark masses close to a scale of grand unification in the realistic SU(5) and flipped SU(5) frameworks. The most and the least conservative lower bounds on the leptoquark masses are then presented. We furthermore single out a leptoquark without phenomenologically dangerous tree-level exchanges that might explain discrepancy of the forward-backward asymmetries in $t \bar t$ production observed at Tevatron, if relatively light. The same state could also play significant role in explaining muon anomalous magnetic moment. We identify contributions of this leptoquark to dimension-six operators, mediated through a box diagram, and tree-level dimension-nine operators, that would destabilize proton if sizable leptoquark and diquark couplings were to be simultaneously present.

Development of a civil society and social systems for protection of different groups is directly related to well functioning political and economic systems. If the level of economic development or political stability is not continuous the implementation of antidiscrimination laws would most likely be at a very low level. In this case development of social rights along with implementation of antidiscrimination rights may be marginalized due to three factors: lack of cooperation among political and economic spheres, lack of knowledge about antidiscrimination laws and absence of political will for adoption and implementation of antidiscrimination laws. Therefore, we focus on the examination of specific issues concerning the three aforementioned factors primarily focusing on EU and divergence in the level of political and economic development among the member states.We will argue that antidiscrimination laws are not welcome in new member states, especially since they increase political and economic costs for the governments of respective countries. Level of political development has much to do with the acceptance and inclusion of AD laws in the decision making process. Economic development has much to do with social and living standards within a country which is directly related to the general perception of the population on AD laws. Therefore, one could say that implementation of AD laws heavily depends on the preparedness of people, economic and political system and their will to cope with costs and benefits of implementing those laws