Interval Semirings

This book has seven chapters. In chapter one we give the basics needed to make this book a self contained one. Chapter two introduces the notion of interval semigroups and interval semifields and are algebraically analysed. Chapter three introduces special types of interval semirings like matrix interval semirings and interval polynomial semirings. Chapter four for the first time introduces the notion of group interval semirings, semigroup interval semirings, loop interval semirings and groupoid interval semirings and these structures are studied. Interval neutrosophic semirings are introduced in chapter five. Applications of these structures are given in chapter six. The final chapter suggests around 120 problems for the reader.Comment: 155 pages; Published by Kappa & Omega in 201

Bounded Representations of Interval and Proper Interval Graphs

Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals L_v and R_v called bounds. We ask whether there exists a bounded representation in which each interval I_v has its left endpoint in L_v and its right endpoint in R_v. We show that the problem can be solved in linear time for interval graphs and in quadratic time for proper interval graphs. Robert's Theorem states that the classes of proper interval graphs and unit interval graphs are equal. Surprisingly the bounded representation problem is polynomially solvable for proper interval graphs and NP-complete for unit interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the proper and unit interval representations behave very differently. The bounded representation problem belongs to a wider class of restricted representation problems. These problems are generalizations of the well-understood recognition problem, and they ask whether there exists a representation of G satisfying some additional constraints. The bounded representation problems generalize many of these problems

Interval Running Exercise Reduces Running TIME of 800 Meters Dash Without Causing Increased Level of Sgot – Sgpt in Male Students of the Faculty of Sports Sciences, Manado State University

The effort to gain best achievement in sports by means of exercise has twodilemmatic sides, both for the coaches and sport promoters. On one side, exercise shouldbe done intensely and maximally, but on the other side, it is a known fact that excessiveand maximal exercises can damage the body organs. The purposes of this study were toobserve the side effects of interval running exercise of 800 meters, to find out level offatigue by examining lactate acid produced by each model, and to assess the negativeeffects on organs as indicated by the level of SGOT-SGPT. The exercise model appliedin the study comprised interval running of 2 x 800 meters, 4 x 400 meters, 8 x 200meters, 16 x 100 meters and one standard of comparison exercise, which was runningexercise of 2 x 800 meters with passive rest. This study was true experimental usingrandomized pre-test-post-test control group design. Samples of this study were 27 malestudents of the Faculty of Sports Sciences, Manado State University, who were dividedinto five groups. Group 1 was with interval running exercise of 2 x 800 meters. Group 2was assigned to interval running exercise of 4 x 400 meters. Group 3 was with intervalrunning exercise of 8 x 200 meters. Group 4 was with interval running exercise of 16 x100 meters. Group 5 as comparison standard was with running exercise of 2 x 800 meterspassive rest. All the exercise models were carried out for six weeks, each with afrequency of three times a week. Results of the study showed that the five groupsdemonstrated reduction of running time of 800 meters dash (p<0.05), lactate acidproduction differed in some of the groups (p>0.05), levels of SGOT and SGPT of allgroups did not show significant increase (p>0.05). From the above findings, it can beconcluded that all exercise models of interval running 2 x 800 meters, 4 x 400 meters, 8 x200 meters, 16 x 100 meters and 2 x 800 meters with passive rest lowered the runningtime of 800 meters dash and did not increase level of SGOT-SGPT

Interval Algebraic Bistructures

This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with the intervals of the form [0, a] where a \in Zn or Z+ \cup {0} or R+ \cup {0} or Q+ \cup {0} unless otherwise specified. Also interval bistructures of the form interval loop-group, interval groupgroupoid so on are introduced and studied. In chapter two n-interval structures are introduced. n-interval groupoids, n-interval semigroups, n-interval loops and so on are introduced and analysed. Using these notions n-interval mixed algebraic structure are defined and described. Some probable applications are discussed. Only in due course of time several applications would be evolved by researchers as per their need. The final chapter suggests around 295 problems of which some are simple exercises, some are difficult and some of them are research problems.Comment: 208 page

Interval type-2 fuzzy automata and Interval type-2 fuzzy grammar

The purpose of the present work is to introduce and study the concept of interval type-2 (IT2) fuzzy grammar which recognizes the given IT2 fuzzy languages. The relationship between IT2 fuzzy automata and IT2 fuzzy (weak) regular grammars is discussed. Specifically, the results we obtained here are (i ) IT2 fuzzy weak regular grammar and IT2 fuzzy regular grammar generate the same classes of IT2 fuzzy languages (ii ) for a given IT2 fuzzy regular grammars, there exists an IT2 fuzzy automata such that they accept the same IT2 fuzzy languages, and vice versa. In addition, we define some operations on IT2 fuzzy languages and it is shown that IT2 fuzzy languages recognized by IT2 fuzzy automata are closed under the operations of union, intersection, concatenation and Kleene closure, but are not closed under complement

Improved time-interval analysis

Several extensions of the halflife analysis method recently suggested by Horvat and Hardy are put forward. Goodness-of-fit testing is included, and the method is extended to cases where more information is available for each decay event which allows applications also for e.g. $\gamma$ decay data. The results are tested with Monte Carlo simulations and are applied to the decays of $^{64}$Cu and $^{56}$Mn.Comment: 16 pages, 3 figure

Interval estimations in metrology

This paper investigates interval estimation for a measurand that is known to be positive. Both the Neyman and Bayesian procedures are considered and the difference between the two, not always perceived, is discussed in detail. A solution is proposed to a paradox originated by the frequentist assessment of the long-run success rate of Bayesian intervals.Comment: 11 pages, 5 figures, submitted to Metrologi