A Generalization of Niho’s Theorem

In this note, we generalize Niho’s theorem on cross-correlation functions of binary m-sequences. Our theorem applies both to binary and non-binary sequences. AMS Classification: 11T24, 94A55 Research supported by the Academy of Finland, grant 200213.     

On the transitivity property

In this short note general transitivity properties of fuzzy binary relations are discussed. It is shown that under some weak conditions any fuzzy binary relation can be regarded as a transitive one with respect to a properly chosen t-norm. A representation theorem for such relations is formulated.     

The structure of solid binary algebras

A solid binary algebra in an abstract characterisation of the idempotents of a completely regular semigroup. We present here a structure theorem for solid binary algebras in terms of semilattices and rectangular bands. We also show that a free solid binary algebra can be embedded in a free completely regular semigroup; thus the word problem for the free solid binary algebra can be solved by using a solution of the word problem for the free completely regular semigroup.Presented by B. M. Schein.The author gratefully acknowledges the financial support of an Australian Postgraduate Research Award.     

Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing

Assembly line balancing generally requires a set of acceptable solutions to the several conflicting objectives. In this study, a binary fuzzy goal programming approach is applied to assembly line balancing. Models for balancing straight and U-shaped assembly lines with fuzzy goals (the number of workstations and cycle time goals) are proposed. The binary fuzzy goal programming models are solved using the methodology introduced by Chang [Chang, C.T., 2007. Binary fuzzy goal programming. European Journal of Operational Research 180 (1), 29–37]. An illustrative example is presented to demonstrate the validity of the proposed models and to compare the performance of straight and U-shaped line configurations.     

Exact and heuristic methods to solve a bi-objective problem of sustainable cultivation

Annals of Operations Research - This work proposes a binary nonlinear bi-objective optimization model for the problem of planning the sustainable cultivation of crops. The solution to the problem...     

An improved version of Lloyd's theorem

The generalisation of Lloyd's theorem to distance-transitive graphs can be improved in the case of antipodal graphs by looking at the derived graph. In the case of binary perfect codes the roots of the Lloyd polynomial are even integers. This can be applied to give a short proof of the binary perfect code theorem.     

On the integer-valued variables in the linear vertex packing problem

Given a graph with weights on vertices, the vertex packing problem consists of finding a vertex packing (i.e. a set of vertices, no two of them being adjacent) of maximum weight. A linear relaxation of one binary programming formulation of this problem has these two well-known properties: (i) every basic solution is (0, 1/2, 1)-valued, (ii) in an optimum linear solution, an integer-valued variable keeps the same value in an optimum binary solution.As an answer to an open problem from Nemhauser and Trotter, it is shown that there is a unique maximal set of variables which are integral in optimal (VLP) solutions.This research was supported by National Research Council of Canada GRANT A8528 and RD 804.     

On a free group of transformations defined by an automaton

We prove that three automorphisms of the rooted binary tree defined by a certain 3-state automaton generate a free non-Abelian group of rank 3. Both authors are supported by the NSF grants DMS-0308985 and DMS-0456185. Yaroslav Vorobets is supported by a Clay Research Scholarship.     

Profust reliability of a gracefully degradable system

Research in traditional reliability theory is based mainly on probist reliability, which uses a binary state assumption and classical reliability distributions. In the present paper the binary state assumption has been replaced by a fuzzy state assumption, thereby leading to profust reliability estimates of a powerloom plant, which is modelled as a two unit gracefully degradable system. Results of Bowles and Palaez [Application of fuzzy logic to reliability engineering, Proc. IEEE 83(3) (1995) 435–449] have been deduced as a particular case of results presented here. It is also recognized that estimation of system parameters such as failure rates, is vital in reliability estimation. Available methods for such estimation do not cover the underlying uncertainty in the failure data collection involving human judgment, evaluation and decision. In this paper we introduce a new approach based on fuzzy set theory to estimate such system parameters.     

Global Dynamics of a Multi-group SEIR Epidemic Model with Infection Age

National Natural Science Foundation of China (No. 12022113),Henry Fok Foundation for Young Teachers, China (No. 171002), Outstanding Young Talents Support Plan of Shanxi Province, Science and Engineering Research Board (SERB for short), India(No. ECR/2017/002786), UGC-BSR Research Start-Up-Grant, India (No. F.30-356/2017(BSR)), and Senior Research Fellowship from the Council of Scientific and Industrial Research (CSIR for short),India (No. 09/1131(0006)/2017-EMR-I).     

Covering radii are not matroid invariants

We show by example that the covering radius of a binary linear code is not generally determined by the Tutte polynomial of the matroid. This answers Problem 361 (P.J. Cameron (Ed.), Research problems, Discrete Math. 231 (2001) 469-478).     

On the copositive representation of binary and continuous nonconvex quadratic programs

In this paper, we model any nonconvex quadratic program having a mix of binary and continuous variables as a linear program over the dual of the cone of copositive matrices. This result can be viewed as an extension of earlier separate results, which have established the copositive representation of a small collection of NP-hard problems. A simplification, which reduces the dimension of the linear conic program, and an extension to complementarity constraints are established, and computational issues are discussed. Research partially supported by NSF Grant CCF-0545514.     

Double Basic Algebras

To any bounded lattice with section antitone bijections can be assigned an algebra with two binary, two unary and a nullary operations satisfying similar axioms as a basic algebra. Due to the doubled similarity type, this algebra is called a double basic algebra. Also conversely, every double basic algebra induces a bounded lattice equipped with antitone bijections in every section. We study properties of double basic algebras, their interval algebras and several conclusions of the so-called pseudo-commutativity. This work is supported by the Research Project MSM 6198959214 by Czech Government.     

Codes with given distances

One of the main results says that ifC is a binary linear code of length 4t and of dimension greater than 2t, thenC contains a word of weight 2t and this bound is best possible. Several results of similar flavor are established both for linear and non-linear codes. For the proof a lemma introducing the binormal forms of binary matrices is needed. The results are applied to determine the coset chromatic number of Hadamard graphs, to solve a problem of Galvin and to give a short proof of a theorem of Gleason on self-dual doubly-even codes.     

Central European journal of operations research (CJOR) “operations research applied to health services (ORAHS) in Europe: general trends and ORAHS 2020 conference in Vienna,Austria”

Central European Journal of Operations Research - This articles provides a short summary of the research topics and latest research results of the European Working Group “Operations Research...     

社会调查中二分数据的转换与解读——以《2005年中国青少年网瘾调查报告》中的数据分析为例

社会调查中常常使用尽可能简短的问卷,为此将会收集到大量的二分数据。本文讨论了产生二分数据的两种主要形式,探讨了如何在遵循统计分析程序的基本要求下,对二分变量进行转换和解读,从中挖掘出丰富而深入的信息,并以《2005年中国青少年网瘾调查报告》中的数据分析为例进行了说明。     

Ginzburg-Landau equation and motion by mean curvature, II: Development of the initial interface

In this paper, we study the short time behavior of the solutions of a sequence of Ginzburg-Landau equations indexed by ∈. We prove that under appropriate assumptions on the initial data, solutions converge to ±1 in short time and behave like the one-dimensional traveling wave across the interface. In particular, energy remains uniformly bounded in ∈. Partially supported by the NSF Grant DMS-9200801 and by the Army Research Office through the Center for Nonlinear Analysis.     

The subdirectly irreducible algebras in the variety generated by graph algebras

We show that every non-trivial subdirectly irreducible algebra in the variety generated by graph algebras is either a two-element left zero semigroup or a graph algebra itself. We characterize all the subdirectly irreducible algebras in this variety. From this we derive an example of a groupoid (graph algebra) that generates a variety with NP-complete membership problem. This is an improvement over the result of Z. Székely who constructed an algebra with similar properties in the signature of two binary operations. The second author was supported by OTKA grants no. T043671, NK67867, K67870 and by NKTH (National Office for Research and Technology, Hungary).     

Slim sets of binary trees

A classical problem in phylogenetic tree analysis is to decide whether there is a phylogenetic tree T that contains all information of a given collection P of phylogenetic trees. If the answer is “yes” we say that P is compatible and T displays P. This decision problem is NP-complete even if all input trees are quartets, that is binary trees with exactly four leaves. In this paper, we prove a sufficient condition for a set of binary phylogenetic trees to be compatible. That result is used to give a short and self-contained proof of the known characterization of quartet sets of minimal cardinality which are displayed by a unique phylogenetic tree.     

Gainfree Leontief substitution flow problems

Leontief substitution systems have been studied by economists and operations researchers for many years. We show how such linear systems are naturally viewed asLeontief substitution flow problems on directed hypergraphs, and that important solution properties follow from structural characteristics of the hypergraphs. We give a strongly polynomial, non-simplex algorithm for Leontief substitution flow problems that satisfy againfree property leading to acyclic extreme solutions. Integrality conditions follow easily from this algorithm. Another structural property,support disjoint reachability, leads to necessary and sufficient conditions for extreme solutions to be binary. In a survey of applications, we show how the Leontief flow paradigm links polyhedral combinatorics, expert systems, mixed integer model formulation, and some problems in graph optimization.Dedicated to the memory of Robert G. JeroslowSee Acknowledgement section.Research supported in part by the ONR (Office of Naval Research) under URI Grant number N00014-86-K-0689, and Center for Operations Research and Econometrics, Universite Catholique de Louvain.