This paper revisits a combinatorial structure called the large set of ordered design (LOD). Among others, we introduce a novel structure called Latin matching and prove that a Latin matching of order ...n leads to an LOD(n−1,n,2n−1); thus, we obtain constructions for LOD(1,2,3), LOD(2,3,5), and LOD(4,5,9). Moreover, we show that constructing a Latin matching of order n is at least as hard as constructing a Steiner system S(n−2,n−1,2n−2); therefore, the order of a Latin matching must be prime. We also show some applications in multiagent systems.
Numerical Semigroups García-Sánchez, P. A; Rosales, J. C
2010, 2009, 20090821, 2009-09-01, Volume:
20
eBook
Open access
"This monograph is the first devoted exclusively to the development of the theory of numerical semigroups. In this concise, self-contained text, graduate students and researchers will benefit from ...this broad exposition of the topic. Key features of ""Numerical Semigroups"" include: - Content ranging from the basics to open research problems and the latest advances in the field, - Exercises at the end of each chapter that expand upon and support the material, - Emphasis on the computational aspects of the theory, algorithms are presented to provide effective calculations, - Many examples that illustrate the concepts and algorithms, - Presentation of various connections between numerical semigroups and number theory, coding theory, algebraic geometry, linear programming, and commutative algebra would be of significant interest to researchers."
Full text
Available for:
FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
3.
Classes of Finite Groups Ballester-Bolinches, Adolfo; Ezquerro, Luis M
2006, 2006-06-01, Volume:
584
eBook
Many group theorists all over the world have been trying in the last twenty-five years to extend and adapt the magnificent methods of the Theory of Finite Soluble Groups to the more ambitious ...universe of all finite groups. This is a natural progression after the classification of finite simple groups but the achievements in this area are scattered in various papers. Our objectives in this book were to gather, order and examine all this material, including the latest advances made, give a new approach to some classic topics, shed light on some fundamental facts that still remain unpublished and present some new subjects of research in the theory of classes of finite, not necessarily solvable, groups.
Full text
Available for:
FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
. We present an identification of the spectra of local conserved operators of integrable quantum lattice models and the density distributions of their thermodynamic particle content. This is derived ...explicitly for the Heisenberg XXZ spin chain. As an application we discuss a quantum quench scenario, in both the gapped and critical regimes. We outline an exact technique which allows for an efficient implementation on periodic matrix product states. In addition, for certain simple product states we obtain closed-form expressions for the density distributions in terms of solutions to Hirota difference equations. Remarkably, no reference to a maximal entropy principle is invoked.
We study systems of equations over graphs, posets and matroids. We give the criteria when a direct power of such algebraic structures is equationally Noetherian. Moreover, we prove that any direct ...power of any finite algebraic structure is weakly equationally Noetherian.
•A collective degree of consensus for group decision making with HFLTSs is defined.•An individual degree of consensus for group decision making with HFLTSs is defined.•These degrees explicitly take ...into account how far non-overlapping assessments are.•A comparison study with existing measures is presented.•A precision-dissension profile for each decision maker is presented.
Display omitted
Present measures of the degree of agreement in group decision-making using hesitant fuzzy linguistic term sets allow consensus or agreement measurement when decision makers’ assessments involve hesitance. Yet they do not discriminate with different degrees of consensus among situations with discordant or polarized assessments. The visualization of differences among groups for which there is no agreement but different possible levels of disagreement is an important issue in collective decision-making situations. In this paper, we propose new collective and individual consensus measures that explicitly consider the hesitance of the decision makers’ hesitance in giving an opinion and also the gap between non-overlapping assessments, thus allowing the measurement of the polarization present within the group’s opinions. In addition, an expert’s profile is defined by considering the expert’s behavior in previous assessments in group decision-making processes in terms of precision and dissension.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
We consider quantum quenches in the integrable -invariant spin chain (Lai-Sutherland model) which admits a Bethe ansatz description in terms of two different quasiparticle species, providing a ...prototypical example of a model solvable by nested Bethe ansatz. We identify infinite families of integrable initial states for which analytic results can be obtained. We show that they include special families of two-site product states which can be related to integrable 'soliton non-preserving' boundary conditions in an appropriate rotated channel. We present a complete analytical result for the quasiparticle rapidity distribution functions corresponding to the stationary state reached at large times after the quench from the integrable initial states. Our results are obtained within a quantum transfer matrix (QTM) approach, which does not rely on the knowledge of the quasilocal conservation laws or of the overlaps between the initial states and the eigenstates of the Hamiltonian. Furthermore, based on an analogy with previous works, we conjecture analytic expressions for such overlaps: this allows us to employ the quench action method to derive a set of integral equations characterizing the quasi-particle distribution functions of the post-quench steady state. We verify that the solution to the latter coincides with our analytic result found using the QTM approach. Finally, we present a direct physical application of our results by providing predictions for the propagation of entanglement after the quench from such integrable states.
•We develop a mathematical framework that allows for the definition of interval principal component analysis.•Interval-valued principal components are defined as linear combinations of the original ...interval-valued variables of maximum symbolic variance.•The projection of the original symbolic observations on the reduced space spanned by the first principal components allows for the use of interval principal component analysis as a dimensionality reduction method.•We develop an outlier-detection method based on the first interval-valued principal components.•We explore real world data from the telecommunications sector, to detect Internet redirection attacks.
Principal Component Analysis is a well-known method that can be used for dimensionality reduction, a useful technique in the Big Data era. There have been a series of proposed adaptations of the Principal Component Analysis method for interval-valued symbolic data, all of which have the downside of having intermediate steps that deal with conventional data. In this work, we put forward an interval Principal Component Analysis that only deals with symbolic data by developing a theoretical framework that allows for the definition of symbolic principal components. This framework provides the mathematical tools needed to use the symbolic principal components to transform the original data in a way that is mathematically coherent with the remainder of the framework and defines the principal components as solutions to maximisation problems, similarly to what is done in conventional Principal Component Analysis. After the theoretical foundations are laid down, we explore real-world data from the telecommunications sector, in an attempt to detect Internet redirection attacks in real-time. In particular, we use our symbolic method to improve and simplify an anomaly detection method that has been proposed in the literature for conventional data.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
PDF
