scholarly journals On Relative $t$-Designs in Polynomial Association Schemes

10.37236/4889 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Eiichi Bannai ◽  
Etsuko Bannai ◽  
Sho Suda ◽  
Hajime Tanaka
Keyword(s):  
Lower Bounds ◽  
Association Scheme ◽  
Point Of View ◽  
Association Schemes ◽  
Algebraic Characterization ◽  
Terwilliger Algebra ◽  
C Algebra ◽  
Irreducible Modules

Motivated by the similarities between the theory of spherical $t$-designs and that of $t$-designs in $Q$-polynomial association schemes, we study two versions of relative $t$-designs, the counterparts of Euclidean $t$-designs for $P$- and/or $Q$-polynomial association schemes. We develop the theory based on the Terwilliger algebra, which is a noncommutative associative semisimple $\mathbb{C}$-algebra associated with each vertex of an association scheme. We compute explicitly the Fisher type lower bounds on the sizes of relative $t$-designs, assuming that certain irreducible modules behave nicely. The two versions of relative $t$-designs turn out to be equivalent in the case of the Hamming schemes. From this point of view, we establish a new algebraic characterization of the Hamming schemes.

scholarly journals Butson-type complex Hadamard matrices and association schemes on Galois rings of characteristic 4

2018 ◽  
Vol 6 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Takuya Ikuta ◽  
Akihiro Munemasa
Keyword(s):  
Association Scheme ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Association Schemes ◽  
Roots Of Unity ◽  
Galois Rings ◽  
Type Complex ◽  
Complex Hadamard Matrix

Abstract We consider nonsymmetric hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of commutative nonsymmetric association schemes. First, we give a characterization of the eigenmatrix of a commutative nonsymmetric association scheme of class 3 whose Bose-Mesner algebra contains a nonsymmetric hermitian complex Hadamard matrix, and show that such a complex Hadamard matrix is necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.We also give nonsymmetric association schemes X of class 6 on Galois rings of characteristic 4, and classify hermitian complex Hadamard matrices belonging to the Bose-Mesner algebra of X. It is shown that such a matrix is again necessarily a Butson-type complex Hadamard matrix whose entries are 4-th roots of unity.

scholarly journals On the Connectivity of Graphs in Association Schemes

10.37236/6820 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Brian G. Kodalen ◽  
William J. Martin
Keyword(s):  
Lower Bounds ◽  
Connected Graph ◽  
Association Scheme ◽  
Undirected Graph ◽  
Association Schemes ◽  
Vertex Connectivity ◽  
Edge Connectivity

Let $(X,\mathcal{R})$ be a commutative association scheme and let $\Gamma=(X,R\cup R^\top)$ be a connected undirected  graph where $R\in \mathcal{R}$. Godsil (resp., Brouwer) conjectured that the edge connectivity (resp., vertex connectivity) of $\Gamma$ is equal to its valency. In this paper, we prove that the deletion of the neighborhood of any vertex leaves behind at most one non-singleton component. Two vertices $a,b\in X$  are called "twins" in $\Gamma$ if they have identical neighborhoods: $\Gamma(a)=\Gamma(b)$. We characterize twins in polynomial association schemes and show that, in the absence of twins, the deletion of any vertex and its neighbors in $\Gamma$ results in a connected graph. Using this and other tools, we find lower bounds on the connectivity of $\Gamma$, especially in the case where $\Gamma$ has diameter two.

scholarly journals A symbolic projection of Langton's Ant

2003 ◽  
Vol DMTCS Proceedings vol. AB,... (Proceedings) ◽  
Author(s):  
Anahi Gajardo
Keyword(s):  
Point Of View ◽  
Algebraic Characterization ◽  
Transition Rule ◽  
Regular Graphs ◽  
New Approach ◽  
The Family ◽  
International Audience ◽  
Topological Dynamical Systems

International audience The Langton's ant is studied from the point of view of topological dynamical systems. A new approach which associate a subshift to the system is proposed.The transition rule is generalized to the family of bi-regular graphs $\Gamma(k,d)$ and the dependence of the dynamical system on $k$ and $d$ is analyzed. A classification of the $\Gamma (k,d)$ graphs based on the dynamical properties of the subshift is established. Also a hierarchy is defined on the graphs through the subset relation of the respective subshifts. The analysis are worked out by establishing an algebraic characterization of the forbidden words of the subshift.

The Analyses of Learning Strategies in English as a Second Language: Theoretical Classification and Measurement Test

2020 ◽  
Vol 4 (2) ◽  
pp. 118-129
Author(s):  
Asti Gumartifa ◽  
◽  
Indah Windra Dwie Agustiani
Keyword(s):  
Language Learning ◽  
Learning Outcomes ◽  
Learning Strategies ◽  
Learning Process ◽  
English Learners ◽  
English Language ◽  
Point Of View ◽  
Effective Learning ◽  
The Impact

Gaining English language learning effectively has been discussed all years long. Similarly, Learners have various troubles outcomes in the learning process. Creating a joyful and comfortable situation must be considered by learners. Thus, the implementation of effective learning strategies is certainly necessary for English learners. This descriptive study has two purposes: first, to introduce the classification and characterization of learning strategies such as; memory, cognitive, metacognitive, compensation, social, and affective strategies that are used by learners in the classroom and second, it provides some questionnaires item based on Strategy of Inventory for Language Learning (SILL) version 5.0 that can be used to examine the frequency of students’ learning strategies in the learning process. The summary of this study explains and discusses the researchers’ point of view on the impact of learning outcomes by learning strategies used. Finally, utilizing appropriate learning strategies are certainly beneficial for both teachers and learners to achieve the learning target effectively.

The Algorithm of Characterization of an Action as a Jointly Committed Crime

2018 ◽  
pp. 37-44
Keyword(s):  
Criminal Code ◽  
Point Of View

The article discusses a sequence of activities to identify a crime as jointly committed. The requirements to the algorithm of such activities are formulated. Programme-based and targeted methods applied by the authors allowed detecting a range of stages of the algorithm. The first four stages aim at defining mandatory elements of a crime allowing to characterize it as a jointly committed action. The rest of the stages focus on identifying a type of criminal complicity. In the article, each stage is described. It is emphasized that in each stage there is a special objective. At the same time, all these stages, taken together, constitute a separate module of the program of criminal characterization of an action. From the authors’ point of view, algorithms are necessary not only for detection of crimes and their criminal characterization, but also for answering the question on existence of criminal complicity in each case. Also the authors give their opinions on interpretation of criminal complicity as a legal category. In particular, it is emphasized that not all of crimes merely committed with participation of two or more persons should be understood as jointly committed. It is joint participation that makes a crime jointly committed. Various forms of criminal complicity and types of co-offenders are considered in the article as well. In various crimes, criminal complicity manifests itself differently. Therefore the proposed algorithm can be applied only after identification a specific article of the Russian Criminal Code stipulating the responsibility for the crime committed.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

scholarly journals Processing Effect and Characterization of Olive Oils from Spanish Wild Olive Trees (Olea europaea var. sylvestris)

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1304
Author(s):  
Francisco Espínola ◽  
Alfonso M. Vidal ◽  
Juan M. Espínola ◽  
Manuel Moya
Keyword(s):  
Phenolic Compounds ◽  
Volatile Compounds ◽  
Olive Tree ◽  
Extraction Yield ◽  
Point Of View ◽  
Human Consumption ◽  
Analytical Point ◽  
Wild Olive ◽  
Olive Trees

Wild olive trees have important potential, but, to date, the oil from wild olives has not been studied significantly, especially from an analytical point of view. In Spain, the wild olive tree is called “Acebuche” and its fruit “Acebuchina”. The objective of this work is to optimize the olive oil production process from the Acebuchina cultivar and characterize the oil, which could be marketed as healthy and functional food. A Box–Behnken experimental design with five central points was used, along with the Response Surface Methodology to obtain a mathematical experimental model. The oils from the Acebuchina cultivar meet the requirements for human consumption and have a good balance of fatty acids. In addition, the oils are rich in antioxidants and volatile compounds. The highest extraction yield, 12.0 g oil/100 g paste, was obtained at 90.0 min and the highest yield of phenolic compounds, 870.0 mg/kg, was achieved at 40.0 °C, and 90.0 min; but the maximum content of volatile compounds, 26.9 mg/kg, was obtained at 20 °C and 30.0 min. The oil yield is lower than that of commercial cultivars, but the contents of volatile and phenolic compounds is higher.

scholarly journals Characterization of Dissipative Structures for First-Order Symmetric Hyperbolic System with General Relaxation

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 728
Author(s):  
Yasunori Maekawa ◽  
Yoshihiro Ueda
Keyword(s):  
Hyperbolic System ◽  
Dissipative Structure ◽  
Dissipative Structures ◽  
Algebraic Characterization ◽  
Symmetric Hyperbolic System ◽  
Full Generality ◽  
Order Linear ◽  
First Order

In this paper, we study the dissipative structure of first-order linear symmetric hyperbolic system with general relaxation and provide the algebraic characterization for the uniform dissipativity up to order 1. Our result extends the classical Shizuta–Kawashima condition for the case of symmetric relaxation, with a full generality and optimality.

scholarly journals Grounding semantic transparency in context

Morphology ◽  
2021 ◽  
Author(s):  
Rossella Varvara ◽  
Gabriella Lapesa ◽  
Sebastian Padó
Keyword(s):  
Large Scale ◽  
Point Of View ◽  
Distributional Semantics ◽  
Semantic Transparency ◽  
Inclusion Measure ◽  
The Difference ◽  
Semantic Point ◽  
The Many ◽  
The Relationship

AbstractWe present the results of a large-scale corpus-based comparison of two German event nominalization patterns: deverbal nouns in -ung (e.g., die Evaluierung, ‘the evaluation’) and nominal infinitives (e.g., das Evaluieren, ‘the evaluating’). Among the many available event nominalization patterns for German, we selected these two because they are both highly productive and challenging from the semantic point of view. Both patterns are known to keep a tight relation with the event denoted by the base verb, but with different nuances. Our study targets a better understanding of the differences in their semantic import.The key notion of our comparison is that of semantic transparency, and we propose a usage-based characterization of the relationship between derived nominals and their bases. Using methods from distributional semantics, we bring to bear two concrete measures of transparency which highlight different nuances: the first one, cosine, detects nominalizations which are semantically similar to their bases; the second one, distributional inclusion, detects nominalizations which are used in a subset of the contexts of the base verb. We find that only the inclusion measure helps in characterizing the difference between the two types of nominalizations, in relation with the traditionally considered variable of relative frequency (Hay, 2001). Finally, the distributional analysis allows us to frame our comparison in the broader coordinates of the inflection vs. derivation cline.

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