scholarly journals Aperiodic Two-Dimensional Words of Small Abelian Complexity

10.37236/8580 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Svetlana Puzynina
Keyword(s):  
The Other ◽  
Two Dimensional ◽  
Other Hand ◽  
Recurrent Word

In this paper we prove an abelian analog of the famous Nivat's conjecture linking complexity and periodicity for two-dimensional words: We show that if a two-dimensional recurrent word contains at most two abelian factors for each pair $(n,m)$ of integers, then it has a periodicity vector. Moreover, we show that a two-dimensional aperiodic recurrent word must have more than two abelian factors infinitely often. On the other hand, there exist aperiodic recurrent words with abelian complexity bounded by $3$, as well as aperiodic words having abelian complexity $1$ for some pairs $(m,n)$.

Polymorphs of phenazine hexacyanoferrate(II) hydrate: supramolecular isomerism in a 2D hydrogen-bonded network

2021 ◽  
Vol 77 (2) ◽  
pp. 211-218
Author(s):  
Ivica Cvrtila ◽  
Vladimir Stilinović
Keyword(s):  
Hydrogen Bonding ◽  
Hydrogen Bonds ◽  
Crystal Structures ◽  
The Other ◽  
Two Dimensional ◽  
Structural Motifs ◽  
Supramolecular Isomerism ◽  
Other Hand ◽  
Π Stacking ◽  
Hydrogen Bonded

The crystal structures of two polymorphs of a phenazine hexacyanoferrate(II) salt/cocrystal, with the formula (Hphen)3[H2Fe(CN)6][H3Fe(CN)6]·2(phen)·2H2O, are reported. The polymorphs are comprised of (Hphen)2[H2Fe(CN)6] trimers and (Hphen)[(phen)2(H2O)2][H3Fe(CN)6] hexamers connected into two-dimensional (2D) hydrogen-bonded networks through strong hydrogen bonds between the [H2Fe(CN)6]2− and [H3Fe(CN)6]− anions. The layers are further connected by hydrogen bonds, as well as through π–π stacking of phenazine moieties. Aside from the identical 2D hydrogen-bonded networks, the two polymorphs share phenazine stacks comprising both protonated and neutral phenazine molecules. On the other hand, the polymorphs differ in the conformation, placement and orientation of the hydrogen-bonded trimers and hexamers within the hydrogen-bonded networks, which leads to different packing of the hydrogen-bonded layers, as well as to different hydrogen bonding between the layers. Thus, aside from an exceptional number of symmetry-independent units (nine in total), these two polymorphs show how robust structural motifs, such as charge-assisted hydrogen bonding or π-stacking, allow for different arrangements of the supramolecular units, resulting in polymorphism.

On Wake-Induced Flutter of a Circular Conductor in the Wake of Another

1980 ◽  
Vol 102 (2) ◽  
pp. 125-137 ◽  
Author(s):  
Y. T. Tsui ◽  
C. C. Tsui
Keyword(s):  
Transmission Line ◽  
Coupling Coefficient ◽  
Frequency Ratio ◽  
Horizontal Axis ◽  
The Other ◽  
Two Dimensional ◽  
Coupling Ratio ◽  
Aeroelastic Stability ◽  
Other Hand ◽  
The Stability

This paper, which is an extension of [1], treats two-dimensional aeroelastic stability of two coupled conductors. It is found that the wake-induced flutter is symmetric with respect to the horizontal axis of the wake for all cases provided that the sign of the static coupling coefficient, ε = kxy/kxx, is changed. It appears that the spacer coupling ratio, K/kxx = Ω/ωx, is the most important factor in determining stability. For practical purposes, the system is almost always stable for K/kxx = Ω/ωx = 0.8, because the frequency ratio, κ = ωy/ωx, deviates less than ten percent from unity for a typical transmission line. On the other hand, within our range of interest, damping has little or no effect on the stability of coupled conductors. When the windward conductor is fixed, i.e., K = 0, then damping does influence the stability of the leeward conductor.

CONTEXT-SENSITIVITY OF TWO-DIMENSIONAL REGULAR ARRAY GRAMMARS

1989 ◽  
Vol 03 (03n04) ◽  
pp. 295-319 ◽  
Author(s):  
YASUNORI YAMAMOTO ◽  
KENICHI MORITA ◽  
KAZUHIRO SUGATA
Keyword(s):  
Context Sensitivity ◽  
The Other ◽  
Two Dimensional ◽  
Regular Array ◽  
Nonterminal Symbol ◽  
Left Hand ◽  
Other Hand ◽  
Context Free ◽  
Rewriting Rules

Regular array grammars (RAGs) are the lowest subclass in the Chomsky-like hierarchy of isometric array grammars. The left-hand side of each rewriting rule of RAGs has one nonterminal symbol and at most one "#" (a blank symbol). Therefore, the rewriting rules cannot sense contexts of non-# symbols. However, they can sense # as a kind of context. In this paper, we investigate this #-sensing ability. and study the language generating power of RAGs. Making good use of this ability, We show a method for RAGs to sense the contexts of local shapes of a host array in a derivation. Using this method, we give RAGs which generate the sets of all solid upright rectangles and all solid squares. On the other hand. it is proved that there is no context-free array grammar (and thus no RAG) which generates the set of all hollow upright rectangles.

scholarly journals Investigation of the Relationship Between the Two-Dimensional Self-Esteem Perceptions and Leadership Orientations of the Faculty of Sports Sciences Students

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Ismail Karatas ◽  
◽  
Hayri Akyuz
Keyword(s):  
Charismatic Leadership ◽  
Self Esteem ◽  
The Self ◽  
The Other ◽  
Two Dimensional ◽  
Leadership Orientations ◽  
Other Hand ◽  
Questionnaire Form ◽  
Sports Sciences ◽  
The Relationship

This research was carried out to investigate of the relationship between the two-dimensional self-esteem perceptions and leadership orientations of the students of the faculty of sports sciences. In this context, the relational survey model, which is consistent with the main purpose of the study, was used in this quantitative study. A total of 323 students, 125 females and 198 males at the Faculty of Sports Sciences of Bartın University constitute the sample of the research. Convenience sampling method, one of the non-probabilistic sampling approaches, was used in the selection of the research group. Questionnaire form was used as data collection tool and this form consisted of three parts. The first part includes the “Personal Information Form,” the second part includes the “Two-Dimensional Self-Esteem: Self-Liking/Self-Competence Scale” and the third part includes the “Multidimensional Leadership Orientations Scale.” The descriptive statistics of the raw data obtained through the questionnaire form were first calculated by considering the data type. Then, the reliability of the scales related to the obtained data were investigated, and the difference and correlation tests were used in the statistical evaluation. In this direction, it has been determined that there are significant correlations within the scope of age and family income level variables. However, there was no significant relationship within the scope of personal income level variable. On the other hand, it was found that there are significant differences in the scope of department and actively doing sports variables. However, it was observed that there were no significant differences in the scope of gender, grade, and place of residence variables. On the other hand, it was determined that there were positive and moderately significant correlations between the participants’ scores of self-liking and political leadership, human resources leadership, charismatic leadership and structural leadership. In addition, it was found that there were positive and moderately significant correlations between the self-competence scores of the participants and the scores of political leadership, charismatic leadership and structural leadership. On the other hand, it was understood that there was a statistically significant positive and low-level correlation between the participants' self-competence scores and their human resources leadership scores. As a result, it can be said that as the self-esteem of the participants increases, their leadership orientation also increases. In this context, it can be said that increasing the self-esteem of the participants is an important concept in the context of leadership orientations.

The Relationship between Legality and Legitimacy: A Double-Edged Sword

2019 ◽  
pp. 302-310
Author(s):  
Dana Burchardt
Keyword(s):  
The Other ◽  
Two Dimensional ◽  
Legal Norms ◽  
Other Hand ◽  
Norm Theory ◽  
The One ◽  
The Relationship

This comment on Thilo Marauhn’s chapter addresses the relationship between legality and legitimacy from a norm-related perspective. It inquires into the reasons for the two-dimensional relationship between legality and legitimacy through the lens of norm theory. It considers legal norms on the one hand and legitimacy norms on the other hand, interrogating how these different kinds of norms can coexist, interrelate, and influence each other and what functions they can fulfil in the international sphere. By doing so, it highlights to what extent legal norms and legitimacy norms compete and complement each other—where the double-edged sword in the relationship between legality and legitimacy can be used for undercutting or rather for defending each other.

Automata with cyclic move operations for picture languages

2018 ◽  
Vol 52 (2-3-4) ◽  
pp. 235-251
Author(s):  
Friedrich Otto ◽  
František Mráz
Keyword(s):  
Finite Number ◽  
Expressive Power ◽  
Single Step ◽  
The Other ◽  
Cyclic Extension ◽  
Two Dimensional ◽  
Other Hand ◽  
Picture Languages ◽  
Restarting Automaton

Here, we study the cyclic extensions of Sgraffito automata and of deterministic two-dimensional two-way ordered restarting automata for picture languages. Such a cyclically extended automaton can move in a single step from the last column (or row) of a picture to the first column (or row). For Sgraffito automata, we show that this cyclic extension does not increase the expressive power of the model, while for deterministic two-dimensional two-way restarting automata, the expressive power is strictly increased by allowing cyclic moves. In fact, for the latter automata, we take the number of allowed cyclic moves in any column or row as a parameter, and we show that already with a single cyclic move per column (or row) the deterministic two-dimensional extended two-way restarting automaton can be simulated. On the other hand, we show that two cyclic moves per column or row already give the same expressive power as any finite number of cyclic moves.

Two-dimensional partial orderings: Undecidability

1980 ◽  
Vol 45 (1) ◽  
pp. 133-143 ◽  
Author(s):  
Alfred B. Manaster ◽  
Joseph G. Rosenstein
Keyword(s):  
Bipartite Graph ◽  
Bipartite Graphs ◽  
The Other ◽  
Two Dimensional ◽  
One Dimensional ◽  
Recursive Model ◽  
Linear Orderings ◽  
Other Hand ◽  
Partial Orderings ◽  
Planar Lattices

In this paper we examine the class of two-dimensional partial orderings from the perspective of undecidability. We shall see that from this perspective the class of 2dpo's is more similar to the class of all partial orderings than to its one-dimensional subclass, the class of all linear orderings. More specifically, we shall describe an argument which lends itself to proofs of the following four results:(A) the theory of 2dpo's is undecidable:(B) the theory of 2dpo's is recursively inseparable from the set of sentences refutable in some finite 2dpo;(C) there is a sentence which is true in some 2dpo but which has no recursive model;(D) the theory of planar lattices is undecidable.It is known that the theory of linear orderings is decidable (Lauchli and Leonard [4]). On the other hand, the theories of partial orderings and lattices were shown to be undecidable by Tarski [14], and that each of these theories is recursively inseparable from its finitely refutable statements was shown by Taitslin [13]. Thus, the complexity of the theories of partial orderings and lattices is, by (A), (B) and (D), already reflected in the 2dpo's and planar lattices.As pointed out by J. Schmerl, bipartite graphs can be coded into 2dpo's, so that (A) and (B) could also be obtained by applying a Rabin-Scott style argument [9] to Rogers' result [11] that the theory of bipartite graphs is undecidable and to Lavrov's result [5] that the theory of bipartite graphs is recursively inseparable from the set of sentences refutable in some finite bipartite graph. (However, (C) and (D) do not seem to follow from this type of argument.)

ENTANGLEMENT, PURITY AND VIOLATION OF BELL INEQUALITY

2009 ◽  
Vol 07 (07) ◽  
pp. 1313-1320 ◽  
Author(s):  
DONG-LING DENG ◽  
JING-LING CHEN
Keyword(s):  
Bell Inequality ◽  
The Other ◽  
Two Dimensional ◽  
Entanglement Of Formation ◽  
Other Hand ◽  
Chsh Inequality ◽  
The One ◽  
The Relationship ◽  
Qubit States

We use the Clauser–Horne–Shimony-Holt (CHSH) inequality to investigate the relationship among entanglement, purity and violation of the Bell inequality. On the one hand, we show numerically that all two-dimensional (qubit) states, whose entanglement of formation (EOF) is larger than [Formula: see text], violate the CHSH inequality. On the other hand, any state with purity smaller than 0.5562 may not violate it.

scholarly journals n-Homogeneous C*-algebras

2021 ◽  
Vol 57 (2) ◽  
pp. 185-189
Author(s):  
M. V. Shchukin
Keyword(s):  
Residue Class ◽  
The Other ◽  
Two Dimensional ◽  
3 Dimensional ◽  
C Algebras ◽  
Residue Classes ◽  
Other Hand ◽  
Primitive Ideals

The classical results by J. Fell, J. Tomiyama, M. Takesaki describe n-homogeneous С*-algebras as algebras of all continuous sections for an appropriate algebraic bundle. By using this realization, several authors described the set of n-homogeneous С*-algebras with different spaces of primitive ideals. In 1974 F. Krauss and T. Lawson described the set of all n-homogeneous С*-algebras whose space Prim of primitive ideals is homeomorphic to the sphere S2. Suppose the space PrimA of primitive ideals is homeomorphic to the sphere S3 for some n-homogeneous С*-algebra A. In this case, these authors showed that the algebra A is isomorphic to the algebra C(S3,Cn×n). If n ≥ 2 then there are countably many pairwise non-isomorphic n-homogeneous С*-algebras A such that PrimA ≅ S 4. Further, let n ≥ 3. There is only one n-homogeneous С*-algebra A such that PrimA ≅ S 5. There are two non-isomorphic 2-homogeneous С*-algebras A and B with space PrimA ≅ S 5. On the other hand, algebraic bundles over the torus T 2 are described by a residue class [p] in Z/nZ = π1(PUn). Two such bundles with classes [pi] produce isomorphic С*-algebras if and only if [p1] = ±[p2]. An algebraic bundle over the torus T 3 is determined by three residue classes in Z/nZ. Anatolii Antonevich and Nahum Krupnik introduced some structures on the set of algebraic bundles over the sphere S2. Algebraic bundles over the compact connected two-dimensional oriented manifolds were considered by the author. In this case, the set of non-equivalent algebraic bundles over such space is like the set of algebraic bundles over the torus T2. Further advances could be in describing the set of algebraic bundles over the 3-dimensional manifolds.

scholarly journals Investigation of the Relationship Between the Two-Dimensional Self-Esteem Perceptions and Leadership Orientations of the Faculty of Sports Sciences Students

2021 ◽  
Author(s):  
Ismail Karatas ◽  
Hayri Akyuz
Keyword(s):  
Charismatic Leadership ◽  
Self Esteem ◽  
The Self ◽  
The Other ◽  
Two Dimensional ◽  
Leadership Orientations ◽  
Other Hand ◽  
Questionnaire Form ◽  
Sports Sciences ◽  
The Relationship

This research was carried out to investigate of the relationship between the two-dimensional self-esteem perceptions and leadership orientations of the students of the faculty of sports sciences. In this context, the relational survey model, which is consistent with the main purpose of the study, was used in this quantitative study. A total of 323 students, 125 females and 198 males at the Faculty of Sports Sciences of Bartın University constitute the sample of the research. Convenience sampling method, one of the non-probabilistic sampling approaches, was used in the selection of the research group. Questionnaire form was used as data collection tool and this form consisted of three parts. The first part includes the “Personal Information Form,” the second part includes the “Two-Dimensional Self-Esteem: Self-Liking/Self-Competence Scale” and the third part includes the “Multidimensional Leadership Orientations Scale.” The descriptive statistics of the raw data obtained through the questionnaire form were first calculated by considering the data type. Then, the reliability of the scales related to the obtained data were investigated, and the difference and correlation tests were used in the statistical evaluation. In this direction, it has been determined that there are significant correlations within the scope of age and family income level variables. However, there was no significant relationship within the scope of personal income level variable. On the other hand, it was found that there are significant differences in the scope of department and actively doing sports variables. However, it was observed that there were no significant differences in the scope of gender, grade, and place of residence variables. On the other hand, it was determined that there were positive and moderately significant correlations between the participants’ scores of self-liking and political leadership, human resources leadership, charismatic leadership and structural leadership. In addition, it was found that there were positive and moderately significant correlations between the self-competence scores of the participants and the scores of political leadership, charismatic leadership and structural leadership. On the other hand, it was understood that there was a statistically significant positive and low-level correlation between the participants' self-competence scores and their human resources leadership scores. As a result, it can be said that as the self-esteem of the participants increases, their leadership orientation also increases. In this context, it can be said that increasing the self-esteem of the participants is an important concept in the context of leadership orientations.

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