complete sets

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Dirichlet's problem, conformal mapping and complete sets in Hilbert space

Dirichlet's problem, conformal mapping and complete sets in Hilbert space

The solution of the bOU?Jdary value problem for harmonic functions leads readily to the conformal mapping of simply connected domains on the interior or a circle.. the corresponding pola[r]

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New examples of complete sets, with connections to a Diophantine theorem of Furstenberg

New examples of complete sets, with connections to a Diophantine theorem of Furstenberg

contains only those numbers whose base a expansion consists of zeros and ones, FS(Γ(a)) is of density zero (so Γ(a) is incomplete), while if α ∈ T is an irrational whose base a expansion is missing some digit, then the set Γ(a)α is nowhere dense in T (so Γ(a) is not dispersing). So it makes sense to augment the semigroup property with some information on the size of the set in question: the sets Γ(a, b) are larger than the sets Γ(a), and in general it is easier for larger sets to be complete and dispersing. In the case of the sets Γ(a, b), information on the size is provided by the following lemma due to Furstenberg:
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New examples of complete sets, with connections to a Diophantine theorem of Furstenberg

New examples of complete sets, with connections to a Diophantine theorem of Furstenberg

By contrast, the notion of a “dispersing” set has not appeared explicitly in the literature before. It bears some resemblance to the notion of a “Glasner set” (cf. [12, 3], and see [2] for a generalization). 1 However, the differences between these definitions are significant, and we will not discuss Glasner sets in this paper. Although their definitions are very different, the notions of completeness and dispersion do share some relation. Both describe some notion of “largeness” of a set of integers which measures not just the growth rate but also in some sense the arithmetical properties of the set in question. This is manifested in the following classical results about complete and dispersing sets, which are due to Birch and Furstenberg, respectively:
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Clinical use of computational modeling for surgical planning of arteriovenous fistula for hemodialysis

Clinical use of computational modeling for surgical planning of arteriovenous fistula for hemodialysis

As far as effective usability of the computational tool, the complete sets of data collected and the feedback provided by clinicians indicated that AVF.SIM system is easy to use and well accepted in clinical routine, with a limited additional workload for pre-operative examin- ation by the clinicians. Actually the computed prediction of patient-specific BFVs after VA maturation are ob- tained using the AVF.SIM system on the basis of demo- graphic information, clinical data and pre-operative DUS measurements, that are today all standard of care for patients in need of VA for HD treatment. Time required to fill up the pre-operative form and send data to the Simulation Center was estimated to extend the routine vascular mapping of approximately 10–15 min only. Pre-operative physical examination and DUS evaluation currently recommended by international guidelines [16] have several potential benefits, but only a system that takes into account the complex interplay of demographic and clinical factors, as well as vessel dimensions and local BFV, could really help the surgeon in identifying the best site for AVF placement, as well as in preventing very low or very high BFV, likely associated with VA complications. The establishment of effective usability of AVF.SIM in the clinical environment is a significant step forward allowing computer assisted clinical decision making on type and location of AVF, as well as for the
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Comparable contributions of structural-functional constraints and expression level to the rate of protein sequence evolution

Comparable contributions of structural-functional constraints and expression level to the rate of protein sequence evolution

of genes [34]. The distributions typically are broad but fol- low a general bell-shaped form (some are bimodal), in support of the notion of an intrinsic rate of domain evo- lution for which the mean (or median) of the respective distribution can be taken as a reasonable proxy. Domains present within multidomain proteins do not show sys- tematic differences in evolutionary rates compared to solo domains as illustrated by two examples in Figure 3. We then addressed the issue of homogenization of the rates of evolution of domains that is predicted by the MIM hypothesis to result from the fusion of domains within a multidomain protein. Figure 4 shows anecdotal evidence for two proteins, each consisting of 3 distinct domains. For one of these proteins, homogenization is obvious (Figure 4A) whereas the other one shows no obvious sign of homogenization (Figure 4B). These examples are char- acteristic of the diversity of the evolutionary regimes of domains, so that homogenization is seen in many but by no means all multidomain proteins, and some actually display the opposite trend (Additional Files 1 and 2, and see below). This striking variability notwithstanding, the results of the analysis of the complete sets of domains unequivocally reveal substantial homogenization as illus- trated by the comparison of the probability density func- tions for the difference (ratio) of the evolutionary rates for all domain combinations and for domain pairs fused within multidomain proteins. The difference in evolu- tionary rates between a pair of domains within a multid- omain protein tends to be substantially less than the difference between rates for the same pair of domains found in different proteins in both human (Figure 5A) and Arabidopsis (Figure 5B).
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Comparison of complete nuclear receptor sets from the human, Caenorhabditis elegans and Drosophila genomes

Comparison of complete nuclear receptor sets from the human, Caenorhabditis elegans and Drosophila genomes

coactivators and corepressors to activate and suppress target gene expression [4]. The transcriptional activities of about half of the NRs studied in humans are regulated by small lipophilic ligands whereas the other, so-called orphan, receptors await ligand identification. Because of their poten- tial for modulation by exogenous compounds and their central roles in metabolism, these receptors are extremely important targets in human disease. Additionally, NRs rep- resent possible new targets for the control of invertebrate pests in agriculture. The latter approach would be especially promising if certain classes of NRs are shown to be specific to selected invertebrate subgroups. Comparison of complete sets of NRs from evolutionarily divergent organisms should tell us more about the feasibility of these approaches as well as shed light on general phylogenetic relationships among NRs and among species.
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Implementing sustainable development education in the school curriculum : learning for ITE from teachers' experiences

Implementing sustainable development education in the school curriculum : learning for ITE from teachers' experiences

Ten assessment portfolios were selected for analysis on the basis that these provided the most complete sets of data identified for close analysis: rationales for their topic selection, on-going reflective commentaries in the form of learning logs and a final evaluation of the topic in terms of both their own and the pupils’ learning. Ethical approval procedures were completed and all teachers gave permission for their work to be analysed and findings published and

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Groups whose locally maximal product free sets are complete

Groups whose locally maximal product free sets are complete

A group G of order p m is said to be of maximal class if m > 2 and the nilpotence class of G is m − 1. It is well known (for example see Theorem 1.2 and Corollary 1.7 of [3]) that the 2-groups of maximal class are dihedral, semidihedral and generalised quaternion. Moreover, by [3, Theorem 1.2], if G is a 2-group of maximal class of order at least 16, then G/Z(G) is dihedral of order 1 2 | G | . A detailed examination of locally maximal product-free sets in 2-groups of maximal class, which among other things results in an alternative proof of Lemma 3.3, appears in [1]. However, since we need the result here we thought it would be useful to include a short proof for ease of reference.
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Complete Stationary Fuzzy Metric Space of The Bounded Closed Fuzzy Sets and Common Fixed Point Theorems

Complete Stationary Fuzzy Metric Space of The Bounded Closed Fuzzy Sets and Common Fixed Point Theorems

Denote by B (X ), C (X ) and C B (X), the totality of fuzzy sets which satisfy that for each α ∈ I, the α-cut of µ is nonempty bounded, nonempty closed and nonempty bounded closed in X , respectively. Next, we give the definition of the function M ∞ on F (X ) × F (X), which is induced by H M

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I- sets and C- sets

I- sets and C- sets

We have that an intuitionistic fuzzy topological space can be associated with two fuzzy topological spaces and vice versa [1]. . If (X, 𝜏) is an IFTS and 𝜏₁= { μₐ / ∃ γₐ ∊ Iˣ such that (μₐ , γₐ) ∊ 𝜏 }, 𝜏₂ = { 1- γₐ / ∃ μₐ ∊ Iˣ such that (μₐ, γₐ) ∊ 𝜏},then (X, 𝜏₁) and (X, 𝜏₂) are fuzzy topological spaces. Similarly if (X, 𝜏₁) and (X, 𝜏₂) are two fuzzy topological space, 𝜏 = {(u,1- v)/ u∊ 𝜏₁, v∊ 𝜏₂ and u ⊆ v} is an intuitionistic fuzzy topology and (X, 𝜏) is an intuitionistic fuzzy topological spaces. We study some relationships connecting the closures and interiors of an intuitionistic fuzzy set in an intuitionistic fuzzy topological space and the closures and interiors of its co- ordinate fuzzy sets in its corresponding fuzzy topological spaces. .
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Maximum Oriented Forcing Number for Complete Graphs

Maximum Oriented Forcing Number for Complete Graphs

This inequality is sharp when q = 2 or when q = 3 and each part has at least two vertices. Proof. The inequality comes from substituting k = 1 into the above corollary. To see that equality holds when q = 2, the complete bipartite case, we first note that MOF(G) ≤ n − 1 for any non-empty graph G. This is because there is always a vertex v with in-degree at least one in such cases, and the set of all vertices other than v is a forcing set. To see that MOF(G) ≥ n − 1, let A and B be the two parts and direct all edges from A to B. Now each vertex of A is necessarily in any forcing set and nothing can be forced unless at least |B| − 1 vertices from B are included. Therefore, MOF(G) = n − 1 = n − q + 1, as claimed.
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Lattices of fuzzy objects

Lattices of fuzzy objects

they are isomorphic to the fuzzification of the complete lattice of crisp objects subsets, closed sets, subalgebras, etc... FUZZY SUBSETS Theorem 5.1.[r]

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Order-clustered fixed point theorems on chain-complete preordered sets and their applications to extended and generalized Nash equilibria

Order-clustered fixed point theorems on chain-complete preordered sets and their applications to extended and generalized Nash equilibria

In traditional game theory, fixed point theory in topological spaces or metric spaces has been an essential tool for the proof of the existence of Nash equilibria of noncooperative games, in which the payoff functions of the players take real values (see [–]). Recently, the concept of nonmonetized noncooperative games has been introduced where the pay- off functions of the players take values in ordered sets, on which the topological structure may not be equipped. The existence of generalized and extended Nash equilibria of non- monetized noncooperative games has been studied by applying fixed point theorems to ordered sets. These games are also named generalized games by some authors (see [– ]). Naturally, fixed point theory on ordered sets has revealed its crucial importance in this new subject in game theory.
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Experimental and biological variability in CFSE-based flow cytometry data

Experimental and biological variability in CFSE-based flow cytometry data

• The black horizontal lines above and below the box (which are in most cases connected to the box via dashed vertical lines) represent the maximimum and minimum value, respectively, excluding outliers. These figures provide a wealth of information concerning the variability and identifiability of parameter estimates. Individually, the box plots within each figure can be used to determine a median parameter estimate and to visualize the variation (spread) in parameter estimates for a given donor and cell type when multiple five-day data sets are considered. Each box plot can also be used to conclude whether or not a particular parameter is likely to be identifiable for any particular donor and cell type. For example, Figures 16 and 17 reveal extremely large spreads in many of the box plots, indicating that the parameters E
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More on vague sets

More on vague sets

Attanassov, K.T., Gargov, G. 1989. Interval valued intuitionstics fuzzy sets; Fuzzy sets and system. 343-349. Bustince, H., Buriuo, P. 1996. Vague sets are intutionistics fuzzy sets. Fuzzy sets and system 79 403-405. Dubois, D. and Prade , H. 1980. Fuzzy sets and systems : Theory and Applications, Academic press, New York. Gau, W. L., Daniel, J. B. 1993. Vague sets, IEEE transactions on systems, man Cybernetics 23 610-614. Zadeh, L.A. 1965. fuzzy sets. Information and control 8 338-353.

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Vol 4, No 12 (2013)

Vol 4, No 12 (2013)

In this paper, we study the undirected graph Γ 𝐼𝐼 (𝑀𝑀) of Gamma near rings for any completely reflexive ideal I of M. Throughout this paper M stands for a non zero Gamma near -ring with zero element and I is a completely reflexive ideal of M. For distinct vertices x and y of a Graph G, let d(x, y) be the length of the shortest path from x to y. The diameter of a connected graph is the supremum of the distances between vertices. For any graph G, the girth of G is the length of a shortest cycle in G and is denoted by gr(G). If G has no cycle, we define the girth of G to be infinite. A clique of a graph is a maximal complete subgraph and the number of graph vertices in the largest clique or graph G, denoted by ω(G) is called the clique number of G. A graph G is bipartite with vertex classes 𝑉𝑉 1 , 𝑉𝑉 2 if the set of all vertices of G is 𝑉𝑉 1 ∪ 𝑉𝑉 2 , 𝑉𝑉 1 ∩ 𝑉𝑉 2 = ∅ , and edge of G joins a vertex from 𝑉𝑉 1 to a vertex of 𝑉𝑉 2 .
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Generating Sets of the Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ2 (X,4)

Generating Sets of the Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ2 (X,4)

Generating Sets of the Complete Semigroups of Binary Relations Defined by Semilattices of the Class Σ 2 X ,4 Bariş Albayrak1, Omar Givradze2, Guladi Partenadze2 Department of Banking a[r]

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Aspects of Constructive Dynamical Systems

Aspects of Constructive Dynamical Systems

As we have seen, the difficulty in finding Brouwerian counterexamples to The- orems 1 and 2 arises in finding abelian groups which are ‘nice’ enough to be complete, but which are not periodic or noncompact, respectively. In fact, our one successful Brouwerian counterexample concerning the generalisation of COP required us to assume a non-constructive principle (LLPO) in order to establish the completeness of the abelian group under consideration. Given that being complete appears to impose so much structure on our complete abelian groups, it seems likely that Theorems 1 and 2 admit constructive proofs. On the other hand, it is interesting to note that there is some similarity between the extra hypothesis assumed in Theorems 18 and 36. In Theorem 18 we are concerned with showing that G is ‘small’, in that it is periodic and therefore the image, under a uniformly continuous mapping, of a compact space. Here we assume that θ(0, ∞) is open, in which case θ(−∞, 0) is also open, so S 1 is
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Existence of mixed strategy equilibria in a class of discontinuous games with unbounded strategy sets

Existence of mixed strategy equilibria in a class of discontinuous games with unbounded strategy sets

The aim of this paper is to show the existence of Nash equilibria in mixed strategies for a class of two-player discontinuous games with complete in- formation in which the strategy sets are non-compact. The problem of the existence of equilibria in discontinuous games has been already addressed by Dasgupta and Maskin (1986a, 1986b), Maskin (1986), Simon (1987), Simon and Zame (1990), and, more recently by Reny (1999). Unlike the existing pa- pers, we construct Nash equilibria in mixed strategies when players’ strategy sets coincides with the set of real numbers.

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Vol 8, No 7 (2017)

Vol 8, No 7 (2017)

A nonempty subset 𝑆 of 𝑉(𝐺), where 𝐺 is any graph, is a clique in 𝐺 if the graph 𝐺 [𝑆] = 〈 𝑆 〉 induced by 𝑆 is complete. A clique 𝑆 in 𝐺 is a \textit{clique dominating} set if it is a dominating set. It is a secure clique dominating set in 𝐺 if for every 𝑢 ∈ 𝑉(𝐺) ∖ 𝑆 , there exists 𝑣 ∈ 𝑆 ∩ 𝑁 𝐺 (𝑢) such that (𝑆 ∖ { 𝑣 }) ∪ { 𝑢 } is a clique dominating set in 𝐺 . The secure clique domination number of 𝐺 , denoted by 𝛾 𝑠𝑐𝑙 (𝐺), is the minimum cardinality of a secure clique dominating set of 𝐺.
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