Báo cáo toán học: "COMPOSITION SUM IDENTITIES RELATED TO THE DISTRIBUTION OF COORDINATE VALUES IN A DISCRETE SIMPLEX" pptx
Báo cáo toán học: "COMPOSITION SUM IDENTITIES RELATED TO THE DISTRIBUTION OF COORDINATE VALUES IN A DISCRETE SIMPLEX" pptx
... ,n} into l disjoint groups. The goal of labelled counting is to establish a relation between the cardinality of the sets of hands and the cardinality of the decks.For example, when dealing with ... multiset of x-coordinates of points in A, andletπy (A) denote the multiset of y-coordinates. We arenow ready to stateTheorem 5.1. For every cardinality l between 2 and n−1, there are more l-element ... imme-diately to the interpretation of the nthFibonacci number as the cardinality of the set of compositions of n by {1, 2} [1, 2.2.23] To date, there are few systematic investigations of composition...
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Báo cáo toán học: "Invariant and coinvariant spaces for the algebra of symmetric polynomials in non-commuting variables" pps
... elu-cidate a relationship between the space SWand the subalgebra TW of W-invariants in T . The subalgebra TWwas first studied in [4, 20] with the aim of obtaining noncommutativeanalogs of classical ... case|x| = ∞, the maps ∆ and ε ar e algebra maps, making N a gra ded connected Hopf algebra.4 The place-action of S on N4.1 Swapping places in Tdand NdOn top of the permutation -a ction of ... normalizing coefficient in (16). Analyzing the abelianization map ab : T → S (the map making the variables x commute), Ro sasand Sagan [15, Thm. 2.1] show that ab|Nsatisfies:ab(m A ) = λ (A) !mλ (A) ....
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Báo cáo y học: "Practical and theoretical barriers to the prevention of accelerated atherosclerosis in systemic lupus erythematosus" docx
... assessment and management of riskfactors [11–17]. There are theoretical and practical barri-ers to improving atherosclerosis -related outcomes in SLEsuggesting that this approach will be challenging, ... Online ISSN 1478-6362)AbstractAccelerated atherosclerotic vascular disease (ASVD) is a major cause of death in systemic lupuserythematosus (SLE). Although many authorities are calling for aggressive ... factormanagement and barriers to acceptance of these measures must also be studied further.Keywords: atherosclerosis, cardiac risk factor, coronary artery disease, systemic lupus erythematosus...
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Báo cáo toán học: "Counting two-graphs related to trees" ppt
... set of vertices corresponds to replacing Tsaranov’sgenerators for vertices in this set with their inverses; so the Tsaranov group is an invariant of the switching class, that is, of the two-graph.Now ... vertex of valency 2. Let ≡ be the reflexive and transitive closure of ∼.Thenan arbitrary permutation of the labels within any equivalence class of ≡ does not change the two-graph. So we have to count ... numbers of labelled reduced two-graphs in each class. The proofs use variousenumeration results for trees. At least some of these results are well-known. To make the paper self-contained, I have included...
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Báo cáo toán học: "√ On Some Partitions Related to Q( 2)" ppsx
... nimal part k, and λ is a partition intodistinct parts where all parts are m plus the minimal part of µ. Further, the part thatis twice the minimal part of µ plus m, and odd parts greater than ... +1 and when it is −1. We leave the details to the reader.3. Conclusions The partition functions contained in this paper are rather curious in that they areall intimately related to the arithmetic ... minimal pa rtk, and λ is a partition into distinct even parts where all parts are > twice the minimalpart of µ, with weight (−1)n(µ), and z still keeping track of the number of even parts...
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Báo cáo toán học: " Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments" pptx
... works in the literature we can cite the following:(1) The deviating argument τ depends at each moment t on the globalbehavior of the solution, and not only on the values that it takes at the instant ... is an elementary matter to check that T is a completely continuous opera-tor from C(I) into itself (one has to take Remark 1 into account). Therefore,Schauder’s Theorem ensures that T has a ... τ.Proof. Reasoning in the same way as in the proof of Proposition 1, weobtain that there exists m ≥ 0 such that α(t) ≤ ϕ∗for all t ∈ I−andα(t) = −m ≤ miny ≥ minIαFα(y) for a. a. t...
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Báo cáo toán học: "Applying Fixed Point Theory to the Initial Value Problem for the Functional Differential Equations with Finite Delay " pot
... neutral differential equation into anequivalent integral equation. Then appropriate mappings were constructed and the Krasnoselskii’s fixed point theorem was employed to show the existence of a periodic ... to the case 1. We conclude that T (D) is equicontinuousand then is relatively compact by the Arzela–Ascoli theorem.By applying the Schauder theorem, T has a fixed point v ∈ D (not in ∂D),that ... the Banach space of allcontinuous functions on [−r, 0] to Rnwith the usual norm ||.||. In what follows,for an interval I ⊂ R, we will use BC(I) to denote the Banach space of boundedcontinuous...
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Báo cáo toán học: "Flattening Antichains with Respect to the Volume" doc
... constraint on s to prove that for every antichain A there exists a flat antichainwith same volume as A. Our main result is:Theorem 1.If A is an antichain then there exists a flat antichain with ... B.Asquashed antichain A isan antichain such that for each i,thesetsinA of size i, together with the sets of sizei contained in all the larger members of A, constitute an initial segment of the sets of ... |A| and itsvolumeis V (A) = A A |A| . The concept of flattening an antichain is illustrated in the proof of Sperner’s seminalresult which establishes the maximal size an antichain can have. In...
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Báo cáo toán học: "Parking functions, empirical processes, and the width of rooted labeled trees" pps
... partly the convergence of moments of the total displacement towards the moments of the Airy law, already obtained by Flajolet et al. [13]: the Airy lawis known as the law of the area below the ... stages of the BFS, the vertex x at the head of the queue is removed from the queue, and all “new” neighbors of x areaddedattheendof the queue, in increasing order. At step 0, the search produces the ... cardinalities a i= #A isatisfy the following set of constraints a 0≥ 1, the electronic journal of combinatorics 8 (2001), #R14 3since either place k − 1 is occupied by car ciand, among the...
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Báo cáo toán học: "Developing new locality results for the Pr¨fer Code u using a remarkable linear-time decoding algorithm" pdf
... presented earlier in the paper contain any additional patterns of interest. The framework developed in this papercould also be used to investigate the locality of other tree representations in greater ... becausethey require one to preprocess the Pr¨ufer string (in the case of decoding) or the tree (in the case of encoding). Furthermore, some of the approaches require the use of additionaldata ... Shin, A generalized enumeration of labeled trees and reverse Pr¨uferalgorithm,” 2005. Available online: arxiv.org/pdf/math/0601009. Due to appear in Journal of Combinatorial Theory (Series A) ,...
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