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Evolutionary-based prediction of ε50 for the lateral load-displacement behavior of piles in clay
Babak Ebrahimian, Aida Nazari, 2013, original scientific article

Abstract: Analyzing piles that are subjected to lateral loads reveals that their behavior depends on the soil’s resistance at any point along the pile as a function of the pile’s deflection, known as the p-y curve. On the other hand, the deformation characteristics of soil defined as “the soil strain at 50% of maximum deviatoric stress (ε50)” have a considerable effect on the generated p-y curve. In this research, several models are proposed to predict ε50 specifically for designing the very long pile foundations of offshore oil and gas platforms in the South Pars field, Persian Gulf, Iran. Herein, ε50 is evaluated using extensive soil data, including in-situ and laboratory test results using evolutionary polynomial regression (EPR). The effects of the undrained shear strength, the normalized tip resistance of the cone penetration test, the over-burden pressure, the plasticity index and the over-consolidation ratio on ε50 are investigated in marine clays. It is demonstrated that the normalized cone tip resistance, which is an indication of the soil’s undrained shear strength, leads to more realistic ε50 values compared with the laboratory-derived undrained shear strength parameter. In addition, the application of the soil-index properties and the over-burden pressure in the models, improves their estimation quality. Furthermore, the results of full-scale lateral pile load tests at different sites are used in order to validate the performance of the proposed models when it comes to predicting the behavior of the lateral piles.
Keywords: p-y curve, laterally loaded pile, piezocone penetration test, PCPT, marine clay, evolutionary polynomial regression, EPR, South Pars field
Published in DKUM: 14.06.2018; Views: 551; Downloads: 56
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Omega polynomial revisited
Mircea V. Diudea, Sandi Klavžar, 2010, original scientific article

Abstract: Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 43-47) to count the opposite topologically parallel edges in graphs, particularly to describe the polyhedral nanostructures. In this paper, the main definitions are re-analyzed and clear relations with other three related polynomials are established. These relations are supported by close formulas and appropriate examples.
Keywords: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, Cluj-Ilmenau index, CI index
Published in DKUM: 24.08.2017; Views: 557; Downloads: 76
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The Hosoya-Wiener polynomial of weighted trees
Blaž Zmazek, Janez Žerovnik, 2007, original scientific article

Abstract: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.
Keywords: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs
Published in DKUM: 05.07.2017; Views: 686; Downloads: 70
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Simplified computation of matchings in polygraphs
Ante Graovac, Damir Vukičević, Damir Ježek, Janez Žerovnik, 2005, original scientific article

Abstract: Matching polynomial and perfect matchings for fasciagraphs, rotagraphs and twisted rotagraphs are treated in the paper. Classical transfer matrix approach makes it possible to get recursions for matching polynomial and perfect matchings, but the order of the matrix grows exponentially in the number of the linking edges between monographs. Novel transfer matrices are introduced whose order is much lower than that in classical transfer matrices. The virtue of the method introduced is especially pronounced when twoor more linking edges end in the same terminal vertex of a monograph. An example of a polyacene polygraph with extended pairings is given where a novel matrix has only 16 entries as compared to 65536 entries in the classical transfer matrix. However, all pairings are treated here on equal footing, but the method introduced can be applied to selected types of pairings of interest in chemistry.
Keywords: polygraphs, matching polynomial, matchings, perfect matchings, Kekulé structures, extended structures, recursive enumeration, transfer matrix method
Published in DKUM: 05.07.2017; Views: 765; Downloads: 68
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On the codimension growth of simple color Lie superalgebras
Dušan Pagon, Dušan Repovš, Mikhail Zaicev, 2012, original scientific article

Abstract: Predmet naših raziskav so polinomske identitete končno razsežnih enostavnih barvnih Liejevih superalgeber nad algebrsko zaprtim poljem z ničelno karakteristiko, gradacijo katerih podaja produkt dveh cikličnih grup reda 2. Dokazujemo, da kodimenzije opisanih identitet naraščajo eksponentno, stopnja te rasti pa je enaka razsežnosti dane algebre. Podoben rezultat smo dobili tudi za gradirane identitete in gradirane kodimenzije.
Keywords: matematika, neasociativna algebra, Liejeve superalgebre, polinomske identitete, kodimenzije, eksponentna rast, mathematics, nonassociative algebra, color Lie superalgebras, polynomial identities, codimensions, exponential growth
Published in DKUM: 10.07.2015; Views: 733; Downloads: 23
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Trace-positive polynomials and the quartic tracial moment problem
Sabine Burgdorf, Igor Klep, 2010, original scientific article

Abstract: V članku podamo nekomutativno različico klasičnega Hilbertovega izreka o pozitivnih polinomih stopnje 4 v 2 spremenljivkah: nekomutativni polinom takšnega tipa, ki ima pozitivno sled, je vsota štirih hermitskih kvadratov in komutatorjev. S pomočjo dualnosti ta rezultat uporabimo za študij problema momentov s sledjo.
Keywords: matematika, nekomutativni polinom, sled, vsota hermitskih kvadratov, problem momentov, prosta pozitivnost, mathematics, noncommutative polynomial, trace, sum of hermitian squares, (truncated) moment problem, free positivity
Published in DKUM: 10.07.2015; Views: 606; Downloads: 95
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The tracial moment problem and trace-positive polynomials
Igor Klep, 2010, published scientific conference contribution abstract

Keywords: algebra, nekomutativni polinom, komutator, sled, algebra, noncommutative polynomial, commutator, trace
Published in DKUM: 10.07.2015; Views: 700; Downloads: 42
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On some polynomially convex maximal real submanifolds in C [sup] {2n} and a related Riemann-Hilbert problem
Matej Zajec, 2009, original scientific article

Abstract: Dokažemo, da so določeni maksimalno realni grafi preslikav iz ▫${mathbb{C}}^n$▫ v ▫${mathbb{C}}^n$▫ polinomsko konveksni. Vpeljemo mnogoterosti, ki so fibrirane nad ▫$partialDelta$▫ in katerih vlakna so taki grafi, in rešujemo pripadajoči Riemann-Hilbertov problem. Dokažemo obstoj rešitve in opišemo njeno lokalno strukturo.
Keywords: matematika, kompleksna analiza, polinomska konveksnost, Riemann-Hilbertov problem, analitični disk, mathematics, complex analysis, polynomial convexity, Riemann-Hilbert problem, analytic disc
Published in DKUM: 10.07.2015; Views: 578; Downloads: 20
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