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Papers

Total Posts 65
15

Large time behavior and Lyapunov functionals for a nonlocal differential equation

산업수학센터 | Danielle Hilhorst, Philippe Laurencot, Thanh-Nam Nguyen | Nonlinear Differential Equations and Applications NoDEA 23 (2016)

A new approach is used to describe the large time behavior of the nonlocal differential equation initially studied in T.-N. Nguyen (On the ω-limit set of a nonlocal differential equation: application of rearrangement theory. Differ. Integr. Equ. arXiv:1601.06491, 2016). Our approach is based upon the existence of infinitely many Lyapunov functionals and allows us to extend the analysis performed in T.-N. Nguyen (On the ωlimit set of a nonlocal differential equation: application of rearrangement theory. Differ. Integr. Equ. arXiv:1601.06491, 2016).

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14

The Multiplicative Inequality for Class Degrees via Relative Transition Classes

산업수학센터 | Soonjo Hong | Qualitative Theory of Dynamical Systems 15(1) (2016)

Generalizing the notion of the degree of a finite-to-one factor code from a shift of finite type, the class degree of a possibly infinite-to-one factor code extends many important properties of degree. In this paper, introducing relative class degree, we study how class degrees change as two factor codes are composed, in comparison with degrees.

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13

A refined enumeration of hex trees and related polynomials

산업수학센터 | HanaKim, Richard P.Stanley | European Journal of Combinatorics 54 (2016)

A hex tree is an ordered tree of which each vertex has updegree 0, 1, or 2, and an edge from a vertex of updegree 1 is either left, median, or right. We present a refined enumeration of symmetric hex trees via a generalized binomial transform. It turns out that the refinement has a natural combinatorial interpretation by means of supertrees. We describe a bijection between symmetric hex trees and a certain class of supertrees. Some algebraic properties of the polynomials obtained in this procedure are also studied.

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12

A link between ordered trees and Green-Red trees

CHEON, GI-SANG; KIM, HANA; SHAPIR, LOUIS W. | Journal of the Korean Mathematical Society 53 (2016)

 The r-ary number sequences given by (b (r) n )n≥0 = 1 (r − 1)n + 1 rn n  are analogs of the sequence of the Catalan numbers 1 n+1 2n n  . Their history goes back at least to Lambert [8] in 1758 and they are of considerable interest in sequential testing. Usually, the sequences are considered separately and the generalizations can go in several directions. Here we link the various r first by introducing a new combinatorial structure related to GR trees and then algebraically as well. This GR transition generalizes to give r-ary analogs of many sequences of combinatorial interest. It also lets us find infinite numbers of combinatorially defined sequences that lie between the Catalan numbers and the Ternary numbers, or more generally, between b (r) n and b (r+1) n 

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11

The relative Hilbert scheme of projection morphisms

Hosung Kim | International Journal of Algebra and Computation 26(1) (2016)

Let YY be a smooth hypersurface of degree dd in a projective space Pn?nand take a point yy in Pn\Y?n\Y. Let Hilb[m]y(Y/Pn−1)Hilby[m](Y/?n−1) be the relative Hilbert scheme parametrizing zero-dimensional subscheme, of length mm, of fibers of the projection morphism Y→Pn−1Y→?n−1 from yy. In this paper we present an embedding of the relative Hilbert scheme Hilb[m]y(Y/Pn−1)Hilby[m](Y/?n−1)into a weighted projective space and describe its defining ideal for general yy. We also study line bundles on the relative Hilbert scheme Hilb[m]y(Y/Pn−1)Hilby[m](Y/?n−1) for n≥4n≥4 and general y y..

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10

Cartan-Fubini rigidity of double covering morphisms of a quadratic manifolds

Hosung Kim | Pacific Journal of Mathematics 282(2) (2016)

Let Z⊂PN be a Fano manifold whose Picard group is generated by the hyperplane section class. Assume that Z is covered by lines and i(Z)≥3. Let ?:XZ→Z be a double cover, branched along a smooth hypersurface section of degree 2m,1≤m≤i(Z)−2. We describe the defining ideal of the variety of minimal rationaltangents at a general point. As an application, we show that if Z⊂PN is defined by quadratic equations and 2≤m≤i(Z)−2, then the morphism ? satisfies the Cartan–Fubini type rigidity property.

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9

Profiles of ordered trees with mutation and associated Riordan matrices

Gi-Sang Cheon, Hana Kim, Louis W. Shapiro | Linear Algebra and Its Applications 511 (2016)

We consider ordered trees with a distinguished vertex which we call a mutator. There are many situations where this model arises. An ordered tree could represent a river network, supply lines, an employee organization chart, a phylogenetic tree, or a family tree. The mutator could be a dam or a source of pollution, a break in a supply line, a corrupt employee, and so on. We look at such things as the number of affected vertices, distance from the root, and the effect of various succession rules. Among the types of trees these results apply to are ordered trees defined by a uniform updegree requirement. We find some profiles of trees with a mutation in terms of Riordan matrices. The asymptotic formulas for the ratios of vertices of the new type to all vertices are also derived by using singularity analysis of generating functions.

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8

Elliptic equations with measurable nonlinearities in nonsmooth domains

Sun-Sig Byun, Youchan Kim | Advances in Mathematics 288 (2016)

We study elliptic equations with measurable nonlinearities in nonsmooth domains. We establish an optimal global W1,p estimate under the condition that the associated nonlinearity is allowed to be merely measurable in one variable but has a sufficiently small BMO semi-norm in the other variables, while the underlying domain is sufficiently flat in the Reifenberg sense that the boundary of the domain is locally trapped between two narrow strips.

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6

A Study of Approximate Normal Distribution Derived from Combinatoric Convolution Sums of Divisor Functions

Daeyeoul Kim, Kwangchul Lee and Gyeong-Sig Seo | Filomat 30(7) (2016)

In this paper, we consider the relations between Bernoulli polynomials, Legendre polynomials and combinatoric convolution sums of divisor functions. In addition, we give examples of approximate normal distribution derived from combinatoric convolution sums of divisor functions.

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