Search results for "combinatoric"
showing 10 items of 1776 documents
Lattices of Jordan algebras
2010
AbstractCommutative Jordan algebras play a central part in orthogonal models. The generations of these algebras is studied and applied in deriving lattices of such algebras. These lattices constitute the natural framework for deriving new orthogonal models through factor aggregation and disaggregation.
Quantitative uniqueness estimates for pp-Laplace type equations in the plane
2016
Abstract In this article our main concern is to prove the quantitative unique estimates for the p -Laplace equation, 1 p ∞ , with a locally Lipschitz drift in the plane. To be more precise, let u ∈ W l o c 1 , p ( R 2 ) be a nontrivial weak solution to div ( | ∇ u | p − 2 ∇ u ) + W ⋅ ( | ∇ u | p − 2 ∇ u ) = 0 in R 2 , where W is a locally Lipschitz real vector satisfying ‖ W ‖ L q ( R 2 ) ≤ M for q ≥ max { p , 2 } . Assume that u satisfies certain a priori assumption at 0. For q > max { p , 2 } or q = p > 2 , if ‖ u ‖ L ∞ ( R 2 ) ≤ C 0 , then u satisfies the following asymptotic estimates at R ≫ 1 inf | z 0 | = R sup | z − z 0 | 1 | u ( z ) | ≥ e − C R 1 − 2 q log R , where C > 0 depends …
The doodle of a finitely determined map germ from R2 to R3
2009
Let f:U⊂R2→R3 be a representative of a finitely determined map germ f:(R2,0)→(R3,0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere Sϵ2 centered at the origin in R3, call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles.
Problemas históricos y dificultades de los estudiantes en la conceptualización de sustancia compuesto químico
2008
Este trabajo ofrece un análisis histórico sobre los problemas que tuvo que resolver la ciencia hasta llegar a la construcción de los conceptos macroscópicos de sustancia y compuesto químico en el contexto de la teoría daltoniana. Por otra parte, en él se muestran algunas de las dificultades de comprensión que estos conceptos ofrecen a los estudiantes. Para determinarlas, se realiza un estudio transversal con alumnos de 15 a 18 años, lo que permite evaluar el significado que otorgan a la idea de sustancia, al tiempo que se constata la necesidad de su comprensión para poder entender los cambios químicos. Por último, se plantea la existencia de ciertas semejanzas entre las ideas sobre la compo…
Fixed point theorems in generalized partially orderedG-metric spaces
2010
In this paper, we consider the concept of a $\Omega$-distance on a complete partially ordered G-metric space and prove some fixed point theorems.
Vertical representation of C∞-words
2015
We present a new framework for dealing with C ∞ -words, based on their left and right frontiers. This allows us to give a compact representation of them, and to describe the set of C ∞ -words through an infinite directed acyclic graph G. This graph is defined by a map acting on the frontiers of C ∞ -words. We show that this map can be defined recursively and with no explicit reference to C ∞ -words. We then show that some important conjectures on C ∞ -words follow from analogous statements on the structure of the graph G.
Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1, 2n)
2003
We prove an Amitsur-Levitzki type theorem for the Lie superalgebras osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We show that the Lie superalgebras gl(p,q) cannot satisfy an Amitsur-Levitzki type super identity if p, q are non zero and conjecture that neither can any other classical simple Lie superalgebra with the exception of osp(1,2n).
Steiner systems and configurations of points
2020
AbstractThe aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner SystemS(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configur…
On semi-fredholm properties of a boundary value problem inR + n
1988
The paper considers a boundary value problem with the help of the smallest closed extensionL ∼ :H k →H k 0×B h 1×...×B h N of a linear operatorL :C (0) ∞ (R + n ) →L(R + n )×L(R n−1)×...×L(R n−1). Here the spacesH k (the spaces ℬ h ) are appropriate subspaces ofD′(R + n ) (ofD′(R n−1), resp.),L(R + n ) andC (0) ∞ (R + n )) denotes the linear space of smooth functionsR n →C, which are restrictions onR + n of a function from the Schwartz classL (fromC 0 ∞ , resp.),L(R n−1) is the Schwartz class of functionsR n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L ∼) and for the uniqueness of solutionsL ∼ U=F are expressed. In addition, ana prio…
Trunk Packing Revisited
2007
For trunk packing problems only few approximation schemes are known, mostly designed for the European standard DIN 70020 [6] with equally sized boxes [8, 9, 11, 12]. In this paper two discretized approaches for the US standard SAE J1100 [10] are presented, which make use of different box sizes. An exact branch-and-bound algorithm for weighted independent sets on graphs is given, using the special structure of the SAE standard. Another branch-and-bound packing algorithm using linear programs is presented. With these algorithms axis-oriented packings of different box sizes in an arbitrary trunk geometry can be computed efficiently.