Search results for "Graph theory"
showing 10 items of 784 documents
Bi-homogeneity and integrability of rational potentials
2020
Abstract In this paper we consider natural Hamiltonian systems with two degrees of freedom for which Hamiltonian function has the form H = 1 2 ( p 1 2 + p 2 2 ) + V ( q 1 , q 2 ) and potential V ( q 1 , q 2 ) is a rational function. Necessary conditions for the integrability of such systems are deduced from integrability of dominate term of the potential which usually is appropriately chosen homogeneous term of V. We show that introducing weights compatible with the canonical structure one can find new dominant terms which can give new necessary conditions for integrability. To deduce them we investigate integrability of a family of bi-homogeneous potentials which depend on two integer para…
On Sets of Words of Rank Two
2019
Given a (finite or infinite) subset X of the free monoid A∗ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆ F∗. A submonoid M generated by k elements of A∗ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆ A∗ primitive if it is the basis of a |X|-maximal submonoid. This extends the notion of primitive word: indeed, w is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆ Y∗. The set Y is therefore called a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive …
A Comparison between Star Products on Regular Orbits of Compact Lie Groups
2001
In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure.
The Many Guises of Nordic Higher Education Mergers
2016
In this final chapter, the volume’s editors reflect upon the empirical and theoretical contributions from the book. The chapter is structured according to a number of ‘dimensions’ which have appeared in the previous chapters. It is concluded that the historical contexts and path dependencies play crucial roles also in the case of mergers. Furthermore, the importance of key actors is highlighted, not least the role played by formal top leaders, but also informal brokers and change agents at the institutional level. In terms of future research, two lines of inquiry are identified. The first is to delve deeper into process-related issues, which is still an unexplored aspect of mergers, and the…
Regularity and h-polynomials of toric ideals of graphs
2020
For all integers 4 ≤ r ≤ d 4 \leq r \leq d , we show that there exists a finite simple graph G = G r , d G= G_{r,d} with toric ideal I G ⊂ R I_G \subset R such that R / I G R/I_G has (Castelnuovo–Mumford) regularity r r and h h -polynomial of degree d d . To achieve this goal, we identify a family of graphs such that the graded Betti numbers of the associated toric ideal agree with its initial ideal, and, furthermore, that this initial ideal has linear quotients. As a corollary, we can recover a result of Hibi, Higashitani, Kimura, and O’Keefe that compares the depth and dimension of toric ideals of graphs.
An inquiry-based learning path to introduce modern physics in high-school
2018
Although Modern Physics (MP) is a scientific field of increasingly interest, due to its mathematical and conceptual difficulty, it was not generally taught in Italian high-schools. Recently, in order to reduce the gap between school curricula and modern technology, the Ministry of Education promoted the inclusion of MP in Italian secondary schools. MP hot topics produce interest and enthusiasm in learners at all ages, but to address this topic in high school in an effective way it is necessary to translate complex theories and highly-advanced experiments into an understandable language appreciated by students. In this contribution, we discuss an inquiry-driven learning sequence suitable to …
Quantum search of spatial regions
2003
Can Grover's algorithm speed up search of a physical region - for example a 2-D grid of size sqrt(n) by sqrt(n)? The problem is that sqrt(n) time seems to be needed for each query, just to move amplitude across the grid. Here we show that this problem can be surmounted, refuting a claim to the contrary by Benioff. In particular, we show how to search a d-dimensional hypercube in time O(sqrt n) for d at least 3, or O((sqrt n)(log n)^(3/2)) for d=2. More generally, we introduce a model of quantum query complexity on graphs, motivated by fundamental physical limits on information storage, particularly the holographic principle from black hole thermodynamics. Our results in this model include a…
Improved Hölder regularity for strongly elliptic PDEs
2019
We establish surprising improved Schauder regularity properties for solutions to the Leray-Lions divergence type equation in the plane. The results are achieved by studying the nonlinear Beltrami equation and making use of special new relations between these two equations. In particular, we show that solutions to an autonomous Beltrami equation enjoy a quantitative improved degree of H\"older regularity, higher than what is given by the classical exponent $1/K$.
Fuzzy Concepts in Small Worlds and the Identification of Leaders in Social Networks
2014
In the study of the Social Networks, the Small World phenomenon appears frequently. We apply some techniques of graph theory and fuzzy sets to characterize the Small World features as well as the existence of the figure of leader in Social Networks. These techniques help to the conceptual formalization in relational networks analysis, by transforming linguistic and human-focused manner concepts related to social networks in some formal representation. These techniques are also applied when the similarity among nodes wants to be measured in order to study the current homophily present in a Network.
2016
Abstract. To date, very little is known about the distribution of natural gas hydrates in sedimentary matrices and its influence on the seismic properties of the host rock, in particular at low hydrate concentration. Digital rock physics offers a unique approach to this issue yet requires good quality, high-resolution 3-D representations for the accurate modeling of petrophysical and transport properties. Although such models are readily available via in situ synchrotron radiation X-ray tomography, the analysis of such data asks for complex workflows and high computational power to maintain valuable results. Here, we present a best-practice procedure complementing data from Chaouachi et al.…