2,149 research outputs found
Maximum Principle for Boundary Control Problems Arising in Optimal Investment with Vintage Capital
No full textThe paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in finite and infinite horizon with Dynamic Programming methods in a series of papers by the same author et al. [26, 27, 28, 29, 30]. Necessary and sufficient optimality conditions for open loop controls are established. Moreover the co-state variable is shown to coincide with the spatial gradient of the value function evaluated along the trajectory of the system, creating a parallel between Maximum Principle and Dynamic Programming. The abstract model applies, as recalled in one of the first sections, to optimal investment with vintage capital.Linear convex control, Boundary control, Hamilton–Jacobi–Bellman equations, Optimal investment problems, Vintage capital
Packing Loose Hamilton Cycles
No full textA subsetCof edges in ak-uniform hypergraphHis aloose Hamilton cycleifCcovers all the vertices ofHand there exists a cyclic ordering of these vertices such that the edges inCare segments of that order and such that every two consecutive edges share exactly one vertex. The binomial randomk-uniform hypergraphHkn,phas vertex set [n] and an edge setEobtained by adding eachk-tuplee∈ () toEwith probabilityp, independently at random.Here we consider the problem of finding edge-disjoint loose Hamilton cycles covering all buto(|E|) edges, referred to as thepacking problem. While it is known that the threshold probability of the appearance of a loose Hamilton cycle inHkn,pisthe best known bounds for the packing problem are aroundp= polylog(n)/n. Here we make substantial progress and prove the following asymptotically (up to a polylog(n) factor) best possible result: forp≥ logCn/nk−1, a randomk-uniform hypergraphHkn,pwith high probability containsedge-disjoint loose Hamilton cycles.Our proof utilizes and modifies the idea of ‘online sprinkling’ recently introduced by Vu and the first author.</jats:p
Perfect matchings (and Hamilton cycles) in hypergraphs with large degrees
No full textAbstractWe establish a new lower bound on the l-wise collective minimum degree which guarantees the existence of a perfect matching in ak-uniform hypergraph, where 1≤l<k/2. For l=1, this improves a long-standing bound of Daykin and Häggkvist (1981) [5]. Our proof is a modification of the approach of Hàn et al. (2009) from [12].In addition, we fill a gap left by the results solving a similar question for the existence of Hamilton cycles
Thresholds for sustainable regeneration in urban restoration plantings in Hamilton City, New Zealand
No full textUrban forest patches have unique environmental and landscape characteristics which may influence the restoration of native plant communities. Urbanisation can lead to a drier and warmer climate, a prevalence of exotic seed sources and isolation from remnant native forest seed sources. This research investigates how these factors influence native species presence in different aged urban forest patches and uses life history traits to identify vulnerable species groups which may require active reintroduction. Seed rain, soil seed banks and vegetation composition was recorded within urban forest restoration plantings (10-36 years old) in Hamilton City, New Zealand with comparison to naturally regenerating forest within the city and a nearby rural forest remnant. To address dispersal limitation for several key mid to late successional forest species an experiment was also undertaken to investigate broadcast seeding as a method to reintroduce trees with large seeds and fleshy fruits into established early successional vegetation.
Seed rain, soil seed banks (fern spores inclusive) and understorey vegetation in urban forest were found to have higher exotic species richness and lower native species density and richness than rural forest. Both understorey vegetation and soil seed banks of urban sites >20 years old had lower exotic species richness than younger (10–20 years) sites, indicating a developmental threshold that provided some resistance to exotic species establishment. A prevalence of exotic species in urban seed rain, however, will allow reinvasion through edge habitat and following any disturbance to canopy vegetation. Persistent soil seed banks from both urban and rural sites were dominated by exotic herbaceous species and native fern species, while few other native forest species were found to persist for >1 year in the seed bank.
Urban native seed rain was greater in quantity than exotic seed rain (reflecting immediately surrounding vegetation) although only when native canopy species had been planted suggesting a benefit of initial planting to encourage restoration of native communities. Novel species arriving in the seed rain, but not present in the immediate vegetation, were often not abundant in quantity but represented three quarters of the native species recorded in urban seed rain providing evidence for some long-distance dispersal (particularly for wind-dispersed species) and potential for new species to establish. Urban and rural seed rain contained a similar number of novel native species arriving, although compositionally dissimilar, whereas a greater number of novel exotic species arrived in urban seed rain. Establishment for some native species arriving in urban seed rain was limited, e.g. ferns, indicating a suitable forest microclimate is still to develop.
It was found that the native forest flora in Hamilton City represented just over half (57%) of the species present in forests of the broader Hamilton Ecological District. This suggests limited natural colonisation from beyond the urban area and the absent species are suggested as priorities for urban reintroduction. In turn only 35% of the city forest flora was found to be represented in the seed supply (annual seed rain and soil seed bank) and understorey sampling in urban forest patches. An over representation of trees in the city forest flora may reflect some relictual long-lived species that are surviving but may no longer have viable populations. Forbs and parasitic plants, highly shade tolerant (i.e. late successional) species and those with biotic pollinators were under represented in the seed supply and understorey indicating some limitation for regeneration or colonisation in young urban forests. The richness of bird-dispersed native species in urban forest patches increased with proximity and size of good quality native vegetation but no other effects of dispersal mode on urban native species presence were found.
To facilitate dispersal, broadcast seeding was found to be a viable method of improving regeneration of large-seeded late successional trees and may be a cost-effective alternative to planting saplings. Seedling establishment can be improved with fruit flesh removal and clay ball treatments, especially in the presence of mammalian seed predators
Seed rain and soil seed banks limit native regeneration within urban forest restoration plantings in Hamilton City, New Zealand
No full textRestoration of native forest vegetation in urban environments may be limited due to isolation from native seed sources and to the prevalence of exotic plant species. To investigate urban seed availability we recorded the composition of seed rain, soil seed banks and vegetation at native forest restoration plantings up to 36 years old in Hamilton City and compared these with naturally regenerating forest within the city and in a nearby rural native forest remnant. Seed rain, soil seed banks (fern spores inclusive) and understorey vegetation in urban forest were found to have higher exotic species richness and lower native species density and richness than rural forest. Both understorey vegetation and soil seed banks of urban sites >20 years old had lower exotic species richness than younger (10–20 years) sites, indicating a developmental threshold that provided some resistance to exotic species establishment. However, the prevalence of exotic species in urban seed rain will allow reinvasion through edge habitat and following disturbance to canopy vegetation. Persistent soil seed banks from both urban and rural sites were dominated by exotic herbaceous species and native fern species, while few other native forest species were found to persist for >1 year in the seed bank. Enrichment planting will be required for those native species with limited dispersal or short-lived seeds, thus improving native seed availability in urban forests as more planted species mature reproductively. Further research into species seed traits and seedling establishment is needed to refine effective management strategies for successful restoration of urban native forests
Volatility Regimes in Central and Eastern European Countries’ Exchange Rates
No full textThe author investigates changes between volatility regimes in five Central and Eastern European countries to analyze whether these changes are consistent with changes in the official exchange rate arrangements. The analysis merges two approaches, the GARCH model (Bollerslev, 1986) and the Markov switching model (Hamilton, 1989). The author discovers switches between high- and low-volatility regimes consistent with policy settings for Hungary, Poland, and, to a lesser extent, the Czech Republic, whereas Romania and Slovakia do not show a clear picture. Furthermore, he checks the robustness of the model regarding the choice of the error distribution and finds that heavy-tailed conditional distributions substantially improve the results.CEEC, exchange rate volatility, regime switching GARCH, Markov switching model, transition economies
Correction to: Unintentional weight loss, its associated burden, and perceived weight status in people with cancer (Supportive Care in Cancer, (2020), 28, 1, (329-339), 10.1007/s00520-019-04797-y)
No full textThe article “Unintentional weight loss, its associated burden, and perceived weight status in people with cancer”, written by Yuen, E.Y.N, Zaleta, A.K., McManus, S., Buzaglo, J.S., LeBlanc, T.W., Hamilton, K., Stein, K., was originally published Online First without Open Access. After publication in volume 28, issue 1, page 329–339 the author decided to opt for Open Choice and to make the article an Open Access publication. Therefore, the copyright of the article has been changed to © The Author(s) 2022 and the article is forthwith distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http:// creat iveco mmons. org/ licen ses/ by/4.0. The original article is corrected
An application of Jordan canonical form to the proof of Cayley-Hamilton theorem
No full textThe statement of Cayley-Hamilton theorem is that every square matrix satisfies its own characteristic equation. Cayley-Hamilton theorem holds both in a vector space over a field and in a module over a commutative ring. The general proof of Cayley-Hamilton theorem is based on the concepts of minimal polynomial and adjoint matrix of a linear map (for the details of the general proof, see Lang (2002), page 561, or Liesen and Mehrmann (2011), page 96, or Shurman). In the case of a diagonalizable matrix A over an algebraically closed field the proof becomes trivial because one can consider the diagonal form D of A and the relation for the k-th power matrix Ak = CDkC−1, where C is the matrix for the basis change to the basis of eigenvectors of A (for the details, see Sernesi (2000) or Lang (1987)). The aim of this paper is to extend the simple proof for diagonalizable matrices to the case of non-diagonalizable ones over a generic field. First, we obtain a proof for non-diagonalizable matrices over an algebraically closed field and then, by virtue of the properties of field extensions, we show that this proof also holds in the case of a generic field
Counting Candy Crush configurations
No full textAk-stablec-coloured Candy Crush grid is a weak properc-colouring of a particular type ofk-uniform hypergraph.In this paper we introduce a fully polynomial randomised approximation scheme (FPRAS) which counts the number of k-stablec-coloured Candy Crush grids of a given size (m,n) for certain values of candk. We implemented this algorithm on Matlab, and found that in a Candy Crush grid with 7 available colours there are approximately 4.3×10613-stable colourings. (Note that, typical Candy Crushgames are played with 6 colours and our FPRAS is not guaranteed to work in expected polynomial time withk=3 andc=6.) We also discuss the applicability of this FPRASto the problem of counting the number of weak c-colourings of other, more general hypergraphs.Adam Hamilton, Giang T.Nguyen, Matthew Rougha
Implicit Partial Differential Equations: different approaching methods
No full textImplicit Partial Differential Equations:
different approaching methods
PhD Thesis of Giovanni Pisante
Abstract
In the last few decades the interest of scientists in nonlinear analysis
has been constantly increasing and nonlinear partial differential
equations have become one of the main tools of modern mathematical
analysis.
In this thesis we deal with a family of nonlinear partial differential
equations, the so called ”implicit partial differential equations”.
The problem of solving this type of equations has been approached
looking at it from different points of view and consequently different
approaching methods were developed. The choice of the method to
apply depends on what properties we require on the solutions of the
equation.
The principal aim of this work is to present some different ways
to establish the existence of solutions of implicit partial differential
equations. In particular we focus our attention on two methods: the
Baire category method and the viscosity method.
The first one is a functional analytic method based essentially on
the Baire category theorem. It was introduced by Cellina in 1980 to
prove density properties of solutions of some differential inclusions and
it has been extensively studied and extended by many authors. In
particular Dacorogna and Marcellini in a series of papers extended the
method to the framework of implicit differential equations looking at
these as differential inclusions. We present this theory, making a survey
on the recent results that we can find in literature and we present new
proofs of general existence theorems. We would point out that the
Baire category method has the ”defect” to be purely existential, that
is it can establish only the existence of solutions (in fact it ensures the
existence of infinitely many solutions), but it does not give any other
information.
The viscosity approach for this type of equations is one of the oldest
methods applied in this field and it has received much attention
since its introduction by Crandall and Lions in 1982. It deals essentially
with scalar problems, i.e. the Hamilton-Jacobi equations, and it
is less general than the previous one. Nevertheless it has the advantage
that it gives much more information than existence of solutions;
for instance, uniqueness, stability, maximality, and, under suitable hypotheses,
explicit formulas.
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Here we discuss about the existence of viscosity solutions for the
Hamilton-Jacobi equations looking at it from a ”geometrical” point of
view. The interest in finding geometrical conditions comes out from
the idea to compare the two above methods. Indeed, if we want to
use the viscosity method as a criterium to select, among the infinitely
many solutions given by the Baire category method, a preferred one, we
immediately deal with restrictive geometrical compatibility conditions.
In particular, generalizing these results, we present new geometrical
conditions sufficient and, in some cases, necessary for the existence of
viscosity solution of Hamilton-Jacobi equations with non necessarily
convex hamiltonian.
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