Search results for "Geometria"
showing 10 items of 422 documents
Gromov-hyperboliset ryhmät
2016
Meeri Martimo, Gromov-hyperboliset ryhmät (engl. Gromov-hyperbolic groups), matematiikan pro gradu -tutkielma, 51 s., Jyväskylän yliopisto, Matematiikan ja tilastotieteen laitos, syksy 2016. Tässä tutkielmassa käsitellään Gromov-hyperbolisia ryhmiä, jotka ovat geometrisen ryhmäteorian tutkimuskohde. Geometrinen ryhmäteoria on melko uusi matematiikan suuntaus, ja 1980-luvulla Gromov-hyperboliset ryhmät kehittänyt ranskalaisvenäläinen matemaatikko Mikhail Gromov yksi sen uranuurtajista. Gromov-hyperbolisuus määritellään ensin metrisille avaruuksille tietyllä tavalla ohuiden kolmioiden avulla. Kolmiot ovat vaaditulla tavalla ohuita esimerkiksi hyperbolisissa avaruuksissa, mutta eivät reaaliaks…
LO STUDIO DELLE MATRICI GEOMETRICHE DEL PROGETTO PER LA CHIESA DEI PADRI SOMASCHI A MESSINA ATTRAVERSO LA MODELLAZIONE DIGITALE
2016
Il contributo è dedicato all'analisi delle geometrie sottese al progetto della chiesa per i Padri Somaschi di Messina di Guarino Guarini, progetto non datato e mai realizzato, noto grazie alla pubblicazione all'intero del trattato Architettura Civile dell'architetto modenese. L'indagine si avvale del processo di ricostruzione digitale della chiesa, che ha consentito un approfondimento delle geometrie che informano ogni singolo elemento dell'architettura, nonché del constante confronto con le opere esistenti d Guarini, in particolar modo la chiesa di San Lorenzo e la cappella del SS. Sudario di Torino.
Rational normal curves and Hadamard products
2021
AbstractGiven $$r>n$$ r > n general hyperplanes in $$\mathbb P^n,$$ P n , a star configuration of points is the set of all the n-wise intersection of the hyperplanes. We introduce contact star configurations, which are star configurations where all the hyperplanes are osculating to the same rational normal curve. In this paper, we find a relation between this construction and Hadamard products of linear varieties. Moreover, we study the union of contact star configurations on a same conic in $$\mathbb P^2$$ P 2 , we prove that the union of two contact star configurations has a special h-vector and, in some cases, this is a complete intersection.
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
2016
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.
Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method
2021
AbstractIn this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the prop…
A construction of Frobenius manifolds from stability conditions
2018
A finite quiver $Q$ without loops or 2-cycles defines a 3CY triangulated category $D(Q)$ and a finite heart $A(Q)$. We show that if $Q$ satisfies some (strong) conditions then the space of stability conditions $Stab(A(Q))$ supported on this heart admits a natural family of semisimple Frobenius manifold structures, constructed using the invariants counting semistable objects in $D(Q)$. In the case of $A_n$ evaluating the family at a special point we recover a branch of the Saito Frobenius structure of the $A_n$ singularity $y^2 = x^{n+1}$. We give examples where applying the construction to each mutation of $Q$ and evaluating the families at a special point yields a different branch of the m…
Mirror quintics, discrete symmetries and Shioda maps
2008
In a recent paper, Doran, Greene and Judes considered one parameter families of quintic threefolds with finite symmetry groups. A surprising result was that each of these six families has the same Picard Fuchs equation associated to the holomorphic 3-form. In this paper we give an easy argument, involving the family of Mirror Quintics, which implies this result. Using a construction due to Shioda, we also relate certain quotients of these one parameter families to the family of Mirror Quintics. Our constructions generalize to degree n Calabi Yau varieties in (n-1)-dimensional projective space.
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.
MR 2944715 Reviewed Zhu S. On the recursion formula for double Hurwitz numbers. Proceedings of the American Mathematical Society (2012) 140, no. 11, …
2013
Let $\mu = (\mu_{1}, \mu_{2}, \ldots, \mu_{m})$ and $\nu = (\nu_{1}, \nu_{2}, \ldots, \nu_{n})$ be two partitions of a positive integer $d$. In this paper, the author considers degree $d$ branched coverings of $\mathbb{P}^{1}$ with at most two special points, $0$ and $\infty$. Specifically, the purpose of the author is to give a recursion formula for double Hurwitz numbers $H^{g}_{\mu, \nu}$ by the cut-join analysis. Here, $H^{g}_{\mu, \nu}$ denotes the number of genus $g$ branched covers of $\mathbb{P}^{1}$ with branching date corresponding to $\mu$ and $\nu$ over $0$ and $\infty$, respectively. Furthemore, as application, the author gets a polynomial identity for linear Goulden-Jackson-Va…
MR 2827979 Reviewed Lando, S. K. Hurwitz numbers: on the edge between combinatorics and geometry. Proceedings of the International Congress of Mathem…
2012
Object of study in this paper are the Hurwitz numbers. They were introduced by Hurwitz in the end of nineteenth century and still they are of great interest. The Hurwitz numbers are important in topology because they enumerate ramified coverings of two-dimensional surfaces, but not only. The author observes that their importance in modern research is mainly due to their connections with the geometry of the moduli space of curves. Moreover, they are of interest in mathematical physics and group theory. The purpose of this paper is to describe the progress made in the last couple of decades in understanding Hurwitz numbers.