An Artificial Viscosity Approach to Quasistatic Crack Growth

Rodica Toader; Chiara Zanini

Displaying similar documents to “An Artificial Viscosity Approach to Quasistatic Crack Growth”

A New $L^{1}$ -Lower Semicontinuity Result

Daniele Graziani (2007)

Bollettino dell'Unione Matematica Italiana

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The aim of this work is to prove a chain rule and an $L^{1}$ -lower semicontinuity theorems for integral functional defined on $BV(\Omega)$ . Moreover we apply this result in order to obtain new relaxation and $\Gamma$ -convergence result without any coerciveness and any continuity assumption of the integrand $f(x,s,p)$ with respect to the variable $s$ .

Isomorphisms of Royden Type Algebras Over $\mathbb{S}^{1}$

Teresa Radice, Eero Saksman, Gabriella Zecca (2009)

Bollettino dell'Unione Matematica Italiana

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Let $\mathbb{S}^{1}$ and $\mathbb{D}$ be the unit circle and the unit disc in the plane and let us denote by $\mathcal{A}(\mathbb{S}^{1})$ the algebra of the complex-valued continuous functions on $\mathbb{S}^{1}$ which are traces of functions in the Sobolev class $W^{1,2}(\mathbb{D})$ . On $\mathcal{A}(\mathbb{S}^{1})$ we define the following norm $\|u\|=\|u\|_{L^{\infty}(\mathbb{S}^{1})}+\left(\iint_{\mathbb{D}}|\nabla\tilde% {u}|^{2}\right)^{1/2}$ where is the harmonic extension of $u$ to $\mathbb{D}$ . We prove that every isomorphism of the functional algebra $\mathcal{A}(\mathbb{S}^{1})$ is a quasitsymmetric change of variables on $\mathbb{S}^{1}$ .

On the Functional Equation $f (λ) + f (ω λ) f (ω^{- 1} λ) = 1$ , $(ω^{5} = 1)$

Yasutaka Sibuya (1984)

Recherche Coopérative sur Programme n°25

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$L^{p}$ Maximal Regularity for Second Order Cauchy Problems is Independent of $p$

Ralph Chill, Sachi Srivastava (2008)

Bollettino dell'Unione Matematica Italiana

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If the second order problem $\ddot{u}+\dot{u}+Au=f$ has $L^{p}$ maximal regularity for some $p\in(1,\infty)$ , then it has $L^{p}$ maximal regularity for every $p\in(1,\infty)$ .

Partial Hölder continuity for quasilinear parabolic systems of higher order with strictly controlled growth

Mario Marino, Antonino Maugeri (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Sfruttando i risultati di [1], si prova che le derivate spaziali $D^{\alpha}u$ di ordine $|\alpha|$ con $|\alpha|<m-1$ delle soluzioni in $Q$ di un sistema parabolico quasilineare di ordine $2m$ con andamenti strettamente controllati, sono parzialmente hölderiane in $Q$ con esponente di hölderianità decrescente al crescere di $|\alpha|$ .

Relaxation and gamma-convergence of supremal functionals

Francesca Prinari (2006)

Bollettino dell'Unione Matematica Italiana

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We prove that the $\Gamma$ -limit in $L^{\infty}_{\mu}$ of a sequence of supremal functionals of the form $F_{k}(u)=\operatorname{\mu-ess\,sup}_{\Omega}f_{k}(x,u)$ is itself a supremal functional. We show by a counterexample that, in general, the function which represents the $\Gamma$ -lim $F(\cdot,B)$ of a sequence of functionals $F_{k}(u,B)=\operatorname{\mu-ess\,sup}_{B}f_{k}(x,u)$ can depend on the set $B$ and wegive a necessary and sufficient condition to represent $F$ in the supremal form $F(u,B)=\operatorname{\mu-ess\,sup}_{B}f(x,u)$ . As a corollary, if $f$ represents a supremal functional, then the level convex envelope of $f$ represents its weak* lower semicontinuous envelope. ...

A Regular Threefold of General Type with $p_{g}=0$ and $P_{2}=6$

M. Cristina Ronconi (2009)

Bollettino dell'Unione Matematica Italiana

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The range of the bigenus $P_{2}$ is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with $p_{g}=0$ : The examples in the literature have $P_{2}\leq 5$ . In the present paper we present a non-singular threefold with $p_{g}=q_{1}=q_{2}=0$ ; $P_{2}=6$ ; the bicanonical map is stably birational.

A Montel Type Result for Subharmonic Functions

R. Supper (2009)

Bollettino dell'Unione Matematica Italiana

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This article is devoted to sequences $(u_{n})_{n}$ of subharmonic functions in $\mathbb{R}^{N}$ , with finite order, whose means $J_{u_{n}}(r)$ (over spheres centered at the origin, with radius r) satisfy such a condition as: $\forall r>0$ , $\exists A_{r}>0$ such that $J_{u_{n}}(r)\leq A_{r}$ , $\forall n\in\mathbf{N}$ . The paper investigates under which conditions one may extract a pointwise or uniformly convergent subsequence.

On locally $S$ -closed spaces

Takashi Noiri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si studiano le condizioni sotto cui l’immagine (o l'immagine inversa) di uno spazio localmente $S$ -chiuso sia localmente $S$ -chiuso.

Convergence to Equilibrium of the Solution of Kac's Kinetic Equation. A Probabilistic View

Eugenio Regazzini (2009)

Bollettino dell'Unione Matematica Italiana

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Let $f(\cdot,t)$ be the probability density function representing the solution of Kac's Boltzmann-like equation at time $t$ , with initial data $f_{0}$ , and let $g_{\sigma}$ be the Gaussian density with zero mean and variance $\sigma^{2}$ , $\sigma^{2}$ being the value of the second moment of $f_{0}$ . Henry McKean Jr. put forward the conjecture that the total variation distance between $f(\cdot,t)$ and $g_{\sigma}$ goes to zero, as $t\to+\infty$ , with an exponential rate equal to $-1/4$ . This lecture aims at explaining the main efforts made to a view to validating this conjecture,...

$\bf{L}$ -embedding, Amalgamation and $\bf{L}$ -elementary equivalence

Daniele Mundici (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Ogni logica $L$ genera canonicamente la $L$ -equivalenza $\equiv_{L}$ e la $L$ -immersione $\underset{L}{\rightarrow}$ proprio come la logica del primo ordine genera l’equivalenza elementare $\equiv$ e l’immersione elementare $\lesssim$ . Astraendo da $L$ , è interessante studiare in sè relazioni d’equivalenza e di immersione generali tra strutture. Mostriamo che esiste una corrispondenza biunivoca tra relazioni d’equivalenza con la proprietà di Robinson e relazioni d’immersione con la proprietà di Amalgamazione Forte ( $AP^{+}$ ). Caratterizziamo algebricamente...

A generalized exponential map for an affinely homogeneous cone

Umberto Sampieri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Dato un cono $V$ aperto non vuoto, convesso, regolare e affinemente omogeneo in uno spazio vettoriale reale $W$ di dimensione finita si prova che per ogni $v$ appartenente a $V$ esiste un diffeomorfismo $E_{v}:W\to V$ che soddisfa le condizioni seguenti E1) $E_{v}(0)=v$ ; E2) $\det(dE_{v}(y))=\Phi_{V}(E_{v}(y))^{-1}$ per ogni $y$ appartenente a $W$ ove $\Phi_{V}:V\to\mathbf{R}^{+}$ è la funzione caratteristica di $V$ .

Correctors for Parabolic Equations in a Heterogeneous Fibered Medium

Mourad Sfaxi, Ali Sili (2007)

Bollettino dell'Unione Matematica Italiana

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We study the problem of correctors in the framework of the homogenization of linear parabolic equations posed in a heterogeneous medium $\Omega$ made of two materials. The first one is located in a set $F_{\epsilon}$ of cylindrical parallel fibers periodically distributed with a period of size $\epsilon$ , and the second one is located in the "matrix" $M_{\epsilon}=\Omega\setminus F_{\epsilon}$ . The ratio between the conductivity coefficients of the two materials is of order $1/\epsilon^{2}$ . After writing the homogenized problem, we give a corrector result and prove...

A Note on Sectorial and R-Sectorial Operators

Alberto Venni (2008)

Bollettino dell'Unione Matematica Italiana

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The following results are proved: (i) if $\alpha$ , $\beta\in\mathbb{R}^{+}$ and $A$ is a sectorial operator, then the set $\{t^{\alpha}A^{\beta}(t+A);t>0\}$ is bounded; (ii) the same set of operators is R-bounded if $A$ is R-sectorial.

A note on singular and degenerate abstract equations

Angelo Favini (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si considera l’equazione astratta $BA_{1}u+A_{0}u=h$ , dove $A_{i}$ $(i=0,1)$ e $B$ sono convenienti operatori lineari chiusi fra spazi di Banach, $A_{i}$ non è necessariamente invertibile, e $A_{0}$ , $A_{1}$ non commutano con $B$ . Si studiano esistenza ed unicità delle soluzioni. Si indicano alcune applicazioni a certe equazioni differenziali degeneri o singolari.

Nodal curves in $\mathbb{P}_{3}(\mathbb{C})$

Edoardo Ballico, Paolo Oliverio (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Siano $d$ , $g$ , $t$ interi con $0\leq t\leq g$ ; se esiste in $\mathbb{P}_{3}(\mathbb{C})$ una curva connessa, non singolare di grado $d$ e genere $g$ , allora esiste in $\mathbb{P}_{3}(\mathbb{C})$ una curva irriducibile di grado $d$ , genere aritmetico $g$ e $t$ nodi.

A curve of genus $q$ with a Half-Canonical embedding in $\mathbf{P}^{3}$

Sevin Recillas (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si costruiscono curve di genere $g=4n—3$ , $n\geq 3$ che hanno $2^{n-3}(2^{n-2}-1)$ fasci semicanonici $L$ tali che $h^{0}(L)=4$ . Per $n+3$ si dimostra che gli $L$ sono molto ampi.

Eigenfunctions of the Laplace Operators for a Building of Type $\widetilde{G}_{2}$

A. M. Mantero, A. Zappa (2009)

Bollettino dell'Unione Matematica Italiana

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Let $\Delta$ be thick affine building of type $\widetilde{G}_{2}$ the Laplace operators of $\Delta$ ; associated with a pair $(y_{1},y_{2})$ ; is the Poisson transform of a suitable finitely additive measure on the maximal boundary $\Omega$ of $\Delta$ ; by using only the combinatorial structure of $\Delta$ .

Moving averages

S. V. Butler, J. M. Rosenblatt (2008)

Colloquium Mathematicae

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In ergodic theory, certain sequences of averages $A_{k} f$ may not converge almost everywhere for all f ∈ L¹(X), but a sufficiently rapidly growing subsequence $A_{m_{k}} f$ of these averages will be well behaved for all f. The order of growth of this subsequence that is sufficient is often hyperexponential, but not necessarily so. For example, if the averages are $A_{k} f (x) = 1 / (2^{k}) \sum_{j = 4^{k} + 1}^{4^{k} + 2^{k}} f (T^{j} x)$ , then the subsequence $A_{k ²} f$ will not be pointwise good even on $L^{\infty}$ , but the subsequence $A_{2^{k}} f$ will be pointwise good on L¹. Understanding when the hyperexponential...

On the existence of scrolls in $\bf{P}^{4}$

Antonio Lanteri (1980)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dimostra il seguente risultato. Sia $X$ una superficie proiettivamente rigata, non iperpiana, di $\bf{P}^{4}$ ; allora $X$ è la rigata cubica oppure è una rigata quintica ellittica. Si descrive inoltre una nuova generazione proiettiva delle rigate quintiche ellittiche di $\bf{P}^{4}$ .

The Schreier Property and Gauss' Lemma

Daniel D. Anderson, Muhammad Zafrullah (2007)

Bollettino dell'Unione Matematica Italiana

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Let $D$ be an integral domain with quotient field $D$ . Recall that $D$ is Schreier if $D$ is integrally closed and for all $x,y,z\in D\setminus\{0\}$ , $x|yz$ implies that $x=r\cdot s$ where $r|y$ e $s|z$ . A GCD domain is Schreier. We show that an integral domain $D$ is a GCD domain if and only if (i) for each pair $a,b\in D\setminus\{0\}$ , there is a finitely generated ideal $B$ such that $aD\bigcap bD=B_{v}$ and (ii) every quadratic in $D[X]$ that is a product of two linear polynomials in $K[X]$ is a product of two linear polynomials in $D[X]$ . We also show that $D$ is Schreier if and only if every...

A remark on complex powers of analytic functions

Giuseppe Zampieri (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Sia $K\subset\subset\mathbb{R}^{n}$ un compatto, $f\geq 0$ una funzione analitica all'intorno di $K$ , ed $m$ la massima molteplicità in $K$ degli zeri di $f$ ; si prova che la potenza $f^{\lambda}$ ( $\lambda\in\mathbb{C}$ , $Re\lambda>—\frac{1}{m}$ ) è integrabile in $K$ . L'estensione meromorfa dell'applicazione $\lambda\rightarrow f^{\lambda}$ da $Re\lambda>0$ a tutto $\mathbb{C}$ (con valori in $\mathcal{D}^{\prime}(K)$ anziché in $L^{1}(K)$ ) era già stata provata in [1] e [2].

Geometry of Syzygies via Poncelet Varieties

Giovanna Ilardi, Paola Supino, Jean Vallès (2009)

Bollettino dell'Unione Matematica Italiana

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We consider the Grassmannian $\mathbb{G}r(k,n)$ of $(k+1)$ -dimensional linear subspaces of $V_{n}=H^{0}(\mathbb{P}^{1},\mathcal{O}_{\mathbb{P}_{1}}(n))$ . We define $\mathfrak{X}_{k,r,d}$ as the classifying space of the $k$ -dimensional linear systems of degree $n$ on $\mathbb{P}^{1}$ , whose bases realize a fixed number $r$ of polynomial relations of fixed degree $d$ , say $r$ syzygies of degree $d$ . Firstly, we compute the dimension of $\mathfrak{X}_{k,r,d}$ . In the second part we make a link between $\mathfrak{X}_{k,r,d}$ and the Poncelet varieties. In particular, we prove that the existence of linear syzygies implies the existence of singularities on the...

The Martingale Problem in Hilbert Spaces

Giuseppe Da Prato, Luciano Tubaro (2008)

Bollettino dell'Unione Matematica Italiana

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We consider an SPDE in a Hilbert space $H$ of the form $dX(t)=(AX(t)+b(X(t)))\,dt+\sigma(X(t))\,dW(t)$ , $X(0)=x\in H$ and the corresponding transition semigroup $P_{t}f(x)=\mathbb{E}[f(X(t,x))]$ . We define the infinitesimal generator $\bar{L}$ of $P_{t}$ through the Laplace transform of $P_{t}$ as in [1]. Then we consider the differential operator $L\varphi=\frac{1}{2}\operatorname{Tr}[\sigma(x)\sigma^{*}(x)D^{2}\varphi]+% \langle b(x),D\varphi\rangle$ defined on a suitable set $V$ of regular functions. Our main result is that if $V$ is a core for $\bar{L}$ , then there exists a unique solution of the martingale problem defined in terms of $L$ . Application to the Ornstein-Uhlenbeck equation and to some regular...

A Note on VLO Functions

Francesca Angrisani, Giacomo Ascione (2018)

Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche

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Inspired by a result from Leibov, we ﬁnd that the supremum deﬁning the $B L O$ norm in $[0,1]$ is actually attained by a speciﬁc sub-interval of $[0,1]$ for $f\in VLO([0,1])$

Twinning in minerals and metals: remarks on the comparison of a thermoelastic theory with some experimental results. Mechanical twinning and growth twinning. Nota II

Giovanni Zanzotto (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In this Note II we continue the analysis of the phenomenon of mechanical twinning that we began in a preceding Note I $(^{1})$ . Furthermore, we point out some fundamental properties useful in the study of growth twins, for which a fully comprehensive thermoelastic theory is not yet available.

The Probabilistic Zeta Function of the Alternating Group $\operatorname{Alt}(p+1)$

Marilena Massa (2007)

Bollettino dell'Unione Matematica Italiana

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We study the irreducibility of the Dirichlet polynomial $P_{G}(s)$ when $G$ is the alternating group on $p+1$ elements with $p$ prime and we prove that $P_{G}(s)$ is irreducible for infinitely many choiches of $p$ .

On the lower semicontinuity of certain integral functionals

Ennio De Giorgi, Giuseppe Buttazzo, Gianni Dal Maso (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dimostra che il funzionale $\int_{\Omega}f(u,Du)dx$ è semicontinuo inferiormente su $W_{loc}^{1,1}(\Omega)$ , rispetto alla topologia indotta da $L_{loc}^{1}(\Omega)$ , qualora l’integrando $f(s,p)$ sia una funzione non-negativa, misurabile in $s$ , convessa in $p$ , limitata nell’intorno dei punti del tipo $(s,0)$ , e tale che la funzione $s\mapsto f(s,0)$ sia semicontinua inferiormente su $\mathbf{R}$ .

Some properties of perfect metric spaces

Angelo Bella, Biagio Ricceri (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questa Nota, dati uno spazio metrico perfetto $X$ ed un suo sottoinsieme $K$ chiuso e raro, si dimostra l'esistenza di una funzione continua $f:X\to[0,1]$ tale che $int(f^{-1}(t))=\emptyset$ per ogni $t\in[0,1]$ , $f(x)=0$ per ogni $x\in K$ e $f(y)=1$ per qualche $y\in X\setminus K$ . In particolare, ciò permette di dare risposta simultaneamente a due questioni poste in [2]. Si mettono in evidenza, poi, ulteriori conseguenze di tale risultato.

An Elliptic Problem with a Lower Order Term Having Singular Behaviour

Daniela Giachetti, François Murat (2009)

Bollettino dell'Unione Matematica Italiana

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We prove the existence of distributional solutions to an elliptic problem with a lower order term which depends on the solution $u$ in a singular way and on its gradient $D u$ with quadratic growth. The prototype of the problem under consideration is $\begin{cases}-\Delta u+\lambda u=\pm\frac{|Du|^{2}}{|u|^{k}}+f&\text{in}\,% \Omega,\\ u=0&\text{on}\,\partial\Omega,\end{cases}$ where $\lambda>0$ , $k>0$ ; $f(x)\in L^{\infty}(\Omega)$ , $f(x)\geq 0$ (and so $u\geq 0$ ). If $0<k<1$ , we prove the existence of a solution for both the "+" and the "-" signs, while if $k\geq 1$ , we prove the existence of a solution for the "+" sign only.

Congruences between modular forms and related modules

Miriam Ciavarella (2006)

Bollettino dell'Unione Matematica Italiana

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We fix $\ell$ a prime and let $M$ be an integer such that $\ell\operatorname{\not|}M$ ; let $f\in S_{2}(\Gamma_{1}(M\ell^{2}))$ be a newform supercuspidal of fixed type at $\ell$ and special at a finite set of primes. For an indefinite quaternion algebra over $Q$ , of discriminant dividing the level of $f$ , there is a local quaternionic Hecke algebra $T$ associated to $f$ . The algebra $T$ acts on a module $M_{f}$ coming from the cohomology of a Shimura curve. Applying the Taylor-Wiles criterion and a recent Savitt's theorem, $T$ is the universal deformation ring of a global...

$\bf{L}$ -embedding, Amalgamation and $\bf{L}$ -elementary equivalence

Daniele Mundici (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Conductor and separating degrees for sets of points in $\mathbb{P}^{r}$ and in $\mathbb{P}^{1}\times\mathbb{P}^{1}$

Lucia Marino (2006)

Bollettino dell'Unione Matematica Italiana

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We attempt to generalize conductor degree's results, known in $\mathbb{P}^{2}$ , to the case of 0-dimensional schemes of $\mathbb{P}^{r}$ . In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in $\mathbb{P}^{r}$ and we determine the conductor degree of every point in a $r$ -partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme...

A note on semi-continuous mappings

Takashi Noiri (1973)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Se $X$ ed $Y$ sono spazi topologici, un'applicazione $f:X\to Y$ dicesi semicontinua [3] se, per ogni insieme aperto $V$ di $Y$ , $f^{-1}(V)$ risulta un insieme semiaperto di $X$ . Qui si studiano tali applicazioni e si dànno tre loro caratterizzazioni.

On operators from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ or to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$

Christian Samuel (2010)

Colloquium Mathematicae

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We show that every operator from $ℓ_{s}$ to $ℓ_{p} \otimes ̂ ℓ_{q}$ is compact when 1 ≤ p,q < s and that every operator from $ℓ_{s}$ to $ℓ_{p} \hat{\otimes ̂} ℓ_{q}$ is compact when 1/p + 1/q > 1 + 1/s.

The number of minimum points of a positive quadratic form

G. L. Watson

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CONTENTSIntroduction.......................................................................................61. Definition of certain special forms...........................................62. Statement of results...................................................................83. Proof of Theorem 2.....................................................................94. Preliminaries for Theorem 1.....................................................105. Further preliminaries for Theorem...

Quasi-polynomial mixing of the 2D stochastic Ising model with “plus” boundary up to criticality

Eyal Lubetzky, Fabio Martinelli, Allan Sly, Fabio Lucio Toninelli (2013)

Journal of the European Mathematical Society

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We considerably improve upon the recent result of [37] on the mixing time of Glauber dynamics for the 2D Ising model in a box of side $L$ at low temperature and with random boundary conditions whose distribution $P$ stochastically dominates the extremal plus phase. An important special case is when $P$ is concentrated on the homogeneous all-plus configuration, where the mixing time $T_{M I X}$ is conjectured to be polynomial in $L$ . In [37] it was shown that for a large enough inverse-temperature $β$ and...

A Note on Regular-closed Functions

Takashi Noiri (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Se $X$ ed $Y$ sono spazi topologici, una funzione $f:X\to Y$ è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di $X$ in un insieme chiuso di $Y$ . Si dimostra che una funzione regolarmente chiusa $f:X\to Y$ risulta chiusa se $X$ è normale.

On Relative $\gamma_{k}$ -Sets

Maddalena Bonanzinga, Filippo Cammaroto, Bruno A. Pansera (2007)

Bollettino dell'Unione Matematica Italiana

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In this note we show a relative version of $\gamma_{k}$ -set introduced and studied in [12]. We give several characterizations of this property; in particular one of the characterizations is Ramsey theoretical. Also we give a result involving a property of the corresponding mapping between function spaces.

On the ampleness of $K_{X}\bigotimes L^{n}$ for a polarized threefold $(X,L)$

Antonio Lanteri, Marino Palleschi (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Siano $X$ una varietà algebrica proiettiva complessa non singolare tridimensionale, $L$ un fibrato lineare ampio su $X$ , e $n\geq 2$ un intero. Si prova che, a meno di contrarre un numero finito di $-1$ -piani di $X$ , il fibrato $K_{X}\bigotimes L^{n}$ è ampio ad eccezione di alcuni casi esplicitamente descritti. Come applicazione si dimostra l'ampiezza del divisore di ramificazione di un qualunque rivestimento di $\mathbf{P}^{3}$ o della quadrica liscia di $\mathbf{P}^{4}$ .