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

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

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 Lincei. Matematica e Applicazioni

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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.

An Artificial Viscosity Approach to Quasistatic Crack Growth

Rodica Toader, Chiara Zanini (2009)

Bollettino dell'Unione Matematica Italiana

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We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$ -gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero.

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...

Exponent of growth of polynomial mappings of $C^{2}$ into $C^{2}$

Jacek Chadzyński, Tadeusz Krasiński (1988)

Banach Center Publications

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Groups of given intermediate word growth

Laurent Bartholdi, Anna Erschler (2014)

Annales de l’institut Fourier

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We show that there exists a finitely generated group of growth $\sim f$ for all functions $f : ℝ_{+} \to ℝ_{+}$ satisfying $f (2 R) \leq f {(R)}^{2} \leq f (η_{+} R)$ for all $R$ large enough and $η_{+} \approx 2.4675$ the positive root of $X^{3} - X^{2} - 2 X - 4$ . Set $α_{-} = log 2 / log η_{+} \approx 0.7674$ ; then all functions that grow uniformly faster than $exp (R^{α_{-}})$ are realizable as the growth of a group. We also give a family of sum-contracting branched groups of growth $\sim exp (R^{α})$ for a dense set of $α \in [α_{-}, 1]$ .

Effective finding of the solutions of the form $\sum_{l = 1}^{\infty} \frac{a_{l}}{x^{l}}$ for the differential equations of the finite and infinite order

K. Orlov (1980)

Matematički Vesnik

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On the proximate order of $f^{(s)} (z) * g^{(s)} (z)$ and ${[f (z) * g (z)]}^{(s)}$

M. K. Sen (1971)

Annales Polonici Mathematici

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On the fundamental solution of the equation $∆^{p} u (X) + k (r) u (X) = 0$

J. Musiałek (1969)

Annales Polonici Mathematici

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Existence of discontinuous absolute minima for certain multiple integrals without growth properties

Lamberto Cesari (1988)

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

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In the present paper the author discusses certain multiple integrals $I(u)$ of the calculus of variations satisfying convexity conditions, and no growth property, and the corresponding Serrin integrals $\mathfrak{I}(u)$ , to which the existence theorems in [3,4,5] do not apply. However, in the present paper, the integrals $I(u)$ and $\mathfrak{I}(u)$ are reduced to simpler form $H(v)$ and $\mathcal{H}(v)$ to which the existence theorems above apply. Thus, we derive that $I(u)\leq\mathfrak{I}(u)$ , $H(v)\leq\mathcal{H}(v)$ , we obtain the existence of the absolute minimum for the Serrin forms $\mathfrak{I}(u)$ ...

Semicontinuity in $L^{\infty}$ for polyconvex integrals

Emilio Acerbi, Giuseppe Buttazzo, Nicola Fusco (1982)

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

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Viene studiata la semicontinuità rispetto alla topologia di $L^{\infty}(\Omega;\mathbf{R}^{m})$ per alcuni funzionali del Calcolo delle Variazioni dipendenti da funzioni a valori vettoriali.

A Marchaud type inequality

Jorge Bustamante (2022)

Commentationes Mathematicae Universitatis Carolinae

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We present a new Marchaud type inequality in $𝕃^{p}$ spaces.

Convergence of Taylor series in Fock spaces

Haiying Li (2014)

Studia Mathematica

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It is well known that the Taylor series of every function in the Fock space $F_{α}^{p}$ converges in norm when 1 < p < ∞. It is also known that this is no longer true when p = 1. In this note we consider the case 0 < p < 1 and show that the Taylor series of functions in $F_{α}^{p}$ do not necessarily converge “in norm”.