Indagationes Mathematicae-New Series最新文献

The modeling of risk situations that occur in a space framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial behavior do not characterize the finite-dimensional distributions of the random field, they have the advantage of being immediate to interpret and easier to estimate. The coefficients that we propose give us information about the tendency of a random field for local oscillations of its values in relation to real valued high levels. It is not the magnitude of the oscillations that is being evaluated, but rather the greater or lesser number of oscillations, that is, the tendency of the trajectories to oscillate. We can observe surface trajectories more smooth over a region according to higher crossinggram value. It takes value in $[0,1]$ and increases with the concordance of the variables of the random field.

We deal with the finite family $F$ of continuous maps on the Hausdorff space $X$. A nonempty compact subset $A$ of such space is called a strict attractor if it has an open neighborhood $U$ such that $A={lim}_{n\to \infty }{F}^n\left(S\right)$ for every nonempty compact $S\subset U$. Every strict attractor is a pointwise attractor, which means that the set $\{x\in X;{lim}_{n\to \infty }{F}^n\left(x\right)=A\}$ contains $A$ in its interior.

We present a class of examples of pointwise attractors – from the finite set to the Sierpiński carpet – which are not strict when we add to the system one nonexpansive map.

We give a sufficient condition for a pair of Banach spaces $(X,Y)$ to have the following property: whenever $W_1\subseteq X$ and $W_2\subseteq Y$ are sets such that $\{x\otimes y:x\in W_1,y\in W_2\}$ is weakly precompact in the projective tensor product $X{\hat{\otimes }}_{\pi }Y$, then either $W_1$ or $W_2$ is relatively norm compact. For instance, such a property holds for the pair $({\ell }_p,{\ell }_q)$ if $1<p,q<\infty$ satisfy $1/p+1/q\ge 1$. Other examples are given that allow us to provide alternative proofs to some results on multiplication operators due to Saksman and Tylli. We also revisit, with more direct proofs, some known results about the embeddability of ${\ell }_1$ into $X{\hat{\otimes }}_{\pi }Y$ for arbitrary Banach spaces $X$ and $Y$, in connection with the compactness of all operators from $X$ to $Y^{\ast }$.

This paper is a sequel to a previous paper of the authors in which the cohomology of semi-simple Leibniz algebras was computed by using spectral sequences. In the present paper we generalize the vanishing theorems of Dixmier and Barnes for nilpotent and (super)solvable Lie algebras to Leibniz algebras. Moreover, we compute the cohomology of the one-dimensional Lie algebra with values in an arbitrary Leibniz bimodule and show that it is periodic with period two. As a consequence, we establish the Leibniz analogue of a non-vanishing theorem of Dixmier for nilpotent Leibniz algebras. In addition, we prove a Fitting lemma for Leibniz bimodules

Many results about the geometry of the trianguline variety have been obtained by Breuil–Hellmann–Schraen. Among them, using geometric methods, they have computed a formula for the dimension of the tangent space of the trianguline variety at dominant crystalline generic points, which has a conjectural generalisation to companion (i.e. non-dominant) points. In an earlier work, they proved a weaker form of this formula under the assumption of modularity using arithmetic methods. We prove a generalisation of a result of Bellaïche–Chenevier in $p$-adic Hodge theory and use it to extend the arithmetic methods of Breuil–Hellmann–Schraen to a wide class of companion points.

With this article, we hope to launch the investigation of what we call the Real Zero Amalgamation Problem. Whenever a polynomial arises from another polynomial by substituting zero for some of its variables, we call the second polynomial an extension of the first one. The Real Zero Amalgamation Problem asks when two (multivariate real) polynomials have a common extension (called amalgam) that is a real zero polynomial. We show that the obvious necessary conditions are not sufficient. Our counterexample is derived in several steps from a counterexample to amalgamation of matroids by Poljak and Turzík. On the positive side, we show that even a degree-preserving amalgamation is possible in three very special cases with three completely different techniques. Finally, we conjecture that amalgamation is always possible in the case of two shared variables. The analogue in matroid theory is true by another work of Poljak and Turzík. This would imply a very weak form of the Generalized Lax Conjecture.

Assuming the Generalized Riemann Hypothesis, we establish explicit bounds in the $q$-aspect for the logarithmic derivative $\left(L^{\prime }/L\right)\left(\sigma ,\chi \right)$ of Dirichlet $L$-functions, where $\chi$ is a primitive character modulo $q\ge 10^{30}$ and $1/2+1/loglogq\le \sigma \le 1-1/loglogq$. In addition, for $\sigma =1$ we improve upon the result by Ihara, Murty and Shimura (2009). Similar results for the logarithmic derivative of the Riemann zeta-function are given.