We present a construction that enables one to find Banach spaces $X$ whose sets $\operatorname{NA}(X)$ of norm attaining functionals do not contain two-dimensional subspaces and such that, consequently, $X$ does not contain proximinal subspaces of finite codimension greater than one, extending the results recently provided by Read [Banach spaces with no proximinal subspaces of codimension 2, Israel J. Math. (to appear)] and Rmoutil [Norm-attaining functionals need not contain 2-dimensional subspaces, J. Funct. Anal. 272 (2017), 918–928]. Roughly speaking, we construct an equivalent renorming with the requested properties for every Banach space $X$ where the set $\operatorname{NA}(X)$ for the original norm is not “too large”. The construction can be applied to every Banach space containing $c_{0}$ and having a countable system of norming functionals, in particular, to separable Banach spaces containing $c_{0}$ . We also provide some geometric properties of the norms we have constructed.

We provide exact computations for the drift of random walks in dependent random environments, including k-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment.

Many complex systems can be modeled via Markov jump processes. Applications include chemical reactions, population dynamics, and telecommunication networks. Rare-event estimation for such models can be difficult and is often computationally expensive, because typically many (or very long) paths of the Markov jump process need to be simulated in order to observe the rare event. We present a state-dependent importance sampling approach to this problem that is adaptive and uses Markov chain Monte Carlo to sample from the zero-variance importance sampling distribution. The method is applicable to a wide range of Markov jump processes and achieves high accuracy, while requiring only a small sample to obtain the importance parameters. We demonstrate its efficiency through benchmark examples in queueing theory and stochastic chemical kinetics.

We show that for spaces with 1–unconditional bases lushness, the alternative Daugavet property and numerical index 1 are equivalent. In the class of rearrangement invariant (r.i.) sequence spaces the only examples of spaces with these properties are ${{c}_{0,}}{{\ell }_{1}}$ and ${{\ell }_{\infty }}$ . The only lush r.i. separable function space on $\left[ 0,1 \right]$ is ${{L}_{1}}\left[ 0,1 \right]$ ; the same space is the only r.i. separable function space on $\left[ 0,1 \right]$ with the Daugavet property over the reals.

Arguing from a critical reading of the text, and scientific evidence on the ground, the authors show that the myth of Phaethon – the delinquent celestial charioteer – remembers the impact of a massive meteorite that hit the Chiemgau region in Bavaria between 2000 and 428 BC.

We present an example of a Banach space whose numerical index is strictly greater than the numerical index of its dual, giving a negative answer to a question which has been latent since the beginning of the seventies. We also show a particular case in which the numerical index of the space and the one of its dual coincide.

A class of operators is introduced on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$ into a space with an unconditional basis belongs to this class.

Electromigration(EM)-driven mass transport in “near-bamboo” Al-lines, which consist mostly of “blocking grains” is an important topic of research on ULSI-metallizations. Because the most easy diffusion path, i.e. grain boundaries parallel to the line, is suppressed in bamboo-like Al-lines other paths have to be considered. In this work two other possible paths of diffusion were examined by in-situ observations in a transmission electron microscope (TEM). For these experiments a special sample holder had to be constructed.

One path is EM-driven intragranular diffusion in Al-lines. In this experiment, inert gas-filled voids with a mean diameter of about lOnm, so-called bubbles, which were created after gas implantation and annealing of the Al-lines, serve as indicators of mass (or vacancy) transport. The in-situ EM-tests reveal no intragranular void motion over a period of more than 100h at current densities of l-1.75MA/cm2 and temperatures of 150–225°C. This leads to an estimation of the maximum void diffusion velocity which was compared with calculated values of surface and volume diffusion controlled void motion, respectively. The second point of interest was the behavior of dislocations in Al-lines under an applied EM-force. The importance of their observed motion for intragranular mass transport will be discussed.

Let 1 < p, q < ∞. It is shown for complex scalars that there are no nontrivial M-ideals in ℒ(Lp[0, 1]) if p ≠ 2, and is the only nontrivial M-ideal in .

A subspace X of a Banach space Y is called an M-ideal if there is an L-projection P on Y* whose kernel is X1, the annihilator of X; that is, we have

In the case that Y is the bidual of X, a natural linear projection on X*** = Y* with kernel X1 is available, namely .