Quasi-2D square planar nickelates exhibit key ingredients of high-Tc superconducting cuprates. Whether bulk samples are remains an open question, single crystals ideal platforms for addressing such fundamental questions.

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by balls to quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated groups. Inspired work Benjamini and Schramm, we show under such maps, some kind of dimension increases: exponent volume growth nilpotent groups, the ideal boundary hyperbo...

in this paper, we introduce a new generalization of weakly prime ideals called $i$-prime. suppose $r$ is a commutative ring with identity and $i$ a fixed ideal of $r$. a proper ideal $p$ of $r$ is $i$-prime if for $a, b in r$ with $ab in p-ip$ implies either $a in p$ or $b in p$. we give some characterizations of $i$-prime ideals and study some of its properties.  moreover, we give conditions  ...

For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

Some properties and characterizations for abundant semigroups with generalised quasiadequate transversals are explored. In such semigroups, an interesting property [?a,b ? Re1S, VSo(a) VSo (b) 0 (a) = (b)] is investigated thus the concept of refined quasi-adequate transversals, short, RGQA introduced. It shown that real common generalisations both orthodox adequate in case. Finally, by means tw...

Wenxian Zhang, Paola Cappellaro, Natania Antler, Brian Pepper, David G. Cory, Viatcheslav V. Dobrovitski, Chandrasekhar Ramanathan, and Lorenza Viola* Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA Department of Optical Science and Engineering, Fudan University, Shanghai 200433, China ITAMP Harvard-Smithsonian Center for Astrophysics, Cambridge, Massac...

We study simply connected Lie groups $G$ for which the hull-kernel topology of primitive ideal space $\text{Prim}(G)$ group $C^*$-algebra $C^*(G)$ is $T_1$, that is, finite subsets are closed. Thus, we prove AF-embeddable. To this end, show if solvable and its action on centre $[G, G]$ has at least one imaginary weight, then no nonempty quasi-compact open subsets. in addition locally compact wi...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...