Related papers: A Counterexample for Lightning Flash Modules over …

Hopkins and Mahowald gave a simple description of the mod $p$ Eilenberg Mac Lane spectrum $\mathbb{F}_p$ as the free $\mathbb{E}_2$-algebra with an equivalence of $p$ and $0$. We show for each faithful $2$-dimensional representation…

In the so called lightbulb process, on days $r=1,..., n$, out of $n$ lightbulbs, all initially off, exactly $r$ bulbs, selected uniformly and independent of the past, have their status changed from off to on, or vice versa. With $X$ the…

Blowing up a rational surface singularity in a reflexive module gives a (any) partial resolution dominated by the minimal resolution. The main theorem shows how deformations of the pair (singularity, module) relates to deformations of the…

In this paper, we study superficial elements of an ideal with respect to a module from a geometrical point of view, using blowing-ups. The notion of weak transform is particularly relevant to this study. We use this viewpoint to get a…

Let $p$ be prime. Let $L/K$ be a finite, totally ramified, purely inseparable extension of local fields, $\left[ L:K\right] =p^{n},\;n\geq2.$ It is known that $L/K$ is Hopf Galois for numerous Hopf algebras $H,$ each of which can act on the…

Let $R$ be the associative $k$-algebra generated by two elements $x$ and $y$ with defining relation $yx=1$. A complete description of simple modules over $R$ is obtained by using the results of Irving and Gerritzen. We examine the short…

We obtain a controlled description of a strongly correlated regime of electronic behaviour. We begin by arguing that there are two ways to characterise the electronic degree of freedom, either by the canonical fermion algebra or the graded…

The Poisson spot is a fascinating lecture demonstration. Its simple explanation can lead to further questions, not only the one posed in the title, but also questions such as why the simple model that considers only light passing just…

We construct and classify the free $U(\mathbb{C}L_0\oplus \mathbb{C}M_0\oplus\mathbb{C}Y_0)$-modules of rank $1$ over the Schr\"{o}dinger-Virasoro algebra $\mathfrak{sv}(s)$ for $s=0$.Moreover, we show that the class of free…

After a review of the results in arXiv:1203.3184 [math-ph] about Pythagorean inequalities for products of spectral triples, I will present some new results and discuss classes of spectral triples and states for which equality holds.

Given a local ring $(R, \mathfrak{m})$ and an ideal $\mathfrak{a}$ of positive height, we give a way of computing multiplier module ${J}(\omega_{{T}}, t^{-\lambda})$ for the extended Rees algebra ${T} =R[\mathfrak{a} t, t^{-1}]$ for an…

In this short note we give counterexamples to several results related to extension theorems published recently.

We define and study the notion of a crossed module over an inverse semigroup and the corresponding $4$-term exact sequences, called crossed module extensions. For a crossed module $A$ over an $F$-inverse monoid $T$, we show that equivalence…

We prove analogues of Ramanujan's Master theorem for the radial sections of the line bundles over the Poincar\'{e} upper half plane $\mathrm{SL}(2, \R)/\mathrm{SO}(2)$ and over the complex hyperbolic spaces $\mathrm {SU}(1, n)/…

In a recent work, Gun and co-workers have proposed that $\,\sum_{n=-\infty}^{\infty}{(n+\alpha)^{-k}}\,$ is a transcendental number for all integer $\,k$, $k > 1$, and $\,\alpha \in \mathbb{Q} \backslash \mathbb{Z}$. Here in this work, this…

In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to sl_5 of the Verma module…

Let $H^*(\calB_e)$ be the cohomology of the Springer fibre for the nilpotent element $e$ in a simple Lie algebra $\g$, on which the Weyl group $W$ acts by the Springer representation. Let $\Lambda^i V$ denote the $i$th exterior power of the…

Wang et al. [1] demonstrated different power transmission coefficients for forward and backward propagation in simulation and experiment. From such a demonstration, the central claim of their paper is that "the spatial inversion symmetry…

The $2$-primary Hopf invariant $1$ elements in the stable homotopy groups of spheres form the most accessible family of elements. In this paper we explore some properties of the $\mathcal{E}_\infty$ ring spectra obtained from certain…

Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with coefficients in the field with $5$ elements. We show that the principal block over a splitting field $K$ of characteristic two of the group algebra $KG$ has a…