Related papers: Crystallizations of generalized lens spaces

Theoretical analysis is presented on quantum state evolution of polarization light waves at frequencies $\omega_{o}$ and $\omega_{e}$ in a periodically poled nonlinear crystal (PPNC). It is shown that the variances of all the four Stokes…

In this paper, we construct higher-order generalizations of the $A_6^{(1)}$- and $A_4^{(1)}$-surface type $q$-Painlev\'e equations from the system of partial difference equations with the consistency around a cube property by periodic…

Gravitational lensing by a spiral galaxy occurs when the line-of-sight to a background quasar passes within a few kpc from the center of the galactic disk. Since galactic disks are rich in neutral hydrogen, the quasar spectrum will likely…

We use the p-adic local Langlands correspondence for GL_2(Q_p) to explicitly compute the reduction modulo p of crystalline representations of small slope, and give applications to modular forms.

Extending work of many authors we calculate the higher simple structure sets of lens spaces in the sense of surgery theory in the case when the fundamental group has order a power of $2$. As a corollary we also obtain a calculation of the…

We prove two generalisations of the Binomial theorem that are also generalisations of the q-binomial theorem. These generalisations arise from the commutation relations satisfied by the components of the co-multiplications of non-simple…

Crystallization from an amorphous atomic structure is usually seen as a spontaneous process in pursuit of a lower energy state, but for alloy systems it is often hard to elucidate because of the intrinsic structural and compositional…

We present preliminary polarisation VLBI maps of the gravitational lens system B0218+357, made at 3 different frequencies.

Let $p$ be prime number and $K$ be a $p$-adic field. We systematically compute the higher $\mathrm{Ext}$-groups between locally analytic generalized Steinberg representations (LAGS for short) of $\mathrm{GL}_n(K)$ via a new combinatorial…

We present a natural and explicit multigraded minimal free resolution for each generalized co-letterplace ideal (see Definition 1.1). Our resolution differs significantly from the ones presented in the works of Ene et al. \cite{EHM} and…

We have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images, hence the lens cross section, for realistic…

With the $[0,1,2]$-family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic $q$-equivelar triangulations of orientable and non-orientable…

In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance…

Let $\mathcal P:=\mathcal P_{m\times n}$ denote the quantized coordinate ring of the space of $m\times n$ matrices, equipped with natural actions of the quantized enveloping algebras $U_q(\mathfrak{gl}_m)$ and $U_q(\mathfrak{gl}_n)$. Let…

Liquids crystallize as they cool; however, when crystallization is avoided in some way, they supercool, maintaining their liquidity, and freezing into glass at low temperatures, as ubiquitously observed. These metastable states crystallize…

We identify the largest known lensed images of a single spiral galaxy, lying close to the centre of the distant cluster MACS J1149.5+2223 ($z=0.544$). These images cover a total area of $\simeq 150 \Box\arcsec$ and are magnified $\simeq…

We derive some local properties of abstract crystals with logarithmic poles over a smooth base in positive characteristic and obtain the existence of the canonical coordinates of certain ordinary crystals. We then apply the results to…

The width $\triangle_L$ of the first Bragg's scattering peak in the (111) direction of a face-centered-cubic lattice of air spheres can be well approximated by a simple formula which only involves the volume averaged $\epsilon$ and…

Let $0<p<\infty$, $0<q\leq\infty$, and $s\in\mathbb{R}$. We introduce a new type of generalized Besov-type spaces $B_{p,q}^{s,\varphi}(\mathbb{R}^d)$ and generalized Triebel-Lizorkin-type spaces $F_{p,q}^{s,\varphi}(\mathbb{R}^d)$, where…

We present a framework for studying gravitational lensing in spherically symmetric spacetimes using 1+1+2 covariant methods. A general formula for the deflection angle is derived and we show how this can be used to recover the standard…