on Little Details That Matter on a Mobile Website By feedproxy.google.com Published On :: Fri, 29 Dec 2017 13:23:51 +0000 Oftentimes, the focus on mobile websites isn’t on adding as much information as possible or even as much detail. It’s all about making the mobile viewing experience as simple and enjoyable as the web designer possibly can. People who use their mobile devices for browsing and research do not have as much time or patience … Little Details That Matter on a Mobile Website Read More » Full Article Reference
on 240 Basic Icons Vector Freebie By feedproxy.google.com Published On :: Sat, 30 Dec 2017 19:53:50 +0000 Flat design is everywhere. Nowadays aesthetics is a lot more simple. No more glossy buttons or gradients background, or what a about the shiny table effect every client asked for?.It is all gone now. In favor of a more “undesigned” look a back to basics trend. Following that idea the guys at your favorite resources … 240 Basic Icons Vector Freebie Read More » Full Article Freebies
on Building Your Website All Alone By feedproxy.google.com Published On :: Sun, 31 Dec 2017 18:22:23 +0000 Whether you have created a brand new company, or you’ve been around for a long time, if you do not already have a website, you are going to have to put one up as soon as humanly possible. According to the website Mashable, online shopping accounted for $231 billion in sales in 2012. This means … Building Your Website All Alone Read More » Full Article Reference
on First impressions of the Fuji X-Pro2 (and the Fujinon 100-400mm lens) By feedproxy.google.com Published On :: Wed, 16 Mar 2016 20:16:47 +0000 Fuji released their new flagship camera this month, the X-Pro2. It is the first X-series camera to feature a 24MP sensor (compared to 16MP before) and it has a very interesting hybrid optical & electronic view finder. When I first […] Full Article Hardware Thoughts
on Limiting your options on purpose By feedproxy.google.com Published On :: Mon, 12 Sep 2016 11:55:19 +0000 Being a photographer with some spending money and a bad habit of lusting after gear, I have amassed a lot of photo gear. Due to that I am often carrying at least two lenses and also prefer zoom lenses versus […] Full Article Photo Tip Thoughts
on Implementing Dark Mode In React Apps Using styled-components By feedproxy.google.com Published On :: Tue, 28 Apr 2020 10:30:00 +0000 One of the most commonly requested software features is dark mode (or night mode, as others call it). We see dark mode in the apps that we use every day. From mobile to web apps, dark mode has become vital for companies that want to take care of their users’ eyes. Dark mode is a supplemental feature that displays mostly dark surfaces in the UI. Most major companies (such as YouTube, Twitter, and Netflix) have adopted dark mode in their mobile and web apps. Full Article
on Brighten Up Someone’s May (2020 Wallpapers Edition) By feedproxy.google.com Published On :: Thu, 30 Apr 2020 07:20:00 +0000 May is here! And even though the current situation makes this a different kind of May, with a new routine and different things on our minds as in the years before, luckily some things never change. Like the fact that we start into the new month with some fresh inspiration. Since more than nine years already, we challenge you, the design community, to get creative and produce wallpaper designs for our monthly posts. Full Article
on Mirage JS Deep Dive: Understanding Mirage JS Models And Associations (Part 1) By feedproxy.google.com Published On :: Thu, 30 Apr 2020 09:30:00 +0000 Mirage JS is helping simplify modern front-end development by providing the ability for front-end engineers to craft applications without relying on an actual back-end service. In this article, I’ll be taking a framework-agnostic approach to show you Mirage JS models and associations. If you haven’t heard of Mirage JS, you can read my previous article in which I introduce it and also integrate it with the progressive framework Vue.js. Full Article
on Join Our New Online Workshops On CSS, Accessibility, Performance, And UX By feedproxy.google.com Published On :: Thu, 30 Apr 2020 12:00:00 +0000 It has been a month since we launched our first online workshop and, to be honest, we really didn’t know whether people would enjoy them — or if we would enjoy running them. It was an experiment, but one we are so glad we jumped into! I spoke about the experience of taking my workshop online on a recent episode of the Smashing podcast. As a speaker, I had expected it to feel very much like I was presenting into the empty air, with no immediate feedback and expressions to work from. Full Article
on An Introduction To React With Ionic By feedproxy.google.com Published On :: Mon, 04 May 2020 10:30:00 +0000 The Ionic Framework is an open-source UI toolkit for building fast, high-quality applications using web technologies with integrations for popular frameworks like Angular and React. Ionic enables cross-platform development using either Cordova or Capacitor, with the latter featuring support for desktop application development using Electron. In this article, we will explore Ionic with the React integration by building an app that displays comics using the Marvel Comics API and allows users to create a collection of their favorites. Full Article
on Meet SmashingConf Live: Our New Interactive Online Conference By feedproxy.google.com Published On :: Tue, 05 May 2020 12:50:00 +0000 In these strange times when everything is connected, it’s too easy to feel lonely and detached. Yes, everybody is just one message away, but there is always something in the way — deadlines to meet, Slack messages to reply, or urgent PRs to review. Connections need time and space to grow, just like learning, and conferences are a great way to find that time and that space. In fact, with SmashingConfs, we’ve always been trying to create such friendly and inclusive spaces. Full Article
on How To Build A Vue Survey App Using Firebase Authentication And Database By feedproxy.google.com Published On :: Fri, 08 May 2020 11:00:00 +0000 In this tutorial, you’ll be building a Survey App, where we’ll learn to validate our users form data, implement Authentication in Vue, and be able to receive survey data using Vue and Firebase (a BaaS platform). As we build this app, we’ll be learning how to handle form validation for different kinds of data, including reaching out to the backend to check if an email is already taken, even before the user submits the form during sign up. Full Article
on The Canon EOS R5 release gets closer as it passes Bluetooth certification By feedproxy.google.com Published On :: Thu, 07 May 2020 17:25:13 +0000 We’re a big step closer to a Canon EOS R5 release announcement now, as Nokishita Tweets that it has passed its Bluetooth certification. The belief is that the EOS R5 was originally scheduled to ship in July, and Canon Rumors reports that they’ve been told that’ll still happen. With lockdowns still in effect in much […] The post The Canon EOS R5 release gets closer as it passes Bluetooth certification appeared first on DIY Photography. Full Article DIY Bluetooth Canon EOS R5 Certification EOS R5
on DJI’s new Matrice 300 RTK drone offers a ridiculous 55-minutes of flight time and 2.7kg payload By feedproxy.google.com Published On :: Thu, 07 May 2020 22:27:23 +0000 DJI has announced their new Matrice 300 RTK “flying platform” (big drone) and the Zenmuse H20 hybrid camera series, to provide “a safer and smarter solution” to their enterprise customers. The M300 RTK, DJI says, is their first to integrate modern aviation features, advanced AI, 6-direction sensing and positioning, a UAV health management system and […] The post DJI’s new Matrice 300 RTK drone offers a ridiculous 55-minutes of flight time and 2.7kg payload appeared first on DIY Photography. Full Article DIY dji DJI M300 RTK DJI Matrice 300 RTK Matrice 300 RTK
on Weird glitch lets you post insanely long photos to Instagram By feedproxy.google.com Published On :: Fri, 08 May 2020 10:13:45 +0000 Have you noticed extra-long and weirdly stretched images on your Instagram feed? It looks like some kind of a glitch has appeared, allowing users to post images like this to their followers. Of course, some Instagrammers have made the use of it to draw attention, and if you want to have some fun (or annoy […] The post Weird glitch lets you post insanely long photos to Instagram appeared first on DIY Photography. Full Article news glitch Instagram
on Nikon has confirmed that their flagship D6 DSLR will start shipping on May 21st By feedproxy.google.com Published On :: Fri, 08 May 2020 11:06:35 +0000 It feels like forever since Nikon announced their newest flagship DSLR; the Nikon D6. It’s actually only been three months, but that hasn’t stopped some people getting anxious. Recently, customers were being told that the D6 would start shipping right about now, but now Nikon has officially come out to announce that the Nikon D6 […] The post Nikon has confirmed that their flagship D6 DSLR will start shipping on May 21st appeared first on DIY Photography. Full Article news Availability Nikon D6
on #COVIDwear: a hilarious photo series showing quarantine fashion of remote workers By feedproxy.google.com Published On :: Fri, 08 May 2020 12:04:34 +0000 With the coronavirus pandemic, many folks switched to working online. Things like teaching, business meetings and other face-to-face activities have been replaced with video calls. Home has become both home and workplace, and admit it: your wardrobe totally reflects this. Creative duo The Workmans shows this “fashion crossover” in their latest photo series #COVIDwear. The […] The post #COVIDwear: a hilarious photo series showing quarantine fashion of remote workers appeared first on DIY Photography. Full Article Inspiration Alex Workman Chelsea Workman Coronavirus COVID-19 funny portraits quarantine self-isolation The Workmans
on Godox’s new SL150/SL200 Mark II LED lights offer fanless “silent mode” operation By feedproxy.google.com Published On :: Sat, 09 May 2020 11:14:24 +0000 The Godox SL series LED lights have proven to be extremely popular due to their low cost. Two of the models in that range, the SL150 and SL200 have seen a Mark II update today, according to an email that Godox has been sending out today. One of the features of the new SL150II and […] The post Godox’s new SL150/SL200 Mark II LED lights offer fanless “silent mode” operation appeared first on DIY Photography. Full Article news Gear Announcement godox LED lights SL150II SL200II
on Matin calme à St-Donat By feedproxy.google.com Published On :: Tue, 31 Mar 2020 22:36:52 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat neige printemps village
on Paysage donatien By feedproxy.google.com Published On :: Wed, 01 Apr 2020 23:26:11 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat espace printemps rural
on Le village de St-Donat au coucher de soleil By feedproxy.google.com Published On :: Sun, 05 Apr 2020 22:47:50 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat printemps riviere village
on Après les nuages, on retrouve toujours la lumière By feedproxy.google.com Published On :: Tue, 07 Apr 2020 22:39:57 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage St-Donat campagne lumière rural
on Nuages au-dessus du Mont-Comi By feedproxy.google.com Published On :: Wed, 15 Apr 2020 22:05:18 +0000 St-Donat, Bas-St-Laurent, Québec Full Article Paysage Printemps St-Donat campagne nuages printemps
on Ça fond à St-Donat By feedproxy.google.com Published On :: Sun, 19 Apr 2020 15:19:24 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Noir et blanc Paysage Printemps St-Donat printemps riviere village
on En route vers St-Donat By feedproxy.google.com Published On :: Tue, 21 Apr 2020 22:42:23 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat printemps route rural
on À l’ombre de la montagne By feedproxy.google.com Published On :: Fri, 01 May 2020 22:40:44 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat montagne rural village
on Légère inondation By feedproxy.google.com Published On :: Sun, 03 May 2020 00:13:42 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat eau riviere village
on Légère inondation II By feedproxy.google.com Published On :: Mon, 04 May 2020 22:21:29 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat printemps riviere village
on The Visual Evolution of the “Flattening the Curve” Information Graphic By eagereyes.org Published On :: Mon, 16 Mar 2020 04:10:24 +0000 Communication has been quite a challenge during the COVID-19 pandemic, and data visualization hasn't been the most helpful given the low quality of the data – see Amanda Makulec's plea to think harder about making another coronavirus chart. A great example of how to do things right is the widely-circulated Flatten the Curve information graphic/cartoon. […] Full Article Blog 2020 COVID-19 Visual Communication
on In Praise of the Diagonal Reference Line By eagereyes.org Published On :: Tue, 24 Mar 2020 05:51:19 +0000 Annotations are what set visual communication and journalism apart from just visualization. They often consist of text, but some of the most useful annotations are graphical elements, and many of them are very simple. One type I have a particular fondness for is the diagonal reference line, which has been used to provide powerful context […] Full Article Blog 2020 COVID-19 Visual Communication
on Double Chance Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:01:41 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/double-chance-picks-monday-18-september-2017/Double Chance Picks *** Monday *** 18 September 2017 DOUBLE CHANCE PICKS To return: ??? USD Odds: 2.03 Stake: 100 USD Starting in Teams Our Prediction Odds Espanyol - Celta Vigo Soccer: Spain - LaLiga 1X 1.29 AFC Eskilstuna - Sundsvall Soccer: Sweden -… Full Article double chance picks double chance tips DOUBLE CHANCE Monday Matches
on Fulltime Result Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:02:01 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/fulltime-result-picks-monday-18-september-2017/Fulltime Result Picks *** Monday *** 18 September 2017 FULLTIME PICKS To return: ??? USD Odds: 3.77 Stake: 100 USD Starting in Teams Our Prediction Odds Plzen - Zlin Soccer: Czech Republic - 1. Liga 1 1.39 Odd - Aalesund Soccer: Norway -… Full Article fulltime predictions fulltime tips and picks FULLTIME RESULT Monday Matches
on Both teams to score Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:02:38 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/teams-score-picks-monday-18-september-2017/Both teams to score Picks *** Monday *** 18 September 2017 BOTH TEAMS TO SCORE To return: ??? USD Odds: 5.26 Stake: 100 USD Starting in Teams BTS Our Pick Odds Lokomotiv Moscow - Amkar Soccer: Russia - Premier League Both to score NO 1.50 Astra - FC… Full Article both teams to score picks both teams to score tips Both teams to score Monday Matches
on Corners Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:03:55 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/corners-picks-monday-18-september-2017/Corners Picks *** Monday *** 18 September 2017 MATCH CORNERS PICKS To return: ??? USD Odds: 1.55 Stake: 100 USD Starting in Teams Our Prediction Odds Espanyol - Celta Vigo Soccer: Spain - LaLiga OVER 9.5 CORNERS 1.55 Full Article corners picks corners predictions MATCH CORNERS Monday Matches
on Asian Handicap Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:04:59 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/asian-handicap-picks-monday-18-september-2017/Asian Handicap Picks *** Monday *** 18 September 2017 ASIAN HANDICAP PICKS To return: ??? USD Odds: 5.83 Stake: 100 USD Starting in Teams Our Prediction goes for Odds Lokomotiv Moscow - Amkar Soccer: Russia - Premier League L. Moscow -0.5 1.55 Odd -… Full Article asian handicap picks asian handicap tips ASIAN HANDICAP Monday Matches
on Goals Scored Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:06:27 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/goals-scored-picks-monday-18-september-2017/Goals Scored Picks *** Monday *** 18 September 2017 MATCH GOALS PICKS To return: ??? USD Odds: 4.56 Stake: 100 USD Starting in Teams Our Prediction Odds Astra - FC Viitorul Soccer: Romania - Liga 1 UNDER 2.5 1.60 Espanyol - Celta Vigo Soccer: Spain - LaLiga… Full Article over 2.5 goals tips under 2.5 goals tips MATCH GOALS Monday Matches
on Half Time Picks *** Monday *** 18 September 2017 By dataviz.tumblr.com Published On :: Sun, 17 Sep 2017 19:07:40 -0400 We have a new preview on https://www.007soccerpicks.com/monday-matches/half-time-picks-monday-18-september-2017/Half Time Picks *** Monday *** 18 September 2017 HALF TIME PICKS To return: ??? USD Odds: 8.39 Stake: 100 USD Starting in Teams Half Time Our Pick Odds Espanyol - Celta Vigo Soccer: Spain - LaLiga HALF TIME X 2.07 Lokomotiv Moscow - Amkar Soccer: Russia… Full Article halftime picks and tips halftime predictions HALF TIME RESULT Monday Matches
on Non-associative Frobenius algebras for simply laced Chevalley groups. (arXiv:2005.02625v1 [math.RA] CROSS LISTED) By arxiv.org Published On :: We provide an explicit construction for a class of commutative, non-associative algebras for each of the simple Chevalley groups of simply laced type. Moreover, we equip these algebras with an associating bilinear form, which turns them into Frobenius algebras. This class includes a 3876-dimensional algebra on which the Chevalley group of type E8 acts by automorphisms. We also prove that these algebras admit the structure of (axial) decomposition algebras. Full Article
on The entropy of holomorphic correspondences: exact computations and rational semigroups. (arXiv:2004.13691v1 [math.DS] CROSS LISTED) By arxiv.org Published On :: We study two notions of topological entropy of correspondences introduced by Friedland and Dinh-Sibony. Upper bounds are known for both. We identify a class of holomorphic correspondences whose entropy in the sense of Dinh-Sibony equals the known upper bound. This provides an exact computation of the entropy for rational semigroups. We also explore a connection between these two notions of entropy. Full Article
on A Marstrand type slicing theorem for subsets of $mathbb{Z}^2 subset mathbb{R}^2$ with the mass dimension. (arXiv:2005.02813v2 [math.CO] UPDATED) By arxiv.org Published On :: We prove a Marstrand type slicing theorem for the subsets of the integer square lattice. This problem is the dual of the corresponding projection theorem, which was considered by Glasscock, and Lima and Moreira, with the mass and counting dimensions applied to subsets of $mathbb{Z}^{d}$. In this paper, more generally we deal with a subset of the plane that is $1$ separated, and the result for subsets of the integer lattice follow as a special case. We show that the natural slicing question in this setting is true with the mass dimension. Full Article
on On the affine Hecke category. (arXiv:2005.02647v2 [math.RT] UPDATED) By arxiv.org Published On :: We give a complete (and surprisingly simple) description of the affine Hecke category for $ ilde{A}_2$ in characteristic zero. More precisely, we calculate the Kazhdan-Lusztig polynomials, give a recursive formula for the projectors defining indecomposable objects and, for each coefficient of a Kazhdan-Lusztig polynomial, we produce a set of morphisms with such a cardinality. Full Article
on On the finiteness of ample models. (arXiv:2005.02613v2 [math.AG] UPDATED) By arxiv.org Published On :: In this paper, we generalize the finiteness of models theorem in [BCHM06] to Kawamata log terminal pairs with fixed Kodaira dimension. As a consequence, we prove that a Kawamata log terminal pair with $mathbb{R}-$boundary has a canonical model, and can be approximated by log pairs with $mathbb{Q}-$boundary and the same canonical model. Full Article
on Arthur packets for $G_2$ and perverse sheaves on cubics. (arXiv:2005.02438v2 [math.RT] UPDATED) By arxiv.org Published On :: This paper begins the project of defining Arthur packets of all unipotent representations for the $p$-adic exceptional group $G_2$. Here we treat the most interesting case by defining and computing Arthur packets with component group $S_3$. We also show that the distributions attached to these packets are stable, subject to a hypothesis. This is done using a self-contained microlocal analysis of simple equivariant perverse sheaves on the moduli space of homogeneous cubics in two variables. In forthcoming work we will treat the remaining unipotent representations and their endoscopic classification and strengthen our result on stability. Full Article
on Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations. (arXiv:2005.02311v2 [math.AP] UPDATED) By arxiv.org Published On :: One proves the existence and uniqueness of a generalized (mild) solution for the nonlinear Fokker--Planck equation (FPE) egin{align*} &u_t-Delta (eta(u))+{mathrm{ div}}(D(x)b(u)u)=0, quad tgeq0, xinmathbb{R}^d, d e2, \ &u(0,cdot)=u_0,mbox{in }mathbb{R}^d, end{align*} where $u_0in L^1(mathbb{R}^d)$, $etain C^2(mathbb{R})$ is a nondecreasing function, $bin C^1$, bounded, $bgeq 0$, $Din(L^2cap L^infty)(mathbb{R}^d;mathbb{R}^d)$ with ${ m div}, Din L^infty(mathbb{R}^d)$, and ${ m div},Dgeq0$, $eta$ strictly increasing, if $b$ is not constant. Moreover, $t o u(t,u_0)$ is a semigroup of contractions in $L^1(mathbb{R}^d)$, which leaves invariant the set of probability density functions in $mathbb{R}^d$. If ${ m div},Dgeq0$, $eta'(r)geq a|r|^{alpha-1}$, and $|eta(r)|leq C r^alpha$, $alphageq1,$ $alpha>frac{d-2}d$, $dgeq3$, then $|u(t)|_{L^infty}le Ct^{-frac d{d+(alpha-1)d}} |u_0|^{frac2{2+(m-1)d}},$ $t>0$, and the existence extends to initial data $u_0$ in the space $mathcal{M}_b$ of bounded measures in $mathbb{R}^d$. The solution map $mumapsto S(t)mu$, $tgeq0$, is a Lipschitz contractions on $mathcal{M}_b$ and weakly continuous in $tin[0,infty)$. As a consequence for arbitrary initial laws, we obtain weak solutions to a class of McKean-Vlasov SDEs with coefficients which have singular dependence on the time marginal laws. Full Article
on Almost invariant subspaces of the shift operator on vector-valued Hardy spaces. (arXiv:2005.02243v2 [math.FA] UPDATED) By arxiv.org Published On :: In this article, we characterize nearly invariant subspaces of finite defect for the backward shift operator acting on the vector-valued Hardy space which is a vectorial generalization of a result of Chalendar-Gallardo-Partington (C-G-P). Using this characterization of nearly invariant subspace under the backward shift we completely describe the almost invariant subspaces for the shift and its adjoint acting on the vector valued Hardy space. Full Article
on Cameron-Liebler sets in Hamming graphs. (arXiv:2005.02227v2 [math.CO] UPDATED) By arxiv.org Published On :: In this paper, we discuss Cameron-Liebler sets in Hamming graphs, obtain several equivalent definitions and present all classification results. Full Article
on Nonlinear singular problems with indefinite potential term. (arXiv:2005.01789v3 [math.AP] UPDATED) By arxiv.org Published On :: We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this paper the concave term is parametric. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter $lambda$ varies. This work continues our research published in arXiv:2004.12583, where $xi equiv 0 $ and in the reaction the parametric term is the singular one. Full Article
on Resonances as Viscosity Limits for Exponentially Decaying Potentials. (arXiv:2005.01257v2 [math.SP] UPDATED) By arxiv.org Published On :: We show that the complex absorbing potential (CAP) method for computing scattering resonances applies to the case of exponentially decaying potentials. That means that the eigenvalues of $-Delta + V - iepsilon x^2$, $|V(x)|leq e^{-2gamma |x|}$ converge, as $ epsilon o 0+ $, to the poles of the meromorphic continuation of $ ( -Delta + V -lambda^2 )^{-1} $ uniformly on compact subsets of $ extrm{Re},lambda>0$, $ extrm{Im},lambda>-gamma$, $arglambda > pi/8$. Full Article
on Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization. (arXiv:2005.00989v2 [math.AP] UPDATED) By arxiv.org Published On :: In this paper, for a family of second-order parabolic equation with rapidly oscillating and time-dependent periodic coefficients, we are interested in an approximate two-sphere one-cylinder inequality for these solutions in parabolic periodic homogenization, which implies an approximate quantitative propagation of smallness. The proof relies on the asymptotic behavior of fundamental solutions and the Lagrange interpolation technique. Full Article
on Complete reducibility: Variations on a theme of Serre. (arXiv:2004.14604v2 [math.GR] UPDATED) By arxiv.org Published On :: In this note, we unify and extend various concepts in the area of $G$-complete reducibility, where $G$ is a reductive algebraic group. By results of Serre and Bate--Martin--R"{o}hrle, the usual notion of $G$-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of $G$. We show that other variations of this notion, such as relative complete reducibility and $sigma$-complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties. Full Article