2 Un lac éphémère au village By feedproxy.google.com Published On :: Tue, 14 Apr 2020 14:08:44 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat fonte printemps village
2 Coucher de soleil à la campagne By feedproxy.google.com Published On :: Fri, 17 Apr 2020 12:32:42 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat printemps rural soleil
2 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
2 Printemps à la campagne By feedproxy.google.com Published On :: Sun, 19 Apr 2020 23:27:21 +0000 St-Donat, Bas-St-Laurent, Québec Full Article Paysage Printemps St-Donat campagne champs fonte
2 La vallée de la Neigette By feedproxy.google.com Published On :: Mon, 27 Apr 2020 22:00:06 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat calme printemps vallée
2 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
2 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
2 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
2 Un peu après le coucher du soleil By feedproxy.google.com Published On :: Fri, 08 May 2020 23:04:54 +0000 St-Donat, Bas-St-Laurent, Québec Full Article aérienne Paysage Printemps St-Donat ciel soir village
2 eagereyesTV Episode 2: Unit Charts, Dot Plots, ISOTYPE, and What Makes Them Special By eagereyes.org Published On :: Wed, 09 Oct 2019 07:17:21 +0000 Charts usually show values as visual properties, like the length in a bar chart, the location in a scatterplot, the area in a bubble chart, etc. Unit charts show values as multiples instead. One famous example of these charts is called ISOTYPE, and you may have seen them in information graphics as well. They’re an […] Full Article Blog 2019 eagereyesTV
2 eagereyesTV: What Is Data? Part 2, Are Images Data? By eagereyes.org Published On :: Mon, 16 Dec 2019 13:01:25 +0000 Visualization turns data into images, but are images themselves data? There are often claims that they are, but then you mostly see the images themselves without much additional data. In this video, I look at image browsers, a project classifying selfies along a number of criteria, and the additional information stored in HEIC that makes […] Full Article eagereyesTV
2 Corners Picks *** Sunday *** 17 September 2017 By dataviz.tumblr.com Published On :: Sat, 16 Sep 2017 19:05:08 -0400 We have a new preview on https://www.007soccerpicks.com/sunday-matches/corners-picks-sunday-17-september-2017/Corners Picks *** Sunday *** 17 September 2017 MATCH CORNERS PICKS To return: ??? USD Odds: 1.55 Stake: 100 USD Starting in Teams Our Prediction Odds Chelsea - Arsenal Soccer: Premier League OVER 9.5 CORNERS 1.55 Full Article corners free picks corners tips and picks MATCH CORNERS Sunday Matches
2 Half Time Picks *** Sunday *** 17 September 2017 By dataviz.tumblr.com Published On :: Sat, 16 Sep 2017 19:14:31 -0400 We have a new preview on https://www.007soccerpicks.com/sunday-matches/half-time-picks-sunday-17-september-2017/Half Time Picks *** Sunday *** 17 September 2017 HALF TIME PICKS To return: ??? USD Odds: 7.43 Stake: 100 USD Starting in Teams Half Time Our Pick Odds Alaves - Villarreal Soccer: Spain - LaLiga HALF TIME X 2.01 Zenit Petersburg - Ufa Soccer: Russia -… Full Article halftime picks and tips halftime predictions HALF TIME RESULT Sunday Matches
2 Goals Scored Picks *** Sunday *** 17 September 2017 By dataviz.tumblr.com Published On :: Sat, 16 Sep 2017 19:14:54 -0400 We have a new preview on https://www.007soccerpicks.com/sunday-matches/goals-scored-picks-sunday-17-september-2017/Goals Scored Picks *** Sunday *** 17 September 2017 MATCH GOALS PICKS To return: ??? USD Odds: 6.44 Stake: 100 USD Starting in Teams Our Prediction Odds Amiens - Marseille Soccer: France - Ligue 1 UNDER 2.5 1.85 AC Milan - Udinese Soccer: Italy - Serie A… Full Article over 2.5 goals tips under 2.5 goals tips MATCH GOALS Sunday Matches
2 Fulltime Result Picks *** Sunday *** 17 September 2017 By dataviz.tumblr.com Published On :: Sat, 16 Sep 2017 19:44:09 -0400 We have a new preview on https://www.007soccerpicks.com/sunday-matches/fulltime-result-picks-sunday-17-september-2017/Fulltime Result Picks *** Sunday *** 17 September 2017 FULLTIME PICKS To return: ??? USD Odds: 3.88 Stake: 100 USD Starting in Teams Our Prediction Odds Waregem - Mouscron Soccer: Belgium - Jupiler League 1 1.61 Sassuolo - Juventus Soccer: Italy - Serie… Full Article fulltime predictions fulltime tips and picks FULLTIME RESULT Sunday Matches
2 Double Chance Picks *** Sunday *** 17 September 2017 By dataviz.tumblr.com Published On :: Sat, 16 Sep 2017 19:45:05 -0400 We have a new preview on https://www.007soccerpicks.com/sunday-matches/double-chance-picks-sunday-17-september-2017/Double Chance Picks *** Sunday *** 17 September 2017 DOUBLE CHANCE PICKS To return: ??? USD Odds: 2.80 Stake: 100 USD Starting in Teams Our Prediction Odds Las Palmas - Ath Bilbao Soccer: Spain - LaLiga X2 1.45 Chievo - Atalanta Soccer: Italy - Serie… Full Article double chance picks double chance tips DOUBLE CHANCE Sunday Matches
2 Both teams to score Picks *** Sunday *** 17 September 2017 By dataviz.tumblr.com Published On :: Sat, 16 Sep 2017 19:52:01 -0400 We have a new preview on https://www.007soccerpicks.com/sunday-matches/teams-score-picks-sunday-17-september-2017/Both teams to score Picks *** Sunday *** 17 September 2017 BOTH TEAMS TO SCORE To return: ??? USD Odds: 5.36 Stake: 100 USD Starting in Teams BTS Our Pick Odds Tosno - Spartak Moscow Soccer: Russia - Premier League Both to score NO 1.53 Chelsea - Arsenal Soccer:… Full Article both teams to score picks both teams to score tips Both teams to score Sunday Matches
2 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
2 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
2 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
2 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
2 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
2 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
2 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
2 Goals Scored Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:05:01 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/goals-scored-picks-tuesday-19-september-2017/Goals Scored Picks *** Tuesday *** 19 September 2017 MATCH GOALS PICKS To return: ??? USD Odds: 6.27 Stake: 100 USD Starting in Teams Our Prediction Odds Burnley - Leeds Soccer: England - Carabao Cup OVER 2.5 2.00 Schalke - Bayern Munich Soccer: Germany -… Full Article over 2.5 goals tips under 2.5 goals predictions MATCH GOALS Tuesday Matches
2 Half Time Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:05:21 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/half-time-picks-tuesday-19-september-2017/Half Time Picks *** Tuesday *** 19 September 2017 HALF TIME PICKS To return: ??? USD Odds: 6.93 Stake: 100 USD Starting in Teams Half Time Our Pick Odds Crystal Palace - Huddersfield Soccer: England - Carabao Cup HALF TIME X 2.10 FC Augsburg - RB… Full Article halftime picks halftime predictions and tips HALF TIME RESULT Tuesday Matches
2 Asian Handicap Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:05:22 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/asian-handicap-picks-tuesday-19-september-2017/Asian Handicap Picks *** Tuesday *** 19 September 2017 ASIAN HANDICAP PICKS To return: ??? USD Odds: 4.08 Stake: 100 USD Starting in Teams Our Prediction goes for Odds West Ham - Bolton Soccer: England - Carabao Cup West Ham -0.5 1.55 Bologna - Inter Soccer:… Full Article asian handicap picks asian handicap tips ASIAN HANDICAP Tuesday Matches
2 Double Chance Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:05:25 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/double-chance-picks-tuesday-19-september-2017/Double Chance Picks *** Tuesday *** 19 September 2017 DOUBLE CHANCE PICKS To return: ??? USD Odds: 1.95 Stake: 100 USD Starting in Teams Our Prediction Odds Bournemouth - Brighton Soccer: England - Carabao Cup 1X 1.20 Wolfsburg - SV Werder Bremen Soccer: Germany… Full Article double chance predictions double chance tips DOUBLE CHANCE Tuesday Matches
2 Fulltime Result Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:05:34 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/fulltime-result-picks-tuesday-19-september-2017/Fulltime Result Picks *** Tuesday *** 19 September 2017 FULLTIME PICKS To return: ??? USD Odds: 5.40 Stake: 100 USD Starting in Teams Our Prediction Odds GAIS - Frej Soccer: Sweden - Superettan 1 1.82 Bologna - Inter Soccer: Italy - Serie… Full Article fulltime picks fulltime predictions and tips FULLTIME RESULT Tuesday Matches
2 Corners Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:05:38 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/corners-picks-tuesday-19-september-2017/Corners Picks *** Tuesday *** 19 September 2017 MATCH CORNERS PICKS To return: ??? USD Odds: 1.55 Stake: 100 USD Starting in Teams Our Prediction Odds Valencia - Malaga Soccer: Spain - LaLiga OVER 9.5 CORNERS 1.55 Full Article corners free tips corners picks MATCH CORNERS Tuesday Matches
2 Both teams to score Picks *** Tuesday *** 19 September 2017 By dataviz.tumblr.com Published On :: Mon, 18 Sep 2017 16:07:46 -0400 We have a new preview on https://www.007soccerpicks.com/tuesday-matches/teams-score-picks-tuesday-19-september-2017/Both teams to score Picks *** Tuesday *** 19 September 2017 BOTH TEAMS TO SCORE To return: ??? USD Odds: 4.75 Stake: 100 USD Starting in Teams BTS Our Pick Odds Schalke - Bayern Munich Soccer: Germany - Bundesliga Both to score YES 1.60 Leicester -… Full Article both teams to score picks both teams to score tips Both teams to score Tuesday Matches
2 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
2 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
2 Regular Tur'an numbers of complete bipartite graphs. (arXiv:2005.02907v2 [math.CO] UPDATED) By arxiv.org Published On :: Let $mathrm{rex}(n, F)$ denote the maximum number of edges in an $n$-vertex graph that is regular and does not contain $F$ as a subgraph. We give lower bounds on $mathrm{rex}(n, F)$, that are best possible up to a constant factor, when $F$ is one of $C_4$, $K_{2,t}$, $K_{3,3}$ or $K_{s,t}$ when $t>s!$. Full Article
2 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
2 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
2 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
2 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
2 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
2 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
2 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
2 Some Quot schemes in tilted hearts and moduli spaces of stable pairs. (arXiv:2005.02202v2 [math.AG] UPDATED) By arxiv.org Published On :: For a smooth projective variety $X$, we study analogs of Quot functors in hearts of non-standard $t$-structures of $D^b(mathrm{Coh}(X))$. The technical framework is that of families of $t$-structures, as studied in arXiv:1902.08184. We provide several examples and suggest possible directions of further investigation, as we reinterpret moduli spaces of stable pairs, in the sense of Thaddeus (arXiv:alg-geom/9210007) and Huybrechts-Lehn (arXiv:alg-geom/9211001), as instances of Quot schemes. Full Article
2 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
2 Entropy and Emergence of Topological Dynamical Systems. (arXiv:2005.01548v2 [math.DS] UPDATED) By arxiv.org Published On :: A topological dynamical system $(X,f)$ induces two natural systems, one is on the probability measure spaces and other one is on the hyperspace. We introduce a concept for these two spaces, which is called entropy order, and prove that it coincides with topological entropy of $(X,f)$. We also consider the entropy order of an invariant measure and a variational principle is established. Full Article
2 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
2 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
2 Solving an inverse problem for the Sturm-Liouville operator with a singular potential by Yurko's method. (arXiv:2004.14721v2 [math.SP] UPDATED) By arxiv.org Published On :: An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution, and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases Full Article
2 An embedding of the Morse boundary in the Martin boundary. (arXiv:2004.14624v2 [math.GR] UPDATED) By arxiv.org Published On :: We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic. Full Article
2 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
2 Lagrangian geometry of matroids. (arXiv:2004.13116v2 [math.CO] UPDATED) By arxiv.org Published On :: We introduce the conormal fan of a matroid M, which is a Lagrangian analog of the Bergman fan of M. We use the conormal fan to give a Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M. This allows us to express the h-vector of the broken circuit complex of M in terms of the intersection theory of the conormal fan of M. We also develop general tools for tropical Hodge theory to prove that the conormal fan satisfies Poincar'e duality, the hard Lefschetz theorem, and the Hodge-Riemann relations. The Lagrangian interpretation of the Chern-Schwartz-MacPherson cycle of M, when combined with the Hodge-Riemann relations for the conormal fan of M, implies Brylawski's and Dawson's conjectures that the h-vectors of the broken circuit complex and the independence complex of M are log-concave sequences. Full Article