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First impressions of the Fuji X-Pro2 (and the Fujinon 100-400mm lens)

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 […]




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Best of 2016

This year went by in a hurry and now it is late December already and Jim Goldstein is running his blog project again, asking for galleries of everyones best photos of the year. Of course I knew I had to […]




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Best of 2017

As in years past Jim Goldstein is running his annual “Best Of” photography blog project in which I have participated since 2008. Usually I had a few thousand images to sort through. This year has been a rather sparse photo […]




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Best of 2018

Another year has almost passed and as has become tradition Jim Goldstein is running his annual Blog Project. You can find my entries for years past right here on my blog. This year I took a lot of images early […]




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Best of 2019

Another year – and in this case another decade – coming to an end. I haven’t had many chances to go take photos this year. In fact my battery charger got lost for months… just so you know how little […]




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How To Succeed In Wireframe Design

For the most part, we tend to underestimate things that are familiar to us. It is also very likely that we will underestimate those things that though new, seem very simple to process. And that is correct to some degree. But, when we are faced with complex cases and all measures are taken, a good and solid understanding of the basics could help us to find the right solutions. In this article, we will take a deeper look at one of the most simple, thus, quite often underrated activities in web development that is the design of wireframes.




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Join Our New Online Workshops On CSS, Accessibility, Performance, And UX

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.




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Reducing Design Risk

Lean, agile, do more with less. Again, and again, design culture urges us to move quickly and trim research and design operations to the point where design becomes a mere thread in the larger corporate spool. Author and designer Nikki Anderson explains the consequences of this pressure to conduct research at lightning speed: “When we’re asked to synthesize at the speed of light, user research becomes a way for teams to take a shortcut — to invent assumptions based on quickly made correlations, opinions, and quotes.




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The Canon EOS R5 release gets closer as it passes Bluetooth certification

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.




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Aputure announces new LS-60D daylight and LX-60X bicolour LED lights

Aputure’s been coming pretty thick and fast on the announcements lately, and now they’ve announced their new Light Storm 60D daylight and 60X bi-colour adjustable focusing LED lights. As the name suggests, these are 60 Watt LEDs, and everything is built inside the head, meaning there’s no external control unit to have to deal with. […]

The post Aputure announces new LS-60D daylight and LX-60X bicolour LED lights appeared first on DIY Photography.




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Google Lens now copies handwritten text and pastes it straight to your computer

Are there still folks among you who, like me, prefer handwriting to typing? If you’re in this group, you’ll love this new feature on Google Lens. The app now lets you scan your handwritten notes, copy them, and paste them straight to your computer. I gave it a spin, and I bring you my impressions […]

The post Google Lens now copies handwritten text and pastes it straight to your computer appeared first on DIY Photography.




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DJI’s new Matrice 300 RTK drone offers a ridiculous 55-minutes of flight time and 2.7kg payload

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.



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Photography Life makes all their paid premium courses free

Photography Life has just contributed to the selection of online courses that you can take for free. While their premim courses are normally paid $150 per course, you can now access them free of charge. The founders have released them on YouTube, available for everyone to watch. The Photography Life team came to the decision […]

The post Photography Life makes all their paid premium courses free appeared first on DIY Photography.




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#COVIDwear: a hilarious photo series showing quarantine fashion of remote workers

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.




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Godox’s new SL150/SL200 Mark II LED lights offer fanless “silent mode” operation

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.








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eagereyesTV Episode 2: Unit Charts, Dot Plots, ISOTYPE, and What Makes Them Special

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 […]




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eagereyesTV Episode 3: 3D Pie Charts For Science!

How do we read pie charts? This seems like a straightforward question to answer, but it turns out that most of what you’ve probably heard is wrong. We don’t actually know whether we use angle, area, or arc length. In a short paper at the VIS conference this week I’m presenting a study I ran […]




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eagereyesTV: What is Data? Part 1, File Formats and Intent

We all use data all the time, but what exactly is data? How do different programs know what to do with our data? How is visualizing data different from other uses of data? And isn’t everything inside a computer data in the end? The latest episode of eagereyesTV looks at what data is and what […]




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eagereyesTV: What Is Data? Part 2, Are Images Data?

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 […]




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Fulltime Result Picks *** Sunday *** 17 September 2017

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…




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Fulltime Result Picks *** Monday *** 18 September 2017

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 -…




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Goals Scored Picks *** Tuesday *** 19 September 2017

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 -…




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Half Time Picks *** Tuesday *** 19 September 2017

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…




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Asian Handicap Picks *** Tuesday *** 19 September 2017

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:…




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Double Chance Picks *** Tuesday *** 19 September 2017

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…




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Fulltime Result Picks *** Tuesday *** 19 September 2017

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…




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Corners Picks *** Tuesday *** 19 September 2017

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




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Both teams to score Picks *** Tuesday *** 19 September 2017

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 -…



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The entropy of holomorphic correspondences: exact computations and rational semigroups. (arXiv:2004.13691v1 [math.DS] CROSS LISTED)

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.




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On the finiteness of ample models. (arXiv:2005.02613v2 [math.AG] UPDATED)

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.




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Arthur packets for $G_2$ and perverse sheaves on cubics. (arXiv:2005.02438v2 [math.RT] UPDATED)

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.




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Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations. (arXiv:2005.02311v2 [math.AP] UPDATED)

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.




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Almost invariant subspaces of the shift operator on vector-valued Hardy spaces. (arXiv:2005.02243v2 [math.FA] UPDATED)

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.




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Some Quot schemes in tilted hearts and moduli spaces of stable pairs. (arXiv:2005.02202v2 [math.AG] UPDATED)

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.




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Resonances as Viscosity Limits for Exponentially Decaying Potentials. (arXiv:2005.01257v2 [math.SP] UPDATED)

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$, $arglambda > pi/8$.




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Triangles in graphs without bipartite suspensions. (arXiv:2004.11930v2 [math.CO] UPDATED)

Given graphs $T$ and $H$, the generalized Tur'an number ex$(n,T,H)$ is the maximum number of copies of $T$ in an $n$-vertex graph with no copies of $H$. Alon and Shikhelman, using a result of ErdH os, determined the asymptotics of ex$(n,K_3,H)$ when the chromatic number of $H$ is greater than 3 and proved several results when $H$ is bipartite. We consider this problem when $H$ has chromatic number 3. Even this special case for the following relatively simple 3-chromatic graphs appears to be challenging.

The suspension $widehat H$ of a graph $H$ is the graph obtained from $H$ by adding a new vertex adjacent to all vertices of $H$. We give new upper and lower bounds on ex$(n,K_3,widehat{H})$ when $H$ is a path, even cycle, or complete bipartite graph. One of the main tools we use is the triangle removal lemma, but it is unclear if much stronger statements can be proved without using the removal lemma.




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Finite dimensional simple modules of $(q, mathbf{Q})$-current algebras. (arXiv:2004.11069v2 [math.RT] UPDATED)

The $(q, mathbf{Q})$-current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic $q$-Schur algebras. In this paper, we study the $(q, mathbf{Q})$-current algebra $U_q(mathfrak{sl}_n^{langle mathbf{Q} angle}[x])$ associated with the special linear Lie algebra $mathfrak{sl}_n$. In particular, we classify finite dimensional simple $U_q(mathfrak{sl}_n^{langle mathbf{Q} angle}[x])$-modules.




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Automorphisms of shift spaces and the Higman--Thomspon groups: the one-sided case. (arXiv:2004.08478v2 [math.GR] UPDATED)

Let $1 le r < n$ be integers. We give a proof that the group $mathop{mathrm{Aut}}({X_{n}^{mathbb{N}}, sigma_{n}})$ of automorphisms of the one-sided shift on $n$ letters embeds naturally as a subgroup $mathcal{h}_{n}$ of the outer automorphism group $mathop{mathrm{Out}}(G_{n,r})$ of the Higman-Thompson group $G_{n,r}$. From this, we can represent the elements of $mathop{mathrm{Aut}}({X_{n}^{mathbb{N}}, sigma_{n}})$ by finite state non-initial transducers admitting a very strong synchronizing condition.

Let $H in mathcal{H}_{n}$ and write $|H|$ for the number of states of the minimal transducer representing $H$. We show that $H$ can be written as a product of at most $|H|$ torsion elements. This result strengthens a similar result of Boyle, Franks and Kitchens, where the decomposition involves more complex torsion elements and also does not support practical extit{a priori} estimates of the length of the resulting product.

We also give new proofs of some known results about $mathop{mathrm{Aut}}({X_{n}^{mathbb{N}}, sigma_{n}})$.




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Equivalence of classical and quantum completeness for real principal type operators on the circle. (arXiv:2004.07547v3 [math.AP] UPDATED)

In this article, we prove that the completeness of the Hamilton flow and essential self-dajointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators.




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Hessian quotient equations on exterior domains. (arXiv:2004.06908v2 [math.AP] UPDATED)

It is well-known that a celebrated J"{o}rgens-Calabi-Pogorelov theorem for Monge-Amp`ere equations states that any classical (viscosity) convex solution of $det(D^2u)=1$ in $mathbb{R}^n$ must be a quadratic polynomial. Therefore, it is an interesting topic to study the existence and uniqueness theorem of such fully nonlinear partial differential equations' Dirichlet problems on exterior domains with suitable asymptotic conditions at infinity. As a continuation of the works of Caffarelli-Li for Monge-Amp`ere equation and of Bao-Li-Li for $k$-Hessian equations, this paper is devoted to the solvability of the exterior Dirichlet problem of Hessian quotient equations $sigma_k(lambda(D^2u))/sigma_l(lambda(D^2u))=1$ for any $1leq l<kleq n$ in all dimensions $ngeq 2$. By introducing the concept of generalized symmetric subsolutions and then using the Perron's method, we establish the existence theorem for viscosity solutions, with prescribed asymptotic behavior which is close to some quadratic polynomial at infinity.




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Output feedback stochastic MPC with packet losses. (arXiv:2004.02591v2 [math.OC] UPDATED)

The paper considers constrained linear systems with stochastic additive disturbances and noisy measurements transmitted over a lossy communication channel. We propose a model predictive control (MPC) law that minimizes a discounted cost subject to a discounted expectation constraint. Sensor data is assumed to be lost with known probability, and data losses are accounted for by expressing the predicted control policy as an affine function of future observations, which results in a convex optimal control problem. An online constraint-tightening technique ensures recursive feasibility of the online optimization and satisfaction of the expectation constraint without bounds on the distributions of the noise and disturbance inputs. The cost evaluated along trajectories of the closed loop system is shown to be bounded by the optimal predicted cost. A numerical example is given to illustrate these results.




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Set theoretic Yang-Baxter & reflection equations and quantum group symmetries. (arXiv:2003.08317v3 [math-ph] UPDATED)

Connections between set theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and twisted algebras and we derive the associated defining algebra relations for $R$-matrices being Baxterized solutions of the $A$-type Hecke algebra ${cal H}_N(q=1)$. We show in the case of the reflection algebra that there exists a "boundary" finite sub-algebra for some special choice of "boundary" elements of the $B$-type Hecke algebra ${cal B}_N(q=1, Q)$. We also show the key proposition that the associated double row transfer matrix is essentially expressed in terms of the elements of the $B$-type Hecke algebra. This is one of the fundamental results of this investigation together with the proof of the duality between the boundary finite subalgebra and the $B$-type Hecke algebra. These are universal statements that largely generalize previous relevant findings, and also allow the investigation of the symmetries of the double row transfer matrix.




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The Shearlet Transform and Lizorkin Spaces. (arXiv:2003.06642v2 [math.FA] UPDATED)

We prove a continuity result for the shearlet transform when restricted to the space of smooth and rapidly decreasing functions with all vanishing moments. We define the dual shearlet transform, called here the shearlet synthesis operator, and we prove its continuity on the space of smooth and rapidly decreasing functions over $mathbb{R}^2 imesmathbb{R} imesmathbb{R}^ imes$. Then, we use these continuity results to extend the shearlet transform to the space of Lizorkin distributions, and we prove its consistency with the classical definition for test functions.




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Weak-strong uniqueness for an elastic plate interacting with the Navier Stokes equation. (arXiv:2003.04049v2 [math.AP] UPDATED)

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of the fluid and as such determines the variable part of a time changing domain (that is hence a part of the solution) containing the fluid. The uniqueness result is a consequence of a stability estimate where the difference of two solutions is estimated by the distance of the initial values and outer forces. For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same. The estimate holds under the assumption that one of the two weak solutions possesses some additional higher regularity. The additional regularity is exclusively requested for the velocity of one of the solutions resembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the framework of variable domains.




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The $kappa$-Newtonian and $kappa$-Carrollian algebras and their noncommutative spacetimes. (arXiv:2003.03921v2 [hep-th] UPDATED)

We derive the non-relativistic $c oinfty$ and ultra-relativistic $c o 0$ limits of the $kappa$-deformed symmetries and corresponding spacetime in (3+1) dimensions, with and without a cosmological constant. We apply the theory of Lie bialgebra contractions to the Poisson version of the $kappa$-(A)dS quantum algebra, and quantize the resulting contracted Poisson-Hopf algebras, thus giving rise to the $kappa$-deformation of the Newtonian (Newton-Hooke and Galilei) and Carrollian (Para-Poincar'e, Para-Euclidean and Carroll) quantum symmetries, including their deformed quadratic Casimir operators. The corresponding $kappa$-Newtonian and $kappa$-Carrollian noncommutative spacetimes are also obtained as the non-relativistic and ultra-relativistic limits of the $kappa$-(A)dS noncommutative spacetime. These constructions allow us to analyze the non-trivial interplay between the quantum deformation parameter $kappa$, the curvature parameter $eta$ and the speed of light parameter $c$.




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Solitary wave solutions and global well-posedness for a coupled system of gKdV equations. (arXiv:2002.09531v2 [math.AP] UPDATED)

In this work we consider the initial-value problem associated with a coupled system of generalized Korteweg-de Vries equations. We present a relationship between the best constant for a Gagliardo-Nirenberg type inequality and a criterion for the existence of global solutions in the energy space. We prove that such a constant is directly related to the existence problem of solitary-wave solutions with minimal mass, the so called ground state solutions. To guarantee the existence of ground states we use a variational method.