la

Save the Planet; Eat an Insect

By David Suzuki David Suzuki Foundation People sometimes get bugged by insects, but we need them. They play essential roles in pollination, combating unwanted agricultural pests, recycling organic matter, feeding fish, birds and bats, and much more. They’re the most … Continue reading




la

The DOJ's Lawless Reversal on Michael Flynn

Randall D. Eliason: The government's motion to dismiss the case against former national security adviser Michael Flynn is like nothing I've ever seen. It's a political screed dressed up as legal analysis, promoting the "deep state" conspiracy fantasies of President Trump. It epitomizes the politicization of the Justice Department under Attorney General William P. Barr. It is, in the truest sense of the word, lawless.




la

More Than 1,000 Workers at Tyson Plant Have Coronavirus

More than 1,000 workers at the Tyson Foods plant in Waterloo have tested positive for the coronavirus, a county public health leader said Thursday -- more than double the number Gov. Kim Reynolds had said were infected the day before.




la

Trump Declares, 'I Learned a Lot from Nixon'

During an interview on "Fox and Friends," Trump explained why he chose not to go on a firing spree amid Special Counsel Robert Mueller's Russia investigation a la Nixon's Saturday Night Massacre during the Watergate scandal. "I learned a lot from Richard Nixon: Don't fire people," the President said. "I learned a lot. I study history, and the firing of everybody ... .I should've, in one way," he continued. "But I'm glad I didn't because look at the way it turned out."




la

GOP Plans to Spend at least $20 million to Combat Voting Rights Lawsuits

The Republican National Committee and President Donald Trump's reelection campaign have doubled their litigation budget to $20 million, Politico reported Thursday. RNC chief of staff Richard Walters told Politico that the GOP is prepared to sue Democrats "into oblivion" by spending "whatever is necessary" to prevail in legal fights against its rivals leading up to the November election.




la

Say Yes, Figure It Out Later. Starting from the Start with Tyler Babin

“It’s impossible to move forward while staying the same”. That’s what motivated Tyler Babin, a 25 year old up & coming filmmaker, who hustled his way into his dream job only to leave it to pursue the riskier thing, an even bigger bet – on himself. I’ve had literally hundreds of requests over the years to have someone on the show who isn’t Richard Branson or Brene Brown or {fill in the blank star}…ie. host someone who hasn’t “made it big” and is, instead, on the come-up themselves…someone from within our very own community who has been listening for years, connecting dots, gleaning knowledge and is now taking major action on that.  Well THIS is Tyler’s story. If you’ve  followed my pal Gary Vaynerchuk, it’s likely you’ve actually seen some of Tyler’s work. For the last 3-4 years, he’s been a whirlwind tour traveling the world with Gary, shooting photo + video, creative directing projects at Vayner… and it all started right here on this show nearly 8 years ago.  This episode goes full circle, friends. Also – instead of the usual studio conversation, Tyler and I recorded the show while grabbing a burger & margarita just around the corner […]

The post Say Yes, Figure It Out Later. Starting from the Start with Tyler Babin appeared first on Chase Jarvis Photography.




la

Everything I Know In One Place

It was surreal to sit down at the mic and record this show after spending the last few years (5 a.m. mornings, late, late nights, and many long weekends hunkered down) writing a book that I’m proud and beyond excited to share with YOU and the world.  It’s called CREATIVE CALLING and it’s officially available for pre-order TODAY! In this episode, you get the little sneak peek at the book (yes, I read a little from it) and a little background on why I needed to write it.  After all, life isn’t about “finding” fulfillment and success – it’s about creating it. Creativity is a force inside every person that, when unleashed, transforms our lives and delivers vitality to everything we do. Establishing a creative practice is therefore our most valuable and urgent task – as important to our well-being as exercise or nutrition. The good news? Creativity isn’t a skill—it’s a habit available to everyone:  beginners and lifelong creators, entrepreneurs to executives, astronauts to zookeepers, and everyone in between. It’s only through small, daily actions that we can supercharge our innate creativity and (re-)discover our personal power in life. Everything you need is inside you right now. Whether your ambition is a creative career, completing a creative […]

The post Everything I Know In One Place appeared first on Chase Jarvis Photography.




la

Harmony > Balance with Jason Calacanis

Today we’re going back to San Francisco with myself and Jason Calacanis on stage during my tour stop for my book Creative Calling. Jason is an investor and long time host of the This Week in Startups podcast. And, of course, Jason wastes no time in our conversation. He goes right to the heart of the matter by getting into failure, venture capitol, knowing when to quit, and when to push through. Enjoy! FOLLOW JASON: facebook | twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post Harmony > Balance with Jason Calacanis appeared first on Chase Jarvis Photography.




la

Workplace Revolution with Amy Nelson

Amy Nelson is the founder and CEO of The Riveter. If you’re not familiar with The Riveter, it’s a modern day union of women and their allies. It’s a community, a workspace and resource that supports women in building business and careers. The Riveter has locations all throughout the US and is growing rapidly. I cannot wait for you to hear this story. Amy Nelson practiced corporate litigation for over a decade in New York City and Seattle and worked in politics under several presidents. But it wasn’t until she was a mother that she started noticing something. Conversations no longer were about her career, but how motherhood would impact her career. Why was it not possible to “have it all”: be the best lawyer, the best wife, and mother? Looking for inspiration, she discovered a telling statistic: 43% of highly trained professional women “off-ramp” after having kids. It was then an idea started to form. In this episode we explore: How a bold concept can go from idea to reality. How Amy raised money and grew a national company in 2.5 years Being a vulnerable leader + the emotional journey of exploring and building something new How can we all […]

The post Workplace Revolution with Amy Nelson appeared first on Chase Jarvis Photography.




la

Start in a Place That’s True with IN-Q

Storytelling is one of the oldest art forms. It connects us. Our brains our wired for it. Story is not only a way for us to share and connect with others, but a path to deeper understanding and vulnerability. That’s why I’m very excited to have on the show award winning Poet, Author, and Performer, IN-Q. In addition to his poetry, live performances and storytelling workshops, IN-Q is a multi-platinum songwriter having worked with Selena Gomez, Aloe Black, Miley Cyrus, Mike Posner, and Foster the People. Oprah named him on her SuperSoul 100 list of the world’s most influential thought leaders. He’s been featured all over the place including A&E, ESPN, HBO, and companies such as Nike, Instagram, Spotify, and many more. In our conversation, we get into his new book, Inquire Within. In fact, he reads a bit of it on the show. It’s an awe-inspiring rhythmic exploration of transforming love, loss, and forgiveness into growth. Super excited for you to hear it. We also get into: Developing your own voice by focusing on what’s moving and meaningful for you How to find calm in the chaos Using vulnerability to short-cut and deepen relationships in our lives and much, […]

The post Start in a Place That’s True with IN-Q appeared first on Chase Jarvis Photography.




la

The Code of the Extraordinary Mind with Vishen Lakhiani

Join me + bestselling author Vishen Lakhiani LIVE Tuesday April 7 at 6:30pm PST. Vishen Lakhiani is one of today’s most influential minds in the fields of education and human consciousness. He is the founder of Mindvalley University and its 2 million-strong student base and creator of the Quests learning platform: a next-generation method of online learning, which attains an unheard-of 60% completion rate on courses, in an industry where 8% is average. Vishen’s book, The Code of the Extraordinary Mind, made the New York Times Business Best Sellers List, and hit the coveted #1 spot on Amazon five times in 2017. Enjoy! FOLLOW VISHEN: instagram | facebook | website Listen to the Podcast coming soon … Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, Grammy Award winners, New York Times best selling authors and the best entrepreneurs of our times.

The post The Code of the Extraordinary Mind with Vishen Lakhiani appeared first on Chase Jarvis Photography.




la

Hope in a Sea of Endless Calamity with Mark Manson

Today on the show, I’m chatting with New York Times bestselling author Mark Manson. He is the #1 New York Times Bestselling author of Everything is F*cked and The Subtle Art of Not Giving a F*ck, the mega-bestseller that reached #1 in fourteen different countries. Mark also runs one of the largest personal growth websites in the world, MarkManson.net, a blog with more than two million monthly readers and half a million subscribers, making him one of the largest and most successful independent publishers in the world. In this episode, we take a deep dive into the creative process. How to spend your time when you’re trying get comfortable with being uncomfortable. Mark helps bring into focus the up-side that this moment has created for us while also sharing some of the tactics he while quarantined. Enjoy! FOLLOW MARK: instagram | twitter | website Listen to the Podcast Subscribe   This podcast is brought to you by CreativeLive. CreativeLive is the world’s largest hub for online creative education in photo/video, art/design, music/audio, craft/maker, money/life and the ability to make a living in any of those disciplines. They are high quality, highly curated classes taught by the world’s top experts — Pulitzer, Oscar, […]

The post Hope in a Sea of Endless Calamity with Mark Manson appeared first on Chase Jarvis Photography.




la

Star Wars Playing Card Deck

I am huge fan of the universe of Star Wars, it is amazing how vast and detailed this it can be. I am also a lover of the playing cards designs, you can big array of topics from sexy to nerdy ones. Just like this ones, a complete set of playing cards based on the …

Star Wars Playing Card Deck Read More »




la

Why Collaborative Coding Is The Ultimate Career Hack

Taking your first steps in programming is like picking up a foreign language. At first, the syntax makes no sense, the vocabulary is unfamiliar, and everything looks and sounds unintelligible. If you’re anything like me when I started, fluency feels impossible. I promise it isn’t. When I began coding, the learning curve hit me — hard. I spent ten months teaching myself the basics while trying to stave off feelings of self-doubt that I now recognize as imposter syndrome.




la

Nikon has confirmed that their flagship D6 DSLR will start shipping on May 21st

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.




la

#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.













la

The Visual Evolution of the “Flattening the Curve” Information Graphic

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. […]




la

Non-associative Frobenius algebras for simply laced Chevalley groups. (arXiv:2005.02625v1 [math.RA] CROSS LISTED)

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.




la

Regular Tur'an numbers of complete bipartite graphs. (arXiv:2005.02907v2 [math.CO] UPDATED)

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 $t>s!$.




la

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.




la

Nonlinear singular problems with indefinite potential term. (arXiv:2005.01789v3 [math.AP] UPDATED)

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.




la

Solving an inverse problem for the Sturm-Liouville operator with a singular potential by Yurko's method. (arXiv:2004.14721v2 [math.SP] UPDATED)

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




la

Lagrangian geometry of matroids. (arXiv:2004.13116v2 [math.CO] UPDATED)

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.




la

On the exterior Dirichlet problem for a class of fully nonlinear elliptic equations. (arXiv:2004.12660v3 [math.AP] UPDATED)

In this paper, we mainly establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for a class of fully nonlinear second-order elliptic equations related to the eigenvalues of the Hessian, with prescribed generalized symmetric asymptotic behavior at infinity. Moreover, we give some new results for the Hessian equations, Hessian quotient equations and the special Lagrangian equations, which have been studied previously.




la

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.




la

$L^p$-regularity of the Bergman projection on quotient domains. (arXiv:2004.02598v2 [math.CV] UPDATED)

We relate the $L^p$-mapping properties of the Bergman projections on two domains in $mathbb{C}^n$, one of which is the quotient of the other under the action of a finite group of biholomorphic automorphisms. We use this relation to deduce the sharp ranges of $L^p$-boundedness of the Bergman projection on certain $n$-dimensional model domains generalizing the Hartogs triangle.




la

Tori Can't Collapse to an Interval. (arXiv:2004.01505v3 [math.DG] UPDATED)

Here we prove that under a lower sectional curvature bound, a sequence of manifolds diffeomorphic to the standard $m$-dimensional torus cannot converge in the Gromov-Hausdorff sense to a closed interval.




la

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.




la

$5$-rank of ambiguous class groups of quintic Kummer extensions. (arXiv:2003.00761v2 [math.NT] UPDATED)

Let $k ,=, mathbb{Q}(sqrt[5]{n},zeta_5)$, where $n$ is a positive integer, $5^{th}$ power-free, whose $5-$class group is isomorphic to $mathbb{Z}/5mathbb{Z} imesmathbb{Z}/5mathbb{Z}$. Let $k_0,=,mathbb{Q}(zeta_5)$ be the cyclotomic field containing a primitive $5^{th}$ root of unity $zeta_5$. Let $C_{k,5}^{(sigma)}$ the group of the ambiguous classes under the action of $Gal(k/k_0)$ = $<sigma>$. The aim of this paper is to determine all integers $n$ such that the group of ambiguous classes $C_{k,5}^{(sigma)}$ has rank $1$ or $2$.




la

Co-Seifert Fibrations of Compact Flat Orbifolds. (arXiv:2002.12799v2 [math.GT] UPDATED)

In this paper, we develop the theory for classifying all the geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to affine equivalence. We apply our classification theory to classify all the geometric fibrations of compact, connected, flat $2$-orbifolds, over a 1-orbifold, up to affine equivalence. This paper is an essential part of our project to give a geometric proof of the classification of all closed flat 4-manifolds.




la

A stochastic approach to the synchronization of coupled oscillators. (arXiv:2002.04472v2 [nlin.AO] UPDATED)

This paper deals with an optimal control problem associated to the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are aligned on the same phase. This control is computed via the minimization of a given cost functional associated with the dynamics considered. For this minimization, we propose a novel approach based on the combination of a standard Gradient Descent (GD) methodology with the recently-developed Random Batch Method (RBM) for the efficient numerical approximation of collective dynamics. Our simulations show that the employment of RBM improves the performances of the GD algorithm, reducing the computational complexity of the minimization process and allowing for a more efficient control calculation.




la

Quasistatic evolution for dislocation-free finite plasticity. (arXiv:1912.10118v2 [math.AP] UPDATED)

We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.




la

Regularized vortex approximation for 2D Euler equations with transport noise. (arXiv:1912.07233v2 [math.PR] UPDATED)

We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot-Savart kernel and the same common noise. The approximation happens by sending the number of particles $N$ to infinity and the regularization $epsilon$ in the Biot-Savart kernel to $0$, as a suitable function of $N$.




la

Eigenvalues of the Finsler $p$-Laplacian on varying domains. (arXiv:1912.00152v4 [math.AP] UPDATED)

We study the dependence of the first eigenvalue of the Finsler $p$-Laplacian and the corresponding eigenfunctions upon perturbation of the domain and we generalize a few results known for the standard $p$-Laplacian. In particular, we prove a Frech'{e}t differentiability result for the eigenvalues, we compute the corresponding Hadamard formulas and we prove a continuity result for the eigenfunctions. Finally, we briefly discuss a well-known overdetermined problem and we show how to deduce the Rellich-Pohozaev identity for the Finsler $p$-Laplacian from the Hadamard formula.




la

Monochromatic Equilateral Triangles in the Unit Distance Graph. (arXiv:1909.09856v2 [math.CO] UPDATED)

Let $chi_{Delta}(mathbb{R}^{n})$ denote the minimum number of colors needed to color $mathbb{R}^{n}$ so that there will not be a monochromatic equilateral triangle with side length $1$. Using the slice rank method, we reprove a result of Frankl and Rodl, and show that $chi_{Delta}left(mathbb{R}^{n} ight)$ grows exponentially with $n$. This technique substantially improves upon the best known quantitative lower bounds for $chi_{Delta}left(mathbb{R}^{n} ight)$, and we obtain [ chi_{Delta}left(mathbb{R}^{n} ight)>(1.01446+o(1))^{n}. ]




la

Integrability of moduli and regularity of Denjoy counterexamples. (arXiv:1908.06568v4 [math.DS] UPDATED)

We study the regularity of exceptional actions of groups by $C^{1,alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of continuity $alpha$. Let $G$ be a finitely generated group admitting a $C^{1,alpha}$ action $ ho$ with a free orbit on the circle, and such that the logarithms of derivatives of group elements are uniformly bounded at some point of the circle. We prove that if $G$ has spherical growth bounded by $c n^{d-1}$ and if the function $1/alpha^d$ is integrable near zero, then under some mild technical assumptions on $alpha$, there is a sequence of exceptional $C^{1,alpha}$ actions of $G$ which converge to $ ho$ in the $C^1$ topology. As a consequence for a single diffeomorphism, we obtain that if the function $1/alpha$ is integrable near zero, then there exists a $C^{1,alpha}$ exceptional diffeomorphism of the circle. This corollary accounts for all previously known moduli of continuity for derivatives of exceptional diffeomorphisms. We also obtain a partial converse to our main result. For finitely generated free abelian groups, the existence of an exceptional action, together with some natural hypotheses on the derivatives of group elements, puts integrability restrictions on the modulus $alpha$. These results are related to a long-standing question of D. McDuff concerning the length spectrum of exceptional $C^1$ diffeomorphisms of the circle.




la

Nonlinear stability of explicit self-similar solutions for the timelike extremal hypersurfaces in R^{1+3}. (arXiv:1907.01126v2 [math.AP] UPDATED)

This paper is devoted to the study of the singularity phenomenon of timelike extremal hypersurfaces in Minkowski spacetime $mathbb{R}^{1+3}$. We find that there are two explicit lightlike self-similar solutions to a graph representation of timelike extremal hypersurfaces in Minkowski spacetime $mathbb{R}^{1+3}$, the geometry of them are two spheres. The linear mode unstable of those lightlike self-similar solutions for the radially symmetric membranes equation is given. After that, we show those self-similar solutions of the radially symmetric membranes equation are nonlinearly stable inside a strictly proper subset of the backward lightcone. This means that the dynamical behavior of those two spheres is as attractors. Meanwhile, we overcome the double roots case (the theorem of Poincar'{e} can't be used) in solving the difference equation by construction of a Newton's polygon when we carry out the analysis of spectrum for the linear operator.




la

Mirror Symmetry for Non-Abelian Landau-Ginzburg Models. (arXiv:1812.06200v3 [math.AG] UPDATED)

We consider Landau-Ginzburg models stemming from groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors for Fermat type polynomials.




la

On $p$-groups with automorphism groups related to the exceptional Chevalley groups. (arXiv:1810.08365v3 [math.GR] UPDATED)

Let $hat G$ be the finite simply connected version of an exceptional Chevalley group, and let $V$ be a nontrivial irreducible module, of minimal dimension, for $hat G$ over its field of definition. We explore the overgroup structure of $hat G$ in $mathrm{GL}(V)$, and the submodule structure of the exterior square (and sometimes the third Lie power) of $V$. When $hat G$ is defined over a field of odd prime order $p$, this allows us to construct the smallest (with respect to certain properties) $p$-groups $P$ such that the group induced by $mathrm{Aut}(P)$ on $P/Phi(P)$ is either $hat G$ or its normaliser in $mathrm{GL}(V)$.




la

On the rationality of cycle integrals of meromorphic modular forms. (arXiv:1810.00612v3 [math.NT] UPDATED)

We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these results is an extension of the Shintani theta lift to meromorphic modular forms of positive even weight.




la

Extremal values of the Sackin balance index for rooted binary trees. (arXiv:1801.10418v5 [q-bio.PE] UPDATED)

Tree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are more likely than balanced ones. Therefore, different methods to measure the balance of trees were introduced. The Sackin index is one of the most frequently used measures for this purpose. In many contexts, statements about the minimal and maximal values of this index have been discussed, but formal proofs have never been provided. Moreover, while the number of trees with maximal Sackin index as well as the number of trees with minimal Sackin index when the number of leaves is a power of 2 are relatively easy to understand, the number of trees with minimal Sackin index for all other numbers of leaves was completely unknown. In this manuscript, we fully characterize trees with minimal and maximal Sackin index and also provide formulas to explicitly calculate the number of such trees.