math Episode 960 Scott Adams: Fake News, Bad Math, Bad Mind-Reading, Bad Behavior in the News By feed.dilbert.com Published On :: Thu, 07 May 2020 15:59:07 +0000 My new book LOSERTHINK, available now on Amazon https://tinyurl.com/rqmjc2a Content: Is the record unambiguous…it was a coup attempt? Mind-readers confirm, Schiff is panicked Tim Graham’s visual writing style Ahmaud Arbery shooting The Plandemic video If you would like to enjoy this same content plus bonus content from Scott Adams, including micro-lessons on lots of useful […] The post Episode 960 Scott Adams: Fake News, Bad Math, Bad Mind-Reading, Bad Behavior in the News appeared first on Scott Adams' Blog. Full Article Podcast Ahmaud Arbery Coronavirus Joe Biden Plandemic politics president trump Remdesivir Scott Adams Tim Graham
math Parents' math skills 'rub off' on their children By esciencenews.com Published On :: Fri, 02 Sep 2016 10:08:23 +0000 Parents who excel at math produce children who excel at math. This is according to a recently released University of Pittsburgh study, which shows a distinct transfer of math skills from parent to child. The study specifically explored intergenerational transmission--the concept of parental influence on an offspring's behavior or psychology--in mathematic capabilities. read more Full Article Psychology & Sociology
math Refinance Dominates Mortgage Applications in the Aftermath of Brexit By zillow.mediaroom.com Published On :: Fri, 08 Jul 2016 08:00:00 -0400 Refinance requests increased 132 percent following the Brexit vote as borrowers capitalize on historically low mortgage rates, according to Zillow Group Mortgages analysis Full Article
math Michele Bachmann's fuzzy gas math By www.mnn.com Published On :: Fri, 19 Aug 2011 14:14:52 +0000 The Republican presidential candidate from Minnesota thinks she has the magic touch for lowering prices at the pump. Full Article Politics
math 'The Great Invisible' explores the environmental and psychological aftermath of the Gulf oil spill By www.mnn.com Published On :: Fri, 24 Oct 2014 19:07:13 +0000 Margaret Brown shares her insights about the Deepwater Horizon spill with MNN. Full Article Wilderness & Resources
math How good are you at math? By www.mnn.com Published On :: Wed, 24 Feb 2016 18:34:49 +0000 There are those of us who aced AP calculus, and there are those of who can't figure out the tip. Take our quiz to find out just how much of a math whiz you are. Full Article Arts & Culture
math Mark Zuckerberg and other tech billionaires create $3 million mathematics prize By www.mnn.com Published On :: Mon, 16 Dec 2013 16:25:15 +0000 Funding for the newest Breakthrough Prize is announced as the awards for life sciences and physics are given at a California ceremony. Full Article Research & Innovations
math Aging is mathematically inevitable, say researchers By www.mnn.com Published On :: Tue, 31 Oct 2017 05:49:59 +0000 Humans have always been searching for a cure for aging, but researchers claim to have developed a mathematical proof that shows it's impossible to avoid. Full Article Fitness & Well-Being
math Turn your shower into a spa with these DIY aromatherapy squares By www.mnn.com Published On :: Mon, 24 Apr 2017 15:57:05 +0000 Homemade aromatherapy shower squares can help relieve stress and even allergies. Here's how to make them yourself. Full Article Fitness & Well-Being
math Why we need to make math relevant to kids By www.mnn.com Published On :: Mon, 12 Dec 2016 20:43:09 +0000 Plus, 5 ideas to use at home to get kids thinking numerically. Full Article Family Activities
math 5 math holidays everyone should know By www.mnn.com Published On :: Fri, 13 Mar 2020 20:21:28 +0000 Mark your calendar for math holidays that celebrate moles, spirals and an endless string of numbers! Full Article Arts & Culture
math How to help in the aftermath of a mass shooting By www.mnn.com Published On :: Tue, 06 Aug 2019 16:21:32 +0000 El Paso and Dayton are in the news this week for all the wrong reasons. If you're wondering what you can do as individual, here are steps you can take. Full Article Responsible Living
math Aromatherapy For Female Hair Loss By www.articlegeek.com Published On :: The essential oil formulas felt so healing and energizing on my scalp. It was as if I could "feel" them working! Within three months I began seeing and feeling soft new growth. Full Article
math Aromatherapy for Hair Loss-Top Eight Essential Oils to Promote Growth By www.articlegeek.com Published On :: For fifteen years now I have been able to control my hair loss and maintain healthy hair with aromatherapy. This article contains what I consider to be the top eight essential oils to stimulate and maintain hair growth. Full Article
math How to Motivate Buyers in the Age of Infinite Media: Mathew Sweezey on Marketing Smarts [Podcast] By rss.marketingprofs.com Published On :: Thu, 20 Feb 2020 10:00 EST Mathew Sweezey of Salesforce offers tips and insights from his forthcoming book, 'Context Marketing Revolution: How to Motivate Buyers in the Age of Infinite Media.' Full Article 15 to 30 minutes Beginner Content Create Intermediate
math Sudershan Kumar Mathavan Presented with the Albert Nelson Marquis Lifetime Achievement Award by Marquis Who's Who By www.24-7pressrelease.com Published On :: Fri, 03 Jan 2020 07:00:00 GMT Dr. Mathavan has been endorsed by Marquis Who's Who as a leader in the engineering industry Full Article
math E Publishing Honors Christopher Mathewson By www.24-7pressrelease.com Published On :: Mon, 22 Oct 2018 07:00:00 GMT E Publishing Honors Christopher Mathewson for his expertise in the field of geology. Full Article
math Walter Koroljow is Celebrated as a Leader in Physics and Mathematics By www.24-7pressrelease.com Published On :: Wed, 29 Apr 2020 07:00:00 GMT Dr. Koroljow has found much success in his decades-spanning career Full Article
math Math Nation Offering 6-8 OER Math Program at Half The Price By www.24-7pressrelease.com Published On :: Tue, 02 Jul 2019 07:00:00 GMT Math Nation is making OER Math curriculum more accessible for all school systems. Full Article
math MATH NATION Releases 6-8 Math Designed To Save Schools Money By www.24-7pressrelease.com Published On :: Tue, 16 Jul 2019 07:00:00 GMT MATH NATION, a leading provider of high school math tutorials, releases 6-8 Mathematics program just in time for back to school. Full Article
math Math and Architectures of Deep Learning By feedproxy.google.com Published On :: Wed, 22 Apr 2020 13:00:59 +0000 This hands-on book bridges the gap between theory and practice, showing you the math of deep learning algorithms side by side with an implementation in PyTorch. You can save 40% off Math and Architectures of Deep Learning until May 13! Just enter the code nlkdarch40 at checkout when you buy from manning.com. Full Article 2020 Apr News Education Deep Learning Manning Mathematics
math Top April Stories: Mathematics for Machine Learning: The Free eBook By feedproxy.google.com Published On :: Fri, 08 May 2020 20:36:00 +0000 Also: Introducing MIDAS: A New Baseline for Anomaly Detection in Graphs; The Super Duper NLP Repo: 100 Ready-to-Run Colab Notebooks; Five Cool Python Libraries for Data Science. Full Article 2020 May Top Stories Tweets Top stories
math Hooda Math Provides Educational Math Games By feedproxy.google.com Published On :: Thu, 31 May 2018 11:52:00 EST Hooda Math is a provider of free educational math games.The games include Day Trader, Transformation Golf 2 and many more. It is free with ads or you can purchase a membership. Read more on howtoweb.com Full Article math games
math Improvements at the Grand Canyon Visitor Center and Mather Point in Grand Canyon National Park Continue to Progress By www.nps.gov Published On :: Sun, 23 Aug 2009 20:00:00 EST Construction on Phase I of the improvements called for in Grand Canyon National Parkâs South Rim Visitor Transportation Plan (SRVTP) continues to progress. https://www.nps.gov/grca/learn/news/news_2009-08-24_phase_i.htm Full Article
math Transition to New Road Alignment to Begin September 8 as Improvements at the Grand Canyon Visitor Center and Mather Point Continue By www.nps.gov Published On :: Tue, 01 Sep 2009 20:00:00 EST As the first phase of improvements called for in Grand Canyon National Park's South Rim Visitor Transportation Plan nears completion, the transition to the new South Entrance Road alignment will begin on Tuesday, September 8. https://www.nps.gov/grca/learn/news/news_2009-09-02_phasei.htm Full Article
math Improved Mather Point and Visitor Center Plaza Areas Now Open to Public By www.nps.gov Published On :: Wed, 05 Jan 2011 19:00:00 EST Phase II of the improvements called for in the South Rim Visitor Transportation Plan/Environmental Assessment (Transportation Plan) is now substantially complete; and Mather Point and the Visitor Center plaza areas have reopened for public use. https://www.nps.gov/grca/learn/news/2011-01-06_phaseii.htm Full Article
math Grand Canyon to celebrate improvements to Mather Point and Grand Canyon Visitor Center area By www.nps.gov Published On :: Wed, 25 May 2011 20:00:00 EST On Wednesday, June 15, Grand Canyon National Park will celebrate the completion of two years of improvements to the Mather Point and Grand Canyon Visitor Center area. https://www.nps.gov/grca/learn/news/2011-05-26_mather.htm Full Article
math Grand Canyon Rangers Respond to Over the Edge Call at Mather Point By www.nps.gov Published On :: Wed, 06 Jul 2016 05:36:00 EST On Monday, June 27 at approximately 4:45 pm, the Grand Canyon Regional Communications Center received a call reporting a visitor over the edge at Mather Point. https://www.nps.gov/grca/learn/news/mather-point-over-the-edge.htm Full Article
math Grand Canyon National Park Rangers Recover Body below Mather Point By www.nps.gov Published On :: Wed, 15 Mar 2017 12:43:00 EST On Tuesday, March 14, at 4:17 pm, the Grand Canyon Regional Communications Center received a call reporting that a visitor had fallen from the rim of the canyon west of Mather Point. https://www.nps.gov/grca/learn/news/mather-point-fatality.htm Full Article
math Northwest Forest Plan-the first 10 years (1994-2003): socioeconomic monitoring of the Klamath National Forest and three local communities. By www.fs.fed.us Published On :: Thu, 06 Nov 2008 08:00:00 PST This report examines socioeconomic changes that took place between 1990 and 2003 on and around lands managed by the Klamath National Forest in California to assess the effects of the Northwest Forest Plan (the Plan) on rural economies and communities there. Three case communities were studied: Scott Valley, Butte Valley, and Mid-Klamath. Full Article
math An Inclusive Vision of Math By rss.sciam.com Published On :: Sat, 07 Mar 2020 20:00:00 GMT Francis Su’s book Mathematics for Human Flourishing is both an invitation and a challenge -- Read more on ScientificAmerican.com Full Article The Sciences Math
math Mathematical Proof That Rocked Number Theory Will Be Published By rss.sciam.com Published On :: Fri, 03 Apr 2020 16:30:00 GMT But some experts say author Shinichi Mochizuki failed to fix a fatal flaw in the solution of a major arithmetic problem -- Read more on ScientificAmerican.com Full Article The Sciences Math
math Remembering Mathematical Magician John Conway By rss.sciam.com Published On :: Mon, 20 Apr 2020 13:00:00 GMT His creative and influential ideas spilled over into quantum physics, philosophy and computer science -- Read more on ScientificAmerican.com Full Article The Sciences Math
math Ampersand, the Aftermath By feedproxy.google.com Published On :: Wed, 22 Jun 2011 12:28:38 PDT The first Ampersand web typography conference took place in Brighton last Friday. Ampersand was ace. I’m going to say that again with emphasis: Ampersand was ace! Like the Ready Brek kid from the 80s TV ads I’m glowing with good vibes. Imagine you’d just met some of the musicians that created the soundtrack to your life. That’s pretty much how I feel. Nerves and all… Photo by Ben Mitchell. For a long, long time I’ve gazed across at the typography community with something akin to awe at the work they do. I’ve lurked quietly on the ATypI mailing list, in the Typophile forum, and behind the glass dividing my eyes from the blogs, portfolios, and galleries. I always had a sneaking suspicion the web and type design communities had much in common: Excellence born from actual client work; techniques and skills refined by practice, not in a lab or classroom; a willingness to share and disseminate, most clearly demonstrated at Typophile and through web designer’s own blogs. The people of both professions have a very diverse set of backgrounds from graphic design all the way through to engineering, to accidentally working in a print shop. We’ve been apprenticed to our work, and Ampersand was a celebration of what we’ve achieved so far and what’s yet to come. Of course, web design is a new profession. Type design has a history that spans hundreds of years. Nevertheless, both professions are self-actualising. Few courses exist of any real merit. There is no qualifications authority. The work from both arenas succeeds or fails based on whether it works or not. Ampersand was the first event of its kind. Folks from both communities came together around the mutal fascination, frustration, challenge and opportunity of web type. Like Brooklyn Beta, the audience was as fantastic as the line up. I met folks like Yves Peters of the FontFeed, Mike Duggan of Microsoft Typography, Jason Smith, Phil Garnham, Fernando Mello, and Emanuela Conidi of Fontsmith, Veronica Burian of TypeTogether, Adam Twardoch of Fontlab and MyFonts, Nick Sherman of of Webtype, Mandy Brown of A Book Apart and Typekit, and many, many others. (Sorry for stopping there, but wow, it would be a huge list.) Rich Rutter Rich Rutter opened the day on behalf of Clearleft and Fontdeck at the Brighton Dome. Rich and I had talked about a web typography conference before. He just went out and did it. Hats off to him, and people like Sophie Barrett at Clearleft who helped make the day run so smoothly. Others have written comprehensive, insightful summaries of the day and the talks. Much better than I could, sitting there on the day, rapt, taking no notes. What follows are a few snippets my memory threw out when prodded. Vincent Connare Who knew the original letterforms for Comic Sans were inspired by a copy of The Watchmen Vincent Connare had in his office? Or that Vincent, who also designed Trebuchet, considers himself an engineer rather than type designer, and is working at the moment on the Ubuntu fonts with colleagues at Dalton Maag. Jason Santa Maria declared himself a type nerd, and gave a supremely detailed talk about selecting, setting, and understanding web type. Wonderful stuff. Jason Santa Maria Jonathan Hoefler talked in rapid, articulate, and precise terms about the work behind upcoming release of pretty-much all of H&FJ’s typefaces as web fonts. (Hooray!) He clearly and wonderfully explained how they took the idea behind their typefaces, and moved them through a design process to produce a final form for a specific purpose. In this case, the web, as a distinct and different environment from print. Jonathan Hoefler Photo by Sean Johnson. I spoke between Jason and Jonathan. Gulp. After staying up until 4am the night before, anxiously working on slides, I was carried along by the privilege and joy of being there, hopefully without too much mumbling or squinting with bleary eyes. After lunch, David Berlow continued the story of web fonts, taking us on a journey through his own trials and tribulations at Font Bureau when re-producing typefaces for the web crude media. His dry, droll, richly-flavoured delivery was a humorous counterpoint to some controversial asides. David Berlow Photo by Jeremy Keith. John Daggett of Mozilla, editor of the CSS3 Fonts Module, talked with great empathy for web designers about the amazing typographic advances we’re about to see in browsers. Tim Brown of Typekit followed. Tim calmly and thoroughly advocated the extension of modular scales to all aspects of a web interface, taking values from the body type and building all elements with those values as the common denominator. Finally, Mark Boulton wrapped up the day brilliantly, describing the designer’s role as the mitigator of entropy, reversing the natural trend for things to move from order to chaos, and a theme he’s exploring at the moment: designing from the content out. Mark Boulton The tone of the day was fun, thoughtful, articulate, and exacting. All the talks were a mix of anecdotal and observational humour, type nerdery, and most of all an overwhelming commitment to excellence in web typography. It was a journey in itself. Decades of experience from plate and press, screen, and web was being distilled into 45-minute presentations. I loved it. As always, one of the most enjoyable bits for me was the hallway track. I talked to heaps of people both in the pre- and after-party, and in between the talks on the day itself. I heard stories, ideas, and opinions from print designers, web designers, type designers, font developers, and writers. We talked late into the night. We talked more the next day. Now the talking has paused for a while, my thoughts are manifold. I can honestly say, I’ve never been so filled with positivity about where we are, and where we’re going. Web typography is here, it works, it’s better all the time, and one day web and type designers everywhere will wonder, perplexed, as they try to imagine what the web was like before. Here’s to another Ampersand next year! I’m now going to see if Rich needs any encouragement to do it again. I’m guessing not, but if he does, I aim to provide it, vigorously. I hope I see you there! Furthermore Rich Rutter back in May on The Ampersand Story Eye Magazine: Web typography comes of age at Brighton’s Ampersand conference Anthony Stonehouse: Ampersand 2011 Laura Kalbag: Notes from Ampersand Dave Bushell: Ampersand Conference! Last but not least, did I mention that Rich Rutter, Mark Boulton, and I are writing a book? We are! More on that another time, but until then, follow @webtypography for intermittent updates. Full Article
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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
math 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