ens Diagnosing and treating resistant hypertension By newsroom.heart.org Published On :: Thu, 13 Sep 2018 09:00:00 GMT Statement Highlight: Resistant blood pressure affects 12 percent to 15 percent of people currently being treated for high blood pressure. Full Article
ens Specific gut bacteria may be associated with pulmonary arterial hypertension By newsroom.heart.org Published On :: Mon, 24 Feb 2020 10:00:00 GMT Research Highlights: Researchers have found a specific bacterial profile in the gut of people with pulmonary arterial hypertension, a chronic and progressive disease that causes constriction of arteries in the lungs. The unique bacterial profile... Full Article
ens Dos artículos de perspectivas sobre los medicamentos para la hipertensión y su uso continuo a fin de combatir el COVID-19 By newsroom.heart.org Published On :: Wed, 01 Apr 2020 09:00:00 GMT DALLAS, 1 de abril del 2020 — Algunos cardiólogos de Wuhan, China y otros países recomiendan a los pacientes con hipertensión arterial que continúen tomando sus medicamentos, aunque los efectos de algunos se hayan visto afectados por las infecciones ... Full Article
ens Maternal hypertensive disorders may lead to mental health disorders in children By newsroom.heart.org Published On :: Mon, 20 Apr 2020 09:00:00 GMT Research Highlights: Hypertensive pregnancy disorders, especially preeclampsia – may increase the risk of psychological development disorders and behavioral and emotional disorders in children. This is the first study to show that preeclampsia... Full Article
ens More than 200 patient groups call on Administration to take additional action to alleviate critical shortage of ventilators, PPE, ensure safety of providers, patients By newsroom.heart.org Published On :: Mon, 06 Apr 2020 16:10:00 GMT Today, more than patient advocacy, medical and public health organizations sent a letter to senior Trump Administration officials, appealing to the Administration to take immediate action to alleviate the critical shortage across the nation ventilators... Full Article
ens Federal district court strikes down USDA rule that weakens national school nutrition programs By newsroom.heart.org Published On :: Tue, 14 Apr 2020 22:45:00 GMT WASHINGTON, D.C., April 14, 2020 — Yesterday, a federal district court struck down a rule by the U.S. Department of Agriculture (USDA) that rolled back nutrition standards in schools. Last fall, The American Heart Association, the world’s leading... Full Article
ens Más pasos por día se relaciona con reducciones significativas de la diabetes y la hipertensión arterial By newsroom.heart.org Published On :: Thu, 05 Mar 2020 21:00:00 GMT Puntos destacados de la investigación: Los adultos de mediana edad que caminaron una mayor cantidad de pasos al día mostraron un 43% menos de riesgo de padecer diabetes y un 31% menos de riesgo de hipertensión arterial, en comparación con personas de... Full Article
ens Big Ten extends suspension of team activities through June 1 By feedproxy.google.com Published On :: Mon, 04 May 2020 13:17:56 PDT Last week, University of Iowa President Bruce Harreld made some waves when he announced at a Board of Regents meeting UI athletics plans to resume practice on June 1. Monday, the Big Ten announced... Full Article Iowa Football
ens Former Hawkeye defensive lineman Jeff Koeppel tackled COVID-19 and prevailed By feedproxy.google.com Published On :: Fri, 08 May 2020 11:31:14 PDT Jeff Koeppel, a North Liberty businessman who played on Iowa’s football team from 1986 to 1989 — was a second-team All-Big Ten defensive lineman for two years — caught COVID-19... Full Article Iowa Football
ens How to Sell Online Courses with Sensei LMS By feedproxy.google.com Published On :: Thu, 07 May 2020 15:00:00 +0000 Any business can increase revenue with online courses. No physical contact required! Here are the 4 tools you’ll need to get started fast & generate sales! The post How to Sell Online Courses with Sensei LMS appeared first on WooCommerce. Full Article Blog
ens Phinney: County needs common sense, smarter government By www.thegazette.com Published On :: Wed, 6 May 2020 11:43:05 -0400 I have been a Johnson County resident since 1977. I grew up in Clear Lake, a small farming community in North Central Iowa. I came to Iowa City after being recruited by Dan Gable to wrestle for the University of Iowa Hawkeye wrestling team and placed 3rd place in the 1980 NCAA Division I.I met my wife Teresa and we settled in Iowa City. I have two children, Melissa, 36, and Anthony, 25; and grandchildren Emma, 9, Ellie and Emilia, 4-month-old twin girls, and Jack, who passed two just before his 2nd birthday. I am a cancer survivor and support cancer research and patient support. I was a maintenance supervisor at the old Cantebury Inn, I owned and operated Advance Property Management for 23 years and drove a school bus for First Student, Inc. While working at First Student I was one of the driving forces in the campaign for the workers to unionize with the Teamsters. I was asked to join the Teamsters as a full-time organizer after the campaign, which I did for 13 years. I found my calling as an organizer because I was able to help others stand up for themselves and really change their lives. I made the decision to run for Johnson County supervisor because we need to bring some common sense back to Johnson County government, and run a smarter government that works for all. The supervisors need to oversee the county departments better to stop wasting county funds paying settlements to individuals because of illegal action by department employees. Rules are for everyone and if you work outside the rules there will be costs and consequences.I want to bring new blood to the board as well as new ideas. County supervisor is a public service position of honor and trust. Being a supervisor is about following through on jobs you were elected to do for the people. The supervisors need to finish jobs that they started but never completed. You should never leave a job half done!I hope the voters agree the Johnson County Board of Supervisors need to answer to the public for their actions and their employees. We can no long just “sweep issues under the rug.” Dean Phinney is a candidate in the Democratic primary for Johnson County Board of Supervisors. Full Article Guest Columnist
ens Lensing: Leadership on education funding, mental health and accessible voting By www.thegazette.com Published On :: Wed, 6 May 2020 15:39:39 -0400 Serving as state representative of House District 85 for the past few years has been a privilege and an honor. I have worked hard to stand for the people of my district fighting for issues that are important to them and to the voters of Iowa City. I want to continue that advocacy and am running for another term in the Iowa House and ask for your vote.I vigorously support adequate funding for education from pre-school to our community colleges and universities. Our young people are Iowa’s future and deserve the best start available through our excellent education system in Iowa. But we need to provide the dollars necessary to keep our teachers in the classroom so our children are prepared for whatever may lie ahead of them.I have advocated for the fair treatment of workers in Iowa and support their right to organize. I have worked on laws for equal pay for equal work and whistle blower protection.I am for essential funding for mental health services for Iowans of all ages. Children and adults who are struggling with mental health issues should have services available to them no matter where they live in this state. I have fought to keep government open and accessible to Iowans. I support open records and open meetings laws to ensure that availability and transparency to all Iowans.Keeping voting easy and accessible to voters has been a priority of mine. I support a fair and balanced redistricting system for voting in Iowa.I have advocated to keep the bottle deposit law in place and expand it to cover the many new types of containers available.I have worked on oversight legislation after several investigations into defrauding government which involved boarding homes, government agencies and pharmacy benefit managers (the “middleman” between pharmacies/Medicaid and the healthcare insurance companies.) I cannot avoid mentioning the challenge of the coronavirus in Iowa. It has impacted our health, jobs, families and businesses. No one could have predicted this pandemic but as Iowans, we need to do our best to limit contact and the spread of this disease. My sincere appreciation goes to those workers on the frontlines of this crisis: the healthcare workers, store owners, businesses, farmers, teachers and workers who show up every day to keep this state moving forward. Thank you all!There is still much work to be done to keep Iowa the great place where we live, work and raise our families. I am asking for your vote to allow me the privilege of continuing that work.Vicki Lensing is a candidate in the Democratic primary for Iowa House District 85. Full Article Guest Columnist
ens How to Use apply_filters() and do_action() to Create Extensible WordPress Plugins By feedproxy.google.com Published On :: Thu, 13 Oct 2016 21:01:47 +0000 How does a single plugin become the basis of a thriving technology ecosystem? Partly by leveraging the extensibilitythat WordPress’s event-driven Hooks system makes possible. Full Article Plugins
ens Through The Lens of Photographer Jessica Antola By www.fubiz.net Published On :: Sat, 09 May 2020 06:52:58 +0000 Au carrefour de la mode et de l’image documentaire, Jessica Antola photographie des tissus, mais avant tout des personnes. Elle construit avec eux une relation de confiance et en retour, ses modèles lui offrent une petite fenêtre ouverte sur leur vie. Tout d’abord, vous avez travaillé dans l’industrie de la mode. Ainsi, votre amour pour […] Full Article Photography Travel
ens What happens if my visa is refused or cancelled due to my character? By feedproxy.google.com Published On :: Wed, 04 Dec 2019 07:16:08 +0000 If you have your visa refused or cancelled, you need to get expert advice a soon as possible. Strict time limits apply to drafting submissions and appeals. A visa refusal or cancellation can limit the type or visas you can apply for in the future or even prohibit you from applying for any visa to […] The post What happens if my visa is refused or cancelled due to my character? appeared first on Visa Australia - Immigration Lawyers & Registered Migration Agents. Full Article Visa Cancellation cancelled visa character issues character test character visa conviction criminal conduct criminal conviction criminal record minister's delegate ministerial direction 65 refused visa substantial criminal record visa cancelled visa refusal visa refused
ens Student visa holders and New Zealand citizens in Australia and the Coronavirus (COVID-19) crisis? By feedproxy.google.com Published On :: Sun, 19 Apr 2020 20:30:00 +0000 International students who have been in Australia for longer than 12 months who find themselves in financial hardship will be able to access their Australian superannuation. The Government will undertake further engagement with the international education sector who already provide some financial support for international students facing hardship. International students working in supermarkets will have […] The post Student visa holders and New Zealand citizens in Australia and the Coronavirus (COVID-19) crisis? appeared first on Visa Australia - Immigration Lawyers & Registered Migration Agents. Full Article Student Visas aged care Australian welfare payments Coronavirus covid-19 extended hours international students JobKeeper payment new zealand citizens nurses special category subclass 444 subclass 444 visa conditions working hours
ens Own This Extensive Font Library Worth $4265 for Just $29 By blog.spoongraphics.co.uk Published On :: Wed, 15 Apr 2020 07:00:40 +0000 High-quality fonts can be really expensive and are often the most costly tool a designer needs, so when a massive saving like this comes along it’s hard to let it pass by! This brand new bundle contains 16 hand-picked typefaces, containing hundreds of individual fonts, chosen specifically for their quality and versatility. These fonts are […] The post Own This Extensive Font Library Worth $4265 for Just $29 appeared first on Spoon Graphics. Full Article News bundle deal design cuts fonts
ens Top 5 Best Internet Live Support Extension To Increase Customers Interactions By icanbecreative.com Published On :: Fri, 27 Mar 2020 03:19:08 PDT Creative interactions call for creative measures - numerous extensions reduce, minimize or dilute the frustration of the customers and resolve issues quickly without the customer support team need.... Full Article Learning
ens Playable simulations to decide what happens next By flowingdata.com Published On :: Mon, 04 May 2020 07:21:03 +0000 The timelines keep shifting and people are getting antsy for many valid (and…Tags: coronavirus, Marcel Salathé, Nicky Case, simulation Full Article Infographics coronavirus Marcel Salathé Nicky Case simulation
ens Intel’s Parallel Extensions for JavaScript By feedproxy.google.com Published On :: Sat, 08 Oct 2011 17:38:07 +0000 Intel’s Parallel Extensions for JavaScript, code named River Trail, hooks into on-chip vector extensions to improve performance of Web applications. Details of Intel’s attempt to get on the JavaScript juggernaut emerged last month at its developer event. The prototype JavaScript extension offered by Intel is intended to allow JavaScript apps to take advantage of modern parallel Read the rest... Full Article Front Page JavaScript
ens Using Funds from Disability Compensation and the GI Bill for Going Back to School By feedproxy.google.com Published On :: Mon, 11 Nov 2013 00:00:00 EST Receiving service-related disability compensation does not interfere with the funds veterans receive from the GI Bill, explains Adam. Full Article
ens Test or Meet at WordCamp San Francisco and Win a Plugin License! By wpengineer.com Published On :: Mon, 20 Oct 2014 06:12:30 +0000 Next week I will be at WordCamp San Francisco and a week later at the WooConf! Maybe one or antoher […] Full Article WPengineer Misc
ens First impressions of the Fuji X-Pro2 (and the Fujinon 100-400mm lens) By feedproxy.google.com Published On :: Wed, 16 Mar 2016 20:16:47 +0000 Fuji released their new flagship camera this month, the X-Pro2. It is the first X-series camera to feature a 24MP sensor (compared to 16MP before) and it has a very interesting hybrid optical & electronic view finder. When I first […] Full Article Hardware Thoughts
ens Google Lens now copies handwritten text and pastes it straight to your computer By feedproxy.google.com Published On :: Thu, 07 May 2020 19:59:08 +0000 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. Full Article news AI Artificial Intelligence Google AI Google Lens hadwriting handwritten
ens 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
ens Triangles in graphs without bipartite suspensions. (arXiv:2004.11930v2 [math.CO] UPDATED) By arxiv.org Published On :: 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. Full Article
ens Convergent normal forms for five dimensional totally nondegenerate CR manifolds in C^4. (arXiv:2004.11251v2 [math.CV] UPDATED) By arxiv.org Published On :: Applying the equivariant moving frames method, we construct convergent normal forms for real-analytic 5-dimensional totally nondegenerate CR submanifolds of C^4. These CR manifolds are divided into several biholomorphically inequivalent subclasses, each of which has its own complete normal form. Moreover it is shown that, biholomorphically, Beloshapka's cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question. Full Article
ens Finite dimensional simple modules of $(q, mathbf{Q})$-current algebras. (arXiv:2004.11069v2 [math.RT] UPDATED) By arxiv.org Published On :: 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. Full Article
ens $5$-rank of ambiguous class groups of quintic Kummer extensions. (arXiv:2003.00761v2 [math.NT] UPDATED) By arxiv.org Published On :: 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 $2$. Full Article
ens Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets. (arXiv:2002.01023v2 [math.OC] UPDATED) By arxiv.org Published On :: Willems et al.'s fundamental lemma asserts that all trajectories of a linear system can be obtained from a single given one, assuming that a persistency of excitation condition holds. This result has profound implications for system identification and data-driven control, and has seen a revival over the last few years. The purpose of this paper is to extend Willems' lemma to the situation where multiple (possibly short) system trajectories are given instead of a single long one. To this end, we introduce a notion of collective persistency of excitation. We will then show that all trajectories of a linear system can be obtained from a given finite number of trajectories, as long as these are collectively persistently exciting. We will demonstrate that this result enables the identification of linear systems from data sets with missing data samples. Additionally, we show that the result is of practical significance in data-driven control of unstable systems. Full Article
ens Compact manifolds of dimension $ngeq 12$ with positive isotropic curvature. (arXiv:1909.12265v4 [math.DG] UPDATED) By arxiv.org Published On :: We prove the following result: Let $(M,g_0)$ be a compact manifold of dimension $ngeq 12$ with positive isotropic curvature. Then $M$ is diffeomorphic to a spherical space form, or a compact quotient manifold of $mathbb{S}^{n-1} imes mathbb{R}$ by diffeomorphisms, or a connected sum of a finite number of such manifolds. This extends a recent work of Brendle, and implies a conjecture of Schoen in dimensions $ngeq 12$. The proof uses Ricci flow with surgery on compact orbifolds with isolated singularities. Full Article
ens Infinite dimensional affine processes. (arXiv:1907.10337v3 [math.PR] UPDATED) By arxiv.org Published On :: The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for such processes, which has been missing in the literature so far. For the existence proof, we will regard affine processes as solutions to infinite dimensional stochastic differential equations with values in Hilbert spaces. This requires a suitable version of the Yamada-Watanabe theorem, which we will provide in this paper. Several examples of infinite dimensional affine processes accompany our results. Full Article
ens A stand-alone analysis of quasidensity. (arXiv:1907.07278v8 [math.FA] UPDATED) By arxiv.org Published On :: In this paper we consider the "quasidensity" of a subset of the product of a Banach space and its dual, and give a connection between quasidense sets and sets of "type (NI)". We discuss "coincidence sets" of certain convex functions and prove two sum theorems for coincidence sets. We obtain new results on the Fitzpatrick extension of a closed quasidense monotone multifunction. The analysis in this paper is self-contained, and independent of previous work on "Banach SN spaces". This version differs from the previous version because it is shown that the (well known) equivalence of quasidensity and "type (NI)" for maximally monotone sets is not true without the monotonicity assumption and that the appendix has been moved to the end of Section 10, where it rightfully belongs. Full Article
ens Representations of the Infinite-Dimensional $p$-Adic Affine Group. (arXiv:1906.08964v2 [math.RT] UPDATED) By arxiv.org Published On :: We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions. Full Article
ens Gabriel-Roiter measure, representation dimension and rejective chains. (arXiv:1903.05555v2 [math.RT] UPDATED) By arxiv.org Published On :: The Gabriel-Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The concept of Gabriel-Roiter measure can be extended to abelian length categories and every such category has multiple Gabriel-Roiter measures. Using this notion, we prove the following broader statement: given any object $X$ and any Gabriel-Roiter measure $mu$ in an abelian length category $mathcal{A}$, there exists an object $X'$ which depends on $X$ and $mu$, such that $Gamma = operatorname{End}_{mathcal{A}}(X oplus X')$ has finite global dimension. Analogously to Iyama's original results, our construction yields quasihereditary rings and fits into the theory of rejective chains. Full Article
ens Twisted Sequences of Extensions. (arXiv:1808.07936v3 [math.RT] UPDATED) By arxiv.org Published On :: Gabber and Joseph introduced a ladder diagram between two natural sequences of extensions. Their diagram is used to produce a 'twisted' sequence that is applied to old and new results on extension groups in category $mathcal{O}$. Full Article
ens Conservative stochastic 2-dimensional Cahn-Hilliard equation. (arXiv:1802.04141v2 [math.PR] UPDATED) By arxiv.org Published On :: We consider the stochastic 2-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution $Y$ to the shifted equation (see (1.4) below), then $X:=Y+{Z}$ is the unique solution to stochastic Cahn-Hilliard equaiton, where ${Z}$ is the corresponding O-U process. Moreover, we use Dirichlet form approach in cite{Albeverio:1991hk} to construct the probabilistically weak solution the the original equation (1.1) below. By clarifying the precise relation between the solutions obtained by the Dirichlet forms aprroach and $X$, we can also get the restricted Markov uniquness of the generator and the uniqueness of martingale solutions to the equation (1.1). Full Article
ens High dimensional expanders and coset geometries. (arXiv:1710.05304v3 [math.CO] UPDATED) By arxiv.org Published On :: High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are abundant. In this work, we construct new families of bounded degree high dimensional expanders obeying the local spectral expansion property. This property has a number of important consequences, including geometric overlapping, fast mixing of high dimensional random walks, agreement testing and agreement expansion. Our construction also yields new families of expander graphs which are close to the Ramanujan bound, i.e., their spectral gap is close to optimal. The construction is quite elementary and it is presented in a self contained manner; This is in contrary to the highly involved previously known construction of the Ramanujan complexes. The construction is also very symmetric (such symmetry properties are not known for Ramanujan complexes) ; The symmetry of the construction could be used, for example, in order to obtain good symmetric LDPC codes that were previously based on Ramanujan graphs. The main tool that we use for is the theory of coset geometries. Coset geometries arose as a tool for studying finite simple groups. Here, we show that coset geometries arise in a very natural manner for groups of elementary matrices over any finitely generated algebra over a commutative unital ring. In other words, we show that such groups act simply transitively on the top dimensional face of a pure, partite, clique complex. Full Article
ens Surjective endomorphisms of projective surfaces -- the existence of infinitely many dense orbits. (arXiv:2005.03628v1 [math.AG]) By arxiv.org Published On :: Let $f colon X o X$ be a surjective endomorphism of a normal projective surface. When $operatorname{deg} f geq 2$, applying an (iteration of) $f$-equivariant minimal model program (EMMP), we determine the geometric structure of $X$. Using this, we extend the second author's result to singular surfaces to the extent that either $X$ has an $f$-invariant non-constant rational function, or $f$ has infinitely many Zariski-dense forward orbits; this result is also extended to Adelic topology (which is finer than Zariski topology). Full Article
ens Minimal acceleration for the multi-dimensional isentropic Euler equations. (arXiv:2005.03570v1 [math.AP]) By arxiv.org Published On :: Among all dissipative solutions of the multi-dimensional isentropic Euler equations there exists at least one that minimizes the acceleration, which implies that the solution is as close to being a weak solution as possible. The argument is based on a suitable selection procedure. Full Article
ens Phase Transitions for one-dimensional Lorenz-like expanding Maps. (arXiv:2005.03558v1 [math.DS]) By arxiv.org Published On :: Given an one-dimensional Lorenz-like expanding map we prove that the conditionlinebreak $P_{top}(phi,partial mathcal{P},ell)<P_{top}(phi,ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied for all continuous potentials $phi:[0,1]longrightarrow mathbb{R}$. We apply this to prove that quasi-H"older-continuous potentials (see, subsection 2.2 for definition) have at most one equilibrium measure and we construct a family of continuous but not H"older and neither weak H"older continuous potentials for which we observe phase transitions. Indeed, this class includes all H"older and weak-H"older continuous potentials and form an open and [2]. Full Article
ens On completion of unimodular rows over polynomial extension of finitely generated rings over $mathbb{Z}$. (arXiv:2005.03485v1 [math.AC]) By arxiv.org Published On :: In this article, we prove that if $R$ is a finitely generated ring over $mathbb{Z}$ of dimension $d, dgeq2, frac{1}{d!}in R$, then any unimodular row over $R[X]$ of length $d+1$ can be mapped to a factorial row by elementary transformations. Full Article
ens Solving equations in dense Sidon sets. (arXiv:2005.03484v1 [math.CO]) By arxiv.org Published On :: We offer an alternative proof of a result of Conlon, Fox, Sudakov and Zhao on solving translation-invariant linear equations in dense Sidon sets. Our proof generalises to equations in more than five variables and yields effective bounds. Full Article
ens A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz. (arXiv:2005.03377v1 [math.AP]) By arxiv.org Published On :: In this paper, we study the regularity criterion of weak solutions to the three-dimensional (3D) MHD equations. It is proved that the solution $(u,b)$ becomes regular provided that one velocity and one current density component of the solution satisfy% egin{equation} u_{3}in L^{frac{30alpha }{7alpha -45}}left( 0,T;L^{alpha ,infty }left( mathbb{R}^{3} ight) ight) ext{ with }frac{45}{7}% leq alpha leq infty , label{eq01} end{equation}% and egin{equation} j_{3}in L^{frac{2eta }{2eta -3}}left( 0,T;L^{eta ,infty }left( mathbb{R}^{3} ight) ight) ext{ with }frac{3}{2}leq eta leq infty , label{eq02} end{equation}% which generalize some known results. Full Article
ens Pointwise densities of homogeneous Cantor measure and critical values. (arXiv:2005.03269v1 [math.DS]) By arxiv.org Published On :: Let $Nge 2$ and $ hoin(0,1/N^2]$. The homogenous Cantor set $E$ is the self-similar set generated by the iterated function system [ left{f_i(x)= ho x+frac{i(1- ho)}{N-1}: i=0,1,ldots, N-1 ight}. ] Let $s=dim_H E$ be the Hausdorff dimension of $E$, and let $mu=mathcal H^s|_E$ be the $s$-dimensional Hausdorff measure restricted to $E$. In this paper we describe, for each $xin E$, the pointwise lower $s$-density $Theta_*^s(mu,x)$ and upper $s$-density $Theta^{*s}(mu, x)$ of $mu$ at $x$. This extends some early results of Feng et al. (2000). Furthermore, we determine two critical values $a_c$ and $b_c$ for the sets [ E_*(a)=left{xin E: Theta_*^s(mu, x)ge a ight}quad extrm{and}quad E^*(b)=left{xin E: Theta^{*s}(mu, x)le b ight} ] respectively, such that $dim_H E_*(a)>0$ if and only if $a<a_c$, and that $dim_H E^*(b)>0$ if and only if $b>b_c$. We emphasize that both values $a_c$ and $b_c$ are related to the Thue-Morse type sequences, and our strategy to find them relies on ideas from open dynamics and techniques from combinatorics on words. Full Article
ens On the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph. (arXiv:2005.03259v1 [math.CO]) By arxiv.org Published On :: In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $ngeq 3$ and there is no odd cycle without chord and length at least 5. Full Article
ens Cohomological dimension of ideals defining Veronese subrings. (arXiv:2005.03250v1 [math.AC]) By arxiv.org Published On :: Given a standard graded polynomial ring over a commutative Noetherian ring $A$, we prove that the cohomological dimension and the height of the ideals defining any of its Veronese subrings are equal. This result is due to Ogus when $A$ is a field of characteristic zero, and follows from a result of Peskine and Szpiro when $A$ is a field of positive characteristic; our result applies, for example, when $A$ is the ring of integers. Full Article
ens Generalized Cauchy-Kovalevskaya extension and plane wave decompositions in superspace. (arXiv:2005.03160v1 [math-ph]) By arxiv.org Published On :: The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the bi-axial Dirac operator. In the classical commuting case, this result can be written as a power series of Bessel type of certain differential operators acting on a single initial function. In the superspace setting, novel structures appear in the cases of negative even superdimensions. In these cases, the CK-extension depends on two initial functions on which two power series of differential operators act. These series are not only of Bessel type but they give rise to an additional structure in terms of Appell polynomials. This pattern also is present in the structure of the Pizzetti formula, which describes integration over the supersphere in terms of differential operators. We make this relation explicit by studying the decomposition of the generalized CK-extension into plane waves integrated over the supersphere. Moreover, these results are applied to obtain a decomposition of the Cauchy kernel in superspace into monogenic plane waves, which shall be useful for inverting the super Radon transform. Full Article
ens Hydrodynamic limit of Robinson-Schensted-Knuth algorithm. (arXiv:2005.03147v1 [math.CO]) By arxiv.org Published On :: We investigate the evolution in time of the position of a fixed number inthe insertion tableau when the Robinson-Schensted-Knuth algorithm is applied to asequence of random numbers. When the length of the sequence tends to infinity, a typical trajectory after scaling converges uniformly in probability to some deterministiccurve. Full Article
ens On the Brown-Peterson cohomology of $BPU_n$ in lower dimensions and the Thom map. (arXiv:2005.03107v1 [math.AT]) By arxiv.org Published On :: For an odd prime $p$, we determined the Brown-Peterson cohomology of $BPU_n$ in dimensions $-(2p-2)leq ileq 2p+2$, where $BPU_n$ is the classifying space of the projective unitary group $PU_n$. We construct a family of $p$-torsion classes $eta_{p,k}in BP^{2p^{k+1}+2}(BPU_n)$ for $p|n$ and $kgeq 0$ and identify their images under the Thom map with well understood cohomology classes in $H^*(BPU_n;mathbb{Z}_{(p)})$. Full Article