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per unit analyzer writes: According to Consumerist, an attorney has filed a classaction lawsuit charging Home Depot (PDF) and Menards (PDF) with deceptive advertising practices by selling "lumber products that were falsely advertised and labeled as having product dimensions that were not the actual dimensions of the products sold." Now granted, this may be news to the novice DIYer, but overall most folks who are purchasing lumber at home improvement stores know that the socalled trade sizes don't match the actual dimensions of the lumber. Do retailers need to educate naive consumers about every aspect of the items they sell? (Especially industry quirks such as this...) Furthermore, as the article notes, it's hard to see how the plaintiffs have been damaged when these building materials are compatible with the construction of the purchaser's existing buildings. i.e., An "actual" 2x4 would not fit in a wall previously built with standard 2x4s  selling the something as advertised woul
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Netflix announced that it's launching an allnew interactive format that turns viewers in storytellers, letting them dictate each choice and direction the story takes. "In each interactive title, you can make choices for the characters, shaping the story as you go," according to Netflix. "Each choice leads to a different adventure, so you can watch again and again, and see a new story each time." The Next Web reports: The first two interactive shows that will be available on Netflix are Puss in Book: Trapped in an Epic Tale and Buddy Thunderstruck: The Maybe Pile. Puss in Book launches globally today, with Buddy Thunderstruck slated to make its debut a month from now on July 14. The new experience will be available on most television setups and iOS devices. "Content creators have a desire to tell nonlinear stories like these, and Netflix provides the freedom to roam, try new things and do their best work," Product Innovation director Carla Fisher said. "The intertwining of our enginee
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An anonymous reader quotes a report from The Guardian: Scientists have worked out why suitcases tend to to rock violently from one wheel to the other until they overturn on the race through the airport. This most pressing of modern mysteries was taken on by physicists in Paris, who devised a scale model of a twowheeled suitcase rolling on a treadmill and backed up their observations with a pile of equations and references to holonomic restraints, finite perturbations and the morphing of bifurcation diagrams. Fortunately for nonphysicists, the findings can be reduced to simpler terms. For the suitcase to rock it had to hit a bump or be struck in some other manner; the faster the suitcase was being pulled, the more minor the bump needed to set it off. So far, so obvious. But Sylvain Courrech du Pont wanted to know more. Why did a rocking suitcase swerve and make such violent movements that it might eventually topple over? After more treadmill tests and more equations, the answer popped
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The European Space Agency has approved the Laser Interferometer Space Antenna mission designed to study gravitational waves in space. The spacecraft is slated for launch in in 2034. New Scientist reports: LISA will be made up of three identical satellites orbiting the sun in a triangle formation, each 2.5 million kilometers from the next. The sides of the triangle will be powerful lasers bounced to and fro between the spacecraft. As large objects like black holes move through space they cause gravitational waves, ripples which stretch and squeeze spacetime. The LISA satellites will detect how these waves warp space via tiny changes in the distance the laser beams travel. In order to detect these minuscule changes, on scales less than a trillionth of a meter, LISA will have to shrug off cosmic rays and the particles and light from the sun. The LISA Pathfinder mission, a solo probe launched in December 2015, proved that this sensitivity was possible and galvanized researchers working to
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Viewers of BBC's News at Ten were entranced last night when a glitch in its system produced over four minutes of surreal beauty. Two readers share a report: Huw Edwards was left sitting in silence for four minutes at the start of BBC News at Ten on Tuesday night after a technical fault delayed the start of the programme and bemused viewers. Viewers on some devices and channels were left watching the presenter sitting in silence as he waited for his cue to start. The BBC News Channel showed Edwards sitting mute for the entirety of the delay, while BBC1 put up a message apologising for the fault and played saxophone music. On BBC iPlayer an announcer apologised for the glitch and breaking news alerts also appeared during the delay. When the programme started at 22:04, Edwards apologised for what he described as a "few technical problems." The presenter said on Wednesday that nobody had told him he was on air until two minutes into the delay. However, Edwards told Radio 4's The Media Show
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Security updates have been issued by Arch Linux (lxterminal, lxterminalgtk3, openvpn, and pcmanfm), CentOS (thunderbird), Debian (jython, spip, tomcat7, and tomcat8), openSUSE (openvpn), Oracle (thunderbird), Slackware (openvpn), SUSE (openvpn), and Ubuntu (kernel, linuxltstrusty, nss, and valgrind).
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The class, denoted by $\mathscr{S}$, of totally disconnected locally compact groups which are nondiscrete, compactly generated, and topologically simple contains many compelling examples. In recent years, a general theory for these groups, which studies the interaction between the compact open subgroups and the global structure, has emerged. In this article, we study the nondiscrete totally disconnected locally compact groups $H$ that admit a continuous embedding with dense image into some $G\in \mathscr{S}$; that is, we consider the dense locally compact subgroups of groups $G\in \mathscr{S}$. We identify a class $\mathscr{R}$ of almost simple groups which properly contains $\mathscr{S}$ and is moreover stable under passing to a nondiscrete dense locally compact subgroup. We show that $\mathscr{R}$ enjoys many of the same properties previously obtained for $\mathscr{S}$ and establish various original results for $\mathscr{R}$ that are also new for the subclass $\mathscr{S}$, notabl
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In this paper, we introduce Durrmeyer type modification of MeyerKonigZeller operators based on (p,q)integers. Rate of convergence of these operators are explored with the help of Korovkin type theorems. We establish some direct results for proposed operators. We also obtain statistical approximation properties of operators. In last section, we show rate of convergence of (p,q)MeyerKonigZeller Durrmeyer operators for some functions by means of Matlab programming.
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Plane increasing trees are rooted labeled trees embedded into the plane such that the sequence of labels is increasing on any branch starting at the root. Relaxed binary trees are a subclass of unlabeled directed acyclic graphs. We construct a bijection between these two combinatorial objects and study the therefrom arising connections of certain parameters. Furthermore, we show central limit theorems for two statistics on leaves. We end the study by considering more than 20 subclasses and their bijective counterparts. Many of these subclasses are enumerated by known counting sequences, and thus enrich their combinatorial interpretation.
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Given a Borel measure $\mu$ on ${\mathbb R}^{n}$, we define a convex set by \[ M({\mu})=\bigcup_{\substack{0\le f\le1,\\ \int_{{\mathbb R}^{n}}f\,{\rm d}{\mu}=1 } }\left\{ \int_{{\mathbb R}^{n}}yf\left(y\right)\,{\rm d}{\mu}\left(y\right)\right\} , \] where the union is taken over all $\mu$measurable functions $f:{\mathbb R}^{n}\to\left[0,1\right]$ with $\int_{{\mathbb R}^{n}}f\,{\rm d}{\mu}=1$. We study the properties of these measuregenerated sets, and use them to investigate natural variations of problems of approximation of general convex bodies by polytopes with as few vertices as possible. In particular, we study an extension of the vertex index which was introduced by Bezdek and Litvak. As an application, we provide a lower bound for certain average norms of centroid bodies of nondegenerate probability measures.
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In our previous work we found sufficient conditions to be imposed on the parameters of the generalized hypergeometric function in order that it be completely monotonic or of Stieltjes class. In this paper we collect a number of consequences of these properties. In particular, we find new integral representations of the generalized hypergeometric functions, evaluate a number of integrals of their products, compute the jump and the average value of the the generalized hypergeometric function over the branch cut, establish new inequalities for this function in the half plane Re(z)<1. Furthermore, we discuss integral representations of absolutely monotonic functions and present a curious formula for a finite sum of products of gamma ratios as an integral of Meijer's G function.
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Hartshorne in "Ample vector bundles" proved that $E$ is ample if and only if $\OOO_{P(E)}(1)$ is ample. Here we generalize this result to flag manifolds associated to a vector bundle $E$ on a complex manifold $X$: For a partition $a$ we show that the line bundle $\it Q_a^s$ on the corresponding flag manifold $\mathcal{F}l_s(E)$ is ample if and only if $ \SSS_aE $ is ample. In particular $\det Q$ on $\it{G}_r(E)$ is ample if and only if $\wedge ^rE$ is ample.\\ We give also a proof of the Ampleness Dominance theorem that does not depend on the saturation property of the LittlewoodRichardson semigroup.
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In the semidiscrete version of Monge's problem one tries to find a transport map $T$ with minimum cost from an absolutely continuous measure $\mu$ on $\mathbb{R}^d$ to a discrete measure $\nu$ that is supported on a finite set in $\mathbb{R}^d$. The problem is considered for the case of the Euclidean cost function. Existence and uniqueness is shown by an explicit construction which yields a onetoone mapping between the optimal $T$ and an additively weighted Voronoi partition of $\mathbb{R}^d$. From the proof an algorithm is derived to compute this partition.
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We study the onedimensional nonlinear KleinGordon (NLKG) equation with a convolution potential, and we prove that solutions with small analytic norm remain small for exponentially long times. The result is uniform with respect to $c \geq 1$, which however has to belong to a set of large measure.
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Delay and Disruption Tolerant Networks (DTNs) may lack continuous network connectivity. Routing in DTNs is thus a challenge since it must handle network partitioning, long delays, and dynamic topology. Meanwhile, routing protocols of the traditional Mobile Ad hoc NETworks (MANETs) cannot work well due to the failure of its assumption that most network connections are available. In this article, a geographic routing protocol is proposed for MANETs in delay tolerant situations, by using no more than onehop information. A utility function is designed for implementing the undercontrolled replication strategy. To reduce the overheads caused by message flooding, we employ a criterion so as to evaluate the degree of message redundancy. Consequently a message redundancy coping mechanism is added to our routing protocol. Extensive simulations have been conducted and the results show that when node moving speed is relatively low, our routing protocol outperforms the other schemes such as Epide
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Optimal channel allocation is a key performance engineering aspect in singlecarrier frequencydivision multiple access (SCFDMA). It is of significance to consider minimum sum power (MinPower), subject to meeting specified user's demand, since mobile users typically employ batterypowered handsets. In this paper, we prove that MinPower is polynomialtime solvable for interleaved SCFDMA (IFDMA). Then we propose a channel allocation algorithm for IFDMA, which is guaranteed to achieve global optimum in polynomial time. We numerically compare the proposed algorithm with optimal localized SCFDMA (LFDMA) for MinPower. The results show that LFDMA outperforms IFDMA in the maximal supported user demand. When the user demand can be satisfied in both LFDMA and IFDMA, LFDMA performs slightly better than IFDMA. However Min Power is polynomialtime solvable for IFDMA whereas it is not for LFDMA.
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This paper is concerned with the analysis of a new stable spacetime finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on the FEM space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the FEM spaces yields an a priori discretization error estimate with respect to the discrete norm. Finally, we confirm the theoretical results with numerical experiments in spatial moving domains to confirm the theory presented.
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We relate the operad FMan controlling the algebraic structure on the tangent sheaf of an $F$manifold (weak Frobenius manifold) defined by Hertling and Manin to the operad PreLie of preLie algebras: for the filtration of PreLie by powers of the ideal generated by the Lie bracket, the associated graded object is FMan.
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We consider a spherically symmetric stellar model in general relativity whose interior consists of a pressureless fluid undergoing microscopic velocity diffusion in a cosmological scalar field. We show that the diffusion dynamics compel the interior to be spatially homogeneous, by which one can infer immediately that within our model, and in contrast to the diffusionfree case, no naked singularities can form in the gravitational collapse. We then study the problem of matching an exterior Bondi type metric to the surface of the star and find that the exterior can be chosen to be a modified Vaidya metric with variable cosmological constant. Finally, we study in detail the causal structure of an explicit, selfsimilar solution.
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Given two finite sequences of positive integers $\alpha$ and $\beta$, we associate a square free monomial ideal $I_{\alpha,\beta}$ in a ring of polynomials $S$, and we recursively compute the algebraic invariants of $S/I_{\alpha,\beta}$. Also, we give precise formulas in special cases.
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Let $\bar{X}$ be a smooth quasiprojective $d$dimensional variety over a field $k$ and let $D$ be an effective Cartier divisor on it. In this note, we construct cycle class maps from (a variant of) the higher Chow group with modulus of the pair $(\bar{X},D)$ in the range $(d+n, n)$ to the relative $K$groups $K_n(\bar{X}, D)$ for every $n\geq 0$.
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In this paper, we give a nonexistence result on certain Drinfeld modules over global function fields. This is applied to prove special cases of a function field analogue of a conjecture of Rasmussen and Tamagawa related with nonexistence of certain abelian varieties over number fields.
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Let $G$ be a simple graph with $n\geq4$ vertices and $d(x)+d(y)\geq n+k$ for each edge $xy\in E(G)$. In this work we prove that $G$ either contains a spanning closed trail containing any given edge set $X$ if $X\leq k$, or $G$ is a well characterized graph. As a corollary, we show that line graphs of such graphs are $k$hamiltonian.
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In this paper we deal with the following fractional Kirchhoff equation \begin{equation*} \left(p+q(1s) \iint_{\mathbb{R}^{2N}} \frac{u(x) u(y)^{2}}{xy^{N+2s}} \, dx\,dy \right)(\Delta)^{s}u = g(u) \mbox{ in } \mathbb{R}^{N}, \end{equation*} where $s\in (0,1)$, $N\geq 2$, $p>0$, $q$ is a small positive parameter and $g: \mathbb{R}\rightarrow \mathbb{R}$ is an odd function satisfying BerestyckiLions type assumptions. By using minimax arguments, we establish a multiplicity result for the above equation, provided that $q$ is sufficiently small.
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Recently \cite{AsimitFurmanVernic:2016} used EM algorithm to estimate singular MarshallOlkin bivariate Pareto distribution. We describe \textbf{absolutely continuous} version of this distribution. We study estimation of the parameters by EM algorithm both in presence and without presence of location and scale parameters. Some innovative solutions are provided for different problems arised during implementation of EM algorithm. A reallife data analysis is also shown for illustrative purpose.
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An antimagic labeling of a directed graph $D$ with $n$ vertices and $m$ arcs is a bijection from the set of arcs of $D$ to the integers $\{1, \cdots, m\}$ such that all $n$ oriented vertex sums are pairwise distinct, where an oriented vertex sum is the sum of labels of all arcs entering that vertex minus the sum of labels of all arcs leaving it. An undirected graph $G$ is said to have an antimagic orientation if $G$ has an orientation which admits an antimagic labeling. Hefetz, M{\"{u}}tze, and Schwartz conjectured that every connected undirected graph admits an antimagic orientation. In this paper, we support this conjecture by proving that every biregular bipartite graph admits an antimagic orientation.
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An anonymous reader quotes a report from The Verge: In 2014, Tumblr was on the front lines of the battle for net neutrality. The company stood alongside Amazon, Kickstarter, Etsy, Vimeo, Reddit, and Netflix during Battle for the Net's day of action. Tumblr CEO David Karp was also part of a group of New York tech CEOs that met with thenFCC chairman Tom Wheeler in Brooklyn that summer, while the FCC was fielding public comment on new Title II rules. President Obama invited Karp to the White House to discuss various issues around public education, and in February 2015 The Wall Street Journal reported that it was the influence of Karp and a small group of liberal tech CEOs that swayed Obama toward a philosophy of internet as public utility. But three years later, as the battle for net neutrality heats up once again, Tumblr has been uncharacteristically silent. The last mention of net neutrality on Tumblr's staff blog  which frequently posts about political issues from civil rights to cl
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We consider the Cauchy problem in R^n for some types of damped wave equations. We derive asymptotic profiles of solutions with weighted L^{1,1}(R^n) initial data by employing a simple method introduced by the first author. The obtained results will include regularity loss type estimates, which are essentially new in this kind of equations.
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Kara Swisher, writing for Recode: It was Lao Tzu who said that "the journey of a thousand miles begins with a single step." In the case of complete and utter change reeling through Uber right now  culminating in the resignation of its once untouchable CEO Travis Kalanick  it turns out that it began with one of the most epic blog posts to be written about what happens when a hot company becomes hostage to its increasingly dysfunctional and toxic behaviors. It was clear from the moment you read the 3,000word post by former engineer Susan Fowler about her time at the carhailing company that nothing was going to be the same. Titled simply, "Reflecting on one very, very strange year at Uber," the essay deftly and surgically laid out the map that the media and others would use to prove to its outtolunch board and waffling investors that Uber CEO Travis Kalanick had to go. In her account, Fowler was neither mean nor selfrighteous, although in reading the story that she laid out about
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A crossdiffusion system describing ion transport through biological membranes or nanopores in a bounded domain with mixed DirichletNeumann boundary conditions is analyzed. The ion concentrations solve strongly coupled diffusion equations with a drift term involving the electric potential which is coupled to the concentrations through a Poisson equation. The globalintime existence of bounded weak solutions and the uniqueness of weak solutions under moderate regularity assumptions are shown. The main difficulties of the analysis are the crossdiffusion terms and the degeneracy of the diffusion matrix, preventing the use of standard tools. The proofs are based on the boundednessbyentropy method, extended to nonhomogeneous boundary conditions, and the uniqueness technique of Gajewski. A finitevolume discretization in one space dimension illustrates the largetime behavior of the numerical solutions and shows that the equilibration rates may be very small.
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In this paper, we first prove the equivalence between the $(K, \infty)$super Perelman Ricci flows and two families of logarithmic Sobolev inequalities, Poincar\'e inequalities and a gradient estimate of the heat semigroup generated by the Witten Laplacian on manifolds equipped with time dependent metrics and potentials. As a byproduct, we derive the Hamilton Harnack inequality for the heat semigroup of the time dependent Witten Laplacian on manifolds equipped with a $(K, \infty)$super Perelman Ricci flow. Based on a new second order time derivative formula on the BoltzmannShannon entropy for the heat equation of the Witten Laplacian, we introduce the $W_K$entropy and prove its monotonicity for the heat equation of the Witten Laplacian on complete Riemannian manifolds satisfying $CD(K, \infty)$condition and on compact manifolds equipped with a $(K, \infty)$super Perelman Ricci flow. Our results characterize the $(K, \infty)$Ricci solitons and the $(K, \infty)$Perelman Ricci flow
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