WASHINGTON, D.C., March 30, 2020 — As longstanding organizations representing and supporting those on the front lines who are risking their lives caring for the world’s most vulnerable patients, we stand united in voicing our concern over the ...

WASHINGTON, D.C., April 1, 2020 – 28 patient and consumer groups representing millions of people nationwide with pre-existing health conditions issued the following statement regarding the administration’s decision not to initiate a special enrollment...

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...

Today, the U.S. Environmental Protection Agency (EPA) announced a final rule that threatens to undermine the Mercury and Air Toxics Standards. The American Lung Association, Allergy & Asthma Network, Alliance of Nurses for Healthy Environments, American...

What would happen if the logos of famous brands suddenly wake up in the bed of another? Thats what the new tumblr blog Logo Mashups explores. It makes us think in the in the connections they share and how they are constantly appealing to our consumer mind through the commons grounds of symbology and typography.

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.

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.

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

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

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

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 $2$.

Motivated by quotient algorithms, such as the well-known $p$-quotient or solvable quotient algorithms, we describe how to compute extensions $ ilde H$ of a finite group $H$ by a direct sum of isomorphic simple $mathbb{Z}_p H$-modules such that $H$ and $ ilde H$ have the same number of generators. Similar to other quotient algorithms, our description will be via a suitable covering group of $H$. Defining this covering group requires a study of the representation module, as introduced by Gasch"utz in 1954. Our investigation involves so-called Fox derivatives (coming from free differential calculus) and, as a by-product, we prove that these can be naturally described via a wreath product construction. An important application of our results is that they can be used to compute, for a given epimorphism $G o H$ and simple $mathbb{Z}_p H$-module $V$, the largest quotient of $G$ that maps onto $H$ with kernel isomorphic to a direct sum of copies of $V$. For this we also provide a description of how to compute second cohomology groups for the (not necessarily solvable) group $H$, assuming a confluent rewriting system for $H$. To represent the corresponding group extensions on the computer, we introduce a new hybrid format that combines this rewriting system with the polycyclic presentation of the module.

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 $mathrm{GL}(V)$.

Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$, a conjecture of Amit states that $N_w(1) ge |G|^{k-1}$, where $N_w(1)$ is the number of $k$-tuples $(g_1,...,g_k)in G^{(k)}$ such that $w(g_1,...,g_k)=1$. Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit's conjecture, and prove that $N_w(g) ge |G|^{k-2}$, where $g$ is a $w$-value in $G$, for finite groups $G$ of odd order and nilpotency class 2. If $w$ is a word in two variables, we further show that $N_w(g) ge |G|$, where $g$ is a $w$-value in $G$ for finite groups $G$ of nilpotency class 2. In addition, for $p$ a prime, we show that finite $p$-groups $G$, with two distinct irreducible complex character degrees, satisfy the generalized Amit conjecture for words $w_k =[x_1,y_1]...[x_k,y_k]$ with $k$ a natural number; that is, for $g$ a $w_k$-value in $G$ we have $N_{w_k}(g) ge |G|^{2k-1}$.

Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.

In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein's homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous groups. In this environment, the theory of Hardy type inequalities becomes intricately intertwined with the properties of sub-Laplacians and more general subelliptic partial differential equations. Particularly, we discuss the Badiale-Tarantello conjecture and a conjecture on the geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant.

Let the group $G = AB$ be the product of subgroups $A$ and $B$, and let $p$ be a prime. We prove that $p$ does not divide the conjugacy class size (index) of each $p$-regular element of prime power order $xin Acup B$ if and only if $G$ is $p$-decomposable, i.e. $G=O_p(G) imes O_{p'}(G)$.

We introduce a notion of c-group, which is a group up to congruence relation and consider the corresponding category. Extensions, actions and crossed modules (c-crossed modules) are defined in this category and the semi-direct product is constructed. We prove that each categorical group gives rise to c-groups and to a c-crossed module, which is a connected, special and strict c-crossed module in the sense defined by us. The results obtained here will be applied in the proof of an equivalence of the categories of categorical groups and connected, special and strict c-crossed modules.

We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ a quadratic extension of p-adic fields the associated unitary group $G=mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with Levi component $L$ isomorphic to $mathrm{GL}_n(E)$. Let $pi$ be an irreducible supercuspidal representation of $L$ of depth zero. We use Hecke algebra methods to determine when the parabolically induced representation $iota_P^G pi$ is reducible.

The congruence subgroup problem for a finitely generated group $Gamma$ and $Gleq Aut(Gamma)$ asks whether the map $hat{G} o Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(G,Gamma ight)$? Here $hat{X}$ denotes the profinite completion of $X$. In the case $G=Aut(Gamma)$ we denote $Cleft(Gamma ight)=Cleft(Aut(Gamma),Gamma ight)$.

Let $Gamma$ be a finitely generated group, $ar{Gamma}=Gamma/[Gamma,Gamma]$, and $Gamma^{*}=ar{Gamma}/tor(ar{Gamma})congmathbb{Z}^{(d)}$. Denote $Aut^{*}(Gamma)= extrm{Im}(Aut(Gamma) o Aut(Gamma^{*}))leq GL_{d}(mathbb{Z})$. In this paper we show that when $Gamma$ is nilpotent, there is a canonical isomorphism $Cleft(Gamma ight)simeq C(Aut^{*}(Gamma),Gamma^{*})$. In other words, $Cleft(Gamma ight)$ is completely determined by the solution to the classical congruence subgroup problem for the arithmetic group $Aut^{*}(Gamma)$.

In particular, in the case where $Gamma=Psi_{n,c}$ is a finitely generated free nilpotent group of class $c$ on $n$ elements, we get that $C(Psi_{n,c})=C(mathbb{Z}^{(n)})={e}$ whenever $ngeq3$, and $C(Psi_{2,c})=C(mathbb{Z}^{(2)})=hat{F}_{omega}$ = the free profinite group on countable number of generators.

In this paper, we give new constructions of strongly regular Cayley graphs on abelian groups as generalizations of a series of known constructions: the construction of covering extended building sets in finite fields by Xia (1992), the product construction of Menon-Hadamard difference sets by Turyn (1984), and the construction of Paley type partial difference sets by Polhill (2010). Then, we obtain new large families of strongly regular Cayley graphs of Latin square type or negative Latin square type.

A coalition of immigrant-focused organizations has created the Spokane Relief Fund for Undocumented Immigrants, in order to help families who are unable to access federal aid during the coronavirus shutdowns. The partners sponsoring the work include the Spokane Immigrant Rights Coalition (SIRC), the Hispanic Business and Professional Association, Latinos en Spokane, Mujeres in Action and Raiz.…

Polysubstituted cyclopentadiene compound wherein at least two different substituents are present from the group consisting of linear, branched and cyclic alkyls, aralkyls and alkenyls, and a process for the preparation of a cyclopentadiene compound substituted with at least two different groups chosen from the group consisting of linear, branched, cyclic and aromatic alkyls and alkenyls, characterized in that it comprises the reacting of a halide of a first substituting group in a mixture of the cyclopentadiene compound and an aqueous solution of a base, in which the quantity of the base relative to the cyclopentadiene compound is between 5 and 30 mol/mol, in the presence of a phase transfer catalyst, followed by the addition of a halide of a second or optionally a third substituting group to the reaction mixture.

The present invention is directed towards microcapsules, uses and methods of microencapsulation with improved properties regarding agglomeration, bleeding and control of the reaction. The invention is especially suitable for chemical compounds with at least one carboxamide group, preferably for microencapsulation of those compounds wherein the carbonyl group is attached to a nitrogen atom or nitrogenated heterocycle and wherein the microencapsulation reaction may be too vigorous. The microcapsules are characterized by a mixed glycoluril-polyurea polymer wall, wherein the polyurea groups come from a urea-formaldehyde resin and not from isocyanate monomers or prepolymers. The process of making such microcapsules a dispersant in the oil phase of the type of block copolymer of vinylpyrrolidone/vinylalkene and/or vinylpyrrolidone/vinyl acetate and the microencapsulation reaction may be carried out without the presence of any polyamine/polyol acting as a catalyst.

The invention relates to indolesulfonyl halogenides which are useful for the protection of organic compounds comprising at least one guanidino moiety and/or at least one amino group. The invention further relates to a process for their preparation and their use as protecting reagents. The invention also relates to the process for the protecting reaction and to the protected compounds thereof.

The present application relates to novel monomers comprising polycarbosiloxane monomers useful in certain specific embodiments in the manufacture of devices. More particularly, the present application relates to certain ethylenically unsaturated free radical polymerizable monomers comprising polycarbosiloxane monomers. Even more particularly, the present application pertains to monomers comprising polycarbosiloxane monomers which further comprise at least two ethylenically unsaturated free radical polymerizable groups.

An ion conducting membrane for fuel cells involves coupling a compound having a sulfonic acid group with a polymeric backbone. Each of the compounds having a sulfonic acid group and the polymeric backbone are first functionalized with a halogen.

An improved polymerization and process method allows the production of special nitrile rubbers which are characterized by a specific anion content and an excellent storage stability and allow a particularly good vulcanization rate and moreover result in vulcanized materials that have advantageous properties, especially with regard to the contact with metal components of molded parts based on said vulcanized materials.

A method by which a halogen atom of a halogen compound can be efficiently replaced with an electrophilic group. Also provided are: a reagent for converting a functional group through a halogen-metal exchange reaction, characterized by comprising either a mixture of a magnesium compound represented by the formula R1—Mg—X (I) (wherein R1 represents a halogen atom or an optionally substituted hydrocarbon residue; and X1 represents a halogen atom) and an organolithium compound represented by the formula R2—Li (II)(wherein R2 represents an optionally substituted hydrocarbon residue) or a product of the reaction of the magnesium compound with the organolithium compound; and a process for producing with the reagent a compound in which a halogen atom of a halogen compound has been replaced with an electrophilic group.

A water heater system comprises a water tank, a burner plenum, a flue, a blower, a combustion air passageway, a dilution air passageway, an upstream manifold, and a downstream manifold. The upstream manifold divides air from the blower so that some air flows through the combustion air passageway to the burner plenum and some air flows through the dilution air passageway to the downstream manifold. The downstream manifold combines the air from the dilution air passageway with combustion products from the flue.

Includes a low flow-rate region (R2) that is disposed on an upstream side of a combustion region (R1) within a second pipe (2), and that has a relatively slow flow-rate of combustion gas (G1) within the second pipe, and a flame kernel formation unit (3a) is disposed in the low flow-rate region.

A boot accessory for limiting how far a user can push his/her boot into a stirrup comprises an arch for hugging a front edge of the boot; a first hook disposed on the first end of the arch and a second hook disposed on the second end of the arch. The first hook curves outwardly from the first end of the arch and further a first end of the first hook curves back toward the front edge of the boot. The second hook curves outwardly from the second end of the arch and further a first end of the second hook curves back toward the front edge of the boot. A gap exists between the first end of the first hook and the arch and between the first end of the second hook and the arch, wherein the gaps are for engaging sides of the stirrup.

An improved organic photoconductor drum having a protective overcoat layer and method to make the same is provided. The protective overcoat layer is prepared from a curable composition including a crosslinkable hole transport molecule containing four radical polymerizable functional groups in combination with a crosslinkable acrylate having at least 6 functional groups.

A method of detecting a cancer progression observation index gene group, comprising: a) preparing a plurality of AKR/J mice in which an oncogene is inserted into a thymocyte; b) dividing the AKR/J mice into three groups, raising the first group of the AKR/J mice after high-dose ionizing radiation of 0.8 Gy/min, raising the second group of the AKR/J mice after low-dose ionizing radiation of 0.7 mGy/hr, and raising the third group of the AKR/J mice in a general environment; c) obtaining a thymus of a dead mouse of the first or second group of the AKR/J mice throughout the b) operation and diagnosing cancer when a weight of the thymus is increased to twice or more than before radiation; d) extracting thymuses by sacrificing the first to third groups of the AKR/J mice at the time at which the third group of the AKR/J mice initially die; and e) selecting only a thymus having no change in weight compared to the organs of the same-aged non-irradiated AKR/J mice from the organs extracted in d) and detecting a gene of the organ whose weight is increased or decreased by a factor of two or more through gene analysis.

The sequel to Disney Family Singalong will be aired on Mother's Day with Jennifer Hudson and John Legend set to deliver their version of the 'Beauty and the Beast' theme.

The valet's positive diagnosis sparks fear of COVID-19 spread in the West Wing, but the White House assures that the president and Vice President Mike Pence 'have since tested negative for the virus.'

Funding available to help local residents.

Birmingham St Mary’s Hospice has unveiled its latest venture aimed at supporting the services on which so many rely.

Joint Lib Dem and Conservative call for demolition plans to be scrapped.

West Midlands charities receive donations from Mondelēz International.

In April, Zomato initiated a voluntary salary reduction programme, which also offers affected employees’ additional stock in lieu of the cash cut from their pay cheques.

Green Visor Capital backed-Simpl, that allows users to buy now and checkout with pay-later function, said the surge in the number of transactions done for daily essentials increased despite supply and workforce issues by merchant partners.

“For incubators, we want to look at India as the first starting point,” said Manish Agarwal, CEO of Reliance Entertainment.

The mobile app development companies as well as independent developers are leveraging this to pitch their apps into the market.

Corgi Con is a semi-annual celebration of short, sausage-shaped dogs called Corgis. Hundreds of dogs and their families descend on Ocean Beach for a day of events and festivities.

Updated at 11:35 a.m. ET on Saturday A pair of armed robbers and two others, including the driver of a hijacked UPS truck, were killed in an exchange of gunfire with South Florida police officers after the suspects led authorities on a high-speed chase. The robbers held up a jewelry store on Thursday before commandeering the UPS truck and holding its driver hostage, according to Coral Gables Police . After fleeing the scene and evading police for dozens of miles, the truck stopped in the middle of rush-hour traffic as armed officers surrounded it. "There was exchanged fire between law enforcement and the suspects, and unfortunately, the suspects are now deceased," George Piro, the special agent in charge of the FBI's Miami office, said . "But two additional innocent civilians were also deceased." Former Department of Housing and Urban Development official Brandon Friedman described the shootout as "appalling." He said the police department should be held accountable for "choosing to

Wein erweist sich in Corona-Zeiten als krisenfest. Davon profitieren vor allem Gründer und ihre Internetshops. Dabei halten typische Käufer eigentlich nicht viel vom Online-Shopping. Das könnte sich nun ändern.

There is an observation in psychology that looks at how people behave when they have not lived up to the expectations they set for themselves; The What The Hell Effect. In this episode of Two Guys on Your Head, Dr. Art Markman, and Dr. Bob Duke discussion about TWTHE and how it relates to identity,...

The coronavirus-shutdown crisis has ripped through Seattle’s arts and culture scene, guillotining income for individual artists and organizations while they scramble to cut expenses.