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It is well-known that a celebrated J"{o}rgens-Calabi-Pogorelov theorem for Monge-Amp`ere equations states that any classical (viscosity) convex solution of $det(D^2u)=1$ in $mathbb{R}^n$ must be a quadratic polynomial. Therefore, it is an interesting topic to study the existence and uniqueness theorem of such fully nonlinear partial differential equations' Dirichlet problems on exterior domains with suitable asymptotic conditions at infinity. As a continuation of the works of Caffarelli-Li for Monge-Amp`ere equation and of Bao-Li-Li for $k$-Hessian equations, this paper is devoted to the solvability of the exterior Dirichlet problem of Hessian quotient equations $sigma_k(lambda(D^2u))/sigma_l(lambda(D^2u))=1$ for any $1leq l<kleq n$ in all dimensions $ngeq 2$. By introducing the concept of generalized symmetric subsolutions and then using the Perron's method, we establish the existence theorem for viscosity solutions, with prescribed asymptotic behavior which is close to some quadratic polynomial at infinity.

Miller and Sheffield introduced a notion of an imaginary surface as an equivalence class of pairs of simply connected proper subdomains of $mathbb{C}$ and Gaussian free fields (GFFs) on them under conformal equivalence. They considered the situation in which the conformal transformations are given by a chordal Schramm--Loewner evolution (SLE). In the present paper, we construct processes of GFF on $mathbb{H}$ (the upper half-plane) and $mathbb{O}$ (the first orthant of $mathbb{C}$) by coupling zero-boundary GFFs on these domains with stochastic log-gases defined on parts of boundaries of the domains, $mathbb{R}$ and $mathbb{R}_+$, called the Dyson model and the Bru--Wishart process, respectively, using multiple SLEs evolving in time. We prove that the obtained processes of GFF are stationary. The stationarity defines an equivalence relation between GFFs, and the pairs of time-evolutionary domains and stationary processes of GFF will be regarded as generalizations of the imaginary surfaces studied by Miller and Sheffield.

We introduce a Gaussian measure formally preserved by the 2-dimensional Primitive Equations driven by additive Gaussian noise. Under such measure the stochastic equations under consideration are singular: we propose a solution theory based on the techniques developed by Gubinelli and Jara in cite{GuJa13} for a hyperviscous version of the equations.

We give an efficient algorithm for robustly clustering of a mixture of two arbitrary Gaussians, a central open problem in the theory of computationally efficient robust estimation, assuming only that the the means of the component Gaussians are well-separated or their covariances are well-separated. Our algorithm and analysis extend naturally to robustly clustering mixtures of well-separated strongly logconcave distributions. The mean separation required is close to the smallest possible to guarantee that most of the measure of each component can be separated by some hyperplane (for covariances, it is the same condition in the second degree polynomial kernel). We also show that for Gaussian mixtures, separation in total variation distance suffices to achieve robust clustering. Our main tools are a new identifiability criterion based on isotropic position and the Fisher discriminant, and a corresponding Sum-of-Squares convex programming relaxation, of fixed degree.

We utilize recent results on the exact block error probability of Gaussian random codes in additive white Gaussian noise to analyze Gaussian random coding for massive multiple-access at finite message length. Soft iterative interference cancellation is found to closely approach the performance bounds recently found in [1]. The existence of two fundamentally different regimes in the trade-off between power and bandwidth efficiency reported in [2] is related to much older results in [3] on power optimization by linear programming. Furthermore, we tighten the achievability bounds of [1] in the low power regime and show that orthogonal constellations are very close to the theoretical limits for message lengths around 100 and above.

We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how replica symmetry in the strong sense of concentration of all multioverlaps can be established as a consequence of the Franz-de Sanctis identities; the identities themselves in the current setting are obtained via a novel perturbation of the prior distribution of the signal. Concentration of multioverlaps means that asymptotically the posterior distribution has a particularly simple structure encoded by a random probability measure (or, in the case of binary signal, a non-random probability measure). We believe that such strong control of the model should be key in the study of inference problems with underlying sparse graphical structure (error correcting codes, block models, etc) and, in particular, in the derivation of replica symmetric formulas for the free energy and mutual information in this context.

A method and apparatus for euthanizing poultry by rapidly impacting the spinal column of the bird.

The present invention relates to a process of synthesis of α-sialyl oligosaccharides and in particular of 6'-sialyllactose and its salts comprising a step of coupling by Koenigs-Knorr reaction under conditions that allow its use on an industrial scale.

The invention relates to an optical resonator, laser apparatus and a method of generating a laser beam inside an optical resonator. The optical resonator (100) includes an optical cavity (102) and an optical element (104.1, 104.2) at either end thereof, operable to sustain a light beam (108) therein, characterized in that each optical element (104.1, 104.2) is a phase-only optical element operable to alter a mode of the beam (108) as it propagates along the length of the optical resonator (100), such that in use the beam (108) at one end of the optical resonator (100) has a Gaussian profile while the beam (108) at the other end of the optical resonator (100) has a non-Gaussian profile.

[Problem to be Solved] The importance of sugar chains having α2,3- or α2,6-linked sialic acid at their non-reducing ends is known. Industrial production has been demanded for these sugar chain compounds. Particularly, the production of glycoprotein drugs or the like inevitably requires producing in quantity sugar chains having homogeneous structures by controlling the linking pattern (α2,6-linkage or α2,3-linkage) of sialic acid. Particularly, a triantennary or tetraantennary N-type complex sugar chain having sialic acid at each of all non-reducing ends is generally considered difficult to chemically synthesize. There has been no report disclosing that such a sugar chain was chemically synthesized. Furthermore, these sugar chains are also difficult to efficiently prepare enzymatically.[Solution]The present inventors have newly found the activity of sialyltransferase of degrading sialic acid on a reaction product in the presence of CMP and also found that formed CMP can be degraded enzymatically to thereby efficiently produce a sialic acid-containing sugar chain. The present inventors have further found that even a tetraantennary N-type sugar chain having four α2,6-linked sialic acid molecules, which has previously been difficult to synthesize, can be prepared at high yields by one-pot synthesis comprising the elongation reaction of a biantennary sugar chain used as a starting material without performing purification after each enzymatic reaction.

An anesthesia workstation includes a sliding track system attached to the front of the anesthesia workstation for the mounting of one or more displays. The displays are horizontally slidable along the front of the anesthesia workstation along the sliding track. In addition, the sliding track system includes pivot points which enable outward pivoting of the displays up to 90 degrees. Sliding and pivoting of the displays is possible both independently and simultaneously. The sliding track system allows the anesthetist to slide and pivot the displays across the front of the workstation along the length of the track to the most preferable viewing position. Additional storage space is positioned within the anesthesia workstation behind the displays and becomes exposed and accessible when the displays are manipulated via the sliding track system.

Models, kits and methods useful in the demonstration of sialendoscopy devices and techniques are described. An exemplary demonstration apparatus comprises a support structure, an insert structure contacting the support structure, and a duct structure contacting the insert structure. The insert structure has a top surface defining a first opening and a bottom surface defining a second opening, and defines a channel with a first end in communication with the first opening and a second end in communication with the second opening. The duct structure comprises an elongate tubular member and has a first end in fluid communication with the first opening of the insert member, a second end, and defines a lumen extending from the first end to the second end. A portion of the duct structure is releasably disposed within the channel defined by the insert structure.

A method and a control program for operating an anesthesia apparatus, as well as an anesthesia apparatus (12), which operates according to the method are provided. The anesthesia apparatus includes a breathing gas feed unit (22) intended for displacing a breathing gas volume in a breathing circuit (10). A piston (23) brings about the displacement of the breathing gas. Switching over between a first mode of operation and a second mode of operation during the return of the piston (23) allows for a presetting of a corresponding piston return velocity. The piston return velocity depends on a volume flow in an exhalation branch (34) of the breathing circuit (10) in the first mode of operation. The piston return velocity depends on a minimally necessary piston return velocity in the second mode of operation.

An antenna array includes a plurality of patch antennas including a plurality of layers. Each of the plurality of layers are separated by a distance and each support a portion of the plurality of patch antennas. A plurality of connectors are each associated with one of the plurality of layers and supply a signal for transmission by the associated layer. A feed network on each of the plurality of layers provides a connection between a connector associated with the layer and the portion of the patch antennas located on the layer. Each layer transmits a signal having a different orthogonal function applied thereto that multiplexes each of the signals having a different orthogonal function applied thereto onto a single transmission beam. A parabolic reflector reflects the single transmission beam from the plurality of layers of the antenna array.

This month alone, Oakland-based, family-owned Mr. Espresso has already donated more than 2,500 pounds of coffee to Bay Area COVID-19 relief efforts.

BHANGRA dancers provided the entertainment for hundreds of people looking to get inspiration for their forthcoming wedding at a Southampton hotel.

LEISURE bosses are today bracing themselves to make the next step towards the development of a huge, multi-million-pound, Las Vegas-style casino planned for Southampton.

Release date : TBA 2020
Synopsis : The film follows Vietnam veterans who return to the jungle to find their lost innocence. Searching for the remains of ...

'The Hangover' star Ed Helms, in the meantime, is on board as an executive producer for the planned project that will chronicle the rise and fall of the former Mayor of Toronto.

The 'I the Heights' helmer is disgusted by the casting scam for the sequels of the 2018 hit film, calling it a 'direct attack' to Asian American actors pursuing 'this dream that they never thought was possible before.'

Sister Jamie Lynn Spears reveals in a new interview that the 'Toxic' singer has to return to her own Los Angeles home because of 'her children and all that stuff.'

Back in 2004, the 'Iron Man' actress generated a pop culture phenomenon when she and then-husband Chris Martin shared with the world the name they chose for their daughter.

Back in 2004, the 'Iron Man' actress generated a pop culture phenomenon when she and then-husband Chris Martin shared with the world the name they chose for their daughter.

Gabriel Iglesias, a stand up comedian with multiple Netflix and Comedy Central specials, actor seen in "Magic Mike" and on his own Netflix show, "Mr. Iglesias,"  joins Joey Diaz and Lee Syatt live in studio.

Festival marks thirtieth birthday of community group.

Sonic Sirius has announced availability of the Abc Soundset, a collection of 128 presets for the Messiah by Memory Moon, a software synthesizer inspired by the Prophet-5 polyphonic analog synth by Sequential Circuits. The soundset is suitable for Synth-Pop, New Wave, Electro, and other modern synth music. It includes arpeggios, bass, keys, leads, pads, and […]

The post Sonic Sirius releases free Abc Soundset for Memory Moon Messiah appeared first on rekkerd.org.

Kansai Nerolac Paints reported 16% drop in profit at Rs 122 crore for September quarter.

Consolidated revenue of the company increased 24 per cent to Rs 5,293.99 crore in Q3FY19.

Total expenses rose 15.65 per cent to Rs 4,340.64 crore in the quarter as against Rs 3,752.94 crore in the year-ago period.

The number beat ET Now's poll estimate of Rs 547 crore profit.

Dhingra indicated that the company they would look for acquisition should be bigger than its existing operations in Russia. BPIL now runs the Russian operations through its subsidiary in Cyprus.

The decorative business segment in India recorded high double digit volume growth.

"The Commission is of the view that evidence provided by JSW Paints is prima-facie sufficient to indicate that Asian Paints has denied access to the distribution channels in the relevant market to JSW Paints by threatening and coercing such dealers through various means," the fair trade regulator said.

Asian Paints' revenue from operations rose 3% to Rs 5,420.28 crore from Rs 5,263.04 crore.

“As a socially responsible company, Asian Paints is committed to providing necessary support towards various relief measures announced by the government to combat Covid-19” said K.B.S. Anand, Managing Director & CEO, Asian Paints Limited.

The sanitiser is being manufactured at Asian Paints’ plant in Ankleshwar, Gujarat and the company has obtained all necessary permissions from authorities. Other brands which started making hand sanitisers after the Covid-19 pandemic spread to India include Dabur, Emami, Patanjali, Nivea India, and Raymond Consumer Care, among several others.

On March 23, the company had informed bourses about disruption of operations across the country on account of COVID -19 pandemic.

'Our foray into sanitizers is an effort to help the fight against Covid-19'

Russia has imported leather and footwear worth USD 3.9 billion in 2018, and India's exports to that country stood at only USD 52.6 million, said Panaruna Aqeel Ahmed, chairman of Council for Leather Exports (CLE).

The production of high-tech running shoes at its so-called speedfactories in Germany's Ansbach and in the US city of Atlanta "will be discontinued by April 2020 at the latest", Adidas said in a statement.

In a letter to the brand’s business partners, Bjorn Gulden, global CEO of Puma SE, announced Ganguly’s elevation in the company adding that that he will continue to work out of Puma’s India head office in Bengaluru.

India’s largest maker of writing & printing paper has been in talks with Nine Dragons for some time now. Discussions are likely to lead to a binding agreement soon, sources said.

Concept Group, one of Russia’s leading fashion retailers, creates collections and sells women’s clothing, accessories as well as children’s wear through its own retail stores.

The affordable gyms under Talwalkar-Snap Fitness tieup to open first in Singapore and Malaysia.

Ambrosia Sipping Chocolate is a brand new, gourmet hot chocolate that’s made in Traverse City. It hits the market on April 15th. “It’s literally like you’re drinking chocolate bars because that’s exactly what it is,” says co-owner Matt Shepler.

Updated at 4:56 p.m. ET Peril from foreign interference in American elections will persist through the 2020 presidential race, former special counsel Robert Mueller warned on Wednesday. Asked whether Russia would attempt to attack future U.S. elections, as it did in 2016, Mueller replied: "They're doing it as we sit here." Mueller didn't detail a prescription for how he believes Congress or the United States should respond, but he recommended generally that intelligence and law enforcement agencies should work together. "They should use the full resources that we have to address this," Mueller said. That warning came during hours of hearings, first before the House Judiciary Committee and then the intelligence committee, in which Democrats sought to underscore that Mueller had not cleared Trump of obstruction allegations and that he had found many contacts between Trump's campaign and the Russian interference in the 2016 election. "Did you actually totally exonerate the president?"

Russian President Vladimir Putin sent telegrams on Friday to US President Donald Trump and British Prime Minister Boris Johnson suggesting the need to rekindle their nations' cooperation during World War II to solve today's problems. Putin's overture was the latest in a series of contacts with Washington with which Moscow is keen to rebuild relations frayed over everything from election hacking allegations to Syria. Ties with London remain badly strained over the poisoning of a former Russian spy and his daughter in England. The telegrams were among many Putin dispatched to the Soviet Union's World War II allies on the 75th anniversary of the end of the conflict in Europe. Related:   Coronavirus postponed Russia's Victory Day. For Putin, it's a problem. Russia, which marks the unconditional surrender of Nazi Germany on May 9, the day after "Victory in Europe" Day, has been forced to scale back commemorations due to the coronavirus. Fiona Hill served as the senior director for European

Since President Donald Trump took office, we’ve heard plenty about Russia. Some have said tensions with the country could lead to conflict – even another world war.

In this podcast special, Al Letson talks to former top NATO commander Richard Shirreff, who spells out these fears – which are very real for him – in his new novel.

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