The computation of multiple roots of a Bernstein basis polynomial

This paper describes the algorithms of Musser and Gauss for the computation of multiple roots of a theoretically exact Bernstein basis polynomial ˆ 5 f(y) when the coefficients of its given form f(y) are corrupted by noise. The exact roots of f(y) can therefore be assumed to be simple, and thus the problem reduces to the calculation of multiple roots of a polynomial f˜(y) that is near f(y), such that the backward error is small. The algorithms require many greatest common divisor (GCD) computations and polynomial deconvolutions, both of which are implemented by a structure-preserving matrix method. The motivation of these algorithms arises from the unstructured and structured condition numbers of a multiple root of a polynomial. These condition numbers have an elegant interpretation in terms of the pejorative manifold of ˆ 12 f(y), which allows the geometric significance of the GCD computations and polynomial deconvolutions to be considered. A variant of the Sylvester resultant matrix is used for the GCD computations because it yields better results than the standard form of this matrix, and the polynomial deconvolutions can be computed in several different ways, sequentially or simultaneously, and with the inclusion or omission of the preservation of the structure of the coefficient matrix. It is shown that Gauss’ algorithm yields better results than Musser’s algorithm, and the reason for these superior results is explained

Simulations of spin-driven AGN jets in gas-rich galaxy mergers

In this work, we use hydrodynamical simulations to explore the effects of kinetic AGN jet feedback on the progression and outcome of the major merger of two isolated, gas-rich galaxies. We present simulations that use the moving-mesh code AREPO to follow the progression of the merger through first passage and up to the final coalescence, modelling the black holes at the centres of both of the merging galaxies using our prescription for black hole accretion via an $\alpha$-disc and feedback in the form of a spin-driven jet. We find that the jets drive large-scale, multiphase outflows which launch large quantities of cold gas out to distances greater than 100 kpc and with velocities that reach $\sim 2500 \, {\rm km \, s^{-1}}$. Gas in the outflows that decelerates, cools and falls back on the galaxies can provide a rich source of fuel for the black hole, leading to intense episodes of jet activity in which the jet can become significantly misaligned. The presence of AGN jets affects the growth of the stellar component: star formation is moderately suppressed at all times during the merger and the peak of the star formation rate, attained during the final coalescence of the galaxies, is reduced by a factor of $\sim 2$. Analysis of simulations such as these will play a central role in making precise predictions for multimessenger investigations of dual radio-AGN, which next-generation observational facilities such as LISA, Athena and SKA will make possible.Comment: 20 pages, 10 figures, submitted to MNRA

The shock Hugoniot of hydroxy-terminated polybutadiene

The response of polymers to shock loading is becoming of increasing importance, both as binder systems in plastic-bonded explosives (PBXs) and as structural materials in their own right. In this paper, we report on the shock Hugoniot of hydroxy-terminated polybutadiene (HTPB), which is commonly used as a binder system in PBXs, but whose shock response has yet to be presented in the open literature. Results indicate that the shock velocity --- particle velocity relationship is linear, similar to some but not all polymer-based materials

An approximate factorisation of three bivariate Bernstein basis polynomials defined in a triangular domain

This paper considers an approximate factorisation of three bivariate Bernstein basis polynomials that are defined in a triangular domain. This problem is important for the computation of the intersection points of curves in computer-aided design systems, and it reduces to the determination of an approximate greatest common divisor (AGCD) d (y) of the polynomials. The Sylvester matrix and its subresultant matrices of these three polynomials are formed and it is shown that there are four forms of these matrices. The most difficult part of the computation is the determination of the degree of d (y) because it reduces to the determination of the rank loss of these matrices. This computation is made harder by the presence of trinomial terms in the Bernstein basis functions because they cause the entries of the matrices to span many orders of magnitude. The adverse numerical effects of this wide range of magnitudes of the entries of the four forms of the Sylvester matrix and its subresultant matrices are mitigated by processing the polynomials before these matrices are formed. It is shown that significantly improved results are obtained if the polynomials are processed before computations are performed on their Sylvester matrices and subresultant matrices

Mesosphere and Lower Thermosphere Changes Associated With the 2 July 2019 Total Eclipse in South America Over the Andes Lidar Observatory, Cerro Pachon, Chile

This article presents the results of a week of observations around the 2 July 2019, total Chilean eclipse. The eclipse occurred between 19:22 and 21:46 UTC, with complete sun disc obscuration at 20:38–20:40 UTC (16:38–16:40 LT) over the Andes Lidar Observatory (ALO) at (30.3°S, 70.7°W). Observations were carried out using ALO instrumentation with the goal to observe possible eclipse-induced effects on the mesosphere and lower thermosphere region (MLT; 75–105 km altitude). To complement our data set, we have also utilized TIMED/SABER temperatures and ionosonde electron density measurements taken at the University of La Serena\u27s Juan Soldado Observatory. Observed events include an unusual fast, bow-shaped gravity wave structure in airglow images, mesosphere temperature mapper brightness as well as in lidar temperature with 150 km horizontal wavelength 24 min observed period, and vertical wavelength of 25 km. Also, a strong zonal wind shear above 100 km in meteor radar scans as well as the occurrence of a sporadic E layer around 100 km from ionosonde measurements. Finally, variations in temperature and density and the presence of a descending sporadic sodium layer near 98 km were seen in lidar data. We discuss the effects of the eclipse in the MLT, which can shed light on a sparse set of measurements during this type of event. Our results point out several effects of eclipse-associated changes in the atmosphere below and above but not directly within the MLT

Fast neutron spectrum unfolding for nuclear nonproliferation and safeguards applications

We present new neutron spectrum unfolding results obtained from measurements with Cf-252 and plutonium-oxide sources. The precise knowledge of the neutron energy spectrum provides information about the presence or absence of fissile material and about the characteristics of the material. We used a neutron spectrum unfolding technique based on a modification of the least-squares method. The main innovation is the use of a Krylov subspace iteration which performs better on ill-conditioned systems of linear equations than standard direct-solution methods. The proposed technique performed well in the unfolding of measured neutron pulseheight distributions from a Cf-252 neutron source and from plutonium-oxide samples and could be easily implemented in a portable neutron spectroscopy system for nuclear nonproliferation and safeguard applications

Primjena tehnologije rekombinantne DNA za pripravke kolinesteraza kao antidota i detektora organofosfata

To develop new avenues for synthesizing novel antidotes for organophosphate poisoning and for detection of the organophosphates, we have turned to recombinant DNA methods to synthesize cholinesterases with unusual properties. For antidotal therapy we describe mutations of the native mouse and human enzymes that allow for enhanced rates of oxime reactivation. Such enzymes, when localized in the circulation, would enable the circulating cholinesterase to become a catalytic rather than simply a stoichiometric scavenger. Hence, “oxime-assisted catalysis” provides a means for scavenging the organophosphates in the circulation thereby minimizing their tissue penetration and toxicity. Accordingly, the oxime antidote or prophylactic agent has a dual action within the circulation and at the tissue level. Second, through a novel chemistry, termed freeze-frame, click chemistry, we have used organophosphate conjugates of acetylcholinesterase as templates for the synthesis of novel nucleophilic reactivating agents. Finally, acetylcholinesterase can be modified through cysteine substitution mutagenesis and attachment of fluorophores at the substitution positions. When linked at certain locations in the molecule, the attached fluorophore is sensitive to organophosphate conjugation with acetylcholinesterase, and thus the very target of insecticide or nerve agent action becomes a detection molecule for organophosphate exposure.Razvijajući novi pristup sintezi antidota pri otrovanju organofosfatima kao i njihovu detekciju, primijenili smo metode rekombinantne DNA za pripremu kolinesteraza s neuobičajenim svojstvima. Za antidotsku terapiju istražili smo mutacije prirodnih enzima miša i čovjeka koje povećavaju brzine reaktivacije oksimom. Takvi enzimi bi po unosu u cirkulaciju postali katalitički, a ne samo stehiometrijski odstranjivači organofosfata. Na taj način “oksimom potpomognuta kataliza” omogućava čišćenje organofosfata iz cirkulacije umanjujući prodiranje organofosfata u tkiva i njihovu toksičnost. Prema tome, oksim kao antidot ima dvojaku ulogu: u cirkulaciji i na razini tkiva. S druge strane, uporabom novog sintetskog pristupa u oblikovanju biološki aktivnih spojeva poznatog kao “klik kemija” diskretnih proteinskih konformacija, organofosforilirani konjugati acetilkolinesteraze služe kao kalup u sintezi novih nukleofilnih reaktivatora. Naposljetku, acetilkolinesteraza se može mutagenezom modificirati uvo|enjem cisteina na koje se mogu vezati fluorofori. Fluorofori uvedeni na određena mjesta u molekuli acetilkolinesteraze mijenjaju svoja fluorescentna svojstva pri konjugaciji organofosfata s enzimom koji na taj način od objekta djelovanja insekticida i živčanih bojnih otrova postaje molekula za detekciju izloženosti organofosfatima