Fractional differentiability for solutions of nonlinear elliptic equations

We study nonlinear elliptic equations in divergence form $${\operatorname{div}}{\mathcal A}(x,Du)={\operatorname{div}}G.$$ When ${\mathcal A}$ has linear growth in $Du$, and assuming that $x\mapsto{\mathcal A}(x,\xi)$ enjoys $B^\alpha_{\frac{n}\alpha, q}$ smoothness, local well-posedness is found in $B^\alpha_{p,q}$ for certain values of $p\in[2,\frac{n}{\alpha})$ and $q\in[1,\infty]$. In the particular case ${\mathcal A}(x,\xi)=A(x)\xi$, $G=0$ and $A\in B^\alpha_{\frac{n}\alpha,q}$, $1\leq q\leq\infty$, we obtain $Du\in B^\alpha_{p,q}$ for each $p<\frac{n}\alpha$. Our main tool in the proof is a more general result, that holds also if ${\mathcal A}$ has growth $s-1$ in $Du$, $2\leq s\leq n$, and asserts local well-posedness in $L^q$ for each $q>s$, provided that $x\mapsto{\mathcal A}(x,\xi)$ satisfies a locally uniform $VMO$ condition

Synthesis and reactivity of an iridium complex based on a tridentate aminophosphano ligand

The iridium(iii) hydride compound IrH{¿3C, P, P'-(SiNP-H)}(CNtBu)2]PF6] (1PF6) was obtained by reaction of Ir(SiNP)(cod)]PF6] with CNtBu as the result of the intramolecular oxidative addition of the SiCH2-H bond to iridium(i) SiNP = Si(CH3)2{N(4-tolyl)PPh2}2, SiNP-H = CH2Si(CH3){N(4-tolyl)PPh2}2]. The mechanism of the reaction was investigated by NMR spectroscopy and DFT calculations showing that the pentacoordinated intermediate Ir(SiNP)(cod)(CNtBu)]PF6] (2PF6) forms in the first place and that further reacts with CNtBu, affording the square planar intermediate Ir(SiNP)(CNtBu)2]PF6] (3PF6) that finally undergoes the intramolecular oxidative addition of the SiCH2-H bond. The reactivity of 1PF6 was investigated. On one hand, the reaction of 1PF6 with N-chlorosuccinimide or N-bromosuccinimide provides the haloderivatives IrX{¿3C, P, P'-(SiNP-H)}(CNtBu)2]PF6] (X = Cl, 4PF6; Br, 5PF6), and the reaction of 5PF6 with AgPF6 in the presence of acetonitrile affords the solvato species Ir{¿3C, P, P'-(SiNP-H)}(CH3CN)(CNtBu)2]2+ (62+) isolated as the hexafluorophosphate salt. On the other hand, the reaction of 1PF6 with HBF4 gives the iridium(iii) compound IrH(CH2SiF2CH3)(HNP)2(CNtBu)2]BF4] (7BF4) as the result of the formal addition of hydrogen fluoride to the Si-N bonds of 1+ HNP = HN(4-tolyl)PPh2]. A similar outcome was observed in the reaction of 1PF6 with CF3COOH rendering 7PO2F2. In this case the intermediate IrH{¿2C, P-CH2SiMeFN(4-tolyl)PPh2}(HNP)(CNtBu)2]+ (8+) was observed and characterised in situ by NMR spectroscopy. DFT calculations suggests that the reaction goes through the sequential protonation of the nitrogen atom of the Si-N-P moiety followed by the formal addition of fluoride ion to silicon. Also, the crystal structures of SiNP, 1PF6, 4PF6 and 7BF4 have been determined by X-ray diffraction measurements. © 2022 The Royal Society of Chemistr

Reactivity of Ir(i)-aminophosphane platforms towards oxidants

The iridium(I)-aminophosphane complex [Ir{κ3C,P,P′-(SiNP-H)}(cod)] has been prepared by reaction of [IrCl(cod)(SiNP)] with KCH3COO. DFT calculations show that this reaction takes place through an unexpected outer sphere mechanism (SiNP = SiMe2{N(4-C6H4Me)PPh2}2; SiNP-H = CH2SiMe{N(4-C6H4Me)PPh2}2). The reaction of [IrCl(cod)(SiNP)] or [Ir{κ3C,P,P′-(SiNP-H)}(cod)] with diverse oxidants has been explored, yielding a range of iridium(III) derivatives. On one hand, [IrCl(cod)(SiNP)] reacts with allyl chloride rendering the octahedral iridium(III) derivative [IrCl2(η3-C3H5)(SiNP)], which, in turn, reacts with tert-butyl isocyanide yielding the substitution product [IrCl(η3-C3H5)(CNtBu)(SiNP)]Cl via the observed intermediate [IrCl2(η1-C3H5)(CNtBu)(SiNP)]. On the other hand, the reaction of [Ir{κ3C,P,P′-(SiNP-H)}(cod)] with [FeCp2]X (X = PF6, CF3SO3), I2 or CF3SO3CH3 results in the metal-centered two-electron oxidation rendering a varied assortment of iridium(III) compounds. [Ir{κ3C,P,P′-(SiNP-H)}(cod)] reacts with [FeCp2]+ (1 : 2) in acetonitrile affording [Ir{κ3C,P,P′-(SiNP-H)}(CH3CN)3]2+ isolated as both the triflato and the hexafluorophosphato derivatives. Also, the reaction of [Ir{κ3C,P,P′-(SiNP-H)}(cod)] with I2 (1 : 1) yields a mixture of iridium(III) derivatives, namely the mononuclear compound [IrI(κ2P,P′-SiNP)(η2,η3-C8H11)]I, containing the η2,η3-cycloocta-2,6-dien-1-yl ligand, and two isomers of the dinuclear derivative [Ir2{κ3C,P,P′-(SiNP-H)}2(μ-I)3]I, the first species being isolated in low yield. DFT calculations indicate that [IrI(κ2P,P′-SiNP)(η2,η3-C8H11)]I forms as the result of a bielectronic oxidation of iridium(I) followed by the deprotonation of the cod ligand by iodide and the protonation of the methylene moiety of the [Ir{κ3C,P,P′-(SiNP-H)}] platform by the newly formed HI. Finally, the oxidation of [Ir{κ3C,P,P′-(SiNP-H)}(cod)] by methyl triflate proceeds via a hydride abstraction from the cod ligand, with the elimination of methane and the formation of the η2,η3-cycloocta-2,6-dien-1-yl ligand with the concomitant two-electron oxidation of the iridium centre. The crystal structures of selected compounds have been determined

Intramolecular C-H oxidative addition to iridium(I) triggered by trimethyl phosphite in N,N′-diphosphanesilanediamine complexes

The reaction of [Ir(SiNP)(cod)][PF] ([1][PF]) and of IrCl(SiNP)(cod) (5) (SiNP = SiMe{N(4-CHCH)PPh}) with trimethyl phosphite affords the iridium(iii) derivatives of the formula [IrHCl(SiNP-H){P(OMe)}] (x = 0, 3; x = 1, 6) containing the κC,P,P′-coordinated SiNP-H ligand (SiNP-H = Si(CH)(CH){N(4-CHCH)PPh}). The thermally unstable pentacoordinated cation [Ir(SiNP){P(OMe)}(cod)] (2) has been detected as an intermediate of the reaction and has been fully characterised in solution. Also, the mechanism of the C-H oxidative addition has been elucidated by DFT calculations showing that the square planar iridium(i) complexes of the formula [IrCl(SiNP){P(OMe)}] (x = 0, 4; x = 1, 7) should be firstly obtained from 2 and finally should undergo the C-H oxidative addition to iridium(i) via a concerted intramolecular mechanism. The influence of the counterion of 2 on the outcome of the C-H oxidative addition reaction has also been investigated.Financial support from Spanish “Ministerio de Economía y Competitividad” (CTQ2013–42532–P), “Diputación General de Aragón” (Group E07) and University of Zaragoza (UZCUD2014–CIE–13) is gratefully acknowledged.Peer Reviewe

Intramolecular C-H oxidative addition to iridium(I) in complexes containing a N,N'-diphosphanosilanediamine ligand

The iridium(I) complexes of formula Ir(cod)(SiNP)+ (1+) and IrCl(cod)(SiNP) (2) are easily obtained from the reaction of SiMe2{N(4-C6H4CH3)PPh2}2 (SiNP) with [Ir(cod)(CH3CN)2]+ or [IrCl(cod)]2, respectively. The carbonylation of [1][PF6] affords the cationic pentacoordinated complex [Ir(CO)(cod)(SiNP)]+ (3+), while the treatment 2 with CO gives the cation 3+ as an intermediate, finally affording an equilibrium mixture of IrCl(CO)(SiNP) (4) and the hydride derivative of formula IrHCl(CO)(SiNP–H) (5) resulting from the intramolecular oxidative addition of the C–H bond of the SiCH3 moiety to the iridium(I) center. Furthermore, the prolonged exposure of [3]Cl or 2 to CO resulted in the formation of the iridium(I) pentacoordinated complex Ir(SiNP–H)(CO)2 (6). The unprecedented κ3C,P,P′ coordination mode of the [SiNP–H] ligand observed in 5 and 6 has been fully characterized in solution by NMR spectroscopy. In addition, the single-crystal X-ray structure of 6 is reported.Financial support from Spanish “Ministerio de Economía y Competitividad” (CTQ2010– 15221) and “Diputación General de Aragón” (Group E07) is gratefully acknowledged.Peer Reviewe

The stress shadow induced by the 1975-1984 Krafla rifting episode

It has been posited that the 1975\u20131984 Krafla rifting episode in northern Iceland was responsible for a significant drop in the rate of earthquakes along the H\ufasav\uedk\u2010Flatey Fault (HFF), a transform fault that had previously been the source of several magnitude 6\u20137 earthquakes. This compelling case of the existence of a stress shadow has never been studied in detail, and the implications of such a stress shadow remain an open question. According to rate\u2010state models, intense stress shadows cause tens of years of low seismicity rate followed by a faster recovery phase of rate increase. Here, we compare the long\u2010term predictions from a Coulomb stress model of the rifting episode with seismological observations from the SIL catalog (1995\u20132011) in northern Iceland. In the analyzed time frame, we find that the rift\u2010induced stress shadow coincides with the eastern half of the fault where the observed seismicity rates are found to be significantly lower than expected, given the historical earthquake activity there. We also find that the seismicity rates on the central part of the HFF increased significantly in the last 17 years, with the seismicity progressively recovering from west to east. Our observations confirm that rate\u2010state theory successfully describes the long\u2010term seismic rate variation during the reloading phase of a fault invested by a negative Coulomb stress. Coincident with this recovery, we find that the b\u2010value of the frequency\u2010magnitude distribution changed significantly over time. We conclude that the rift\u2010induced stress shadow not only decreased the seismic rate on the eastern part of the HFF but also temporarily modified how the system releases seismic energy, with more large magnitude events in proportion to small ones. This behavior is currently being overturned, as rift\u2010induced locking is now being compensated by tectonic forcing

The Distant Horizon: investigating the relationship between social sciences academic research and game development

Research in the social sciences devotes a great amount of attention to investigating the impact of video games on the individual and on society. However, results generated by this research often fail to inform game development. The present study investigated the outreach of research conducted by the academic community by interviewing 30 game developers and 14 researchers, highlighting critical aspects in the relationship between game research and game industry. Specifically, we found that the difference in priorities, speed cycles, and dissemination practices between these two contexts hinder communication. Subsequently, we carried out a focus group for a set of developers and researchers (N=6) with the aim of eliciting recommendation for improving communication between academics and developers. Among the recommendations to emerge were calls to diversify dissemination channels, promote joint conferences and develop research-production partnerships. It was felt such measures could strengthen the influence of research results outside the academic community

Joint Effect of Childhood Abuse and Family History of Major Depressive Disorder on Rates of PTSD in People with Personality Disorders

Objective. Childhood maltreatment and familial psychopathology both lead to an increased risk of the development of posttraumatic stress disorder (PTSD) in adulthood. While family history of psychopathology has traditionally been viewed as a proxy for genetic predisposition, such pathology can also contribute to a stress-laden environment for the child. Method. Analyses were conducted to evaluate the joint effect of childhood abuse and a family history of major depressive disorder (MDD) on diagnoses of PTSD and MDD in a sample of 225 adults with DSM-IV Axis II disorders. Results. Results showed that the rate of PTSD in the presence of both childhood abuse and MDD family history was almost six-fold (OR = 5.89, P = .001) higher relative to the absence of both factors. In contrast, the rate of MDD in the presence of both factors was associated with a nearly three-fold risk relative to the reference group (OR = 2.75, P = .01). Conclusions. The results from this observational study contribute to a growing understanding of predisposing factors for the development of PTSD and suggest that joint effects of family history of MDD and childhood abuse on PTSD are greater than either factor alone

Impedance measurements and simulations on the TCT and TDI LHC collimators

The LHC collimation system is a critical element for the safe operation of the LHC machine and it is subject to continuous performance monitoring, hardware upgrade and optimization. In this work we will address the impact on impedance of the upgrades performed on the injection protection target dump (TDI), where the absorber material has been changed to mitigate the device heating observed in machine operation, and on selected secondary (TCS) and tertiary (TCT) collimators, where beam position monitors (BPM) have been embedded for faster jaw alignment. Con- cerning the TDI, we will present the RF measurements per- formed before and after the upgrade, comparing the result to heating and tune shift beam measurements. For the TCTs, we will study how the higher order modes (HOM) intro- duced by the BPM addition have been cured by means of ferrite placement in the device. The impedance mitigation campaign has been supported by RF measurements whose results are in good agreement with GdfidL and CST simula- tions. The presence of undamped low frequency modes is proved not to be detrimental to the safe LHC operation

Analysis and functional annotation of expressed sequence tags from the fall armyworm Spodoptera frugiperda

BACKGROUND: Little is known about the genome sequences of lepidopteran insects, although this group of insects has been studied extensively in the fields of endocrinology, development, immunity, and pathogen-host interactions. In addition, cell lines derived from Spodoptera frugiperda and other lepidopteran insects are routinely used for baculovirus foreign gene expression. This study reports the results of an expressed sequence tag (EST) sequencing project in cells from the lepidopteran insect S. frugiperda, the fall armyworm. RESULTS: We have constructed an EST database using two cDNA libraries from the S. frugiperda-derived cell line, SF-21. The database consists of 2,367 ESTs which were assembled into 244 contigs and 951 singlets for a total of 1,195 unique sequences. CONCLUSION: S. frugiperda is an agriculturally important pest insect and genomic information will be instrumental for establishing initial transcriptional profiling and gene function studies, and for obtaining information about genes manipulated during infections by insect pathogens such as baculoviruses