Unique Invariant Point Theorems for Random operators In Hilbert Space

We find unique common random fixed point of two random operators in closed subset of a separable Hilbert space by considering a sequence of measurable functions satisfying  Theorem 1.1 and Theorem 1.2. Keywords: Separable Hilbert space, random operators, common random fixed point

Some Result on fixed point Theorem in Hilbert Space

This paper puts up a result regarding the generalization of the Banach contraction  principle in the Hilbert space, It consist of four rational square terms in the inequality. Further the corollary of Koparde and Wag mode was obtained by considering vanishing values to some constant towards the end of this result. Keywords: Hilbert space, closed subset, Cauchy sequence, Completeness

Bulk Viscosity of Magnetized Neutron Star Matter

We study the effect of magnetic field on the bulk viscosity of nuclear matter in neutron stars. We employ the framework of relativistic mean field theory to observe the dense nuclear matter in neutron stars. The effects are first studied for the case when the magnetic field does not exceed the critical value to confine the electrons to the lowest Landau levels. We then consider the case of intense magnetic field to evaluate viscosity for the URCA processes and show that the inequality $p_{F}(e)+p_{F}(p)\geq p_{F}(n)$ is no longer required to be satisfied for the URCA processes to proceed.Comment: Latex 2e file with four postscripts figure

Cellular mechanisms underlying steroid-resistant asthma

© ERS 2019. Severe steroid-resistant asthma is clinically important, as patients with this form of the disease do not respond to mainstay corticosteroid therapies. The heterogeneity of this form of asthma and poor understanding of the pathological mechanisms involved hinder the identification of therapeutic targets and the development of more effective therapies. A major limiting factor in the understanding of severe steroid-resistant asthma is the existence of multiple endotypes represented by different immunological and inflammatory phenotypes, particularly in adults. Several clinical and experimental studies have revealed associations between specific respiratory infections and steroid-resistant asthma in adults. Here, we discuss recent findings from other authors as well as our own studies that have developed novel experimental models for interrogating the association between respiratory infections and severe steroid-resistant asthma. These models have enabled the identification of new therapies using macrolides, as well as several novel disease mechanisms, including the microRNA-21/phosphoinositide 3-kinase/histone deacetylase 2 axis and NLRP3 inflammasomes, and highlight the potential of these mechanisms as therapeutic targets

Dating Howardite Melt Clasts: Evidence for an Extended Vestan Bombardment?

Howardites are polymict breccias that, together with eucrites and diogenites (HED), likely originate from the vestan surface (regolith/ megaregolith), and display a heterogeneous distribution of eucritic and diogenitic material. Melt clasts are also present alongside other regolithic features within howardites, and are noteworthy for their compositional variability and appearance. Melt clasts formed by impact events provide a snapshot of the timings and conditions of surface gardening and bombardment on the vestan surface. By dating such clasts, we aim to better constrain the timings of impact events on Vesta, and to establish whether the impact flux in the asteroid belt was similar to that on the Moon. As the Moon is used as the basis for characterising impact models of the inner solar system, it is necessary to verify that apparent wide-scale events are seen in other planetary bodies. In particular, the observed clustering of Apollo melt clast ages between 3.8-4.0 Ga has led to two hypotheses: 1) The Moon was subjected to a sudden event - 'Lunar Cataclysm' or period of 'Late Heavy Bombardment' (LHB), 2) The age cluster represents the end of an epoch of declining bombardment or 'Heavy Bombardment. No consensus has emerged regarding one or other hypothesis. We are testing these hypotheses by seeking evidence for such events in materials other than those derived from the Moon

Impact History on Vesta: Petrographic, Compositional and Future Chronological Studies of Melt Clasts in Howardites

Howardite meteorites are polymict breccias composed mainly of eucritic and diogenitic material that likely originate from the surface of the Asteroid 4 Vesta. They can be separated into two subtypes: Regolithic, which represent the lithified remains of the active vestan regolith; Fragmental, which represent simpler polymict breccias. Amongst the regolithic features observed in the former, melt clasts are particularly striking for their appearance and compositional variability. They range from glassy spherules to finely crystalline (i.e., devitrified) clasts, and clasts containing only relict mineral grains to those containing only phenocrysts. Glasses can be separated into compositional sub-types including those with low FeO/MgO ratios (less than 5) -low alkali glasses, K-rich (K2O greater than 0.2 wt.%), Na-rich (Na2O greater than 0.6 wt.%) and CaO-rich, and those with high FeO/MgO ratios (greater than 10). There is also a distinction to be made between primary volcanic melt clasts and those produced by impacts. While suggested that a lack of chemical homogeneity among their studied melt clasts ruled out a primary volcanic origin, the low siderophile element contents observed in such clasts suggest less compositional influence from impactors than commonly assumed. Studying the chronology of the impact melt clasts in howardites can help us to better determine the timing of impact events on Vesta and the asteroid belt. In this research, we are launching an investigation into the petrology, composition (major/trace element and noble gas) and chronology of melt clasts in howardites. We have selected a set of howardites known to contain large quantities of melt clasts, and have begun the petrological and compositional studies of these materials. Once the melt clasts have been fully classified, we aim to perform chronological studies of individual clasts using both the Ar-40/Ar-39 and Pb-Pb chronometers, as well as determine the noble gas components present. Of particular note, the study will take advantage of the laser ablation techniques associated with the noble gas facilities at ASU, which will allow high-resolution, in-situ analysis of individual clasts. The broader aim of this work is to ascertain whether the impact flux in the region of the asteroid belt was similar to that on the Moon. Our understanding of impact events in the inner Solar System relies heavily on our analyses of lunar meteorites and returned samples, and there is currently some debate regarding whether there was a "Lunar Cataclysm" event around approx. 3.9 Ga, or the end of an epoch of "Late Heavy Bombardment" (LHB) at this time. New and more comprehensive constraints on howardite melt clast ages may help determine whether the asteroid belt experienced such a cataclysm or LHB

M1 muscarinic receptor is a key target of neuroprotection, neuroregeneration and memory recovery by i-Extract from Withania somnifera

Memory loss is one of the most tragic symptoms of Alzheimer's disease. Our laboratory has recently demonstrated that 'i-Extract' of Ashwagandha (Withania somnifera) restores memory loss in scopolamine (SC)-induced mice. The prime target of i-Extract is obscure. We hypothesize that i-Extract may primarily target muscarinic subtype acetylcholine receptors that regulate memory processes. The present study elucidates key target(s) of i-Extract via cellular, biochemical, and molecular techniques in a relevant amnesia mouse model and primary hippocampal neuronal cultures. Wild type Swiss albino mice were fed i-Extract, and hippocampal cells from naïve mice were treated with i-Extract, followed by muscarinic antagonist (dicyclomine) and agonist (pilocarpine) treatments. We measured dendritic formation and growth by immunocytochemistry, kallikrein 8 (KLK8) mRNA by reverse transcription polymerase chain reaction (RT-PCR), and levels of KLK8 and microtubule-associated protein 2, c isoform (MAP2c) proteins by western blotting. We performed muscarinic receptor radioligand binding. i-Extract stimulated an increase in dendrite growth markers, KLK8 and MAP2. Scopolamine-mediated reduction was significantly reversed by i-Extract in mouse cerebral cortex and hippocampus. Our study identified muscarinic receptor as a key target of i-Extract, providing mechanistic evidence for its clinical application in neurodegenerative cognitive disorders

Phase-based video motion processing

We introduce a technique to manipulate small movements in videos based on an analysis of motion in complex-valued image pyramids. Phase variations of the coefficients of a complex-valued steerable pyramid over time correspond to motion, and can be temporally processed and amplified to reveal imperceptible motions, or attenuated to remove distracting changes. This processing does not involve the computation of optical flow, and in comparison to the previous Eulerian Video Magnification method it supports larger amplification factors and is significantly less sensitive to noise. These improved capabilities broaden the set of applications for motion processing in videos. We demonstrate the advantages of this approach on synthetic and natural video sequences, and explore applications in scientific analysis, visualization and video enhancement.Shell ResearchUnited States. Defense Advanced Research Projects Agency. Soldier Centric Imaging via Computational CamerasNational Science Foundation (U.S.) (CGV-1111415)Cognex CorporationMicrosoft Research (PhD Fellowship)American Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Toric Calabi-Yau supermanifolds and mirror symmetry

We study mirror symmetry of supermanifolds constructed as fermionic extensions of compact toric varieties. We mainly discuss the case where the linear sigma A-model contains as many fermionic fields as there are U(1) factors in the gauge group. In the mirror super-Landau-Ginzburg B-model, focus is on the bosonic structure obtained after integrating out all the fermions. Our key observation is that there is a relation between the super-Calabi-Yau conditions of the A-model and quasi-homogeneity of the B-model, and that the degree of the associated superpotential in the B-model is given in terms of the determinant of the fermion charge matrix of the A-model.Comment: 20 pages, v2: references adde