Direct and Inverse Problems for the Heat Equation with a Dynamic type Boundary Condition

This paper considers the initial-boundary value problem for the heat equation with a dynamic type boundary condition. Under some regularity, consistency and orthogonality conditions, the existence, uniqueness and continuous dependence upon the data of the classical solution are shown by using the generalized Fourier method. This paper also investigates the inverse problem of finding a time-dependent coefficient of the heat equation from the data of integral overdetermination condition

Synchronization, Control and Stability of Fractional Order Hyperchaotic Systems in The Context of The Generalized Memory

In the article offered fractional kinetic model of networks with generalized memory. On the basis of fractional kinetic model network with hyperchaotic systems, embedded in a percolation structure, realized task topologically synchronization. While tracing control and stability. Criterion ndash ldquoproximityrdquo capture average return time Poincare. Shows a visualization of results

An inverse coefficient problem for the heat equation in the case of nonlocal boundary conditions

This paper investigates the inverse problem of finding a time-dependent coefficient in a heat equation with nonlocal boundary and integral overdetermination conditions. Under some regularity and consistency conditions on the input data, the existence, uniqueness and continuous dependence upon the data of the solution are shown by using the generalized Fourier method

PHASES High Precision Differential Astrometry of delta Equulei

delta Equulei is among the most well-studied nearby binary star systems. Results of its observation have been applied to a wide range of fundamental studies of binary systems and stellar astrophysics. It is widely used to calibrate and constrain theoretical models of the physics of stars. We report 27 high precision differential astrometry measurements of delta Equulei from the Palomar High-precision Astrometric Search for Exoplanet Systems (PHASES). The median size of the minor axes of the uncertainty ellipses for these measurements is 26 micro-arcseconds. These data are combined with previously published radial velocity data and other previously published differential astrometry measurements using other techniques to produce a combined model for the system orbit. The distance to the system is determined to within a twentieth of a parsec and the component masses are determined at the level of a percent. The constraints on masses and distance are limited by the precisions of the radial velocity data; we outline plans improve this deficiency and discuss the outlook for further study of this binary.Comment: Accepted by AJ. Complete versions of tables 2-7 now available at http://stuff.mit.edu/~matthew1/deltaEquTables/ (removed from astroph server

Multi-band analyses of the bright GRB~230812B and the associated SN2023pel

GRB~230812B is a bright and relatively nearby ($z =0.36$) long gamma-ray burst that has generated significant interest in the community and therefore has been subsequently observed over the entire electromagnetic spectrum. We report over 80 observations in X-ray, ultraviolet, optical, infrared, and sub-millimeter bands from the GRANDMA (Global Rapid Advanced Network for Multi-messenger Addicts) network of observatories and from observational partners. Adding complementary data from the literature, we then derive essential physical parameters associated with the ejecta and external properties (i.e. the geometry and environment) and compare with other analyses of this event (e.g. Srinivasaragavan et al. 2023). We spectroscopically confirm the presence of an associated supernova, SN2023pel, and we derive a photospheric expansion velocity of v $\sim$ 17$\times10^3$ km $s^{-1}$. We analyze the photometric data first using empirical fits of the flux and then with full Bayesian Inference. We again strongly establish the presence of a supernova in the data, with an absolute peak r-band magnitude $M_r = - 19.41 \pm 0.10$. We find a flux-stretching factor or relative brightness $k_{\rm SN}=1.04 \pm 0.09$ and a time-stretching factor $s_{\rm SN}=0.68 \pm 0.05$, both compared to SN1998bw. Therefore, GRB 230812B appears to have a clear long GRB-supernova association, as expected in the standard collapsar model. However, as sometimes found in the afterglow modelling of such long GRBs, our best fit model favours a very low density environment ($\log_{10}({n_{\rm ISM}/{\rm cm}^{-3}}) = -2.16^{+1.21}_{-1.30}$). We also find small values for the jet's core angle $\theta_{\rm core}={1.70^{+1.00}_{-0.71}} \ \rm{deg}$ and viewing angle. GRB 230812B/SN2023pel is one of the best characterized afterglows with a distinctive supernova bump

Preliminary Evidence for Cell Membrane Amelioration in Children with Cystic Fibrosis by 5-MTHF and Vitamin B12 Supplementation: A Single Arm Trial

Cystic fibrosis (CF) is one of the most common fatal autosomal recessive disorders in the Caucasian population caused by mutations of gene for the cystic fibrosis transmembrane conductance regulator (CFTR). New experimental therapeutic strategies for CF propose a diet supplementation to affect the plasma membrane fluidity and to modulate amplified inflammatory response. The objective of this study was to evaluate the efficacy of 5-methyltetrahydrofolate (5-MTHF) and vitamin B12 supplementation for ameliorating cell plasma membrane features in pediatric patients with cystic fibrosis.A single arm trial was conducted from April 2004 to March 2006 in an Italian CF care centre. 31 children with CF aged from 3 to 8 years old were enrolled. Exclusion criteria were diabetes, chronic infections of the airways and regular antibiotics intake. Children with CF were supplemented for 24 weeks with 5-methyltetrahydrofolate (5-MTHF, 7.5 mg /day) and vitamin B12 (0.5 mg/day). Red blood cells (RBCs) were used to investigate plasma membrane, since RBCs share lipid, protein composition and organization with other cell types. We evaluated RBCs membrane lipid composition, membrane protein oxidative damage, cation content, cation transport pathways, plasma and RBCs folate levels and plasma homocysteine levels at baseline and after 24 weeks of 5-MTHF and vitamin B12 supplementation. In CF children, 5-MTHF and vitamin B12 supplementation (i) increased plasma and RBC folate levels; (ii) decreased plasma homocysteine levels; (iii) modified RBC membrane phospholipid fatty acid composition; (iv) increased RBC K(+) content; (v) reduced RBC membrane oxidative damage and HSP70 membrane association.5-MTHF and vitamin B12 supplementation might ameliorate RBC membrane features of children with CF.ClinicalTrials.gov NCT00730509

Heterosynaptic plasticity in the neocortex

Ongoing learning continuously shapes the distribution of neurons’ synaptic weights in a system with plastic synapses. Plasticity may change the weights of synapses that were active during the induction—homosynaptic changes, but also may change synapses not active during the induction—heterosynaptic changes. Here we will argue, that heterosynaptic and homosynaptic plasticity are complementary processes, and that heterosynaptic plasticity might accompany homosynaptic plasticity induced by typical pairing protocols. Synapses are not uniform in their susceptibility for plastic changes, but have predispositions to undergo potentiation or depression, or not to change. Predisposition is one of the factors determining the direction and magnitude of homo- and heterosynaptic changes. Heterosynaptic changes which take place according to predispositions for plasticity may provide a useful mechanism(s) for homeostasis of neurons’ synaptic weights and extending the lifetime of memory traces during ongoing learning in neuronal networks

GRANDMA and HXMT Observations of GRB 221009A -- the Standard-Luminosity Afterglow of a Hyper-Luminous Gamma-Ray Burst

GRB 221009A is the brightest Gamma-Ray Burst (GRB) detected in more than 50 years of study. In this paper, we present observations in the X-ray and optical domains after the GRB obtained by the GRANDMA Collaboration (which includes observations from more than 30 professional and amateur telescopes) and the Insight-HXMT Collaboration. We study the optical afterglow with empirical fitting from GRANDMA+HXMT data, augmented with data from the literature up to 60 days. We then model numerically, using a Bayesian approach, the GRANDMA and HXMT-LE afterglow observations, that we augment with Swift-XRT and additional optical/NIR observations reported in the literature. We find that the GRB afterglow, extinguished by a large dust column, is most likely behind a combination of a large Milky-Way dust column combined with moderate low-metallicity dust in the host galaxy. Using the GRANDMA+HXMT-LE+XRT dataset, we find that the simplest model, where the observed afterglow is produced by synchrotron radiation at the forward external shock during the deceleration of a top-hat relativistic jet by a uniform medium, fits the multi-wavelength observations only moderately well, with a tension between the observed temporal and spectral evolution. This tension is confirmed when using the extended dataset. We find that the consideration of a jet structure (Gaussian or power-law), the inclusion of synchrotron self-Compton emission, or the presence of an underlying supernova do not improve the predictions, showing that the modelling of GRB22109A will require going beyond the most standard GRB afterglow model. Placed in the global context of GRB optical afterglows, we find the afterglow of GRB 221009A is luminous but not extraordinarily so, highlighting that some aspects of this GRB do not deviate from the global known sample despite its extreme energetics and the peculiar afterglow evolution.Comment: Accepted to ApJL for the special issue, 37 pages, 23 pages main text, 6 tables, 13 figure