The delay effect on reaction–diffusion equations

In this work we study a reaction–diffusion problem with delay and we make an analysis of the stability of solutions by means of bifurcation theory. We take the delay constant as a parameter. Special conditions on the vector field assure existence of a spatially nonconstant positive equilibrium U_k , which is stable for small values of the delay. An increase of the delay destabilizes the equilibrium of U_k and leads to super or subcritical Hopf bifurcation.     

Sensitivity analysis of nondifferentiable sums of singular values of rectangular matrices

Let K(x) be an s-by-r rectangular matrix depending on a parameter x ε E and denote by g(x) the sum of its m largest singular values (1 ≤ m ≤ Min{s,r}). If K(x) depends affinely on x, then g is a nondifferentiable convex function. In this paper we consider first the affine case and give some formulas for the conjugate, subdifferential, and ε-subdifferential of g. These formulas are then used to obtain perturbation bounds for g(x). We study next the nonaffine case and discuss some questions related with the regularity, generalized subdifferentiability, and directional differentiability of g.     

Chebyshev and L1 solutions of overdetermined systems of linear equations with bounded variables

Two algorithms are here presented. The first one is for obtaining a Chebyshev solution of an overdetermined system of linear equations subject to bounds on the elements of the solution vector. The second algorithm is for obtaining an L₁ solution of an overdetermined system of linear equations subject to the same constraints. Efficient solutions are obtained using linear programming techniques. Numerical results and comments are given.     

An alternative proof of Lickorish–Wallace theorem

We introduce the concept of s-distance of an unstabilized Heegaard splitting. We prove if a 3-manifold admits an unstabilized genus g Heegaard splitting with s-distance m  , then surgery on some (m−1)$(m-1)$ components link may produce a 3-manifold which admits a stabilized genus g Heegaard splitting. We also give an alternative proof of the fundamental theorem of surgery theory, which states that every closed orientable 3-manifold is obtained by surgery on some link in 3-sphere.     

Surface tension of dimethyl ether + propane from 243 to 333 K

The surface tension of the binary refrigerant mixture dimethyl ether (RE170)(1) + propane (R290)(2) at three mass fraction of w₁=0.3007,0.4975 ??and ??0.6949$w_1=\mathrm{0.3007,0.4975}\text{\hspace{0.17em}??}\text{and}\text{\hspace{0.17em}??}0.6949$ was measured in the temperature range from 243 to 333 K with a differential capillary rise method. The uncertainties of the measurement of the temperature and the surface tension were estimated to be within ±10 mK and ±0.2 mN m⁻¹, respectively. A correlation for the surface tension of the binary refrigerant mixture RE170 + R290 was developed as a function of the composition.     

Improvement of magnetic intergranular isolation and evaluation of read/write characteristics on SmCo5 perpendicular magnetic thin films

SmCo₅ alloy is a promising candidate for ultra-high-density perpendicular magnetic recording (PMR) media because of its high uniaxial magnetocrystalline anisotropy K_u of more than 1.1×10⁸ erg/cm³. Previously, we successfully achieved high K_u in a sputter-deposited SmCo₅ thin film by introducing a Cu/Ti dual underlayer. However, in order to apply the SmCo₅ films to practical PMR media, it is necessary to decrease medium noise. A granulated magnetic film comprising of small and magnetically decoupled grains is effective in reducing the medium noise. In this paper, we have proposed a new granular film that is fabricated by partial thermodiffusion of Cu between the Sm-Co continuous layer and the Cu underlayer, which is granulated using compositional segregation caused by the addition of Ta₂O₅. We have analyzed the magnetic properties, magnetic domain size, and magnetization reversal process of the proposed SmCo₅ film. The magnetic domain size decreased and the magnetization reversal process changed from the magnetic-wall-motion mode to a coherent rotation mode to some extent on isolation of magnetic grains. The read/write characteristics of granulated SmCo₅ double-layered media were also evaluated. The medium noise decreased and the signal-to-noise ratio increased for the granulated double-layered (PMR) medium.     

Constraints on dark energy and modified gravity models by the Cosmological Redshift Drift test

We study cosmological constraints on the various accelerating models of the universe using the time evolution of the cosmological redshift of distant sources. The important characteristic of this test is that it directly probes the expansion history of the universe. In this work we analyze the various models of the universe which can explain the late time acceleration, within the framework of General Theory of Relativity (GR) (XCDM, scalar field potentials) and beyond GR (f(R)$f(R)$ gravity model).     

Surface‐enhanced resonance Raman spectroscopic characterization of cytochrome c immobilized on 2‐mercaptoethanesulfonate monolayers on silver

Single‐component self‐assembled monolayers (SAMs) of mercaptoethanesulfonate (MES) on Ag surfaces were studied with surface‐enhanced resonance Raman scattering (SERRS) spectroscopy with a view to their application to immobilize (ferro)cytochrome c (cyt c). SERS studies revealed that MES molecules adopt primarily trans (T) conformation even at early stages of the SAM growth and over wide range of pH values. High accessibility of the negatively charged groups for (bio)molecules in solution makes single‐component MES SAMs suitable linkage monolayers for electrostatic attachment of cyt c, which was verified with SERRS. Cyt c was successfully anchored to MES‐coated Ag at natural (∼5), neutral, and isoelectric point (10.6) pH. At pH = 7.0 and 10.6, SERRS bands characteristic of native six‐coordinated low‐spin (6cLS) heme iron configuration were detected. Lack of buffering resulted in additional appearance of five‐coordinated high‐spin (5cHS) SERRS markers and the presence of bands indicating ferric ion. An electrostatic attraction between protein and SAM was confirmed to exclude the hydrophobic interactions involved in cyt c binding. Cyt c attached to MES SAM on Ag was found to be electroactive at neutral pH, and protein oxidation was assisted with reversible conversion of 6cLS to the non‐native 5cHS state. Alteration of heme orientation deduced from SERRS spectra upon change of redox state allowed us to propose the protein dynamics as the electron transfer rate‐limiting step. Copyright © 2010 John Wiley & Sons, Ltd.     

Assessment of cardiac iron by MRI susceptometry and R2* in patients with thalassemia

A magnetic resonance imaging cardiac magnetic susceptometry (MRI-CS) technique for assessing cardiac tissue iron concentration based on phase mapping was developed. Normal control subjects (n=9) and thalassemia patients (n=13) receiving long-term blood transfusion therapy underwent MRI-CS and MRI measurements of the cardiac relaxation rate R2*. Using MRI-CS, subepicardium and subendocardium iron concentrations were quantified exploiting the hemosiderin/ferritin iron specific magnetic susceptibility. The average of subepicardium and subendocardium iron concentrations and R2* of the septum were found to be strongly correlated (r=0.96, P<.0001), and linear regression analysis yielded CIC (μg Fe/g_{wet tissue})=(6.4±0.4)·R2* _septum (s⁻¹) − (120±40). The results demonstrated that septal R2* indeed measures cardiac iron level.