Fast iterative methods for symmetric sinc-Galerkin systems

The symmetric sinc-Galerkin method developed by Lund, when appliedto the second-order self-adjoint boundary value problem, givesrise to a symmetric coefficient matrix has a special structureso that it can be advantageously used in solving the discretesystem. In this paper, we employ the preconditioned conjugategradient method with banded matrices as preconditioners. Weprove that the condition number of the preconditioned matrixis uniformly bounded by a constant independent of the size ofthe matrix. In particular, we show that the solution of an n-by-ndiscrete symmetric sinc-Galerkin system can be obtained in O(nlog n) operations. We also extend our method to the self-adjointelliptic partial differential equation. Numerical results aregiven to illustrate the effectiveness of our fast iterativesolvers.     

Viscometric,light scattering,and size‐exclusion chromatography studies on the structural changes of aqueous poly(vinyl alcohol) induced by γ‐ray irradiation

The crosslinking processes of aqueous poly(vinyl alcohol) (PVA) by γ‐ray irradiation were studied by viscometry, dynamic and static light scattering (DLS and SLS), as well as size exclusion chromatography (SEC). Increases in the intrinsic viscosity ([η]), molecular weight (M_w), hydrodynamic radius (R_h), and radius of gyration (R_g), and a decrease in second virial coefficient (A₂) were observed after γ‐ray irradiation. However, both the values of [η] and A₂ for irradiated PVA fell below the data of unirradiated PVA solutions, suggesting a conformational change of PVA chains after γ‐ray irradiation. This structural change of PVA as a result of γ‐ray irradiation was also indicated by the decreases in R_g/R_h from 1.5 to 1.39 by SLS and DLS, and in Mark–Houwink exponent α_η from 0.54 to 0.26 by SEC‐Viscometry. The broadening of the M_w distribution (MWD) as indicated by the polydispersity index increased from 2.2 to 6.5 because of γ‐ray irradiation. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 214–221, 2000     

(e, 3e) Differential cross section of He (21 S) and He (23 S)

The angular distribution of the five-fold differential cross section for the electron impact double ionization of He (2¹ S) and He (2³ S) has been studied. The kinematical conditions for maxima/minima in the angular distribution for the two cases have been compared. The two-step process for the double ionization is found to contribute very little in the triplet case.     

Microwave absorption studies of MgB2 superconductor

Microwave absorption studies have been carried out on MgB₂ superconductor using a standard X-band EPR spectrometer. The modulated low-field microwave absorption signals recorded for polycrystalline (grain size ∼ 10 μm) samples suggested the absence of weak-link character. The field dependent direct microwave absorption has been found to obey a ✓H dependence with two different slopes, which indicated a transition from strongly pinned lattice to flux flow regime.     

Potentiometric titration behavior of poly(acrylic acid) within a cross-linked polymer network having amide groups

This study aimed to investigate the effect of COOH group distribution within a polymer network having amide groups, with which the COOH could form hydrogen bonds. We employed here two polyelectrolyte gels composed of N-isopropylacrylamide (NIPA) networks, either copolymerized with acrylic acid (AA) or within which poly(acrylic acid) (PAA) was entrapped. Both gels (AA–NIPA ∼ 1:4 mol/mol) were prepared by aqueous red-ox polymerization with N,N’-methylenebisacrylamide as the cross-linker. Finely divided gels in NaCl solutions (0.025 and 0.1 M) were titrated with NaOH and back-titrated with HCl at 25 °C. The results of the copolymer gel (CG) agreed well with those of a linear copolymer and a nanoscale gel which had a similar AA content to CG. However, marked differences were observed in the titration behaviors of the AA-copolymerized and PAA-entrapped gels, mainly due to the hydrogen bonding between the entrapped PAA chain and its surrounding NIPA network.     

Light scattering study of complex formation between protein and polyelectrolyte at various ionic strengths

Formation of protein-polyelectrolyte complexes (PPCs) between bovine serum albumin (BSA) and potassium poly (vinyl alcohol) sulfate (KPVS) was studied at pH 3 as a function of ionic strength. Turbidimetric titration was employed by a combination of dynamic light scattering (DLS) and electrophoretic light scattering (ELS). The formal charge (Z(PPC)) of the resulting PPCs at different ionic strengths were estimated from ELS data by assuming the free draining and the non-free draining model. The radius of a BSA molecule in the complex was used in the former model for calculation of Z(PPC) with the Henry's equation, while in the latter case the hydrodynamic radius of a PPC particle determined from DLS was employed. The results obtained were compared with the Z(PPC) values calculated using a relation of Z(PPC)=n(b)Z(BSA)+alphaZ(KPVS), where Z(BSA) (> or =0) and Z(KPVS) (< or =0) denote the formal charge of BSA and KPVS, respectively. Moreover, n(b) is the number of bound proteins per complex composed of alpha polymer chains. It was suggested that the PPC between BSA and KPVS behaves as a free draining molecule during the electrophoresis, at least at a high ionic strength. Also suggested is that the PPC formation at low ionic strength follows a 1:1 stoichiometry in the charge neutralization.     

Thermo-sensitive N-n-propylacrylamide gels

Thermo-sensitive gels were prepared by irradiating aqueous solutions of poly(N-n-propylacrylamide) (NNPA) and its copolymers with acrylic acid (AA) with γ-rays from a ⁶⁰Co source. The equilibrium swelling volume of the gel in water was determined as a function of temperature. NNPA gel showed a discontinuous and reversible volume phase transition. The transition temperature and the volume change at the transition decreased with irradiation time. The transition temperature was approximately 12°C lower than that of poly(N-isopropylacrylamide) gel. A discontinuous volume transition was also observed in the copolymer gels of NNPA and AA. The dependence of the transition temperature on the concentration of carboxyl groups revealed a marked difference depending on whether they were protonated or dissociated. For gels having side groups of COONa, the transition temperature rose and the volume change at the transition was elevated as the COONa concentration increased. In contrast, an increase in the COOH concentration resulted in a decrease in the transition temperature. These results are discussed in terms of an equation of state constructed based on scaling theory.     

Electrochemically induced aggregation of intra-particle cationic nanogel complexes with a stoichiometric amount of bound polyanions

The present study aimed to see the effect of an applied electric field on the stability of a colloid system in which overall electroneutrality is maintained in a metastable state. We employed two polyelectrolyte nanogels (PENG) based on N,N′-methylenebisacrylamide (MBA)-cross-linked terpolymer composed of N-isopropylacrylamide (NIPA), acrylic acid (AAc) and 1-vinylimidazole (VI) and MBA-cross-linked copolymer of NIPA and VI. The complexes of these PENG particles with potassium poly(vinyl alcohol) sulfate (KPVS) were formed in an aqueous HCl solution (1 mM, pH 3) which allows a complete ionization of the PENG-fixed imidazole groups. The amount of KPVS anions was adjusted so as to become equivalent to that of PENG-fixed cations. The complex dispersion was electrolyzed in a simple cell made of a glass tube. A fine platinum wire was used as an electrode for both cathode and anode. It was suggested that the electrochemically induced increase in pH in the cathodic side causes the aggregation of the complex particles due to a partial dissociation of the bound polyanions from the complex.     

Effects of lipopolysaccharide-induced inflammation on expression of growth-associated genes by corticospinal neurons

Background  

Inflammation around cell bodies of primary sensory neurons and retinal ganglion cells enhances expression of neuronal growth-associated genes and stimulates axonal regeneration. We have asked if inflammation would have similar effects on corticospinal neurons, which normally show little response to spinal cord injury. Lipopolysaccharide (LPS) was applied onto the pial surface of the motor cortex of adult rats with or without concomitant injury of the corticospinal tract at C4. Inflammation around corticospinal tract cell bodies in the motor cortex was assessed by immunohistochemistry for OX42 (a microglia and macrophage marker). Expression of growth-associated genes c-jun, ATF3, SCG10 and GAP-43 was investigated by immunohistochemistry or in situ hybridisation.     

Conductometric and light scattering studies on the complexation between cationic polyelectrolyte nanogel and anionic polyion

This work aims to provide a basic understanding of the water dispersibility of a 1:1 stoichiometric polyelectrolyte complex (SPEC) in water in the absence of low-molecular-weight salts. We studied the complexation of a linear polyanion, potassium poly(vinyl alcohol sulfate) (KPVS), with a cationic polyelectrolyte nanogel (CPENG) composed of a lightly cross-linked copolymer of N-isopropylacrylamide and 1-vinylimidazole, in an aqueous salt-free solution (pH 3 and 25 °C), as a function of the molar mixing ratio (Mmr) of anionic to cationic groups. Also studied for comparison was the complexation of KPVS with poly(diallyldimethylammonium chloride) (PDDA), which is a standard reaction in colloid titration. Turbidimetric and conductometric measurements were used in combination of dynamic light scattering (DLS). An abrupt increase of turbidity curve and a break of conductivity curve were observed at Mmr =1 when KPVS was added to the CPENG or PDDA solution, indicating the formation of SPEC. All the complexes formed at Mmr ≤ 1 were water-dispersible and hence characterized by DLS. The CONTIN analysis of DLS data showed that (i) an increase of Mmr causes a decrease of the hydrodynamic radius (R(h)) of the nanogel complex particle but (ii) the R(h) of the PDDA complex remains unchanged at Mmr < 0.8. Taking these into account, we discussed the conductometric results in terms of the random model (RM) and all-or-none model (AONM) in polyelectrolyte complex formations. It was found that KPVS and PDDA yield a water-dispersible SPEC particle at each Mmr, accompanying the uptake of counterions (K(+) and Cl(-)) by the complex. This uptake amount was about 7% of the stoichiometric release of the counterions. In the nanogel system, a complete release of the counterions was observed at Mmr < 0.2 at which one or two KPVS chains were bound to a CPENG particle, but further KPVS binding led to about 20% of the counterion uptake to maintain electroneutrality. Thus, we suggest that the counterion uptake becomes a key factor to understand the water dispersibility of SPEC particles.