Birational extensions of a noetherian UFD

We construct two nonisomorphic groups G and Q of order 96 which have isomorphic tables of marks, but such that the centre of G has order 8 and the centre of Q has order 4. We also note that G has an abelian subgroup of order 48, whereas Q has no abelian subgroup of that order. This also leads us to conclude that this isomorphism of tables of marks does not preserve normalizers.     

Invariance property of anisotropic hele-shaw flows

The invariance of the noncoincidence set for the varia-tional inequalities govening anisotropic Hele-Shaw flows is proven by introducing weighted elliptic quadrature domains.     

Fictitious domain method with penalty for an incompressible fluid

Fictitious domain method shows great advantages when handling problems with complex and constantly varying domains. In this article, we propose an algorithm which extends the fictitious domain method by introducing penalties. Test results with the numerical examples of backward facing step problem and the flow around steady and dynamic cylinder problem show that the algorithm we propose is highly efficient for solving incompressible fluid problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Terahertz time domain spectroscopy of hydrothermally synthesized boehmite and ammonium dawsonite nanostructures

The frequency dependent optical and dielectric properties of boehmite (AlOOH) and ammonium aluminum carbonate hydroxide (AACH) nanostructures, prepared at different temperatures via hydrothermal synthesis, were studied by using terahertz time domain spectroscopy (THz-TDS). The complex refractive indices, absorption coefficients and complex dielectric constants were determined and compared for different synthesis temperatures. X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) were also performed to confirm the formation of boehmite and AACH. Scanning electron microscopy (SEM) was performed to study the morphology of nanostructures. The study reveals the formation of AACH at higher temperatures and decrease in refractive index with increasing synthesis temperature. The higher absorption coefficient and lower refractive index and dielectric constant were observed for AACH than for boehmite.     

Parallelization of the algorithm of asymptotic partial domain decomposition in thin tube structures

The method of asymptotic partial domain decomposition for thin tube structures (finite unions of thin cylinders) is revisited. Its application to the Newtonian and non-Newtonian flows in great systems of vessels is considered. The possibility of a parallelization of its algorithm is discussed for linear and non-linear models.     

A study of the stripe domain phase at the spin reorientation transition of two-dimensional magnetic system

Stripe domain phase in a two-dimensional magnetic system was studied using model calculation and Monte-Carlo simulation in the spin reorientation transition (SRT) region. We find that near the SRT point the stripe domains evolve into a static spin wave structure with a fractional in-plane magnetization along the stripe direction and a fractional out-of-plane magnetization in a sinusoidal form. With increase in the uniaxial perpendicular anisotropy, both the wavelength and the height of the static spin wave increase slowly until the saturation of the wave height, after which the stripe width increases exponentially with the magnetic anisotropy. Our theoretical result is in good agreement with experimental observations.     

Temperature‐dependent location of a weakly segregated block copolymer in binary blends of block copolymers

The phase behaviors of binary blends of poly(styrene‐b‐butadiene) block copolymers were investigated by a small‐angle X‐ray scattering technique. The blends were composed of weakly segregated one in a random micellar phase and the other in a cylindrical phase with similar molecular weights and complementary volume fractions. Morphologies, domain spacings, and order–disorder transition temperatures of the blends indicated that the junctions of the constituent block copolymers share the interface at low temperatures. The domain spacing decreased as temperature increased in a blend with a small amount of the weakly segregated block copolymer. In the cases of the blends with a large amount of the weakly segregated constituent, domain spacing increased with increasing temperature. These results implied that some of the weakly segregated block copolymer moved from the interface to one microdomain at higher temperatures. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 470–476     

Vector Bundle-Valued Poisson and Cauchy Kernel Functions on Classical Domains

In this paper we investigate the vector bundle-valued Cauchy and Poisson kernel functions. We compute explicitly matrix-valued eigenfunctions of an invariant differential operator on the classical domain of Type I. Furthermore, a special choice of a vector bundle gives us a matrix-valued Cauchy and Poisson kernel function which satisfies the matrix-valued Laplacian operator on the classical domain of Type I.     

Gravitational Field of Spherical Domain Walls

In this paper we have considered a spherically symmetric domain wall with non vanishing stress component in the direction perpendicular to the plane of the wall. The exact solutions are obtained using functional separability of metric coefficients. Also we have studied the motion of the test particles in different situations.