Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Selectively protected galactose derivatives for the synthesis of branched oligosaccharides

Synthesis and characterization of several new anomerically pure galactose derivatives, based on simple and effective protective group manipulations of benzyl β-d-galactopyranoside, are reported. The monosaccharides described contain selectively protected/deprotected hydroxyl functionalities at their 1,2,3,4- and 6-positions rendering them useful as building blocks for construction of branched oligosaccharides.     

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

Riemannian manifolds in noncommutative geometry

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c${}^c$ manifolds; and conversely, in the presence of a spin^c${}^c$ structure. We also show how to obtain an analogue of Kasparov’s fundamental class for a Riemannian manifold, and the associated notion of Poincaré duality. Along the way we clarify the bimodule and first-order conditions for spectral triples.     

Vacuum ultraviolet-induced surface modification of cyclo-olefin polymer substrates for photochemical activation bonding

The surface of cyclo-olefin polymer (COP) was treated with vacuum ultraviolet (VUV) light at 172 nm wavelength to improve the wettability and adhesion properties. Through VUV treatment in air, the terminal groups of the COP surface were oxidized into oxygen functional groups, containing CO, CO, and COO components, making the COP surface hydrophilic. The extent of oxygenation was evaluated by XPS and FTIR-ATR spectra, and it was shown that the surface properties, hydrophilicity, and functionalization were dependent on both VUV irradiation distance and irradiation time, which have an effect on the concentration of oxygen functional groups. VUV-light treatment with a short irradiation distance was more effective in introducing oxygen functional groups.     

Observation of the exchange spring behavior in hard-soft-ferrite nanocomposite

Nanocomposite of hard (BaFe₁₂O₁₉) and soft ferrite (Ni_0.8Zn_0.2Fe₂O₄) are prepared by the mixing of the individual ferrite components at appropriate ratio and subsequent heat treatment. Initially the microstructure of the individual phases is controlled by suitable processing. We have observed the exchange spring behavior in the soft-hard ferrite composite for the first time by tailoring the particle size of the individual phases and by suitable thermal treatment of the composite. It is found that the exchange interaction dominates over the dipolar interaction for smaller particle sizes of the soft ferrite. The magnetization of the composite showed hysteresis loop that is characteristic of the exchange spring system. This gives experimental proof for some theoretical modeling as well as paves way for developing magnet with higher (BH)_max product based on ferrites.     

Subgroups of index 4 of the 2-dimensional space groups

There are 281 subgroups of index 4 for the 17 types of 2-dimension space groups: p1:7, p2:31, pm:19, pg:7, cm:11, p2mm:67, p2mg:23, p2gg:11, c2mm:31, p4:11, p4mm:31, p4gm:11, p3:4, p3m1:4, p31m:4, p6:4, p6mm:5. Every subgroup has been identified by its conventional cell disposition with respect to the conventional cell of the starting group. These subgroups may be arranged in 96 automorphism classes and 184 conjugation classes according to their starting groups.     

Measurement of στ product of solid state laser materials by an alternative method: Application to Nd3+ doped YVO4 crystal for 4 F 3/2→4 I 11/2 transition

In this paper an alternative approach for measurement of στ product for ⁴ F _3/2→⁴ I _11/2 transition of Nd³⁺ doped YVO₄ crystal is reported. In this method a microchip laser is formed by keeping a small piece of the sample in plane-plane resonator and a diode laser (808 nm) is used for pumping. The pump power induced thermal lensing effect is used to make the cavity stable. The cavity mode area is estimated by measuring the thermal lens focal length at the threshold and the average pump area is measured by Gaussian fit to the intensity profiles of the pump beam. The value of στ product of Nd:YVO₄ crystal obtained by this method is within 10% of the reported values. The advantage of this method is that it is a simple method for direct measurement of στ product of laser crystals.     

Effects of the Synergy of Hardness and Resilience on the Akron Abrasion Properties of SBR Vulcanizates

The hardness (H) and resilience (R) of rubber vulcanizates were combined together in this paper, named as hardness–resilience product (H⁴R), and its relationship with the Akron abrasion loss was investigated using various styrene-butadiene rubber (SBR) vulcanizates possessing specific hardness and resilience characteristics as samples. For the unfilled SBR vulcanizates with different chain microstructure, possessing high elastic resilience and low hardness, the results showed that their Akron abrasion loss had a good linear relationship with the log(H⁴100R). This linear relationship also occurred when these SBRs were filled with 50 phr carbon black. For two particular types of SBR, after being filled with different fractions of carbon black and aged for different times, all their Akron abrasion losses (including unaged, aged for 24 h, and aged for 48 h) also had a good linear relationship with the log(H⁴100R). However, this linear relationship weakened for one of the SBRs after being aged for 48 h. In the high H⁴R region (the carbon black fractions being 60 and 70 phr), the data obviously deviated from the fitting curve due to the high hardness of the aged vulcanizates. However, after being filled with 50 phr of various kinds of carbon blacks, the relationships between abrasion loss and log(H⁴100R) were also approximately linear, with the correlation coefficient of the fitting curves being 0.99966 and 0.99878, respectively, for the two types of SBR.     

On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.