Effects of reaction conditions on the structure of graft copolymer

In order to advance the studies of radiation graft copolymerization, we have presented the theory of coupling graft copolymerization and apply it to the investigation of the grafting of methylmethacrylate on to pre-irradiated polystyrene.     

Shift-invariant bi-inner product functionals are inner products

Bi-inner product functionals generated by a pair of Bessel sequences of L² functions are introduced. It is shown that these functionals are constant multiples of the inner products of L² and l², if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L². The research of this author was supported by NSF Grant # DMS-95-05460 and ARO Contract #DAAH-04-95-10193, This author is currently visiting the Department of statistics, Stanford University, Stanford, CA 94305. The research of this author was supported by the Texas Coordinating Board of Higher Education under Grant # 999903-109.     

Two Brominated-sesquiterpene from Alga Laurencia Majuscula

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｒｅｄａｌｇａｏｆｇｅｎｕｓＬａｕｒｅｎｃｉａｉｓｗｅｌｌ ｋｎｏｗｎｔｏｂｅｕｓｅｄｔｏｐｒｏｄｕｃｅｔｅｒｐｅｎｏｉｄｓａｎｄＣ15ａｃｅｔｏｇｅｎｉ ｕｅ[1— 3] .ＷｅｉｎｖｅｓｔｉｇａｔｅｄｔｈｅｔｒｏｐｉｃａｌｒｅｄａｌｇａＬａｕ ｒｅｎｃｉａｍａｊｕｓｃｕｌａ ,ｃｏｌｌｅｔｅｄｆｒｏｍｔｈｅＸｉｓｈａＩｓｌａｎｄｓｉｎｔｈｅＳｏｕｔｈＣｈｉｎａＳｅａ ,ａｎｄｉｓｏｌａｔｅｄｎａｔｕｒａｌｌｙｏｃｃｕｒｒｉｎｇｔｒｉｃｙｃｌｅｓｅｓｑｕｉｔｅｒｐｅｎｅ ,ｐｏｌｙ…     

Stability of the Bose system in Bose-Fermi mixture with attraction between bosons and fermions

An effective Hamiltonian for the Bose system in the mixture of ultracold atomic clouds of bosons and fermions is obtained by integrating out the Fermi degrees of freedom. An instability of the Bose system is found in the case of attractive interaction between components that is in good agreement with an experiment on the bosonic ⁸⁷Rb and fermionic ⁴⁰K mixture.     

Modeling shear modulus distribution in magnetic resonance elastography with piecewise constant level sets

Magnetic resonance elastography (MRE) is designed for imaging the mechanical properties of soft tissues. However, the interpretation of shear modulus distribution is often confusing and cumbersome. For reliable evaluation, a common practice is to specify the regions of interest and consider regional elasticity. Such an experience-dependent protocol is susceptible to intrapersonal and interpersonal variability. In this study we propose to remodel shear modulus distribution with piecewise constant level sets by referring to the corresponding magnitude image. Optimal segmentation and registration are achieved by a new hybrid level set model comprised of alternating global and local region competitions. Experimental results on the simulated MRE data sets show that the mean error of elasticity reconstruction is 11.33% for local frequency estimation and 18.87% for algebraic inversion of differential equation. Piecewise constant level set modeling is effective to improve the quality of shear modulus distribution, and facilitates MRE analysis and interpretation.     

Matrix-valued symmetric templates for interpolatory surface subdivisions: I. Regular vertices

The objective of this paper is to introduce a general procedure for deriving interpolatory surface subdivision schemes with “symmetric subdivision templates” (SSTs) for regular vertices. While the precise definition of “symmetry” will be clarified in the paper, the property of SSTs is instrumental to facilitate application of the standard procedure for finding symmetric weights for taking weighted averages to accommodate extraordinary (or irregular) vertices in surface subdivisions, a topic to be studied in a continuation paper. By allowing the use of matrices as weights, the SSTs introduced in this paper may be constructed to overcome the size barrier limited to scalar-valued interpolatory subdivision templates, and thus avoiding the unnecessary surface oscillation artifacts. On the other hand, while the old vertices in a (scalar) interpolatory subdivision scheme do not require a subdivision template, we will see that this is not the case for the matrix-valued setting. Here, we employ the same definition of interpolation subdivisions as in the usual scalar consideration, simply by requiring the old vertices to be stationary in the definition of matrix-valued interpolatory subdivisions. Hence, there would be another complication when the templates are extended to accommodate extraordinary vertices if the template sizes are not small. In this paper, we show that even for C² interpolatory subdivisions, only one “ring” is sufficient in general, for both old and new vertices. For example, for 1-to-4 split C² interpolatory surface subdivisions, we obtain matrix-valued symmetric interpolatory subdivision templates (SISTs) for both triangular and quadrilateral meshes with sizes that agree with those of the Loop and Catmull–Clark schemes, respectively. Matrix-valued SISTs of similar sizes are also constructed for C² interpolatory and subdivision schemes in this paper. In addition to small template sizes, an obvious feature of matrix-valued weights is the flexibility for introducing shape-control parameters. Another significance is that, in contrast to the usual scalar setting, matrix-valued SISTs can be formulated in terms of the coefficient sequence of some vector refinement equation of interpolating bivariate C² splines with small support. For example, by modifying the spline function vectors introduced in our previous work [C.K. Chui, Q.T. Jiang, Surface subdivision schemes generated by refinable bivariate spline function vectors, Appl. Comput. Harmon. Anal. 15 (2003) 147–162; C.K. Chui, Q.T. Jiang, Refinable bivariate quartic and quintic C²-splines for quadrilateral subdivisions, Preprint, 2004], C² symmetric interpolatory subdivision schemes associated with refinement equations of C² cubic and quartic splines on the 6-directional and 4-directional meshes, respectively, are also constructed in this paper.     

An efficient and expeditious synthesis of di- and monosubstituted 2-aminoimidazoles

A microwave-assisted protocol was developed for the construction of di- and monosubstituted 2-aminoimidazoles. The two-step reaction involves the synthesis of N-(1H-imidazol-2-yl)acetamides from readily available alpha-haloketones and N-acetylguanidine, followed by deacetylation. Significant rate enhancement was observed for both steps of the protocol, and the overall reaction time was shortened to 20 min compared to 48 h of the conventional procedures. A representative set of di- and monosubstituted 2-aminoimidazoles was prepared using commercially available parallel reactors.