Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Limit theorems for sequences of random trees

We consider a random tree and introduce a metric in the space of trees to define the ""mean tree"" as the tree minimizing the average distance to the random tree. When the resulting metric space is compact we have laws of large numbers and central limit theorems for sequence of independent identically distributed random trees. As application we propose tests to check if two samples of random trees have the same law.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Acanthoscurrin Fragment 101-132: Total Synthesis at 60 degrees C of a Novel Difficult Sequence

Glycine-rich proteins (GRP), serve a variety of biological functions. Acanthoscurrin is an antimicrobial GRP isolated front hemocytes-of the Brazilian spider Acanthoscurria gomesiana. Aiming to contribute to the knowledge of the secondary structure and stepwise solid-phase synthesis of GRPs` glycine-rich domains, we attempted to prepare G(101)GGLGGGRGGGYG(113) GGGGYGGGYG(123)GGy(126)GGGKYK(132)-NH(2), acanthoscurrin C-terminal amidated fragment. Although a theoretical prediction did not indicate high aggregation potential for this peptide, repetitive incomplete aminoacylations were observed after incorporating Tyr(126) to the growing peptide-MBHA resin (Boc chemistry) at 60 degrees C. The problem was not solved by varying the coupling reagents or solvents, adding chaotropic salts to the reaction media or changing the resin/chemistry (Rink amide resin/Fmoc chemistry). Some improvement was mode when CLEAR amide resin (Fmoc chemistry) was 32 used, as it allowed for obtaining fragment (G(113)-K(132) NIR-FT-Raman spectra collected for samples of the growing peptide-MBHA, -Rink amide resin and -CLEAR amide resin revealed the presence of beta-sheet structures. Only the combination of CLEAR-amide resin, 60 degrees C, Fmoc-(Fmoc-Hmb)Gly-OH and LiCl (the last two used alternately) was able to inhibit the phenomenon, as proven by NIR-FT-Raman analysis of the growing peptide-resin, allowing the total synthesis of desired 132 fragment Gly(101)-K(132). In summary, this work describes a new difficult sequence, contributes to understanding stepwise solid-phase synthesis of this type of peptide and shows that, at least while protected and linked to a resin, this GRPs glycine-rich motif presents all early tendency to assume beta-sheet structures. (c) 2008 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 92: 65-75, 2009.

Lithium butylchalcogenolate induced Michael-aldol tandem sequence: easy and rapid access to highly functionalized organochalcogenides and unsaturated compounds

Lithium ""butylchalcogenolates are generated in situ by reacting the elements (S, Se, and Te) with (n)butyl-lithium at 0 degrees C. Reaction of the lithium alkylchalcogenolates with activated alkenes and aldehydes gives the corresponding aldol adducts. The selenium-containing products give Morita-Baylis-Hillman adducts after the oxidation/elimination of the selenoxide. The whole sequence can be performed in a one-pot procedure. (C) 2009 Elsevier Ltd. All rights reserved.

Fast Acquisition of (13)C NMR Spectra using the Steady-state Free Precession Sequence

In this paper, we show that the steady-state free precession sequence can be used to acquire (13)C high-resolution nuclear magnetic resonance spectra and applied to qualitative analysis. The analysis of brucine sample using this sequence with 60 degrees flip angle and time interval between pulses equal to 300 ms (acquisition time, 299.7 ms; recycle delay, 300 ms) resulted in spectrum with twofold enhancement in signal-to-noise ratio, when compared to standard (13)C sequence. This gain was better when a much shorter time interval between pulses (100 ms) was applied. The result obtained was more than fivefold enhancement in signal-to-noise ratio, equivalent to more than 20-fold reduction in total data recording time. However, this short time interval between pulses produces a spectrum with severe phase and truncation anomalies. We demonstrated that these anomalies can be minimized by applying an appropriate apodization function and plotting the spectrum in the magnitude mode.