Geometric Mechanics of Curved Crease Origami

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations which allow us to generalize our analysis to study multiply folded structures

Homological algebra for Schwartz algebras of reductive p-adic groups

Let G be a reductive group over a non-Archimedean local field. Then the canonical functor from the derived category of smooth tempered representations of G to the derived category of all smooth representations of G is fully faithful. Here we consider representations on bornological vector spaces. As a consequence, if V and W are two tempered irreducible representations and if V or W is square-integrable, then Ext_G^n(V,W) vanishes for all n>0. We use this to prove in full generality a formula for the formal dimension of square-integrable representations due to Schneider and Stuhler.Comment: 34 pages, version 2 contains, in addition, a discussion about formal dimensions from the point of view of Schwartz algebras and von Neumann algebra

Automorphisms of graphs of cyclic splittings of free groups

We prove that any isometry of the graph of cyclic splittings of a finitely generated free group $F_N$ of rank $N\ge 3$ is induced by an outer automorphism of $F_N$. The same statement also applies to the graphs of maximally-cyclic splittings, and of very small splittings.Comment: 22 pages, 5 figures. Small modifications. To appear in Geometriae Dedicat

Abelian subgroups of Garside groups

In this paper, we show that for every abelian subgroup $H$ of a Garside group, some conjugate $g^{-1}Hg$ consists of ultra summit elements and the centralizer of $H$ is a finite index subgroup of the normalizer of $H$. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups.Comment: This article replaces our earlier preprint "Stable super summit sets in Garside groups", arXiv:math.GT/060258

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

Production of nanoparticles-in-microparticles by a double emulsion method : a comprehensive study

AbstractA method based on a double emulsion system (solid-in-water-in-oil-in-water) has been developed for the production of nanoparticles-in-microparticles (NIMs). The distribution of nanoparticles within the NIMs was explored using light and electron microscopy and through assessment of drug loading and release profiles. The extent of nanoparticle entrapment within the NIMs was found to be dependent on the state (wet vs. dry) in which the nanoparticles were introduced to the formulation. The technique was readily adaptable to produce NIMs of different morphologies. It is proposed that NIMs and this method to produce them have broad application in drug delivery research

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Information gaps for patients requiring craniotomy for benign brain lesion: a qualitative study

Doctor–patient communication in the setting of a life-threatening illness poses considerable challenges. This study aimed to determine the information needs of a subset of neurosurgical patients. Qualitative case study methodology was used. Twenty-five semi-structured interviews were conducted with ambulatory adult patients who had undergone surgery for a benign brain tumor, arteriovenous malformation, or unruptured aneurysm. Interviews were digitally audio recorded and transcribed, and the data subjected to thematic analysis. Six overarching themes emerged from the data: (1) the amount of information patients want varies; (2) the type of information needed is not limited to information about treatment options and risks; (3) patients engage in independent information seeking for a variety of reasons; (4) patients consider compassion from their surgeon as important; (5) direct communication with the surgeon post-operatively is very important; and (6) patients’ information needs are greatest post-operatively. Many patients felt that the amount and quality of information they received was not sufficient, particularly regarding post-operative recovery and long-term life issues, leading many to do their own research. The findings from this study emphasize the need for improved communication with patients so they can participate meaningfully in choices about their treatment, give a truly informed consent, and effectively participate in their own recovery

Effect of Manganese in Test Media on In Vitro Susceptibility of Enterobacteriaceae and Acinetobacter baumannii to Tigecycline

Item does not contain fulltextWe assessed the effect of increasing manganese concentrations in test media (0.001 to 1,024 mg/liter) on MICs of tigecycline. For both broth microdilution (BMD) and Etests, this effect was negligible for physiological concentrations, but MICs increased when concentrations exceeded 8 mg/liter. Susceptibility testing should be performed on media with standardized low manganese content.1 september 201