Pareto Frontier for the time-energy cost vector to an Earth-Moon transfer orbit using the patched-conic approximation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Alternative transfer to the Earth-Moon Lagrangian points L4 and L5 using lunar gravity assist

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Photoelastic determination of stress intensity factors in patched cracked plates

n this paper, the influence of patch parameters on stress intensity factors in edge cracked plates is studied by employing transmission photoelasticity. Edge cracked plates made of photo-elastic material are patched on one side only by E glass-epoxy and carbon-epoxy unidirectional composites. The patch is located on the crack in such a way that the crack tip is not covered. Magnified isochromatic fringes are obtained by using a projection microscope of magnification 50, converted into a polariscope. Irwin's method is used to compute stress intensity factors from photoelastic data. The reduction in stress intensity factors is presented in graphical form as a function of patch parameters, namely stiffness, location and length. An empirical equation connecting reduction in stress intensity factor and these patch parameters is presented.

Analytical estimation of stress intensity factors in patched cracked plates

The fatigue and fracture performance of a cracked plate can be substantially improved by providing patches as reinforcements. The effectiveness of the patches is related to the reduction they cause in the stress intensity factor (SIF) of the crack. So, for reliable design, one needs an accurate evaluation of the SIF in terms of the crack, patch and adhesive parameters. In this investigation, a centrally cracked large plate with a pair of symmetric bonded narrow patches, oriented normally to the crack line, is analysed by a continuum approach. The narrow patches are treated as transversely flexible line members. The formulation leads to an integral equation which is solved numerically using point collocation. The convergence is rapid. It is found that substantial reductions in SIF are possible with practicable patch dimensions and locations. The patch is more effective when placed on the crack than ahead of the crack. The present analysis indicates that a little distance inwards of the crack tip, not the crack tip itself, is the ideal location, for the patch.

Constructing a wire-frame from views on arbitrary view planes for objects with conic sections inclined to all view planes

A new and efficient approach to construct a 3D wire-frame of an object from its orthographic projections is described. The input projections can be two or more and can include regular and complete auxiliary views. Each view may contain linear, circular and other conic sections. The output is a 3D wire-frame that is consistent with the input views. The approach can handle auxiliary views containing curved edges. This generality derives from a new technique to construct 3D vertices from the input 2D vertices (as opposed to matching coordinates that is prevalent in current art). 3D vertices are constructed by projecting the 2D vertices in a pair of views on the common line of the two views. The construction of 3D edges also does not require the addition of silhouette and tangential vertices and subsequently splitting edges in the views. The concepts of complete edges and n-tuples are introduced to obviate this need. Entities corresponding to the 3D edge in each view are first identified and the 3D edges are then constructed from the information available with the matching 2D edges. This allows the algorithm to handle conic sections that are not parallel to any of the viewing directions. The localization of effort in constructing 3D edges is the source of efficiency of the construction algorithm as it does not process all potential 3D edges. Working of the algorithm on typical drawings is illustrated. (C) 2011 Elsevier Ltd. All rights reserved.

On the Behavior of the Homogeneous Self-Dual Model for Conic Convex Optimization

There is a natural norm associated with a starting point of the homogeneous self-dual (HSD) embedding model for conic convex optimization. In this norm two measures of the HSD model’s behavior are precisely controlled independent of the problem instance: (i) the sizes of ε-optimal solutions, and (ii) the maximum distance of ε-optimal solutions to the boundary of the cone of the HSD variables. This norm is also useful in developing a stopping-rule theory for HSD-based interior-point methods such as SeDuMi. Under mild assumptions, we show that a standard stopping rule implicitly involves the sum of the sizes of the ε-optimal primal and dual solutions, as well as the size of the initial primal and dual infeasibility residuals. This theory suggests possible criteria for developing starting points for the homogeneous self-dual model that might improve the resulting solution time in practice

Darboux invariants for planar polynomial differential systems having an invariant conic

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Immunohistochemical Analysis of Human Homologue of Drosophila Patched (PTCH) in Dental Follicles of Impacted Third Molars

This study investigated the immunodetection of PTCH in epithelial components of dental follicles associated with impacted third molars without radiographic signs of pathosis. One hundred and five specimens of dental follicles associated with impacted third molars with incomplete rhizogenesis (between Nolla's stage 6 and 9) were surgically removed from 56 patients. Epithelial cell proliferation was determined by using immunohistochemical labeling. Statistical analysis was performed using Fisher exact test and a level of significance of 5%. Of the 105 dental follicles collected, 3 were PTCH-positive. The specimens with squamous metaplasia and epithelial hyperplasia had higher rates of positivity for PTCH, as well as those with active remnants of odontogenic epithelium. This study suggests that the odontogenic cells of the dental follicle might be proliferating during the rhizogenesis, while the squamous metaplasia and hyperplasia of the epithelial lining and proliferative odontogenic epithelial rests show the differentiation potential of dental follicles.

Characterization of two patched receptors for the vertebrate hedgehog protein family

The multitransmembrane protein Patched (PTCH) is the receptor for Sonic Hedgehog (Shh), a secreted molecule implicated in the formation of embryonic structures and in tumorigenesis. Current models suggest that binding of Shh to PTCH prevents the normal inhibition of the seven-transmembrane-protein Smoothened (SMO) by PTCH. According to this model, the inhibition of SMO signaling is relieved after mutational inactivation of PTCH in the basal cell nevus syndrome. Recently, PTCH2, a molecule with sequence homology to PTCH, has been identified. To characterize both PTCH molecules with respect to the various Hedgehog proteins, we have isolated the human PTCH2 gene. Biochemical analysis of PTCH and PTCH2 shows that they both bind to all hedgehog family members with similar affinity and that they can form a complex with SMO. However, the expression patterns of PTCH and PTCH2 do not fully overlap. While PTCH is expressed throughout the mouse embryo, PTCH2 is found at high levels in the skin and in spermatocytes. Because Desert Hedgehog (Dhh) is expressed specifically in the testis and is required for germ cell development, it is likely that PTCH2 mediates its activity in vivo. Chromosomal localization of PTCH2 places it on chromosome 1p33–34, a region deleted in some germ cell tumors, raising the possibility that PTCH2 may be a tumor suppressor in Dhh target cells.

Sonic hedgehog protein signals not as a hydrolytic enzyme but as an apparent ligand for Patched

The amino-terminal signaling domain of the Sonic hedgehog secreted protein (Shh-N), which derives from the Shh precursor through an autoprocessing reaction mediated by the carboxyl-terminal domain, executes multiple functions in embryonic tissue patterning, including induction of ventral and suppression of dorsal cell types in the developing neural tube. An apparent catalytic site within Shh-N is suggested by structural homology to a bacterial carboxypeptidase. We demonstrate here that alteration of residues presumed to be critical for a hydrolytic activity does not cause a loss of inductive activity, thus ruling out catalysis by Shh-N as a requirement for signaling. We favor the alternative, that Shh-N functions primarily as a ligand for the putative receptor Patched (Ptc). This possibility is supported by new evidence for direct binding of Shh-N to Ptc and by a strong correlation between the affinity of Ptc-binding and the signaling potency of Shh-N protein variants carrying alterations of conserved residues in a particular region of the protein surface. These results together suggest that direct Shh-N binding to Ptc is a critical event in transduction of the Shh-N signal.

Regulation of patched by sonic hedgehog in the developing neural tube.

Ventral cell fates in the central nervous system are induced by Sonic hedgehog, a homolog of hedgehog, a secreted Drosophila protein. In the central nervous system, Sonic hedgehog has been identified as the signal inducing floor plate, motor neurons, and dopaminergic neurons. Sonic hedgehog is also involved in the induction of ventral cell type in the developing somites. ptc is a key gene in the Drosophila hedgehog signaling pathway where it is involved in transducing the hedgehog signal and is also a transcriptional target of the signal. PTC, a vertebrate homolog of this Drosophila gene, is genetically downstream of Sonic hedgehog (Shh) in the limb bud. We analyze PTC expression during chicken neural and somite development and find it expressed in all regions of these tissues known to be responsive to Sonic hedgehog signal. As in the limb bud, ectopic expression of Sonic hedgehog leads to ectopic induction of PTC in the neural tube and paraxial mesoderm. This conservation of regulation allows us to use PTC as a marker for Sonic hedgehog response. The pattern of PTC expression suggests that Sonic hedgehog may play an inductive role in more dorsal regions of the neural tube than have been previously demonstrated. Examination of the pattern of PTC expression also suggests that PTC may act in a negative feedback loop to attenuate hedgehog signaling.

Osculation for conic fibrations.

Smooth projective surfaces fibered in conics over a smooth curve are investigated with respect to their k-th osculatory behavior. Due to the bound for the dimension of their osculating spaces they do not differ at all from a general surface for k = 2, while their structure plays a significant role for k >= 3. The dimension of the osculating space at any point is studied taking into account the possible existence of curves of low degree transverse to the fibers, and several examples are discussed to illustrate concretely the various situations arising in this analysis. As an application, a complete description of the osculatory behavior of Castelnuovo surfaces is given. The case k = 3 for del Pezzo surfaces is also discussed, completing the analysis done for k = 2 in a previous paper by the authors (2001). Moreover, for conic fibrations X subset of P-N whose k-th inflectional locus has the expected codimension, a precise description of this locus is provided in terms of Chern classes. In particular, for N = 8, it turns out that either X is hypo-osculating for k = 3, or its third inflectional locus is 1-dimensional