Lê–Greuel type formula for the Euler obstruction and applications

The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we establish several Lê–Greuel type formulas for germs f:(X,0)→(C,0) and g:(X,0)→(C,0). We give applications when g is a generic linear form and when f and g have isolated singularities.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

Temporal variation in egg-capsule deposition by Nassarius vibex (Gastropoda: Nassariidae)

The morphology and the deposition periods of egg capsules by the bruised nassa Nassarius vibex were investigated on two beaches located on the southeast coast of Brazil. The nassariids were associated with the charru mussel Mytella charruana, which forms beds on soft mud-bottoms. A total of 1558 capsules were collected, only from the fronds of the green alga Ulva lactuca, 859 for Camaroeiro Beach and 699 for Cidade Beach. The mean sizes of the egg capsules and numbers of eggs or larvae per capsule were similar on the two beaches, as were the periods of capsule deposition. At Camaroeiro Beach, capsules first appeared in May 2006, reached a peak in August 2006, and disappeared in December 2006. At Cidade Beach, the first capsules were recorded in July 2006, with a peak in August 2006. A second peak was also observed at this beach between January 2007 and April 2007. The two periods of deposition recorded at the latter beach may indicate two periods of recruitment in the same year for N. vibex. Regarding the influence of intertidal level on capsule deposition, there was a significant difference in the number of capsules between the levels at Camaroeiro Beach (F= 7.445, p<0.05), and for the second capsule-deposition peak at Cidade Beach (F= 6.382, p<0.05). This study revealed a selective pattern of capsule deposition, with individuals of N. vibex using only fronds of U. lactuca. This process was influenced by the morphodynamics of the two beaches, with the nassariids maximizing the survival of embryos by depositing more capsules and more eggs per capsule in better-protected parts of the mytilid beds.

Role of CCR2 in orthodontic tooth movement

Introduction: Cytokines and chemokines regulate bone remodeling during orthodontic tooth movement. CC chemokine ligand 2 (CCL2) is involved in osteoclast recruitment and activity, and its expression is increased in periodontal tissues under mechanical loading. In this study, we investigated whether the CC chemokine receptor 2 (CCR2)-CCL2 axis influences orthodontic tooth movement. Methods: A coil spring was placed in CCR2-deficient (CCR2(-/-)), wild-type, vehicle-treated, and P8A-treated (CCL2 analog) mice. In a histopathologic analysis, the amounts of orthodontic tooth movement and numbers of osteoclasts were determined. The expression of mediators involved in bone remodeling was evaluated by real-time polymerase chain reaction. Results: Orthodontic tooth movement and the number of TRAP-positive cells were significantly decreased in CCR2(-/-) and P8A-treated mice in relation to wild-type and vehicle-treated mice, respectively. The expressions of RANKL, RANK, and osteoblasts markers (COL-1 and OCN) were lower in CCR2(-/-) than in wild-type mice. No significant difference was found in osteoprotegerin levels between the groups. Conclusions: These data suggested a reduction of osteoclast and osteoblast activities in the absence of CCR2. The CCR2-CCL2 axis is positively associated with osteoclast recruitment, bone resorption, and orthodontic tooth movement. Therefore, blockage of the CCR2-CCL2 axis might be used in the future for modulating the extent of orthodontic tooth movement. (Am J Orthod Dentofacial Orthop 2012;141:153-60)

On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

URANS calculations for smooth circular cylinder flow in a wide range of Reynolds Numbers: solution verification and validation

The flow around circular smooth fixed cylinder in a large range of Reynolds numbers is considered in this paper. In order to investigate this canonical case, we perform CFD calculations and apply verification & validation (V&V) procedures to draw conclusions regarding numerical error and, afterwards, assess the modeling errors and capabilities of this (U)RANS method to solve the problem. Eight Reynolds numbers between Re = 10 and Re 5 x 10(5) will be presented with, at least, four geometrically similar grids and five discretization in time for each case (when unsteady), together with strict control of iterative and round-off errors, allowing a consistent verification analysis with uncertainty estimation. Two-dimensional RANS, steady or unsteady, laminar or turbulent calculations are performed. The original 1994 k - omega SST turbulence model by Menter is used to model turbulence. The validation procedure is performed by comparing the numerical results with an extensive set of experimental results compiled from the literature. [DOI: 10.1115/1.4007571]

Lower numbers of natural killer T cells in HIV-1 and Mycobacterium leprae co-infected patients

Natural killer T (NKT) cells are a heterogeneous population of lymphocytes that recognize antigens presented by CD1d and have attracted attention because of their potential role linking innate and adaptive immune responses. Peripheral NKT cells display a memory-activated phenotype and can rapidly secrete large amounts of pro-inflammatory cytokines upon antigenic activation. In this study, we evaluated NKT cells in the context of patients co-infected with HIV-1 and Mycobacterium leprae. The volunteers were enrolled into four groups: 22 healthy controls, 23 HIV-1-infected patients, 20 patients with leprosy and 17 patients with leprosy and HIV-1-infection. Flow cytometry and ELISPOT assays were performed on peripheral blood mononuclear cells. We demonstrated that patients co-infected with HIV-1 and M.leprae have significantly lower NKT cell frequencies [median 0.022%, interquartile range (IQR): 0.0070.051] in the peripheral blood when compared with healthy subjects (median 0.077%, IQR: 0.0320.405, P < 0.01) or HIV-1 mono-infected patients (median 0.072%, IQR: 0.0300.160, P < 0.05). Also, more NKT cells from co-infected patients secreted interferon-? after stimulation with DimerX, when compared with leprosy mono-infected patients (P = 0.05). These results suggest that NKT cells are decreased in frequency in HIV-1 and M.leprae co-infected patients compared with HIV-1 mono-infected patients alone, but are at a more activated state. Innate immunity in human subjects is strongly influenced by their spectrum of chronic infections, and in HIV-1-infected subjects, a concurrent mycobacterial infection probably hyper-activates and lowers circulating NKT cell numbers.