Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells

Chern-Schwartz-MacPherson (CSM) classes generalize to singular and/or noncompact varieties the classical total homology Chern class of the tangent bundle of a smooth compact complex manifold. The theory of CSM classes has been extended to the equivariant setting by Ohmoto. We prove that for an arbitrary complex projective manifold $X$, the homogenized, torus equivariant CSM class of a constructible function $\varphi$ is the restriction of the characteristic cycle of $\varphi$ via the zero section of the cotangent bundle of $X$. This extends to the equivariant setting results of Ginzburg and Sabbah. We specialize $X$ to be a (generalized) flag manifold $G/B$. In this case CSM classes are determined by a Demazure-Lusztig (DL) operator. We prove a `Hecke orthogonality' of CSM classes, determined by the DL operator and its Poincar{\'e} adjoint. We further use the theory of holonomic $\mathcal{D}_X$-modules to show that the characteristic cycle of a Verma module, restricted to the zero section, gives the CSM class of the corresponding Schubert cell. Since the Verma characteristic cycles naturally identify with the Maulik and Okounkov's stable envelopes, we establish an equivalence between CSM classes and stable envelopes; this reproves results of Rim{\'a}nyi and Varchenko. As an application, we obtain a Segre type formula for CSM classes. In the non-equivariant case this formula is manifestly positive, showing that the expansion in the Schubert basis of the CSM class of a Schubert cell is effective. This proves a previous conjecture by Aluffi and Mihalcea, and it extends previous positivity results by J. Huh in the Grassmann manifold case. Finally, we generalize all of this to partial flag manifolds $G/P$.Comment: 40 pages; main changes in v2: removed some unnecessary compactness hypotheses; added remarks 7.2 and 9.6 explaining how orthogonality of characteristic cycles for transversal Schubert cell stratifications leads to orthogonality of stable envelopes and that of CSM classe

Luminescent acetylthiol derivative tripodal osmium(II) and iridium(III) complexes: Spectroscopy in solution and on surfaces

Luminescent Os(II) and Ir(III) complexes containing a tripodal-type structure terminalized with three thiol derivatives are described. The tripod is introduced through derivatization, with a rigid spacer, of a phenanthroline ligand coordinated to the metal ion, and the entire structure possesses axial geometry. The geometry of the complexes combined with the three anchoring sites, the thiol groups, allows the complexes to adopt an almost perpendicular arrangement to the surfaces and the formation of a well-packed monolayer on Au substrates. The photophysical and electrochemical behavior of the complexes is studied in solution and on surfaces. Furthermore, a self-assembled monolayer (SAM) of Os(II) complexes on an ultraflat Au surface is used to fabricate a metal-molecule-metal junction with Au and In Ga eutectic as electrodes. The Os(II) SAM in the tunneling junction exhibits rectification behavior which is opposite in direction to that which we have previously shown for Ru(II) SAM

Luminescent acetylthiol derivative tripodal osmium(II) and iridium(III) complexes: Spectroscopy in solution and on surfaces

Luminescent Os(II) and Ir(III) complexes containing a tripodal-type structure terminalized with three thiol derivatives are described. The tripod is introduced through derivatization, with a rigid spacer, of a phenanthroline ligand coordinated to the metal ion, and the entire structure possesses axial geometry. The geometry of the complexes combined with the three anchoring sites, the thiol groups, allows the complexes to adopt an almost perpendicular arrangement to the surfaces and the formation of a well-packed monolayer on Au substrates. The photophysical and electrochemical behavior of the complexes is studied in solution and on surfaces. Furthermore, a self-assembled monolayer (SAM) of Os(II) complexes on an ultraflat Au surface is used to fabricate a metal–molecule–metal junction with Au and In Ga eutectic as electrodes. The Os(II) SAM in the tunneling junction exhibits rectification behavior which is opposite in direction to that which we have previously shown for Ru(II) SAMs.Chemistry and Chemical Biolog

Generation Of Machined Multiple Flat Surfaces On Circular Bar By Its Rotation And In Synchronism With Cutting Tool

The operation of machining by lathe is one of the most common operations in automobile and machinery industries. The process is able to generate cylindrical bars under a wider variety of diameters/staggerings and using different materials, metallic's or non-metallic's (cupper, wood, aluminum, brass, steel, etc.). However, when more complex geometries are required, additional machines are used, like milling machine and/or machines under numerical control (CNC) and multiple axles. The possibility of joining circles, polygons, angular motion and synchronism, open the mind to multiple figures (shapes) and movements, which can generate different geometries. This paper aims to demonstrate that both operations (turning and milling), can be made at the same time and at the same machine, special but simpler lathe. The studies of geometry, associated with calculus (trigonometry) and angular motion give basis and sustain this statement. Tests in bench materialize the idea and reinforce this thesis.82146155Martin, J.T., Jonathan, M.B., Patrick, R.A., (1998) Fractal Geometry In Digital Imaging, p. 1. , Academic PressLandrini, M., Colagrossi, A., Greco, M., Tulin, M.P., (2012) The Fluid Mechanics of Splashing Bow Waves On Ships: A Hybrid BEM-SPH Analysis, 53, pp. 111-127. , Ocean EngineeringKline, (1972) Mathematical Thought From Ancient to Modern Times, p. 1032. , Oxford University PressFigueiredo, D.G., (2009) Análise De Fourier E Equações Diferenciais, p. 274. , Editora Projeto Euclides, in PortugueseIório, V.M., (2010) EDP: Um Curso De Graduação, p. 275. , Editora Coleção Matemática Universitária, in portugueseIório Jr., R., Iório, V.M., (2010), p. 343. , Equações Diferenciais Parciais: Uma Introdução, Editora Projeto Euclides, in PortugueseKnobloch, E., (2011) Kaspar Schott's "encyclopedia of All Mathematical Sciences", 7, pp. 225-247. , Poiesis Prax(1998) Trigonometric Delights, , by Eli Maor, Princeton University Press, Ebook version, in PDF format, full text presented(1914) Trigonometry, , by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, In images, full text presentedhttp://www.mfg.mtu.edu/cyberman/machining.html, The John W Sutherland Research PageLiang, S.Y., Junz Wang, J.J., (1994), pp. 1177-1190. , Milling force convolution modeling for identification of cutter axis offset, International Journal of Machine Tools and ManufactureMartelloti, M.E., An analysis of the milling process (1941) Transactions of the ASME, 63, pp. 677-700Martellotti, M.E., An analysis of the milling process, Part II-Down milling (1945) Transactions of the ASME, 67, pp. 233-251Ber, A., Feldman, D., (1974) A Mathematical Model of the Radial and Axial Throw of Square Indexable Inserts In a Face Milling Cutter, pp. 19-23. , Annals of CIRP: Manufacturing TechnologyKline, W.A., Devor, R.E., The effect of runout on cutting geometry and forces in end milling (1983) International Journal of Machine Tool Design and Research, pp. 123-140Fu, H.J., Devor, R.E., Kapoor, S.G., A mechanistic model for the prediction of force system in face milling operations (1984) Transactions of the ASME: Journal of Engineering For Industry, pp. 81-88Desai, K.A., Piyush, K.A., Rao, P.V.M., Process geometry modeling with cutter runout for milling of curved surfaces (2009) International Journal of Machine Tools & Manufacture, pp. 1015-1028Boothroyd, G., Knight, W.A., (2006) Fundamentals of Machining and Machine Tools, , CRC Press, Boca Rato

First direct measurement of the total cross section of 12C(alpha,gamma)16O

The total cross section of 12C(alpha,gamma)16O was measured for the first time by a direct and ungated detection of the 16O recoils. This measurement in inverse kinematics using the recoil mass separator ERNA in combination with a windowless He gas target allowed to collect data with high precision in the energy range E=1.9 to 4.9 MeV. The data represent new information for the determination of the astrophysical S(E) factor.Comment: 5 pages, 3 figures, 1 table, accepted for publication Eur.Phys.J. A (Online first available

Scope for Credit Risk Diversification

This paper considers a simple model of credit risk and derives the limit distribution of losses under different assumptions regarding the structure of systematic risk and the nature of exposure or firm heterogeneity. We derive fat-tailed correlated loss distributions arising from Gaussian risk factors and explore the potential for risk diversification. Where possible the results are generalised to non-Gaussian distributions. The theoretical results indicate that if the firm parameters are heterogeneous but come from a common distribution, for sufficiently large portfolios there is no scope for further risk reduction through active portfolio management. However, if the firm parameters come from different distributions, then further risk reduction is possible by changing the portfolio weights. In either case, neglecting parameter heterogeneity can lead to underestimation of expected losses. But, once expected losses are controlled for, neglecting parameter heterogeneity can lead to overestimation of risk, whether measured by unexpected loss or value-at-risk

The arabidopsis DNA polymerase δ has a role in the deposition of transcriptionally active epigenetic marks, development and flowering

DNA replication is a key process in living organisms. DNA polymerase α (Polα) initiates strand synthesis, which is performed by Polε and Polδ in leading and lagging strands, respectively. Whereas loss of DNA polymerase activity is incompatible with life, viable mutants of Polα and Polε were isolated, allowing the identification of their functions beyond DNA replication. In contrast, no viable mutants in the Polδ polymerase-domain were reported in multicellular organisms. Here we identify such a mutant which is also thermosensitive. Mutant plants were unable to complete development at 28°C, looked normal at 18°C, but displayed increased expression of DNA replication-stress marker genes, homologous recombination and lysine 4 histone 3 trimethylation at the SEPALLATA3 (SEP3) locus at 24°C, which correlated with ectopic expression of SEP3. Surprisingly, high expression of SEP3 in vascular tissue promoted FLOWERING LOCUS T (FT) expression, forming a positive feedback loop with SEP3 and leading to early flowering and curly leaves phenotypes. These results strongly suggest that the DNA polymerase δ is required for the proper establishment of transcriptionally active epigenetic marks and that its failure might affect development by affecting the epigenetic control of master genes.Fil: Iglesias, Francisco Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Bruera, Natalia Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Dergan Dylon, Leonardo Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Marino, Cristina Ester. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; ArgentinaFil: Lorenzi, Hernán. J. Craig Venter Institute; Estados UnidosFil: Mateos, Julieta Lisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; Argentina. Max Planck Institute for Plant Breeding Research; AlemaniaFil: Turck, Franziska. Max Planck Institute for Plant Breeding Research; AlemaniaFil: Coupland, George. Max Planck Institute for Plant Breeding Research; AlemaniaFil: Cerdan, Pablo Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigaciones Bioquimicas de Buenos Aires; Argentina. Fundación Instituto Leloir; Argentina. Universidad de Buenos Aires. Departamento de Ciencias Exactas; Argentin

The Role of Industry, Geography and Firm Heterogeneity in Credit Risk Diversification

In theory the potential for credit risk diversification for banks could be substantial. Portfolio diversification is driven broadly by two characteristics: the degree to which systematic risk factors are correlated with each other and the degree of dependence individual firms have to the different types of risk factors. We propose a model for exploring these dimensions of credit risk diversification: across industry sectors and across different countries or regions. We find that full firm-level parameter heterogeneity matters a great deal for capturing differences in simulated credit loss distributions. Imposing homogeneity results in overly skewed and fat-tailed loss distributions. These differences become more pronounced in the presence of systematic risk factor shocks: increased parameter heterogeneity greatly reduces shock sensitivity. Allowing for regional parameter heterogeneity seems to better approximate the loss distributions generated by the fully heterogeneous model than allowing just for industry heterogeneity. The regional model also exhibits less shock sensitivity