Invariant solutions to the Strominger system and the heterotic equations of motion

We construct many new invariant solutions to the Strominger system with respect to a 2-parameter family of metric connections $\nabla^{\varepsilon,\rho}$ in the anomaly cancellation equation. The ansatz $\nabla^{\varepsilon,\rho}$ is a natural extension of the canonical 1-parameter family of Hermitian connections found by Gauduchon, as one recovers the Chern connection $\nabla^{c}$ for $({\varepsilon,\rho})=(0,\frac12)$, and the Bismut connection $\nabla^{+}$ for $({\varepsilon,\rho})=(\frac12,0)$. In particular, explicit invariant solutions to the Strominger system with respect to the Chern connection, with non-flat instanton and positive $\alpha'$ are obtained. Furthermore, we give invariant solutions to the heterotic equations of motion with respect to the Bismut connection. Our solutions live on three different compact non-K\"ahler homogeneous spaces, obtained as the quotient by a lattice of maximal rank of a nilpotent Lie group, the semisimple group SL(2,$\mathbb{C}$) and a solvable Lie group. To our knowledge, these are the only known invariant solutions to the heterotic equations of motion, and we conjecture that there is no other such homogeneous space admitting an invariant solution to the heterotic equations of motion with respect to a connection in the ansatz $\nabla^{\varepsilon,\rho}$.Comment: 27 pages, 3 figure

The ascending central series of nilpotent Lie algebras with complex structure

We obtain several restrictions on the terms of the ascending central series of a nilpotent Lie algebra $\mathfrak g$ under the presence of a complex structure $J$. In particular, we find a bound for the dimension of the center of $\mathfrak g$ when it does not contain any non-trivial $J$-invariant ideal. Thanks to these results, we provide a structural theorem describing the ascending central series of 8-dimensional nilpotent Lie algebras $\mathfrak g$ admitting this particular type of complex structures $J$. Since our method is constructive, it allows us to describe the complex structure equations that parametrize all such pairs $(\mathfrak g, J)$.Comment: 28 pages, 1 figure. To appear in Trans. Amer. Math. So

Symplectically harmonic cohomology of nilmanifolds

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically harmonic cohomology.Comment: 18 page

The anomaly flow on nilmanifolds

We study the Anomaly flow on 2-step nilmanifolds with respect to any Hermitian connection in the Gauduchon line. In the case of flat holomorphic bundle, the general solution to the Anomaly flow is given for any initial invariant Hermitian metric. The solutions depend on two constants K1 and K2, and we study the qualitative behaviour of the Anomaly flow in terms of their signs, as well as the convergence in Gromov–Hausdorff topology. The sign of K1 is related to the conformal invariant introduced by Fu, Wang and Wu. In the non-flat case, we find the general evolution equations of the Anomaly flow under certain initial assumptions. This allows us to detect non-flat solutions to the Hull-Strominger-Ivanov system on a concrete nilmanifold, which appear as stationary points of the Anomaly flow with respect to the Strominger-Bismut connection. © 2021, The Author(s), under exclusive licence to Springer Nature B.V

On non-Kähler compact complex manifolds with balanced and Astheno-Kähler metrics [Sur les variétés compactes complexes non Kähler avec des métriques équilibrées et Asthéno-Kähler]

In this note, we construct, for every n=4, a non-Kähler compact complex manifold X of complex dimension n admitting a balanced metric and an astheno-Kähler metric, which is in addition k-th Gauduchon for any 1<=k<=n-1

Sixty Billion Gallons by 2030: Economic and Agricultural Impacts of Ethanol and Biodiesel Expansion

Agriculture is well positioned as a feedstock source because the fuels can be utilized with current engine technologies and are compatible with the current distribution infrastructure. Commercialization of cellulosic to ethanol technology will enable fuels to be derived from a diverse portfolio of feedstocks from numerous regions of the country. The levels of ethanol production analyzed are 10, 30, and 60 billion gallons of ethanol annually by 2010, 2020 and 2030, respectively. Impacts of producing 1 billion gallons of biodiesel production by 2012 and 1.6 billion gallons by 2030 are also projected. Overall, for the period 2007 to 2030, the estimated accumulated gains in net farm income are over $210 billion; and the accumulated potential savings in government payments are estimated to be$150 billion. Due to the geographic decentralization of the production of feedstock, economic gains are projected to accrue to the majority of regions of the country. Significant expansion beyond 60 billion gallons per year would likely require expansion of the region suitable for the production of bioenergy crops, ability to convert other pastureland (beyond cropland in pasture) into energy crops; allowing CRP acreage to be used in feedstock production, increasing short-rotation wood crops in the Northeast and Northwest regions, increased yields above those assumed in the analysis, and/or increasing the efficiency of cellulosic conversion. Further research should examine the agricultural, environmental, and economic impacts of one or more these factors changing.Resource /Energy Economics and Policy,

On the real homotopy type of generalized complex nilmanifolds

We prove that for any n = 4, there are infinitely many real homotopy types of 2n-dimensional nilmanifolds admitting generalized complex structures of every type k, for 0 = k = n

Six-Dimensional Solvmanifolds with Holomorphically Trivial Canonical Bundle

We determine the 6D solvmanifolds admitting an invariant complex structure with holomorphically trivial canonical bundle. Such complex structures are classified up to isomorphism, and the existence of strong Kähler with torsion, generalized Gauduchon, balanced and strongly Gauduchon metrics is studied. As an application, we construct a holomorphic family (M,Ja) of compact complex manifolds such that (M,Ja) satisfies the ¿¿¯-lemma and admits a balanced metric for any a¿0, but the central limit neither satisfies the ¿¿¯-lemma nor admits balanced metrics

Genotyping strategies for maximizing genomic information in evaluations of the Latxa dairy sheep breed

Genomic selection has been implemented over the years in several livestock species, due to the achievable higher genetic progress. The use of genomic information in evaluations provides better prediction accuracy than do pedigree-based evaluations, and the makeup of the genotyped population is a decisive point. The aim of this work is to compare the effect of different genotyping strategies (number and type of animals) on the prediction accuracy for dairy sheep Latxa breeds. A simulation study was designed based on the real data structure of each population, and the phenotypic and genotypic data obtained were used in genetic (BLUP) and genomic (single-step genomic BLUP) evaluations of different genotyping strategies. The genotyping of males was beneficial when they were genetically connected individuals and if they had daughters with phenotypic records. Genotyping females with their own lactation records increased prediction accuracy, and the connection level has less relevance. The differences in genotyping females were independent of their estimated breeding value. The combined genotyping of males and females provided intermediate accuracy results regardless of the female selection strategy. Therefore, assuming that genotyping rams is interesting, the incorporation of genotyped females would be beneficial and worthwhile. The benefits of genotyping individuals from various generations were highlighted, although it was also possible to gain prediction accuracy when historic individuals were not considered. Greater genotyped population sizes resulted in more accuracy, even if the increase seems to reach a plateau

Complicaciones al uso de Implantes Subdérmico con Etonogestrel en usuarias adscritas al Programa de Planificación Familiar en el C.S.R.D San Pedro Tenayac en los años 2011 - 2013

Objetivo: Analizar las complicaciones al uso de implante subdérmico de Etonogestrel en las usuarias del C.S.R.D San pedro Tenayac adscritas al programa de planificación familiar en los años 2011-2013 Material y método: Se analizaron los expedientes de 178 usuarias de implante subdérmico de Etonogestrel en la unidad, registradas en el tarjetero del programa de planificación familiar en el Centro de Salud. De dichas usuarias por diversas razones fue imposible localizar a 13 quedando un total de 165 mujeres a estudiar. Fueron excluidas al momento del estudio 9, 7 de ellas por que no contaban con el criterio de haber portado el implante por más 6 meses y 2 por deseo de embarazo, quedando como tamaño de la muestra 156 mujeres. Resultados: Se registró ganancia de peso e incremento en el Índice de Masa Corporal en la mayor parte de las usuarias (80%). En cuanto a las alteraciones del patrón de sangrado menstrual, encontramos que la amenorrea fue la alteración que se presentó con más frecuencia (69.6%), seguida en orden decreciente por polimenorrea (56.5%), opsomenorrea (37.0%), hipomenorrea (32.6%), oligomenorrea (28.3%), hipermenorrea (28.3%), sangrado intermenstrual (21.7%) y proiomenorrea (13.0%). De las otras complicaciones referidas, la cefalea se presentó con mayor frecuencia (56.5%), seguida de la mastalgia (47.8%), y las alteraciones de la libido (43.5%). Conclusiones: La información obtenida en nuestro estudio demostró, que como se esperaba, tanto el sobrepeso y obesidad; así como las alteraciones del patrón del sangrado menstrual, son más frecuentes de lo que reporta la literatura