On totally geodesic submanifolds in the Jacobian locus

We study submanifolds of A_g that are totally geodesic for the locally symmetric metric and which are contained in the closure of the Jacobian locus but not in its boundary. In the first section we recall a formula for the second fundamental form of the period map due to Pirola, Tortora and the first author. We show that this result can be stated quite neatly using a line bundle over the product of the curve with itself. We give an upper bound for the dimension of a germ of a totally geodesic submanifold passing through [C] in M_g in terms of the gonality of C. This yields an upper bound for the dimension of a germ of a totally geodesic submanifold contained in the Jacobian locus, which only depends on the genus. We also study the submanifolds of A_g obtained from cyclic covers of the projective line. These have been studied by various authors. Moonen determined which of them are Shimura varieties using deep results in positive characteristic. Using our methods we show that many of the submanifolds which are not Shimura varieties are not even totally geodesic.Comment: To appear on International Journal of Mathematic

Discrete Approximations of a Controlled Sweeping Process

The paper is devoted to the study of a new class of optimal control problems governed by the classical Moreau sweeping process with the new feature that the polyhe- dral moving set is not fixed while controlled by time-dependent functions. The dynamics of such problems is described by dissipative non-Lipschitzian differential inclusions with state constraints of equality and inequality types. It makes challenging and difficult their anal- ysis and optimization. In this paper we establish some existence results for the sweeping process under consideration and develop the method of discrete approximations that allows us to strongly approximate, in the W^{1,2} topology, optimal solutions of the continuous-type sweeping process by their discrete counterparts

Empirical Tests Of Optimal Cognitive Distance

This article provides empirical tests of the hypothesis of ‘optimal cognitive distance’, proposed by Nooteboom (1999, 2000), in two distinct empirical settings. Variety of cognition, needed for learning, has two dimensions: the number of agents with different cognition, and differences in cognition between them (cognitive distance). The hypothesis is that in interfirm relationships optimal learning entails a trade-off between the advantage of increased cognitive distance for a higher novelty value of a partner’s knowledge, and the disadvantage of less mutual understanding. If the value of learning is the mathematical product of novelty value and understandability, it has an inverse-U shaped relation with cognitive distance, with an optimum level that yields maximal value of learning. With auxiliary hypotheses, the hypothesis is tested on interfirm agreements between pharmaceutical companies and biotech companies, as well as on interfirm agreements in ICT industries.innovation;organizational learning;ICT;biotechnology;alliances

Nonlinear elasticity of monolayer graphene

By combining continuum elasticity theory and tight-binding atomistic simulations, we work out the constitutive nonlinear stress-strain relation for graphene stretching elasticity and we calculate all the corresponding nonlinear elastic moduli. Present results represent a robust picture on elastic behavior of one-atom thick carbon sheets and provide the proper interpretation of recent experiments. In particular, we discuss the physical meaning of the effective nonlinear elastic modulus there introduced and we predict its value in good agreement with available data. Finally, a hyperelastic softening behavior is observed and discussed, so determining the failure properties of graphene.Comment: 4 page

The Conservation of Marcus Aurelius' Monument. Technical studies

The equestrian bronze monument of Marcus Aurelius in Rome has been further investigated, after restoration, mainly to foresee possible damages caused by outdoor exposure. At the same time a copy of it has been cast by following a new original method to obtain the intermediate model. New non-destructive tests have heen carried out to execute the above researches and in the end old and new methodologies can be consldered as a complex experimental tool to study and control outdoor bronze monument

Elastic properties of hydrogenated graphene

There exist three conformers of hydrogenated graphene, referred to as chair-, boat-, or washboard-graphane. These systems have a perfect two-dimensional periodicity mapped onto the graphene scaffold, but they are characterized by a $sp^3$ orbital hybridization, have different crystal symmetry, and otherwise behave upon loading. By first principles calculations we determine their structural and phonon properties, as well as we establish their relative stability. Through continuum elasticity we define a simulation protocol addressed to measure by a computer experiment their linear and nonlinear elastic moduli and we actually compute them by first principles. We argue that all graphane conformers respond to any arbitrarily-oriented extention with a much smaller lateral contraction than the one calculated for graphene. Furthermore, we provide evidence that boat-graphane has a small and negative Poisson ratio along the armchair and zigzag principal directions of the carbon honeycomb lattice (axially auxetic elastic behavior). Moreover, we show that chair-graphane admits both softening and hardening hyperelasticity, depending on the direction of applied load.Comment: submitted on Phys.Rev.

The impact of M&A on the R&D process. An empirical analysis of the role of technological and market relatedness.

While the impact of M&A on R&D and innovation examined at the aggregate level left inconclusive evidence, we find that at the level of the R&D process both the technological and market relatedness between the target and acquirer are helpful dimensions to identify effects. Using information on 31 in-depth cases of individual M&A deals we show that technological relatedness between M&A partners directly affects the inputs and organizational structure of the R&D process. M&A partners that operate in the same technological fields tend to reduce their R&D effort and rationalize the R&D process after the M&A compared to firms active in complementary technological fields that merge. These firms will furthermore face less technological competition in the technology market, but risk creating a more bureaucratic R&D process with a less motivated workforce. Market relatedness between partners, while having comparable aggregate effects on the R&D process, operates on different dimensions of the R&D process. Former rivals that engage in a M&A are significantly less likely to expand into new R&D fields or leverage their technological competences across the products and markets of the new entity. Non-rival firms that join forces, on the contrary, significantly increase R&D output and productivity through these activities.Competition; Effects; Field; Firms; Information; Innovation; International; M&A; Market; Market relatedness; Markets; Organizational structure; Processes; Product; R&D; Risk; Scale and scope; Structure; Subsidiaries; Technolocal relatedness; Technology diffusion;

Shimura varieties in the Torelli locus via Galois coverings of elliptic curves

We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list of all such families that satisfy a simple sufficient condition that ensures that the closure of the image of the family via the Torelli map yields a Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author together with A. Ghigi [FGP] similar computations were done in the case $g'=0$. Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$ and we show that these are the only families with $g'=1$ satisfying this sufficient condition. We show that among these examples two families yield new Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.Comment: 18 pages, to appear in Geometriae Dedicat

Hyperbolic Balance Laws with a Non Local Source

This paper is devoted to hyperbolic systems of balance laws with non local source terms. The existence, uniqueness and Lipschitz dependence proved here comprise previous results in the literature and can be applied to physical models, such as Euler system for a radiating gas and Rosenau regularization of the Chapman-Enskog expansion.Comment: 26 page