Geometric second derivative estimates in Carnot groups and convexity

We prove some new a priori estimates for H ₂-convex functions which are zero on the boundary of a bounded smooth domain Ω in a Carnot group . Such estimates are global and are geometric in nature as they involve the horizontal mean curvature of ∂Ω. As a consequence of our bounds we show that if has step two, then for any smooth H ₂-convex function in vanishing on ∂Ω one has

Role of thiol‐disulfide exchange in episulfide polymerization

Episulfide polymerization offers a number of features that are uncommon in other ring‐opening anionic mechanisms. Besides the negligible sensitivity to water, the most distinctive and novel one is likely to be the role of disulfides, which may act both at the levels of chain transfer and end‐capping, producing polymers that feature both terminal and internal disulfides. In this article, we have qualitatively studied the kinetics of chain transfer and measured the thiolate–disulfide exchange equilibrium constants. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2233–2249, 2008     

A kinematically coupled time-splitting scheme for fluid–structure interaction in blood flow

We present a new time-splitting scheme for the numerical simulation of fluid–structure interaction between blood flow and vascular walls. This scheme deals in a successful way with the problem of the added mass effect. The scheme is modular and it embodies the stability properties of implicit schemes at the low computational cost of loosely coupled ones.     

Unitals of PG(2,q2) Containing Conics

A unital in PG(2, q²) is a set of points such that each line meets in 1 or points. The well‐known example is the classical unital consisting of all absolute points of a unitary polarity of PG(2, q²). Unitals other than the classical one also exist in PG(2, q²) for every . Actually, all known unitals are of Buekenhout–Metz type [see F. Buekenhout, Geom Dedicata 5 (1976), 189–194, R. Metz, Geom Dedicata 8 (1979), 125–126.], and they can be obtained by a construction due to F. Buekenhout, (Geom Dedicata 5 (1976), 189–194).. The unitals constructed by R. D. Baker and G. L. Ebert (J Combin Theory Ser A 60 (1992), 67–84), and independently by J. W. P. Hirschfeld and T. Sz?nyi (Discrete Math 97 (1991), 229–242), are the union of q conics. Our Theorem  1.1 shows that this geometric property characterizes the Baker–Ebert–Hirschfeld–Sz?nyi unitals. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 21: 101–111, 2013     

Theoretical study of the performance for short channel carbon nanotube transistors with asymmetric contacts

We have simulated short channel carbon nanotube field-effect transistors with asymmetric source and drain contacts using a coupled mode space approach within the non-equilibrium Green's function framework. The simulated results show that the asymmetric conduction properties under positive and negative drain-to-source voltages are caused by the asymmetric Schottky barriers to carriers at the source and drain contacts. Under negative drain-to-source voltages, hole and electron conduction are dominated by thermionic emission and tunneling through the Schottky barrier, respectively, leading to the different subthreshold behaviors of the hole and electron conduction. With increasing channel length, short channel effects can be suppressed effectively and ON/OFF ratio can be improved.     

Symmetry in a free boundary problem for degenerate parabolic equations on unbounded domains

We use the method of Alexandroff-Serrin to establish the spherical symmetry of the ground domain and of the weak solution to a free boundary problem for a class of quasi-linear parabolic equations in an unbounded cylinder , where , with a simply connected bounded domain. The equations considered are of the type , with modeled on . We consider a solution satisfying the boundary conditions: for , and , as . We show that the overdetermined co-normal condition for , with 0$"> for at least one value , forces the spherical symmetry of the ground domain and of the solution.

     

A multiplicity result for a class of nonlinear boundary value problems of the ambrosetti-prodi type

Summary In this paper we prove the existence of at least two solutions for a nonlinear elliptic boundary value problem of the Ambrosetti-Prodi type in the case when there exist two suitable supersolutions. This result follows from an abstract theorem of existence of multiple solutions which is a variant of a result due to Ambrosetti and Hess, [5].

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Riassunto In questo lavoro si prova che per un problema al contorno del tipo Ambrosetti-Prodi esistono almeno due soluzioni se esistono due opportune soprasoluzioni. Tale risultato discende da un teorema astratto di esistenza di soluzioni multiple che é una variante di un risultato di Ambrosetti ed Hess, [5].

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Paper written under the auspices of G.N.A.F.A., C.N.R., Italy.