We consider linear optimization over a fixed compact convex feasible region that is semi-algebraic (or, more generally, “tame”). Generically, we prove that the optimal solution is unique and lies on a unique manifold, around which the feasible region is “partly smooth”, ensuring finite identification of the manifold by many optimization algorithms. Furthermore, second-order optimality condition...

This article is the second part in the series of articles where we are developing theory of valuations on manifolds. Roughly speaking valuations could be thought as finitely additive measures on a class of nice subsets of a manifold which satisfy some additional assumptions. The goal of this article is to introduce a notion of a smooth valuation on an arbitrary smooth manifold and establish som...

We study a polarized family π : X → R of 2-dimensional complex projective varieties, originally constructed by Catanese and Ciliberto, whose smooth fibers are surfaces of general type with invariants pg = q = 1, K2 = 3. By studying degenerations within a subfamily, we show that the Zariski-closure of the image of the monodromy representation on the second cohomology of a smooth fiber is as larg...

BACKGROUND Notch signaling in vascular smooth muscle precursors is required for smooth muscle differentiation. Jagged1 expression on endothelium activates Notch in vascular smooth muscle precursors including those of neural crest origin to initiate the formation of a smooth muscle layer in a maturing blood vessel. METHODS AND RESULTS Here, we show that Jagged1 is a direct Notch target in smoo...

forage species in mixtures are extensively grown worldwide nowadays, particularly as a step towards sustainable agriculture, however, information on this topic is scanty in our country. thus a 2-year (2001-2003) field experiment was conducted to determine the forage yield, botanical composition, as well as competition of some forage grasses and legumes as mono and dual cultures combinations at ...

We obtain constraints on the topology of families smooth $4$-manifolds arising from a finite dimensional approximation Seiberg-Witten monopole map. Amongst other results these include generalisation Donaldson's diagonalisation theorem and Furuta's $10/8$ theorem. As an application we construct examples continuous $\mathbb{Z}_p$-actions for any odd prime $p$, which can not be realised smoothly. ...

We study the implicit second order ordinary differential equations with complete integral. In this paper, we give a characterization of the implicit second order ordinary differential equations with smooth complete integral which we call Clairaut type equations. Besides, we consider properties of the Clairaut type equations and present the duality among special completely integrable equations w...

A second-order energy-preserving scheme is studied for the solution of the semilinear Cauchy Problem un uxx -uyy + u =0 (t > 0 ; x, y e R). Smooth data functions of compact support are prescribed at t = 0. On any time interval [0, 7"], second-order convergence (up to logarithmic corrections) to the exact solution is established in both the energy and uniform norms.

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

We compare two recent variational-analytic approaches to second-order conditions and sensitivity analysis for nonsmooth optimization. We describe a broad setting where computing the generalized Hessian of Mordukhovich is easy. In this setting, the idea of tilt stability introduced by Poliquin and Rockafellar is equivalent to a classical smooth second-order condition.