We prove a direct theorem for convex polynomial L p-approximation, 0 < p < 1, in terms of the classical modulus of smoothness ! 3 (f; t) p. This theorem may be regarded as an extension to L p of the well-known pointwise estimates of the Timan type and their variants of R. DeVore, Y. K. Hu and D. Leviatan for convex approximation in L p. It leads to a characterization of convex functions in Lips...

Minimizers of the total variation subject to a prescribed L-norm are considered as eigensolutions of the 1-Laplace operator. The derivation of the corresponding eigenvalue equation, which requires particular care due to the lack of smoothness, is carried out in a previous paper by using a special Lagrange multiplier rule based on Degiovanni’s weak slope. The present paper provides a simpler pro...

The single laser irradiation ( SLI ) method was adopted to develop a double DLI investigate the effects of laser-induced structures downward-propagating flames in tube on transition from primary acoustic instability parametric . Previously, effectively used study interaction between oscillation and flame structure by controlling shape front. deformed cellular (either concave or convex) -induced...

A language L is prefix-convex if, whenever words u and w are in L with u a prefix of w, then every word v which has u as a prefix and is a prefix of w is also in L. Similarly, we define suffix-, factor-, and subword-convex languages, where by subword we mean subsequence. Together, these languages constitute the class of convex languages which contains interesting subclasses, such as ideals, clo...

For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of the line segment. Midpoint convexity is a well-known characterization of ordinary convexity under very mild assumptions. For a function defined on the integer...

In a two-capacitated spanning tree of a complete graph with a distinguished root vertex v, every component of the induced subgraph on V\{v} has at most two vertices. We give a complete, non-redundant characterization of the polytope defined by the convex hull of the incidence vectors of two-capacitated spanning trees. This polytope is the intersection of the spanning tree polytope on the given ...

Consider L being a continuous lattice, two functors from the category of convex spaces (denoted by CS) to the category of stratified L-convex spaces (denoted by SL-CS) are defined. The first functor enables us to prove that the category CS can be embedded in the category SL-CS as a reflective subcategory. The second functor enables us to prove that the category CS can be embedded in the categor...

It is shown that every equi-affine invariant and upper semicontinuous valuation on the space of convex discs is a linear combination of the Euler characteristic, area, and affine length. Asymptotic formulae for approximation of convex discs by polygons are derived, extending results of L. Fejes Tóth from smooth convex discs to general convex discs. 1991 AMS subject classification: 52A10, 53A15,...

A new method for the design of fixed-structure dynamic output-feedback Linear Parameter Varying (LPV) controllers for discrete-time LPV systems with bounded scheduling parameter variations is presented. Sufficient conditions for the stability, H2 and induced l2-norm performance of a given LPV system are given through a set of Linear Matrix Inequalities (LMIs) and exploited for design. Extension...

Complex surface structures have stimulated a great deal of interests due to many potential applications in surface devices. However, in the fabrication of complex surface micro-/nanostructures, there are always great challenges in precise design, or good controllability, or low cost, or high throughput. Here, we present a route for the accurate design and highly controllable fabrication of surf...