We make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces revolution and ruled in R3. prove that MCF non-cylindrical R3 are trivial. Moreover, we characterize revolutions under a homothetic helicoidal motion terms generating curve. Finally, cylindrical Explicit families exact also given.

We propose a systematic approach for generating linear implied constraints that link the values returned by several automata with accumulators after consuming the same input sequence. The method handles automata whose accumulators are increased by (or reset to) some non-negative integer value on each transition. We evaluate the impact of the generated linear invariants on conjunctions of two fa...

We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M , generalizing a result of Dolich on o-minimal theories in [4].

Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order control variations, a specific method for generating such variations is proposed. The theory is applied to a number of nontrivial examples.

We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These differential equations are then used to determine the initial counting sequence and for asymptotic analysis. The key tool is the scalar product for symmetric fu...

Families of Borel equivalence relations and quasiorders that are cofinal with respect to the Borel reducibility ordering, ≤B , are constructed. There is an analytic ideal on ù generating a complete analytic equivalence relation and any Borel equivalence relation reduces to one generated by a Borel ideal. Several Borel equivalence relations, among them Lipschitz isomorphism of compact metric spa...

We compute the complexity of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński gasket, and the Schreier graphs of the Hanoi Towers group H(3) acting on the rooted ternary tree. For both of them, we study the weighted generating functions of the spanning trees, associated with several natural labellings of the edge sets.

Hair and nails are skin appendages that share with other ectodermal tissues a common developmental pathway. Inherited disorders affecting these two structures therefore very often involve other epithelial components and present with multiple anomalies, generating both physical and psychological distress among patients and their families. The present review briefly describes major recent advance...

We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the evaluations to be expressed in terms of zeta values or more general polylogarithmic terms. The machinery developed is then applied to evaluation of further families of...

The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function.