By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in Av(4231, 31524, 42513, 351624), a pattern class which has three different connections with algebraic geometry, including the specification of indices of Schubert varieties defined by inclusions. This characterisation leads to the enumeration of the class.

In this paper we study discrete approximations of continuous-time evolution sy~tems governed by differential inclusions with nonconvex compact values in infinite-dimensional spaces. Our crucial result ensures the possibility of a strong Sobolev space approximation of every feasible solution to the continuous-time inclusion by its discrete-time counterparts extended as Euler's "bro~ ken lines." ...

We establish some Filippov type existence theorems for solutions of fractional semilinear differential inclusions involving Caputo’s fractional derivative in Banach spaces.

The present study compared intracytoplasmic inclusion bodies in the locus ceruleus (LC) of mouse with protein bodies in the LC of human. Phosphotungstic acid-hematoxylin (PTAH) and the Mallory method were used as the anionic stains. The inclusion bodies and protein bodies, which stained with PTAH and the Mallory method in the brain, contain proteins that appear to belong to the same family. Alt...

The Byrnes-Martin integral invariance principle for ordinary diierential equations is extended to diierential inclusions on R N. The extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes.

The article is devoted to the describtion of quasitriangular structures (universal R-matrices) on cocommutative Hopf algebras. It is known that such structures are concentrated on finite dimensional Hopf subalgebras. In particular, quasitriangular structure on group algebra is defined by the pairs of normal inclusions of an finite abelian group and by invariant bimultiplicative form on it. The ...

To motivate a study of asymptotic behaviour of nonlinear systems modelled by ordinary differential equations and differential inclusions, we indicate how such equations/inclusions arise naturally in control of dynamical process by feedback. The concept of control pertains to modifying the behaviour of the process, by manipulation of inputs to the process, in order to achieve some prescribed goa...

Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the computationally dense ones) are seen to be the ones whose ‘lifts’ to a kind of completion have right adjoints. We characterize topos inclusions corresponding to a general form of relative computability. We characterize p...

In this paper we examine nonlinear hyperbolic inclusions in Banach spaces. With the aid of a compactness condition involving the ball measure of non-compactness we prove two existence theorems. The rst for problems with convex valued orientor elds and the second for problems with nonconvex valued ones.

This paper serves as a corrigendum to the paper titled Application of Pettis integration to delay second order differential inclusions appearing in EJQTDE no. 88, 2012. We present here a corrected version of Theorem 3.1, because Proposition 2.2 is not true. 1 Correction In the above article, Proposition 2.2 is not true since the normed space P 1 E ([0, 1]) is not complete. Consequently, to corr...