Assume T is superstable and small. Using the multiplicity rankM we find locally modular types in the same manner as U -rank considerations yield regular types. We define local versions of M-rank, which also yield meager types. 0. Introduction. Throughout, T is superstable, small, and we work in C = C. In [Ne1] we defined the multiplicity rank M and proved that M has additivity properties simila...

We consider an operator P which is a sum of squares of vector fields with analytic coefficients. The operator has a nonsymplectic characteristic manifold, but the rank of the symplectic form σ is not constant on CharP . Moreover the Hamilton foliation of the non symplectic stratum of the Poisson-Treves stratification for P consists of closed curves in a ring-shaped open set around the origin. W...

Local search is currently one of the most used methods for finding solutions in real-life problems. It is usually considered when the research is interested in the final solution of the problem instead of the how the solution is reached. In this paper, the authors present an implementation of local search with Membrane Computing techniques applied to the N-queens problem as a case study. A CLIP...

With a view toward fracton theory in condensed matter, we introduce higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector symmetry for p$=0$ and p$=1$ respectively). We relate this of $n$-dimensional space, to lower degree (either higher-moment, e.g., degree-(p-$\ell$)) subdimensional subsystem layers $(n-\ell)$-submanifolds. ...

We prove that every place of an algebraic function field F |K of arbitrary characteristic admits local uniformization in a finite extension F of F. We show that F|F can be chosen to be normal. If K is perfect and P is of rank 1, then alternatively, F can be obtained from F by at most two Galois extensions; if in addition P is zero-dimensional, then we only need one Galois extension. Certain rat...

in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...