Importance of the pseudodifferential symbol calculus extends far beyond the fundamental role it is known to play in Global and Microlocal Analysis. In this article, we demonstrate that algebras of symbols contribute to subtle phenomena in characteristic p > 0. A perfect fit between Smooth Geometry and de Rham Theory in characteristic zero leads many to interpret the situation in characteristic ...

‎Many optimization problems can be reduced to a problem with an increasing and co-radiant objective function by a suitable transformation of variables. Functions, which are increasing and co-radiant, have found many applications in microeconomic analysis. In this paper, the abstract convexity of positive valued affine increasing and co-radiant (ICR) functions are discussed. Moreover, the ...

Postnikov constructed a decomposition of a totally nonnegative Grassmannian (Grkn)≥0 into positroid cells. We provide combinatorial formulas that allow one to decide which cell a given point in (Grkn)≥ belongs to and to determine affine coordinates of the point within this cell. This simplifies Postnikov’s description of the inverse boundary measurement map and generalizes formulas for the top ...

For each Dynkin diagram $D$, we define a ''cluster configuration space'' ${\mathcal{M}}_D$ and partial compactification ${\widetilde {\mathcal{M}}}_D$. $D = A_{n-3}$, have ${\mathcal{M}}_{A_{n-3}} {\mathcal{M}}_{0,n}$, the space of $n$ points on ${\mathbb P}^1$, {\mathcal{M}}}_{A_{n-3}}$ was studied in this case by Brown. The {\mathcal{M}}}_D$ is smooth affine algebraic variety with stratificat...

An adaptive neural network command-filtered backstepping design algorithm is proposed for the underactuated translational oscillator with a rotating actuator (TORA). The system dynamics are transformed into nonlinear cascade through global change of coordinates. Considering weak sinusoid-type interaction and affine-free appearance in model, TORA looked at as pure feedback system. Two networks u...

Let p(t) be an admissible Hilbert polynomial in P of degree d and Gotzmann number r. It is well known that Hilb p(t) can be seen as a closed subscheme of the Grasmannian G(N, s), where N = ` n+r n ́ and s = N − p(r), hence, by Plücker embedding, it becomes a closed subset of a suitable projective space. Let us denote by B the finite set of the Borel fixed ideals in k[X0, . . . ,Xn] generated by ...

The extraction of metric information from image data is highly relevant for the update of geospatial data bases. Photogrammetric methods offer tools to extract such information in a reliable and accurate manner from mostly multiple image setups using appropriate sensor models. These methods require a certain amount of expertise and often expensive software systems to process the image data. An ...

index notation, 7, 88acceleration, 73, 74achronal, 19ADM-mass, 25affine connection, 9analytic at infinity, 49associated 1-from, 95associated H-tensor field, 95asymptotically flat, 22, 23, 40asymptotically flatmanifold, 23asymptotically Schwarzschildian, 28asymptotically spherically round, 28 Bianchi identityfirst, 10second, 34, 92bound...

We investigate the local metrizability of Finsler spaces with $m$-Kropina metric $F = \alpha^{1+m}\beta^{-m}$, where $\beta$ is a closed null 1-form. show that such space Berwald type if and only (pseudo-)Riemannian $\alpha$ 1-form have very specific form in certain coordinates. In particular, when signature Lorentzian, belongs to subclass Kundt class generates corresponding congruence, this ge...