‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...

For an arbitrary solution to the Burgers–KdV hierarchy, we define tau-tuple $$(\tau _1,\tau _2)$$ of solution. We show that product $$\tau _1\tau _2$$ admits Buryak’s residue formula. Therefore, according Alexandrov’s theorem, is a tau-function KP hierarchy. then derive formula for affine coordinates point Sato Grassmannian corresponding explicitly in terms those _1$$ . Applications analogous o...

We describe the boundary of linear subvarieties in moduli space multi-scale differentials. Linear are algebraic strata (possibly) meromorphic differentials that local period coordinates given by equations. The main example such affine invariant submanifolds, is, closures $\operatorname{SL}(2,\mathbb{R})$-orbits. prove any subvariety is again equations generalized boundary. Our technical tool an...

‎let $v$ be a vector space over a field $f$ of characteristic $pgeq 0$ and let‎ ‎$t$ be a regular subgroup of the affine group $agl(v)$‎. ‎in the finite dimensional case we show that‎, ‎if $t$ is abelian or $p>0$‎, ‎then $t$ is unipotent‎. ‎for $t$ abelian‎, ‎pushing forward some ideas used in [a‎. ‎caranti‎, ‎f‎. ‎dalla volta and m‎. ‎sala‎, ‎abelian regular subgroups of the affine group and r...

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

As designers of artificial intelligence try to outwit hackers, both sides continue hone in on AI's inherent vulnerabilities. Designed and trained from certain statistical distributions data, deep neural networks (DNNs) remain vulnerable deceptive inputs that violate a DNN's statistical, predictive assumptions. Before being fed into network, however, most existing adversarial examples cannot mai...

Let p(t) be an admissible Hilbert polynomial in P of degree d. The Hilbert scheme Hilbnp(t) can be realized as a closed subscheme of a suitable Grassmannian G, hence it could be globally defined by homogeneous equations in the Plücker coordinates of G and covered by open subsets given by the non-vanishing of a Plücker coordinate, each embedded as a closed subscheme of the affine space A, D = di...

This paper proposes a novel stratified selfcalibration method of camera based on rotation movement. The proposed method firstly captures more than three images of the same scene in the case of constant internal parameters by panning and rotating the camera with small relative rotation angles among the captured images. After feature extraction and matching of captured images, the pixel coordinat...

Discussed is the structure of classical and quantum excitations of internal degrees of freedom of multiparticle objects like molecules, fullerens, atomic nuclei, etc. Basing on some invariance properties under the action of isometric and affine transformations we reviewed some new models of the mutual interaction between rotational and deformative degrees of freedom. Our methodology and some re...

Laplacian coordinates as a local shape descriptor have been employed in mesh editing. As they are encoded in the global coordinate system, they need to be transformed locally to reflect the changed local features of the deformed surface. We present a novel implicit Laplacian editing framework which is linear and effectively captures local rotation information during editing. Directly representi...