We prove a number of results to the effect that generic quantum graphs (defined via operator systems as in work Duan-Severini-Winter / Weaver) have few symmetries: for Zariski-dense open set tuples $(X_1,\cdots,X_d)$ traceless self-adjoint operators $n\times n$ matrix algebra corresponding system has trivial automorphism group, largest possible range parameters: $2\le d\le n^2-3$. Moreover, gro...

A standard proof of Schur's Theorem yields that any $r$-coloring $\{1,2,\dots,R_r-1\}$ a monochromatic solution to $x+y=z$, where $R_r$ is the classical $r$-color Ramsey number, minimum $N$ such complete graph on vertices triangle. We explore generalizations and modifications this result in higher dimensional integer lattices, showing particular if $k\geq d+1$, then $\{1,2,\dots,R_r(k)^d-1\}^d$...

This paper provides necessary as well sufficient conditions on the Hurst parameters so that continuous time parabolic Anderson model $$\frac{\partial u}{\partial t}=\frac{1}{2}\Delta +u{\dot{W}}$$ $$[0, \infty )\times {{\mathbb {R}}}^d $$ with $$d\ge 1$$ has a unique random field solution, where W(t, x) is fractional Brownian sheet {R}}}^d$$ and formally $$\dot{W} =\frac{\partial ^{d+1}}{\parti...

For $$E \subset \mathbb F_q^d$$ , $$d \ge 2$$ where $$\mathbb F_q$$ is the finite field with $$q$$ elements, we consider distance graph $$\mathcal G^{\textrm{dist}}_t(E)$$ $$t\neq 0$$ vertices are elements of $$E$$ and two $$x$$ $$y$$ connected by an edge if $$\|x-y\| \equiv (x_1-y_1)^2+\dots+(x_d-y_d)^2=t$$ . We prove that $$|E| C_k q^{\frac{d+2}{2}}$$ then contains a statistically ...

In this paper, we study additive properties of finite sets lattice points on spheres in three and four dimensions. Thus, given d , m ? N $d,m \in \mathbb {N}$ let A $A$ be a set ( x 1 ? ) Z $(x_1, \dots x_d) {Z}^d$ satisfying 2 + = $x_1^2 x_{d}^2 m$ . When 4 $d=4$ prove threshold breaking bounds for the energy that is, show there are at most O ? | / 3 ? 2766 $O_{\epsilon }(m^{\epsilon }|A|^{2 1...

A mathematical model of a two-dimensional high-speed flow in terms justification and taking into account several physical assumptions is formulated. The problem solved analytically the plane velocity hodograph to determine all parameters flow. coupling uniform with general form "simple wave" made it possible achieve reduction error model. adequacy pre-sented method shown.
 existing models ...

Abstract In this paper, we study the geometry of GT -varieties $$X_{d}$$ X d with group a finite cyclic $$\Gamma \subset {{\,\mathrm{GL}\,}}(n+1,\mathbb {K})$$ Γ ⊂ GL (</mml...

Polymorphism of haptoglobin (Hp) types was examined among 2,087 unrelated residents of Aichi Prefecture. The phenotypic distribution obtained agreed well with the genetic hypothesis. The frequency of Hpl gene in Aichi Prefecture was estimated to be 0.247, which is quite similar to those observed in other districts of Japan. 57 A genetically determined polymorphism of haptoglobin (Hp) in human s...