Abstract Based on iteration of random-valued functions we study the problem solvability in class continuous and Hölder $$\varphi $$ φ equations $$\begin{aligned} \varphi (x)=F(x)-\int _{\Omega }\varphi \big (f(x,\omega )\big )P(d\omega ),\\ (x)=F(x)+\int ), \end{aligned}$$ <m...

We develop a theory which unifies the universal (co)acting bi/Hopf algebras as studied by Sweedler, Manin and Tambara with recently introduced \cite{AGV1} bi/Hopf-algebras that are among all support equivalent algebras. Our approach uses vector spaces endowed family of linear maps between tensor powers $A$, called $\Omega$-algebras. This allows us to treat algebras, coalgebras, braided many oth...

Every six-dimensional $\mathcal{N}=(2,0)$ SCFT on $\mathbf{R}^6$ contains a set of protected operators whose correlation functions are controlled by two-dimensional chiral algebra. We provide an alternative construction this algebra performing $\Omega$-deformation~of topological-holomorphic twist the theory and restricting to cohomology specific supercharge. In addition, we show that central ch...

In this article, we study Codazzi-couples of an arbitrary connection $\nabla$ with a nondegenerate 2-form $\omega$, isomorphism $L$ on the space derivation $\rho$-commutative algebra $A$, which important examples are almost complex and para-complex structures, metric $g$ that $(g, \omega,L)$ form compatible triple. We statistical structure algebras by classical manner Riemannian manifolds. Then...

We link distinct concepts of geometric group theory and homotopy through underlying combinatorics. For a flag simplicial complex $K$, we specify necessary sufficient combinatorial condition for the commutator subgroup $RC_K'$ right-angled Coxeter group, viewed as fundamental real moment-angle $\mathcal{R}_K$, to be one-relator group; Pontryagin algebra $H_*(\Omega \mathcal{Z}_K)$ algebra. also ...

We show that the nerve of a strict omega-category can be described algebraically as a simplicial set with additional operations subject to certain identities. The resulting structures are called sets with complicial identities. We also construct an equivalence between the categories of strict omega-categories and of sets with complical identities.

We develop a ∗-continuous Kleene ω-algebra of real-time energy functions. Together with corresponding automata, these can be used to model systems which can consume and regain energy (or other types of resources) depending on available time. Using recent results on ∗-continuous Kleene ω-algebras and computability of certain manipulations on real-time energy functions, it follows that reachabili...

Abstract Given a probability space $$(\Omega ,\mathcal {A},\mathbb {P})$$ ( Ω , A P ) , complete separable Banach X with the $$\sigma $$ σ -algebra $$\mathcal B(X)$$ B ...