Related papers: On K-semistable domains -- more examples
For a linear algebraic group $G$ over $\mathbf Q$, we consider the period domains $D$ classifying $G$-mixed Hodge structures, and construct the extended period domains $D_{\Sigma}$. In particular, we give toroidal partial compactifications…
We establish basic results on subrings of finite commutative rings and closely related rings. Among other applications we calculate the number of maximal subrings of a finite commutative local ring.
We characterise piecewise Boolean domains, that is, those domains that arise as Boolean subalgebras of a piecewise Boolean algebra. This leads to equivalent descriptions of the category of piecewise Boolean algebras: either as piecewise…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
In the present paper we generalize the notion of a Heyting algebra to the non-commutative setting and hence introduce what we believe to be the proper notion of the implication in skew lattices. We list several examples of skew Heyting…
We explain how to construct a uniformly random cubic integral domain $S$ of given signature with $|\text{disc}(S)| \leq T$ in expected time $\widetilde O(\log T)$.
We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.
We give a combinatorial proof of a formula giving the partial sums of the $k$-bonacci sequence as alternating sums of powers of two multiplied by binomial coefficients. As a corollary we obtain a formula for the $k$-bonacci numbers.
Let K be a number field. A finite group G is called K-admissible if there exists a G-crossed product K-division algebra. K-admissibility has a necessary condition called K-preadmissibility that is known to be sufficient in many cases. It is…
We suggest an extension of a certain logarithm of the total Johnson map in terms of solvable Lie groups. Here, the domain of the map is extended to a subset consisting of exponential solvable elements in the mapping class group of a…
We show some elementary facts about the semantical analogue of Parikh's Splitting, which we call Factorization.
In this paper, we define locally matchable subsets of a group which is extracted from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…
Data structures known as $k$-d trees have numerous applications in scientific computing, particularly in areas of modern statistics and data science such as range search in decision trees, clustering, nearest neighbors search, local…
Let $A$ be a Dedekind domain, $K$ the fraction field, $\p$ a non-zero prime ideal of $A$, and $K_\pp$ the completion of $K$ with respect to the $\p$-adic topology. At the input of a monic irreducible separable polynomial, $f(x)\in A[x]$,…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We define a topological invariant of complex projective plane curves. As an application, we present new examples of arithmetic Zariski pairs.
The notion of a k-automatic set of integers is well-studied. We develop a new notion - the k-automatic set of rational numbers - and prove basic properties of these sets, including closure properties and decidability.
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
We give algorithms of computing bases of logarithmic cohomology groups for square-free polynomials in two variables. (Fixed typos of v1)
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems