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Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
We consider bicrossed products obtained by twisting compact semi-direct products by a suitable finite subgroup. Under some restriction, we give a practical criterion for the discrete dual of such bicrossed products to have the rapid decay…
The aim of this article is to study basic structures and interrelations of $\delta$-rings, perfectoid towers, and lim Cohen-Macaulay sequences over Noetherian rings in positive or mixed characteristic. Then we discuss some methods for…
We characterize the existence of certain geometric configurations in the fractal percolation limit set $A$ in terms of the almost sure dimension of $A$. Some examples of the configurations we study are: homothetic copies of finite sets,…
It is known that Hall's sextic residue sequence has some desirable features of pseudorandomness: an ideal two-level autocorrelation and linear complexity of the order of magnitude of its period $p$. Here we study its correlation measure of…
A numerical semigroup $S$ is cyclotomic if its semigroup polynomial $P_S$ is a product of cyclotomic polynomials. The number of irreducible factors of $P_S$ (with multiplicity) is the polynomial length $\ell(S)$ of $S.$ We show that a…
This article presents an identification methodology to capture general relationships, with application to piecewise nonlinear approximations of model predictive control for constrained (non)linear systems. The mathematical formulation…
Divisibility sequences are defined by the property that their elements divide each other whenever their indices do. The divisibility sequences that also satisfy a linear recurrence, like the Fibonacci numbers, are generated by polynomials…
The aim of this article is to obtain a better understanding and classification of strictly ergodic topological dynamical systems with discrete spectrum. To that end, we first determine when an isomorphic maximal equicontinuous factor map of…
For any given Salem number, we construct an automorphism on a simple abelian variety whose first dynamical degree is the square of the Salem number. Our construction works for both simple abelian varieties with totally indefinite quaternion…
The starting point of this paper is a duality for sequences of natural numbers which, under mild hypotheses, interchanges subadditive and superadditive sequences and inverts their asymptotic growth constants. We are motivated to explore…
Two perfect matchings $P$ and $Q$ of the complete graph on $2k$ vertices are said to be set-wise $t$-intersecting if there exist edges $P_{1}, \cdots, P_{t}$ in $P$ and $Q_{1}, \cdots, Q_{t}$ in $Q$ such that the union of edges $P_{1},…
We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
The identification of binary sequences with large merit factor (small mean-squared aperiodic autocorrelation) is an old problem of complex analysis and combinatorial optimization, with practical importance in digital communications…
Let $n_1$ and $n_2$ be two distinct primes with $\mathrm{gcd}(n_1-1,n_2-1)=4$. In this paper, we compute the autocorrelation values of generalized cyclotomic sequence of order $4$. Our results show that this sequence can have very good…
We exhibit the first explicit examples of Salem sets in $\mathbb{Q}_p$ of every dimension $0 < \alpha < 1$ by showing that certain sets of well-approximable $p$-adic numbers are Salem sets. We construct measures supported on these sets that…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…
We study the relations between the projective and the almost conformally symplectic structures on a smooth even dimensional manifold. We describe these relations by a single almost conformally symplectic connection with totally trace--free…
This is the second paper of the paper series on multiple Riordan arrays. In this paper, based on the study of multiple Riordan arrays and the multiple Riordan group, we define multiple almost-Riordan arrays and find that the set of all…