Related papers: Hirotaka's problem 028
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given…
Minimax solutions are weak solutions to Cauchy problems involving Hamilton--Jacobi equations, constructed from generating families quadratic at infinity of their geometric solutions. We give a complete description of minimax solutions and…
We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…
We investigate three combinatorial problems considered by Erd\"os, Rivat, Sark\"ozy and Sch\"on regarding divisibility properties of sum sets and sets of shifted products of integers in the context of function fields. Our results in this…
Origami is becoming more and more relevant to research. However, there is no public dataset yet available and there hasn't been any research on this topic in machine learning. We constructed an origami dataset using images from the…
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
We consider the Dirichlet problem in an ellipsoidal cylinder when the data function is entire. Under an additional assumption that the order of the data function is less than one, we show that there is a solution that extends as an entire…
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
The aim of this paper is to deal with the $k$-Hessian counterpart of the Laplace equation involving a nonlinearity studied by Matukuma. Namely, our model is the problem \begin{equation*} (1)\;\;\;\begin{cases} S_k(D^2u)= \lambda…
Relations between differential calculi, quantum groups, integrable systems, and q-analysis are studied. Some new Hirota type formulas are established for qKP along with variations on classical Hirota formulas.
This paper considers the equivalence problem for quasi-cyclic codes over finite fields. The results obtained are used to construct isodual quasi-cyclic codes.
This paper deals with a dynamic Gao beam of infinite length subjected to a moving concentrated Dirac mass. Under appropriate regularity assumptions on the initial data, the problem possesses a weak solution which is obtained as the limit of…
We are concerned with the Dirichlet problem for a class of Hessian type equations. Applying some new methods we are able to establish the $C^2$ estimates for an approximating problem under essentially optimal structure conditions. Based on…
Sudoku is a popular combinatorial puzzle. A new method of solving Sudoku is presented, which involves formulating a puzzle as a special type of transportation problem. This model allows one to solve puzzles with more than one solution,…
This paper gives one set of axioms for origami constructions, and describes the set of constructible points under these axioms. The determination of the set of cunstructible points for this particular set of axioms is related to Hilbert's…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
We investigate a "deep zero problem" proposed by Hedenmalm. We show that there is a natural connection between Hedenmalm's problem and the classical HRT conjecture in time-frequency analysis. This connection allows us to show that…
We explore the capabilities of physical computing with Oscillatory Neural Networks (ONN) to solve combinatorial optimization problems. To solve Sudokus with ONNs, we define a novel mapping strategy that utilizes the unique characteristics…