Related papers: A New Take on Classic 'Pen Problems'
We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence…
This work concerns an alignment problem that has applications in many geospatial problems such as resource allocation and building reliable disease maps. Here, we introduce the problem of optimally aligning $k$ collections of $m$ spatial…
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…
We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.
Practically relevant problems of quadratic optimization often contain multidimensional arrays of variables interconnected by linear constraints, such as equalities and inequalities. The values of each variable depend on its specific meaning…
The purpose of the present work is solving the characterization problem for one class of second order operator pencil with complex periodic coefficients, which consists of identification of necessary and sufficient conditions on the…
We analyze the problem of folding one polyhedron, viewed as a metric graph of its edges, into the shape of another, similar to 1D origami. We find such foldings between all pairs of Platonic solids and prove corresponding lower bounds,…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a rational matrix that preserve its structure of zeros and…
The article explores a simple yet interesting geometric problem: how to fold a notebook page so it is the most visible when the notebook is closed (i.e., as a bookmark). We start with a square page, then proceed to the rectangular page.…
The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…
Some classical graph problems such as finding minimal spanning tree, shortest path or maximal flow can be done efficiently. We describe slight variations of such problems which are shown to be NP-complete. Our proofs use straightforward…
We study linear pencils of curves on normal surface singularities. Using the minimal good resolution of the pencil, we describe the topological type of generic elements of the pencil and characterize the behaviour of special elements. Then…
The Bin Packing Problem (BPP) is a well-established combinatorial optimization (CO) problem. Since it has many applications in our daily life, e.g. logistics and resource allocation, people are seeking efficient bin packing algorithms. On…
We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers,…
A canonical factorization is given for a quadratic pencil of accretive operators in a Hilbert space. Also, we establish some relationships between an m-accretive operator and its Moore-Penorse inverse. As an application, we study a result…
Distributing spatially located heterogeneous workloads is an important problem in parallel scientific computing. We investigate the problem of partitioning such workloads (represented as a matrix of non-negative integers) into rectangles,…