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In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…

We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…

We establish a mixed norm estimate for the Radon transform in the plane when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar…

In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…

We investigate the presence of localized solutions in models described by a single real scalar field with generalized dynamics. The study offers a method to solve very intricate nonlinear ordinary differential equations, and we illustrate…

We discuss first order systems of rational difference equations which have the property that lines through the origin are mapped into lines through the origin. We call such systems projective systems of rational difference equations and we…

Object pose distribution estimation is crucial in robotics for better path planning and handling of symmetric objects. Recent distribution estimation approaches employ contrastive learning-based approaches by maximizing the likelihood of a…

A successive continuation method for locating connecting orbits in parametrized systems of autonomous ODEs is considered. A local convergence analysis is presented and several illustrative numerical examples are given.

Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we…

We consider the problem of testing the stationarity and isotropy of a spatial point pattern based on the concept of local spectra. Using a logarithmic transformation, the mechanism of the proposed test is approximately identical to a simple…

A simple method to generate a two-dimensional binary grid pattern, which allows for absolute and accurate self-location in a finite planar region, is proposed. The pattern encodes position information in a local way so that reading a small…

The far-field pattern of a simple one-dimensional laser array of emitters radiating into free space is considered. In the path of investigating the inverse problem for their near fields leading to a target beam form, surprisingly we found…

Exploration systems are critical for enhancing the autonomy of robots. Due to the unpredictability of the future planning space, existing methods either adopt an inefficient greedy strategy or require a lot of resources to obtain a global…

We study two different methods for inferring the parameters of a spheroid distribution from planar sections of a stationary spatial system of spheroids: one method first unfolds non-parametrically the joint size-shape-orientation…

This paper studies the problem of extracting planar regions in uneven terrains from unordered point cloud measurements. Such a problem is critical in various robotic applications such as robotic perceptive locomotion. While existing…

Arbitrary distributions of radiant exposure may be written by transversely scanning a single known spatially-random screen that is normally illuminated by spatially but not necessarily temporally uniform radiation or matter wave fields. The…

The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to a range of results…

We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

A compact classification of the projective lines defined over (commutative) rings (with unity) of all orders up to thirty-one is given. There are altogether sixty-five different types of them. For each type we introduce the total number of…