Monodromy of projections of hypersurfaces

Let X be an irreducible, reduced complex projective hypersurface of degree d. A point P not contained in X is called uniform if the monodromy group of the projection of X from P is isomorphic to the symmetric group $$S_d$$ S d . We prove that the locus of non-uniform points is finite when X is smooth or a general projection of a smooth variety. In general, it is contained in a finite union of linear spaces of codimension at least 2, except possibly for a special class of hypersurfaces with singular locus linear in codimension 1. Moreover, we generalise a result of Fukasawa and Takahashi on the finiteness of Galois points.

On general convergence behaviours of finite-dimensional approximants for abstract linear inverse problems

In the framework of abstract linear inverse problems in infinite-dimensional Hilbert space we discuss generic convergence behaviours of approximate solutions determined by means of general projection methods, namely outside the standard assumptions of Petrov–Galerkin truncation schemes. This includes a discussion of the mechanisms why the error or the residual generically fail to vanish in norm, and the identification of practically plausible sufficient conditions for such indicators to be small in some weaker sense. The presentation is based on theoretical results together with a series of model examples and numerical tests.

Ecotourism impact assessment on environment in protected areas of Serbia: A case study of Gornje Podunavlje Special nature Reserve

Ecotourism is a nature-based type of tourism, especially represented within protected areas. No matter the fact, just like the other selective types of this sector, ecotourism might affect the environment. In a process of writing the Visitor Management Plan in the Gornje Podunavlje Special Nature Reserve (SNR) in 2019, one part of the study was related to general projection of the ecotourism development impact on eco-educational paths within this SNR. The research was conducted throughout November 2019, in the form of interviews. The sample obtained 12 experts for nature protection, who stated their attitudes on three important topics: tourism in protected areas in general, tourism in the Gornje Podunavlje SNR and ecotourism within three concrete sites: Karapandža, Štrbac and Bestrement.

Projection Methods for Uniformly Convex Expandable Sets

Many problems in medical image reconstruction and machine learning can be formulated as nonconvex set theoretic feasibility problems. Among efficient methods that can be put to work in practice, successive projection algorithms have received a lot of attention in the case of convex constraint sets. In the present work, we provide a theoretical study of a general projection method in the case where the constraint sets are nonconvex and satisfy some other structural properties. We apply our algorithm to image recovery in magnetic resonance imaging (MRI) and to a signal denoising in the spirit of Cadzow’s method.

Novel Image Mosaicking of UAV’s Imagery using Collinearity Condition

This paper presents a preliminary result of ongoing research on unmanned aerial vehicle (UAV) for cooperative mapping to support a large-scale urban city mapping, in Malang, Indonesia. A small UAV can carry an embedded camera which can continuously take pictures of landscapes. A convenient way of monitoring landscape changes might be through accessing a sequence of images. However, since the camera’s field of view is always smaller than human eye’s field of view, the need to combine aerial pictures into a single mosaic is eminent. Through mosaics, a more complete view of the scene can be accessed and analyzed. A semi-automated generation of mosaics is investigated using a photogrammetric approach, namely a perspective projection which is based on collinearity condition. This paper reviews the general projection model based on collinearity condition and uses that to determine a common projective plane from images. The overlapped points for each RGB channel are interpolated onto that of orthographic plane to generate mosaics. An initial attempt shows a promising result.

A general iterative solver for unbalanced inconsistent transportation problems

The transportation problem, as a particular case of a linear programme, has probably the highest relative frequency with which appears in applications. At least in its classical formulation, it involves demands and supplies. When, for practical reasons, the total demand cannot satisfy the total supply, the problem becomes unbalanced and inconsistent, and must be reformulated as e.g. finding a least squares solution of an inconsistent system of linear inequalities. A general iterative solver for this class of problems has been proposed by S. P. Han in his 1980 original paper. The drawback of Han’s algorithm consists in the fact that it uses in each iteration the computation of the Moore-Penrose pseudoinverse numerical solution of a subsystem of the initial one, which for bigger dimensions can cause serious computational troubles. In order to overcome these difficulties we propose in this paper a general projection-based minimal norm solution approximant to be used within Han-type algorithms for approximating least squares solutions of inconsistent systems of linear inequalities. Numerical experiments and comparisons on some inconsistent transport model problems are presented.