On Aristotelian Universals and Individuals: The "Vink" That Is In Body and May Be In Me

G. E. L. Owen, in his infl uential paper “Inherence,” talks of “vink,” a name he has created for a particular shade of the color pink, and this “vink” serves as an individual in the Aristotelian category of quality. Owen was one of the first to aim to discredit the belief that J. L. Ackrill and his camp espoused, the belief that Aristotle thought that “general attributes are not in individuals, particular attributes are not in more than one individual.” I postulate that there is nothing here that does not preclude the existence of transferable nonsubstantial particulars, and base this view on passages from Aristotle’s Categories and certain examples found in Ammonius’s commentary and On Colors. Given this, a nonsubstantial particular of “vink” would not have to rely on having inhered in just one particular body to have existence, however, it would have to inhere in at least one particular body

Min (A)cyclic Feedback Vertex Sets and Min Ones Monotone 3-SAT

In directed graphs, we investigate the problems of finding: 1) a minimum feedback vertex set (also called the Feedback Vertex Set problem, or MFVS), 2) a feedback vertex set inducing an acyclic graph (also called the Vertex 2-Coloring without Monochromatic Cycles problem, or Acyclic FVS) and 3) a minimum feedback vertex set inducing an acyclic graph (Acyclic MFVS). We show that these problems are strongly related to (variants of) Monotone 3-SAT and Monotone NAE 3-SAT, where monotone means that all literals are in positive form. As a consequence, we deduce several NP-completeness results on restricted versions of these problems. In particular, we define the 2-Choice version of an optimization problem to be its restriction where the optimum value is known to be either D or D+1 for some integer D, and the problem is reduced to decide which of D or D+1 is the optimum value. We show that the 2-Choice versions of MFVS, Acyclic MFVS, Min Ones Monotone 3-SAT and Min Ones Monotone NAE 3-SAT are NP-complete. The two latter problems are the variants of Monotone 3-SAT and respectively Monotone NAE 3-SAT requiring that the truth assignment minimize the number of variables set to true. Finally, we propose two classes of directed graphs for which Acyclic FVS is polynomially solvable, namely flow reducible graphs (for which MFVS is already known to be polynomially solvable) and C1P-digraphs (defined by an adjacency matrix with the Consecutive Ones Property)

The minimal components of the Mayr-Meyer ideals

Mayr and Meyer found ideals $J(n,d)$ (in a polynomial ring in $10n+2$ variables over a field $k$ and generators of degree at most $d+2$) with ideal membership property which is doubly exponential in $n$. This paper is a first step in understanding the primary decomposition of these ideals: it is proved here that $J(n,d)$ has $nd^2 + 20$ minimal prime ideals. Also, all the minimal components are computed, and the intersection of the minimal components as well

The common good

Pojęcie dobra wspólnego jest pojęciem szerszym niż pojęcie interesu publicznego, na którym przez lata skupiała się uwaga doktryny i orzecznictwa. W obecnych czasach kryzysu państwa, którego podstawowe elementy omówiono w opracowaniu, refleksja nad pojęciem dobra wspólnego wydaje się szczególnie ważna dla ochrony podstaw idei oraz realizacji rządów prawa. Zakotwiczone w konstytucji ma także poważne konsekwencje dla oceny działań administracji publicznej, jak wskazuje bowiem doktryna, o ile interes publiczny dotyczy zawsze zbiorowości, o tyle dla dobra wspólnego może być niezbędna np. ochrona jednostki, jej godności, pozycji prawnej. Wskazano także, jak naruszenie zasad działania administracji publicznej w procesie legislacyjnym zagraża dobru wspólnemu. W artykule ukazano możliwe konkretyzacje pojęcia dobra wspólnego w prawie administracyjnym. Dotyczyć to może zarówno zadań administracji, jak i wykonywania kierownictwa w administracji publicznej. Przedstawiono postulaty badawcze w tym zakresie.The concept of the common good is a wider concept than the concept of public interest, which has for years been the focus of interest of the doctrine and judicial decisions. At the time of the current State crisis, the fundamental elements of which are discussed in the paper, a reflexion on the common good seems to be of particular importance for the protection of the fundamentals of the idea and the realisation of the rule of law. Both are anchored in the Constitution but have significant consequences for the evaluation of actions taken by public administration. Furthermore, as the doctrine shows, while public interest concerns a collective action, the common good requires the protection of an individual, their dignity and legal position. It has also been shown that the common good may be put in jeopardy as a result of the infringement of the principles according to which public administration functions. Possible concretisations of the concept of the common good in administrative law and consequently in the sphere of the performance of tasks or management in administration have been proposed and relevant directions of research programmes recommended

On global geodesic mappings of nn-dimensional surfaces of revolution

In this paper we study geodesic mappings of $n$-dimensional surfaces of revolution. From the general theory of geodesic mappings of equidistant spaces we specialize to surfaces of revolution and apply the obtained formulas to the case of rotational ellipsoids. We prove that such $n$-dimensional ellipsoids admit non trivial smooth geodesic deformations onto $n$-dimensional surfaces of revolution, which are generally of a different type.Comment: 10 page

A new family of ideals with the doubly exponential ideal membership property

Mayr and Meyer found ideals with the doubly exponential ideal membership property. In the analysis of the associated primes of these ideals (in math.AC/0209344), a new family of ideals arose. This new family is presented and analyzed in this paper. It is proved that this new family also satisfies the doubly exponential ideal membership property. Furthermore, the set of associated primes of this family can be computed inductively