We discuss a number of techniques for determining the Minkowski dimension of bounded subsets of some Euclidean space of any dimension, including: the box-counting dimension and equivalent definitions based on various box-counting functions; the similarity dimension via the Moran equation (at least in the case of self-similar sets); the order of the (box-)counting function; the classic result on...

Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic might be the logic of subsets...

The vertex set of a Kneser graph KG(m,n) consists of all n-subsets of the set [m] = {0, 1, . . . ,m − 1}. Two vertices are defined to be adjacent if they are disjoint as subsets. A subset of [m] is called 2stable if 2 ≤ |a − b| ≤ m − 2 for any distinct elements a and b in that subset. The reduced Kneser graph KG2(m,n) is the subgraph of KG(m,n) induced by vertices that are 2-stable subsets. We ...

The paper presents a combined state and parameter estimation for landslide model using Kalman filter. under investigation is based on underlying mechanics that depicts behavior. This system described by an Ordinary Differential Equation (ODE) with displacement as geometrical material properties parameters. filter approach utilized simplified equation estimation. Finally, the presented validated...

Feature selection is the process of selecting an optimal subset features required for maintaining or improving performance data mining models. Recently, hybrid filter/wrapper feature methods have shown promising results high-dimensional data. However, lack generalisation power, which enables selected to be trainable over different classifiers without having repeat process. To address power prob...

Criteria are obtained for a filter F of subsets of a set I to be an intersection of finitely many ultrafilters, respectively, finitely many κ-complete ultrafilters for a given uncountable cardinal κ. From these, general results are deduced concerning homomorphisms on infinite direct product groups, which yield quick proofs of some results in the literature: the Loś-Eda theorem (characterizing h...

‎in this paper‎, ‎the notion of the radical of a filter in‎ ‎residuated lattices is defined and several characterizations of‎ ‎the radical of a filter are given‎. ‎we show that if f is a‎ ‎positive implicative filter (or obstinate filter)‎, ‎then‎ ‎rad(f)=f‎. ‎we proved the extension theorem for radical of filters in residuated lattices‎. ‎also‎, ‎we study the radical‎ ‎of filters in linearly o...

Reliability of a navigation system is one of great importance for navigation purposes. Therefore, an integrity monitoring system is an inseparable part of aviation navigation system. Failures or faults due to malfunctions in the systems should be detected and repaired to keep the integrity of the system intact. According to the characteristic of GPS (Global Positioning System) receiver noise di...

in this paper, we proposed a novel structure for designing all optical filter based on photonic crystal structure. in designing the proposed filter, we simply employed a point defect localized between input and output waveguides as wavelength selecting part of the filter. the initial form of this filter is capable of selecting optical waves at =1560 nm, the transmission efficiency of the filte...

Abstract Background: Identity disturbance is one of the DSM-IV criteria for borderline personality disorder, but there has been little attention to its nature. Four subsets of identity disturbance (role absorption, painful incoherence, inconsistency and lack of commitment) have been assessed. This study aimed to assess the role of these subsets in patients with borderline person...