Apartness spaces were introduced as a constructive counterpart to proximity spaces which, in turn, aimed to model the concept of nearness of sets in a metric or topological environment. In this paper we introduce apartness algebras and apartness frames intended to be abstract counterparts to the apartness spaces of Bridges and Vîta [3], and we prove a discrete duality for them.

Matrix trace inequalities are finding increased use in many areas such as analysis, where they can be used to generalise several well known classical inequalities, and computational statistics, where they can be applied, for example, to data fitting problems. In this paper we give simple proofs of two useful matrix trace inequalities and provide applications to orthogonal regression and matrix ...

Memahami manusia diantaranya adalah dengan mencermati keberadaannya diantara makhluk lain,potensi yang dimilikinya, serta menyimak penjelasan-penjelasan dari Sang Pencitpa manusia. Adalah Qs. Al Baqarah [2]: 30 merupakan satu beberapa ayat Quran menjelaskan tentang eksistensi manusia, dimana dalam tersebut Allah menegaskan akan menjadikan wakil-Nya di muka bumi (<strong>khalifatullah fi a...

Several features of subfitness are analyzed. Isbell’s Spatiality Theorem leads to the concept of T1-spatiality which is compared with the TD-spatiality. Subfitness is put into relation with other weak separation axioms (and with the existence of nearness), both in spaces and locales, and seeming discrepancies are explained. A new characteristic of subfitness by means of codensity is presented.

BACKGROUND Standard measures of dyspnea rely on self-report. Cognitive impairment and nearness to death may interfere with symptom distress reporting leading to underrecognition and overtreatment or undertreatment. Previous psychometric testing of the Respiratory Distress Observation Scale (RDOS) demonstrated internal consistency and convergent validity with dyspnea self-report and discriminant...

This study was designed to assess in situ the effects of sediment nearness on Crassostrea gigas metabolism. One year-old oysters were reared for 5 months (April-August) in plastic bags on metallic frames at 10 and 60 cm off the sediment at the beginning of April. The management of the energetic resources (storage, consumption) was estimated with respect to biochemical changes of proteins, lipid...

Machine learning can be described as the discipline of automatically “learning” concepts from data eitherwith, or without human guidance. The goal ofmostmachine learning applications is to discover patterns within data so that properties of hitherto unseen data can be predicted reliably. However, the task of learning from data can often be very challenging (naturally contingent upon the concept...