Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl–Titchmarsh–Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac operator up to a gauge transformation. Our result applies in particular to radial Dirac operators and extends the classical results for Dirac operators with one...

MOTIVATION The human microbiome plays an important role in human disease and health. Identification of factors that affect the microbiome composition can provide insights into disease mechanism as well as suggest ways to modulate the microbiome composition for therapeutical purposes. Distance-based statistical tests have been applied to test the association of microbiome composition with enviro...

In this paper, we propose a new type of graph, denoted as ”embedded-graph”, and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated relations, which cannot be expressed by the existing edge-graphs or weighted-graphs. We introduce the mathematical definition of embedded-graph, translation, edg...

The purpose of this study is to investigate the accuracy Inverse Distance Weighted (IDW) interpolation method estimate and map surface water salinity along coastal waters Pulau Tuba, Langkawi. Sea was recorded using a refractometer during two sampling activities that were carried out in November 2018. Global Positioning System (GPS) used record geo-location each point. IDW applied data collecti...

the high hillsides of the tehran metropolis are prone to landslides due to the climatic conditions and the geological, geomorphologicalcharacteristics of the region. therefore, it is vitally important that a landslide susceptibility map of the region be prepared. for thispurpose, thematic layers including landslide inventory, lithology, slope, aspect, curvature, distance to stream, distance to ...