We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a boundedly finite measure. We prove that this space with the ...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

Assessment and monitoring of rangeland in different grazing managements seems necessary to manage rangelands. The plant functional groups can be used as appropriate responders for rangelands condition and management. Therefore, this study was performed and aimed to determine the most important traits that are influenced by rangeland variation and management. In order to this, three areas along ...

We measure the fractal dimension of an African plant that is widely cultivated as ornamental, the Asparagus plumosus. This plant presents self-similarity, remarkable in at least two different scalings. In the following, we present the results obtained by analyzing this plant via the box counting method for three different scalings. We show in a quantitatively way that this species is a fractal.

The present study deals with the analysis of leaf shapes in terms of fractal geometry with medicinal plant like Hibiscus Leaf, by using the techniques of Image Processing. Fractal analysis has been applied to describe various aspects connected with the complexity of plant morphology. In this work we determined the fractal dimension of leaves for four methods like Prewitt , Sobel , Roberts , Can...

For a large Adaptive Optics (AO) system such as a large Segmented Mirror Telescope (SMT), it is often difficult, although not impossible, to directly apply common Multi-Input Multi-Output (MIMO) controller design methods due to the computational burden imposed by the large dimension of the system model. In this paper, a practical controller design method is proposed which significantly reduces ...

Texture is an important visual attribute used to describe the pixel organization in an image. As well as it being easily identified by humans, its analysis process demands a high level of sophistication and computer complexity. This paper presents a novel approach for texture analysis, based on analyzing the complexity of the surface generated from a texture, in order to describe and characteri...

The nature of time has long been an obsession for philosophers, scientists, and laymen. This nearly universal interest in time is encapsulated by the fact that the quotation “Time is nature’s way of keeping everything from happening at once” has been attributed to both Woody Allen and Albert Einstein! Although some argue that time is an illusion, ongoing work has revealed that most organisms po...