On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers

Let (R,𝔪) be a local ring and I an ideal. The aim of the present paper is twofold. At first we continue the investigation to compare fgrade(I,R) with depth R∕I and further we derive some results on the vanishing of Lyubeznik numbers.     

Relationship between bearing capacity and depth of soft layer of paddy fields in South China

The bearing capacity of paddy field in South China was measured with a kind of penetrometer. A straight line relationship is valuable in summarizing the dependence of bearing capacity on depth of soft soil layer.     

Development of a prototype high-current low-energy ion implanter

A high current-low energy implant system for the processing of semiconductor devices at medium-high dopant levels is described. Criteria for selection and design of ion beam components such as ion beam optics, vacuum requirements and reliability are discussed. Variations in wafer uniformities for within wafer, wafer-to-wafer and run-to-run are presented.     

Unique ion beam scattering technique on depth profile determination

Abstract

By combination of energy and time of flight detection in ERDA or NRA measurement, the particles' masses can be determined, additionally to the depth information. This leads to unique depth profile determination even for complex targets. Combination with th concept of Jacobi transformations results in extremely fast measurements. In this paper, a way is shown how this concept can be realized even for accelerators ofenergies as low as about 1 MeV.     

An improved edge detection algorithm for depth map inpainting

Three-dimensional (3D) measurement technology has been widely used in many scientific and engineering areas. The emergence of Kinect sensor makes 3D measurement much easier. However the depth map captured by Kinect sensor has some invalid regions, especially at object boundaries. These missing regions should be filled firstly. This paper proposes a depth-assisted edge detection algorithm and improves existing depth map inpainting algorithm using extracted edges. In the proposed algorithm, both color image and raw depth data are used to extract initial edges. Then the edges are optimized and are utilized to assist depth map inpainting. Comparative experiments demonstrate that the proposed edge detection algorithm can extract object boundaries and inhibit non-boundary edges caused by textures on object surfaces. The proposed depth inpainting algorithm can predict missing depth values successfully and has better performance than existing algorithm around object boundaries.     

On the Center of Continuous Maps of Dendrites

The structure and the depth of the center of a continuous map of a dendrite with a closed countable set of branch points of a finite order are studied. It is proved that the center of that map coincides with the closure of the set of periodic points. It is shown also that for an arbitrary natural number n S 2 there are the dendrite X n with a closed countable set of branch points of a finite order and the continuous map f n : X n M X n with n as the depth of the center.     

Differential 3D shape retrieval

We are presenting a differential three-dimensional (3-D) shape profiling method that is based on the combination of orthogonal fringe projection. It allows us to compute depth gradient maps in a fast and efficient manner. What we are demonstrating is that depth gradients can be computed in a simple way by measuring fringe deformation throughout a novel single-shot approach. We show the usefulness and potential applications of the proposed approach. Validation experiments are presented as well.     

Computer aided measurement of melanoma depth of invasion in microscopic images

This paper presents a novel computer aided technique for measurement of melanoma depth of invasion. Melanoma is the deadliest form of skin cancer with worldwide increasing incidences. For a conclusive diagnosis of melanoma, skin biopsies should be examined under a microscope. Visual inspection of microscopic samples is often subjective, time-consuming, cumbersome and prone to human errors. This fact demonstrates the necessity of developing an automated method which assists pathologists in evaluating histopathological samples more accurately in the busy clinical environment. To the best of our knowledge, this is the first time that a computer-assisted diagnosis algorithm has been applied in measurement of melanoma invasion depth. The proposed method uses a clustering algorithm for granular layer extraction and a pre-trained SVM classifier for detection of malignant melanocytes. The experimental results with average error of 3.9 μm demonstrate that the proposed method is reliable and effective.     

The depth spectrums of constacyclic codes over finite chain rings

In light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n,p)=1$(n,p)=1$.     

Cohen–Macaulayness and Limit Behavior of Depth for Powers of Cover Ideals

Let 𝕂 be a field, and let R = 𝕂[x ₁,…, x _n ] be the polynomial ring over 𝕂 in n indeterminates x ₁,…, x _n . Let G be a graph with vertex-set {x ₁,…, x _n }, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J ^(k) and J ^[k], respectively. In this paper, we give necessary and sufficient conditions for R/J ^k , R/J ^(k), and R/J ^[k] to be Cohen–Macaulay. We also study the limit behavior of the depths of these rings.