Probe method and a Carleman function

A Carleman function is a special fundamental solution with a large parameter for the Laplace operator and gives a formula to calculate the value of the solution of the Cauchy problem in a domain for the Laplace equation. The probe method applied to an inverse boundary value problem for the Laplace equation in a bounded domain is based on the existence of a special sequence of harmonic functions which is called a {\it needle sequence}. The needle sequence blows up on a special curve which connects a given point inside the domain with a point on the boundary of the domain and is convergent locally outside the curve. The sequence yields a reconstruction formula of unknown discontinuity, such as cavity, inclusion in a given medium from the Dirichlet-to-Neumann map. In this paper, an explicit needle sequence in {\it three dimensions} is given in a closed form. It is an application of a Carleman function introduced by Yarmukhamedov. Furthermore, an explicit needle sequence in the probe method applied to the reduction of inverse obstacle scattering problems with an {\it arbitrary} fixed wave number to inverse boundary value problems for the Helmholtz equation is also given.Comment: 2 figures, final versio

Linear sampling method for identifying cavities in a heat conductor

We consider an inverse problem of identifying the unknown cavities in a heat conductor. Using the Neumann-to-Dirichlet map as an input data, we develop a linear sampling type method for the heat equation. A new feature is that there is a freedom to choose the time variable, which suggests that we have more data than the linear sampling methods for the inverse boundary value problem associated with EIT and inverse scattering problem with near field data

Initial structure development in the CO2 laser-heated drawing of poly(trimethylene terephthalate) fiber

Because rapid and uniform laser heating can fix the neck-drawing point in continuous drawing of PTT fiber, we have successfully analyzed the fiber structure development in the continuous drawing process by in-situ measurement with a time resolution of less than 1 ms. In this study, we investigated fiber structure development for PTT around the neck point controlled with a CO2 laser-heated apparatus during continuous drawing, through on-line measurements of WAXD, SAXS, and fiber temperature. Fiber temperature attained by laser radiation initiated a rise around −3 mm in relation to the neck point at 0 mm, and increased to about 90 °C, which is past the 45 °C Tg for PTT. The instantaneous increase in fiber temperature continued with a vertical ascent, with plastic deformation around the neck point. The crystalline diffraction pattern was revealed initially at the elapsed time of 0.415 ms immediately after necking, and remained fairly constant with elapsed time. The ultimate crystalline diffraction pattern for a completely drawn fiber showed little difference from that at the initial stage. In PET a two-dimensionally ordered structure in the form of a mesophase was detected immediately after the necking, whereas in PTT the phenomenon was not observed. With elapsed time, the d spacing of (002) plane decreased gradually due to transformation of the initial all-trans conformation into trans-gauche-gauche-trans conformation, and ultimately the PTT molecular chain could favorably adopt the trans-gauche-gauche-trans conformation. SAXS pattern immediately after the necking revealed an X-shape; the scattering intensity concentrated on meridian directions due to individual crystal development, and at 2 ms two-pointed scattering started to appear. Past 8 ms, the typical two-pointed scattering pattern was prominent and its intensity increased with elapsed time. Long period decreased with increasing elapsed time, but the crystallite size of meridian (002) plane hardly changed. The decrease in long period might be caused by chain relaxation in the amorphous region.ArticlePolymer. 49(26):5705-5713 (2008)journal articl

JAXA EARTH OBSERVATION DASHBOARD WITH COG AND WMS/WMTSS

JAXA has developed and implemented earth observation (EO) dashboard jointly with ESA and NASA. The development of the JAXA dashboard, along with the "Earth-graphy" website and the newly developed "JAXA Earth API" service, demonstrate JAXA's commitment to providing climate change and earth science information to users worldwide. The EO dashboard serves as a platform to deliver valuable data and information related to climate change. The WMS/WMTS technology allows users to visualize and interact with geospatial information by providing web-based mapping services. This technology enhances the user experience by enabling the display of satellite imagery, overlays, and other geospatial data layers within the EO dashboard. To further facilitate the efficient use of satellite data, JAXA has developed the JAXA Earth API service. This service offers a user-friendly interface for accessing and utilizing JAXA's Earth observation satellite image data. By providing an easy-to-use format, JAXA aims to promote the effective utilization of satellite data and encourage its widespread use. Overall, the development and operation of the JAXA dashboard, with its integration of COG format data, WMS/WMTS technology, Python-based API. This paper introduces the status of development of JAXA Earth Observation dashboard with COG format data, WMS/WMTS technology, phyton based API and JAXA Earth Observation missions

Chlamydia trachomatis infection in early neonatal period

BACKGROUND: The clinical characteristics of Chlamydia trachomatis respiratory tract infections in Japanese neonates were investigated. METHODS: Clinical, laboratory and microbiological characteristics of five infants with pneumonia due to C. trachomatis in early neonatal period were analyzed. RESULTS: Only C. trachomatis was identified in 4 infants. Both C. trachomatis and cytomegalovirus was identified in one. Wheezing, tachypnea and cyanosis were common in infants. Mothers of five infants had negative chlamydial EIAs at 20 weeks of gestation. CONCLUSIONS: We identified five cases of C. trachomatis respiratory tract infections in early neonatal period with the possibility of intrauterine infection. Targeted screening, early diagnosis, and effective treatment of perinatal and neonatal chlamydial infections seems to be necessar

Computing Volume Bounds of Inclusions by EIT Measurements

The size estimates approach for Electrical Impedance Tomography (EIT) allows for estimating the size (area or volume) of an unknown inclusion in an electrical conductor by means of one pair of boundary measurements of voltage and current. In this paper we show by numerical simulations how to obtain such bounds for practical application of the method. The computations are carried out both in a 2D and a 3D setting.Comment: 20 pages with figure

Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case

International audienceIn this paper we address some ill-posed problems involving the heat or the wave equation in one dimension, in particular the backward heat equation and the heat/wave equation with lateral Cauchy data. The main objective is to introduce some variational mixed formulations of quasi-reversibility which enable us to solve these ill-posed problems by using some classical La-grange finite elements. The inverse obstacle problems with initial condition and lateral Cauchy data for heat/wave equation are also considered, by using an elementary level set method combined with the quasi-reversibility method. Some numerical experiments are presented to illustrate the feasibility for our strategy in all those situations. 1. Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Latt es and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial ill-posed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary