The enclosure method for the heat equation

This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary value problems whose governing equation is the heat equation is considered. An explicit method to extract an approximation of the value of the support function at a given direction of unknown discontinuity embedded in a heat conductive body from the temperature for a suitable heat flux on the lateral boundary for a fixed observation time is given.Comment: 12pages. This is the final versio

An inverse source problem for the heat equation and the enclosure method

An inverse source problem for the heat equation is considered. Extraction formulae for information about the time and location when and where the unknown source of the equation firstly appeared are given from a single lateral boundary measurement. New roles of the plane progressive wave solutions or their complex versions for the backward heat equation are given.Comment: 23page

On separable and H-separable polynomials in skew polynomial rings of several variables

Let B be a ring with 1, and {ρ1,⋯,ρe} a set of automorphisms of B. Let B[X1,⋯,Xe;ρ1,⋯,ρe;{uij}] be the skew polynomial ring of automorphism type. In this paper, we shall give equivalent conditions that the residue ring of B[X1,⋯,Xe;ρ1,⋯,ρe;{uij}] by the ideal generated by a set {Xm11−u1,⋯,Xmee−ue} to be separable or H-separable over B

Radiating and non-radiating sources in elasticity

In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.Comment: 17 page

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

NeuroD Expression in Podocytes and Interrelationships with Nephrin at Both Nuclear and Cytoplasmic Sites

Background/Aims The research of genes implicated in kidney glomerular function, eliciting cell fate program, is always at the forefront in nephrological studies. Several neurological molecules have been recently the object of study not only for their involvement in the central nervous system differentiation but also for their importance in the functionality of other organs and for mature phenotype, as in kidney. NeuroD, in CNS, is related to two functional roles, the early survival and the differentiation. The aim of our study was to ascertain the presence of NeuroD transcription factor in glomeruli and to understand which targets and mechanisms NeuroD controls. Methods: We used immunofluorescence (IF) studies on both human and mice renal tissues and on cultured podocytes to describe NeuroD distribution; then we investigated NeuroD binding to the nephrin promoter region in cultured podocytes by chromatin-immuno-precipitation (ChIP) assay. The overexpression of NeuroD in podocytes was used to establish first its role in nephrin synthesis, evaluated by real-Time quantitative (RTq) PCR and western-blot (WB) and successively to determine the recovery of cell morphology after adriamycin injury, measuring foot processes length. Results: We identified NeuroD transcription factor in glomeruli, in the same cells positive for WT1 and synaptopodin, namely podocytes; subsequently we observed a differentiation dependent NeuroD distribution in cultured podocytes, and a consistent link of NeuroD with the Nephrin promoter leading to the regulation of Nephrin translation and transcription. Our data also describes NeuroD expression in cytoplasm as phosphoprotein linked to nephrin and actinin4. Preliminary experiments seem to indicate NeuroD involved in dynamics of cell shape regulation after adriamycin injury. Conclusion: we propose that NeuroD possess in podocytes a dual ability acting in the nucleus as a transcription factor and in cytoplasm stabilizing cell shape

Inverse problems with partial data for a magnetic Schr\"odinger operator in an infinite slab and on a bounded domain

In this paper we study inverse boundary value problems with partial data for the magnetic Schr\"odinger operator. In the case of an infinite slab in $R^n$, $n\ge 3$, we establish that the magnetic field and the electric potential can be determined uniquely, when the Dirichlet and Neumann data are given either on the different boundary hyperplanes of the slab or on the same hyperplane. This is a generalization of the results of [41], obtained for the Schr\"odinger operator without magnetic potentials. In the case of a bounded domain in $R^n$, $n\ge 3$, extending the results of [2], we show the unique determination of the magnetic field and electric potential from the Dirichlet and Neumann data, given on two arbitrary open subsets of the boundary, provided that the magnetic and electric potentials are known in a neighborhood of the boundary. Generalizing the results of [31], we also obtain uniqueness results for the magnetic Schr\"odinger operator, when the Dirichlet and Neumann data are known on the same part of the boundary, assuming that the inaccessible part of the boundary is a part of a hyperplane

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

A novel model of in vitro osteocytogenesis induced by retinoic acid treatment

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