scholarly journals Convexification of restricted Dirichlet-to-Neumann map

2017 ◽  
Vol 25 (5) ◽  
Author(s):  
Michael V. Klibanov
Keyword(s):  
Inverse Problem ◽  
Point Source ◽  
Boundary Data ◽  
Neumann Boundary ◽  
The Other ◽  
Coefficient Inverse Problem ◽  
Other Hand ◽  
Straight Line ◽  
Dirichlet To Neumann Map

AbstractBy our definition, “restricted Dirichlet-to-Neumann (DN) map” means that the Dirichlet and Neumann boundary data for a coefficient inverse problem (CIP) are generated by a point source running along an interval of a straight line. On the other hand, the conventional DN data can be generated, at least sometimes, by a point source running along a hypersurface. CIPs with restricted DN data are non-overdetermined in the

Uniqueness for an inverse problem originating from magnetohydrodynamics. A class of smooth domains

2005 ◽  
Vol 135 (2) ◽  
pp. 267-283
Author(s):  
Elena Beretta ◽  
Sergio Vessella
Keyword(s):  
Inverse Problem ◽  
Dirichlet Problem ◽  
Normal Derivative ◽  
The Other ◽  
Nonlinear Source ◽  
Other Hand ◽  
Homogeneous Dirichlet Problem

We consider the homogeneous Dirichlet problem δu = −f(u) ≤ 0 in Ω with u = 0 on ∂Ω. We are interested in the inverse problem of determining the nonlinear source f from knowledge of the normal derivative of u, ∂u/δn, on an open arc Γ of ∂Ω. It is well known that this fails if Ω is a ball. On the other hand, Beretta and Vogelius proved that an analytic source f is uniquely determined from knowledge of (∂u/∂n)|Γ if Γ has at least a true corner. In this paper we try to bridge the gap finding a class of smooth domains for which the determination of analytic f is possible

The Spectra of Red Variables: SC Stars

1979 ◽  
Vol 46 ◽  
pp. 215-222
Author(s):  
Philip C. Keenan
Keyword(s):  
Inverse Problem ◽  
Variable Star ◽  
Point Of View ◽  
The Other ◽  
Spectral Features ◽  
Spectral Classification ◽  
Mira Variables ◽  
Other Hand ◽  
Physical Variables ◽  
The One

The value of recording the spectra of red stars depends upon one’s point of view. On the one side, to those concerned with spectral classification in general, it is of the greatest aid in calibrating the criteria of classification if those criteria are observed in a variable star in which the physical variables change by a known amount. Thus the temperature differences, amounting to three or four hundred degrees, between the maximum and minimum phases of Mira variables, have helped to establish the temperature criteria that are in general use for the coolest stars.On the other hand, I am sure that at this meeting there is more interest in the inverse problem: how to use the behavior of the spectral features to learn more about what is going on in the variable star - or, at least, at their surfaces.

Letters to the Editor

PEDIATRICS ◽  
1982 ◽  
Vol 69 (4) ◽  
pp. 503-503
Author(s):  
Gerald S. Arbus ◽  
Godfrey S. Bacheyie
Keyword(s):  
Serum Creatinine ◽  
Rate Of Change ◽  
The Other ◽  
Letters To The Editor ◽  
Other Hand ◽  
Straight Line ◽  
Line Relationship

Inadvertently we did not reference three articles from 1978—the two mentioned by Leumann and our own abstract.1 Both of Leumann's references confirmed that in children, as in adults with progressive renal failue, a straight-line relationship exists when plotting the reciprocal of the serum creatinine (SC) level or, occasionally, the logarithm vs time. They also examined the rate of change in SC for various disease categories in children, which was also previously investigated in adults.2,3 On the other hand, our recent paper4 considered whether we could have predicted early in the child's illness when he would reach his already known SC value just before dialysis was instituted.

An inverse problem of determining the time-dependent potential in a higher-order Boussinesq-Love equation from boundary data

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mousa Huntul ◽  
Mohammad Tamsir ◽  
Abdullah Ahmadini
Keyword(s):  
Inverse Problem ◽  
Boundary Data ◽  
Numerical Solutions ◽  
Physical Property ◽  
Neumann Boundary ◽  
Higher Order ◽  
Time Dependent ◽  
Potential Coefficient ◽  
Content Type ◽  
Dependent Potential

PurposeThe paper aims to numerically solve the inverse problem of determining the time-dependent potential coefficient along with the temperature in a higher-order Boussinesq-Love equation (BLE) with initial and Neumann boundary conditions supplemented by boundary data, for the first time.Design/methodology/approachFrom the literature, the authors already know that this inverse problem has a unique solution. However, the problem is still ill-posed by being unstable to noise in the input data. For the numerical realization, the authors apply the generalized finite difference method (GFDM) for solving the BLE along with the Tikhonov regularization to find stable and accurate numerical solutions. The regularized nonlinear minimization is performed using the MATLAB subroutine lsqnonlin. The stability analysis of solution of the BLE is proved using the von Neumann method.FindingsThe present numerical results demonstrate that obtained solutions are stable and accurate.Practical implicationsSince noisy data are inverted, the study models real situations in which practical measurements are inherently contaminated with noise.Originality/valueThe knowledge of this physical property coefficient is very important in various areas of human activity such as seismology, mineral exploration, biology, medicine, quality control of industrial products, etc. The originality lies in the insight gained by performing the numerical simulations of inversion to find the potential co-efficient on time in the BLE from noisy measurement.

scholarly journals The Use of Geometric Conceits in Exposition of Love in Metaphysical Poetry

IIUC Studies ◽  
1970 ◽  
Vol 3 ◽  
pp. 45-54
Author(s):  
Md Eftekhar Uddin
Keyword(s):  
John Donne ◽  
The Other ◽  
Human Being ◽  
George Herbert ◽  
Human Beings ◽  
Andrew Marvell ◽  
Metaphysical Poetry ◽  
Other Hand ◽  
Straight Line ◽  
Circular Line

The language, used by Metaphysical poets is highly evocative and infused with multi-dimensional meaning. It demands comprehension and sensitivity on the part of the reader to grasp out the inner aspect of a poem. Love, being a universal feeling gets expression through the hands of different poets in different ways. The exposition of love in Metaphysical poems has shaped up in a unique way because of the juxtaposition of geometry in it. Straight line and circular line are the two components of geometry. Straight line being regarded as imperfect one as it has no limit and end is used as a vehicle to convey the imperfection of love in Metaphysical poems. On the other hand, circular line, being treated as a perfect one is used to express a harmonious union of love between human beings and also between God and human being. The article aims at exploring such conflation of love with geometry in the poetic works of John Donne, Henry Vaughn, Andrew Marvell and George Herbert, the four major Metaphysical Poets. doi: 10.3329/iiucs.v3i0.2663   IIUC STUDIES Vol. - 3, December 2006 (p 31-44)

scholarly journals Consumption of fertilizers in districts of Slovakia in the period 2006–2015

2018 ◽  
pp. 389-398
Author(s):  
Cyril Siman ◽  
Yvetta Velísková
Keyword(s):  
Point Source ◽  
Urban Areas ◽  
Agricultural Land ◽  
Wastewater Treatment Plants ◽  
The Other ◽  
Organic Fertilizers ◽  
Other Hand ◽  
Quality Of Water ◽  
Source Of Pollution

Consumption of fertilizers in districts of Slovakia in the period 2006–2015 Water quality in the surface streams is influenced by several factors. One of important information which can help us to solve problems with quality of water in water body is a distribution of point and non-point pollution sources in a river basin and also amount of pollutants released from them to surface streams. An example of a point source of pollution is the outlet from wastewater treatment plants (industry, urban areas, farms, etc.). On the other hand the most significant non-point source of pollution is considered the application of fertilizers in agriculture. In this paper we have evaluated consumption of organic and industrial fertilizers in Slovakia in the period 2006–2015. Total (in tonnes) and average (in kg ha-1) consumption of industrial and organic fertilizers was analyzed. In monitored period, the amount of applied organic fertilizers was much higher than the amount of applied industrial fertilizers and in addition a significant part of total fertilizers consumption had nitrogenous fertilizers in a group of industrial fertilizers. In a group of industrial fertilizers during the period 2006–2015 we observed just moderately increasing in their consumption, while in the period 2010–2015 the average amount of applied industrial fertilizers per hectare of agricultural land increased by about 20 kg ha-1. On the other hand, in a group of organic fertilizers we observed a decreasing in consumption of fertilizers.

scholarly journals Detour Extra Straight Lines in the Euclidean Plane

2020 ◽  
pp. 237-249
Author(s):  
I. Szalay ◽  
B. Szalay
Keyword(s):  
Euclidean Plane ◽  
Euclidean Geometry ◽  
The Other ◽  
Real Numbers ◽  
Other Hand ◽  
Straight Line ◽  
Axiom Systems ◽  
Straight Lines

Using the theory of exploded numbers by the axiom-systems of real numbers and Euclidean geometry, we explode the Euclidean plane. Exploding the Euclidean straight lines we get super straight lines. The extra straight line is the window phenomenon of super straight line. In general, the extra straight lines are curves in Euclidean sense, but they have more similar properties to Euclidean straight lines. On the other hand, with respect of parallelism we find a surprising property: there are detour straight lines.

scholarly journals An inverse problem for a 2D parabolic equation with nonlocal overdetermination condition

2016 ◽  
Vol 8 (1) ◽  
pp. 107-117
Author(s):  
N.Ye. Kinash
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Existence And Uniqueness ◽  
Boundary Data ◽  
Function Method ◽  
Neumann Boundary ◽  
Fixed Number ◽  
Initial Condition ◽  
Green Function Method ◽  
The Green Function

We consider an inverse problem of identifying the time-dependent coefficient $a(t)$ in a two-dimensional parabolic equation: $$u_t=a(t)\Delta u+b_1(x,y,t)u_x+b_2(x,y,t)u_y+c(x,y,t)u+f(x,y,t),$$ $(x,y,t)\in Q_T,$ with the initial condition, Neumann boundary data and the nonlocal overdetermination condition $$\nu_1(t)u(0,y_0,t)+\nu_2(t)u(h,y_0,t)=\mu_3(t),\quad t\in[0,T],$$ where $y_0$ is a fixed number from $[0,l].$ The conditions of existence and uniqueness of the classical solution to this problem are established. For this purpose the Green function method, Schauder fixed point theorem and the theory of Volterra intergral equations are utilized.

scholarly journals Simulation Of Microlensing Lightcurves By Combining Contouring And Rayshooting

1996 ◽  
Vol 173 ◽  
pp. 275-276
Author(s):  
Stein Vidar Hagfors Haugan
Keyword(s):  
Point Source ◽  
Efficient Algorithm ◽  
Noise Level ◽  
Computing Time ◽  
Source Area ◽  
The Other ◽  
Source Plane ◽  
Source Profile ◽  
Other Hand

The contouring methods described by Lewis et al. (1993) and Witt (1993) are very efficient for obtaining the magnification of a point source moving along a straight track in the source plane. For finite sources, however, the amplification must be computed for numerous parallel tracks and then convolved with the source profile. Rayshooting, on the other hand, is an efficient algorithm for relatively large sources, but the computing time increases with the inverse of the source area for a given noise level.

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