1,821 research outputs found
Parabolic equations with the second order Cauchy conditions on the boundary
The paper studies some ill-posed boundary value problems on semi-plane for
parabolic equations with homogenuous Cauchy condition at initial time and with
the second order Cauchy condition on the boundary of the semi-plane. A class of
inputs that allows some regularity is suggested and described explicitly in
frequency domain. This class is everywhere dense in the space of square
integrable functions.Comment: 7 page
On the number of solutions of a transcendental equation arising in the theory of gravitational lensing
The equation in the title describes the number of bright images of a point
source under lensing by an elliptic object with isothermal density. We prove
that this equation has at most 6 solutions. Any number of solutions from 1 to 6
can actually occur.Comment: 26 pages, 12 figure
Successive Coefficients of Univalent Functions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135332/1/jlms0448.pd
Nondestructive testing of bond integrity in foam insulation/aluminum composites
Nondestructive test methods are used for evaluating bond integrity of low-density polyurethane spray-on foam used as cryogenic insulation on aluminum alloy surfaces
Evaluation of ultrasonics and optimized radiography for 2219-T87 aluminum weldments
Ultrasonic studies are described which are specifically directed toward the quantitative measurement of randomly located defects previously found in aluminum welds with radiography or with dye penetrants. Experimental radiographic studies were also made to optimize techniques for welds of the thickness range to be used in fabricating the External Tank of the Space Shuttle. Conventional and innovative ultrasonic techniques were applied to the flaw size measurement problem. Advantages and disadvantages of each method are discussed. Flaw size data obtained ultrasonically were compared to radiographic data and to real flaw sizes determined by destructive measurements. Considerable success was achieved with pulse echo techniques and with 'pitch and catch' techniques. The radiographic work described demonstrates that careful selection of film exposure parameters for a particular application must be made to obtain optimized flaw detectability. Thus, film exposure techniques can be improved even though radiography is an old weld inspection method
An Arclength Problem for Close‐to‐Convex Functions
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135569/1/jlms0181.pd
Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters
Pathwise predictability of continuous time processes is studied in
deterministic setting. We discuss uniform prediction in some weak sense with
respect to certain classes of inputs. More precisely, we study possibility of
approximation of convolution integrals over future time by integrals over past
time. We found that all band-limited processes are predictable in this sense,
as well as high-frequency processes with zero energy at low frequencies. It
follows that a process of mixed type still can be predicted if an ideal
low-pass filter exists for this process.Comment: 10 page
Interface growth in two dimensions: A Loewner-equation approach
The problem of Laplacian growth in two dimensions is considered within the
Loewner-equation framework. Initially the problem of fingered growth recently
discussed by Gubiec and Szymczak [T. Gubiec and P. Szymczak, Phys. Rev. E 77,
041602 (2008)] is revisited and a new exact solution for a three-finger
configuration is reported. Then a general class of growth models for an
interface growing in the upper-half plane is introduced and the corresponding
Loewner equation for the problem is derived. Several examples are given
including interfaces with one or more tips as well as multiple growing
interfaces. A generalization of our interface growth model in terms of
``Loewner domains,'' where the growth rule is specified by a time evolving
measure, is briefly discussed.Comment: To appear in Physical Review
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