scholarly journals Half-space Gaussian symmetrization: applications to semilinear elliptic problems

2021 ◽  
Vol 10 (1) ◽  
pp. 1201-1221
Author(s):  
J. I. Díaz ◽  
F. Feo ◽  
M. R. Posteraro
Keyword(s):  
Half Space ◽  
Order Term ◽  
Zero Order ◽  
Power Type ◽  
Semilinear Equations ◽  
Suitable Definition ◽  
Semilinear Elliptic Problems ◽  
Growth Restrictions ◽  
Definition Of ◽  
Uniqueness Of A Solution

Abstract We consider a class of semilinear equations with an absorption nonlinear zero order term of power type, where elliptic condition is given in terms of Gauss measure. In the case of the superlinear equation we introduce a suitable definition of solutions in order to prove the existence and uniqueness of a solution in ℝ N without growth restrictions at infinity. A comparison result in terms of the half-space Gaussian symmetrized problem is also proved. As an application, we give some estimates in measure of the growth of the solution near the boundary of its support for sublinear equations. Finally we generalize our results to problems with a nonlinear zero order term not necessary of power type.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

THE HEAT-KERNEL MOST-LIKELY-PATH APPROXIMATION

2012 ◽  
Vol 15 (01) ◽  
pp. 1250001 ◽  
Author(s):  
JIM GATHERAL ◽  
TAI-HO WANG
Keyword(s):  
Heat Kernel ◽  
Implied Volatility ◽  
Order Term ◽  
Time Integration ◽  
Natural Extension ◽  
Approximation Formula ◽  
Local Volatility ◽  
Improved Performance ◽  
Volatility Function ◽  
Definition Of

In this article, we derive a new most-likely-path (MLP) approximation for implied volatility in terms of local volatility, based on time-integration of the lowest order term in the heat-kernel expansion. This new approximation formula turns out to be a natural extension of the well-known formula of Berestycki, Busca and Florent. Various other MLP approximations have been suggested in the literature involving different choices of most-likely-path; our work fixes a natural definition of the most-likely-path. We confirm the improved performance of our new approximation relative to existing approximations in an explicit computation using a realistic S&P500 local volatility function.

scholarly journals On the Inversion of the Gauss Transformation

1957 ◽  
Vol 9 ◽  
pp. 459-464 ◽  
Author(s):  
P. G. Rooney
Keyword(s):  
Differential Operator ◽  
Recent Work ◽  
Suitable Definition ◽  
Inversion Theory ◽  
The Subject ◽  
Definition Of ◽  
Image Position ◽  
Gauss Transformation ◽  
Operational Methods

The inversion theory of the Gauss transformation has been the subject of recent work by several authors. If the transformation is defined by1.1,then operational methods indicate that,under a suitable definition of the differential operator.

Iterative approach for zero-order term elimination in off-axis multiplex digital holography

2017 ◽  
Vol 383 ◽  
pp. 513-517 ◽  
Author(s):  
Dongliang Zhao ◽  
Dongzhuo Xie ◽  
Yong Yang ◽  
Hongchen Zhai
Keyword(s):  
Digital Holography ◽  
Order Term ◽  
Zero Order ◽  
Iterative Approach

The Algebra of Dimension-Linking Operators

1965 ◽  
Vol 8 (2) ◽  
pp. 203-222 ◽  
Author(s):  
R. H. Bruck
Keyword(s):  
Group Theory ◽  
Special Reference ◽  
Mathematical Society ◽  
Summer Institute ◽  
Burnside Problem ◽  
The Third ◽  
Australian Mathematical Society ◽  
Suitable Definition ◽  
Definition Of ◽  
Restricted Burnside Problem

In the course of preparing a book on group theory [1] with special reference to the Restricted Burnside Problem and allied problems I stumbled upon the concept of a dimension-linking operator. Later, when I lectured to the Third Summer Institute of the Australian Mathematical Society [2], G. E. Wall raised the question whether the dimension-linking operators could be made into a ring by introduction of a suitable definition of multiplication. The answer was easily found to be affirmative; the result wasthat the theory of dimen sion-linking operators became exceedingly simple.

scholarly journals On Near-Rings of Quotients

1979 ◽  
Vol 22 (2) ◽  
pp. 77-86 ◽  
Author(s):  
A. Oswald
Keyword(s):  
Finite Rank ◽  
Minimum Condition ◽  
Suitable Definition ◽  
Definition Of ◽  
Rings Of Quotients

In (2), Holcombe investigated near-rings of zero-preserving mappings of a group Γ which commute with the elements of a semigroup S of endomorphisms of Γ and examined the question: under what conditions do near-rings of this type have near-rings of right quotients which are 2-primitive with minimum condition on right ideals? In the first part of this paper (§2) we investigate further properties of near-rings of this type. The second part of the paper (§3) deals with those near-rings which have semisimple near-rings of right quotients. Our results here are analogous to those of Goldie (1); in particular, with a suitable definition of finite rank we prove that a near-ring which has a semisimple near-ring of right quotients has finite rank

An effective approach to removing zero-order term overlap and controlling image distortion in digital off-axis holography

2015 ◽  
Vol 356 ◽  
pp. 589-594
Author(s):  
Weipeng Zhang ◽  
Mingqing Wang ◽  
Ming Zheng ◽  
Jian Wu
Keyword(s):  
Order Term ◽  
Image Distortion ◽  
Zero Order

scholarly journals The Köthe Dual of an Abstract Banach Lattice

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
E. Jiménez Fernández ◽  
M. A. Juan ◽  
E. A. Sánchez-Pérez
Keyword(s):  
Integral Representation ◽  
Banach Lattice ◽  
Broad Class ◽  
Banach Lattices ◽  
Vector Measures ◽  
Integrable Functions ◽  
Suitable Definition ◽  
Integral Structures ◽  
Definition Of ◽  
Köthe Dual

We analyze a suitable definition of Köthe dual for spaces of integrable functions with respect to vector measures defined onδ-rings. This family represents a broad class of Banach lattices, and nowadays it seems to be the biggest class of spaces supported by integral structures, that is, the largest class in which an integral representation of some elements of the dual makes sense. In order to check the appropriateness of our definition, we analyze how far the coincidence of the Köthe dual with the topological dual is preserved.

The possibility of comparing line standards of length photographically

1953 ◽  
Vol 219 (1139) ◽  
pp. 500-515 ◽  
Keyword(s):  
Standard Deviation ◽  
Sufficient Accuracy ◽  
Visual Methods ◽  
Line Position ◽  
Single Measurement ◽  
Photographic Images ◽  
Suitable Definition ◽  
Definition Of ◽  
Better Than

Line standards of length, such as metres or yards, can be compared visually using micrometer microscopes to about one in ten millions in the most precise work. It seems possible that in a photographic comparison appreciably higher precision could be attained with less labour. Photographs of the lines on some line standards have been examined with a densitometer to determine the accuracy with which the distance between two photographic images of such lines could be measured. With suitable definition of line position a single measurement of this distance should have a standard deviation corresponding to less than 0.05 μ . Provided the temperature of the bars is known with sufficient accuracy it should be possible to compare two line standards to much better than one in ten millions in less than half the time taken by present visual methods. A machine for measuring the photographs is suggested. The characteristics of photographs of some lines are given in an appendix.

Depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space in direct current methods

Geophysics ◽  
1981 ◽  
Vol 46 (5) ◽  
pp. 768-780 ◽  
Author(s):  
B. B. Bhattacharya ◽  
M. K. Sen
Keyword(s):  
Half Space ◽  
Direct Current ◽  
Inverse Relationship ◽  
Electrode Arrays ◽  
Definition Of ◽  
Depth Of Investigation

The definition of depth of investigation as suggested by Evjen (1938) [subsequently used by Roy and Apparao (1971) also for the study of depth of investigation of electrode arrays in direct current methods for homogeneous isotropic earth] has been used to study the depth of investigation of various collinear electrode arrays for a homogeneous anisotropic half‐space. It has been shown that some simple transformations are to be applied to the expressions of normalized depth of investigation characteristic (NDIC) of the same arrays over homogeneous isotropic earth to obtain normalized depth of investigation characteristic of various arrays placed over homogeneous anisotropic earth. The novelty of anisotropy is that the depth of investigation of collinear electrode arrays over homogeneous anisotropic half‐space bears an inverse relationship with the coefficient of anisotropy and also depends upon array length and dip of the plane of stratification. The effect of the coefficient of anisotropy is most pronounced for horizontally stratified anisotropic earth and is independent of it for vertically stratified anisotropic earth—entirely consistent with the concept of the “;paradox of anisotropy.” The depth of investigation of all the collinear arrays for inclined stratification lies somewhere between the values obtained for horizontal and vertical stratifications.

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