scholarly journals Phragmén-Lindelöf Alternative Results for a Class of Thermoelastic Plate

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2256
Author(s):  
Shiguang Luo ◽  
Jincheng Shi ◽  
Baiping Ouyang
Keyword(s):  
Energy Method ◽  
Differential Inequality ◽  
Second Order ◽  
Biharmonic Operator ◽  
Spatial Properties ◽  
Energy Expression ◽  
Coupling Equations ◽  
Thermoelastic Plate

The spatial properties of solutions for a class of thermoelastic plate with biharmonic operator were studied. The energy method was used. We constructed an energy expression. A differential inequality which the energy expression was controlled by a second-order differential inequality is deduced. The Phragme´n-Lindelo¨f alternative results of the solutions were obtained by solving the inequality. These results show that the Saint-Venant principle is also valid for the hyperbolic–hyperbolic coupling equations. Our results can been seen as a version of symmetry in inequality for studying the Phragme´n-Lindelo¨f alternative results.

XXIII.—On an Extension to an Integro-differential Inequality of Hardy, Littlewood and Polya

1972 ◽  
Vol 69 (4) ◽  
pp. 295-333 ◽  
Author(s):  
W. N. Everitt
Keyword(s):  
Differential Equation ◽  
Fourth Order ◽  
Differential Inequality ◽  
Order Differential Equation ◽  
Order Equation ◽  
Second Order ◽  
Image Position ◽  
Fourth Order Differential Equation

SynopsisThis paper considers an extension of the following inequality given in the book Inequalities by Hardy, Littlewood and Polya; let f be real-valued, twice differentiable on [0, ∞) and such that f and f are both in the space fn, ∞), then f′ is in L,2(0, ∞) andThe extension consists in replacing f′ by M[f] wherechoosing f so that f and M[f] are in L2(0, ∞) and then seeking to determine if there is an inequality of the formwhere K is a positive number independent of f.The analysis involves a fourth-order differential equation and the second-order equation associated with M.A number of examples are discussed to illustrate the theorems obtained and to show that the extended inequality (*) may or may not hold.

Spatial properties of second-order vestibulo-ocular relay neurons in the alert cat

1990 ◽  
Vol 81 (3) ◽  
pp. 462-478 ◽  
Author(s):  
K. Fukushima ◽  
S. I. Perlmutter ◽  
J. F. Baker ◽  
B. W. Peterson
Keyword(s):  
Second Order ◽  
Spatial Properties ◽  
Alert Cat ◽  
Relay Neurons

Cortical processing of second-order motion

1999 ◽  
Vol 16 (3) ◽  
pp. 527-540 ◽  
Author(s):  
ISABELLE MARESCHAL ◽  
CURTIS L. BAKER
Keyword(s):  
Spatial Frequency ◽  
High Spatial Frequency ◽  
Second Order ◽  
Spatial Properties ◽  
Processing Stream ◽  
Spatial Frequencies ◽  
Nonlinear Input ◽  
Nonlinear Processing ◽  
Frequency Components ◽  
Optimal Values

Neurons in the mammalian visual cortex have been found to respond to second-order features which are not defined by changes in luminance over the retina (Albright, 1992; Zhou & Baker, 1993, 1994, 1996; Mareschal & Baker, 1998a,b). The detection of these stimuli is most often accounted for by a separate nonlinear processing stream, acting in parallel to the linear stream in the visual system. Here we examine the two-dimensional spatial properties of these nonlinear neurons in area 18 using envelope stimuli, which consist of a high spatial-frequency carrier whose contrast is modulated by a low spatial-frequency envelope. These stimuli would fail to elicit a response in a conventional linear neuron because they are designed to contain no spatial-frequency components overlapping the neuron's luminance defined passband. We measured neurons' responses to these stimuli as a function of both the relative spatial frequencies and relative orientations of the carrier and envelope. Neurons' responses to envelope stimuli were narrowband to the carrier spatial frequency, with optimal values ranging from 8- to 30-fold higher than the envelope spatial frequencies. Neurons' responses to the envelope stimuli were strongly dependent on the orientation of the envelope and less so on the orientation of the carrier. Although the selectivity to the carrier orientation was broader, neurons' responses were clearly tuned, suggesting that the source of nonlinear input is cortical. There was no fixed relationship between the optimal carrier and envelope spatial frequencies or orientations, such that nonlinear neurons responding to these stimuli could perhaps respond to a variety of stimuli defined by changes in scale or orientation.

scholarly journals Spatial Behavior of a Coupled System of Wave-Plate Type

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Gusheng Tang ◽  
Yan Liu ◽  
Wenhui Liao
Keyword(s):  
Differential Inequality ◽  
Coupled System ◽  
Second Order ◽  
Spatial Behavior ◽  
Decay Estimates ◽  
Spatial Decay ◽  
Area Measure ◽  
First Order ◽  
Wave Plate ◽  
Plate Type

The spatial behavior of a coupled system of wave-plate type is studied. We get the alternative results of Phragmén-Lindelöf type in terms of an area measure of the amplitude in question based on a first-order differential inequality. We also get the spatial decay estimates based on a second-order differential inequality.

On an inequality of the Kolmogorov type for a second-order differential expression

1993 ◽  
Vol 442 (1916) ◽  
pp. 555-569 ◽  
Keyword(s):  
Differential Expression ◽  
Differential Inequality ◽  
Second Order ◽  
Numerical Treatment ◽  
Kolmogorov Type ◽  
Best Constant

In this paper we discuss an integro-differential inequality formed from the square of a second-order differential expression. A connection between the existence of the inequality and the Titchmarsh–Weyl m -function is established and it is shown that the best constant in the inequality is determined by the behaviour of the m -function. Analytic results are established for specific classes of problems. A numerical treatment of the inequality is also discussed and estimates of the best constant in specific examples are given.

scholarly journals An inverse problem on determining second order symmetric tensor for perturbed biharmonic operator

2021 ◽  
Author(s):  
Sombuddha Bhattacharyya ◽  
Tuhin Ghosh
Keyword(s):  
Inverse Problem ◽  
Vector Field ◽  
Symmetric Matrix ◽  
Symmetric Tensor ◽  
Second Order ◽  
Order Perturbation ◽  
Biharmonic Operator ◽  
First Order ◽  
Dirichlet To Neumann Map ◽  
First Order Perturbation

AbstractThis article offers a study of the Calderón type inverse problem of determining up to second order coefficients of higher order elliptic operators. Here we show that it is possible to determine an anisotropic second order perturbation given by a symmetric matrix, along with a first order perturbation given by a vector field and a zero-th order potential function inside a bounded domain, by measuring the Dirichlet to Neumann map of the perturbed biharmonic operator on the boundary of that domain.

scholarly journals Weighted Second-Order Differential Inequality on Set of Compactly Supported Functions and Its Applications

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2830
Author(s):  
Aigerim Kalybay ◽  
Ryskul Oinarov ◽  
Yaudat Sultanaev
Keyword(s):  
Fourth Order ◽  
Differential Inequality ◽  
Spectral Properties ◽  
Differential Operators ◽  
Second Order ◽  
Independent Interest ◽  
Compactly Supported ◽  
Compactly Supported Functions

In the paper, we establish the oscillatory and spectral properties of a class of fourth-order differential operators in dependence on integral behavior of its coefficients at zero and infinity. In order to obtain these results, we investigate a certain weighted second-order differential inequality of independent interest.

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