scholarly journals Alternating and variable controls for the wave equation

2020 ◽  
Vol 26 ◽  
pp. 38 ◽  
Author(s):  
Antonio Agresti ◽  
Daniele Andreucci ◽  
Paola Loreti
Keyword(s):  
Wave Equation ◽  
Sufficient Conditions ◽  
Dimensional Case ◽  
Equivalent Condition ◽  
Open Problems ◽  
One Dimensional ◽  
Constant Rate ◽  
Exact Observability ◽  
Single Exchange ◽  
The One

The present article discusses the exact observability of the wave equation when the observation subset of the boundary is variable in time. In the one-dimensional case, we prove an equivalent condition for the exact observability, which takes into account only the location in time of the observation. To this end we use Fourier series. Then we investigate the two specific cases of single exchange of the control position, and of exchange at a constant rate. In the multi-dimensional case, we analyse sufficient conditions for the exact observability relying on the multiplier method. In the last section, the multi-dimensional results are applied to specific settings and some connections between the one and multi-dimensional case are discussed; furthermore some open problems are presented.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

Higher Dimensional Asymptotic Cycles

2003 ◽  
Vol 55 (3) ◽  
pp. 636-648 ◽  
Author(s):  
Sol Schwartzman
Keyword(s):  
Invariant Measure ◽  
Compact Manifold ◽  
Invariant Measures ◽  
Sufficient Conditions ◽  
Stationary Points ◽  
Dimensional Case ◽  
One Dimensional ◽  
Smooth Flow ◽  
Higher Dimensional ◽  
The One

AbstractGiven a p-dimensional oriented foliation of an n-dimensional compact manifold Mn and a transversal invariant measure τ, Sullivan has defined an element of Hp(Mn; R). This generalized the notion of a μ-asymptotic cycle, which was originally defined for actions of the real line on compact spaces preserving an invariant measure μ. In this one-dimensional case there was a natural 1—1 correspondence between transversal invariant measures τ and invariant measures μ when one had a smooth flow without stationary points.For what we call an oriented action of a connected Lie group on a compact manifold we again get in this paper such a correspondence, provided we have what we call a positive quantifier. (In the one-dimensional case such a quantifier is provided by the vector field defining the flow.) Sufficient conditions for the existence of such a quantifier are given, together with some applications.

scholarly journals Partial best approximations and the absolute Cesaro summability of multiple Fourier series

2021 ◽  
Vol 103 (3) ◽  
pp. 4-12
Author(s):  
S. Bitimkhan ◽  
◽  
D.T. Alibieva ◽  
Keyword(s):  
Fourier Series ◽  
Sufficient Conditions ◽  
Multiple Fourier Series ◽  
Dimensional Case ◽  
Cesàro Summability ◽  
Best Approximations ◽  
One Dimensional ◽  
Cesaro Summability ◽  
The Absolute ◽  
The One

The article is devoted to the problem of absolute Cesaro summability of multiple trigonometric Fourier series. Taking a central place in the theory of Fourier series this problem was developed quite widely in the one-dimensional case and the fundamental results of this theory are set forth in the famous monographs by N.K. Bari, A. Zigmund, R. Edwards, B.S. Kashin and A.A. Saakyan [1–4]. In the case of multiple series, the corresponding theory is not so well developed. The multidimensional case has own specifics and the analogy with the one-dimensional case does not always be unambiguous and obvious. In this article, we obtain sufficient conditions for the absolute summability of multiple Fourier series of the function f ∈ Lq(Is) in terms of partial best approximations of this function. Four theorems are proved and four different sufficient conditions for the |C; β¯|λ-summability of the Fourier series of the function f are obtained. In the first theorem, a sufficient condition for the absolute |C; β¯|λ- summability of the Fourier series of the function f is obtained in terms of the partial best approximation of this function which consists of s conditions, in the case when β1 = ... = βs = 1/q'. Other sufficient conditions are obtained for double Fourier series. Sufficient conditions for the |C; β1; β2|λ-summability of the Fourier series of the function f ∈ Lq(I2) are obtained in the cases β1 = 1/q', −1 < β2 < 1/q'(in the second theorem), 1/q'< β1 < +∞, β2 = 1/q', (in the third theorem), −1 < β1 < 1/q', 1/q' < β2 < +∞ (in the fourth theorem).

REPETITIONS, FULLNESS, AND UNIFORMITY IN TWO-DIMENSIONAL WORDS

2004 ◽  
Vol 15 (02) ◽  
pp. 355-383 ◽  
Author(s):  
ARTURO CARPI ◽  
ALDO de LUCA
Keyword(s):  
Essential Role ◽  
Finite Alphabet ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Fixed Size ◽  
Open Problems ◽  
One Dimensional ◽  
Combinatorial Properties ◽  
The Difference ◽  
The One

We consider some combinatorial properties of two-dimensional words (or pictures) over a given finite alphabet, which are related to the number of occurrences in them of words of a fixed size (m,n). In particular a two-dimensional word (briefly, 2D-word) is called (m,n)-full if it contains as factors (or subwords) all words of size (m,n). An (m,n)-full word such that any word of size (m,n) occurs in it exactly once is called a de Bruijn word of order (m,n). A 2D-word w is called (m,n)-uniform if the difference in the number of occurrences in w of any two words of size (m,n) is at most 1. A 2D-word is called uniform if it is (m,n)-uniform for all m,n>0. In this paper we extend to the two-dimensional case some results relating the notions above which were proved in the one-dimensional case in a preceding article. In this analysis the study of repeated factors in a 2D-word plays an essential role. Finally, some open problems and conjectures are discussed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

Thermally corrected solutions of the one-dimensional wave equation for the laser-induced ultrasound

2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  
Keyword(s):  
Wave Equation ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

Numerical assessment on the performance of variable area single- and two-stage ejectors: A comparative study

2021 ◽  
pp. 095440892110331
Author(s):  
Anil Kumar ◽  
Virendra Kumar ◽  
PMV Subbarao ◽  
Surendra K Yadav ◽  
Gaurav Singhal
Keyword(s):  
Change Theory ◽  
Single Stage ◽  
Two Stage ◽  
Entrainment Ratio ◽  
Ansys Fluent ◽  
One Dimensional ◽  
Flow Parameters ◽  
Constant Rate ◽  
Numerical Assessment ◽  
The One

The two-stage ejector has been suggested to replace the single-stage ejector geometrical configuration better to utilize the discharge flow’s redundant momentum to induce secondary flow. In this study, the one-dimensional gas dynamic constant rate of momentum change theory has been utilized to model a two-stage ejector along with a single-stage ejector. The proposed theory has been utilized in the computation of geometry and flow parameters of both the ejectors. The commercial computational fluid dynamics tool ANSYS-Fluent 14.0 has been utilized to predict performance and visualize the flow. The performance in terms of entrainment ratio has been compared under on- design and off-design conditions. The result shows that the two-stage ejector configuration has improved (≈57%) entrainment capacity than the single-stage ejector under the on-design condition.

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