scholarly journals Bispectrality and Time–Band Limiting: Matrix-valued Polynomials

2018 ◽  
Vol 2020 (13) ◽  
pp. 4016-4036 ◽  
Author(s):  
F Alberto Grünbaum ◽  
Inés Pacharoni ◽  
Ignacio Zurrián
Keyword(s):  
Signal Processing ◽  
Differential Operator ◽  
Integral Operator ◽  
General Condition ◽  
Integrable Systems ◽  
Joint Work ◽  
The Subject ◽  
Time Band ◽  
Commuting Differential Operator

Abstract The subject of time–band limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its eigenfunctions. Bispectrality is an effort to dig into the reasons behind this miracle and goes back to joint work with H. Duistermaat. This search has revealed unexpected connections with several parts of mathematics, including integrable systems. Here we consider a matrix-valued version of bispectrality and give a general condition under which we can display a constructive and simple way to obtain the commuting differential operator. Furthermore, we build an operator that commutes with both the time-limiting operator and the band-limiting operators.

Time functions revisited

2015 ◽  
Vol 12 (08) ◽  
pp. 1560027 ◽  
Author(s):  
Albert Fathi
Keyword(s):  
Time Function ◽  
Joint Work ◽  
Aubry Set ◽  
The Subject

In this paper we revisit our joint work with Antonio Siconolfi on time functions. We will give a brief introduction to the subject. We will then show how to construct a Lipschitz time function in a simplified setting. We will end with a new result showing that the Aubry set is not an artifact of our proof of existence of time functions for stably causal manifolds.

scholarly journals From the theory to practice: Five years of urban regeneration workshops

2018 ◽  
Vol 8 (3) ◽  
pp. 179
Author(s):  
Raimundo Bambó-Naya ◽  
Pablo De la Cal-Nicolás ◽  
Carmen Díez-Medina ◽  
Sergio García-Pérez ◽  
Javier Monclús-Fraga
Keyword(s):  
Urban Regeneration ◽  
Joint Work ◽  
Teaching Innovation ◽  
Academic Field ◽  
Future Challenges ◽  
Academic Courses ◽  
The Subject ◽  
The University ◽  
Previous Phase ◽  
Selection Of

The aim of this communication is to present the experience of four academic courses in the subject of Integrated Urban and Landscape Design, taught in the framework of the Master in Architecture of the School of Engineering and Architecture of the University of Zaragoza. It addresses urban regeneration interventions in vulnerable areas of the consolidated city with approaches to teaching innovation in the academic field and in the topic of user participation.The workshop methodology is explained in detail, paying more attention to the process followed than to the specific results of the workshop. The different stages of the process are presented: previous phase and selection of the study area, phase of analysis and diagnosis, phase of proposals, where a joint work is carried out with vision of action in the whole of the neighbourhood, and phase of presentation of the results to the Neighbours. Finally, some future challenges of this workshop are outlined.

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.

scholarly journals Assessment of a steel bridge corrosion degree

2018 ◽  
Vol 49 ◽  
pp. 00098 ◽  
Author(s):  
Jacek Selejdak ◽  
Mariusz Urbański ◽  
Marek Winiarski
Keyword(s):  
Structural Steel ◽  
General Condition ◽  
Load Capacity ◽  
Technical Condition ◽  
Steel Bridge ◽  
Railway Line ◽  
Railway Tracks ◽  
The Subject ◽  
Corrosion Assessment ◽  
National Road

The subject of this analysis is connected with the verification of the load capacity of the span structure taking into account the degree of corrosion of the railway viaduct components located at 41.446 km, on the railway line no. 301 of "Kotlarnia" SA Sand Mine built over the national road DK88 and railway tracks PKP-PLK near T. Kościuszki street in Zabrze The general condition of the structure with regard to the corrosion assessment of structural steel is presented in the paper. Static and strength calculations were carried out to determine the load capacity class, and as a result of the analysis it was found that the technical condition of the facility steel girders is suitable for repair.

scholarly journals Integral operators, bispectrality and growth of Fourier algebras

2020 ◽  
Vol 2020 (766) ◽  
pp. 151-194 ◽  
Author(s):  
W. Riley Casper ◽  
Milen T. Yakimov
Keyword(s):  
Differential Operator ◽  
Integral Kernel ◽  
Exact Estimate ◽  
Airy Functions ◽  
Direct Computation ◽  
Infinite Dimensional ◽  
First Order ◽  
Rank 2 ◽  
Commuting Differential Operator ◽  
Algorithmic Procedure

AbstractIn the mid 1980s it was conjectured that every bispectral meromorphic function {\psi(x,y)} gives rise to an integral operator {K_{\psi}(x,y)} which possesses a commuting differential operator. This has been verified by a direct computation for several families of functions {\psi(x,y)} where the commuting differential operator is of order {\leq 6}. We prove a general version of this conjecture for all self-adjoint bispectral functions of rank 1 and all self-adjoint bispectral Darboux transformations of the rank 2 Bessel and Airy functions. The method is based on a theorem giving an exact estimate of the second- and first-order terms of the growth of the Fourier algebra of each such bispectral function. From it we obtain a sharp upper bound on the order of the commuting differential operator for the integral kernel {K_{\psi}(x,y)} leading to a fast algorithmic procedure for constructing the differential operator; unlike the previous examples its order is arbitrarily high. We prove that the above classes of bispectral functions are parametrized by infinite-dimensional Grassmannians which are the Lagrangian loci of the Wilson adelic Grassmannian and its analogs in rank 2.

scholarly journals Starlikeness Condition for a New Differential-Integral Operator

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 694 ◽  
Author(s):  
Mugur Acu ◽  
Gheorghe Oros
Keyword(s):  
Differential Operator ◽  
Integral Operator ◽  
Differential Subordination

A new differential-integral operator of the form I n f ( z ) = ( 1 − λ ) S n f ( z ) + λ L n f ( z ) , z ∈ U , f ∈ A , 0 ≤ λ ≤ 1 , n ∈ N is introduced in this paper, where S n is the Sălăgean differential operator and L n is the Alexander integral operator. Using this operator, a new integral operator is defined as: F ( z ) = β + γ z γ ∫ 0 z I n f ( z ) · t β + γ − 2 d t 1 β , where I n f ( z ) is the differential-integral operator given above. Using a differential subordination, we prove that the integral operator F ( z ) is starlike.

Time-and-band limiting for matrix orthogonal polynomials of Jacobi type

2017 ◽  
Vol 06 (04) ◽  
pp. 1740001 ◽  
Author(s):  
M. Castro ◽  
F. A. Grünbaum
Keyword(s):  
Signal Processing ◽  
Differential Operator ◽  
Orthogonal Polynomials ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Jacobi Polynomials ◽  
Matrix Theory ◽  
Matrix Orthogonal Polynomials

We extend to a situation involving matrix-valued orthogonal polynomials a scalar result that plays an important role in Random Matrix Theory and a few other areas of mathe-matics and signal processing. We consider a case of matrix-valued Jacobi polynomials which arises from the study of representations of [Formula: see text], a group that plays an important role in Random Matrix Theory. We show that in this case an algebraic miracle, namely the existence of a differential operator that commutes with a naturally arising integral one, extends to this matrix-valued situation.

Optimization Strategies for Machine Tool Spindle-Bearing Systems: A Critical Review

1992 ◽  
Vol 114 (2) ◽  
pp. 244-253 ◽  
Author(s):  
J. A. Brandon ◽  
K. J. H. Al-Shareef
Keyword(s):  
Signal Processing ◽  
Machine Tool ◽  
Machine Tools ◽  
High Performance ◽  
Optimization Theory ◽  
Early Research ◽  
Research Activity ◽  
Spindle Bearing ◽  
Machine Tool Spindle ◽  
The Subject

After a period of relative quiescence, optimization of the design of high performance machine tools has become the subject of considerable recent research activity. Advances in the general areas of optimization theory and signal processing have enabled effective solutions to problems regarded as intractable by earlier analysts. There is, however, a danger that valuable early research may be discounted or overlooked when there is a substantial period of dormancy in a discipline. The survey links early work with current activity in the optimization of machine tool spindle bearing systems.

scholarly journals Real Time Detection of R – Peak in QRS Complex of ECG using Microcontroller

2018 ◽  
Vol 11 (1) ◽  
pp. 372
Author(s):  
Santipriya N ◽  
Venkateswara Rao M ◽  
Arun V ◽  
R Karthik
Keyword(s):  
Signal Processing ◽  
Real Time ◽  
Heart Diseases ◽  
Processing Algorithm ◽  
Ecg Signal ◽  
Qrs Complex ◽  
Peak Detector ◽  
Signal Processing Algorithm ◽  
The Subject ◽  
Real Time Detection

<p>Real-time detection of R peaks in QRS complex of ECG signal is the first step in the processing of ECG waveform. Based on this, various other ECG parameters can be extracted. These parameters provide substantial information about various heart diseases. In this paper, we are proposing a method to detect R – peaks of ECG signal dynamically. The most prominent role in the R – peak detector is executed by the microcontroller. This method originates by acquiring signal from the subject and necessary pre-processing is carried out on the signal in order to achieve the denoised signal. Subsequently, this filtered signal is handed over to microcontroller where a pulse is generated for each R – peak that is found in the QRS complex of ECG signal. The microcontroller is embedded with a signal processing algorithm. The algorithm used to determine the R – peaks is double differentiation method which is straightforward and robust.  </p>

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