A letter from Zellig Harris to André Lentin

2021 ◽  
Author(s):  
Bruce Nevin
Keyword(s):  
Point Of View ◽  
French Translation ◽  
Comprehensive Overview ◽  
Mathematical Point

Summary Toward the end of his life, Zellig Harris (1909–1992) wrote a brief account of the origins and development of his work to establish the foundations of a science of language on mathematical principles. A French translation was published in 1990, and in the same publication appeared a parallel appraisal from a mathematical point of view by André Lentin (1913–2015). Early the following year, having reread Lentin’s essay several times, Harris wrote him the letter which is presented here. More than a gesture of thanks and appreciation, this letter further illuminates the comprehensive overview afforded by the two essays, both of which appeared in English in 2002.

scholarly journals Contact interactions in complex fibrous metamaterials

2021 ◽  
Author(s):  
Mario Spagnuolo ◽  
Antonio M. Cazzani
Keyword(s):  
Strain Energy ◽  
Point Of View ◽  
The Other ◽  
Contact Interactions ◽  
Coupling Term ◽  
Dissipation Potential ◽  
Parallel Fibers ◽  
Mathematical Point

AbstractIn this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

scholarly journals Generalizations of the Lagrange mean value theorem and applications

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Miodrag Mateljevic ◽  
Marek Svetlik ◽  
Miloljub Albijanic ◽  
Nebojsa Savic
Keyword(s):  
Economic Growth ◽  
Growth Model ◽  
Arbitrary Function ◽  
Mean Value ◽  
Point Of View ◽  
Neoclassical Economic ◽  
Mean Value Theorem ◽  
Mathematical Point ◽  
Economic Growth Model

In this paper we give a generalization of the Lagrange mean value theorem via lower and upper derivative, as well as appropriate criteria of monotonicity and convexity for arbitrary function f : (a, b) ( R. Some applications to the neoclassical economic growth model are given (from mathematical point of view).

S-matrix Theory

2020 ◽  
pp. 622-675
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Matrix Theory ◽  
Point Of View ◽  
Integrable Models ◽  
Geometrical Interpretation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Recursive Structure ◽  
Mathematical Point ◽  
S Matrix ◽  
Dynamical Principle

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

Congenital adrenal hyperplasia in children

2011 ◽  
pp. 1137-1147
Author(s):  
Felix G. Riepe
Keyword(s):  
Congenital Adrenal Hyperplasia ◽  
Clinical Picture ◽  
Point Of View ◽  
Adrenal Hyperplasia ◽  
Hydroxylase Deficiency ◽  
Comprehensive Overview ◽  
21 Hydroxylase Deficiency ◽  
Paediatric Endocrinologist

Congenital adrenal hyperplasia (CAH) is caused by the genetic impairment of one of the five enzymes required for the biosynthesis of cortisol from cholesterol. In 95% of cases 21-hydroxylase deficiency (21-OHD) is responsible for the disease (1). Classic 21-OHD has an incidence varying from 1:11 800 to 1:21 800, depending on the population background. The pathophysiology, clinical picture, genetics, and the unique aspects of management from the point of view of the paediatric endocrinologist are addressed, and the problems encountered from birth to puberty are described. The child specific issues of rare forms of CAH are summarized thereafter. The reader is referred to Chapter 5.11 for a comprehensive overview of 21-OHD and for more details on all other forms of CAH.

Games of Chance: I. The Banker’s Clock

1933 ◽  
Vol 17 (226) ◽  
pp. 296-297
Author(s):  
S.T Shovelton
Keyword(s):  
Point Of View ◽  
Mathematical Point ◽  
Mathematical Probability ◽  
Games Of Chance ◽  
The Face

The game of Banker’s Clock provides an interesting question in mathematical probability In this game the banker turns up in sequence the first twelve cards of a well-shuffled ordinary pack of 52 cards. He backs himself to turn up at least one card of which the face value corresponds to its position in the sequence, an Ace ranking as one, a Jack as eleven and a Queen as twelve. The interest in the question from the mathematical point of view is in finding the probability that the event will happen.

Note on the FFT Based Computational Code and Its Application

2008 ◽  
Author(s):  
Xiaoqing Jin ◽  
Leon M. Keer ◽  
Qian Wang
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Toeplitz Matrix ◽  
Contact Problems ◽  
Point Of View ◽  
Fast Fourier Transform Algorithm ◽  
Discrete Convolution ◽  
Mathematical Point ◽  
Computational Code

The discrete convolution based Fast Fourier Transform algorithm (DC-FFT) has been successfully applied in numerical simulation of contact problems. The algorithm is revisited from a mathematical point of view, equivalent to a Toeplitz matrix multiplied by a vector. The nature of the convolution property permits one to implement the algorithm with fewer constraints in choosing the computational domains. This advantageous feature is explored in the present work, and is expected to be beneficial to many tribological studies.

A Kind of Enhanced Slotted ALOHA Algorithm for Anti-Collision in RFID System

2013 ◽  
Vol 756-759 ◽  
pp. 3497-3500
Author(s):  
Fan Wei Meng ◽  
Yue Zhao ◽  
Cui Hong Ma ◽  
You Liang Yang
Keyword(s):  
Real Time ◽  
System Performance ◽  
Conflict Situation ◽  
Point Of View ◽  
Slotted Aloha ◽  
Mathematical Point ◽  
Frame Length ◽  
Time Estimates ◽  
Rfid System ◽  
Framed Slotted Aloha

in the RFID system, the conflict caused by the multi-label has been affecting system performance. This paper proposed a grouping dynamic framed slotted ALOHA algorithm based on the analysis of ALOHA algorithm. According to the conflict situation, to make real-time estimates the number of tags on the dynamic framed slotted ALOHA algorithm from the mathematical point of view, Dynamically change the frame length or the labels are grouped to reduce the label probability of collisions, thereby improving the efficiency of the recognition.

Neuro-Technical Interfaces Based on Biocompatible Polymeric Substrates

2007 ◽  
Vol 1009 ◽  
Author(s):  
Thomas Stieglitz
Keyword(s):  
System Integration ◽  
Microelectromechanical Systems ◽  
Electrode Site ◽  
Point Of View ◽  
Multielectrode Arrays ◽  
Electrode Arrays ◽  
Process Technology ◽  
Comprehensive Overview ◽  
Adhesion Properties ◽  
Polymeric Substrates

AbstractMultielectrode arrays create the interfaces between nerves and technical systems in neuroprosthetic devices. MEMS (microelectromechanical systems) technologies offer opportunities to develop high density arrays with large numbers of electrodes and smallest dimensions of electrode site area and pitch. Polymers are promising candidates for flexible substrates of these electrode arrays to meet the requirements of structural biocompatibility. In addition, these substrates must be biostable and should be non-toxic. From an engineering point of view, material processing should be feasible with standard MEMS process technology. Fail-safe integration of electronic circuitry, encapsulation of the systems with substrate-integrated electrodes and connection to cables and connectors is of great importance for reliable (micro-) implants.A comprehensive overview of the application of polymers like silicone rubber, polyimide, and parylene C as substrate, insulation and encapsulation material for multielectrode arrays will be given. Assembling techniques for system integration and encapsulation concepts will be discussed with a special attention on the adhesion properties between substrate, interconnects and insulation and possible failure mechanisms. Application scenarios include peripheral nerve interfaces like cuff and sieve electrodes as well as multielectrode arrays for retinal vision prostheses and shaft and grid arrays for the central nervous system interfaces.

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