scholarly journals A survey of topics related to Functional Analysis and Applied Sciences

2021 ◽  
Vol 20 ◽  
pp. 312-359
Author(s):  
Denise Huet
Keyword(s):  
Applied Sciences ◽  
Functional Analysis ◽  
Quantum Mechanics ◽  
Partial Differential Equations ◽  
Bergman Spaces ◽  
Natural Sciences ◽  
Spectral Flow ◽  
Advanced Students ◽  
Different Types ◽  
Harmonic Bergman Spaces

This survey is the result of investigations suggested by recent publications on functional analysis and applied sciences. It contains short accounts of the above theories not usually combined in a single document and completes the work of D. Huet 2017. The main topics which are dealt with involve spectrum and pseudospectra of partial differential equations, Steklov eigenproblems, harmonic Bergman spaces, rotation number and homeomorphisms of the circle, spectral flow, homogenization. Applications to different types of natural sciences such as echosystems, biology, elasticity, electromagnetisme, quantum mechanics, are also presented. It aims to be a useful tool for advanced students in mathematics and applied sciences.

scholarly journals THE INFLUENCE OF DESIGN BRIEF INFORMATION ON CREATIVE OUTCOMES BY NOVICE AND ADVANCED STUDENTS

2021 ◽  
Vol 1 ◽  
pp. 3041-3050
Author(s):  
Georgios Koronis ◽  
Hernan Casakin ◽  
Arlindo Silva ◽  
Jacob Kai Siang Kang
Keyword(s):  
Design Education ◽  
Design Problems ◽  
Frame Design ◽  
Design Creativity ◽  
Abstract Representations ◽  
Advanced Students ◽  
Different Types ◽  
Fishbone Diagram ◽  
Design Expertise ◽  
Novel Design

AbstractThis study centers on using different types of brief information to support creative outcomes in architectural and engineering design and its relation to design expertise. We explore the influence of design briefs characterized by abstract representations and/or instructions to frame design problems on the creativity of concept sketches produced by novice and advanced students. Abstract representations of problem requirements served as stimuli to encourage associative thinking and knowledge transfer. The Ishikawa/Fishbone Diagram was used to foster design restructuring and to modify viewpoints about the main design drives and goals. The design outcomes generated by novice and advanced engineering/architecture students were assessed for their creativity using a pairwise experimental design. Results indicated that advanced students generated more novel design solutions while also contributing the most useful solutions overall. Implications for creativity in design education and professional practice are presented. Educational programs aimed at promoting creativity in the design studio may find it helpful to consider that the way design briefs are constructed can either promote or inhibit different aspects of design creativity.

scholarly journals Emotions and Cognitions. Fourteenth-Century Discussions on the Passions of the Soul

Vivarium ◽  
2005 ◽  
Vol 43 (2) ◽  
pp. 250-274 ◽  
Author(s):  
Dominik Perler
Keyword(s):  
Functional Analysis ◽  
Fourteenth Century ◽  
Mental States ◽  
Complex Phenomenon ◽  
Emotional Conflict ◽  
Cognitive Component ◽  
Cognitive Components ◽  
Different Types ◽  
William Ockham ◽  
Intellectual Level

AbstractMedieval philosophers clearly recognized that emotions are not simply "raw feelings" but complex mental states that include cognitive components. They analyzed these components both on the sensory and on the intellectual level, paying particular attention to the different types of cognition that are involved. This paper focuses on William Ockham and Adam Wodeham, two fourteenth-century authors who presented a detailed account of "sensory passions" and "volitional passions". It intends to show that these two philosophers provided both a structural and a functional analysis of emotions, i.e., they explained the various elements constituting emotions and delineated the causal relations between these elements. Ockham as well as Wodeham emphasized that "sensory passions" are not only based upon cognitions but include a cognitive component and are therefore intentional. In addition, they pointed out that "volitional passions" are based upon a conceptualization and an evaluation of given objects. This cognitivist approach to emotions enabled them to explain the complex phenomenon of emotional conflict, a phenomenon that has its origin in the co-presence of various emotions that involve conflicting evaluations.

scholarly journals Revolutions in the earth sciences

1999 ◽  
Vol 354 (1392) ◽  
pp. 1915-1919 ◽  
Author(s):  
Claude Allègre ◽  
Vincent Courtillot
Keyword(s):  
Earth Sciences ◽  
Quantum Mechanics ◽  
20Th Century ◽  
Plate Tectonics ◽  
Statistical Physics ◽  
Natural Sciences ◽  
Scientific Revolutions ◽  
The Earth

The 20th century has been a century of scientific revolutions for many disciplines: quantum mechanics in physics, the atomic approach in chemistry, the nonlinear revolution in mathematics, the introduction of statistical physics. The major breakthroughs in these disciplines had all occurred by about 1930. In contrast, the revolutions in the so–called natural sciences, that is in the earth sciences and in biology, waited until the last half of the century. These revolutions were indeed late, but they were no less deep and drastic, and they occurred quite suddenly. Actually, one can say that not one but three revolutions occurred in the earth sciences: in plate tectonics, planetology and the environment. They occurred essentially independently from each other, but as time passed, their effects developed, amplified and started interacting. These effects continue strongly to this day.

Bose-Einstein-type statistics, order statistics and planar random motions with three directions

2004 ◽  
Vol 36 (3) ◽  
pp. 937-970 ◽  
Author(s):  
S. Leorato ◽  
E. Orsingher
Keyword(s):  
Partial Differential Equations ◽  
Order Statistics ◽  
Constant Velocity ◽  
Uniform Motion ◽  
Change Of Direction ◽  
Telegraph Process ◽  
Cyclic Motion ◽  
Different Types ◽  
Random Motions ◽  
Bose Einstein

In this paper we study different types of planar random motions (performed with constant velocity) with three directions, defined by the vectors dj = (cos(2πj/3), sin(2πj/3)) for j = 0, 1, 2, changing at Poisson-paced times. We examine the cyclic motion (where the change of direction is deterministic), the completely uniform motion (where at each Poisson event each direction can be taken with probability ) and the symmetrically deviating case (where the particle can choose all directions except that taken before the Poisson event). For each of the above random motions we derive the explicit distribution of the position of the particle, by using an approach based on order statistics. We prove that the densities obtained are solutions of the partial differential equations governing the processes. We are also able to give the explicit distributions on the boundary and, for the case of the symmetrically deviating motion, we can write it as the distribution of a telegraph process. For the symmetrically deviating motion we use a generalization of the Bose-Einstein statistics in order to determine the distribution of the triple (N0, N1, N2) (conditional on N(t) = k, with N0 + N1 + N2 = N(t) + 1, where N(t) is the number of Poisson events in [0, t]), where Nj denotes the number of times the direction dj (j = 0, 1, 2) is taken. Possible extensions to four directions or more are briefly considered.

scholarly journals Toeplitz operators on weighted harmonic Bergman spaces

2018 ◽  
Vol 12 (4) ◽  
pp. 808-842 ◽  
Author(s):  
Zipeng Wang ◽  
Xianfeng Zhao
Keyword(s):  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Harmonic Bergman Spaces

KORÁNYI’S LEMMA FOR HOMOGENEOUS SIEGEL DOMAINS OF TYPE II. APPLICATIONS AND EXTENDED RESULTS

2014 ◽  
Vol 90 (1) ◽  
pp. 77-89 ◽  
Author(s):  
DAVID BÉKOLLÉ ◽  
HIDEYUKI ISHI ◽  
CYRILLE NANA
Keyword(s):  
Functional Analysis ◽  
Bergman Kernel ◽  
Atomic Decomposition ◽  
Bergman Spaces ◽  
Decomposition Theorem ◽  
Interpolation Theorem ◽  
Type Ii ◽  
Siegel Domain ◽  
Homogeneous Case ◽  
Siegel Domains

AbstractWe show that the modulus of the Bergman kernel $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}B(z, \zeta )$ of a general homogeneous Siegel domain of type II is ‘almost constant’ uniformly with respect to $z$ when $\zeta $ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used it to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces $A^p$ on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents $p$ via functional analysis using recent estimates.

Bose-Einstein-type statistics, order statistics and planar random motions with three directions

2004 ◽  
Vol 36 (03) ◽  
pp. 937-970 ◽  
Author(s):  
S. Leorato ◽  
E. Orsingher
Keyword(s):  
Partial Differential Equations ◽  
Order Statistics ◽  
Constant Velocity ◽  
Uniform Motion ◽  
Change Of Direction ◽  
Telegraph Process ◽  
Cyclic Motion ◽  
Different Types ◽  
Random Motions ◽  
Bose Einstein

In this paper we study different types of planar random motions (performed with constant velocity) with three directions, defined by the vectorsdj= (cos(2πj/3), sin(2πj/3)) forj= 0, 1, 2, changing at Poisson-paced times. We examine the cyclic motion (where the change of direction is deterministic), the completely uniform motion (where at each Poisson event each direction can be taken with probability) and the symmetrically deviating case (where the particle can choose all directions except that taken before the Poisson event). For each of the above random motions we derive the explicit distribution of the position of the particle, by using an approach based on order statistics. We prove that the densities obtained are solutions of the partial differential equations governing the processes. We are also able to give the explicit distributions on the boundary and, for the case of the symmetrically deviating motion, we can write it as the distribution of a telegraph process. For the symmetrically deviating motion we use a generalization of the Bose-Einstein statistics in order to determine the distribution of the triple (N0,N1,N2) (conditional onN(t) =k, withN0+N1+N2=N(t) + 1, whereN(t) is the number of Poisson events in [0,t]), whereNjdenotes the number of times the directiondj(j= 0, 1, 2) is taken. Possible extensions to four directions or more are briefly considered.

scholarly journals Topologies on Z n that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1072 ◽  
Author(s):  
Sang-Eon Han ◽  
Saeid Jafari ◽  
Jeong Kang
Keyword(s):  
Applied Sciences ◽  
Topological Space ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Discrete Topology ◽  
Separation Axiom ◽  
Different Types

The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on.

scholarly journals Stability of observations of partial differential equations under uncertain perturbations

2017 ◽  
Vol 24 (1) ◽  
pp. 45-61 ◽  
Author(s):  
Martin Lazar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Wave Operator ◽  
System Dynamic ◽  
Schrödinger Equations ◽  
Partial Differential ◽  
Main System ◽  
Different Types ◽  
The Stability ◽  
Observability Estimates

We demonstrate the stability of observability estimates for solutions to wave and Schrödinger equations subjected to additive perturbations. This work generalises recent averaged observability/control results by allowing for systems consisting of operators of different types. We also consider the simultaneous observability problem by which one tries to estimate the energy of each component of a system under consideration. Our analysis relies on microlocal defect tools, in particular on standard H-measures when the main system dynamic is governed by the wave operator, and parabolic H-measures in the case of the Schrödinger operator.

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