Kreı̆n Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One

2020 ◽  
pp. 91-112
Author(s):  
Claudio Cacciapuoti
Keyword(s):  
Dimension One

scholarly journals Exact solutions for the total variation denoising problem of piecewise constant images in dimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Total Variation ◽  
Piecewise Constant ◽  
Geometrical Properties ◽  
Total Variation Denoising ◽  
Fidelity Term ◽  
Dimension One

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.

scholarly journals Nonlinear Conditions for Ultradifferentiability

2021 ◽  
Author(s):  
David Nicolas Nenning ◽  
Armin Rainer ◽  
Gerhard Schindl
Keyword(s):  
General Validity ◽  
Dimension One ◽  
Analogous Theorem

AbstractA remarkable theorem of Joris states that a function f is $$C^\infty $$ C ∞ if two relatively prime powers of f are $$C^\infty $$ C ∞ . Recently, Thilliez showed that an analogous theorem holds in Denjoy–Carleman classes of Roumieu type. We prove that a division property, equivalent to Joris’s result, is valid in a wide variety of ultradifferentiable classes. Generally speaking, it holds in all dimensions for non-quasianalytic classes. In the quasianalytic case we have general validity in dimension one, but we also get validity in all dimensions for certain quasianalytic classes.

scholarly journals From non-local Eringen’s model to fractional elasticity

2018 ◽  
Vol 24 (6) ◽  
pp. 1935-1953 ◽  
Author(s):  
Anton Evgrafov ◽  
José C. Bellido
Keyword(s):  
Riesz Potential ◽  
Heterogeneous Material ◽  
Research Literature ◽  
Stress Concentrations ◽  
Uniqueness Of Solutions ◽  
Numerical Studies ◽  
Smooth Kernels ◽  
Ill Posed ◽  
Non Local ◽  
Dimension One

Eringen’s model is one of the most popular theories in non-local elasticity. It has been applied to many practical situations with the objective of removing anomalous stress concentrations around geometric shape singularities, which appear when local modelling is used. Despite the great popularity of Eringen’s model within the mechanical engineering community, even the most basic questions such as the existence and uniqueness of solutions have been rarely considered in research literature for this model. In this work we focus on precisely these questions, proving that the model is in general ill-posed in the case of smooth kernels, the case which appears rather often in numerical studies. We also consider the case of singular, non-smooth kernels and for the paradigmatic case of Riesz potential we establish the well-posedness of the model in fractional Sobolev spaces. For such a kernel, in dimension one the model reduces to the well-known fractional Laplacian. Finally, we discuss possible extensions of Eringen’s model to spatially heterogeneous material distributions.

scholarly journals A Note on One-dimensional Varieties Over the Complex p-adic Field

2018 ◽  
Vol 11 (4) ◽  
pp. 1046-1057
Author(s):  
Amran Dalloul
Keyword(s):  
One Dimensional ◽  
Dimension One

In this paper, we study the varieties V ⊆ C 4 p of dimension one that contain points of the form (x1, x2, exp(x1), exp(x2)) by using tools from Non-Archimedian Analysis.

scholarly journals Extended gradient systems: Dimension one

2000 ◽  
Vol 6 (3) ◽  
pp. 503-518 ◽  
Author(s):  
Siniša Slijepčević
Keyword(s):  
Gradient Systems ◽  
Dimension One

Pole shifting for families of systems: The dimension one case

1988 ◽  
Vol 1 (3) ◽  
pp. 285-292 ◽  
Author(s):  
James Brewer ◽  
Lee Klingler
Keyword(s):  
Dimension One

Perceptual Organization of Speech Sounds by Infants

1983 ◽  
Vol 26 (2) ◽  
pp. 268-282 ◽  
Author(s):  
James Hillenbrand
Keyword(s):  
Perceptual Organization ◽  
Control Group ◽  
Stop Consonants ◽  
Speech Sounds ◽  
Head Turn ◽  
Male And Female ◽  
A Value ◽  
Feature Similarity ◽  
Feature Dimension ◽  
Dimension One

An operant head-turn procedure was used to test whether 6-month-old infants recognize the auditor similarity of speech sounds sharing a value on a phonetic-feature dimension. One group of infants was reinforced for head turns when a change occurred from a series of repeating background stimuli containing nasal consonants ([m, n, ŋ]) to repetitions from a category of syllables containing voiced stop consonants ([b, d, g]), or to a change from stops to nasals. The stimuli were naturally produced by both male and female talkers. The performance of infants in this "phonetic" group was compared to that of infants in a "nonphonetic" control group. Using the same procedures, these infants were reinforced for head turns to a group of phonetically unrelated speech sounds. Results indicated that the performance of infants in the group trained on phonetically related speech sounds was far superior to that of infants in the nonphonetic control group. These findings suggest that prelinguistic infants can perceptually organize speech sounds on the basis of auditory properties related to feature similarity.

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