Search results for "FRACTAL"
showing 10 items of 329 documents
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
Optical-data storage-readout technique based on fractal encrypting masks
2009
We propose the use of fractal structured diffractive masks as keys in secure storage-readout systems. A joint transform correlator based on a photorefractive crystal in the Fourier domain is implemented to perform encryption and decryption. We discuss the advantages of encrypting information using this kind of deterministic keys in comparison to conventional random phase masks. Preliminary experimental results are presented to demonstrate the effectiveness of the proposed system.
Analysis of 55 cases of adenomatoid odontogenic tumor in an Indian population and review of literature
2021
Background This study reviews the demographic, clinical and radiographic features of adenomatoid odontogenic tumor(AOT) diagnosed in an Indian population over 50 years and also evaluate and compare follicular AOT(F-AOT) and extra-follicular AOT(EF-AOT). Material and Methods 55 diagnosed cases of AOT from 1971-2020 were studied retrospectively. The data regarding the age, sex, location, variant of AOT, duration, clinical features, radiographic appearance, treatment and recurrence were collected and analysed. Results Of the 722 odontogenic tumors diagnosed, 7.6% were AOTs with higher prevalence of extra-follicular (67.3%) than follicular (32.7%) variant. All the tumors were intraosseous with …
Benefits of nonlinear analysis indices of walking stride interval in the evaluation of neurodegenerative diseases.
2021
Indices characterising the long-range temporal structure of walking stride interval (SI) variability such as Hurst exponent (H) and fractal dimension (D) may be used in addition to indices measuring the amount of variability like the coefficient of variation (CV). We assess the added value of the former indices in a clinical neurological context. Our aim is to demonstrate that they provide a clinical significance in aging and in frequent neurodegenerative diseases such as Parkinson's disease, Huntington, and amyotrophic lateral sclerosis. Indices assessing the temporal structure of variability are mainly dependent on SI time series length and algorithms used, making quantitative comparisons…
Temporal Structure of Human Gaze Dynamics Is Invariant During Free Viewing.
2015
We investigate the dynamic structure of human gaze and present an experimental study of the frequency components of the change in gaze position over time during free viewing of computer-generated fractal images. We show that changes in gaze position are scale-invariant in time with statistical properties that are characteristic of a random walk process. We quantify and track changes in the temporal structure using a well-defined scaling parameter called the Hurst exponent, H. We find H is robust regardless of the spatial complexity generated by the fractal images. In addition, we find the Hurst exponent is invariant across all participants, including those with distinct changes to higher or…
Products of snowflaked Euclidean lines are not minimal for looking down
2017
We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.
Relationship between particle size and dissolution rate of bulk powders and sieving characterized fractions of two qualities of orthoboric acid
1996
Drug Dev. Ind. Pharm. ISI Document Delivery No.: VN279 Times Cited: 1 Cited Reference Count: 22 Tromelin, A Habillon, S Andres, C Pourcelot, Y Chaillot, B; International audience; We have carried out a study of the particle size distribution and aqueous dissolution rate of two commercially available qualities of orthoboric acid, labeled ''crystal'' (ABC) and ''powder'' (ABP). In a previous work, we have shown that the two commercial qualities of orthoboric acid chosen as model compound (''powder'' and ''crystal'') are related to the same crystal network in spite of their different names. However, these two qualities have very different size particle distributions, as previously determined b…
A regularized Newton method for locating thin tubular conductivity inhomogeneities
2011
We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…
Estimation des dimensions en présence d'erreurs
2018
Journées du GDR Analyse Multifractale, Nouan-le-Fuzelier, FRANCE, 16-/09/2018 - 20/09/2018; Nous nous posons la question de l'estimation des différentes dimensions fractales lorsque nous sommes en présence de bruit additif (à une itération donnée) ou multiplicatif ( qui se propage à travers les itérations), en testant, sur des fractales construites, les méthodes classiques d'estimation et en analysant la structure des résidus d'estimation.
Oscillatory integrals and fractal dimension
2021
Theory of singularities has been closely related with the study of oscillatory integrals. More precisely, the study of critical points is closely related to the study of asymptotic of oscillatory integrals. In our work we investigate the fractal properties of a geometrical representation of oscillatory integrals. We are motivated by a geometrical representation of Fresnel integrals by a spiral called the clothoid, and the idea to produce a classification of singularities using fractal dimension. Fresnel integrals are a well known class of oscillatory integrals. We consider oscillatory integral $$ I(\tau)=\int_{; ; \mathbb{; ; R}; ; ^n}; ; e^{; ; i\tau f(x)}; ; \phi(x) dx, $$ for large value…