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Global discrepancy and small points on elliptic curves  [PDF]
Matthew Baker,Clayton Petsche
Mathematics , 2005,
Abstract: Let E be an elliptic curve defined over a number field k. In this paper, we define the ``global discrepancy'' of a finite set Z of algebraic points on E which in a precise sense measures how far the set is from being adelically equidistributed. We then prove an upper bound for the global discrepancy of Z in terms of the average canonical height of points in Z. We deduce from this inequality a number of consequences. For example, we give a new and simple proof of the Szpiro-Ullmo-Zhang equidistribution theorem for elliptic curves. We also prove a non-archimedean version of the Szpiro-Ullmo-Zhang theorem which takes place on the Berkovich analytic space associated to E. We then prove some quantitative `non-equidistribution' theorems for totally real or totally p-adic small points. The results for totally real points imply similar bounds for points defined over the maximal cyclotomic extension of a totally real field.
Adult Orthodontics  [PDF]
Anita G,Asiya Begum
Indian Journal of Dental Advancements , 2010,
Abstract: Adult orthodontics is becoming a larger proportion of many practices. Adult orthodontics is concerned with striking a balance between achieving optimal proximal and occlusal contact of the teeth, acceptable dentofacial esthetics, normal function, and reasonable stability. With the adult, it is more frequently concerned with physiological adaptation and is often symptom related, whereas with the child the dealing is with the signs. In the past three decades, a major reorientation of orthodontic thinking has occurred regarding adult patients. Changed lifestyles and patient awareness have increased the demands for adult orthodontic treatment and multidisciplinary dental therapy has allowed better management of the more complicated and unique requirements of the adult patient population, thereby greatly improving the quality of care and treatment prognosis. In addition to goal clarification, adult patients desire treatment efficiency, convenience in appointment timings and good communication with other health care professionals. Almost 80% of the adult patients require interdisciplinary treatment planning and treatment execution. With the adult, consultation with another specialist isn’t occasional. It is the rare adult whom one treats orthodontically without finding it necessary to collaborate with another specialist. This represents both the challenge and the excitement of adult orthodontics.
Gingival esthetics: an orthodontic and periodontal approach
Seixas, Máyra Reis;Costa-Pinto, Roberto Amarante;Araújo, Telma Martins de;
Dental Press Journal of Orthodontics , 2012, DOI: 10.1590/S2176-94512012000500025
Abstract: introduction: currently, people's esthetic requirements and expectations have increased substantially. therefore, dentists have been seeking ways to provide excellent treatment results which, consequently, increasingly require a well organized transdisciplinary approach. the link between orthodontics and periodontics became evident from the moment professionals began to understand the biology of tooth movement. as regards smile esthetics, however, such cooperation is now essential. objective: to show clinically how and when orthodontists and periodontists should work jointly to enhance smile esthetics based on the display and harmony of the gingival contour.
Mean square discrepancy bounds for the number of lattice points in large convex bodies  [PDF]
Alexander Iosevich,Eric Sawyer,Andreas Seeger
Mathematics , 2002,
Abstract: We prove various estimates for the mean square lattice point discrepancy for dilates of a convex body.
A characterization theorem for the $L^{2}$-discrepancy of integer points in dilated polygons  [PDF]
Giancarlo Travaglini,Maria Rosaria Tupputi
Mathematics , 2015,
Abstract: Let $C$ be a convex $d$-dimensional body. If $\rho$ is a large positive number, then the dilated body $\rho C$ contains $\rho^{d}\left\vert C\right\vert +\mathcal{O}\left( \rho^{d-1}\right) $ integer points, where $\left\vert C\right\vert $ denotes the volume of $C$. The above error estimate $\mathcal{O}\left( \rho^{d-1}\right) $ can be improved in several cases. We are interested in the $L^{2}$-discrepancy $D_{C}(\rho)$ of a copy of $\rho C$ thrown at random in $\mathbb{R}^{d}$. More precisely, we consider \[ D_{C}(\rho):=\left\{ \int_{\mathbb{T}^{d}}\int_{SO(d)}\left\vert \textrm{card}\left( \left( \rho\sigma(C)+t\right) \cap\mathbb{Z}^d\right) - \rho^{d}\left\vert C\right\vert \right\vert ^{2}d\sigma dt\right\} ^{1/2}\ , \] where $\mathbb{T}^{d}=$ $\mathbb{R}^{d}/\mathbb{Z}^{d}$ is the $d$-dimensional flat torus and $SO\left( d\right) $ is the special orthogonal group of real orthogonal matrices of determinant $1$. An argument of D. Kendall shows that $D_{C}(\rho)\leq c\ \rho^{(d-1)/2}$. If $C$ also satisfies the reverse inequality $\ D_{C}(\rho)\geq c_{1} \ \rho^{(d-1)/2}$, we say that $C$ is $L^{2}$\emph{-regular}. L. Parnovski and A. Sobolev proved that, if $d>1$, a $d$-dimensional unit ball is $L^{2}% $-regular if and only if $d\not \equiv 1\ (\operatorname{mod}4)$. In this paper we characterize the $L^{2}$-regular convex polygons. More precisely we prove that a convex polygon is not $L^{2}$-regular if and only if it can be inscribed in a circle and it is symmetric about the centre.
Internet and Orthodontics.
P. Karvelas
Hellenic Orthodontic Review , 1998,
Abstract: Internet is spreading at on incredible rate. Orthodontics has already started adapting to this new environment and future developments are something to look forward to. This article presents main addresses directly or indirectly related to orthodontics. Because of the Web dynamics, changes occur so fast that some addresses may not be valid by the time this article is published and there may be new ones that are not included.
A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary  [PDF]
W. G. Nowak
Mathematics , 2006, DOI: 10.4064/aa127-3-6
Abstract: Let B denote a three-dimensional body of rotation, with respect to one coordinate axis, whose boundary is sufficiently smooth and of bounded nonzero Gaussian curvature throughout, except for the two boundary points on the axis of rotation, where the curvature may vanish. For a large real variable t, we are interested in the number A(t) of integer points in the linearly dilated body tB, in particular in the lattice discrepancy P(t) = A(t) - volume(tB). We are able to evaluate the contribution of the boundary points of curvature zero to P(t), with a remainder that is fairly small in mean-square.
Lingual Orthodontics
Vasu murthy S,Saritha T
Indian Journal of Dental Advancements , 2009,
Abstract: At the early stages of the 80's, most of the practitioners and the patients have been seduced by lingual But the difficulties of the technique have rapidly given a disappointment. Today ten years later the authors present the progress which have been realized: the evolution of the brackets, the accuracy of their placement in the lab procedures, the making of the wire, the increase in patient's comfort. So this article attempts to review some of the advantages, disadvantages, bracket systems and aboratory procedures of lingual orthodontics.
Detecting Change-Points in Time Series by Maximum Mean Discrepancy of Ordinal Pattern Distributions  [PDF]
Mathieu Sinn,Ali Ghodsi,Karsten Keller
Computer Science , 2012,
Abstract: As a new method for detecting change-points in high-resolution time series, we apply Maximum Mean Discrepancy to the distributions of ordinal patterns in different parts of a time series. The main advantage of this approach is its computational simplicity and robustness with respect to (non-linear) monotonic transformations, which makes it particularly well-suited for the analysis of long biophysical time series where the exact calibration of measurement devices is unknown or varies with time. We establish consistency of the method and evaluate its performance in simulation studies. Furthermore, we demonstrate the application to the analysis of electroencephalography (EEG) and electrocardiography (ECG) recordings.
Assisted Video Sequences Indexing : Motion Analysis Based on Interest Points  [PDF]
Emmanuel Etievent,Frank Lebourgeois,Jean-Michel Jolion
Computer Science , 2000,
Abstract: This work deals with content-based video indexing. Our viewpoint is semi-automatic analysis of compressed video. We consider the possible applications of motion analysis and moving object detection : assisting moving object indexing, summarising videos, and allowing image and motion queries. We propose an approach based on interest points. As first results, we test and compare the stability of different types of interest point detectors in compressed sequences.
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