The containment problem and a rational simplicial arrangement

Since Dumnicki, Szemberg and Tutaj-Gasi\'nska gave in 2013 in [9] the first example of a set of points in the complex projective plane such that for its homogeneous ideal I the containment of the third symbolic power in the second ordinary power fails, there has been considerable interest in searching for further examples with this property and investigating into the nature of such examples. Many examples, defined over various fields, have been found but so far there has been essentially just one example found of 19 points defined over the rationals, see [16, Theorem A, Problem 1]. In [12, Problem 5.1] the authors asked if there are other rational examples. This has motivated our research. The purpose of this note is to flag the existence of a new example of a set of 49 rational points with the same non-containment property for powers of its homogeneous ideal. Here we establish the existence and justify it computationally. A more conceptual proof, based on Seceleanu's criterion [20] will be published elsewhere [17]

Hadamard Products of Symbolic Powers and Hadamard Fat Grids

In this paper we address the question if, for points P, Q ? P-2, I(P)I-m(*)(Q)(n) = I(P(*)Q)(m+n-1 )and we obtain different results according to the number of zero coordinates in P and Q. Successively, we use our results to define the so called Hadamard fat grids, which are the result of the Hadamard product of two sets of collinear points with given multiplicities. The most important invariants of Hadamard fat grids, as minimal resolution, Waldschmidt constant and resurgence, are then computed

Intermittency in MHD turbulence and coronal nanoflares modelling

High resolution numerical simulations, solar wind data analysis, and measurements at the edges of laboratory plasma devices have allowed for a huge progress in our understanding of MHD turbulence. The high resolution of solar wind measurements has allowed to characterize the intermittency observed at small scales. We are now able to set up a consistent and convincing view of the main properties of MHD turbulence, which in turn constitutes an extremely efficient tool in understanding the behaviour of turbulent plasmas, like those in solar corona, where in situ observations are not available. Using this knowledge a model to describe injection, due to foot-point motions, storage and dissipation of MHD turbulence in coronal loops, is built where we assume strong longitudinal magnetic field, low beta and high aspect ratio, which allows us to use the set of reduced MHD equations (RMHD). The model is based on a shell technique in the wave vector space orthogonal to the strong magnetic field, while the dependence on the longitudinal coordinate is preserved. Numerical simulations show that injected energy is efficiently stored in the loop where a significant level of magnetic and velocity fluctuations is obtained. Nonlinear interactions give rise to an energy cascade towards smaller scales where energy is dissipated in an intermittent fashion. Due to the strong longitudinal magnetic field, dissipative structures propagate along the loop, with the typical speed of the Alfvén waves. The statistical analysis on the intermittent dissipative events compares well with all observed properties of nanoflare emission statistics. Moreover the recent observations of non thermal velocity measurements during flare occurrence are well described by the numerical results of the simulation model. All these results naturally emerge from the model dynamical evolution without any need of an ad-hoc hypothesis

Sleep bruxism and sdb in albanian growing subjects: A cross-sectional study

BackgroundThe aim of this study was to evaluate a possible correlation between sleep bruxism and risk factors of developing obstructive sleep apnea syndrome (OSAS) in a sample of growing subjects and to assess parental awareness about sleep bruxism in their children. Methods: The sample was composed of 310 subjects (173 females and 137 males), with a mean age of 8.9 years, attending "Ndre Mjeda" school of Tirana (Albania). All parents of the children participating in the study were asked to fill in a questionnaire manually or via a digital version. The questionnaire was composed of three sections: personal data, sleep quality data, and OSAS risk factors, and it was filled out by both parents. Results: Of our samples, 41.3% presented with bruxism, and 16.5% of the parents ground their teeth. Oral breathing was reported in 11.9% of the subjects, and among these, 40% of the subjects were affected by bruxism (p > 0.05). Of the subjects, 18.7% snore overnight. Comparing it with sleep bruxism, the two phenomena are often related (p = 0.00). Conclusions: Heredity, night-sweating, nycturia, oral breathing, and snoring seem to have a significant correlation with bruxism

Zooplankton Community in the Waters of Lab Faculty of Fisheries and Marine Science East Likupang North Minahasa

Tujuan penelitian ini adalah untuk mengetahui jenis, kepadatan, dan struktur komunitas Zooplankton seperti Indeks Keanekaragaman (H\u27), Indeks Dominansi (C), dan Keseragaman (e). Pengambilan sampel dilakukan pada 12 November 2019 mengunakan planktonet sampai kedalaman 10 m dari permukaan laut, dilakukan secara vertikal sebanyak 3 kali pada setiap titik. Berdasarkan hasil pengamatan diperoleh 22 genus 26 spesies dalam 3 kelas yaitu : Paracalanus sp, Rhincalanus sp, Calanus sp., Corycaeus sp, Acrocalanus sp., Oncaea sp, Oithona sp., Scolecithricella sp., Euterpina sp., Eurytemora sp., Centropages sp., Ctenocalanus sp., Eucalanus sp., Pseudocalanus sp., Microsetella sp., Nauplius sp., Squilla sp., Siriella sp., Pseudeuphausia sp., Nematocelis sp., Zoea., Solenocera sp. Kepadatan Relatif tertinggi terdapat pada Paracalanus sp yakni 39.38%. Keanekaragaman (H\u27) zooplankton di dua titik tergolong sedang. Nilai tersebut menunjukkan komunitas organisme dalam kondisi yang kurang beragam. Dan Dominansi (C) menunjukkan tidak ada spesies yang mendominasi di perairan Likupang Timur

Enamel interproximal reduction during treatment with clear aligners: digital planning versus OrthoCAD analysis

Background The aim of the study was to compare the amount of interproximal enamel reduction (IPR) provided on ClinCheck software with the amount of IPR carried out by the orthodontist during treatment with clear aligners. Methods 30 subjects (14 males, 16 females; mean age of 24.53 +/- 13.41 years) randomly recruited from the Invisalign account of the Department of Orthodontics at the University of Rome "Tor Vergata" from November 2018 to October 2019, were collected according to the following inclusion criteria: mild to moderate dento-alveolar discrepancy (1.5-6.5 mm); Class I canine and molar relationship; full permanent dentition (excluding third molars); both arches treated only using Comprehensive Package by Invisalign system; treatment plan including IPR. Pre- (T0) and post-treatment (T1) digital models (.stl files), created from an iTero scan, were collected from all selected patients. The OrthoCAD digital software was used to measure tooth mesiodistal width in upper and lower arches before (T0) and at the end of treatment (T1) before any refinement. The widest mesio-distal diameter was measured for each tooth excluding molars by "Diagnostic" OrthoCAD tool. The total amount of IPR performed during treatment was obtained comparing the sum of mesio-distal widths of all measured teeth at T0 and T1. Significant T1-T0 differences were tested with dependent sample t-test (P < 0.05). Results In the upper arch, IPR was digitally planned on average for 0.62 mm while in the lower arch was on average for 1.92 mm. As for the amount of enamel actually removed after IPR performing, it was on average 0.62 mm in the maxillary arch. In the mandibular arch, the mean of IPR carried out was 1.93 mm. The difference between planned IPR and performed IPR is described: this difference was on average 0.00 mm in the upper arch and 0.01 in the lower arch. Conclusions The amount of enamel removed in vivo corresponded with the amount of IPR planned by the Orthodontist using ClinCheck software

Non-collinear quasi phase matching and annular profiles in difference frequency generation with focused Gaussian beams.

We present and experimentally test a simple model for difference frequency generation (DFG) in periodically-poled crystals with gaussian pumping beams. Focusing of input beams originates several non-collinear quasi-phase-matching configurations of the interacting wavevectors, which contribute to the idler output field. In this picture, we accurately describe a number of effects, such as the occurrence of annular idler intensity profiles and the asymmetric trend of DFG power vs temperature. Finally, we quantitatively test the model by means of an indirect measurement of the crystal poling period

Modeling a coronal loop heated by MHD-turbulence nanoflares

We model the hydrodynamic evolution of the plasma confined in a coronal loop, 30000 km long, subject to the heating of nanoflares due to intermittent magnetic dissipative events in the MHD turbulence produced by loop footpoint motions. We use the time-dependent distribution of energy dissipation along the loop obtained from a hybrid shell model, occurring for a magnetic field of about 10 G in corona; the relevant heating per unit volume along the loop is used in the Palermo-Harvard loop plasma hydrodynamic model. We describe the results focussing on the effects produced by the most intense heat pulses, which lead to loop temperatures between 1 and 1.5 MK.Comment: 21 pages, 8 figures, journal articl