Minimal Discrepancies Research Articles

ON BOUNDEDNESS OF DIVISORS COMPUTING MINIMAL LOG DISCREPANCIES FOR SURFACES

AbstractLet $\Gamma $ be a finite set, and $X\ni x$ a fixed kawamata log terminal germ. For any lc germ $(X\ni x,B:=\sum _{i} b_iB_i)$ , such that $b_i\in \Gamma $ , Nakamura’s conjecture, which is equivalent to the ascending chain condition conjecture for minimal log discrepancies for fixed germs, predicts that there always exists a prime divisor E over $X\ni x$ , such that $a(E,X,B)=\mathrm {mld}(X\ni x,B)$ , and $a(E,X,0)$ is bounded from above. We extend Nakamura’s conjecture to the setting that $X\ni x$ is not necessarily fixed and $\Gamma $ satisfies the descending chain condition, and show it holds for surfaces. We also find some sufficient conditions for the boundedness of $a(E,X,0)$ for any such E.

Assessment of Gingival Thickness Using CBCT Compared to Transgingival Probing and Its Correlation with Labial Bone Defects: A Cross-Sectional Study.

The aims of this study were to determine the accuracy and repeatability of CBCT for assessing gingival thickness (GT) as compared to transgingival probing and to investigate the correlation between GT and labial bone defects. This cross-sectional study comprised 37 patients who underwent CBCT imaging. A total of 111 sites were examined, and measurements were obtained from the same points on selected index teeth. The GT was measured, and the presence of dehiscence and fenestration defects was evaluated on the CBCT scans. Transgingival probing was performed at the same points as those used on the scans. Intraexaminer reliability for clinical and radiographic measurements and interexaminer reliability for radiographic measurements were tested. Agreement between the measurement methods and the correlations between GT and labial bone defects were assessed using intraclass correlation coefficient (ICC) and chi-square test, respectively. The agreement between both measurement methods was excellent and statistically significant (ICC = 0.888; P < .001), with a bias of 0.04 (95% CI: 0.01 to 0.08). Significant differences in the occurrence of fenestration (P = .023) and dehiscence defects (P < .001) between the thin and thick gingival phenotypes were observed, and the defects were positively correlated with the thin gingival phenotype. CBCT demonstrated high diagnostic accuracy for GT measurements, with minimal discrepancies from the transgingival method. The presence of dehiscence and fenestration defects was positively correlated with thin gingival phenotype.

Структура плоской эквидистантной антенной решетки с радиальной сеткой

The article proposes to consider the radial structure of the placement of radiating elements in the nodes of a flat equidistant antenna array. The known variants of rectangular and hexagonal structures of elements placement in flat antenna arrays are considered. The main calculated ratios of parameters for the radial structure of the pitch are given as well as the linear distances between the emitters in various orthogonal directions, along the radial and angular components. For the proposed structure, using a specific example of an antenna array consisting of nine circles, with a total number of 180 emitters and a uniform amplitude distribution, the radiation patterns in three-dimensional space are calculated, that are represented on the drawing plane by various sections along the angular coordinate φ with a step of 150. The proposed radial structure, unlike the known ones, ensures the identity of the DN with minimal discrepancies from each other in different planes φ at the level of -35 dB.

Small Quotient Minimal Log Discrepancies

We prove that for each positive integer n, there exists a positive number ϵn such that n-dimensional toric quotient singularities satisfy the ACC for MLDs on the interval (0,ϵn). In the course of the proof, we show a geometric Jordan property for finite automorphism groups of affine toric varieties.

On minimal log discrepancies and kollár components

AbstractIn this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that$d$-dimensional$a$-log canonical singularities with standard coefficients, which admit an$\epsilon$-plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on$d,\,a$and$\epsilon$. This result gives a natural geometric stratification of the possible mld's in a fixed dimension by finite sets. As an application, we prove the ascending chain condition for minimal log discrepancies of exceptional singularities. We also introduce an invariant for klt singularities related to the total discrepancy of Kollár components.

Generalization of ray tracing in symmetric gradient-index media by Fermat's ray invariants.

Ray tracing in gradient-index (GRIN) media has been traditionally performed either by using the analytical or numerical solutions to the Eikonal equation or by creating a layered medium where Snell's law is calculated in each layer. In this paper, an exact general method to perform ray tracing in GRIN media is presented based on the invariants of the system as stated by Fermat's principle when the media presents symmetries. Its advantage, compared with other methods reported in the literature, relies on its easy implementation. Besides the GRIN distribution and the initial conditions of the incident ray, once the invariants of the system are stated the resulting math is simple to solve and interpret. To benchmark the algorithm, ray tracing in typical cases of GRIN media is calculated, finding minimal discrepancies between the analytical solutions and our simulations. The used media are axial refractive index and parabolic index fiber and lenses with spherical gradient-index symmetry, such as: Luneburg's, Gutman's, generalized Maxwell's Fish-eye, Eaton's, and concentrator lenses. Our method can be further applied to distributions with symmetries associated with other common curvilinear orthogonal coordinate systems, in particular to those associated to the separability of the Helmholtz equation that would allow us to investigate wave optics in these GRIN media with the associated geometries.

Tekhnicheskiye sredstva i metodika issledovaniya tonkoy struktury techeniya vodnogo potoka s ispol'zovaniyem videoregistratsii

The article discusses developed technical means and methods allowing to obtain in situ spatial distribution of velocity of suspended particle movement by a water flow. A brief description is given of the developed measuring complex based on video recording of the aquatic environment. The method of performing full-scale experiments by the example of study of sea estuaries is described. The article presents measurement results and examples of spatial distributions of flow velocities required for solving various problems related to mass transfer, coast erosion and silting of water areas. Analysis of expedition research results obtained using the developed complex allowed to create methodical approaches to assess the current state of a water body and informative parameters of its state using a visualization method. Based on the created methods, data on the fine structure of the flow in the Chernaya River estuary area were obtained. Comparison of the averaged data on the water flow velocity with the measurement results obtained through standard technical means, namely a hydrometric current meter, showed minimal discrepancies not exceeding 11 %. The developed method and technical means make it possible to study the water flow dynamics and to describe the flow fine structure, which is necessary for studying the mechanisms of erosion, sediment accumulation and transport.

Minimal log discrepancies in positive characteristic

We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive characteristic if the exponent of an ideal is less than the log canonical threshold of the ideal.

Characterization of two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic

We characterize two-dimensional semi-log canonical hypersurfaces in arbitrary characteristic from the viewpoint of the initial term of the defining equation. As an application, we prove a conjecture about a uniform bound of divisors computing minimal log discrepancies for two-dimensional varieties, which is a conjecture by Ishii and also a special case of the conjecture by Mustaţă–Nakamura.

A gap theorem for minimal log discrepancies of noncanonical singularities in dimension three

We show that there exists a positive real numberδ&gt;0\delta &gt;0such that for any normal quasi-projectiveQ\mathbb {Q}-Gorenstein33-foldXX, ifXXhas worse than canonical singularities, that is, the minimal log discrepancy ofXXis less than11, then the minimal log discrepancy ofXXis not greater than1−δ1-\delta. As applications, we show that the set of all noncanonical klt Calabi–Yau33-folds are bounded modulo flops, and the global indices of all klt Calabi–Yau33-folds are bounded from above.

Motion‐insensitive susceptibility weighted imaging

To enable SWI that is robust to severe head movement. Prospective motion correction using a markerless optical tracker was applied to all pulse sequences. Three-dimensional gradient-echo and 3D EPI were used as reference sequences, but were expected to be sensitive to motion-induced B0 changes, as the long TE required for SWI allows phase discrepancies to accumulate between shots. Therefore, 2D interleaved snapshot EPI was investigated for motion-robust SWI and compared with conventional 2D EPI. Repeated signal averages were retrospectively corrected for motion. The sequences were evaluated at 3 T through controlled motion experiments involving two cooperative volunteers and SWI of a tumor patient. The performed continuous head motion was in the range of 5-8° rotations. The image quality of the 3D sequences and conventional 2D EPI was poor unless the rotational motion axis was parallel to B0 . Interleaved snapshot EPI had minimal intraslice phase discrepancies due to its small temporal footprint. Phase inconsistency between signal averages was well tolerated due to the high-pass filter effect of the SWI processing. Interleaved snapshot EPI with prospective and retrospective motion correction demonstrated similar image quality, regardless of whether motion was present. Lesion depiction was equal to 3D EPI with matching resolution. Susceptibility-based imaging can be severely corrupted by head movement despite accurate prospective motion correction. Interleaved snapshot EPI is a superior alternative for patients who are prone to move and offers SWI which is insensitive to motion when combined with prospective and retrospective motion correction.

A novel UV-fluorescence approach to assess the long wear efficacy of foundations.

The long wear properties of foundations are regarded as a must-have in terms of claims. Here, we propose an instrumental approach based on UV-fluorescence imaging as an alternative to clinical grading methods. A method was developed, with UV-fluorescence images captured with the Visia CR as a first step, followed by images analysis using Image-Pro plus. Repeated-measures correlation was used to assess the degree of association between the UV-fluorescence method and a grading method when removing the foundation incrementally from the skin using wipes. Thresholds to ascertain whether a foundation pass or fail long-wearing using the newly developed method were established using a mixed linear model and cross-validated using two subsets of a panel of 20 women. The method could measure incremental removal of foundation using wipes, in a similar fashion to a grading method, as outlined with repeated measures correlation (r=-.86). Pass/fail thresholds established with the mixed linear model were tested versus the grading method when assessing a foundation under real conditions for a duration over 24hours, with minimal discrepancies between the two methods. By capitalising on foundation physical/chemical properties, the proposed method allows to assess their long wear properties, irrespective of basal skin tone or foundation shade. It offers the advantage of appealing visuals for efficacy and to be less resource intensive than a clinical grading approach.

Pediatric Osteopathic Manipulative Medicine: A Scoping Review.

A common reproach precluding the use of osteopathic manipulative medicine (OMM) in pediatrics is a lack of evidence regarding its safety, feasibility, and effectiveness. We conducted a systematic, scoping review of pediatric osteopathic medicine to identify gaps in the literature and make recommendations for future research. We searched 10 databases using 6 key words and medical subject heading terms for any primary articles reporting OMM use in children published from database inception until initiation of the study. Articles were selected if they reported primary data on OMM conducted in the United States on patient(s) 0 to 18 years old. Baseline study characteristics were collected from each article and the Grading of Recommendations, Assessment, Development, and Evaluations system was used to critically appraise each study. Database search yielded 315 unique articles with 30 studies fulfilling inclusion and exclusion criteria. Of these, 13 reported the data required to demonstrate statistically significant results, and no significant adverse events were reported. The majority of studies were graded as providing weak clinical evidence because of significant methodologic flaws and biases. The review was limited to US-based studies and reports. Minimal discrepancies between reviewers were resolved via an objective third reviewer. There is little strong, scientific, evidence-based literature demonstrating the therapeutic benefit of OMM for pediatric care. No strong clinical recommendations can be made, but it can be medically tolerated given its low risk profile. High-quality, scientifically rigorous OMM research is required to evaluate safety, feasibility, and efficacy in pediatrics.

An optimal gap of minimal log discrepancies of threefold non-canonical singularities

We show that the minimal log discrepancy of any Q -Gorenstein non-canonical threefold is ≤ 12 13 , which is an optimal bound.

Evaluation of dental parameters perception by Lebanese prosthodontists, orthodontists and aesthetic doctors

The aim of this study was to compare the effect of varying smile parameters with respect to three indices between Lebanese dentists (prosthodontists and orthodontists) and medical doctors. 245 participants were divided into 3 groups. A photograph of the smile that conforms to a woman’s aesthetic standards has been digitally altered to provide a reference image. Next, images where modified then evaluated. The collected data was analyzed. Dental professionals critically judged dental aesthetics by focusing on the gingivo-dental characteristics that make the smile less pleasant. Dental professionals detected minimal dental discrepancies in a smile, unlike doctors who assessed the smile in relation to the entire face since their judgment is global. Lebanese doctors have a different perception of oral aesthetics from Lebanese prosthodontists and orthodontists.

New protocol for in-house management of computer assisted orthognathic surgery

The aim of this study was to evaluate retrospectively the accuracy of a protocol for completely in-house, computer-assisted, orthognathic surgery, generating resin printed intermediate surgical guides. A retrospective, observational study was made on a cohort of 15 patients treated consecutively from September 2017 to May 2019, who underwent bimaxillary orthognathic surgery planned with the same 3-dimensional program and whose surgical intermediate splints were obtained with the same all-in-house protocol. Virtual planned surgical movements were compared with the real surgical outcome. The differences were not significant for eight of the 12 variables considered. The p values, calculated with the Wilcoxon signed rank test, were evenly distributed and ranged from p=0.001 to p=0.820. Significant differences were reported in four measurements: angle between sella-nasion plane and a line connecting the incisal edge and the apex of the root of the most prominent incisor (U1-SN) (p=0.001), angle between Frankfort plane and a line connecting the incisal edge and the root apex of the most prominent upper incisor (p=0.008), dental midline discrepancies (p=0.006), and occlusal plane tilt (U1-FH) (p=0.001), basically due to intraoperative settings. The 3-dimensional resin printed surgical guides were shown to be a reliable alternative to the commercial ones and showed high rate of accuracy for most of the variables assessed. Four out of 12 of these showed significant errors, but two of them were only minimal discrepancies with no clinical implications.

Minimal log discrepancies of determinantal varieties via jet schemes

We compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs (Dk,∑αiDki) consisting of a determinantal variety (of square matrices) and an R-linear sum of determinantal subvarieties. Our result implies the semicontinuity conjecture for minimal log discrepancies of such pairs. For these computations, we use the description of minimal log discrepancies via codimensions of cylinders in the space of jets; this necessitates the computations of an explicit generator for the canonical differential forms and the Nash ideal of determinantal varieties, which may be of independent interest.

On equivalent conjectures for minimal log discrepancies on smooth threefolds

On smooth varieties, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. In dimension three, we reduce it to the case when the boundary is the product of a canonical part and the maximal ideal to some power. We prove the reduced assertion when the log canonical threshold of the maximal ideal is either at most one-half or at least one.

The minimal log discrepancies on a smooth surface in positive characteristic

This paper shows that Mustaţǎ–Nakamura’s conjecture holds for pairs consisting of a smooth surface and a multiideal with a real exponent over the base field of positive characteristic. As corollaries, we obtain the ascending chain condition of the minimal log discrepancies and of the log canonical thresholds for those pairs. We also obtain finiteness of the set of the minimal log discrepancies of those pairs for a fixed real exponent.

The Performance of Emergency Department Nurses Across Sectors in Jordan: An Application of the Work Functioning Model.

Work functioning is a relatively new conceptual model developed to embrace various aspects surrounding work performance, work participation, and individual capacity. The assessment of work performance (AWP) in nursing has gained inconsistent evidence due to examining it from multidimensional aspects. This study aimed to perform the AWP in nurses working in the emergency departments (EDs) at different healthcare sectors in Jordan. A descriptive, cross-sectional design was used in which ED nurses completed a questionnaire. ED nurses were recruited conveniently from four referral hospitals located in Amman (two government and two private hospitals). The Nursing Work Functioning Questionnaire (NWFQ), in addition to the demographic questionnaire were completed. A total of 179 ED nurses participated in the study (100 government and 79 private nurses). A few differences were found between government and private sector nurses in respect to work functioning domains. Overall, nurses from both sectors reported minimal impairments in their performance represented in seven domains. However, ED nurses from the private sector claimed more frequent work incidences compared to ED nurses from the government sector (p = .043). In addition, associate nurses showed higher avoidance behavior than registered nurses in both sectors (p = .031). Contrary to former studies, this study found minimal discrepancies in work performance between government and private sectors, and employing the work functioning model is useful to gain a thorough understanding of the AWP.