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In this paper, we introduce an algorithm for computing p-adic integrals on bad reduction hyperelliptic curves. For bad reduction curves, there are two notions of p-adic integration: Berkovich-Coleman integrals which can be performed locally; and abelian integrals with desirable number-theoretic properties. By covering a bad reduction hyperelliptic curve by annuli and basic wide open sets, we reduce the computation of Berkovich-Coleman integrals to the known algorithms on good reduction hyperelliptic curves. These are due to Balakrishnan, Bradshaw, and Kedlaya, and to Balakrishnan and Besser for regular and meromorphic 1-forms on good reduction curves, respectively. We then employ tropical geometric techniques due to the first-named author with Rabinoff and Zureick-Brown to convert the Berkovich-Coleman integrals into abelian integrals. We provide examples of our algorithm, verifying that certain abelian integrals between torsion points vanish., Comment: Comments Welcome! figure taken from arxiv::1606.09618; v2 minor revisions

We show that for smooth and proper varieties over local fields with no non-trivial vector fields, good reduction descends over purely inseparable extensions. We use this to extend the Neron-Ogg-Shafarevich criterion for K3 surfaces to the equicharacteristic $p>0$ case., 15 pages, comments welcome!

We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under some assumptions. These criteria are higher dimensional versions of the good reduction criterion for hyperbolic curves given by Oda and Tamagawa.

Let F be a totally real number field which is unramified at 3 , 5 , and 7. We give explicit conditions on a finite place v 0 of F such that any elliptic curve over F with potential good reduction at v 0 is modular. The main point is to prove that there exist no elliptic curves with reducible mod 5, and 7 representations (or mod 3, 5, and 7 representations) under our assumptions.

Let $E$ be an elliptic curve defined over a number field $K$ where $p$ splits completely. Suppose that $E$ has good reduction at all primes above $p$. Generalizing previous works of Kobayashi and Sprung, we define multiply signed Selmer groups over the cyclotomic $\mathbb{Z}_p$-extension of a finite extension $F$ of $K$ where $p$ is unramified. Under the hypothesis that the Pontryagin duals of these Selmer groups are torsion over the corresponding Iwasawa algebra, we show that the Mordell-Weil ranks of $E$ over a subextension of the cyclotomic $\mathbb{Z}_p$-extension are bounded. Furthermore, we derive an aysmptotic formula of the growth of the $p$-parts of the Tate-Shafarevich groups of $E$ over these extensions., Comment: 20 pages

For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E. Hasse’s theorem asserts that $$|a_p| \le 2\sqrt{p}$$ . In this paper we establish average asymptotics for primes p for which $$a_p \in \left( 2\sqrt{p} - f(p), 2\sqrt{p}\right) $$ or $$a_p \in \left( c\sqrt{p} - f(p), c\sqrt{p}\right) $$ , where $$f(x) = o(\sqrt{x})$$ is a function satisfying mild growth conditions and $$0< c < 2$$ is a constant.

The goal of this manuscript is to provide a survey of good reduction criteria for hyperbolic polycurves. In particular, we give outlines of the proofs of the main theorems of the papers [19] and [20], which are details of the talk “Criteria for good reduction of hyperbolic polycurves” given at “Algebraic Number Theory and Related Topics 2018”. Also, this paper contains a proof of a specialization theorem of pro-L fundamental groups., Algebraic Number Theory and Related Topics 2018. November 26-30, 2018. edited by Takao Yamazaki and Shuji Yamamoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

Background Laser hair reduction is one of the most common laser procedures in dermatology. Laser systems available are Ruby at 694 nm, Alexandrite (755 nm), Diode (810nm), and Nd:YAG (1064 nm). Recently, devices presenting a combination of wavelengths have shown to produce high effective hair reduction with no related risks. This study was conducted with the Soprano Ice Platinum (Alma Lasers, GMBH, Germany) that emits a combination of three wavelengths at 755, 810, and 1064 nm in a single pulse. Aims To establish the efficacy and safety of novel triple wavelength laser hair reduction technology in skin types IV to V. Patients and methods This was an investigator initiated, single-center, prospective clinical study conducted between December 2017 and June 2019 with a total of 25 patients (23 female and two male) above 18 years with skin types IV and V, areas included are face, beard, neck, chest, and others. Results Hair reduction was assessed using the physician GAIS (global esthetic improvement scale) score: no results 0% reduction, poor 0%-25% reduction, average 25%-50%, good 50%-75%, and excellent 75%-100%. All 25 patients (mean age 28 years, range 18-52 y/o) completed all six sessions of the study. Conclusion Objective clinical assessment of hair reduction using the physician GAIS score in 90 anatomical sites scores an excellent reduction in 95.5% areas and good reduction in 80% areas. This current study shows that a synergistic combination of three diode laser wavelengths used for hair removal (755, 810, 1064 nm) is effective and safe to use in subjects skin types IV and V for facial and body hair.

We implement two-cover descent for plane quartics over Q with all 28 bitangents rational and show that on a significant collection of test cases, it resolves the existence of rational points. We also review a classical description of the relevant moduli space and use it to generate examples. We observe that local obstructions are quite rare for such curves, and only seem to occur in practice at primes of good reduction. In particular, having good reduction at 11 implies having no rational points. We also gather numerical data on two-Selmer ranks of Jacobians of these curves, which suggests that these often have non-trivial Tate-Shafarevich groups. We implement two-cover descent for plane quartics over Q with all 28 bitangents rational and show that on a significant collection of test cases, it resolves the existence of rational points. We also review a classical description of the relevant moduli space and use it to generate examples. We observe that local obstructions are quite rare for such curves and only seem to occur in practice at primes of good reduction. In particular, having good reduction at 11 implies having no rational points. We also gather numerical data on two-Selmer ranks of Jacobians of these curves, providing evidence these behave differently from those of general abelian varieties due to the frequent presence of an everywhere locally trivial torsor., 15 pages; Some minor improvements to algorithm and rank data analysis

This survey article is an outline of author's talk at the RIMS Workshop Algebraic Number Theory and Related Topics (2017). We study arithmetic properties of K3 surfaces with complex multiplication (CM) generalizing the results of Shimada for K3 surfaces with Picard number 20. Then, following Taelman's strategy and using Matsumoto's good reduction criterion for K3 surfaces with CM, we construct K3 surfaces over finite fields with given L-function, up to finite extensions of the base fields. We also prove the Tate conjecture for self-products of K3 surfaces over finite fields by CM lifts and the Hodge conjecture for self-products of K3 surfaces with CM proved by Mukai and Buskin., Algebraic Number Theory and Related Topics 2017. December 4-8, 2017. edited by Hiroshi Tsunogai, Takao Yamazaki and Yasushi Mizusawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.

We define affinoids in the Lubin–Tate curve in even equal characteristic, and compute the reductions of them. Each reduction is isomorphic to a smooth affine curve with Artin–Schreier type equation. We expect that the cohomology of the reductions realizes the local Langlands correspondence and local Jacquet–Langlands correspondence for representations of conductor five.

Food sector produces million tons of waste. Out of which some is discarded as animal feed, as fertilizer or mostly treated as waste which further creates environmental hazards. The present study was done to utilize the waste pomace from vegetables – carrot and beetroot after juice extraction in the formation of Cellulose Nano Particles (CNPs). Pomaces of carrot and beetroot were treated with alkali treatment and bleaching treatment separately.So formed CNPs have shown good adsorption behavior and have shown good reduction in polluting parameters , specially colour was reduced upto 80 % in waste water.

Mandibular condylar fractures are among the most common facial fractures and some of the most difficult to manage. Opinions about the management of mandibular condylar fractures differ among surgeons. With the implementation of new technology, an increased understanding of fracture management, and better functional and morphological outcomes reported in the literature, open reduction and internal fixation is becoming many surgeons’ preferred choice for the treatment of condylar fractures. Because surgical treatment of such fractures is complex, certain factors must be considered to achieve satisfactory outcomes. In this article, we summarise six key points in the management of mandibular condylar fractures: virtual evaluation of condylar fracture, a suitable surgical approach, good reduction, stable internal fixation, repair of the articular disc, and restoration of the mandibular arch width. We believe that these points will help to improve the prognosis of mandibular condyle fractures. Keywords: Mandibular fractures, Condylar fractures, Template

We obtain two results about the p-primary part of the Brauer group of a p-adic curve X. First, assuming enough roots of unity and that X has good reduction, we construct indecomposable K(X)-divisio...

Let E be an elliptic curve with good reduction at a fixed odd prime p and K an imaginary quadratic field where p splits. We give a growth estimate for the Mordell-Weil rank of E over finite extensions inside the $$\mathbb{Z}_p^2$$-extension of K.

Introduction: Today’s society is always more interested to the concept of aesthetics. The patients frequently ask to dentist to resolve unaesthetic problems of teeth, in particular that of the upper frontal group. The WSLs are enamel white alterations due to alteration during the demineralization and remineralization of enamel. This effect is caused by alteration of the pH in the oral cavity and buffer action of saliva. An alteration of this relationship leads to a progressive demineralization of enamel until the formation of a dental cavitation. Materials and Methods: For this study are selected 11 patients, of which 3 men and 8 women, with total of 17 WSLs. The inclusion criteria included WLSs with ICDAS = 2 and WLSs caused by hypomineralization of traumatic origin. These patients were subjected to treatment with infiltrating resin according to operative procedure. Discussion: The therapy with infiltrating resin gave great results in 12 lesions out of 17. In the lesions where there weren’t a complete remission we obtained a great aesthetic improvement and a good reduction of lesions. The follow up could improve the result after a better rehydration of hard tissue. Conclusions: With a correct selection of cases and good operative procedure, the use of the micro-infiltrative technique by low viscosity resin is a good procedure to resolve WSLs problems of non-orthodontic origins. Other studies with a larger sample are required to validate this clinical approach.

Instance-based classifiers become inefficient when the size of their training dataset or model is large. Therefore, they are usually applied in conjunction with a Data Reduction Technique that collects prototypes from the available training data. The set of prototypes is called the condensing set and has the benefit of low computational cost during classification, while, at the same time, accuracy is not negatively affected. In case of imbalanced training data, the number of prototypes collected for the minority (rare) classes may be insufficient. Even worse, the rare classes may be eliminated. This paper presents three methods that preserve the rare classes when data reduction is applied. Two of the methods apply data reduction only on the instances that belong to common classes and avoid costly under-sampling or over-sampling procedures that deal with class imbalances. The third method utilizes SMOTE over-sampling before data reduction. The three methods were tested by conducting experiments on twelve imbalanced datasets. Experimental results reveal high recall and very good reduction rates.

Let $p$ be an odd prime number, and $E$ an elliptic curve defined over a number field with good reduction at every prime of $F$ above $p$. In this short note, we compute the Euler characteristics of the signed Selmer groups of $E$ over the cyclotomic $\Zp$-extension. The novelty of our result is that we allow the elliptic curve to have mixed reduction types for primes above $p$ and that we allow mixed signs in the definition of the signed Selmer groups., 9 pages

We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves.