Valuation Semigroups of Two Dimensional Local Rings

We consider the question of when a semigroup is the semigroup of a valuation dominating a two dimensional noetherian local domain, giving some surprising examples. We give a necessary and sufficient condition for the pair of a semigroup S and a field extension L/k to be the semigroup and residue field of a valaution dominating a regular local ring R of dimension two with residue field k, generalizing the theorem of Spivakovsky for the case when there is no residue field extension.Comment: 34 pages. Final versio

Long-Term Outcome Of Once Daily Saline Irrigation For The Treatment Of Pediatric Chronic Rhinosinusitis

Objectives:Chronic rhinosinusitis (CRS) results in significant morbidity and healthcare expenditure. The safety and effectiveness of nasal irrigation for the treatment of pediatric CRS has been demonstrated, but its long-term outcomes are unknown. This study's goals were to assess the effectiveness of nasal irrigation after first-time use for pediatric CRS and to determine the short- and long-term outcomes of treating nasal symptoms with irrigation. Methods: This was a two-part study. First, we performed a retrospective cohort study on pediatric CRS patients who were treated by a single pediatric otolaryngologist between July 2003 and January 2012 and were prescribed a 6-week course of nasal irrigation. Demographics, presenting symptoms, Lund-Mackay scores, and treatment outcomes were summarized. Second, we surveyed parents from 1 to 9 years later to assess each patient's symptom recurrence, parent-initiated use of nasal irrigation for recurrent symptoms, and any subsequent surgical interventions. Results: One hundred four patients were reviewed. The mean age was 8.0 years, and 65.4% were male. Presenting symptoms included congestion(95.2%), cough(79.8%), and rhinorrhea(60.6%). Comorbid conditions include asthma(57.3%) and positive allergy test(50.0%). After the initial 6 weeks of irrigation, 57.7% of patients reported complete resolution of symptoms, and 10.6% patients underwent FESS. Reductions in Lund-Mackay scores were 4.14 and 4.38 on the left and right sides, respectively (pConclusion: Nasal irrigation may well be effective as a first line treatment for pediatric CRS as well as for recurring symptoms. Once nasal irrigation is used as a treatment modality for pediatric CRS, parents and caretakers are likely to utilize it again for recurrent symptoms. Patients with symptoms of CRS, even when refractory to other medical therapies, should utilize nasal irrigation before consideration for FESS

Distinct spreads in vector spaces over finite fields

In this short note, we study the distribution of spreads in a point set $\mathcal{P} \subseteq \mathbb{F}_q^d$, which are analogous to angles in Euclidean space. More precisely, we prove that, for any $\varepsilon > 0$, if $|\mathcal{P}| \geq (1+\varepsilon) q^{\lceil d/2 \rceil}$, then $\mathcal{P}$ generates a positive proportion of all spreads. We show that these results are tight, in the sense that there exist sets $\mathcal{P} \subset \mathbb{F}_q^d$ of size $|\mathcal{P}| = q^{\lceil d/2 \rceil}$ that determine at most one spread

腐食した鋼トラス橋格点ガセット・プレートの残存耐荷力と炭素繊維シートによる補修

国立大学法人長岡技術科学大