Regulator constants of integral representations of finite groups

Let G be a finite group and p be a prime. We investigate isomorphism invariants of $\mathbb{Z}_{p}[G]$-lattices whose extension of scalars to $\mathbb{Q}_p$ is self-dual, called regulator constants. These were originally introduced by Dokchitser--Dokchitser in the context of elliptic curves. Regulator constants canonically yield a pairing between the space of Brauer relations for G and the subspace of the representation ring for which regulator constants are defined. For all G, we show that this pairing is never identically zero. For formal reasons, this pairing will, in general, have non-trivial kernel. But, if G has cyclic Sylow p-subgroups and we restrict to considering permutation lattices, then we show that the pairing is non-degenerate modulo the formal kernel. Using this we can show that, for certain groups, including dihedral groups of order 2p for p odd, the isomorphism class of any $\mathbb{Z}_p[G]$-lattice whose extension of scalars to $\mathbb{Q}_p$ is self-dual, is determined by its regulator constants, its extension of scalars to $\mathbb{Q}_p$, and a cohomological invariant of Yakovlev.Comment: 43 pages. Restated the main theorem (Thm 6.8) in terms of $\mathbb{Z}_p$-lattices as opposed to $\mathbb{Z}_{(p)}$-lattices and added Section 6.3 providing criteria for the theorem to apply. To appear in Math. Proc. Cambridge Philos. So

Functoriality of motivic lifts of the canonical construction

Let (G,X) be a Shimura datum and K a neat open compact subgroup of $G(\mathbb{A}_f)$. Under mild hypothesis on (G,X), the canonical construction associates a variation of Hodge structure on $\textrm{Sh}_K(G,X)(\mathbb{C})$ to a representation of G. It is conjectured that this should be of motivic origin. Specifically, there should be a lift of the canonical construction which takes values in relative Chow motives over $\textrm{Sh}_K(G,X)$ and is functorial in (G,X). Using the formalism of mixed Shimura varieties, we show that such a motivic lift exists on the full subcategory of representations of Hodge type {(-1,0),(0,-1)}. If (G,X) is equipped with a choice of PEL-datum, Ancona has defined a motivic lift for all representations of G. We show that this is independent of the choice of PEL-datum and give criteria for it to be compatible with base change.Comment: 25 pages, v2 has some mostly typographical improvements. To appear in Manuscripta Mathematic

Capability of load-time history reconstruction and fatigue crack growth rate estimation for 2024-T3 aluminium alloy on the basis of fractographic analysis

The subject of the paper is the considerations of the capability of load-time history reconstruction for the component under variable amplitude loading and fatigue crack growth rate estimation for the 2024-T3 Alclad aluminium alloy on the basis of microfracture analysis. For this goal three variable amplitude (VA) load sequences with multiple overloads and differing from the level of load sequence complexity were applied. These loads are employed when simulating the fatigue behaviour of aeronautical alloys. To reveal the load sequence effect on crack growth behaviour the microfracture analysis were provided by means of TEM microscope

Fatigue research 2024-T3 aluminium alloy

В роботі представлено дослідження втомного руйнування листів алюмінієвого сплаву 2024-Т3 товщиною 3 мм при трьох видах блокового змінно амплітудного навантаження. Прикладене навантаження моделює реальний спектр навантажень нижньої частини крила літака. Метою дослідження було виявлення впливу спектру навантаження на формування втомних борозенок на поверхні руйнування та перевірка можливості відтворення історії навантаження на основі фрактографічного аналізу. Результати дослідження швидкості руйнування відносяться до довгих тріщин. Експериментально визначена швидкість руйнування була порівняна з швидкістю отриманою на основі аналізу відстані між втомними борозенками. Фрактографічний аналіз дозволяє отримати кількісний опис залежності між міжборозенковою відстанню на поверхні руйнування та швидкістю втомного руйнування в цілому діапазоні довжини тріщини.The subject of the paper is fatigue crack growth rate investigation for 2024-T3 3 mm thick Alclad aluminium alloy sheet under three variable amplitude load programs with multiple overloadsunderloads. These programs correspond to a flight simulation spectrum of a lower skin wing structure. The research was undertaken in order to learn an interaction between applied load and formation of fatigue striations on the specimen fracture surfaces as well as to check the capability for load-time history reconstruction on the basis of microfracture analysis. All considerations in the terms of fatigue crack growth behaviour refer mainly to long cracks. Experimentally determined crack growth rates were compared with the growth rates that were evaluated from the striations spacing. Quantitative fractography allowed to deliver the relation between surface crack and crack depth growth rates for whole range of crack growth.W pracy przedstawiono badania zmęczeniowego pękania 3 mm blachy ze stopu aluminium 2024-T3 pod wpływem trzech zmiennoamplitudowych programów obciążeń. Zastosowane obciążenia były związane z widmem obciążeń dolnego pokrycia skrzydła samolotu. Badania miały na celu określenie wpływu widma obciążeń na kształtowanie się prążków zmęczeniowych na powierzchni przełomu oraz sprawdzenie możliwości odtwarzania historii obciążenia na podstawie analizy fraktograficznej. Wyniki badań prędkości pękania dotyczyły długich pęknięć. Doświadczalnie wyznaczone prędkości zmęczeniowego pękania były porównywane z prędkościami wyznaczonymi na podstawie odległości międzyprążkowych. Analiza fraktograficzna pozwala na określenie ilościowych relacji między odległościami międzyprążkowymi na powierzchni przełomu a prędkością zmęczeniowego pękania w całym zakresie długości pęknięcia

Atrial Fibrillation-Induced Cardiac Shock: First Manifestation of a Congenitally Corrected Transposition of the Great Arteries in a 45-Year-Old Man

Background. The congenitally corrected transposition of the great arteries (L-TGA) is a very rare congenital heart defect, which often remains undetected for several decades of life. Case Presentation. We report on a 45-year-old man without prior history of heart disease, presenting with cardiac shock related to a first episode of tachycardic atrial fibrillation. The diagnostic work-up identified a L-TGA as the underlying cause for acute heart failure. Discussion. L-TGA is a very rare congenital heart defect, which is characterized by an atrioventricular as well as a ventriculoarterial discordance. By this means, the physiological sequence of pulmonary and systemic circulation is still maintained. On the basis of an ongoing strain of the right ventricle, which has to carry the burden of the systemic blood pressure, after more than four decades without symptoms, acute heart failure was triggered by a tachycardic atrial fibrillation

Diagnostic accuracy of C-reactive protein and white blood cell counts in the early detection of inflammatory complications after open resection of colorectal cancer: a retrospective study of 1,187 patients

Purpose: Although widely used, there is a lack of evidence concerning the diagnostic accuracy of C-reactive protein (CRP) and white blood cell counts (WBCs) in the postoperative period. The aim of this study was to evaluate the diagnostic accuracy of CRP and WBCs in predicting postoperative inflammatory complications after open resection of colorectal cancer. Methods: In this retrospective study, clinical data and the CRP and WBCs, routinely measured until postoperative day5 (POD 5), were available for 1,187 patients who underwent colorectal cancer surgery between 1997 and 2009. Using the receiver-operating characteristic (ROC) methodology, the diagnostic accuracy was evaluated according to the area under the curve (AUC). Results: Three hundred forty-seven patients (29.2%; 95% CI, 26.7-31.9%) developed various inflammatory complications. Anastomotic leakage occurred in 8.0% (95% CI, 6.1-9.1%) of patients. The CRP level on POD 4 (AUC 0.76; 95% CI, 0.71-0.81) had the highest diagnostic accuracy for the early detection of inflammatory complications. With a cutoff of 123mg/l, the sensitivity was 0.66 (95% CI, 0.56-0.74), and the specificity was 0.77 (95% CI, 0.71-0.82). The diagnostic accuracy of the WBC was significantly lower compared to CRP. Conclusion: Measurement of CRP on POD 4 is recommended to screen for inflammatory complications. CRP values above 123mg/l on POD 4 should raise suspicion of inflammatory complications, although the discriminatory performance was insufficient to provide a single threshold that could be used to correctly predict inflammatory complications in clinical practice. WBC measurement contributes little to the early detection of inflammatory complications. Registered at www.clinicaltrials.gov (NCT01221324

Functoriality of motivic lifts of the canonical construction

Let (G,X) be a Shimura datum and K a neat open compact subgroup of $G(\mathbb{A}_f)$. Under mild hypothesis on (G,X), the canonical construction associates a variation of Hodge structure on $\textrm{Sh}_K(G,X)(\mathbb{C})$ to a representation of G. It is conjectured that this should be of motivic origin. Specifically, there should be a lift of the canonical construction which takes values in relative Chow motives over $\textrm{Sh}_K(G,X)$ and is functorial in (G,X). Using the formalism of mixed Shimura varieties, we show that such a motivic lift exists on the full subcategory of representations of Hodge type {(-1,0),(0,-1)}. If (G,X) is equipped with a choice of PEL-datum, Ancona has defined a motivic lift for all representations of G. We show that this is independent of the choice of PEL-datum and give criteria for it to be compatible with base change

Public transport accessibility and the prices of nearby properties: the case of the first metro line in Warsaw

This paper identifies the relation between metro proximity and the prices of residential properties in Warsaw. The analysis is based on 2006-2013 AMRON-SARFiN data. The results show that metro has a positive impact on property prices if it is located at most 1.5 km from the property. The greatest increase in price of 8-13 per cent is observed when metro is located 400-800 meters from the property. The results indicate that when the metro transportation is poor, it causes a large increase in property prices, which is not comparable to the impact of other transports, such as bus or tram

The Product Issues Tracking System: An Educational Module for Staff Nurses

An event reporting system that is intended for the documentation and reporting of near-miss events involving defective medical devices is an important component of a healthcare facilities\u27 safety culture and enables the staff to exercise a stewardship role focused on reducing healthcare costs. The Mayo Clinic in Rochester Minnesota does have an internal near-miss documentation system in place to report near-miss events that arise from the discovery and removal of a medical device that is defective before potential harm can occur. This documentation and reporting is termed The Product Issue Tracking System (PITS). Education for staff nurses, which instructs on the use and importance of PITS is essential to ensure the system is utilized. Jean Watson\u27s Caring Science Theory (2008) provides a theoretical foundation for this module because of its emphasis on caring. A component of authentic caring is an attention to the environment where care is given because it recognizes that a safe environment is critical to healing. Hills and Watson curriculum for Caring Science provides a framework for teaching methodology and content of an educational module that is congruent with Caring Science principles

Bounds on the number of rational points of curves in families

In this note, we give an alternative proof of uniform boundedness of the number of integral points of smooth projective curves over a fixed number field with good reduction outside of a fixed set of primes. We use that due to Bertin-Romagny, the Kodaira-Parshin families constructed by Lawrence-Venkatesh can themselves be assembled into a family. We then repeat Lawrence-Venkatesh's study of the p-adic period map, together with the comparison of nearby fibres.Comment: 12 pages, version to appear in the Bulletin of the London Mathematical Societ