An elementary proof of Hilbert's theorem on ternary quartics

In 1888, Hilbert proved that every non-negative quartic form f=f(x,y,z) with real coefficients is a sum of three squares of quadratic forms. His proof was ahead of its time and used advanced methods from topology and algebraic geometry. Up to now, no elementary proof is known. Here we present a completely new approach. Although our proof is not easy, it uses only elementary techniques. As a by-product, it gives information on the number of representations f=p_1^2+p_2^2+p_3^2 of f up to orthogonal equivalence. We show that this number is 8 for generically chosen f, and that it is 4 when f is chosen generically with a real zero. Although these facts were known, there was no elementary approach to them so far.Comment: 26 page

Applying Laser Doppler Anemometry inside a Taylor-Couette geometry - Using a ray-tracer to correct for curvature effects

In the present work it will be shown how the curvature of the outer cylinder affects Laser Doppler anemometry measurements inside a Taylor-Couette apparatus. The measurement position and the measured velocity are altered by curved surfaces. Conventional methods for curvature correction are not applicable to our setup, and it will be shown how a ray-tracer can be used to solve this complication. By using a ray-tracer the focal position can be calculated, and the velocity can be corrected. The results of the ray-tracer are verified by measuring an a priori known velocity field, and after applying refractive corrections good agreement with theoretical predictions are found. The methods described in this paper are applied to measure the azimuthal velocity profiles in high Reynolds number Taylor-Couette flow for the case of outer cylinder rotation

Effects of temporal floral resource availability and non-crop habitats on broad bean pollination

Context Flowering plants can enhance wild insect populations and their pollination services to crops in agricultural landscapes, especially when they flower before the focal crop. However, characterizing the temporal availability of specific floral resources is a challenge. Objectives Developing an index for the availability of floral resources at the landscape scale according to the specific use by a pollinator. Investigating whether detailed and temporally-resolved floral resource maps predict pollination success of broad bean better than land cover maps. Methods We mapped plant species used as pollen source by bumblebees in 24 agricultural landscapes and developed an index of floral resource availability for different times of the flowering season. To measure pollination success, patches of broad bean (Vicia faba), a plant typically pollinated by bumblebees, were exposed in the center of selected landscapes. Results Higher floral resource availability before bean flowering led to enhanced seed set. Floral resource availability synchronous to broad bean flowering had no effect. Seed set was somewhat better explained by land cover maps than by floral resource availability, increasing with urban area and declining with the cover of arable land. Conclusions The timing of alternative floral resource availability is important for crop pollination. The higher explanation of pollination success by land cover maps than by floral resource availability indicates that additional factors such as habitat disturbance and nesting sites play a role in pollination. Enhancing non-crop woody plants in agricultural landscapes as pollen sources may ensure higher levels of crop pollination by wild pollinators such as bumblebees

Программа расчёта математической модели теплового контура электролизного узла производства фтора

Объектом исследования является модель теплового контура электролизного узла производства фтора. Цель работы – разработка принципов организации и создания программы для ЭВМ расчета модели электролизного узла на примере создания программы расчета модели теплового контура узла. В процессе работы проводился анализ структуры и математического описания МЭУ с целью выбора технологии программирования и определения принципов структурной организации программы. Руководствуясь определенными принципами структурной организации и используя выбранную технологию программирования разработана программа расчета модели теплового контура электролизного узла.The object of research is a model of the thermal circuit of the electrolysis unit of fluorine production. The aim of work is development of principles of the organization and the creation of a computer program for calculating the model of the electrolysis unit by creating a program of calculation models thermal unit circuit. During the process of research analyzed the structure and the mathematical description of the EUM to select programming technology and the definition of the principles of structural organization of the program. Guided by certain principles of structural organization and using the selected programming technology developed program for calculating thermal circuit model electrolysis unit

A pan-European model of landscape potential to support natural pest control services

Pest control by natural enemies (natural pest control) is an important regulating ecosystem service with significant implications for the sustainability of agro-ecosystems. The presence of semi-natural habitats and landscape heterogeneity are key determinants of the delivery of this service. However, to date, synthetic and consistent indicators at large scales are lacking. We developed a pan-European, spatially-explicit model to map and assess the landscape potential to sustain natural pest control. The model considers landscape composition in terms of semi-natural habitats types, abundance, spatial configuration and distance from the focal field. It combines recent high-resolution geospatial layers with empirical results from extensive field surveys measuring the specific contribution of different semi-natural habitats to support insects flying enemies providing natural pest control. The resulting maps facilitate a comparison of the relative biological control potential of different areas and show that currently a large proportion of high-productive agricultural areas in Europe has low potential. The obtained indicator can inform the formulation of policies and planning strategies aimed at increasing biodiversity and ecosystem services and can be used to assess trade-offs between different services. Potential fields of application include the Common Agricultural Policy and the EU Biodiversity Strategy, in particular the implementation of Green Infrastructure

Outcomes of men with HIV and germ cell cancer : Results from an international collaborative study

Background: Previous studies have shown that men with HIV and germ cell cancer (HIV-GCC) have inferior overall survival (OS) in comparison with their HIV-negative counterparts. However, little information is available on treatments and outcomes of HIV-GCC in the era of combination antiretroviral therapy (cART). Methods: This study examined men living with HIV who were 18 years old or older and had a diagnosis of histologically proven germ cell cancer (GCC). The primary outcomes were OS and progression-free survival (PFS). Results: Data for 89 men with a total of 92 HIV-GCCs (2 synchronous GCCs and 1 metachronous bilateral GCC) were analyzed; among them were 64 seminomas (70%) and 28 nonseminomas (30%). The median age was 36 years, the median CD4 T-cell count at GCC diagnosis was 420 cells/µL, and 77% of the patients on cART had an HIV RNA load < 500 copies/mL. Stage I disease was found in 44 of 79 gonadal GCCs (56%). Among 45 cases with primary disseminated GCC, 78%, 18%, and 4% were assigned to the good-, intermediate-, and poor-prognosis groups, respectively, of the International Germ Cell Cancer Collaborative Group. Relapses occurred in 14 patients. Overall, 12 of 89 patients (13%) died. The causes of death were refractory GCC (n = 5), an AIDS-defining illness (n = 3), and other causes (n = 4). After a median follow-up of 6.5 years, the 5- and 10-year PFS rates were 81% and 73%, respectively, and the 5- and 10-year OS rates were 91% and 85%, respectively. Conclusions: The 5- and 10-year PFS and OS rates of men with HIV-GCC were similar to those reported for men with HIV-negative GCC. Patients with HIV-GCC should be managed identically to HIV-negative patients. Lay Summary: Men living with HIV are at increased risk for germ cell cancer (GCC). Previous studies have shown that the survival of men with HIV-associated germ cell cancer (HIV-GCC) is poorer than the survival of their HIV-negative counterparts. This study examined the characteristics, treatments, and outcomes of 89 men with HIV-GCC in the era of effective combination antiretroviral therapies. The long-term outcomes of men with HIV-GCC were similar to those reported for men with HIV-negative GCC. Patients with HIV-GCC should be managed identically to HIV-negative patients

Specific detection of methionine 27 mutation in histone 3 variants (H3K27M) in fixed tissue from high-grade astrocytomas

Studies in pediatric high-grade astrocytomas (HGA) by our group and others have uncovered recurrent somatic mutations affecting highly conserved residues in histone 3 (H3) variants. One of these mutations leads to analogous p.Lys27Met (K27M) mutations in both H3.3 and H3.1 variants, is associated with rapid fatal outcome, and occurs specifically in HGA of the midline in children and young adults. This includes diffuse intrinsic pontine gliomas (80 %) and thalamic or spinal HGA (>90 %), which are surgically challenging locations with often limited tumor material available and critical need for specific histopathological markers. Here, we analyzed formalin-fixed paraffin-embedded tissues from 143 pediatric HGA and 297 other primary brain tumors or normal brain. Immunohistochemical staining for H3K27M was compared to tumor genotype, and also compared to H3 tri-methylated lysine 27 (H3K27me3) staining, previously shown to be drastically decreased in samples carrying this mutation. There was a 100 % concordance between genotype and immunohistochemical analysis of H3K27M in tumor samples. Mutant H3K27M was expressed in the majority of tumor cells, indicating limited intra-tumor heterogeneity for this specific mutation within the limits of our dataset. Both H3.1 and H3.3K27M mutants were recognized by this antibody while non-neoplastic elements, such as endothelial and vascular smooth muscle cells or lymphocytes, did not stain. H3K27me3 immunoreactivity was largely mutually exclusive with H3K27M positivity. These results demonstrate that mutant H3K27M can be specifically identified with high specificity and sensitivity using an H3K27M antibody and immunohistochemistry. Use of this antibody in the clinical setting will prove very useful for diagnosis, especially in the context of small biopsies in challenging midline tumors and will help orient care in the context of the extremely poor prognosis associated with this mutation. Electronic supplementary material The online version of this article (doi:10.1007/s00401-014-1337-4) contains supplementary material, which is available to authorized users