Sums of two squares and a power

We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a congruence condition is imposed on $z$. These examples are of interest as there is no congruence obstruction itself for the representation of these $n$. This way we provide a new family of counterexamples to the Hasse principle or strong approximation.Comment: 6 pages, to appear in the memorial volume "From Arithmetic to Zeta-Functions - Number Theory in Memory of Wolfgang Schwarz

Characterization of plant-based protein sources for use in canine and feline nutrition

The objective of this study was to determine the macronutrient composition and standardized amino acid digestibility of 14 novel, plant-based, protein sources. The 14 protein sources are comprised of protein concentrates (pea, potato, faba bean, yeast, and soy concentrates), pulses (garbanzo beans, navy beans, black beans, lentils, and peas), and byproducts (corn gluten meal, peanut flour, soybean meal, and soy flakes). Macronutrient compositions and a complete amino acid profile were analyzed for all 14 protein sources. Cecectomized roosters (n=4/treatment) were utilized in a precision-fed rooster assay to measure standardized amino acid digestibility and true metabolizable energy corrected for nitrogen (TMEn). The roosters were precision-fed 30g of a 1:1 ratio of an ingredient and corn mixture. Excreta was collected after 48h, freeze-dried, and analyzed for a complete amino acid profile. Due to the high amino acid digestibility and well-balanced essential amino acid profiles, these plant-based proteins have the potential to become viable protein sources in canine and feline diets

Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov's mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed

Aplicação de produtos químicos na repicagem da figueira

Como a repicagem de mudas de figueira (Ficus carica L. cv. Roxo de Valinhas) apresen ta frequentemente problemas no transplante, estudou-se o efeito de produtos químicos nesta fase crftica para a formação do figueiral. Procedeu-se aos tratamentos de redução da área foliar, pulverização com Transplantone 10 g/l água, Oed green (oxietileno docosanol) 40 ml/1 ,Good-rite peps (polisulfeto de polietíleno) 0,6 ml/l e Mobileaf 200 ml/l, além do controle. Redução da área foliar ou pulverização com oxietileno docasonol aumentaram a porcentagem de sobrevivência das figueiras transplantadas. Os produtos químicos não promoveram variações significativas na altura das mudas de figueira 'Roxo de Valinhos'. Auxinas componentes do Transplantone (naftalenacetamida e àcido naftalenacético) causaram aumento no número de folhas da figueira transplantada.This research deals with the effects of chemicals on, transplantation of Ficus carica L. cv. Roxo de Valinhos. Fig plants were sprayed with Transplantone (naphthaleneacetamide plusnaphtaleneacetic acid) 10 g/1 , Oed green (oxyethylene docosanol) 40 ml/1, Good-rite peps (polyethylene polysulfite) 0,6 ml/1, and Mobileaf 200 ml/1. A check treatment and aereduction to half of leaf area were also established. Reduction of leaf area and application of oxyethylene docosanol promoted higher plant survival. The chemicals did not affect the growth of transplanted plants. Auxins constituents of Transplantone increased leaf number of fig plants

The biased apelin receptor agonist, MM07, reverses Sugen/hypoxia-induced pulmonary arterial hypertension as effectively as the endothelin antagonist macitentan

Introduction: Pulmonary arterial hypertension (PAH) is characterised by endothelial dysfunction and pathological vascular remodelling, resulting in the occlusion of pulmonary arteries and arterioles, right ventricular hypertrophy, and eventually fatal heart failure. Targeting the apelin receptor with the novel, G protein-biased peptide agonist, MM07, is hypothesised to reverse the developed symptoms of elevated right ventricular systolic pressure and right ventricular hypertrophy. Here, the effects of MM07 were compared with the clinical standard-of-care endothelin receptor antagonist macitentan. Methods: Male Sprague-Dawley rats were randomised and treated with either normoxia/saline, or Sugen/hypoxia (SuHx) to induce an established model of PAH, before subsequent treatment with either saline, macitentan (30 mg/kg), or MM07 (10 mg/kg). Rats were then anaesthetised and catheterised for haemodynamic measurements, and tissues collected for histopathological assessment. Results: The SuHx/saline group presented with significant increases in right ventricular hypertrophy, right ventricular systolic pressure, and muscularization of pulmonary arteries compared to normoxic/saline controls. Critically, MM07 was as at least as effective as macitentan in significantly reversing detrimental structural and haemodynamic changes after 4 weeks of treatment. Discussion: These results support the development of G protein-biased apelin receptor agonists with improved pharmacokinetic profiles for use in human disease

Equidistribution of expanding translates of curves and Dirichlet's theorem on Diophantine approximation

We show that for almost all points on any analytic curve on R^{k} which is not contained in a proper affine subspace, the Dirichlet's theorem on simultaneous approximation, as well as its dual result for simultaneous approximation of linear forms, cannot be improved. The result is obtained by proving asymptotic equidistribution of evolution of a curve on a strongly unstable leaf under certain partially hyperbolic flow on the space of unimodular lattices in R^{k+1}. The proof involves ergodic properties of unipotent flows on homogeneous spaces.Comment: 26 page

Altered Brain Structure in Infants with Turner Syndrome

Turner syndrome (TS) is a genetic disorder affecting approximately 1:2000 live-born females. It results from partial or complete X monosomy and is associated with a range of clinical issues including a unique cognitive profile and increased risk for certain behavioral problems. Structural neuroimaging studies in adolescents, adults, and older children with TS have revealed altered neuroanatomy but are unable to identify when in development differences arise. In addition, older children and adults have often been exposed to years of growth hormone and/or exogenous estrogen therapy with potential implications for neurodevelopment. The study presented here is the first to test whether brain structure is altered in infants with TS. Twenty-six infants with TS received high-resolution structural MRI scans of the brain at 1 year of age and were compared to 47 typically developing female and 39 typically developing male infants. Results indicate that the typical neuroanatomical profile seen in older individuals with TS, characterized by decreased gray matter volumes in premotor, somatosensory, and parietal-occipital cortex, is already present at 1 year of age, suggesting a stable phenotype with origins in the prenatal or early postnatal period

A Current Mode Detector Array for Gamma-Ray Asymmetry Measurements

We have built a CsI(Tl) gamma-ray detector array for the NPDGamma experiment to search for a small parity-violating directional asymmetry in the angular distribution of 2.2 MeV gamma-rays from the capture of polarized cold neutrons by protons with a sensitivity of several ppb. The weak pion-nucleon coupling constant can be determined from this asymmetry. The small size of the asymmetry requires a high cold neutron flux, control of systematic errors at the ppb level, and the use of current mode gamma-ray detection with vacuum photo diodes and low-noise solid-state preamplifiers. The average detector photoelectron yield was determined to be 1300 photoelectrons per MeV. The RMS width seen in the measurement is therefore dominated by the fluctuations in the number of gamma rays absorbed in the detector (counting statistics) rather than the intrinsic detector noise. The detectors were tested for noise performance, sensitivity to magnetic fields, pedestal stability and cosmic background. False asymmetries due to gain changes and electronic pickup in the detector system were measured to be consistent with zero to an accuracy of $10^{-9}$ in a few hours. We report on the design, operating criteria, and the results of measurements performed to test the detector array.Comment: 33 pages, 20 figures, 2 table

Modeling of droplet generation in a top blowing steelmaking process

Quantification of metal droplets ejected due to impinging gas jet on the surface of liquid metal is an important parameter for the understanding and for the modeling of the refining kinetics of reactions in slag-metal emulsion zone. In the present work, a numerical study has been carried out to critically examine the applicability of droplet generation rate correlation previously proposed by Subagyo et al. on the basis of dimensionless blowing number (N B). The blowing number was re-evaluated at the impingement point of jet with taking into account the temperature effect of change in density and velocity of the gas jet. The result obtained from the work shows that the modified blowing number N B,T at the furnace temperature of 1873 K (1600 °C) is approximately double in magnitude compared to N B calculated by Subagyo and co-workers. When N B,T has been employed to the Subagyo’s empirical correlation for droplet generation, a wide mismatch is observed between the experimental data obtained from cold model and hot model experiments. The reason for this large deviation has been investigated in the current study, and a theoretical approach to estimate the droplet generation rate has been proposed. The suitability of the proposed model has been tested by numerically calculating the amount of metals in slag. The study shows that the weight of metals in emulsion falls in the range of 0 to 21 wt pct of hot metal weight when droplet generation rate has been calculated at ambient furnace temperature of 1873 K (1600 °C)