DEVELOPMENT OF RURAL AMERICA

Community/Rural/Urban Development,

Non-existence of Ramanujan congruences in modular forms of level four

Ramanujan famously found congruences for the partition function like p(5n+4) = 0 modulo 5. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on Gamma_{1}(4) which is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpartitions, crank differences, and 2-colored F-partitions.Comment: 19 page

First observation of the depolarization of Thomson scattering radiation by a fusion plasma

Peer reviewe

A Review on Applications of Machine Learning in Shipping Sustainability

The shipping industry faces a significant challenge as it needs to significantly lower the amounts of Green House Gas emissions at the same time as it is expected to meet the rising demand. Traditionally, optimising the fuel consumption for ships is done during the ship design stage and through operating it in a better way, for example, with more energy-efficient machinery, optimising the speed or route. During the last decade, the area of machine learning has evolved significantly, and these methods are applicable in many more fields than before. The field of ship efficiency improvement by using Machine Learning methods is significantly progressing due to the available volumes of data from online measuring, experiments and computations. This amount of data has made machine learning a powerful tool that has been successfully used to extract information and intricate patterns that can be translated into attractive ship energy savings. This article presents an overview of machine learning, current developments, and emerging opportunities for ship efficiency. This article covers the fundamentals of Machine Learning and discusses the methodologies available for ship efficiency optimisation. Besides, this article reveals the potentials of this promising technology and future challenges

Phase composition and transformations in magnetron-sputtered (Al,V)2O3 coatings

Coatings of (Al1-xVx)2O3, with x ranging from 0 to 1, were deposited by pulsed DC reactive sputter deposition on Si(100) at a temperature of 550 {\deg}C. XRD showed three different crystal structures depending on V-metal fraction in the coating: {\alpha}-V2O3 rhombohedral structure for 100 at.% V, a defect spinel structure for the intermediate region, 63 - 42 at.% V. At lower V-content, 18 and 7 at.%, a gamma-alumina-like solid solution was observed, shifted to larger d-spacing compared to pure {\gamma}-Al2O3. The microstructure changes from large columnar faceted grains for {\alpha}-V2O3 to smaller equiaxed grains when lowering the vanadium content toward pure {\gamma}-Al2O3. Annealing in air resulted in formation of V2O5 crystals on the surface of the coating after annealing to 500 {\deg}C for 42 at.% V and 700 {\deg}C for 18 at.% V metal fraction respectively. The highest thermal stability was shown for pure {\gamma}-Al2O3-coating, which transformed to {\alpha}-Al2O3 after annealing to 1100{\deg} C. Highest hardness was observed for the Al-rich oxides, ~24 GPa. The latter decreased with increasing V-content, larger than 7 at.% V metal fraction. The measured hardness after annealing in air decreased in conjunction with the onset of further oxidation of the coatings

Sink strength simulations using the Monte Carlo method : Applied to spherical traps

The sink strength is an important parameter for the mean-field rate equations to simulate temporal changes in the micro-structure of materials. However, there are noteworthy discrepancies between sink strengths obtained by the Monte Carlo and analytical methods. In this study, we show the reasons for these differences. We present the equations to estimate the statistical error for sink strength calculations and show the way to determine the sink strengths for multiple traps. We develop a novel, very fast Monte Carlo method to obtain sink strengths. The results show that, in addition to the well-known sink strength dependence of the trap concentration, trap radius and the total sink strength, the sink strength also depends on the defect diffusion jump length and the total trap volume fraction. Taking these factors into account, allows us to obtain a very accurate analytic expression for the sink strength of spherical traps. (C) 2017 Elsevier B. V. All rights reserved.Peer reviewe

Association between Plasma Homocysteine Levels and Neuronal Injury in HIV Infection

OBJECTIVE: To investigate the role of homocysteine in neuronal injury in HIV infection. METHODS: Using a cross-sectional design and archived samples, we compared concentrations of plasma homocysteine and cerebrospinal fluid (CSF) neurofilament light protein (NFL), a sensitive marker of neuronal injury, in 83 HIV-1-infected subjects without antiretroviral treatment. We also analyzed plasma vitamin B12, serum folate, CSF, and plasma HIV RNA, the immune activation marker neopterin in CSF and serum, and albumin ratio as a marker of blood-brain barrier integrity. Twenty-two subjects provided a second sample median of 12.5 months after antiretroviral treatment initiation. RESULTS: A significant correlation was found between plasma homocysteine and CSF NFL concentrations in untreated individuals (r = 0.52, p < 0.0001). As expected, there was a significant inverse correlation between homocysteine and B12 (r = –0.41, p < 0.001) and folate (r = –0.40, p = < 0.001) levels. In a multiple linear regression analysis homocysteine stood out as an independent predictor of CSF NFL in HIV-1-infected individuals. The correlation of plasma homocysteine and CSF NFL was also present in the group receiving antiretroviral therapy (r = 0.51, p = 0.016). CONCLUSION: A correlation between plasma homocysteine and axonal injury, as measured by CSF NFL, was found in both untreated and treated HIV. While this study is not able to prove a causa

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$