Zagier's weight 3/23/2 mock modular form

Mock modular forms have their origins in Ramanujan's pioneering work on mock theta functions. In a 1975 paper, Zagier proved certain transformation properties of the generating function of the Hurwitz class numbers $H(n)$ for the discriminant $(-n)$. In the modern framework, these results show that the generating function of $H(n)$ is a mock modular form of weight 3/2 with the theta function being the shadow. In this expository paper, we provide a detailed proof of Zagier's result.Comment: 24 page

Thin films sensor devices for mycotoxins detection in foods: applications and challenges

Mycotoxins are a group of secondary metabolites produced by different species of filamentous fungi and pose serious threats to food safety due to their serious human and animal health impacts such as carcinogenic, teratogenic and hepatotoxic effects. Conventional methods for the detection of mycotoxins include gas chromatography and high-performance liquid chromatography coupled with mass spectrometry or other detectors (fluorescence or UV detection), thin layer chromatography and enzyme-linked immunosorbent assay. These techniques are generally straightforward and yield reliable results; however, they are time-consuming, require extensive preparation steps, use large-scale instruments, and consume large amounts of hazardous chemical reagents. Rapid detection of mycotoxins is becoming an increasingly important challenge for the food industry in order to effectively enforce regulations and ensure the safety of food and feed. In this sense, several studies have been done with the aim of developing strategies to detect mycotoxins using sensing devices that have high sensitivity and specificity, fast analysis, low cost and portability. The latter include the use of microarray chips, multiplex lateral flow, Surface Plasmon Resonance, Surface Enhanced Raman Scattering and biosensors using nanoparticles. In this perspective, thin film sensors have recently emerged as a good candidate technique to meet such requirements. This review summarizes the application and challenges of thin film sensor devices for detection of mycotoxins in food matrices.This work was funded by Project POCI-01–0145-FEDER-006984 - Associate Laboratory LSRE-LCM, Project UID/BIO/04469/2013 - CEB and strategic project PEst-OE/AGR/UI0690/2014 - CIMO all funded by European Regional Development Fund (ERDF) through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI)—and by national funds through FCT—Fundação para a Ciência e a Tecnologia I.P. Andréia O. Santos also acknowledges the research grant provided by the Associate Laboratory LSRE-LCM under the Projects UID/EQU/50020/2013 and POCI-01-0145-FEDER-006984. Andreia Vaz acknowledges the research grant provided by the Portuguese Foundation for Science and Technology (FCT), reference number SFRH/BD/129775/2017. The APC was kindly waived by MDPI.info:eu-repo/semantics/publishedVersio

Biofuels: Production and Properties as Substitute Fuels

Renewable sources include plants and animal fats, which are the main components of biofuels. Biofuels are free from sulfur, aromatics, metals, and crude oil residues. Since biofuels are more lubricating than petroleum diesel fuel, they are nonflammable and extend the life of diesel engines. As a result of this study, the main chemical and physical properties of biofuels were investigated, including their lubricity, viscosity, calorific value, and cetane number, which indicate the quality of renewable fuels, and compared with the other. We examined and compared the combustion characteristics of various types of biofuels as an alternative fuel, as well as their emissions characteristics. Biodiesel and biodiesel blends are compared to mineral diesel, as well as their performance in CI engines in this study’s review. With modified combustion equipment, biodiesel fuels can potentially reduce air pollution in diesel engines and are a very good substitute for fossil fuels. There is a need for more research and technological development in order for biofuels to become economically viable. Biofuel/biodiesel research should therefore be supported with policies that make their prices competitive with other conventional sources of energy. In the current state of affairs, biofuels are more effective when used alongside other sources of energy

Geodesic Reduction via Frame Bundle Geometry

A manifold with an arbitrary affine connection is considered and the geodesic spray associated with the connection is studied in the presence of a Lie group action. In particular, results are obtained that provide insight into the structure of the reduced dynamics associated with the given invariant affine connection. The geometry of the frame bundle of the given manifold is used to provide an intrinsic description of the geodesic spray. A fundamental relationship between the geodesic spray, the tangent lift and the vertical lift of the symmetric product is obtained, which provides a key to understanding reduction in this formulation

Journey of india’s first anaerobic digestion waste to biogas plant

Organic Recycling Systems Pvt. Ltd. which was established in 2008 and functions through its SPV-Solapur Bio-Energy Systems Pvt. Ltd (SBESPL), has established India’s first demonstration plant for MSW processing facility based on indigenously developed technology at Solapur, Maharashtra. The company is currently processing 200 Tons per day (TPD) of un-segregated MSW, and now is being upgraded to full working capacity of 400 TPD. Besides this, Bangalore 1000 tonnes and Meerut 800 tonnes are also in advanced stage

A High Sensitivity Micro Format Chemiluminescence Enzyme Inhibition Assay for Determination of Hg(II)

A highly sensitive and specific enzyme inhibition assay based on alcohol oxidase (AlOx) and horseradish peroxidase (HRP) for determination of mercury Hg(II) in water samples has been presented. This article describes the optimization and miniaturization of an enzymatic assay using a chemiluminescence reaction. The analytical performance and detection limit for determination of Hg(II) was optimized in 96 well plates and further extended to 384 well plates with a 10-fold reduction in assay volume. Inhibition of the enzyme activity by dissolved Hg(II) was found to be linear in the range 5–500 pg·mL−1 with 3% CV in inter-batch assay. Due to miniaturization of assay in 384 well plates, Hg(II) was measurable as low as 1 pg·mL−1 within 15 min. About 10-fold more specificity of the developed assay for Hg(II) analysis was confirmed by challenging with interfering divalent metal ions such as cadmium Cd(II) and lead Pb(II). Using the proposed assay we could successfully demonstrate that in a composite mixture of Hg(II), Cd(II) and Pb(II), inhibition by each metal ion is significantly enhanced in the presence of the others. Applicability of the proposed assay for the determination of the Hg(II) in spiked drinking and sea water resulted in recoveries ranging from 100–110.52%

A High-Throughput Enzyme Assay for Organophosphate Residues in Milk

A rapid, high-sensitivity, chemiluminescence (CL) enzyme assay for the determination of organophosphate (OP) residues in milk is presented. The assay for quantification of OP residues in milk is based on the inhibition of enzyme butyrylcholinesterase (BuChE). BuChE was stabilized and preloaded in 384 well plates at 30 °C. The assay permits rapid determination of OPs in milk within 12 min including an incubation step. The enzyme assay was tested for individual and mixtures of OPs such as methyl paraoxon (MPOx), methyl parathion (MP) and malathion (MT) in milk to evaluate their synergistic effect on BuChE inhibition. Good linearity was obtained in the range 0.005–50 μg·L−1 for MPOx and 0.5–1,000 μg·L−1 for MP as well as MT in milk. Mean recovery of 93.2%–98.6% was obtained for MPOx spiked milk samples with 0.99%–1.67% reproducibility (RSD). The proposed method facilitated rapid screening of milk samples in 384 well plate formats with further miniaturization presented in 1,536 well plates

Evaluating the potential of thermal read-out techniques combined with molecularly imprinted polymers for the sensing of low-weight organic molecules

In recent years, there has been a tremendous increase in the papers published on synthetic recognition elements. Molecularly imprinted polymers (MIPs), also referred to as “man-made mimics” of antibodies, are able to rebind their template molecules with high affinity. Advantages compared with those of natural receptors include their excellent thermal and chemical stability, low cost, and ease of the production process. However, their use in commercial biosensors is limited owing to the difficulty to incorporate MIPs into suitable sensing platforms and traditional detection techniques, such as chromatography, that require bulky and sophisticated equipment. In this review, we evaluate the potential to use MIPs combined with thermal read-out for the detection of low-weight organic molecules. We discuss thermal methods to study MIP-template complexation and to determine neurotransmitters concentrations. In particular, we highlight the heat-transfer method, a recent technique that is straightforward and low cost and requires minimal instrumentation. Until now, sample preparation involves a 2-step process, making it time-consuming, and measuring biological samples is difficult owing to the noise in the signal. Different sample preparation methods are discussed, and it will be demonstrated how this affects the thermal response. An outlook is given in novel methods that can simplify and speed up sample preparation. Finally, we show a novel thermal technique, which is based on the analysis of transport of thermal waves rather than evaluating the fixed heat-transfer resistance. Through applying the concept of thermal waves, signal-noise ratio is significantly increased, which results in lower detection limits and has potential for the study of biological samples