On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.

     

Photoionization of some closed shell atoms and ions

Dipole-allowed single photoionization of some closed shell atoms and ions has been investigated in the relativistic random-phase approximation (RRPA). Application of relativisticmultichannel quantum defect theory (RMQDT) is made together with RRPA to analyse autoionizing resonances. Analysis points to the importance of interchannel coupling in high energy photoionization and reveals various degeneracies in relativistic atomic spectra to influence the low energy dynamics. Interesting threshold behavior in photoelectron spin polarization has been seen. Prospective future studies have been indicated.     

Brans-Dicke Cosmology–A Generalization in Anisotropic Space-Time Models

The generalized Brans-Dicke (BD) Cosmology has been studied for Bianchi-I, Bianchi-III and Kantowski-Sachs anisotropic space-time models. Solutions have been obtained for radiation-dominated era, stiff matter epoch and other equations of state.     

Synthesis of Nitrogen Doped Multilayered Graphene Flakes: Selective Non‐enzymatic Electrochemical Determination of Dopamine and Uric Acid in presence of Ascorbic Acid.

Nitrogen doped multilayered graphene (NDMLG) is synthesized by annealing the black fluffy mass obtained by decomposing the complex prepared from Zn(OAc)₂, diethanolamine and triethanolamine. The NDMLG has been characterized by HRTEM, FESEM, XRD, XPS, Raman spectroscopy, BET which indicate formation of nitrogen doped multilayer graphene flakes with high surface area. NDMLG shows better electrochemical oxidation property towards Dopamine, Uric acid and Ascorbic acid. The linear response ranges for determination of DA, UA and AA are 0.5–150 µM, 3–60 µM and 80–2000 µM respectively and the detection limits (S/N=3) are 15 nM, 15 nM, 580 nM, respectively in the mixture.     

Synthesis of Some Novel Bisisoxazolidine Derivatives from Glyoxal‐derived Bisnitrones via Simultaneous Double Cycloaddition Reactions in Water

Simultaneous double 1,3‐dipolar cycloaddition reactions of glyoxal‐derived bisnitrones have been described in water. Significant rate acceleration and improved yields of exclusively diastereoselective and regioselective bisisoxazolidines in water have been observed at room temperature in a short reaction time compared with conventional solvents.     

Carrageenan for encapsulation and immobilization of flavor,fragrance, probiotics,and enzymes: A review

Carrageenans are sulfated polysaccharides obtained from sea weed. There are six types of carrageenans. They have been explored as gelling agents, control release vehicles, and encapsulating agents. It has been established that carrageenans, in the form of gels, beads and films, can efficiently encapsulate flavors, fragrances, probiotics, and enzymes. Flavors and fragrances are encapsulated to reduce their volatility. Probiotic encapsulation results in enhanced stability. Immobilization of enzymes in carrageenans improves their biocatalytic performance and stability. This review has summarized how carrageenans have been extensively investigated as potential encapsulating agents for the above-mentioned attributes.     

Polyoxometalate-Engineered Building Blocks with Gold Cores for the Self-Assembly of Responsive Water-Soluble Nanostructures

The controlled assembly of gold nanoparticles (AuNPs) with the size of quantum dots into predictable structures is extremely challenging as it requires the quantitatively and topologically precise placement of anisotropic domains on their small, approximately spherical surfaces. We herein address this problem by using polyoxometalate leaving groups to transform 2 nm diameter gold cores into reactive building blocks with hydrophilic and hydrophobic surface domains whose relative sizes can be precisely tuned to give dimers, clusters, and larger micelle-like organizations. Using cryo-TEM imaging and ¹H DOSY NMR spectroscopy, we then provide an unprecedented “solution-state” picture of how the micelle-like structures respond to hydrophobic guests by encapsulating them within 250 nm diameter vesicles whose walls are comprised of amphiphilic AuNP membranes. These findings provide a versatile new option for transforming very small AuNPs into precisely tailored building blocks for the rational design of functional water-soluble assemblies.     

Redefining the transparency order

In this paper, we consider the multi-bit Differential Power Analysis (DPA) in the Hamming weight model. In this regard, we revisit the definition of Transparency Order (\(\mathsf {TO}\)) from the work of Prouff (FSE 2005) and find that the definition has certain limitations. Although this work has been quite well referred in the literature, surprisingly, these limitations remained unexplored for almost a decade. We analyse the definition from scratch, modify it and finally provide a definition with better insight that can theoretically capture DPA in Hamming weight model for hardware implementation with precharge logic. At the end, we confront the notion of (revised) transparency order with attack simulations in order to study to what extent the low transparency order of an s-box impacts the efficiency of a side channel attack against its processing. To the best of our knowledge, this is the first time that such a critical analysis is conducted (even considering the original notion of Prouff). It practically confirms that the transparency order is indeed related to the resistance of the s-box against side-channel attacks, but it also shows that it is not sufficient alone to directly achieve a satisfying level of security. Regarding this point, our conclusion is that the (revised) transparency order is a valuable criterion to consider when designing a cryptographic algorithm, and even if it does not preclude to also use classical countermeasures like masking or shuffling, it enables to improve their effectiveness.     

Use of EM algorithm for data reduction under sparsity assumption

Recent scientific applications produce data that are too large for storing or rendering for further statistical analysis. This motivates the construction of an optimum mechanism to choose only a subset of the available information and drawing inferences about the parent population using only the stored subset. This paper addresses the issue of estimation of parameter from such filtered data. Instead of all the observations we observe only a few chosen linear combinations of them and treat the remaining information as missing. From the observed linear combinations we try to estimate the parameter using EM based technique under the assumption that the parameter is sparse. In this paper we propose two related methods called ASREM and ESREM. The methods developed here are also used for hypothesis testing and construction of confidence interval. Similar data filtering approach already exists in signal sampling paradigm, for example, Compressive Sampling introduced by Candes et al. (Commun Pure Appl Math 59(8):1207–1223, 2006) and Donoho (IEEE Trans Inf Theory 52: 1289–1306, 2006). The methods proposed in this paper are not claimed to outperform all the available techniques of signal recovery, rather our methods are suggested as an alternative way of data compression using EM algorithm. However, we shall compare our methods to one standard algorithm, viz., robust signal recovery from noisy data using min-\(\ell _{1}\) with quadratic constraints. Finally we shall apply one of our methods to a real life dataset.     

Acid Catalyzed Efficient Syntheses of Aryl‐5H‐dibenzo[b,i]xanthene‐5,7,12,14‐(13H)‐tetraones and 3,3‐(Arylmethylene)bis(2‐hydroxynaphthalene‐1,4‐diones) and In Vitro Evaluation of their Antioxidant Activity

A simple and efficient synthesis of aryl‐5H‐dibenzo[b,i]xanthene‐5,7,12,14‐(13H)‐tetraones and 3,3‐(arylmethylene)bis(2‐hydroxynaphthalene‐1,4‐diones) by the condensation of aromatic aldehydes and 2‐hydroxy‐1,4‐naphthoquinone under extremely mild conditions using catalytic amount of H₂SO₄ or in the presence of acidic ionic liquid 1‐butyl‐3‐methylimidazolium hydrogen sulphate, which could be recycled, has been reported. The radical scavenging capacity of the synthesized compounds has been examined towards the stable free radical 2,2‐diphenyl‐1‐picrylhydrazyl (DPPH), and the compounds 2 were found to scavenge DPPH free radical efficiently.