Maximal Contractive Tuples

Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained.     

Small secret exponent attack on RSA variant with modulus N=p^rq

We consider an RSA variant with Modulus \(N=p^rq\) . This variant is known as Prime Power RSA. In PKC 2004, May proved when decryption exponent \(d<N^{ \frac{r}{(r+1)^2}}\) or \(d< N^{\left( \frac{r-1}{r+1}\right) ^2}\) , one can factor \(N\) in polynomial time. In this paper, we improve this bound when \(r \le 5\) . We provide detailed experimental results to justify our claim.     

Two valued measure and summability of double sequences

In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure μ called the (APO₂) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure μ has the condition (APO₂).     

Copper catalyzed atom transfer radical copolymerization of glycidyl methacrylate and 2‐ethylhexyl acrylate

This investigation reports the atom transfer radical copolymerization (ATRcP) of glycidyl methacrylate (GMA) and 2‐ethylhexyl acrylate (EHA). Poly(glycidyl methacrylate) (PGMA) has easily transformable pendant oxirane group and poly(2‐ethylhexyl acrylate) (PEHA) has very low T_g. They are the important components of coating and adhesive materials. Copolymerization of GMA and EHA was carried out in bulk and in toluene at 70 °C at different molar feed ratios using CuCl as catalyst in combination with 2,2′‐bypyridine (bpy) as well as N,N,N′,N″,N″‐pentamethyl diethylenetriamine (PMDETA) as ligand. The molecular weight (M_n) and the polydispersity index (PDI) of the polymers were determined by GPC analysis. The molar composition of the copolymers was determined by ¹H NMR analysis. The reactivity ratios of GMA (r₁) and EHA (r₂) were determined using Finemann‐Ross and Kelen‐Tudos linearization methods and those had been compared with the literature values for conventional free radical copolymerization. The thermal properties of the copolymers were studied by DSC and TGA analysis. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6526–6533, 2009     

Millimeter wave attenuation in relation to rain rate distribution over a tropical station

Rain, perhaps, is the worst offender for utilising Millimeterwaves in practice. This paper describes the rain rate distribution from which millimeterwave attenuation distribution have been attempted. Results reveal that in our location (Calcutta: lat 23°N long 88.5°E) the rain rate distribution fits well with normal distribution. The cumulative distribution of rain rate also prompted the present authors to find out rain attenuation cumulative distribution for both terrestrial and earth-space paths in millimeterwave band.     

Cation transport in polymer electrolytes: a microscopic approach

A microscopic theory for cation diffusion in polymer electrolytes is presented. Based on a thorough analysis of molecular dynamics simulations on poly(ethylene) oxide with LiBF4, the mechanisms of cation dynamics are characterized. Cation jumps between polymer chains can be identified as renewal processes. This allows us to obtain an explicit expression for the lithium ion diffusion constant DLi by invoking polymer-specific properties such as the Rouse dynamics. This extends previous phenomenological and numerical approaches. In particular, the chain length dependence of DLi can be predicted and compared with experimental data. This dependence can be fully understood without referring to entanglement effects.     

Self-assembled nanoribbons and nanotubes in water: energetic vs entropic networks

We present a comparative investigation of two opposite classes of self-assembled fibrillar networks. Ribbons and tubes having cross-sectional dimensions in the nanoscale can be formed in aqueous solutions of steroids derived, respectively, from deoxycholic (DC) and lithocholic (LC) acids. Rheological features distinguish energetic networks of DC ribbons rigidly fixed in cylindrical bundles and entropic transient networks of LC tubes weakly interacting in shear-sensitive suspensions. The two classes are characterized by their frequency sweep profiles, viscoelastic linear domains, scaling laws of the elastic shear modulus vs concentration, kinetics of formation of the networks, and their optical birefringence aspects. A theoretical context for networks of rigid fibers is used to account for the scaling exponents α in the G’ (and σ*) ∝C ^α laws (α=2.0 and 1.0, respectively, for DC and LC). The evolution observed in DC gels from ribbons to cylindrical fibers with monodisperse sections made up with four ribbons is an indication of an equilibrated balance between face-to-face attractions and untwisting elastic processes of the constitutive ribbons.Paper presented at the Annual Meeting of the European Society of Rheology, Grenoble, April 2005     

Imprinted ZnO nanostructure-based electrochemical sensing of calcitonin: A clinical marker for medullary thyroid carcinoma

The present work describes an exciting method for the selective and sensitive determination of calcitonin in human blood serum samples. Adopting the surface molecular imprinting technique, a calcitonin-imprinted polymer was prepared on the surface of the zinc oxide nanostructure. Firstly, a biocompatible tyrosine derivative as a monomer was grafted onto the surface of zinc oxide nanostructure followed by their polymerization on vinyl functionalized electrode surface by activator regenerated by electron transfer–atom transfer radical polymerization (ARGET–ATRP) technique. Such sensor can predict the small change in the concentration of calcitonin in the human body and it may also consider to be as cost-effective, renewable, disposable, and reliable for clinical studies having no such cross-reactivity and matrix effect from real samples. The morphologies and properties of the proposed sensor were characterized by scanning electron microscopy, cyclic voltammetry, difference pulse voltammetry and chronocoulometry. The linear working range was found to be 9.99 ng L⁻¹ to 7.919 mg L⁻¹ and the detection limit as low as 3.09 ± 0.01 ng L⁻¹ (standard deviation for three replicate measurements) (S/N = 3).     

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.