On standardized models of isogenous elliptic curves

Let be isogenous elliptic curves over given by standardized Weierstrass models. We show that (in the obvious notation)

and, moreover, that there are integers such that

where .

     

Ultrasonic pretreatment of corn slurry for saccharification: A comparison of batch and continuous systems

The effects of ultrasound on corn slurry saccharification yield and particle size distribution was studied in both batch and continuous-flow ultrasonic systems operating at a frequency of 20 kHz. Ground corn slurry (28% w/v) was prepared and sonicated in batches at various amplitudes (192–320 μm_{peak-to-peak (p–p)}) for 20 or 40 s using a catenoidal horn. Continuous flow experiments were conducted by pumping corn slurry at various flow rates (10–28 l/min) through an ultrasonic reactor at constant amplitude of 12 μm_p–p. The reactor was equipped with a donut shaped horn. After ultrasonic treatment, commercial alpha- and gluco-amylases (STARGEN^TM 001) were added to the samples, and liquefaction and saccharification proceeded for 3 h. The sonicated samples were found to yield 2–3 times more reducing sugars than unsonicated controls. Although the continuous flow treatments released less reducing sugar compared to the batch systems, the continuous flow process was more energy efficient. The reduction of particle size due to sonication was approximately proportional to the dissipated ultrasonic energy regardless of the type of system used. Scanning electron microscopy (SEM) images were also used to observe the disruption of corn particles after sonication. Overall, the study suggests that both batch and continuous ultrasonication enhanced saccharification yields and reduced the particle size of corn slurry. However, due to the large volume involve in full scale processes, an ultrasonic continuous system is recommended.     

Aggregated CdS quantum dots: Host of biomolecular ligands

In this contribution, we have studied structural and photophysical properties of aggregated CdS quantum dots (QDs) capped with 2-mercaptoethanol in aqueous medium. The hydrodynamic diameter of the nanostructures in aqueous solution was found to be approximately 160 nm with the dynamic light scattering (DLS) technique, which is in close agreement with atomic force microscopy (AFM) studies (diameter approximately 150 nm). However, the UV-vis absorption spectroscopy, powder X-ray diffraction (XRD), and transmission electron microscopy (TEM) studies confirm the average particle size (QD) in the nanoaggregate to be 4.0 +/- 0.5 nm. The steady-state and time-resolved photoluminescence studies on the QDs further confirm preservation of electronic band structure of the QDs in the nanoaggregate. To study the nature of the nanoaggregate we have used small fluorescent probes, which are widely used as biomolecular ligands (2,6-p-toluidinonaphthalene sulfonate (TNS) and Oxazine 1), and found the pores of the aggregate to be hydrophobic in nature. The significantly large spectral overlap of the host quantum dots (donor) with that of the guest fluorescent probe Oxazine 1 (acceptor) allows us to carry out F?rster resonance energy transfer (FRET) studies to estimate average donor-acceptor distance in the nanostructure, found to be approximately 25 Angstrom. The quantum dot aggregate and the characterization techniques reported here could have implications in the future application of the QD-nanoaggregate as host of small ligand molecules of biological interest.     

The Imaginary Point Spectrum and Hypercyclicity

Let A be a generator of a C₀-semigroup T(·) on a separable Banach space. Under suitable conditions on the imaginary point spectrum of A, we show that T(·) is hypercyclic.     

An unusual approach to spirolactones and related structures

Spirocyclic structures can be obtained by an ipso-type radical cyclisation onto a furan or a suitably substituted pyrrole followed by oxidation of the stabilised radical adduct.     

Algorithms for non-uniform size data placement on parallel disks

We study an optimization problem that arises in the context of data placement in a multimedia storage system. We are given a collection of M multimedia objects (data items) that need to be assigned to a storage system consisting of N disks d₁,d₂,…,d_N. We are also given sets U₁,U₂,…,U_M such that U_i is the set of clients seeking the ith data item. Data item i has size s_i. Each disk d_j is characterized by two parameters, namely, its storage capacity C_j which indicates the maximum total size of data items that may be assigned to it, and a load capacity L_j which indicates the maximum number of clients that it can serve. The goal is to find a placement of data items to disks and an assignment of clients to disks so as to maximize the total number of clients served, subject to the capacity constraints of the storage system.We study this data placement problem for homogeneous storage systems where all the disks are identical. We assume that all disks have a storage capacity of k and a load capacity of L. Previous work on this problem has assumed that all data items have unit size, in other words s_i=1 for all i. Even for this case, the problem is NP-hard. For the case where s_i{1,…,Δ} for some constant Δ, we develop a polynomial time approximation scheme (PTAS). This result is obtained by developing two algorithms, one that works for constant k and one that works for arbitrary k. The algorithm for arbitrary k guarantees that a solution where at least -fraction of all clients are assigned to a disk (under certain assumptions). In addition we develop an algorithm for which we can prove tight bounds when s_i{1,2}. In fact, we can show that a -fraction of all clients can be assigned (under certain natural assumptions), regardless of the input distribution.     

First high-resolution analysis of the 4ν1+ν3 band of nitrogen dioxide near 1.5 μm

The high-resolution absorption spectrum of the 4ν₁+ν₃ band of the ¹⁴N¹⁶O₂ molecule was recorded by CW-Cavity Ring Down Spectroscopy between 6575 and 6700 cm⁻¹. The assignments involve energy levels of the (4,0,1) vibrational state with rotational quantum numbers up to K_a=8 and N=48. A large majority of the spin-rotation energy levels were reproduced within their experimental uncertainty using a theoretical model which takes explicitly into account the Coriolis interactions between the spin-rotational levels of the (4,0,1) vibrational state and those of the (4,2,0) and of (0,9,0) dark states, the anharmonic interactions between the (4,2,0) and (0,9,0) states together with the electron spin-rotation resonances within the (4,0,1), (4,2,0) and (0,9,0) states. Precise vibrational energies, rotational, spin-rotational, and coupling constants were determined for the {(4,2,0), (0,9,0), (4,0,1)} triad of interacting states. Using these parameters and the value of the transition dipole-moment operator determined from a fit of a selection of experimental line intensities, the synthetic spectrum of the 4ν₁+ν₃ band was generated and is provided as Supplementary Material.     

Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators

We give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on Hilbert spaces, which is subject to a Lipschitz continuous perturbation depending on the state. These sets are not necessarily weakly closed as in [3], [4], while the invariance criteria are still written by using only the data of the system. So, no need to the explicit knowledge of neither the solution of this differential inclusion, nor the semi-group generated by the maximal monotone operator. These invariant/viability results are next applied to derive explicit criteria for a-Lyapunov pairs of lower semi-continuous (not necessarily weakly-lsc) functions associated to these differential inclusions. The lack of differentiability of the candidate Lyapunov functions and the consideration of general invariant sets (possibly not convex or smooth) are carried out by using techniques from nonsmooth analysis.