Duality, Tangential Interpolation, and Töplitz Corona Problems

In this paper, we extend a method of Arveson (J Funct Anal 20(3):208–233, 1975) and McCullough (J Funct Anal 135(1):93–131, 1996) to prove a tangential interpolation theorem for subalgebras of H ^∞. This tangential interpolation result implies a Töplitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent and Wick (Complex Anal Oper Theory 3(3):729–738, 2009) and Douglas and Sarkar (Proc CRM, 2009).     

Diazotized reagent for spectrophotometric determination of glyphosate pesticide in environmental and agricultural samples

A new sensitive spectrophotometric method for the determination of glyphosate herbicide in environmental and agricultural samples is developed. The reaction is based on diazotization followed by coupling of glyphosate with p-dimethyl amino benzaldehyde. The resulted complex absorption spectra was observed at λ_max = 420 nm. The effects of other metal ions and pesticides were also tested for selective determination of glyphosate. The analytical parameters were optimized and have been successfully applied for determination of glyphosate in various environmental samples such as soil, water and vegetables. This method has a lower limit detection of 6 μg of glyphosate. Beer's law is obeyed over the concentration range of 6.0 μg–24.0 μg glyphosate in 25 mL of the final solution at 420 nm. The standard deviation and relative standard deviation calculated are 0.0055 and 1.023, respectively. The molar absorptivity of the colored system is 1.91 × 10¹⁰ L mol^?1cm^?1 and Sandell's sensitivity is found 0.408 × 10^?5 μg cm^?2. The proposed method is simple, sensitive, highly reproducible and time saving as compare to those complicated time consuming methods.     

Abrahamse's interpolation theorem and Fuchsian groups

We generalize Abrahamse's interpolation theorem from the setting of a multiply connected domain to that of a more general Riemann surface. Our main result provides the scalar-valued interpolation theorem for the fixed-point subalgebra of H^∞ associated to the action of a Fuchsian group. We rely on two results from a paper of Forelli. This allows us to prove the interpolation result using duality techniques that parallel Sarason's approach to the interpolation problem for H^∞ [Donald Sarason, Generalized interpolation in H^∞, Trans. Amer. Math. Soc. 127 (1967) 179-203, MR0208383. [26]]. In this process we prove a more general distance formula, very much like Nehari's theorem, and obtain relations between the kernel function for the character automorphic Hardy spaces and the Szegö kernel for the disk. Finally, we examine our interpolation results in the context of the two simplest examples of Fuchsian groups acting on the disk.     

Graviton emission in the bulk from a higher-dimensional Schwarzschild black hole

We consider the evaporation of (4+n)$(4+n)$-dimensional non-rotating black holes into gravitons. We calculate the energy emission rate for gravitons in the bulk obtaining analytical solutions of the master equation satisfied by all three types (S, V, T) of gravitational perturbations. Our results, valid in the low-energy regime, show a vector radiation dominance for every value of n. The calculated low-energy emission rate, for all types of degrees of freedom, is found to decrease with the number of extra dimensions n, as in the previously studied case of a bulk scalar field. By comparing the emission rates in the bulk for scalars and gravitons, we find that the one for gravitons remains well below that for a scalar field in the low-energy regime.     

On a lower bound of commutativity degree

The commutativity degree of a finite group G, denoted by Pr(G), is the probability that a randomly chosen pair of elements of G commute. The object of this paper is to derive a lower bound for Pr(G) and study some of its consequences towards characterizing G.     

Microstrip Coupled-Line Lowpass Filter with Wide Stopband for RF/Wireless Systems

We present the design of a compact microstrip lowpass filter with a wide stopband which is up to ten times the cutoff frequency. The filter is based on a coupled-line configuration and shunt open stubs. The open stubs create additional transmission zeros, which are used to extend the stopband of the filter without any additional components or cascaded units. A prototype lowpass filter with a 3 dB cutoff frequency of 0.428 GHz and a 15 dB stopband extended up to 4.77 GHz is fabricated to validate the theoretical predictions.     

Characterization of the tryptophan residues of human placental ribonuclease inhibitor and its complex with bovine pancreatic ribonuclease A by steady-state and time-resolved emission spectroscopy

Human placental ribonuclease inhibitor (hRI) containing six tryptophan (Trp) residues located at positions 19, 261, 263, 318, 375, and 438 and its complex with RNase A have been studied using steady-state and time-resolved fluorescence (298 K) as well as low-temperature phosphorescence (77 K). Two Trp residues in wild-type hRI and also in the protein-protein complex with RNase A are resolved optically. The accessible surface area values of Trp residues in the wild-type hRI and its complex and consideration of inter-Trp energy transfer in the wild-type hRI reveal that one of the Trp residues is Trp19, which is located in a hydrophobic buried region. The other Trp residue is tentatively assigned as Trp375 based on experimental results on wild-type hRI and its complex. This residue in the wild-type hRI is more or less solvent exposed. Both the Trp residues are perturbed slightly on complex formation. Trp19 moves slightly toward a more hydrophobic region, and the environment of Trp375 becomes less solvent exposed. The complex formation also results in a more heterogeneous environment for both the optically resolved Trp residues.     

A New Unified Approach for the Simulation of a Wide Class of Directional Distributions

The need for effective simulation methods for directional distributions has grown as they have become components in more sophisticated statistical models. A new acceptance–rejection method is proposed and investigated for the Bingham distribution on the sphere using the angular central Gaussian distribution as an envelope. It is shown that the proposed method has high efficiency and is also straightforward to use. Next, the simulation method is extended to the Fisher and Fisher–Bingham distributions on spheres and related manifolds. Together, these results provide a widely applicable and efficient methodology to simulate many of the standard models in directional data analysis. An R package simdd, available in the online supplementary material, implements these simulation methods.     

Ti(III)-mediated radical cyclization of β-aminoacrylate containing epoxy alcohol moieties: synthesis of highly substituted azacycles

Ti(III)-mediated radical cyclization of β-aminoacrylate containing 2,3-epoxy alcohol moieties led to the formation of highly substituted piperidine and pyrrolidine rings. The pyrrolidine ring system was then transformed into an indolizidine framework present in many natural products.     

Substituent effect on diastereoselectivity in Type-II ene cyclisation: a theoretical study

Methyl and methoxy substituted transition states (TS) of Type-II ene cyclisation have been optimized by ab-initio method and relative stability of the diastereomeric TSs have been calculated. In all TSs, equatorial substituent positions have been found to be preferred over the axial positions except for the 4′-substituted methoxy derivative, in which the methoxy group prefers to retain axial position. It has also been noted that the presence of the methoxy group(s) in other position(s) may affect the stability of axially oriented TS and thus alters the overall stereoselectivity of the reaction.