On a conjecture of Pomerance

We say that k is a P-integer if the first phi(k) primes coprime to k form a reduced residue system modulo k. In 1980 Pomerance proved the finiteness of the set of P-integers and conjectured that 30 is the largest P-integer. We prove the conjecture assuming the Riemann Hypothesis. We further prove that there is no P-integer between 30 and 10^11 and none above 10^3500.Comment: 10 pages. Submitted to Acta Arithmetic

Thiol-Disulfide Exchange in Human Growth Hormone

The biopharmaceutical industry has been growing at a tremendous rate, with sales of $63.6 billion 2012 in the US [1]. Nevertheless, the successful development of many protein drugs has been impeded by physical and chemical instabilities arising from their inherent chemical complexity and often leading to protein aggregation. The formation of non-native disulfide bonds is a common route to covalent aggregation of therapeutic proteins and other biologics [2, 3]. Disulfide bonds participate in hydrolytic and oxidative degradation reactions that form non-native disulfide bonds and other reactive species. The mechanisms responsible for protein aggregation are poorly understood and formulations are currently optimized on a trial and error basis. This approach contributes to high development costs and increases the time to market. The main goal of our research is to elucidate the mechanisms of thiol-disulfide exchange and disulfide scrambling in therapeutic proteins. To accomplish this goal, model peptides derived from human growth hormone (hGH) and intact hGH were used to investigate reaction mechanisms and kinetics in solution and solid-state environments. The results will be useful in the rational development of stable, safe and efficacious protein formulations that contain free cysteines and disulfides

On a problem of Recaman and its generalization

AbstractWe solve some cases of a conjecture of Pomerance concerning reduced residue systems modulo k consisting of the first φ(k) primes not dividing k. We cover the case when k is a prime, thus giving a complete solution to a problem of Recaman

A functional link network based adaptive power system stabilizer

An on-line identifier using Functional Link Network (FLN) and Pole-shift (PS) controller for power system stabilizer (PSS) application are presented in this thesis. To have the satisfactory performance of the PSS controller, over a wide range of operating conditions, it is desirable to adapt PSS parameters in real time. Artificial Neural Networks (ANNs) transform the inputs in a low-dimensional space to high-dimensional nonlinear hidden unit space and they have the ability to model the nonlinear characteristics of the power system. The ability of ANNs to learn makes them more suitable for use in adaptive control techniques. On-line identification obtains a mathematical model at each sampling period to track the dynamic behavior of the plant. The ANN identifier consisting of a Functional link Network (FLN) is used for identifying the model parameters. A FLN model eliminates the need of hidden layer while retaining the nonlinear mapping capability of the neural network by using enhanced inputs. This network may be conveniently used for function approximation with faster convergence rate and lesser computational load. The most commonly used Pole Assignment (PA) algorithm for adaptive control purposes assign the pole locations to fixed locations within the unit circle in the z-plane. It may not be optimum for different operating conditions. In this thesis, PS type of adaptive control algorithm is used. This algorithm, instead of assigning the closed-loop poles to fixed locations within the unit circle in the z-plane, this algorithm assumes that the pole characteristic polynomial of the closed-loop system has the same form as the pole characteristic of the open-loop system and shifts the open-loop poles radially towards the centre of the unit circle in the z-plane by a shifting factor α according to some rules. In this control algorithm, no coefficients need to be tuned manually, so manual parameter tuning (which is a drawback in conventional power system stabilizer) is minimized. The PS control algorithm uses the on-line updated ARMA parameters to calculate the new closed-loop poles of the system that are always inside the unit circle in the z-plane. Simulation studies on a single-machine infinite bus and on a multi-machine power system for various operating condition changes, verify the effectiveness of the combined model of FLN identifier and PS control in damping the local and multi-mode oscillations occurring in the system. Simulation studies prove that the APSSs have significant benefits over conventional PSSs: performance improvement and no requirement for parameter tuning

Irreducibility of some orthogonal polynomials

AbstractWe give an explicit upper bound for the degree of reducible generalized Hermite–Laguerre polynomials in some particular cases

In vitro antioxidant activity and polyphenol estimation of methanolic extract of endangered medicinal tree species, Hildegardia populifolia (Roxb.) Schott & Endl.

Antioxidant property of methanolic leaf and stem bark extracts of the endangered medicinal tree species, Hildegardia populifolia was evaluated by studying the contents of total phenolics, tannins and flavonoids, free radical scavenging activity using 1,1-diphenyl-2-picryl hydrozyl (DPPH), hydroxyl radical scavenging activity, reducing power activity, ABTS·+ assay and metal chelating activity. The results of the study revealed that both the parts studied were found to have potent antioxidant activity against DPPH, hydroxyl and ABTS·+ radicals with the IC50 value of 92.86 and 309.83 for methanolic extracts of leaf and stem bark respectively for DPPH radicals and 820.30 (leaf) and 456.71 (stem bark) for hydroxyl radicals. Therefore methanolic extracts of both leaf and stem bark of H. populifolia can be considered as a new potential source of natural antioxidants for pharmaceutical industries