Root locus diagrams by digital computer

Adaptation of root locus method to programming on IBM 7074 digital compute

Differential equations for generalized Jacobi polynomials

We look for spectral type differential equations satisfied by the generalized Jacobi polynomials, which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with two point masses at the endpoints of the interval of orthogonality. We show that such a differential equation is uniquely determined and we give explicit representations for the coefficients. In case of nonzero mass points the order of this differential equation is infinite, except for nonnegative integer values of (one of) the parameters. Otherwise, the finite order is explictly given in terms of the parameters.Comment: 33 pages, submitted for publicatio

On the limit of non-standard q-Racah polynomials

The aim of this article is to study the limit transitions from non-standard q-Racah polynomials to big q-Jacobi, dual q-Hahn, and q-Hahn polynomials such that the orthogonality properties and the three-term recurrence relations remain valid

Asparagine promotes cancer cell proliferation through use as an amino acid exchange factor.

Cellular amino acid uptake is critical for mTOR complex 1 (mTORC1) activation and cell proliferation. However, the regulation of amino acid uptake is not well-understood. Here we describe a role for asparagine as an amino acid exchange factor: intracellular asparagine exchanges with extracellular amino acids. Through asparagine synthetase knockdown and altering of media asparagine concentrations, we show that intracellular asparagine levels regulate uptake of amino acids, especially serine, arginine and histidine. Through its exchange factor role, asparagine regulates mTORC1 activity and protein synthesis. In addition, we show that asparagine regulation of serine uptake influences serine metabolism and nucleotide synthesis, suggesting that asparagine is involved in coordinating protein and nucleotide synthesis. Finally, we show that maintenance of intracellular asparagine levels is critical for cancer cell growth. Collectively, our results indicate that asparagine is an important regulator of cancer cell amino acid homeostasis, anabolic metabolism and proliferation

Gamma-Ray Burst Afterglow: Polarization and Analytic Light Curves

GRB afterglow polarization is discussed. We find an observable, up to 10%, polarization, if the magnetic field coherence length grows at about the speed of light after the field is generated at the shock front. Detection of a polarized afterglow would show that collisionless ultrarelativistic shocks can generate strong large scale magnetic fields and confirm the synchrotron afterglow model. Non-detection, at a 1% level, would imply that either the synchrotron emission model is incorrect, or that strong magnetic fields, after they are generated in the shock, somehow manage to stay un-dissipated at ``microscopic'', skin depth, scales. Analytic lightcurves of synchrotron emission from an ultrarelativistic self-similar blast wave are obtained for an arbitrary electron distribution function, taking into account the effects of synchrotron cooling. The peak synchrotron flux and the flux at frequencies much smaller than the peak frequency are insensitive to the details of the electron distribution function; hence their observational determination would provide strong constraints on blast wave parameters.Comment: 19 pages, submitted to Ap

Stable Electromyographic Sequence Prediction During Movement Transitions using Temporal Convolutional Networks

Transient muscle movements influence the temporal structure of myoelectric signal patterns, often leading to unstable prediction behavior from movement-pattern classification methods. We show that temporal convolutional network sequential models leverage the myoelectric signal's history to discover contextual temporal features that aid in correctly predicting movement intentions, especially during interclass transitions. We demonstrate myoelectric classification using temporal convolutional networks to effect 3 simultaneous hand and wrist degrees-of-freedom in an experiment involving nine human-subjects. Temporal convolutional networks yield significant $(p<0.001)$ performance improvements over other state-of-the-art methods in terms of both classification accuracy and stability.Comment: 4 pages, 5 figures, accepted for Neural Engineering (NER) 2019 Conferenc

On the Krall-type Askey-Wilson Polynomials

In this paper the general Krall-type Askey-Wilson polynomials are introduced. These polynomials are obtained from the Askey-Wilson polynomials via the addition of two mass points to the weight function of them at the points $\pm1$. Several properties of such new family are considered, in particular the three-term recurrence relation and the representation as basic hypergeometric series

Attracted Diffusion-Limited Aggregation

In this paper, we present results of extensive Monte Carlo simulations of diffusion-limited aggregation (DLA) with a seed placed on an attractive plane as a simple model in connection with the electrical double layers. We compute the fractal dimension of the aggregated patterns as a function of the attraction strength \alpha. For the patterns grown in both two and three dimensions, the fractal dimension shows a significant dependence on the attraction strength for small values of \alpha, and approaches to that of the ordinary two-dimensional (2D) DLA in the limit of large \alpha. For non-attracting case with \alpha=1, our results in three dimensions reproduce the patterns of 3D ordinary DLA, while in two dimensions our model leads to formation of a compact cluster with dimension two. For intermediate \alpha, the 3D clusters have quasi-2D structure with a fractal dimension very close to that of the ordinary 2D-DLA. This allows one to control morphology of a growing cluster by tuning a single external parameter \alpha.Comment: 6 pages, 6 figures, to appear in Phys. Rev. E (2012