The Limit Behavior Of The Trajectories of Dissipative Quadratic Stochastic Operators on Finite Dimensional Simplex

The limit behavior of trajectories of dissipative quadratic stochastic operators on a finite-dimensional simplex is fully studied. It is shown that any dissipative quadratic stochastic operator has either unique or infinitely many fixed points. If dissipative quadratic stochastic operator has a unique point, it is proven that the operator is regular at this fixed point. If it has infinitely many fixed points, then it is shown that $\omega-$ limit set of the trajectory is contained in the set of fixed points.Comment: 14 pages, accepted in Difference Eq. App

Photovoltaic stand-alone modular systems, phase 2

The final hardware and system qualification phase of a two part stand-alone photovoltaic (PV) system development is covered. The final design incorporated modular, power blocks capable of expanding incrementally from 320 watts to twenty kilowatts (PK). The basic power unit (PU) was nominally rated 1.28 kWp. The controls units, power collection buses and main lugs, electrical protection subsystems, power switching, and load management circuits are housed in a common control enclosure. Photo-voltaic modules are electrically connected in a horizontal daisy-chain method via Amp Solarlok plugs mating with compatible connectors installed on the back side of each photovoltaic module. A pair of channel rails accommodate the mounting of the modules into a frameless panel support structure. Foundations are of a unique planter (tub-like) configuration to allow for world-wide deployment without restriction as to types of soil. One battery string capable of supplying approximately 240 ampere hours nominal of carryover power is specified for each basic power unit. Load prioritization and shedding circuits are included to protect critical loads and selectively shed and defer lower priority or noncritical power demands. The baseline system, operating at approximately 2 1/2 PUs (3.2 kW pk.) was installed and deployed. Qualification was successfully complete in March 1983; since that time, the demonstration system has logged approximately 3000 hours of continuous operation under load without major incident

Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant

A bistochastic matrix B of size N is called unistochastic if there exists a unitary U such that B_ij=|U_{ij}|^{2} for i,j=1,...,N. The set U_3 of all unistochastic matrices of order N=3 forms a proper subset of the Birkhoff polytope, which contains all bistochastic (doubly stochastic) matrices. We compute the volume of the set U_3 with respect to the flat (Lebesgue) measure and analytically evaluate the mean entropy of an unistochastic matrix of this order. We also analyze the Jarlskog invariant J, defined for any unitary matrix of order three, and derive its probability distribution for the ensemble of matrices distributed with respect to the Haar measure on U(3) and for the ensemble which generates the flat measure on the set of unistochastic matrices. For both measures the probability of finding |J| smaller than the value observed for the CKM matrix, which describes the violation of the CP parity, is shown to be small. Similar statistical reasoning may also be applied to the MNS matrix, which plays role in describing the neutrino oscillations. Some conjectures are made concerning analogous probability measures in the space of unitary matrices in higher dimensions.Comment: 33 pages, 6 figures version 2 - misprints corrected, explicit formulae for phases provide

The educational potential of the Harmony Project

This research, funded by Canterbury Christ Church University, involved semi-structured interviews with senior leaders from ten schools in England who are engaging with principles of Harmony. Interviews were conducted between May and July 2019 by research intern Julie Marshall and the project was led by Nicola Kemp and Alan Pagden. The aim was to explore the educational potential of the Harmony approach in different school contexts

Discovering cellular mitochondrial heteroplasmy heterogeneity with single cell RNA and ATAC sequencing

Next generation sequencing technologies have revolutionised the study of biological systems by enabling the examination of a broad range of tissues. Its application to single cell genomics has generated a dynamic and evolving field with a vast amount of research highlighting heterogeneity in transcriptional, genetic and epigenomic state between cells. However, compared to these aspects of cellular heterogeneity, relatively little has been gleaned from the single cell datasets regarding cellular mitochondrial heterogeneity. Single cell sequencing techniques can provide coverage of the mitochondrial genome which allows researchers to probe heteroplasmies 0at the level of the single cell, and observe interactions with cellular function. In this review we give an overview of two popular single cell modalities — single cell RNA sequencing and single cell ATAC sequencing — whose throughput and widespread usage offers researchers the chance to probe heteroplasmy combined with cell state in detailed resolution across thousands of cells. After summarising these technologies in the context of mitochondrial research, we give an overview of recent methods which have used these approaches for discovering mitochondrial heterogeneity. We conclude by highlighting current limitations of these approaches and open problems for future consideration

A Census of X-ray gas in NGC 1068: Results from 450ks of Chandra HETG Observation

We present models for the X-ray spectrum of the Seyfert 2 galaxy NGC 1068. These are fitted to data obtained using the High Energy Transmission Grating (HETG) on the Chandra X-ray observatory. The data show line and radiative recombination continuum (RRC) emission from a broad range of ions and elements. The models explore the importance of excitation processes for these lines including photoionization followed by recombination, radiative excitation by absorption of continuum radiation and inner shell fluorescence. The models show that the relative importance of these processes depends on the conditions in the emitting gas, and that no single emitting component can fit the entire spectrum. In particular, the relative importance of radiative excitation and photoionization/recombination differs according to the element and ion stage emitting the line. This in turn implies a diversity of values for the ionization parameter of the various components of gas responsible for the emission, ranging from log(xi)=1 -- 3. Using this, we obtain an estimate for the total amount of gas responsible for the observed emission. The mass flux through the region included in the HETG extraction region is approximately 0.3 Msun/yr assuming ordered flow at the speed characterizing the line widths. This can be compared with what is known about this object from other techniques.Comment: 39 pages, 12 figures, Ap. J. in pres

Expressive vocabulary predicts non-verbal executive function: a 2-year longitudinal study of deaf and hearing children

Numerous studies suggest an association between language and executive function (EF), but evidence of a developmental relationship remains inconclusive. Data were collected from 75 deaf/hard-of-hearing (DHH) children and 82 hearing age-matched controls. Children were 6-11 years old at first time of testing, and completed a battery of nonverbal EF tasks and a test of expressive vocabulary. These tasks were completed again two years later. Both groups improved their scores on all tasks over this period. DHH children performed significantly less well than hearing peers on some EF tasks and the vocabulary test at both time points. Cross-lagged panel models showed that vocabulary at Time 1 predicted change in EF scores for both DHH and hearing children but not the reverse

Gratings photowritten in ion-exchanged glass channel waveguides

Gratings are photowritten in ion-exchanged glass channel waveguides. The transmission of these waveguides shows a rejection dip of almost 20dB. The polarisation dependence of these waveguide gratings is measured and discussed

Grating formation in BGG31 glass by UV exposure

A three-dimensional index variation grating in bulk BGG31 glass written using neither hydrogen loading nor germanium doping is demonstrated. This material is useful for fabricating ion-exchanged waveguides, and its photosensitivity to ultraviolet (UV) radiation at 248nm has not been previously explored. Intensity measurements of the Bragg diffracted spots indicated a maximum index variation (Delta n) of similar to 4 x 10(-5)