Spectral Properties of Non-Unitary Band Matrices

We consider families of random non-unitary contraction operators defined as deformations of CMV matrices which appear naturally in the study of random quantum walks on trees or lattices. We establish several deterministic and almost sure results about the location and nature of the spectrum of such non-normal operators as a function of their parameters. We relate these results to the analysis of certain random quantum walks, the dynamics of which can be studied by means of iterates of such random non-unitary contraction operators.Comment: updated version, to appear in Annales Henri Poincar

Product Vacua and Boundary State Models in d Dimensions

We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Lambda subset of Z^d, which we call `Product Vacua with Boundary States' (PVBS). We characterize their ground state spaces on arbitrary finite volumes and study the thermodynamic limit. Using the martingale method, we prove that the models have a gapped excitation spectrum on Z^d except for critical values of the parameters. For special values of the parameters we show that the excitation spectrum is gapless. We demonstrate the sensitivity of the spectrum to the existence and orientation of boundaries. This sensitivity can be explained by the presence or absence of edge excitations. In particular, we study a PVBS models on a slanted half-plane and show that it has gapless edge states but a gapped excitation spectrum in the bulk

Approximating the ground state of gapped quantum spin systems

We consider quantum spin systems defined on finite sets $V$ equipped with a metric. In typical examples, $V$ is a large, but finite subset of Z^d. For finite range Hamiltonians with uniformly bounded interaction terms and a unique, gapped ground state, we demonstrate a locality property of the corresponding ground state projector. In such systems, this ground state projector can be approximated by the product of observables with quantifiable supports. In fact, given any subset, X, of V the ground state projector can be approximated by the product of two projections, one supported on X and one supported on X^c, and a bounded observable supported on a boundary region in such a way that as the boundary region increases, the approximation becomes better. Such an approximation was useful in proving an area law in one dimension, and this result corresponds to a multi-dimensional analogue

Synthesis and screening of anticancer potentials of some new terephthaldehyde-derived nitrone compounds

Purpose: To synthesize and screen some new nitrone compounds derived from terephthaldehyde for their anticancer potential. Methods: Six new compounds (H, p-Me,p-Br, p-Cl, o-Cl and m-Me) were synthesized via a condensation reaction between terephthaldehyde and a variety of aryl hydroxylamine compounds derived from nitrobenzene and its derivatives. The chemical structures of these compounds were identified using elemental CHN analysis and were elucidated using Fourier Transform infra-red (FT-IR), 1H-nuclear magnetic resonance (1H NMR), mass spectrometry (MS), and elemental analysis. The anticancer effects of the compounds were screened in vitro with respect to their cytotoxicity on MCF7 human cancer cells line. The IC50 values were obtained by MTT assay and their effects on apoptosis of MCF-7 cells were assessed using Acridine orange-ethidium bromide AO/EtBr staining method under a fluorescence microscope. Results: Only four compounds (2b, 2d, 2e, and 2f) inhibited more than 50 % of the growth of MCF-7 cells. The strongest anti-proliferation effect against MCF-7 cells was exhibited by 2f (m-Me), producing more apoptosis which increased membrane disruption and consistency of lysosome vacuoles; it also exhibited higher cytotoxic effects on human cancer cell lines (IC50 < 7.5) than the other synthesized compounds. Conclusion: The new nitrone compounds (2b, 2d, 2e, and 2f) synthesized from terephthaldehyde exhibit some anticancer properties, and so are potential anticancer agents. Keywords: Terephthaldehyde, Nitrone, Cytotoxicity, Anticancer, MCF-7 cell

Estimation and prediction of temperature in Iraq using the multi-layered neural network model

The forecasting using the multi-layered neural network model is one of the methods used recently in forecasting, especially in climate forecasts for certain regions, because of its accuracy in forecasting, which sometimes reaches levels close to the real collected data. In this research, the daily temperatures in the climate of Iraq were predicted, by taking data from the Iraqi Meteorological Authority by (228) observations, which represent the daily temperatures of Karbala Governorate in the year (2021), The results of the autocorrelation and partial autocorrelation showed that the daily temperature series of Karbala governorate is unstable, and this was confirmed by conducting the augmented Dickey Fuller test. The data was analyzed using the multi-layered neural network model in two stages, and it was later shown that the accuracy of estimation and prediction using the multi-layered neural network even if the time series is not stable, The results showed an indication of an rising increase in temperatures during the coming years. The researcher concluded that it is necessary to pay attention to the vegetation cover and to conduct many predictive studies of the climate using the multi-layered neural network

Hepcidin and its Related Hematological Biomarkers of Anemia in Children on Hemodialysis: Role of Carnitine Deficiency

BACKGROUND: Anemia is one of the most common complications in end-stage renal disease (ESRD) patients. Hepcidin is a hormone that regulates iron homeostasis in patients with ESRD. Carnitine deficiency is commonly seen in hemodialysis (HD) patients. AIM: This study aimed to investigate the relationship between hepcidin and inflammatory and other anemia markers in children with ESRD and to evaluate the association of carnitine deficiency with anemia in these patients. SUBJECTS AND METHODS: Thirty pediatric patients with ESRD undergoing HD, and thirty healthy, age- and sex-matched children served as controls were included in the study. Serum levels hepcidin, iron status, high-sensitivity C-reactive protein, and total carnitine were measured. RESULTS: Statistically significant increases in serum levels of hepcidin (100.7 ± 0.99 ng\ml vs. 77.43 ± 0.8 ng\ml, p = 0.000), was found in HD children as compared to healthy controls. Statistically significant increase in serum levels of hs-CRP (3.94 ± 0.19 mg/l vs. 1.36 ± 0.07 mg/l, p = 0.04) was found in HD children as compared to healthy controls. However, serum levels of carnitine (29.59 ± 2.46 μmol/L vs. 36 ± 2.39 μmol/L, p = 0.000) showed statistically significant decreases in HD children as compared to healthy controls positive correlation was found between hepcidin and hs-CRP (r = 0.059, p = 0.042). Furthermore, a positive correlation was present between serum carnitine levels and serum iron levels (r = 0.651, p = 0.042). CONCLUSION: Serum hepcidin may be a more useful biomarker of functional iron deficiency in children on HD. The efficacy of carnitine treatment for children on HD with carnitine deficiency and its effect on anemia needs to be studied

Diffusive propagation of wave packets in a fluctuating periodic potential

We consider the evolution of a tight binding wave packet propagating in a fluctuating periodic potential. If the fluctuations stem from a stationary Markov process satisfying certain technical criteria, we show that the square amplitude of the wave packet after diffusive rescaling converges to a superposition of solutions of a heat equation.Comment: 13 pages (v2: added a paragraph on the history of the problem, added some references, correct a few typos; v3 minor corrections, added keywords and subject classes