Functions preserving nonnegativity of matrices

The main goal of this work is to determine which entire functions preserve nonnegativity of matrices of a fixed order $n$ -- i.e., to characterize entire functions $f$ with the property that $f(A)$ is entrywise nonnegative for every entrywise nonnegative matrix $A$ of size $n\times n$. Towards this goal, we present a complete characterization of functions preserving nonnegativity of (block) upper-triangular matrices and those preserving nonnegativity of circulant matrices. We also derive necessary conditions and sufficient conditions for entire functions that preserve nonnegativity of symmetric matrices. We also show that some of these latter conditions characterize the even or odd functions that preserve nonnegativity of symmetric matrices.Comment: 20 pages; expanded and corrected to reflect referees' remarks; to appear in SIAM J. Matrix Anal. App

On the growth of the Bergman kernel near an infinite-type point

We study diagonal estimates for the Bergman kernels of certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range -- roughly speaking -- from being ``mildly infinite-type'' to very flat at the infinite-type points.Comment: Significant revisions made; simpler estimates; very mild strengthening of the hypotheses on Theorem 1.2 to get much stronger conclusions than in ver.1. To appear in Math. An

Decision Making in Optimizing a Product of a Small Scale Industry: A Bayesian Analysis Approach

This paper intends to find Expected monetary value (EMV), Expected opportunity loss (EOL) and conditional profit of the main product (Mukta) of a small scale industry–“ORGAMAN” situated at Jorhat District of Assam. To meet the above specific objectives, the method of Bayesian Analysis has been adopted. The data used in this endeavor is secondary in nature, collected by direct personal investigation. As per prior information, the target of the industry is to produce a minimum of 50 MT (low production) of product and a maximum of 350 MT (high production) of the same per month. The prior analysis reveals that the expected monetary value and expected opportunity loss are optimum against high production. Based on both the prior analysis and posterior analysis, it is observed that the profit for the product of the industry is maximum against high production of 350 MT per month. Although, the profit based on posterior analysis is slightly high, it seems that the additional amount of money has to be spend to collect additional information for posterior analysis

On spectra of Hermitian Randic matrix of second kind

We propose the Hermitian Randi\'c matrix $R^\omega(X)=(R^\omega_{ij})$, where $\omega=\frac{1+i \sqrt{3}}{2}$ and $R^\omega_{ij}={1}/{\sqrt{d_id_j}}$ if $v_iv_j$ is an unoriented edge, ${\omega}/{\sqrt{d_id_j}}$ if $v_i\rightarrow v_j$, ${\overline{\omega}}/{\sqrt{d_id_j}}$ if $v_i\leftarrow v_j$, and 0 otherwise. This appears to be more natural because of $\omega+\overline{\omega}=1$ and $|\omega|=1$. In this paper, we investigate some features of this novel Hermitian matrix and study a few properties like positiveness, bipartiteness, edge-interlacing etc. We also compute the characteristic polynomial for this new matrix and obtain some upper and lower bounds for the eigenvalues and the energy of this matrix

Re-awakening of GRS 1716–249 after 23 yr, observed by Swift/XRT and NuSTAR

In this work, we present a spectral and temporal analysis of Swift/XRT and NuSTAR observations of GRS 1716–249 during its recent 2016–2017 outburst. This low-mass X-ray binary underwent an extraordinary outburst after a long quiescence of 23 yr, since its last major outburst in 1993. The source was observed over two different epochs during 2017 April 7 and 10. The best-fitting joint spectral fitting in the energy range 0.5–79.0 keV indicates that the spectrum is best described by relatively cold, weak disc blackbody emission, dominant thermal Comptonization emission, and a relativistically broadened fluorescent iron K α emission line. We observed a clear indication of a Compton hump around 30 keV. We also detected an excess feature of 1.3 keV. Assuming a lamp-post geometry of the corona, we constrained the inner disc radius for both observations to 11.92^(+8.62)_(−11.92) R_(ISCO) (i.e. an upper limit) and 10.39^(+9.51)_(−3.02) R_(ISCO)(where R_(ISCO) ≡ radius of the innermost stable circular orbit) for the first epoch (E1) and second epoch (E2), respectively. A significant (5σ) type C quasi-periodic oscillation (QPO) at 1.20 ± 0.04 Hz is detected for the first time for GRS 1716–249, which drifts to 1.55 ± 0.04 Hz (6σ) at the end of the second observation. The derived spectral and temporal properties show a positive correlation between the QPO frequency and the photon index

Amino-Functionalized Silica Nanoparticles: In Vitro Evaluation for Targeted Delivery and Therapy of Pancreatic Cancer

We report a method of synthesis and optimization of amino-functionalized silica nanoparticles (SiNPs) and their in vitro evaluation as targeted delivery vehicles for the potential treatment of pancreatic cancer. SiNPs can efficiently encapsulate doxorubicin and can be attached to a targeting moiety such as anti-Claudin-4 (CLN4). The preferential uptake in pancreatic cancer cells, where CLN4 is overexpressed, of SiNPs when conjugated to CLN4 antibody (compared to nonconjugated SiNPs) was confirmed by confocal microscopy. SiNPs encapsulating doxorubicin had greater efficacy in MTT assays than free doxorubicin, and when conjugated to CLN4, the efficacy was dramatically increased (at 1 μM). No apparent carrier toxicity was observed when void SiNPs were used. SiNPs carrying a chemotherapeutic drug have the potential to be used as a targeted therapy for lethal cancers, such as pancreatic cancer. Also, incorporation of fluorescent probes in these SiNPs creates the possibility of their use as an imaging probe for diagnostic purposes

Control of Ni/Ce1-xMxOy Catalyst Properties Via the Selection of Dopant M = Gd, La, Mg. Part 2. Catalytic Activity

To elucidate the role of support composition in autothermal reforming of ethanol (ATR of C2H5OH), a series of Ni catalysts (Ni content 2–15 wt.%) supported on different ceria-based oxides (Ce1-xGdxOy, Ce1-xLaxOy and Ce1-xMgxOy; x = 0.1–0.9) were prepared. The synthetized materials were tested in ATR of ethanol at 200–700 °C. It was established that supports themselves show catalytic activity in ATR of C2H5OH and provide 10–15% yield of H2 at 700 °C. Upon the increase of Ni content from 2 to 15 wt.% the temperature of 100% ethanol conversion decreases from 700 tо 300 °С, hydrogen yield increases from 25 to 60%, the inhibition of С2-С3 by-products formation, as well as the promotion of decomposition of acetaldehyde occur. The enhancement of catalyst performance in ATR of C2H5OH has been observed in the next series of supports: Ce1-xMgxOy < Ce1-xGdxOy < Ce1-xLaxOy and with a decrease of x to an optimal value that correlates with the improvement of Ni active component reducibility. At 600 °C on 10Ni/Ce0.8La0.2O1.9 catalyst the H2 yield of 50% was achieved at C2H5OH conversion of 100%. Stable and high performance of developed catalysts in ATR of C2H5OH indicates the promise of their use in the production of hydrogen