Further refinements of the Heinz inequality

The celebrated Heinz inequality asserts that $2|||A^{1/2}XB^{1/2}|||\leq |||A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}|||\leq |||AX+XB|||$ for $X \in \mathbb{B}(\mathscr{H})$, A,B\in \+, every unitarily invariant norm $|||\cdot|||$ and $\nu \in [0,1]$. In this paper, we present several improvement of the Heinz inequality by using the convexity of the function $F(\nu)=|||A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}|||$, some integration techniques and various refinements of the Hermite--Hadamard inequality. In the setting of matrices we prove that \begin{eqnarray*} &&\hspace{-0.5cm}\left|\left|\left|A^{\frac{\alpha+\beta}{2}}XB^{1-\frac{\alpha+\beta}{2}}+A^{1-\frac{\alpha+\beta}{2}}XB^{\frac{\alpha+\beta}{2}}\right|\right|\right|\leq\frac{1}{|\beta-\alpha|} \left|\left|\left|\int_{\alpha}^{\beta}\left(A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\right)d\nu\right|\right|\right|\nonumber\\ &&\qquad\qquad\leq \frac{1}{2}\left|\left|\left|A^{\alpha}XB^{1-\alpha}+A^{1-\alpha}XB^{\alpha}+A^{\beta}XB^{1-\beta}+A^{1-\beta}XB^{\beta}\right|\right|\right|\,, \end{eqnarray*} for real numbers $\alpha, \beta$.Comment: 15 pages, to appear in Linear Algebra Appl. (LAA

Crystal structure of 3-benzoyl-2-[(5-bromo-2-Hydroxy-3-methoxybenzylidene)amino]-4,5,6,7-tetrahydrobenzo[b]thiophene

In the cyclo­hexene ring of the title compound, C23H20BrNO3S, the -(CH2)4- atoms are positionally disordered [occupancy ratio = 0.753 (6):0.247 (6)]. The ring has a half-chair conformation for both the major and minor components. The dihedral angles between the mean plane of the thio­phene ring and those of the benzene and phenyl rings are 35.2 (4) and 57.7 (3)°, respectively. The planes of the two aryl rings are twisted with respect to each other by 86.4 (6)°. In the mol­ecule, there is an O-H...N hydrogen bond forming an S(6) ring motif. In the crystal, mol­ecules are linked via C-H...O hydrogen bonds, forming chains parallel to [100].Publisher PDFPeer reviewe

Revealing a new symbiotic X-ray binary with Gemini NIFS

We use K-band spectroscopy of the counterpart to the rapidly variable X-ray transient XMMU J174445.5-295044 to identify it as a new symbiotic X-ray binary. XMMU J174445.5-295044 has shown a hard X-ray spectrum (we verify its association with an Integral/IBIS 18-40 keV detection in 2013 using a short Swift/XRT observation), high and varying N$_H$, and rapid flares on timescales down to minutes, suggesting wind accretion onto a compact star. We observed its near-infrared counterpart using the Near-infrared Integral Field Spectrograph (NIFS) at Gemini-North, and classify the companion as ~ M2 III. We infer a distance of $3.1^{+1.8}_{-1.1}$ kpc (conservative 1-sigma errors), and therefore calculate that the observed X-ray luminosity (2-10 keV) has reached to at least 4$\times10^{34}$ erg/s. We therefore conclude that the source is a symbiotic X-ray binary containing a neutron star (or, less likely, black hole) accreting from the wind of a giant.Comment: 7 pages, 3 figures, MNRAS in pres

Amelioration of Obesity, Glucose Intolerance, and Oxidative Stress in High-Fat Diet and Low-Dose Streptozotocin-Induced Diabetic Rats by Combination Consisting of “Curcumin with Piperine and Quercetin”

Curcumin is an important nutraceutical that has enormous potential for a variety of diseases, but the medicinal properties of curcumin cannot be utilized due to its low in vivo bioavailability. Therefore, in view of the foregoing, there is an extensive need for combinatorial extract “curcumin with piperine and quercetin” which may enhance bioavailability of oral curcumin by inhibiting the enzymes responsible for the metabolism of curcumin. Thus, the present study investigated the effect of combinatorial extract of curcumin on obesity, glucose intolerance, and oxidative stress in high fat diet and low-dose streptozotocin-induced rats. Oral administration of combinatorial extract for 28 days significantly (P < 0.05) reduced PGL (64.84%), PTG (88.94%), LDL (26.38%) and PTC (50.23%) levels, respectively and improved glucose tolerance (P < 0.05) significantly to exogenously administered glucose (2 g/kg) at 60, 90, and 120 min interval on OGTT. The results for antioxidant potential indicate that at 100 mg/kg dose of combinatorial extract of curcumin significantly prevented the high-fat diet and low-dose streptozotocin-induced changes in the oxidative stress parameters (P < 0.01) which supports popular medicinal uses of this combinatorial extract as antihyperglycemic and hypolipidemic and is likely to bring this promising natural product to the forefront of therapeutic agents in the in the treatment of “metabolic syndrome”

Fermentation Of Multigrain Dough – An Approach To Reduce Glycemic Index For Healthy Bread

The use of sourdough as the starter culture for bread making is one of the oldest processes in food fermentation and is very much prevalent in being used for the manufacture of various multigrain breads. The fermentation process of breads from mixed flours is one way, reported to reduce the glycemic index as compared to white bread. In this paper, we have discussed the use of (autochthonous) native culture vs pure culture use, in fermentation to prepare a starter culture sourdough by propagative fermentation. Since such a dough is incorporated in the sourdough bread making process (1:3), by the initial process of intermittent back-slopping (at intervals of 3.5 and 7 days) to propagate sourdough with a starter culture, as a part of the process, we observed the reduction in glycaemic index of the sourdough itself to as low as GI=40, at 3rd day of fermentation when the pure consortium and at 5th day of fermentation GI=43, when the native consortium was used. The sourdough process is thus an essential tool, aimed to make healthy breads, as it is incorporated as an ingredient in the process, to make sourdough bread

Near-infrared counterparts of three transient very faint neutron star X-ray binaries

We present near-infrared (NIR) imaging observations of three transient neutron star X-ray binaries, SAX J1753.5-2349, SAX J1806.5-2215 and AX J1754.2-2754. All three sources are members of the class of `very faint' X-ray transients which exhibit X-ray luminosities $L_X\lesssim10^{36}$ erg s$^{-1}$. The nature of this class of sources is still poorly understood. We detect NIR counterparts for all three systems and perform multi-band photometry for both SAX J1753.5-2349 and SAX J1806.5-2215, including narrow-band Br$_{\gamma}$ photometry for SAX J1806.5-2215. We find that SAX J1753.5-2349 is significantly redder than the field population, indicating that there may be absorption intrinsic to the system, or perhaps a jet is contributing to the infrared emission. SAX J1806.5-2215 appears to exhibit absorption in Br$_{\gamma}$, providing evidence for hydrogen in the system. Our observations of AX J1754.2--2754 represent the first detection of a NIR counterpart for this system. We find that none of the measured magnitudes are consistent with the expected quiescent magnitudes of these systems. Assuming that the infrared radiation is dominated by either the disc or the companion star, the observed magnitudes argue against an ultracompact nature for all three systems.Comment: 10 pages, 10 figures, accepted for publication in MNRA

Influence of phosphate dispersing agents on particle size distribution of soil fines

Abstract: The particle size distribution of a fine portion of soils is usually determined using sedimentation principles and hydrometer method. Some hydrometer test methods, such as South African Standard (SANS3001, 2014) and Guidelines laid by International Soil Reference and Information centre (ISRIC, 2002) make provision for the effect of the dispersing agent in the solution on readings recorded during the test. Test methods that do not make such provision may be incorrectly yielding inflated fines (including clay) contents. This paper discusses the results of an investigation into the effect of dispersants when applying TMH1 (1986) test method. The results have been compared using phosphate dispersants such as Calgon, sodium pyrophos-phate decahydrate and sodium tetra pyrophosphate in various concentrations. The use of dispersants in higher concentrations produced anomalous increases in the hydrometer readings and the results indicated the im-portance of understanding the effect of dispersants on fine soil particle size distribution analyses