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

Exploring the S-Matrix of Massless Particles

We use the recently proposed generalised on-shell representation for scattering amplitudes and a consistency test to explore the space of tree-level consistent couplings in four-dimensional Minkowski spacetime. The extension of the constructible notion implied by the generalised on-shell representation, i.e. the possibility to reconstruct at tree level all the scattering amplitudes from the three-particle ones, together with the imposition of the consistency conditions at four-particle level, allow to rediscover all the known theories and their algebra structure, if any. Interestingly, this analysis seems to leave room for high-spin couplings, provided that at least the requirement of locality is weakened. We do not claim to have found tree-level consistent high-spin theories, but rather that our methods show signatures of them and very likely, with a suitable modification, they can be a good framework to perform a systematic search.Comment: 44 pages, 1 figur

A neuroanatomical correlate of sensorimotor recovery in response to repeated vaginocervical stimulation in rats

Gentle probing against the cervix via the vagina (vaginocervical stimulation, VCS) increases tail flick latency (TFL) to radiant heat; greater force abolishes the tail flick response and other withdrawal responses. This effect occurs in spinal cord-transected rats and in intact rats. On the basis of our earlier finding that VCS releases vasoactive intestinal peptide (VIP) into the spinal cord, and others’ reports of neurotrophic effects of VIP in vitro, we hypothesized that repeated VCS would stimulate sprouting and sensorimotor function of terminals of genital nerve primary afferents in the sacral spinal cord. To test this hypothesis, in the present study, we denervated the genital tract only unilaterally, which significantly reduced the TFL-elevating effect of VCS. Then we applied repeated daily VCS for 1 week and compared the subsequent effectiveness of acute VCS in elevating TFL. The rats that received the repeated daily VCS showed a significantly greater elevation in TFL in response to acute VCS than control rats that did not receive the repeated stimulation. Then, to test whether daily repeated VCS stimulates sprouting of genital primary afferents in such unilaterally genital tract-denervated rats, we transected the contralateral remaining intact pelvic nerve, applied horseradish peroxidase (HRP) to its proximal cut end for 1–2 h, and 2–3 days later counted HRP particles in its terminal zone (L6–S1) in the spinal cord. There were significantly more HRP particles in the rats that received the daily repeated VCS than in the control rats. In the context of these findings, we conclude that VCS in rats can produce a functional sensorimotor recovery via a neurotrophic effect on compromised primary afferents in the spinal cord

Nurse Practice Environment and Quality of Care in a Multigenerational Workforce

In recent years, the nurse practice environment included nurses from multigenerational [1, 2, 3, 4] presenting organizational hurdles as they collaborate on nursing teams [5, 6] that affected the quality of care they render. Thus, the present study was conducted to ascertain the relationship of nurse practice environment (NPE) and quality of care (QoC) in a multigenerational workforce. The Practice Environment Scale of the Nursing Work Index (PES-NWI; Lake, 2002) and Karen-Personnel Instrument (Lindgren & Andersson, 2010) were employed to measure the NPE and QoC, respectively. Data from randomly selected staff nurses (N=213) from two (2) private tertiary hospitals in Metro Manila were analyzed using Multiple Linear Regression (MLR). Results indicated that multigenerational workforce does not influence nurse practice environment and quality of care (β=0.004; p>0.05). Nonetheless, findings of this study could expectedly yield valuable insights that would assist nursing leaders to further examine the nurse practice environment so that nurses could function at the highest scope of clinical practice

recent developments in cancer nanomedicine

Since decades, conventional diagnosis and treatment strategies for cancer have been practiced widely despite their expensive and time-consuming process. These conventional contrast and therapeutic agents suffer from various side-effects such as low radiodensity and image resolution, rapid clearance, non-specific biodistribution, poor tumor accumulation, high-dose and multiple-dose requirements, nephrotoxicity, uncontrolled exposure of high electromagnetic radiations, whole-body scans, and so on. Therefore, nanosized imaging and therapeutic probes have been proposed recently owing to their promising efficacy and negligible side-effects. However, these nanoplatforms are struggling deeply to find their clinical translational relevance. Integrating targeting ligands with diagnostic and therapeutic agents within a single system at the nanoscale resulted in localized nanotheranostics. Furthermore, the conceptualized nanotheranostics has been recognized as a clinical ‘weapon’ for localized cancer nanomedicine. In this review, we have covered a wide spectrum of recent developments in cancer nanotheranostics. Numerous examples of functional nanohybrids and clinical relevant materials with their multimode imaging and therapeutics have been addressed here. On the other hand, the importance of combination therapies, imaging-guided tumor regression, deep tissue visualization, localized diagnosis and tumor ablation, manipulation of the tumor microenvironment, and so on have been discussed here. Overall, localized and stimuli responsive nanosized multifunctional platforms have proved their superiority over conventional diagnosis and therapies.publishersversionpublishe