Lp mean estimates for an operator preserving inequalities between polynomials

If $P(z)$ be a polynomial of degree at most $n$ which does not vanish in $|z| < 1$, it was recently formulated by Shah and Liman \cite[\textit{Integral estimates for the family of $B$-operators, Operators and Matrices,} \textbf{5}(2011), 79 - 87]{wl} that for every $R\geq 1$, $p\geq 1$, $$\left\|B[P\circ\sigma](z)\right\|_p \leq\frac{R^{n}|\Lambda_n|+|\lambda_{0}|}{\left\|1+z\right\|_p}\left\|P(z)\right\|_p,$$ where $B$ is a $\mathcal{B}_{n}$-operator with parameters $\lambda_{0}, \lambda_{1}, \lambda_{2}$ in the sense of Rahman \cite{qir}, $\sigma(z)=Rz$ and $\Lambda_n=\lambda_{0}+\lambda_{1}\frac{n^{2}}{2} +\lambda_{2}\frac{n^{3}(n-1)}{8}$. Unfortunately the proof of this result is not correct. In this paper, we present a more general sharp $L_p$-inequalities for $\mathcal{B}_{n}$-operators which not only provide a correct proof of the above inequality as a special case but also extend them for $0 \leq p <1$ as well.Comment: 16 Page

Immune boosting and anti-influenza effects of an Unani decoction in influenza like illness and COVID-19 like epidemics: a rationale approach

The Unani system of medicine is one of the traditional systems of medicine practised since centuries in many parts of the world including India. At a time when the coronavirus disease 2019 (COVID-19) pandemic is still raging across the globe and there is still no appreciable satisfactory management available with vaccination being the only panacea in the near future, unani medicine chiefly composed of herbal drugs is replete with many classical references for the management of influenza like illness and COVID-19 like epidemics. In Unani medicine, nazla-i-wabāi is referred as influenza for which a decoction containing Behidana (Cydonia oblonga), Unnab (Ziziphus jujuba) and Sapistan (Cordia myxa) are recommended to relieve the clinical features of nazla-i-wabāi and other COVID-19 like epidemics. All the three ingredients of this formulation are also individually used for the treatment of sore throat, cough, septicaemia, fever, dyspnoea, pharyngitis, chest pain etc. Certain scientific studies have validated various pharmacological actions of these drugs as claimed by unani physicians. A concerted rational approach has been attempted to highlight the effect of the unani decoction as to its immune boosting property both as prophylactic and therapeutic use in the treatment of influenza like illness and COVID-19 like epidemics in the light of ancient Unani classics and recent scientific studies

Systematic investigation of quadrupole properties in deformed and transitional nuclei

In the present work, we address a long-standing problem in nuclear physics on how to decipher the nature of collective motion from electromagnetic transition probabilities. A systematic analysis of the $B(E2)$ transitions is performed for thirty nuclei using the triaxial projected shell model (TPSM) approach. It is shown that $I \rightarrow (I-2)$ transitions for the $\gamma$-bands depict a staggering phase and this phase reverses with the inclusion of the quasiparticle excitations for all the nuclei, except for the six nuclei of $^{76}$Ge, $^{112}$Ru, $^{170}$Er, $^{182}$Os, $^{192}$Pt and $^{232}$Th. This feature is analogous to the energy staggering phase obtained for these nuclei. It is noted that the energy staggering phase with even-spin-down (odd-spin-down), which is considered as a signature of $\gamma$-softness ($\gamma$-rigidity), corresponds to even-spin-up (odd-spin-up) staggering phase of the $B(E2)$ transitions. Further, TPSM predicted values for both energies and transition are shown to be in good agreement with the corresponding experimental values.Comment: 24 pages, 28 figure

Triaxial projected shell model approach for negative parity states in even-even nuclei

The triaxial projected shell model (TPSM) approach is generalized to investigate the negative parity band structures in even-even systems. In the earlier version of the TPSM approach, the quasiparticle excitations were restricted to one major oscillator shell and it was possible to study only positive parity states in even-even systems. In the present extension, the excited quasiparticles are allowed to occupy two major oscillator shells, which makes it possible to generate the negative parity states. As a major application of this development, the extended approach is applied to elucidate the negative parity high-spin band structures in $^{102-112}$Ru and it is shown that energies obtained with neutron excitation are slightly lower than the energies calculated with proton excitation. However, the calculated aligned angular momentum ($i_x$) clearly separates the two spectra with neutron $i_x$ in reasonable agreement with the empirically evaluated $i_x$ from the experimental data, whereas proton $i_x$ shows large deviations. Furthermore, we have also deduced the transition quadrupole moments from the TPSM wavefunctions along the negative-parity yrast- and yrare- bands and it is shown that these quantities exhibit rapid changes in the bandcrossing region.Comment: 14 pages, 17 figure

Complementing chronic frailty assessment at hospital admission with an electronic frailty index (FI-Laboratory) comprising routine blood test results

BACKGROUND: Acutely ill and frail older adults have complex social and health care needs. It is important to understand how this complexity affects acute outcomes for admission to hospital. We validated a frailty index using routine admission laboratory tests with outcomes after patients were admitted to hospital. METHODS: In a prospective cohort of older adults admitted to a large tertiary hospital in the United Kingdom, we created a frailty index from routine admission laboratory investigations (FI-Laboratory) linked to data comprising hospital outcomes. We evaluated the association between the FI-Laboratory and total days spent in hospital, discharge to a higher level of care, readmission and mortality. RESULTS: Of 2552 admissions among 1750 older adults, we were able to generate FI-Laboratory values for 2254 admissions (88.3% of the cohort). More than half of admitted patients were women (55.3%) and the mean age was 84.6 (SD 14.0) years. We found that the FI-Laboratory correlated weakly with the Clinical Frailty Scale (CFS; r2 = 0.09). An increase in the CFS and the equivalent of 3 additional abnormal laboratory test results in the FI-Laboratory, respectively, were associated with an increased proportion of inpatient days (rate ratios [RRs] 1.43, 95% confidence interval [CI] 1.35-1.52; and 1.47, 95% CI 1.41-1.54), discharge to a higher level of care (odd ratios [ORs] 1.39, 95% CI 1.27-1.52; and 1.30, 95% CI 1.16-1.47) and increased readmission rate (hazard ratios [HRs] 1.26, 95% CI 1.17-1.37; and 1.18, 95% CI 1.11-1.26). Increases in the CFS and FI-Laboratory were associated with increased mortality HRs of 1.39 (95% CI 1.28-1.51) and 1.45 (95% CI 1.37-1.54), respectively. INTERPRETATION: We determined that FI-Laboratory, distinct from baseline frailty, could be used to predict risk of many adverse outcomes. The score is therefore a useful way to quantify the degree of acute illness in frail older adults

Converting simulated total dry matter to fresh marketable yield for field vegetables at a range of nitrogen supply levels

Simultaneous analysis of economic and environmental performance of horticultural crop production requires qualified assumptions on the effect of management options, and particularly of nitrogen (N) fertilisation, on the net returns of the farm. Dynamic soil-plant-environment simulation models for agro-ecosystems are frequently applied to predict crop yield, generally as dry matter per area, and the environmental impact of production. Economic analysis requires conversion of yields to fresh marketable weight, which is not easy to calculate for vegetables, since different species have different properties and special market requirements. Furthermore, the marketable part of many vegetables is dependent on N availability during growth, which may lead to complete crop failure under sub-optimal N supply in tightly calculated N fertiliser regimes or low-input systems. In this paper we present two methods for converting simulated total dry matter to marketable fresh matter yield for various vegetables and European growth conditions, taking into consideration the effect of N supply: (i) a regression based function for vegetables sold as bulk or bunching ware and (ii) a population approach for piecewise sold row crops. For both methods, to be used in the context of a dynamic simulation model, parameter values were compiled from a literature survey. Implemented in such a model, both algorithms were tested against experimental field data, yielding an Index of Agreement of 0.80 for the regression strategy and 0.90 for the population strategy. Furthermore, the population strategy was capable of reflecting rather well the effect of crop spacing on yield and the effect of N supply on product grading