Harmonic Mean Cordial labeling of some graphs

All the graphs considered in this article are simple and undirected. Let G = (V(G), E(G)) be a simple undirected Graph. A function f : V (G) → {1, 2} is called Harmonic Mean Cordial if the induced function f*: E(G) → {1, 2} defined by f* (uv) = [2f(u)f(v)/f(u)+f(v)] satisfies the condition |vf (i) − vf (j)| ≤ 1 and |ef (i) − ef (j)| ≤ 1 for any i, j ∈ {1, 2}, where vf (x) and ef (x) denotes the number of vertices and number of edges with label x respectively and bxc denotes the greatest integer less than or equals to x. A Graph G is called Harmonic Mean Cordial graph if it admits Harmonic Mean Cordial labeling. In this article, we have provided some graphs which are not Harmonic Mean Cordial and also we have provided some graphs which are Harmonic Mean Cordial.Publisher's Versio

Derivation and Improvements of the Quantum Canonical Ensemble from a Regularized Microcanonical Ensemble

We develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by giving an explanation for the, at the first sight unreasonable, effectiveness of the canonical ensemble when applied to certain small, isolated, systems. This method also allows a direct identification between the parameters of the microcanonical and the canonical ensemble and it yields simple indicators and rigorous bounds for the effectiveness of the approximation. Finally, we derive an asymptotic expansion of the microcanonical corrections to the canonical ensemble for those systems, which are near, but not quite, at the thermodynamical limit and show how and why the canonical ensemble can be applied also for systems with exponentially increasing density of states. The aim throughout the paper is to keep mathematical rigour intact while attempting to produce results both physically and practically interesting.Comment: 17 pages, latex2e with iopar

Spin-orbit coupled Bose-Einstein condensate in a tilted optical lattice

Bloch oscillations appear for a particle in a weakly tilted periodic potential. The intrinsic spin Hall effect is an outcome of a spin-orbit coupling. We demonstrate that both these phenomena can be realized simultaneously in a gas of weakly interacting ultracold atoms exposed to a tilted optical lattice and to a set of spatially dependent light fields inducing an effective spin-orbit coupling. It is found that both the spin Hall as well as the Bloch oscillation effects may coexist, showing, however, a strong correlation between the two. These correlations are manifested as a transverse spin current oscillating in-phase with the Bloch oscillations.Comment: 12 pages, 7 figure

Higher-order mesoscopic fluctuations in quantum wires: Conductance and current cumulants

We study conductance cumulants $>$ and current cumulants $C_j$ related to heat and electrical transport in coherent mesoscopic quantum wires near the diffusive regime. We consider the asymptotic behavior in the limit where the number of channels and the length of the wire in the units of the mean free path are large but the bare conductance is fixed. A recursion equation unifying the descriptions of the standard and Bogoliubov--de Gennes (BdG) symmetry classes is presented. We give values and come up with a novel scaling form for the higher-order conductance cumulants. In the BdG wires, in the presence of time-reversal symmetry, for the cumulants higher than the second it is found that there may be only contributions which depend nonanalytically on the wire length. This indicates that diagrammatic or semiclassical pictures do not adequately describe higher-order spectral correlations. Moreover, we obtain the weak-localization corrections to $C_j$ with $j\le 10$.Comment: 7 page

Self-assembly, nematic phase formation and organocatalytic behaviour of a proline-functionalized lipopeptide

The self-assembly of the amphiphilic lipopeptide PAEPKI-C16 (P = proline, A = alanine, E = glutamic acid, K = lysine, I = isoleucine, C16 = hexadecyl) was investigated using a combination of spectroscopic, microscopic and scattering methods and compared to C16-IKPEAP with the same (reversed) peptide sequence and the alkyl chain positioned N-terminally and which lacks a free N-terminal proline residue. The catalytic activity of these peptides were then compared using a model aldol reaction system. For PAEPKI-C16, Cryo-TEM images showed the formation of micrometer length fibers, which by Small-angle X-ray scattering (SAXS) were found to have a radius of 2.5 - 2.6 nm. Spectroscopic analysis shows these fibers are built from -sheets. This behaviour is in complete contrast to that of C16-IKPEAP which forms spherical micelles with peptides in a disordered conformation [Hutchinson, J. A. et al. J. Phys. Chem. B 2019, 123, 613]. For PAEPKI-C16, the spontaneous alignment of fibers was observed upon increasing pH, which was accompanied by observed birefringence and anisotropy of SAXS patterns. This shows the formation of a nematic liquids and unprecedented nematic hydrogel formation was also observed these lipopeptides at sufficiently high concentrations. SAXS shows retention of an ultrafine (1.7 nm core radius) fibrillar network within the hydrogel. PAEPKI-C16 with free N-terminal proline shows enhanced anti:syn diastereoselectivity and better conversion compared to C16-IKPEAP. The cytotoxicity of PAEPKI-C16 was also lower than C16-IKPEAP for both fibroblast and cancer cell lines. These results highlight the sensitivity of lipopeptide properties to the presence of a free proline residue. The spontaneous nematic phase formation by PAEPKI-C16 points to the highly anisotropy of its ultrafine fibrillar structure and the formation of such a phase at low concentration in aqueous solution may be valuable for future applications

Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory

We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as a common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasiconservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On superkinetic time scales, density quasiconservation is lost while energy remains conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. However, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.Peer reviewe

A Fuzzy Criticality Assessment System of Process Equipment for Optimized Maintenance Management.

yesIn modern chemical plants, it is essential to establish an effective maintenance strategy which will deliver financially driven results at optimised conditions, that is, minimum cost and time, by means of a criticality review of equipment in maintenance. In this article, a fuzzy logic-based criticality assessment system (FCAS) for the management of a local company’s equipment maintenance is introduced. This fuzzy system is shown to improve the conventional crisp criticality assessment system (CCAS). Results from case studies show that not only can the fuzzy logic-based system do what the conventional crisp system does but also it can output more criticality classifications with an improved reliability and a greater number of different ratings that account for fuzziness and individual voice of the decision-makers

Study of effects of oligohydramnios on perinatal outcome

Background: Oligohydramnios has got a noteworthy influence on perinatal outcome. Hence, early detection and its timely management will aid in curtailing of perinatal morbidity and mortality and leading to decreased operative interventions. Therefore, the present study is conducted to look for the effects of oligohydramnios.Methods: This comparative study was a prospective observational study conducted at study institution. The women were divided into study and control groups based on AFI (amniotic fluid index), 100 cases were selected in each group.Results: Out of the 200 women, included in the present study, 35% of the patients in the study group had non-reactive non-stress test (NST) while in the control group 7% had it. Caesarean section was performed in 58% of cases in the study group as compared to 30% in the control group. Amongst these, Fetal distress was the most common indication for LSCS (lower segment caesarean section). There were no perinatal deaths in this study.Conclusions: Based on this study it has been observed that, amniotic fluid index of ≤5 cm was commonly associated with increased LSCS rates, intrauterine growth restriction, non-reactive NST, and abnormal Doppler velocimetry studies. Therefore, every case of oligohydramnios requires to be assessed meticulously. Prompt detection; timely management and treating the underlying condition improve outcome

Impact of the introduction of a specialist critical care pharmacist on the level of pharmaceutical care provided to the critical care unit

Objectives To evaluate the impact of a dedicated specialist critical care pharmacist service on patient care at a UK critical care unit (CCU). Methods Pharmacist intervention data was collected in two phases. Phase 1 was with the provision of a non-specialist pharmacist chart review service and Phase 2 was after the introduction of a specialist dedicated pharmacy service. Two CCUs with established critical care pharmacist services were used as controls. The impact of pharmacist interventions on optimising drug therapy or preventing harm from medication errors was rated on a 4-point scale. Key findings There was an increase in the mean daily rate of pharmacist interventions after the introduction of the specialist critical care pharmacist (5.45 versus 2.69 per day, P < 0.0005). The critical care pharmacist intervened on more medication errors preventing potential harm and optimised more medications. There was no significant change to intervention rates at the control sites. Across all study sites the majority of pharmacist interventions were graded to have at least moderate impact on patient care. Conclusion The introduction of a specialist critical care pharmacist resulted in an increased rate of pharmacist interventions compared to a non-specialist pharmacist service thus improving the quality of patient care

A study of gestational diabetes mellitus and fetal outcome in a tertiary care center

Background: Modern desk-bound lifestyle and unhealthy dietary changes have brought a rise in the prevalence of obesity and gestational diabetes mellitus (GDM). It is associated with severe hazards to the mother and the baby. It is mandatory that early diagnosis ensues and timely and congruous management is undertaken.Methods: In this observational study, 1250 women were included. A standardized questionnaire was formed and their details were noted. Tests for glucose levels, complete blood picture, urine examination were performed. An oral glucose tolerance test was performed on all the patients. Neonatal outcomes in terms of birth weight and the presence of complications were noted.Results: A total 201 (16.1%) of all women were having gestational diabetes mellitus (GDM). Most mothers were in the 25-30 age group. The majority of the women had a BMI between 26-30. 21.9% of babies were having weight >3.5 kgs. 11.4% of babies were <2.5 kgs. Out of 201 neonates, 90 babies were having complications. Major complications in neonates were macrosomia and respiratory distress. Therefore, early diagnosis, glycemic control, and timely and congruous management are advantageous to both mother and baby.Conclusions: GDM complicating the pregnancy results in a higher prevalence of complications in the mother and the neonate. Therefore, appropriate control of the sugar level in mothers is necessary and it decreases the morbidity and mortality rates in the babies as well as the mothers.