Deformation of Leibniz Algebra Morphisms Over Commutative Local Algebra Base

We study deformations of Leibniz algebra morphisms over a commutative local algebra base with 1. We construct the associated deformation cohomology that controls deformations using the cochain complex defining the Leibniz cohomology.     

Optimised polychromatic field-mediated suppression of H-atom tunnelling in a coupled symmetric double well: two-dimensional malonaldehyde model

The cis–cis isomerisation motion of malonaldehyde can be modelled as a symmetric double well coupled with an asymmetric double well, which includes the effect of the cis–trans out-of-plane motion on the cis–cis motion. We have presented an effective method for having control over the tunnelling dynamics of the symmetric double well which is coupled with the asymmetric double well by monitoring tunnelling splitting. When a suitable external field is allowed to interact with the system, the tunnelling splitting gets modified. As the external time perturbation is periodic in nature, the Floquet theory can be applied to calculate the quasi-energies of the perturbed system and hence the tunnelling splitting. The Floquet analysis is coupled with a stochastic optimiser in order to minimise the tunnelling splitting, which is related to slowering of the tunnelling process. The minimisation has been done by one of the stochastic optimisers, simulated annealing. Optimisation has been performed on the parameters which define the external polychromatic field, such as intensities and frequencies of the components of the polychromatic field. With the optimised sets of parameters, we have followed the dynamics of the system and have found suppression of tunnelling which is manifested by a much higher tunnelling time.     

Birefringence and Order Parameter of Some Alkyl and Alkoxycyanobiphenyl Liquid Crystals

The refractive indices and densities of six liquid crystals—two alkylcyanobiphenyls, three alkoxycyanobiphenyls and one mixture of two alkylcyanobiphenyls have been reported as a function of temperature. The effective polarizabilities α_eand α_o in the nematic phase calculated using the methods due to Neugebauer, Vuks and Saupe and Maier, are found to be appreciably different, though the order parameter S evaluated with those values of (α_e - α_o) are in good agreement. The preference of one method over the other two is discussed.     

Solutions of Strominger System from Unitary Representations of Cocompact Lattices of {{\rm SL}(2, \mathbb{C})}

Given an irreducible unitary representation of a cocompact lattice of ${{\rm SL}(2, \mathbb{C})}$ SL ( 2 , C ) , we explicitly write down a solution of the Strominger system of equations. These solutions satisfy the equation of motion, and the underlying holomorphic vector bundles are stable.     

Ultrasonic emulsification of food-grade nanoemulsion formulation and evaluation of its bactericidal activity

Basil oil (Ocimum basilicum) nanoemulsion was formulated using non-ionic surfactant Tween80 and water by ultrasonic emulsification method. Process of nanoemulsion development was optimized for parameters such as surfactant concentration and emulsification time to achieve minimum droplet diameter with high physical stability. Surfactant concentration was found to have a negative correlation with droplet diameter, whereas emulsification time had a positive correlation with droplet diameter and also with intrinsic stability of the emulsion. Stable basil oil nanoemulsion with droplet diameter 29.3 nm was formulated by ultrasonic emulsification for 15 min. Formulated nanoemulsion was evaluated for antibacterial activity against Escherichia coli by kinetics of killing experiment. Fluorescence microscopy and FT-IR results showed that nanoemulsion treatment resulted alteration in permeability and surface features of bacterial cell membrane.     

Co-existence of competing prey with a shared predator

This paper deals with a complex prey?–?predator system, consisting of two competing prey species and one predator. We derive conditions for persistence. In the presence of a delay, we estimate the length of delay to maintain persistence of the system.     

First principle studies on structural,electronic, elastic,optical, and thermoelectric properties of XGeCl3 (X = Rb/Cs): Promising compounds for green energy application

This study employed density functional theory (DFT) embedded in Wien2K code to evaluate the physical features of the XGeCl₃ (X = Rb/Cs) cubic halide perovskites. The structural optimization has been performed considering generalized gradient approximation (GGA) and electronic properties have been computed considering modified Becke-Johnson potential (mBJ). The formation energy and phonon dispersion analysis establish the stability of the investigated compounds. Mechanical stability is further confirmed by the computed diverse elastic coefficients. It has been discovered that the examined substances are naturally ductile. The refractive index, reflectivity, and absorption coefficient, are among the optical parameters that have been estimated and analyzed. Interesting results have been obtained for the transport properties of XGeCl₃ (X = Rb/Cs). The XGeCl₃ (X = Rb/Cs) exhibits a high Seebeck coefficient (X = Rb/Cs) and the largest figure of merit (about 0.99), indicating significant potential for thermoelectric applications.     

Ontological Models,Preparation Contextuality and Nonlocality

The ontological model framework for an operational theory has generated much interest in recent years. The debate concerning reality of quantum states has been made more precise in this framework. With the introduction of generalized notion of contextuality in this framework, it has been shown that completely mixed state of a qubit is preparation contextual. Interestingly, this new idea of preparation contextuality has been used to demonstrate nonlocality of some \(\psi \) -epistemic models without any use of Bell’s inequality. In particular, nonlocality of a non maximally \(\psi \) -epistemic model has been demonstrated from preparation contextuality of a maximally mixed qubit and Schrödinger’s steerability of the maximally entangled state of two qubits (Leifer and Maroney, Phys Rev Lett 110:120401, 2013). In this paper, we, show that any mixed state is preparation contextual. We, then, show that nonlocality of any bipartite pure entangled state, with Schmidt rank two, follows from preparation contextuality and steerability provided we impose certain condition on the epistemicity of the underlying ontological model. More interestingly, if the pure entangled state is of Schmidt rank greater than two, its nonlocality follows without any further condition on the epistemicity. Thus our result establishes a stronger connection between nonlocality and preparation contextuality by revealing nonlocality of any bipartite pure entangled states without any use of Bell-type inequality.     

Meson screening masses from lattice QCD with two light quarks and one strange quark

We present results for screening masses of mesons built from light and strange quarks in the temperature range of approximately between 140 MeV to 800 MeV. The lattice computations were performed with 2+1 dynamical light and strange flavors of improved (p4) staggered fermions along a line of constant physics defined by a pion mass of about 220 MeV and a kaon mass of 500 MeV. The lattices had temporal extents N _τ =4, 6 and 8 and aspect ratios of N _s /N _τ ≥4. At least up to a temperature of 140 MeV the pseudo-scalar screening mass remains almost equal to the corresponding zero temperature pseudo-scalar (pole) mass. At temperatures around 3T _c (T _c being the transition temperature) the continuum extrapolated pseudo-scalar screening mass approaches very close to the free continuum result of 2πT from below. On the other hand, at high temperatures the vector screening mass turns out to be larger than the free continuum value of 2πT. The pseudo-scalar and the vector screening masses do not become degenerate even for a temperature as high as 4T _c . Using these mesonic spatial correlation functions we have also investigated the restoration of chiral symmetry and the effective restoration of the axial symmetry. We have found that the vector and the axial-vector screening correlators become degenerate, indicating chiral symmetry restoration, at a temperature which is consistent with the QCD transition temperature obtained in previous studies. On the other hand, the pseudo-scalar and the scalar screening correlators become degenerate only at temperatures larger than 1.3T _c , indicating that the effective restoration of the axial symmetry takes place at a temperature larger than the QCD transition temperature.