PERSISTENCE AND STABILITY IN ARATIO‐DEPENDENT PREDATOR‐PREY SYSTEM WITH DELAY AND HARVESTING

ABSTRACT. . This paper aims to study the effect of time‐delay and combined harvesting on a Michaelis‐Menten type ratio‐dependent predator‐prey system. Dynamical behaviors such as persistence, stability, bifurcation, et cetera, are studied critically. Computer simulations are carried out to illustrate our analytical findings.     

The effect of nonlinearity in relativistic nucleon–nucleon potential

A simple form for nucleon–nucleon (NN) potential is introduced as an alternative to the popular M3Y form using the relativistic mean field theory (RMFT) with the non-linear terms in σ-meson for the first time. In contrast to the M3Y form, the new interaction becomes exactly zero at a finite distance and the expressions are analogous with the M3Y terms. Further, its applicability is examined by the study of proton and cluster radioactivity by folding it with the RMFT-densities of the cluster and daughter nuclei to obtain the optical potential in the region of proton-rich nuclides just above the double magic core¹⁰⁰Sn. The results obtained were found comparable with the widely used M3Y NN interactions.     

Quantum restoration of broken symmetry in one-dimensional loop space

For one-dimensional loop space, a nonlinear nonlocal transformation of fields is given to make the action of the self-interacting quantum field to the free one. A specific type of classically broken symmetry is restored in quantum theory. One-dimensional sine-Gordon system and sech interactions are treated as the explicit examples.     

A pilgrimage through superheavy valley

We searched for the shell closure proton and neutron numbers in the superheavy region beyond Z = 82 and N = 126 within the framework of non-relativistic Skryme–Hartree–Fock (SHF) with FITZ, SIII, SkMP and SLy4 interactions. We have calculated the average proton pairing gap Δ_p, average neutron pairing gap Δ_n, two-nucleon separation energy S _2q and shell correction energy E _shell for the isotopic chain of Z = 112–126. Based on these observables, Z = 120 with N = 182 is suggested to be the magic numbers in the present approach.     

Subwavelength propagation and localization of light using surface plasmons: A brief perspective

Surface plasmons at the metal–dielectric interface have emerged as an important candidate to propagate and localize light at subwavelength scales. By tailoring the geometry and arrangement of metallic nanoarchitectures, propagating and localized surface plasmons can be obtained. In this brief perspective, we discuss: (1) how surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs) can be optically excited in metallic nanoarchitectures by employing a variety of optical microscopy methods; (2) how SPPs and LSPs in plasmonic nanowires can be utilized for subwavelength polarization optics and single-molecule surface-enhanced Raman scattering (SERS) on a photonic chip; and (3) how individual plasmonic nanowire can be optically manipulated using optical trapping methods.     

B s data at Tevatron and possible new physics

The new physics (NP) is parametrized with four model-independent quantities: the magnitudes and phases of the dispersive part M ₁₂ and the absorptive part ??₁₂ of the NP contribution to the effective Hamiltonian. We constrain these parameters using the four observables ??M _s, ????_s, the mixing phase $\beta_\mathrm{s}^{J/\psi\phi}$ and $A^b_{\rm sl}$ . This formalism is extended to include charge-parity-time reversal (CPT) violation, and it is shown that CPT violation by itself, or even in the presence of CPT-conserving NP without an absorptive part, helps only marginally in the simultaneous resolution of these anomalies.     

SUSY formalism for the symmetric double well potential

Using first- and second-order supersymmetric Darboüx formalism and starting with symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique.