A hypergraph is a generalization of a graph where edges can connect any number of vertices. In this paper, we extend the study of locating-dominating sets to hypergraphs. Along with some basic results, sharp bounds for the location-domination number
of hypergraphs in general and exact values with specified conditions are investigated. Moreover, locating-dominating sets in some specific hypergraphs are found.
Let $G=QD_{8k}~$ be the quasi-dihedral group of order $8n$ and $theta$ be an automorphism of $QD_{8k}$ of finite order. The fixed-point set $H$ of $theta$ is defined as $H_{theta}=G^{theta}={xin G mid theta(x)=x}$ and generalized symmetric space $Q$
of $theta$ given by $Q_{theta}={gin G mid g=xtheta(x)^{-1}~mbox{for some}~xin G}.$ The characteristics of the sets $H$ and $Q$ have been calculated. It is shown that for any $H$ and $Q,~~H.Q eq QD_{8k}.$ the $H$-orbits on $Q$ are obtained under different conditions. Moreover, the formula to find the order of $v$-th root of unity in $mathbb{Z}_{2k}$ for $QD_{8k}$ has been calculated. The criteria to find the number of equivalence classes denoted by $C_{4k}$ of the involution automorphism has also been constructed. Finally, the set of twisted involutions $R=R_{theta}={~xin G~mid~theta(x)=x^{-1}}$ has been explored.
In software modelling, the designers have to produce UML visual models with software constraints. Similarly, in business modelling, designers have to model business processes using business constraints (business rules). Constraints are the key compon
ents in the skeleton of business or software models. A designer has to write constraints to semantically compliment business models or UML models and finally implementing the constraints into business processes or source code. Business constraints/rules can be written using SBVR (Semantics of Business Vocabulary and Rules) while OCL (Object Constraint Language) is the well-known medium for writing software constraints. SBVR and OCL are two significant standards from OMG. Both standards are principally different as SBVR is typically used in business domains and OCL is employed to compliment software models. However, we have identified a few similarities in both standards that are interesting to study. In this paper, we have performed a comparative analysis of both standards as we are looking for a mechanism for automatic transformation of SBVR to OCL. The major emphasis of the study is to highlight principal features of SBVR and OCL such as similarities, differences and key parameters on which these both standards can work together.
A fraction of multiple planet candidate systems discovered from transits by the Kepler mission contain pairs of planet candidates that are in orbital resonance or are spaced slightly too far apart to be in resonance. We focus here on the four planet
system, KOI 730, that has planet periods satisfying the ratios 8:6:4:3. By numerically integrating four planets initially in this resonant configuration in proximity to an initially exterior cold planetesimal disk, we find that of the order of a Mars mass of planet-orbit-crossing planetesimals is sufficient to pull this system out of resonance. Approximately one Earth mass of planet-orbit-crossing planetesimals increases the interplanetary spacings sufficiently to resemble the multiple planet candidate Kepler systems that lie just outside of resonance. This suggests that the closely spaced multiple planet Kepler systems, host only low mass debris disks or their debris disks have been extremely stable. We find that the planetary inclinations increase as a function of the mass in planetesimals that have crossed the orbits of the planets. If systems are left at zero inclination and in resonant chains after depletion of the gas disk then we would expect a correlation between distance to resonance and mutual planetary inclinations. This may make it possible to differentiate between dynamical mechanisms that account for the fraction of multiple planet systems just outside of resonance.
Optical resonant microcavities with ultra high quality factors are widely used for biosensing. Until now, the primary method of detection has been based upon tracking the resonant wavelength shift as a function of biodetection events. One of the sour
ces of noise in all resonant-wavelength shift measurements is the noise due to intensity fluctuations of the laser source. An alternative approach is to track the change in the quality factor of the optical cavity by using phase shift cavity ring down spectroscopy, a technique which is insensitive to the intensity fluctuations of the laser source. Here, using biotinylated microtoroid resonant cavities, we show simultaneous measurement of the quality factor and the wavelength shift by using phase shift cavity ring down spectroscopy. These measurements were performed for disassociation phase of biotin-streptavidin reaction. We found that the disassociation curves are in good agreement with the previously published results. Hence, we demonstrate not only the application of phase shift cavity ring down spectroscopy to microcavities in the liquid phase but also simultaneous measurement of the quality factor and the wavelength shift for the microcavity biosensors in the application of kinetics measurements.
By logging encounters between planetesimals and planets we compute the distribution of encounters in a numerically integrated two planet system that is migrating due to interactions with an exterior planetesimal belt. Capture of an irregular satellit
e in orbit about a planet through an exchange reaction with a binary planetesimal is only likely when the binary planetesimal undergoes a slow and close encounter with the planet. In our simulations we find that close and slow encounters between planetesimals and a planet primarily occur with the outermost and not innermost planet. Taking care to consider where a planet orbit crossing binary planetesimal would first be tidally disrupted, we estimate the probability of both tidal disruption and irregular satellite capture. We estimate that the probability that the secondary of a binary planetesimal is captured and becomes an irregular satellite about a Neptune mass outer planet is about 1/100 for binaries with masses and separations similar to transneptunian planetesimal binaries. If young exoplanetary debris disks host a binary planetesimal population then outwards migrating outer planets should host captured irregular satellite populations. We discuss interpretation of emission associated with the exoplanet Fomalhaut b in terms of collisional evolution of a captured irregular satellite population that is replenished due to planetary migration.
Electron transport through molecular bridge shows novel quantum features. Propogation of electronic wave function through molecular bridge is completely different than individual atomic bridge employed between two contacts. In case of molecular bridg
e electronic wave propagators interfere and effect conduction through molecular bonding and anti-bonding states.In the present work i showed through simple calculation that interference of electronic wave propagators cause asymmetric propagation of electronic wave through bonding and anti-bonding state. While for hydrogenic molecule these propagators interfere completely destructively for bonding state and constructively for anti-bonding state, giving rise to only one peak in spectral function for anti- bonding state.
In this study we explain the role of applied magnetic field in inelastic conduction properties of a Quantum Dot coupled with an oscillator . In the presence of strong applied magnetic field coulomb blockade effects become weak due to induced Zeeman s
plitting in spin degenerate eigen states of Quantum Dot.By contacting Quantum Dot by identical metallic leads tunneling rates of spin down and spin up electrons between Quantum Dot and electrodes will be symmetric. For symmetric tunneling rates of spin down and spin up electrons onto Quantum Dot, first oscillator get excited by spin down electrons and then spin up elctrons could excite it further. Where as average energy transferred to oscillator coupled with Quantum Dot by spin down electrons will further increase by average energy transferred by spin up electrons to oscillator. Here we have also discussed that with increasing Quantum Dot and electrodes coupling strength phononic side band peaks start hiding up, which happens because with increasing tunneling rates electronic states of Quantum Dot start gettting broadened.
In this work, we have investigated conduction through an artificial molecule comprising two coupled quantum dots. The question addressed is the role of inter-dot coupling on electronic transport. We find that the current through the molecule exhibits
step-like features as a function of the voltage between the leads, where the step size increases as the inter-dot coupling is increased. These step-like features disappear with increasing tunneling rate from the leads, but we find that in the presence of coupling, this smooth behavior is not observed rather two kinks are seen in the current voltage curve. This shows that the resolution of the two levels persists if there is finite inter-dot coupling. Furthermore, we also consider the effects of electron-phonon interaction as well as dissipation on conduction in this system. Phononic side bands in the differential conductance survive for finite inter-dot coupling even for strong lead to molecule coupling.
Due to ultra high quality factor ($10^6-10^9$), axisymmetric optical microcavities are popular platforms for biosensing applications. It has been recently demonstrated that a microcavity biosensor can track a biodetection event as a function of its q
uality factor by using phase shift cavity ring down spectroscopy (PS-CRDS). However, to achieve maximum sensitivity, it is necessary to optimize the microcavity parameters for a given sensing application. Here, we introduce an improved finite element model which allows us to determine the optimized geometry for the PS-CRDS sensor. The improved model not only provides fast and accurate determination of quality factors but also determines the tunneling distance of axisymmetric resonators. The improved model is validated numerically, analytically, and experimentally.
