Parabolic Region Research Articles

On Starlike and Convex Functions in a Parabolic Region

On Starlike and Convex Functions in a Parabolic Region

In-plane spectrum in superlattices

We show that the existing theory does not give correct in-plane spectrum of superlattices at small in-plane momentum. Magnetoabsorption experiments demonstrate that the energy range of the parabolic region of the spectrum near the electron sub-band bottom is lower by an order of magnitude than the value predicted by the traditional approach. We developed a modified theory according to which the energy range of the parabolic region and carrier in-plane effective masses are determined by the effective band gap of the superlattice rather than by the bulk band gaps of the superlattice layers. The results of this theory are consistent with the experiment.

The exact Taylor formula of the implied volatility

In a model driven by a multidimensional local diffusion, we study the behavior of the implied volatility ${\sigma}$ and its derivatives with respect to log-strike $k$ and maturity $T$ near expiry and at the money. We recover explicit limits of the derivatives ${\partial_{T}^{q}} \partial_{k}^{m} \sigma$ for $(T,x-k)$ approaching the origin within the parabolic region $|x-k|\leq\lambda\sqrt{T}$ , with $x$ denoting the spot log-price of the underlying asset and where $\lambda$ is a positive and arbitrarily large constant. Such limits yield the exact Taylor formula for the implied volatility within the parabola $|x-k|\leq\lambda\sqrt{T}$ . In order to include important models of interest in mathematical finance, e.g. Heston, CEV, SABR, the analysis is carried out under the weak assumption that the infinitesimal generator of the diffusion is only locally elliptic.

Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice

Matter in nontrivial topological phase possesses unique properties, such as support of unidirectional edge modes on its interface. It is the existence of such modes which is responsible for the wonderful properties of a topological insulator – material which is insulating in the bulk but conducting on its surface, along with many of its recently proposed photonic and polaritonic analogues. We show that exciton-polariton fluid in a nontrivial topological phase in kagome lattice, supports nonlinear excitations in the form of solitons built up from wavepackets of topological edge modes – topological edge solitons. Our theoretical and numerical results indicate the appearance of bright, dark and grey solitons dwelling in the vicinity of the boundary of a lattice strip. In a parabolic region of the dispersion the solitons can be described by envelope functions satisfying the nonlinear Schrödinger equation. Upon collision, multiple topological edge solitons emerge undistorted, which proves them to be true solitons as opposed to solitary waves for which such requirement is waived. Importantly, kagome lattice supports topological edge mode with zero group velocity unlike other types of truncated lattices. This gives a finer control over soliton velocity which can take both positive and negative values depending on the choice of forming it topological edge modes.

Experimental investigation on oxidation kinetics of germanium by ozone

Oxidation kinetics of germanium surface by ozone at low temperature (≤400°C) is experimentally investigated. The growth process contains two regions: initial linear growth region and following parabolic growth region. The GeOx thickness vs. oxidation time plot obeys the well-known Deal-Grove or linear parabolic model. The linear growth region contains reaction of oxygen atoms with surface bond and back bonds of outmost Ge layer. And the activation energy is experimentally estimated to be 0.06eV. Such small activation energy indicates that the linear growth region is nearly barrier-less. The parabolic growth region starts when the oxygen atoms diffuse into back bonds of second outmost Ge layers. And the activation energy for this process is found to be 0.54eV. Furthermore, in the ozone oxidation it is not O3 molecules but O radicals that go through the GeOx film.

The Exact Taylor Formula of the Implied Volatility

In a model driven by a multi-dimensional local diffusion, we study the behavior of implied volatility {\sigma} and its derivatives with respect to log-strike k and maturity T near expiry and at the money. We recover explicit limits of these derivatives for (T,k) approaching the origin within the parabolic region |x-k|^2

Some properties of branched continued fractions of special form

The fact that the values of the approximates of the positive definite branched continued fraction of special form are all in a certain circle is established for the certain conditions. The uniform convergence of branched continued fraction of special form, which is a particular case of the mentioned fraction, in the some limited parabolic region is investigated.

Study of the Effect of Linear and Parabolic Density Region in Settling Tanks for Potable Water

AbstractComputational fluid dynamics (CFD) methods are employed to evaluate the influence of temperature variations on the flow field in an actual sedimentation tank for potable-water treatment. A series of experimental measurements of temperature variation has been conducted in that sedimentation tank. The mixed-convection problem caused by the density variations and the horizontal stream is considered at low temperatures (0–10°C) where the variation of water density is strongly nonlinear. Three cases have been examined: (1) one in the ascending, (2) one in the descending parabolic density region, and (3) one in the linear density region. The thermophysical properties of water have been incorporated into the CFD code. All simulations have been conducted for a transient, turbulent flow field. The momentum exchange between the primary and the secondary phase (particles) is considered. The results show that in the parabolic density region, only a few particles are trapped in the bottom, whereas many of them...

ON TRIANGLES ASSOCIATED WITH A CURVE

It is well-known that the area of parabolic region between a parabola and any chord <TEX>$P_1P_2$</TEX> on the parabola is four thirds of the area of triangle <TEX>${\Delta}P_1P_2P$</TEX>. Here we denote by P the point on the parabola where the tangent is parallel to the chord <TEX>$P_1P_2$</TEX>. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles <TEX>${\Delta}P_1P_2PQ$</TEX> where Q is the intersection point of two tangents to X at <TEX>$P_1$</TEX> and <TEX>$P_2$</TEX> we establish some characterization theorems for parabolas.

Numerical Simulation of the Fluid Flow, Heat Transfer, and Solidification in a Twin-Roll Strip Continuous Casting Machine

In this paper, a three-dimensional enthalpy–porosity mixture solidification model is employed to describe the basic rules of heat transfer and solidification in a twin-roll strip continuous casting machine equipped with a multi-port trough-shaped feeding system, and reasons for the formation of these rules are analyzed. The two-layer zonal turbulence model is used to incorporate the turbulence in fluid flow, and the fluid flow in the wedge-shaped pool region in various conditions is studied. The results show that the fluid flow field in the pool region is quite different with/without the consideration of rotating rolls when the solidification is ignored, which indicates the importance of the consideration of rotating rolls in the water modeling equipment design. There are three aspects including molten steel jet impingement, roll rotating, and backward flow of the mushy zone, which strongly influence the temperature distribution in the pool region. The solidification process in the pool region could be divided into three stages: at the first stage, there exists a fast solidification region which obeys the square root law, and an approximately linear growth region could be found at the second stage, while a parabolic growth region could be found at the last stage. The formation of the first stage and the last stage could be mainly due to the geometry of the feeding system and the backward flow of the mushy zone, respectively. The first stage of solidification could be modified by a better designed feeding system, but the backward flow of mushy zone determined by the properties of metals and casting parameters could be one of the biggest obstacles for commercial production of steel sheets by a twin-roll caster.

DISCOVERY OF SUB- TO SUPERLUMINAL MOTIONS IN THE M87 JET: AN IMPLICATION OF ACCELERATION FROM SUB-RELATIVISTIC TO RELATIVISTIC SPEEDS

The velocity field of the M87 jet from milli-arcsecond (mas) to arcsecond scales is extensively investigated together with new radio images taken by EVN observations. We detected proper motions of components located at between 160 mas from the core and the HST-1 complex for the first time. Newly derived velocity fields exhibits a systematic increase from sub-to-superluminal speed in the upstream of HST-1. If we assume that the observed velocities reflect the bulk flow, we here suggest that the M87 jet may be gradually accelerated through a distance of 10^6 times of the Schwarzschild radius of the supermassive black hole. The acceleration zone is co-spatial with the jet parabolic region, which is interpreted as the collimation zone of the jet (Asada & Nakamura 2012). The acceleration and collimation take place simultaneously, which we suggest a characteristic of magnetohydrodynamic flows. Distribution of the velocity field has a peak at HST-1, which is considered as the site of over-collimation, and shows a deceleration downstream of HST-1 where the jet is conical. Our interpretation of the velocity map in the M87 jet gives a hypothesis in AGNs that the acceleration and collimation zone of relativistic jets extends over the whole scale within the sphere of influence of the supermassive black hole.

Engineering parabolic beams with dynamic intensity profiles

We present optical fields formed by superposing nondiffracting parabolic beams with distinct longitudinal wave-vector components, generating light profiles that display intensity fluxes following parabolic paths in the transverse plane. Their propagation dynamics vary depending on the physical mechanism originating interference, where the possibilities include constructive and destructive interference between traveling parabolic beams, interference between stationary parabolic modes, and combinations of these. The dark parabolic region exhibited by parabolic beams permits a straightforward superposition of intensity fluxes, allowing formation of a variety of profiles, which can exhibit circular, elliptic, and other symmetries.

Robust resolution of Kepler’s equation in all eccentricity regimes

In this paper we discuss the resolution of Kepler’s equation in all eccentricity regimes. To avoid rounding off problems we find a suitable starting point for Newton’s method in the hyperbolic case. Then, we analytically prove that Kepler’s equation undergoes a smooth transition around parabolic orbits. This regularity allows us to fix known numerical issues in the near parabolic region and results in a non-singular iterative technique to solve Kepler’s equation for any kind of orbit. We measure the performance and the robustness of this technique by comprehensive numerical tests.

LOW-FIELD MOBILITY MODEL ON PARABOLIC BAND ENERGY OF GRAPHENE NANORIBBON

The carrier mobility in low-field specifically in parabolic energy region of one-dimensional graphene nanoribbon (GNR) band energy is presented in this work. Low-field mobility model describe the carrier transport and its dependency factors when dealing with degenerate and non-degenerate principals. The result shows that the low-field mobility strongly depends on the temperature in the non-degenerate regime in which it sharply decreases with increasing temperature in the range of 10–250 K but the mobility is less affected by the temperature above 250 K. The effect of varying the GNR width to the mobility is also demonstrated in this work. In addition, it is also shown that the mobility depends on the carrier concentration in degenerate domain in which it increases at higher carrier concentrations.

Spectral Multipliers for Laplacians Associated with some Dirichlet Forms

AbstractLet be the self-adjoint operator associated with the Dirichlet formwhere ϕ is a positive C2 function, dλϕ = ϕdλ and λ denotes Lebesgue measure on ℝd. We study the boundedness on Lp(λϕ) of spectral multipliers of . We prove that if ϕ grows or decays at most exponentially at infinity and satisfies a suitable ‘curvature condition’, then functions which are bounded and holomorphic in the intersection of a parabolic region and a sector and satisfy Mihlin-type conditions at infinity are spectral multipliers of Lp(λϕ). The parabolic region depends on ϕ, on p and on the infimum of the essential spectrum of the operator on L2(λϕ). The sector depends on the angle of holomorphy of the semigroup generated by on Lp(λϕ).

Characterization of tensile behavior of a two-dimensional woven carbon/silicon carbide composite fabricated by chemical vapor infiltration

The tensile behavior of a two-dimensional woven carbon/silicon carbide composite has been characterized both by monotonic and loading/unloading tests. The composite shows markedly non-linear behavior with evident hysteresis loops, appreciable residual strains and continuously decreasing moduli. Both the loop width and residual strain have a continuous acceleration with applied stress, implying the composite failure precedes matrix cracking saturation. The shape of hysteresis loops is characterized by an initial parabolic region followed by a linear region. The preexisting matrix microcracks in as-processed specimens and multiple microcracks accompanied by extensive fiber pull-out in the failed specimens were observed, indicating large thermal residual stresses and relatively weak interfacial bonding exist in the present composite, respectively. Then the interfacial sliding stress and residual stress were quantitatively derived from the hysteresis analysis, and further used to predict matrix cracking stress and stress–strain behavior. Excellent agreement between predictions and experimental results was obtained.

Impact of Solvent Quality on the Density Profiles of Looped Triblock Copolymer Brushes by Neutron Reflectivity Measurements

Preferential adsorption of poly(2-vinylpyridine)-deuterated polystyrene-poly(2-vinylpyridine) (PVP-dPS-PVP) triblock copolymers from toluene onto silicon leads to the formation of dPS loops tethered by the PVP end blocks. Using neutron reflectometry, we have determined the segment density profiles of these looped polymer brushes in toluene, a good solvent for the dPS block, and in cyclohexane at 20 C (poor solvent), 32 C, (near- solvent), and 50 C (marginal solvent). While the swelling behavior qualitatively agrees with that observed for singly grafted brushes, there are interesting differences in the local structural details: In a good solvent, the segment density profiles are composed of an inner parabolic region and a long, extended tail. In cyclohexane, the profiles are described by exponential decays. We ascribe these features to a novel polydispersity effect that arises due to tethering the PS loops by both ends. The results also show that the less dense layers undergo more significant changes in swollen height as solvent quality is changed and that the looped brushes of different molecular weight, asymmetry, and tethering density adhere to scaling relationships derived for lightly cross-linked polymer gels.

Neighborhoods of Starlike and Convex Functions Associated with Parabola

Let be a normalized analytic function defined on the unit disk and for . For , a function if lies in the parabolic region . Let be the corresponding class consisting of functions such that lies in the region . For an appropriate , the -neighbourhood of a function is shown to consist of functions in the class .

TRANSPORT PROPERTIES OF DELTA-DOPED FIELD EFFECT TRANSISTOR

The first calculation of mobility and conductivity between source and drain as function of gate voltage in a δ-doped Field Effect Transistor is presented. The calculation was performed with a model for the δ-FET that was shown in (1). The mobility was calculated using a phenomenological expression that was presented in (2). That expression does not have empirical form, neither empirical parameter. For the first time a phenomenological expression of the conductivity is presented, which is derived from the mobility expression. The conductivity shows three different regions: a parabolic region and two linear regions. The parabolic region represents the region at which the conduction channel begins to close. On the other hand, the mobility shows a more different behavior. In the mobility there are four regions. These regions correspond to the disappearance of the different conduction channels that form the subbands of the delta- doped quantum well. The different behavior between mobility and conductivity relies on the depletion of the delta-doped quantum well as the gate potential grows.

Homogenization of Degenerate Two-Phase Flow Equations with Oil Trapping

We consider the one-dimensional degenerate two-phase flow equations as a model for water drive in oil recovery. The effect of oil trapping is observed in strongly heterogeneous materials with large variations in the permeabilities and in the capillary pressure curves. In such materials, a vanishing oil saturation may appear at interior interfaces and inhibit the oil recovery. We introduce a free boundary problem that separates a critical region with locally vanishing permeabilities from a strictly parabolic region and we give a rigorous derivation of the effective conservation law.