Linear Growth Coefficient Research Articles

General Mean-Field BDSDEs with Continuous and Stochastic Linear Growth Coefficients

General Mean-Field BDSDEs with Continuous and Stochastic Linear Growth Coefficients

Existence Solution for Fractional Mean-Field Backward Stochastic Differential Equation with Stochastic Linear Growth Coefficients

We deal with fractional mean field backwardWe deal with fractional mean field backward stochastic differential equations with hurst parameter $H\in (\frac{1}{2},1)$ when the coefficient $f$ satisfy a stochastic Lipschitz conditions, we prove the existence and uniqueness of solution and provide a comparison theorem. Via an approximation and comparison theorem, we show the existence of a minimal solution when the drift satisfies a stochastic growth condition.

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients

Generalized Backward Doubly Stochastic Differential Equations Driven by Lévy Processes with Discontinuous and Linear Growth Coefficients

Lp -Solutions of backward doubly SDEs with continuous and stochastic linear growth coefficients and p ∈ (1,2)

In this paper, we are interested in solving backward doubly stochastic differential equations in Lp , for any p ∈ ( 1 , 2 ) , when the coefficients are continuous with stochastic linear growth. Via approximation and comparison theorem, the existence of L p − minimal and L p − maximal solutions are obtained.

Generalized Risk-Sensitive Optimal Control and Hamilton–Jacobi–Bellman Equation

In this article, we consider the generalized risk-sensitive optimal control problem, where the objective functional is defined by the controlled backward stochastic differential equation (BSDE) with quadratic growth coefficient. We extend the earlier results of the risk-sensitive optimal control problem to the case of the objective functional given by the controlled BSDE. Note that the risk-neutral stochastic optimal control problem corresponds to the BSDE objective functional with linear growth coefficient, which can be viewed as a special case of the article. We obtain the generalized risk-sensitive dynamic programming principle for the value function via the backward semigroup associated with the BSDE. Then we show that the corresponding value function is a viscosity solution to the Hamilton-Jacobi-Bellman equation. Under an additional parameter condition, the viscosity solution is unique, which implies that the solution characterizes the value function. We apply the theoretical results to the risk-sensitive European option pricing problem.

Holographic complexity of local quench at finite temperature

This paper is devoted to the study of the evolution of holographic complexity after a local perturbation of the system at finite temperature. We calculate the complexity using both the complexity=action(CA) and the complexity=volume(CA) conjectures and find that the CV complexity of the total state shows the unbounded late time linear growth. The CA computation shows linear growth with fast saturation to a constant value. We estimate the CV and CA complexity linear growth coefficients and show, that finite temperature leads to violation of the Lloyd bound for CA complexity. Also it is shown that for composite system after the local quench the state with minimal entanglement may correspond to the maximal complexity.

Theoretical and numerical analysis of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients

In this paper, we consider the theoretical and numerical analysis of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients. The existence, uniqueness and pth moment boundedness of the analytic solutions are investigated. Euler method is shown to be divergent in the strong mean square sense for super linear growth coefficients, so the truncated Euler-Maruyama method is presented and its moment boundedness and Lq-convergence are shown. Moreover, its pth moment boundedness and Lq-convergence (q∈[2,p) and p is a parameter in Khasminskii-type condition) rate are given under Local Lipschitz condition and Khasminskii-type condition. The theoretical results are illustrated by some numerical examples.

A discretized version of Krylov’s estimate and its applications

In this paper we prove a discretized version of Krylov's estimate for discretized It\^o's processes. As applications, we study the weak and strong convergences for Euler's approximation of mean-field SDEs with measurable discontinuous and linear growth coefficients. Moreover, we also show the propagation of chaos for Euler's approximation of mean-field SDEs.

Induced mixing electrokinetics in a charged corrugated nano-channel: towards a controlled ionic transport

To perform a fluid analysis for electroosmotic flows in micro- and nano-channels, it is necessary to mix various fluid contents in micro- and nano-scales. It is observed that fluids in electroosmotic flow exhibits Reynolds number effect as the flow exerts very weak inertial force and it requires long channel for mixing of different layers and species through diffusion process. Hence, if the desired length scale of mixing is large, an enormous time is needed for the molecules to be thoroughly mixed by diffusion. The theory of dynamic equations on time scale is used to study the stability of these systems. It is found that such a system may exhibits an unstable nature for overlapping electric double layer field with fluctuating velocities and stability is preserved for zero linear growth coefficient. To obtain an improved understanding of mixing performance, a numerical study is performed with the variation of channel height when more than one ionic species with channels patterned with heterogeneity is considered. The wall heterogeneity may be created by placing some blocks of unequal size (with or without charged) close to the channel wall or some external potential patches. The analytical results for the transport characteristics of electroosmotic flow obtained are compared with the direct numerical simulation of the Navier–Stokes equation, Nernst–Plank equation, and Poisson equation, simultaneously. It is shown that heterogeneous potential could generate complex flow structures and the increment of species layers at different levels of the channel cross section from inlet to outlet significantly improve the mixing rate.

Backward doubly SDEs with continuous and stochastic linear growth coefficients

Abstract We study backward doubly stochastic differential equations when the coefficients are continuous with stochastic linear growth. Via an approximation and comparison theorem, the existence of minimal and maximal solutions are obtained.

Closed and asymptotic formulas for energy of some circulant graphs

We consider circulant graphs G(r, N) where the vertices are the integers modulo N and the neighbours of 0 are . The energy of G(r, N) is a trigonometric sum of terms. For low values of r we compute this sum explicitly. We also study the asymptotics of the energy of G(r, N) for . There is a known integral formula for the linear growth coefficient, we find a new expression of the form of a finite trigonometric sum with r terms. As an application we show that in the family G(r, N) for there is a finite number of hyperenergetic graphs. On the other hand, for each there is at most a finite number of non-hyperenergetic graphs of the form G(r, N). Finally, we show that the graph minimizes the energy among all the regular graphs of degree 2r.

Electric-Field-Induced Instabilities in Thin Liquid Trilayers Confined between Patterned Electrodes

Electric-field-induced instabilities of trilayer of immiscible thin films confined between both planar and patterned electrodes have been explored by the linear stability analysis (LSA) and the long-wave nonlinear simulations. The twin liquid–liquid interfaces of a trilayer can undergo either in-phase bending or antiphase squeezing or mixed modes of evolution. The linear and nonlinear analyses together uncover the conditions under which these modes evolve and subsequently form an array of interesting, complex patterns. The study confirms that when the middle layer is of the highest or lowest dielectric permittivity than the other layers the interfaces undergo a squeezing mode of deformation. In other cases, the interfaces evolve in the bending mode, except for the situations where the linear growth coefficient versus wavenumber curves in the LSA show a bimodal behavior and the interfaces evolve in a mixed mode. The LSA also highlights the importance of the ratios of the thermodynamic parameters such as th...

Predictors of Morphosyntactic Growth in Typically Developing Toddlers: Contributions of Parent Input and Child Sex

Theories of morphosyntactic development must account for between-child differences in morphosyntactic growth rates. This study extends Legate and Yang's (2007) theoretically motivated cross-linguistic approach to determine if variation in properties of parent input accounts for differences in the growth of tense productivity. Fifteen toddlers (and parents) participated. None were producing tense morphemes productively at 21 months. Two dependent measures of morphosyntactic growth between 21 and 30 months were used: empirical Bayes linear coefficients at 21 months and predicted productivity scores at 30 months. Predictor variables included child sex, vocabulary, and mean length of utterance as well as 4 measures of parent language input at 21 months. Input informativeness for tense was the most consistent predictor of morphosyntactic growth, explaining 28.3% of the unique variance in children's linear growth coefficients at 21 months and 23.0% of the unique variance in predicted tense productivity scores at 30 months. General input measures were unrelated. Child sex explained an additional 24.7% of the variance in early linear growth. Child vocabulary at 21 months did not explain a significant proportion of unique variance. The findings provide evidence that input informativeness, an abstract and distributed property of input, contributes to morphosyntactic growth.

Effect of process conditions on particle growth for spouted bed coating of urea

The aim of this work was to analyze the influences of operational variables on particle growth for urea coating in a conventional spouted bed (CSB). An aqueous polymeric suspension was the coating liquid sprayed on the spouted particles. The effects of inlet air temperature, coating suspension flow rate and atomizing air pressure on particle growth were analyzed by a central composite rotatable design (CCRD) of experiments. The results showed particle growth in the range of 1.1–2.6%, therefore, some results below the expected for a film coating (2–8%). A second-order polynomial model was obtained for estimating particle growth as a function of the statistically significant variables: air temperature, suspension flow rate and atomizing air pressure, with percentage of explained variation R 2 = 90.72%. The urea growth kinetics during coating was analyzed for the optimal operating condition and a linear growth coefficient of 1.13 × 10 −3 min −1 was obtained. The volatilization analyses showed that the polymer film coating provided a decrease of the nitrogen loss in the range of 3–57%. And, SEM analyses demonstrated a total, uniform and homogeneous covering of the urea particles surface.

Erratum to: “Linear growth coefficients in quasilinear equations”

A remark concerning the use of Leray-Schauder theorem in the article “Linear growth coefficients in quasilinear equations” [NoDEA 13 (2007), 605–617, DOI 10.1007/s00030-006-4026-8] 10.1007/s00030-006-4026-8] is considered.

Linear growth coefficients in quasilinear equations

In the paper the author proves properties of existence, uniqueness and regularity for divergence form elliptic equations, extending these results from the linear case to the quasilinear one.

Vortex-merger statistical-mechanics model for the late time self-similar evolution of the Kelvin–Helmholtz instability

The nonlinear growth, of the multimode incompressible Kelvin–Helmholtz shear flow instability at all density ratios is treated by a large-scale statistical-mechanics eddy-pairing model that is based on the behavior of a single eddy and on the two eddy pairing process. From the model, a linear time growth of the mixing zone is obtained and the linear growth coefficient is derived for several density ratios. Furthermore, the asymptotic eddy size distribution and the average eddy life time probability are calculated. Very good agreement with experimental results and full numerical simulations is achieved.

Evolution of dendritic patterns during alloy solidification: onset of the initial instability.

The evolution of a dendritic pattern from a planar solid-liquid interface during directional solidification of a binary alloy was investigated experimentally. The model alloy used was the transparent organic crystal succinonitrile doped with the laser dye coumarin 152. The buildup of solute ahead of the initially stable planar interface and the subsequent instability of the planar front were measured in detail and compared with recent theoretical calculations by Warren and Langer [Warren, J. A. & Langer, J. S. (1993) Phys. Rev. E 47, 2702- 2712]. The fluorescence of coumarin 152 was used for direct observations of the evolution of the solute concentration profile ahead of the initially planar solid-liquid interface. UV absorption was used to produce thermal perturbations of the sample that generated spatially periodic modulations of the planar interface. This technique allows for measurement of both positive and negative linear growth coefficients (determined from the growth or decay rate of the modulation after the perturbation is switched off) for a large range of wave vectors. Measurements of the evolution of the concentration profile and the linear growth coefficients, and the occurrence of the initial instability, were in good agreement with the Warren-Langer predictions.

Reflected solutions of backward stochastic differential equations with continuous coefficient

We prove the existence of a reflected solution of one-dimensional backward stochastic differential equations with continuous and linear growth coefficient and squared integrable terminal condition.