Anomalous Scaling of Surface Growth Equations with Spatially and Temporally Correlated Noise

Based on the scaling idea of local slopes by Lopez et al. [Phys. Rev. Lett. 94 （2005） 166103], we investigate anomalous dynamic scaling of （d ＋ 1）-dimensional surface growth equations with spatially and temporally correlated noise. The growth equations studied include the Kardar-Parisi-Zhang （KPZ）, Sun-Guo-Grant （SGG）, and Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the weak- and strong-coupling regions are obtained, respectively.

A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

GLOBAL STABILITY FOR MICHAELIS-MENTEN SINGLE-SPECIES GROWTH EQUATIONS

Consider the so-called Michaelis-Menten single-species growth equation with.ai,ti∈(0,+∞),ci∈(0,1),r(t)∈C([0,∞),(0,+∞)),ai(1+ci)-1=1and n is a positive integer. We establish a new sufficient condition for the global stability of the positive equilibrium N*=1. This condition generalizes and improves some known results and is different from a recent result of Yu J.S..

A Logistic-growth-equation-based Intensity Prediction Scheme for Western North Pacific Tropical Cyclones

Accurate prediction of tropical cyclone(TC)intensity remains a challenge due to the complex physical processes involved in TC intensity changes.A seven-day TC intensity prediction scheme based on the logistic growth equation(LGE)for the western North Pacific(WNP)has been developed using the observed and reanalysis data.In the LGE,TC intensity change is determined by a growth term and a decay term.These two terms are comprised of four free parameters which include a time-dependent growth rate,a maximum potential intensity(MPI),and two constants.Using 33 years of training samples,optimal predictors are selected first,and then the two constants are determined based on the least square method,forcing the regressed growth rate from the optimal predictors to be as close to the observed as possible.The estimation of the growth rate is further refined based on a step-wise regression(SWR)method and a machine learning(ML)method for the period 1982−2014.Using the LGE-based scheme,a total of 80 TCs during 2015−17 are used to make independent forecasts.Results show that the root mean square errors of the LGE-based scheme are much smaller than those of the official intensity forecasts from the China Meteorological Administration(CMA),especially for TCs in the coastal regions of East Asia.Moreover,the scheme based on ML demonstrates better forecast skill than that based on SWR.The new prediction scheme offers strong potential for both improving the forecasts for rapid intensification and weakening of TCs as well as for extending the 5-day forecasts currently issued by the CMA to 7-day forecasts.

Study on visualization simulation soybean leaf based on growth equation

According to the virtual crops model research＇s need, the paper emphasized on the modeling theory and dynamic modeling methods, and took the soybean leaf as the example, introduced the establishment of leaf growth model based on growth equation, finally realized the visualization result based on OpenGL in VC＋＋ platform. The paper has great significance on establishing the whole growth model and researching the crops growth principles.

Growth Characteristics and Resource Evaluation of Sebastes schlegelii in Zhangzidao Artificial Reef Area

[Objective]The paper was to formulate catchable size and total allowable catch of Sebastes schlegelii in Zhangzidao artificial reef area.[Method]Based on analysis of length-weight formula,body length and weight growth equations,and instantaneous mortality rate,the inflection age and critical age of weight growth were calculated,and the biomass of S.schlegelii in Zhangzidao artificial reef area was estimated.[Result]The growth equation of body length was Lt=412.5×[1-e^-0.21（t＋0.65）]and the growth equation of body weight was Wt=1 734.2×[1-e^-0.21（t＋0.65）]^2.92.The inflection age and critical age for weight growth of S.schlegelii were 4.45 and 4.82 a,respectively.The biomass in Zhangzidao artificial reef area was about 456.8 t.[Conclusion]For S.schlegelii flock in Zhangzidao artificial reef area,the catchable length was about 271.2-281.7 mm,the catchable weight as about 509.4-569.5 g,and the total allowable catch was about 60.43 t.

Evidence for the anomalous scaling behaviour of the molecular-beam epitaxy growth equation

According to the scaling idea of local slope, we investigate numerically and analytically anomalous dynamic scaling behaviour of （1＋ 1）-dimensional growth equation for molecular-beam epitaxy. The growth model includes the linear molecular-beam epitaxy （LMBE） and the nonlinear Lai-Das Sarma-Villain （LDV） equations. The anomalous scaling exponents in both the LMBE and the LDV equations are obtained, respectively. Numerical results are consistent with the corresponding analytical predictions.

Invariance of specific mass increment in the case of non-equilibrium growth

The invariance of specific mass increments of crystalline structures that co-exist in the case of non-equilibrium growth is grounded for the first time by using the maximum entropy production principle. Based on the hypothesis of the existence of a universal growth equation, and through the dimensional analysis, an explicit form of the time-dependent specific mass increment is proposed. The applicability of the obtained results for describing growth in animate nature is discussed.

Relationship between age and prostate size

In a community-based study, the relationship between age and human prostate size was investigated in a population of men between the ages of 40 and 70 years to determine the normal prostate increase curve equation. One thousand male volunteers were randomly recruited from the Shanghai community, and the length, width, height, volume of the transition zone （TZ） and the whole prostates were measured by transrectal ultrasound （TRUS）. Each volunteer was evaluated bythe International Prostate Symptom Score （IPSS）. Among those who completed the examination, the mean prostate parameters were all positively associated with increased age. There were statistically significant differences between each age group （P〈O.05）. The mean transition zone volume （TZV） had a higher increase rate with age than the mean total prostate volume （TPV）, indicating that the enlargement of the TZ contributed the most to the increase in TPV. While all prostate parameters were positively correlated with the IPSS, the strongest correlation was associated with the TZ length （TZL） and TZV. The growth curve equations for prostate width, height and length were also positively associated with increasing

Estimating the Age of Oil-tea Camellia Trees

To determine the age of oil-tea camellia trees, regression equations including Logistic, Mitscherlich, Gompertz, Korf, and Richards were used to calculate accumulative growth rate using basal trunk disc and investigate the relations between the age of oil-tea camellia trees and their growth rate of secondary trunk. The Gompertz equation Y=71.296 1exp （-3.874 4exp （-0.006 4t）） was the most optimal equation to simulate the accumulative growth rate of basal trunk disc. This equation could be used to estimate the age of oil-tea camellia trees that grow under similar environmental conditions. The Korf equation Y=576.900 1exp （-4.153 0x -0.314 2 ） was the best equation to describe the relation between the age and growth rate of different secondary trunks. With the adjustment coefficient and average growth of different secondary trunk discs, it is possible to predict the age of ancient oil-tea camellia trees that grow under similar environmental conditions. In addition, taking three or more discs from the same diameter group and calculating their average growth rate could lead to more accurate results. For trees that grow in different areas, environmental conditions should be carefully considered when using the above two equations to predict the age of ancient oil-tea camellia trees.

The Existence of a Weak Solution of Inhomogeneous Quasilinear Elliptic Equation with Critical Growth Conditions

In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|m-1eb|u|γat +∞, with γ=N/N-1, m≥1, b】0.

SOLVABILITY OF A THREE-POINT BOUNDARY VALUE PROBLEM WITH NONLINEAR GROWTH

In this paper, we study the existence of solutions to a three-point boundary value problem with nonlinear growth. Sufficient conditions for the existence of solutions to the system in the resonance and non-resonance cases are established by employing Leray-Schauder continuation theorem and the coincidence degree theory.