ON THE SHARP GROWTH,COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN C^n

In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cn is considered, where z = 0 is a zero of order k ＋ 1 of f（z） - z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the construction of the above mappings on bounded starlike circular domain in Cn is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.

On Growth and Covering Theorem for Almost Spiallike Mapping of Type β with Order α

Let f（x） be an almost spirallike mapping of type β with order B on unit ball B of complex Banach space X. In this paper, we consider the growth and covering theorems for f（x）, we also prove that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.

On Growth and Covering Theorem for Spiallike Mapping of Type β with Order α

In this paper, we consider growth and covering theorem for f（x）, where f（x） is spiallike mapping of type β with order α defined on unit ball B of complex Banach space, and x=0 is zero of order k＋1 for f（x）-x. We also dicate that the estimation is precise when β=0 and still give growth upper bound and distortion upper bound for subordinate mapping. This result include some results known.

On Growth and Covering Theorem for Strongly Spirallike Mapping of Type β with Order α

In this paper, we deduce growth and covering theorem for f（x） by the other means,where f（x） is strongly spirallike mapping of type β with order α defined on Unit Ball B of complex Banach space, and still give growth upper bound and distortion upper bound for subordinate mapping.

On Growth and Covering Theorem for a Kind of Spiral-like Mappings

In this paper, we deduce growth and covering theorem for f（x） by the othermeans where f（x） is strongly spiral-like mapping of type β with order α defined on UnitBall B of complex Banach space and still give growth upper bound and distortionbound for subordinate mapping.

The Growth Theorem for Convex Maps on the Banach Space

In this paper,the growth theorem for convex maps on the Banach space is given, this is: ‖f(x)‖≤‖x‖/(1-‖x‖),x∈B the estimate is best possible for Hilbert space.

The Growth Theorem for Almost Starlike Mappings of Order α on Bounded Starlike Circular Domains

In this paper,we extend the definition of almost starlike mappings of order 1/2 on B n to the almost starlike mappings of order α on the bounded starlike circular domains in C n,and give the growth theorem of it. This type of domain on which we discuss is rather general,in the sense that the domain must be starlike if there exists a normalized biholomorphic starlike mapping on it.

The Growth Theorem for Strongly Starlike Mappings of Order α on Bounded Starlike Circular Domains

The authors obtain the growth and covering theorems for strongly starlike mappings of order α on bounded starlike circular domains.This kind of domain discussed is rather general,since the domain must be starlike if exists a normalized biholomorphic starlike mapping on it.

Semi-Circle Theorem of Unstable Spectrum Distribution of Heterotropic Perturbation and the Upper Bound Estimation of Its Growth Rate

Based on the theoretical analysis on the unstable spectrum distribution of heterotropic perturbation, the semi–circle theorem of such spectrum distribution is obtained — the spectrum distributed within an upper semi–circle domain with radius R0 and taking origin as its circle center in the complex plane, and the upper bound estimation of growth rate is given simultaneously. It is found that the smaller the horizontal scale of perturbation is, the higher the model top located, the greater the estimated value of upper bound of such growth rate is. Also the increase of vertical shear of wind and latitude have the positive contribution to the increase of such growth rate. Finally when stratified stability decreases, the relative maximal growth rate increases, while the maximal growth rate decreases instead.

Growth Theorem and Distortion Theorem for a Sub class of Parab olic Starlike Mappings

In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established.

On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space

A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space is confined to ?n, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge.

Covering Theorems on Two Classes of Quasi-conformal Mappings

In this paper we define two classes of quasiconformal mappings, and study theircovering properties by methods of module. We obtain some new results. In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.

The Covering Theorems for Normalized Holomorphic Mappings on Bounded Starlike Circular Domains in C^n

In this paper, we will investigate convex domains and starlike domains which contain the image set of normalized holomorphic mappings on bounded starlike circular domains in Cn.

EXISTENCE RESULT FOR A CLASS OF N-LAPLACIAN EQUATIONS INVOLVING CRITICAL GROWTH

In this paper, we consider a class of N-Laplacian equations involving critical growth{-?_N u = λ|u|^(N-2) u + f(x, u), x ∈ ?,u ∈ W_0^(1,N)(?), u(x) ≥ 0, x ∈ ?,where ? is a bounded domain with smooth boundary in R^N(N > 2), f(x, u) is of critical growth. Based on the Trudinger-Moser inequality and a nonstandard linking theorem introduced by Degiovanni and Lancelotti, we prove the existence of a nontrivial solution for any λ > λ_1, λ = λ_?(? = 2, 3, · · ·), and λ_? is the eigenvalues of the operator(-?_N, W_0^(1,N)(?)),which is defined by the Z_2-cohomological index.

Remote Sensing Data and SLEUTH Urban Growth Model:As Decision Support Tools for Urban Planning

Sri Lanka is experiencing speedy urbanization by converting the agriculture land and other natural land cover into built-up land. The urban population of Sri Lanka is expected to reach to 60% by 2030 from 14% in 2010. The rapid growth in urban population and urban areas in Sri Lanka may cause serious socioeconomic disparities, if they are not handled properly. Thus, planners in Sri Lanka are in need of information about past and future urban growth patterns to plan a better and sustainable urban future for Sri Lanka. In this paper, we analyzed the characteristics of past land use and land cover trends in Matara City of Sri Lanka from 1980 to 2010 to assess the historic urban dynamics. The land use change detection analysis based on remote sensing datasets reveal that the conversion of homestead/garden and paddy into urban land is evident in Matara City. The historic urban trends are projected into the near future by using SLEUTH urban growth model to identify the hot spots of future urbanization and as well as the urban growth patterns in Matara City up to the basic administrative level, i.e., Grama Niladari Divisions(GND). The urban growth simulations for the year 2030 reveal that 29 GNDs out of 66 GNDs in Matara City will be totally converted into urban land. Whereas, 28 GNDs will have urban land cover from 75% to 99% by 2030. The urban growth simulations are further analyzed with respect to the proposed Matara city development plan by the Urban Development Authority(UDA) of Sri Lanka. The results show that the UDA's city development plan of Matara will soon be outpaced by rapid urbanization. Based on the calibration and validation results, the SLEUTH model proved to be a useful planning tool to understand the near future urbanization of Sri Lankan cities.

Gibberellic Acid Promotes Early Growth of Winter Wheat and Rye

Winter wheat (Triticum aestivum) planting in Nebraska is recommended for mid Sep but summer crops are often harvested around Oct 1. Also, weather may delay planting. Could gibberellic acid (GA3), a growth stimulant, overcome the delayed seedling growth from late planting? Irrigated field trials were planted from 2005 to 2010 applying GA3 to wheat seed of cvs. Goodstreak and Wesley. In 2005, dip, spray and furrow GA3 applications to seed were tested. Dip and spray gave similar results. Furrow application was calculated too costly. Further tests used seed dips. In 2006 to 2008 planting, wheat was planted about 15 Sep, 1 Oct and 15 Oct. Trials planted in 2007 and 2008 included winter rye (Secale cereale) cv. Rymin. Heights in mid Nov showed a reduction with later planting. When planted about 1 Oct and 15 Oct, the delayed growth of Goodstreak, compared to planting two weeks earlier, was fully overcome by GA3 at 250 ppm. For Wesley, 1000 ppm GA3 was needed to nearly overcome later planting. Rymin rye gave an intermediate response between the two wheat cultivars. Spring and summer heights were not affected by GA3. Spring biomass, yield and harvested seed germination showed no GA3 effect. In later trials (planted in 2009 and 2010), the cytokinin 6-benzyl adenine (6BA) was added to GA3 to stimulate tiller formation. In the 1st year, 6BA at 2000 ppm depressed height, weight and yield without tiller promotion. Repeating the trial with lower rates (31 - 125 ppm 6BA) did not offer an additional advantage to GA3. The results indicate that seed application of GA3 can overcome delayed growth resulting from delayed planting of winter wheat and rye under irrigation.

α-times Integrated Cosine Operator Functions with Growth ω

For a continuous,increasing functionω:[0,∞)→C of finite exponential type,we establish a Hille-Yosida type theorem for strongly continuous α-times(α>0)integrated cosine operator functions with O(ω).It includes the corresponding results for n-times integrated cosine operator functions that are polynomially bounded and exponentially bounded.

STRONGLY CONTINUOUS INTEGRATED COSINE OPERATOR FUNCTIONS WITH GROWTHω

For a continuous increasing function ω ： [0, ∞） → （0, ∞） of finite exponetial type, we establish a Hille-Yosida type theorem for strongly continuous integrated cosine operator functions with O（ω）. It includes the well-known polynomially bounded and exponentially bounded cases.

On Kirchhoff Problems Involving Critical Exponent and Critical Growth

In this paper, we establish the existence of multiple solutions to a class of Kirchhoff type equations involving critical exponent, concave term and critical growth. Our main tools are the Nehari manifold and mountain pass theorem.

Future Land-Use Land-Cover Scenarios for the Flint River Watershed in Northern Alabama Using the Prescott Spatial Growth Model

A changing mosaic of natural vegetation and human land uses has evolved within and around the Flint River Watershed (FRW) in Alabama and Tennessee over the past several decades. To determine the cause of change and linkage between human activities and environmental change can prove problematic. Subsequently, there is a need to produce projections of future environments based on planning instruments and socio-economic parameters. Scenarios of potential future land use land cover (LULC) change are required in order to better manage potential impacts on many environmental issues. This study creates future scenarios for the year 2030 from baseline land use of 2001, relative to three projected land use scenarios which include differences related to conservation, planning, and development. The future growth scenarios were created using the ArcGIS tool, Prescott Spatial Growth Model (PSGM). The model allows users to build different future growth scenarios based on socio-economic projections such as population, employment and other controlling factors. The simulation results indicate that LULC changes associated with future urbanization can increase by ~23% - 43% within the FRW, which will lead to significant environmental issues if not managed properly. The overall analysis and model results demonstrate the ability of future growth scenarios to explore and evaluate options for a future environment. Spatial modeling and analysis tools, such as PSGM, provide a powerful approach to evaluate potential impacts of LULC change in the future and should be used to manage urbanization in areas with more intense development.