A Theoretical Evaluation of Water Surface Changes in a Circular Reservoir

The purpose of this project is primarily to develop an equation to estimate the time that it will take for the water surface to decrease to another depth in an inverted conical-shaped reservoir behind an earth dam by means of the falling head permeability concept. This equation can be applied to the earth embankment either with or without underdrain. Since the derived equation for time span is a complicated and tedious matter, a computer program has been developed for solving this equation. The computer program is written in BASIC language and executed on a Tektronix 4051 microcomputer. Primary effort has been used to set up the program in a universal BASIC so that it can be easily executed on any microcomputer with the BASIC language. This program also has been tested on an IBM P.C

Diffusive Logistic Equations with Harvesting and Heterogeneity Under Strong Growth Rate

We consider the equation −Δu=au−b(x)u2−ch(x) in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, b(x) and h(x) are nonnegative functions, and there exists Ω0⊂⊂Ω such that {x:b(x)=0}=Ω¯¯¯0. We investigate the existence of positive solutions of this equation for c large under the strong growth rate assumption a≥λ1(Ω0), where λ1(Ω0) is the first eigenvalue of the −Δ in Ω0 with Dirichlet boundary condition. We show that if h≡0 in Ω∖Ω¯¯¯0, then our equation has a unique positive solution for all c large, provided that a is in a right neighborhood of λ1(Ω0). For this purpose, we prove and utilize some new results on the positive solution set of this equation in the weak growth rate case

Positive solutions to logistic type equations with harvesting

AbstractWe use comparison principles, variational arguments and a truncation method to obtain positive solutions to logistic type equations with harvesting both in RN and in a bounded domain Ω⊂RN, with N⩾3, when the carrying capacity of the environment is not constant. By relaxing the growth assumption on the coefficients of the differential equation we derive a new equation which is easily solved. The solution of this new equation is then used to produce a positive solution of our original problem

Global L∞L^\infty-estimate for general quasilinear elliptic equations in arbitrary domains of RN\mathbb{R}^N

In this paper our main goal is to present a new global $L^\infty$-estimate for a general class of quasilinear elliptic equations of the form $$-div \mathcal{A}(x,u,\nabla u)=\mathcal{B}(x,u,\nabla u)$$ under minimal structure conditions on the functions $\mathcal{A}$ and $\mathcal{B}$, and in arbitrary domains of $\mathbb{R}^N$. The main focus and the novelty of the paper is to prove $L^\infty$-estimate of the form $$|u|_{\infty, \Omega}\le C \Phi(|u|_{\beta,\Omega})$$ where $\Phi: \mathbb{R}^+\to \mathbb{R}^+$ is a data independent function with $\lim_{s\to 0^+}\Phi(s)=0$

VEHICLE DETECTION FOR NIGHTTIME USING MONOCULAR IR CAMERA WITH DISCRIMINATELY TRAINED MIXTURE OF DEFORMABLE PART MODELS

Vehicle detection at night time is a challenging problem due to low visibility and light distortion caused by motion and illumination in urban environments. This paper presents a method based on the deformable object model for detecting and classifying vehicles using monocular infra-red camera. In proposed method, features of vehicles are learned as a deformable object model through the combination of a latent support vector machine (LSVM) and histograms of oriented gradients (HOG). The proposed detection algorithm is flexible enough in detecting various types and orientations of vehicles as it can effectively integrate both global and local information of vehicle textures and shapes. Experimental results prove the effectiveness of the algorithm for detecting close and medium range vehicles in urban scenes at night time