In the present research, the effects of delamination size and location on vibration characteristics of laminated composite beams are investigated both analytically and numerically. In the analytical method, the delaminated beam is modeled as four interconnected Euler–Bernoulli beams and the constrained and free mode models are both simulated. The differential stretching and the bending-extensio...

In this chapter, we present distance mapping, a technique for adding small-scale displacement mapping to objects in a pixel shader. We treat displacement mapping as a ray-tracing problem, beginning with texture coordinates on the base surface and calculating texture coordinates where the viewing ray intersects the displaced surface. For this purpose, we precompute a three-dimensional distance m...

BACKGROUND Stereotactic Body Radiotherapy (SBRT) has excellent control rates for low- and intermediate-risk prostate carcinoma.The role of SBRT for high-risk disease remains less studied. We present long-term results on a cohort of patients with NCCN-defined high-risk disease treated with SBRT. METHODS We retrospectively studied 97 patients treated as part of prospective trial from 2006-2010 ...

OBJECTIVE Obesity has been demonstrated to predict biochemical progression in men undergoing radical prostatectomy for prostate adenocarcinoma, and is associated with a higher risk of biochemical and clinical relapse after radiation therapy (RT). We evaluated if obesity, determined by body mass index (BMI), is associated with adverse disease characteristics, pre-treatment serum testosterone, bi...

In this paper, we propose a numerical method based on the generalized hat functions (GHFs) and improved hat functions (IHFs) to find numerical solutions for stochastic Volterra-Fredholm integral equation. To do so, all known and unknown functions are expanded in terms of basic functions and replaced in the original equation. The operational matrices of both basic functions are calculated and em...

Our goal in this section is to define and develop the six basic trigonometric functions. We start with two of the more important transcendental functions, namely the sine function and the cosine function. These are universally denoted by y = sinx and y = cos x respectively. In order to define sinx and cosx, we first need to agree on how we are going to measure angles. An angle, θ, consists of t...

We use the following convention: x, t, t1, t2, r, a, b are real numbers and F , G are partial functions from R to R. Let F be a partial function from R to R and let t be a real number. We say that t is a period of F if and only if: (Def. 1) t 6= 0 and for every x holds x ∈ domF iff x+t ∈ domF and if x ∈ domF, then F (x) = F (x+ t). Let F be a partial function from R to R. We say that F is perio...

The notion of function is indispensable to our understanding of distinctions such as that between being broken and being in working order (for artifacts) and between being diseased and being healthy (for organisms). A clear account of the ontology of functions and functioning is thus an important desideratum for any top-level ontology intended for application to domains such as engineering or m...