In “Shape From Specular Flow: Is One Flow Enough?” (Vasilyev, et al., 2011 [5]) we show that mirror shape can often be reconstructed from the observation of a single specular flow. In this technical report we provide additional details that, due to space constraints, could not be included in the paper. First we provide a derivation of the linear system for the reflection field derivative in the...

with D(φ(·,u)) ⊂ j for all u ∈ = ∏N j=1 j . The existence of an open loop of (1.1), (1.2) with φ independent of the control u, has been established in Ton [7]. With optimal shape design and with inverse problems inmind, we will consider the case when φ depends on the control u as it appears in the top order term of the partial differential operators involved in the problems. Optimal design of d...

in this paper, we ask “can proximity to towns reduces poverty in rural areas?” for this study we have mapped all the villages in orissa. the study is based on small area poverty estimation methodology as well as the secondary data covering 47,395 villages and 109 towns. our main findings are (i) there is a relationship between the distance to nearest town and rural poverty and (ii) poverty leve...

A fourth-degree Substrate Integrated Waveguide (SIW) crossed coupled band pass filter for WLAN band is designed by using a new negative coupling structure. It consists of two U shape microstrip lines on top and bottom planes with via holes at the center of them. This paper investigates the phase characteristics of negative and positive coupling structures and their effects. The design, fabricat...

W both retail distribution and less-than-truckload transportation networks crossdocks vary greatly in shape. Docks in the shape of an I, L, or T are most common, but unusual ones may be found, including those in the shape of a U, H, or E. Is there a best shape? We show that the answer depends on the size of the facility and on the pattern of freight flows inside. Our results suggest that many l...

All our words (strings) are over a fixed alphabet. A square is a subword of the form uu=u, where u is a nonempty word. Two squares are distinct if they are of different shape, not just translates of each other. A word u is primitive if u cannot be written in the form u=v j for some j 2. A square u with u primitive is primitive rooted. Let M(n) denote the maximum number of distinct squares, P(n)...

Here u = u(x, t) and f(u) is smooth, convex, and satisfies f(0) = f′(0) = 0. The choice f(u) = u/2 has been shown previously to arise in connection with the physical problem of upward flame-front propagation in a vertical channel in a particular parameter regime. In this context, the shape y = y(x, t) of the flame-front interface satisfies u = −yx. For this problem, it is shown that the princip...

We study the stability of noncompact critica of parametric elliptic functionals with a volume constraint. Let F : U ⊂ S → R be a smooth function. For a smooth, oriented hypersurface X : Σ → E whose Gauss map ν : Σ → S is assumed to lie in U , we define the functional FΛ(X) = ∫ Σ F (ν)dΣ + ΛV (X), Λ ∈ R, (1) where V (X) denotes the algebraic n + 1 dimensional volume enclosed by X, V (X) := 1 n +...