The cascade algorithm that is used for extended surface analysis depends on a new parameterization called the thermal transmission matrix to represent a single fin. This thermal transmission matrix, which is intended ...
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The cascade algorithm that is used for extended surface analysis depends on a new parameterization called the thermal transmission matrix to represent a single fin. This thermal transmission matrix, which is intended to replace the more familiar fin efficiency as a design and analysis parameterization, is a linear transformation that maps conditions of heat flow and temperature at the fin tip to heat flow and temperature conditions at the fin base. The cascade algorithm was derived by resorting to an analogy between a fin and the electrical transmission line. The cascade algorithm permits a fin to be subdivided into many subfins each having a thermal transmission matrix and then the individual transmission matrices for each of the subfins can be used, via a simple matrix product to form an overall equivalent thermal transmission matrix for the entire fin. This thesis develops a thermal transmission matrix for the radiating rectangular, trapezoidal, and triangular fins both for the free space and non-free space environments. Test cases have been run and their solutions exactly match those contained in the literature. The thesis concludes with optimization studies for each profile considered where it is observed that simple algebraic equations can be employed to describe the optimum geometry.
Let A be a dilation matrix, an n x n expansive matrix that maps Z(n) into itself. Let. be a finite subset of Z(n), and for kappa is an element of Lambda let c kappa be r x r complex matrices. The refinement equation c...
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Let A be a dilation matrix, an n x n expansive matrix that maps Z(n) into itself. Let. be a finite subset of Z(n), and for kappa is an element of Lambda let c kappa be r x r complex matrices. The refinement equation corresponding to A, Z(n),Lambda and c = {c(kappa)}(kappa is an element of Lambda) is f(x) = Sigma(kappa is an element of Lambda)c(kappa) f(Ax - kappa). A solution f : R-n -> C-r, if one exists, is called a refinable vector function or a vector scaling function of multiplicity r. This paper characterizes the higher-order smoothness of compactly supported solutions of the refinement equation, in terms of the p-norm joint spectral radius of a finite set of finite matrices determined by the coefficients c(kappa).
We consider the univariate two-scale refinement equation phi (x) = Sigma (N)(k=0) c(k)phi (2x - k), where c(0),..., c(N) are complex values and Sigmac(k) = 2. This paper analyzes the correlation between the existence ...
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We consider the univariate two-scale refinement equation phi (x) = Sigma (N)(k=0) c(k)phi (2x - k), where c(0),..., c(N) are complex values and Sigmac(k) = 2. This paper analyzes the correlation between the existence of smooth compactly supported solutions of this equation and the convergence of the corresponding cascade algorithm/subdivision scheme. We introduce a criterion that expresses this correlation in terms of the mask of the equation. We show that the convergence of the subdivision scheme depends on values that the mask takes at the points of its generalized cycles. This means in particular that the stability of shifts of refinable function is not necessary for the convergence of the subdivision process. This also leads to some results on the degree of convergence of subdivision processes and on factorizations of refinable functions.
Constrained iterative deconvolution (CID) super-resolution algorithm and its fast version, i.e., fast constrained-iterative deconvolution (FCID) are studied. These approaches are able to break through the aperture lim...
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ISBN:
(纸本)9781467386456
Constrained iterative deconvolution (CID) super-resolution algorithm and its fast version, i.e., fast constrained-iterative deconvolution (FCID) are studied. These approaches are able to break through the aperture limiting to angular resolutions and can be applicable to two-dimensional imaging of non-coherent radars. However, FCID algorithm suffers fromd ivergence, which limits the improvement of angular resolutions. A cascade algorithm that FCID iterations alternate with CID iterations is developed in this paper. This algorithm significantly increases permissible FCID iterations, thus higher angular resolution of two-dimensional imaging is achieved with less computational burden.
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