Closed-Form Solutions for Broad-Band Equivalent Circuit of Vertical Rod Buried in Lossy Grounds Subjected to Lightning Strokes

Closed-Form Solutions to Forward-Backward Smoothing

We propose a closed form Gaussian sum smoother and, more importantly, closed form smoothing solutions for increasingly complex problems arising from practice, including tracking in clutter, joint detection and tracking (in clutter), and multiple target tracking (in clutter) via the Probability Hypothesis Density. The solutions are based on the corresponding forward-backward smoothing recursions...

Closed-Form Solutions to Minimal Absolute Pose Problems with Known Vertical Direction

In this paper we provide new simple closed-form solutions to two minimal absolute pose problems for the case of known vertical direction. In the first problem we estimate absolute pose of a calibrated camera from two 2D-3D correspondences and a given vertical direction. In the second problem we assume camera with unknown focal length and radial distortion and estimate its pose together with the...

Closed Form Solutions for Nonuniform Transmission Lines

In this paper, three analytic closed form solutions are introduced for arbitrary Nonuniform Transmission Lines (NTLs). The differential equations of NTLs are written in three suitable matrix equation forms, first. Then the matrix equations are solved to obtain the chain parameter matrix of NTLs. The obtained solutions are applicable to arbitrary lossy and dispersive NTLs. The validation of the ...

Closed-Form Solutions for Robust Inventory Management

Copyright: © 2016 INFORMS Abstract. We propose and analyze robust optimization models of an inventory management problem, where cumulative purchase, inventory, and shortage costs over n periods are minimized for correlated nonidentically distributed demand. We assume that the means and covariance matrix of stochastic demand are known; the distributions are not needed. We derive closed-form orde...

Optimization of Conformal Mapping Functions used in Developing Closed-Form Solutions for Underground Structures with Conventional cross Sections

Elastic solutions applicable to single underground openings usually suffer from geometry related simplification. Most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. D-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). In the present...

On Certain Closed-form Solutions to Problems of Wave Prop- Agation in a Strain-hardening Rod* By