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At a particular frequency, most materials and objects of interest exhibit a polarization signature, or Mueller matrix, of limited dimensionality, with many matrix elements either negligibly small or redundant due to symmetry. Robust design of a polarization sensor for a particular material or object of interest, or for an application with a limited set of materials or objects, will adapt to the signature subspace, as well as the available modulators, in order to avoid unnecessary measurements and hardware and their associated budgets, errors, and artifacts. At the same time, measured polarization features should be expressed in the Stokes–Mueller basis to allow use of known phenomenology for data interpretation and processing as well as instrument calibration and troubleshooting. This approach to partial Mueller-matrix polarimeter (pMMP) design begins by defining a vector space of reduced Mueller matrices and an instrument vector representing the polarization modulators and other components of the sensor. The reduced-Mueller vector space is proven to be identical to R15 and to provide a completely linear description constrained to the Mueller cone. The reduced irradiance, the inner product of the reduced instrument and target vectors, is then applied to construct classifiers and tune modulator parameters, for instance to maximize representation of a specific target in a fixed number of measured channels. This design method eliminates the use of pseudo-inverses and reveals the optimal channel compositions to capture a particular signature feature, or a limited set of features, under given hardware constraints. Examples are given for common optical division-of-amplitude (DoA) 2-channel passive and serial/DoT-DoA 4-channel active polarimeters with rotating crystal modulators for classification of targets with diattenuation and depolarization characteristics.

In this paper we investigate a class of nonlinear integral equations for existence of global classical solutions. We give conditions under which the considered equations have at least one, at least two and at least three solutions. To prove our main results we propose a new approach based upon recent theoretical results.

A non-constructive existence theory for certain operator equations L u = D u , using the substitution u = B 1 2 ξ with B  =  L −1 , is developed, where L is a linear operator (in a suitable Banach space) and D is a homogeneous nonlinear operator such that Dλu  =  λ α D u for all λ  ≥ 0 and some α ∈ R ,   α  ≠ ~1. This theory is based on the positive-operator approach of Krasnosel’skii. The method has the advantage of being able to tackle the nonlinear right-hand side D in cases where conventional operator techniques fail. By placing the requirement that the operator B must have a positive square root, it is possible to avoid the usual regularity condition on either the mapping D or its Fréchet derivative. The technique can be applied in the case of elliptic PDE problems, and we show the existence of solitary waves for a generalization of Benjamin’s fluid dynamics problem.

Waverider is a hypersonic vehicle that improves the lift-to-drag ratio using the shockwave attached to the leading edge of the lifting surface. Owing to its superior aerodynamic performance, it exhibits a viable external configuration in hypersonic flight conditions. Most of the existing studies on waverider employ the inverse design method to generate vehicle configuration. However, the waverider inverse design method exhibits two limitations; inaccurate definition of design space and unfeasible performance estimation during the design process. To address these issues, a novel framework to directly optimize the waverider is proposed in this paper. The osculating cone theory is adopted as a waverider inverse design method. A general methodology to define the design space is suggested by analyzing the design curves of the osculating cone theory. The performance of the waverider is estimated accurately and rapidly via combining a high-fidelity computational fluid dynamics solver and a surrogate model. A comparison study shows that the proposed direct optimization framework enables a more accurate design space and efficient performance estimation. The framework is applied to the multi-objective optimization problem, which maximizes internal volume and minimizes aerodynamic drag. Finally, general characteristics for waverider are presented by analyzing the optimized results with data mining methods such as K-means.

The purpose of this paper is to present a procedure for the estimation of the smallest eigenvalues and their associated eigenfunctions of nth order linear boundary value problems with homogeneous boundary conditions defined in terms of quasi-derivatives. The procedure is based on the iterative application of the equivalent integral operator to functions of a cone and the calculation of the Collatz–Wielandt numbers of such functions. Some results on the sign of the Green functions of the boundary value problems are also provided.

In this paper, we investigate the existence of minimal nonnegative solution for a class of nonlinear fractional integro-differential equations on semi-infinite intervals in Banach spaces by applying the cone theory and the monotone iterative technique. An example is given for the illustration of main results.

By using the cone theory and the Banach contraction mapping principle, we study the existence and uniqueness of an iterative solution to the singular n th-order nonlocal boundary value problems.

In this paper, we investigate the existence of a positive solution to the third-order boundary value problem where k is a positive constant, ϕ ∈ L (0;+ ∞) is nonnegative and does vanish identically on (0;+ ∞) and the function f : ℝ × (0;+ ∞) × (0;+ ∞) → ℝ is continuous and may be singular at the space variable and at its derivative.

This paper deals with the existence of positive ω-periodic solutions for third-order ordinary differential equation with delay u‴(t)+Mu(t)=f(t,u(t),u(t−τ)),t∈R, where ω>0 and M>0 are constants, f:R3→R is continuous, f(t,x,y) is ω-periodic in t, and τ>0 is a constant denoting the time delay. We show the existence of positive ω-periodic solutions when 0

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