Helmholtz stereopsis has been introduced recently as a surface reconstruction technique that does not assume a model of surface reflectance. In the reported formulation, correspondence was established using a rank constraint, necessitating at least three viewpoints and three pairs of images. Here, it is revealed that the fundamental Helmholtz stereopsis constraint defines a nonlinear partial di...

Electroweak unification is implied by the local structure theorem of distribution theory applied to the causal interval R = X − Z between two space-time points X and Z . Taking R as generating function, the potentials of the electromagnetic and weak interactions are obtained by applying the causal d’Alembertian operator onR, and both potentials can be given a proper physical interpretation prov...

To be more precise, in [2] is proved the existence of u { weak solution belonging to W 1,2 0 (Ω) ∩ L ∗∗ (Ω), if m ≥ 2N N+2 (“Stampacchia” theory); distributional solution belonging to W 1,m ∗ 0 (Ω), if 1 < m < 2N N+2 (“Calderon-Zygmund” theory); (5) where m∗ = mN N−m (1 ≤ m < N) and m ∗∗ = mN N−2m (1 ≤ m < N 2 ). Note that the above existence results are exactly the results proved with E = 0 in...

We establish conditions for an exponential rate of forgetting of the initial distribution of nonlinear filters in V -norm, allowing for unbounded test functions. The analysis is conducted in an general setup involving nonnegative kernels in a random environment which allows treatment of filters and prediction filters in a single framework. The main result is illustrated on two examples, the fir...

Results on singular products of the distributions x ± and x −p for natural p are derived when the products are balanced so that their sum exists in the distribution space. These results follow the pattern of a known distributional product published by Jan Mikusiński in 1966. The results are obtained in Colombeau algebra of generalized functions, which is most relevant algebraic construction for...

Nonlinear operations such as multiplication of distributions are not allowed in the classical theory of distributions. As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity andmultifluid flows, or some new cosmological models such as signature changing space-times. Colombeau’s new theory of generalized fun...

AbsfraclThe influence of specifying a roll moment distribution to effect the handling dynamics of automobiles has long been appreciated by conventional automotive designers. With the advent of active suspension systems, it is now possible to actively vary the roll moment distribution via feedback control. Nonlinear vehicle dynamics are developed to describe the effect of roll moment distributio...

A recent asymptotic model of cascading failure in two-domain, coupled infrastructure systems is used to pose and solve a generic degree-distribution design problem. A low-order nonlinear analysis exposes the mechanisms by which optimized graphs can form star-like clusters, as embedded into specialized distributions. Several other design rules are developed. Through examples on coupled systems o...

In this paper we have constructed an optimal eighth-order method with four function evaluations to solve the nonlinear equations. The proposed method is a three-step method in which no derivative is required. Our scheme is optimal in the sense of Kung and Traub. Moreover, some test functions have been also included to confirm the superiority of the proposed method. At the end, we have presented...

We extend the functional analytic approach to Colombeautype spaces of nonlinear generalized functions in order to study algebras of tempered generalized functions. We obtain a definition of Fourier transform of nonlinear generalized functions which has a strict inversion theorem, agrees with the classical Fourier transform for tempered distributions and preserves well-known classical properties...