Let L be a finite distributive lattice and μ : L → R a logsupermodular function. For functions k : L → R let Eμ(k; q) def = ∑ x∈L k(x)μ(x)q ∈ R[q]. We prove for any pair g, h : L → R of monotonely increasing functions, that Eμ(g; q) ·Eμ(h; q) ≪ Eμ(1; q) · Eμ(gh; q), where “≪ ” denotes coefficientwise inequality of real polynomials. The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) is ...

We examine how aggregate output and income distribution interact with accumulation of intangible capital over time and across individuals. We consider an overlapping generations economy in which managerial skill (intangible capital) is essential for production, and it is acquired by young workers through on-the-job training by old managers. We show that, when young trainees are not committed to...

Inverse kinematics (IK) problems are important in the study of robotics and have found applications in other fields such as structural biology. The conventional formulation of IK in terms of joint parameters amounts to solving a system of nonlinear equations, which is considered to be very hard for general chains, especially for those with many links. In this paper, we study IK for a serial cha...

In this paper, for handling general minimum-effort inverse-kinematic problems, the nonuniqueness condition is investigated. A set of nonlinear equations and inequality is presented for online nonuniqueness-checking. The concept and utility of primal neural networks (NNs) are introduced in this context of dynamical inequalities and constraints. The proposed primal NN can handle well such a nonli...

In this paper we study the local behavior of a solution to the Lamé system when the Lamé coefficients λ and μ satisfy that μ is Lipschitz and λ is essentially bounded in dimension n ≥ 2. One of the main results is the local doubling inequality for the solution of the Lamé system. This is a quantitative estimate of the strong unique continuation property. Our proof relies on Carleman estimates w...

The problem of giving a spectral factorization of a class of matrices arising in Wiener filtering theory and network synthesis is tackled via an kgebralc procedure. A quadratic matrix quation involving only constant matrices is shown to possess solutions which directly define a solution to the spectral factorization problem. A spectral factor with a stable inverse is defined by that unique solu...

We introduce a new hybrid extragradient viscosity approximationmethod for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for β-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed i...

Hierarchical least-square optimization is often used in robotics to inverse a direct function when multiple incompatible objectives are involved. Typical examples are inverse kinematics or dynamics. The objectives can be given as equalities to be satisfied (e.g. point-to-point task) or as areas of satisfaction (e.g. the joint range). This paper proposes a complete solution to solve multiple lea...

In this paper, we introduce a new iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inversestrongly-monotone mapping in a Banach space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common el...