This paper presents several basic results on compiling indefinite and GCWA(Generalized Closed World Assumption) inference in IDDB(Indefinite Dedutive Databases). We do not allow function symbols, but do allow non-Horn clauses. Further, although the GCWA is used to derive negative assumptions, we do also allow negative clauses to occur explicitly. We show a fundamental relationship between indef...

where Q is an indefinite quadratic form on Z, f(m,n) is a doubly periodic function on Z such that the sums of f(m,n)q over all vertical and all horizontal lines in Z vanish. Some of these series appeared as coefficients in univalued triple Massey products on elliptic curves computed via homological mirror symmetry in [3]. In particular, in this context the condition of vanishing of sums over ve...

This paper is concerned with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation methods to obtain our results.

A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE), which is a matrix-valued quadratic backward stochastic differential equation along with an algebraic constraint involving the unknown. Either the optimal control problem or the SRE is solvable only if the g...

This paper considers optimal (minimizing) control of stochastic linear quadratic regulators (LQRs). The assumption that the control weight costs must be positive definite, inherited from the deterministic case, has been taken for granted in the literature. It is, however, shown in this paper that some stochastic LQR problems with indefinite (in particular, negative) control weight costs may sti...

Abstract We prove an analogue of Kronecker’s second limit formula for a continuous family “indefinite zeta functions”. Indefinite functions were introduced in the author’s previous paper as Mellin transforms indefinite theta functions, defined by Zwegers. Our is valid dimension $$g=2$$ g = <mm...

λ0 = λ0(1, P, Ω) := sup{λ ∈ R : ∃u > 0 s.t. (P − λ)u ≥ 0 in Ω}, where 1 is the constant function on Ω, taking at any point x ∈ Ω the value 1. Using the Krein-Rutman theorem, the author proved in [13, 14] generalized maximum principles and anti-maximum principles (in brief, GMPs and AMPs, respectively) for the problem (P − λ)uλ = f 0 in Ω. (1.1) In particular, these GMPs and AMPs (without weight...