In general, Picard-Fuchs systems in N = 2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independe...

For an R-bounded families of operators on L1 we associate a family of representing measures and show that they form a weakly compact set. We consider a sectorial operator A which generates an R-bounded semigroup on L1. We show that given 2 > 0 there is an invertible operator U : L1 → L1 with ‖U − I‖ < 2 such that for some positive Borel function w we have U(D(A)) ⊃ L1(w).

The class of weakly algebrizable logics is defined as the class of logics having monotonic and injective Leibniz operator. We show that “monotonicity” cannot be discarded on this definition, by presenting an example of a system with injective and non monotonic Leibniz operator. We also show that the non injectivity of the non protoalgebraic inf-sup fragment of the Classic Propositional Calculus...

The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operatorvalued free probability. The paper presents constructions for maps with similar properties to the H and K transforms from the literature, semi inner-product bimodule analogues for the monotone and weakly monotone product of Hilbert spaces, an ad-hoc versio...

The paper investigates invariants of compactified Picard modular surfaces by principal congruence subgroups of Picard modular groups. The applications to the surface classification and modular forms are also discussed.

In general, Picard-Fuchs systems in N = 2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independe...

Necessary and sufficient geometric conditions for the equivalence of a nonlinear time– delay system with one output, under bicausal change of coordinates and output transformation, to a linear weakly observable time–delay system up to output injection are given. These conditions are derived through the use of the Extended Lie Bracket operator recently introduced in the literature for dealing wi...