We study multiplicities of jumping numbers multiplier ideals in a smooth variety arbitrary dimension. prove that the multiplicity function is quasi-polynomial, hence proving Poincar\'e series rational function. further when various components quasi-polynomial have highest possible degree and relate it to contributed by Rees valuations. Finally, we special case monomial ideals.

We study the L2 → L∞ norms of spectral projections and spectral multipliers of left-invariant elliptic and subelliptic second-order differential operators on homogeneous Lie groups. We obtain a precise description of the L2 → L∞ norms of spectral multipliers for some class of operators which we call quasi-homogeneous. As an application we prove a stronger version of Alexopoulos’ spectral multip...

We fabricated 1 mm-thick periodically-poled lithium niobate (PPLN) crystals by using a high-voltage amplifier for standard electric field poling combined with a voltage multiplier. Furthermore, two 1 mm-thick PPLNs were directly bonded to make a 2 mm-thick PPLN. The large aperture allowed broad angular tuning, and a broad spectral range of quasi-phase matched second-harmonic generation can be a...

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asympotically. Because of that, this paper analyses the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carl...

This paper considers the design of robust`1 estimators based on multiplier theory (which is intimately related to the mixed structured singular value). Speciically, the Popov-Tsypkin multiplier is used to develop an upper bound on an`1 cost function over an uncertainty set. The robust`1 estimation problem is formulated as a parameter optimization problem in which the upper bound is minimized su...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theor...

This paper presents a self-adaptive differential evolution with augmented Lagrange multiplier method (SADE_ALM) for solving optimal power flow (OPF) problems with non-smooth generator fuel cost curves. The SADE_ALM is a modified version of conventional differential evolution (DE) by integrating mutation factor (F ) and crossover constant (CR ) as additional control variables. An augmented Lagra...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theor...

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. This space is a natural setting for studying global invariants of singularities involving multiplier ideals. We show that multiplier ideals provide natural stratifications of this space. We prove a structure theor...