Introduction. In classical algebraic geometry the adjoint curves to an irreducible plane curve are an essential tool in the study of the geometry on the curve. In this paper we shall give an algebro-arithmetic development of the theory of adjoint curves, and shall extend the classical results to irreducible plane curves with arbitrary singularities defined over arbitrary ground fields. Our defi...

New formulas on the inverse problem for the continuous skewself-adjoint Dirac type system are obtained. For the discrete skewself-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. BorgMarchenko type uniqueness theorems are derived for both discrete and ...

One-dimensional δ ′ -function potential is discussed in the framework of Green’s function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green’s function for this case is crucially dependent on the boundary conditions which are provided by self-adjoint extension method. The most general Green’s function which contains four real self-adjoint extension pa...

For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we first extend the ranges of exponents for the classical linear or bilinear adjoint restriction conjectures for such functions and verify the linear adjoint restriction conjecture for the paraboloid. We also interpret the r...

For any even positive integer 2n and any positive integermwe construct a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most (2n − 1)m + 1 eigenvalues. Our main result reduces to previously known results for the cases n = 1 and n = 2. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n(m + 1)...

S U M M A R Y We compare finite-frequency phase and amplitude sensitivity kernels calculated based on frequency-domain surface wave mode summation and a time-domain adjoint method. The adjoint calculations involve a forward wavefield generated by an earthquake and an adjoint wavefield generated at a seismic receiver. We determine adjoint sources corresponding to frequency-dependent phase and am...

A differential operator on a directed graph with weighted edges is characterized as a system of ordinary differential operators. A class of local operators is introduced to clarify which operators should be considered as defined on the graph. When the edge lengths have a positive lower bound, all local self-adjoint extensions of the minimal symmetric operator may be classified by boundary condi...

1. Introduction While aerodynamic prediction methods based CFD are now well established , and quite accurate and robust, the ultimate need in the design process is to find the optimum shape which maximizes the aerodynamic performance. One way to approach this objective is to view it as a control problem, in which the wing is treated as a device which controls the flow to produce lift with minim...

In this paper we present an approach to shape optimization which is based on continuous adjoint computations. If the exact discrete adjoint equation is used, the resulting formula yields the exact discrete reduced gradient. We first introduce the adjoint-based shape derivative computation in a Banach space setting. This method is then applied to the instationary NavierStokes equations. Finally,...

A generalization of the Aleksandrov operator is provided, in order to represent the adjoint of a weighted composition operator on H2 by means of an integral with respect to a measure. In particular, we show the existence of a family of measures which represents the adjoint of a weighted composition operator under fairly mild assumptions, and we discuss not only uniqueness but also the generaliz...