相关论文: Adjoint and Its roles in Sciences, Engineering, an…

Adjoint methods enable the accurate calculation of the sensitivities of a quantity of interest. The sensitivity is obtained by solving the adjoint system, which can be derived by continuous or discrete adjoint strategies. In acoustic wave…

A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of…

The solving of scientific and practical application connected with conducting of satellite experiments and measurement demand analysis of geometric and physic conditions according to different kind of models. This is forced in connect of…

The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms…

A geometrical formulation for adjoint-symmetries as 1-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution…

Ordered logics and type systems have been used in a variety of applications including computational linguistics, memory allocation, stream processing, logical frameworks, parametricity, and enforcing security protocols. In most…

Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return sets of canonical solutions rather than a unique one. In the…

We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…

In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has…

This chapter uses categorical techniques to describe relations between various sets of operators on a Hilbert space, such as self-adjoint, positive, density, effect and projection operators. These relations, including various…

This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory…

We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions,…

For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from…

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

We show how to use formal desingularizations (defined earlier by the first author) in order to compute the global sections (also called adjoints) of twisted pluricanonical sheaves. These sections define maps that play an important role in…

We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular…

Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like…

Uncertainty quantification and sensitivity analyses are a vital component for predictive modeling in the sciences and engineering. The adjoint approach to sensitivity analysis requires solving a primary system of equations and a…