An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents in an ordered monoid. We study when a generalized power series ring has a Rota-Baxter operator and how this is related to the ordered monoid.

In this work we study action theories of the situation calculus such that the initial KB is a generalized database with equality constraints (GFDBs). We show that GFDBs characterize the class of definitional KBs and that they are closed under progression. We also show that, under conditions, generalized projection queries can be decided based on an induced transition system and evaluation of lo...

Matrix valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, B-derivative, directional derivative, and se...

Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, -derivative, directional derivative, and sem...

In the context of generalized finite element methods for elliptic equations with rough coefficients a(x), efficiency and accuracy of the numerical method depend critically on the use of appropriate basis functions. This work explores several random sampling strategies for construction of basis functions, and proposes a quantitative criterion to analyze and compare these sampling strategies. Num...

It is known (see [5, 6]) that when K is a closed convex cone, problems NCP( f ,K) and VI( f ,K) are equivalent. To study the existence of solutions of the NCP( f ,K) and VI( f ,K) problems, many authors have used the techniques of KKM mappings, and the Fan-KKM theorem from fixed point theory (see [1, 5, 6, 7, 8, 9, 10]). In case B is a Hilbert space, Isac and other authors have used the notion ...

In this paper we consider the numerical solution of projected generalized continuous-time Lyapunov equations with low-rank right-hand sides. The interest in this problem stems from stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. Two projection methods are proposed for calculating low-rank approximate solutions. One is based ...

In this paper, a new statistical projection-based method called Two-DimensionalOriented Linear Discriminant Analysis (2DO-LDA) is presented. While in the Fisherfaces method the 2D image matrices are first transformed into 1D vectors by merging their rows of pixels, 2DO-LDA is directly applied on matrices, as 2D-PCA. Within and between-class image covariance matrices are generalized, and 2DO-LDA...

Output-feedback control for trajectory tracking is an important research topic of various engineering systems. In this paper, a novel online hybrid direct/indirect adaptive Petri fuzzy neural network (PFNN) controller with stare observer for uncertain nonlinear multivariable dynamical systems using generalized projection-update laws is presented. This new approach consists of control objectives...

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naiv...