Related papers: Bundle-theoretic methods for higher-order variatio…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We obtain necessary optimality conditions for higher-order infinite horizon problems of the calculus of variations via discrete quantum operators.
We propose a variational scheme to represent composite quantum systems using multiple parameterized functions of varying accuracies on both classical and quantum hardware. The approach follows the variational principle over the entire…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions in the calculus of variations and optimal control. Motivated by this fact, we construct a new, right-weighted…
New constructions in the theory of fields for multiple integrals are designed. Generalizations of the Legendre - Weyl - Caratheodory transforms and corresponding invariant integrals are introduced and explored. Connection and curvature of…
The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical…
We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…
Jet manifolds and vector bundles allow one to employ tools of differential geometry to study differential equations, for example those arising as equations of motions in physics. They are necessary for a geometrical formulation of…
Given an ordered set partition, when one insert a number of bars in-between the blocks of the ordered set partition the result is a barred preferential arrangement. In this study, using the notion of barred preferential arrangements we…
We consider the algebro-geometric consequences of integration by parts.
These notes survey the theory of (twisted) conformal blocks from an algebro-geometric perspective and have two main goals. The first one is to summarize the construction of conformal blocks from vertex operator algebras, and to describe…
A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the Lagrangian is replaced by a section of a…
In this work we look at the original fractional calculus of variations problem in a somewhat different way. As a simple consequence, we show that a fractional generalization of a classical problem has a solution without any restrictions on…
One popular way for lifted inference in probabilistic graphical models is to first merge symmetric states into a single cluster (orbit) and then use these for downstream inference, via variations of orbital MCMC [Niepert, 2012]. These…
In this paper we determine a number of meaningful compositions of higher order of a set of functions, which is considered in Malesevic (1998), in implicit and explicit form. Results which are obtained are applied to the vector analysis in…
In this paper, we introduce and develop the circle embedding method. This method hinges essentially on a combinatorial-geometric structure which we choose to call circles of partition. We provide applications in the context of problems that…
We present both the Lagrangian and Hamiltonian procedures for treating higher-order equations of motion for mechanical models by adopting the Riemann-Liouville Fractional integral to describe their action. We point out and discuss its…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
Let $X$ be the wonderful compactification of a complex adjoint symmetric space $G/K$ such that $rk(G/K)=rk(G)-rk(K)$. We show how to extend equivariant vector bundles on $G/K$ to equivariant vector bundles on $X$, generated by their global…