相关论文: The contingent epiderivative and the calculus of v…

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…

E727 in the Enestrom index. This is a translation from the Latin original "Accuratior evolutio problematis de linea brevissima in superficie quacunque ducenda" (1779). Given a surface $pdx+qdy+rdz=0$, Euler wants to develop equations that…

This work contains an exposition of foundations of the variational calculus in fibered manifolds. The emphasis is laid on the geometric aspects of the theory. Especially functionals defined by real functions (Lagrange functions) or…

In the present paper we will give some new notions, such as {\Delta}-convergence and {\Delta}-Cauchy, by using the {\Delta}-density and investigate their relations. It is important to say that, the results presented in this work generalize…

Decision makers may suffer from uncertainty induced by limited data. This may be mitigated by accounting for epistemic uncertainty, which is however challenging to estimate efficiently for large neural networks. To this extent we…

Developed turbulent motion of fluid still lacks an analytical description despite more than a century of active research. Nowadays phenomenological ideas are widely used in practical applications, such as small-scale closures for numerical…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

This paper proposes a method for modeling event sequences with ambiguous timestamps, a time-discounting convolution. Unlike in ordinary time series, time intervals are not constant, small time-shifts have no significant effect, and…

We study a minimisation problem in $L^p$ and $L^\infty$ for certain cost functionals, where the class of admissible mappings is constrained by the Navier-Stokes equations. Problems of this type are motivated by variational data assimilation…

In this article we focus our attention on the relation between a singular linear discrete time system and a singular linear system of fractional nabla difference equations whose coefficients are square constant matrices. By using matrix…

In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many of the properties considered for shift invariant difference operators satisfying the…

Variational principles play a fundamental role in deriving evolution equations of physics. They are working well in case of nondissipative evolution but for dissipative systems they are not unique, not predictive and not constructive. With…

The work described here shows that the known variational principle for the Navier-Stokes equations and the adjoint system can be modified to produce a set of Euler-Lagrange variational equations which have the same order and same solution…

Here we study the long time behavior of an advection-diffusion equation with a general time varying (including random) shear flow imposing no-flux boundary conditions on channel walls. We derive the asymptotic approximation of the scalar…

We investigate model assessment and selection in a changing environment, by synthesizing datasets from both the current time period and historical epochs. To tackle unknown and potentially arbitrary temporal distribution shift, we develop…

Time series are difficult to monitor, summarize and predict. Segmentation organizes time series into few intervals having uniform characteristics (flatness, linearity, modality, monotonicity and so on). For scalability, we require fast…

In this paper we develop a geometric approach to convex subdifferential calculus in finite dimensions with employing some ideas of modern variational analysis. This approach allows us to obtain natural and rather easy proofs of basic…

The mathematical theory of a novel variational approximation scheme for general second and fourth order partial differential equations \begin{equation}\label{eq: A} \partial_t u - \nabla\cdot\Big(u\nabla\frac{\delta\phi}{\delta…

We prove a more general version of the Gruss inequality by using the recent theory of combined dynamic derivatives on time scales and the more general notions of diamond-alpha derivative and integral. For the particular case when alpha = 1,…

This paper provides a quite simple method of Tonelli's calculus of variations with positive definite and superlinear Lagrangians. The result complements the classical literature of calculus of variations before Tonelli's modern approach.…