We give a simple characterization of all single-item truthrevealing auctions under some mild (and natural) assumptions about the auctions. Our work opens up the possibility of using variational calculus to design auctions having desired properties.

P. A. Griffiths established the so-called mixed endpoint conditions for variational problems with non-holonomic constraints. We will present some results in this context and discuss the inverse problem of calculus of variations.

Fractional action-like variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multi-dimensional fractional action-like problems of the calculus of variations. 2000 Mathematics Subject Classification: 49K10, 49S05.

We show that for any variational symmetry of the problem of the calculus of variations on time scales there exists a conserved quantity along the respective Euler-Lagrange extremals. Mathematics Subject Classification 2000: 49K05, 39A12.

We prove a Noether’s theorem for fractional variational problems with Riesz-Caputo derivatives. Both Lagrangian and Hamiltonian formulations are obtained. Illustrative examples in the fractional context of the calculus of variations and optimal control are given.

We extend the DuBois–Reymond necessary optimality condition and Noether’s symmetry theorem to the time delay variational setting. Both Lagrangian and Hamiltonian versions of Noether’s theorem are proved, covering problems of the calculus of variations and optimal control with delays.

Abstract: This paper provides an overview of the applications that calculus of variations found in two major fields of interest, namely signal processing and image processing. We will describe the significant role of calculus of variations in modeling and optimizing a variety of signal and image processing problems. Specifically, the key role of calculus of variations in deriving the worst-case...

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

In this paper, we introduce fractional calculus into image inpainting and propose a new class of fractional-order variational image inpainting models, in both space and wavelet domains, inspired by the works of Bai and Feng. The corresponding Euler-Lagrange equations are given and proper numerical algorithm is analyzed. According to the simulations on several testing images, our algorithm demon...

In this paper, a new theory of generalized micropolar thermoelasticity is derived by using fractional calculus. The generalized heat conduction equation in micropolar thermoelasticity has been modified with two distinct temperatures, conductive temperature and thermodynamic temperature by fractional calculus which depends upon the idea of the RiemannLiouville fractional integral operators. A un...