The optimality conditions for the optimal shape remodelling of linearly elastic plates are obtained by introducing the total variation of a function defined on a variable domain, although the variation of a function has been taken on a fixed domain in most literature on calculus of variations. Using these optimality conditions, a solution scheme involving an iterative algorithm is proposed, tog...

introduction here we report an unusual case of massive stone formation in augmented urinary bladder. case presentation a 25-year-old man presented with recurrent urinary tract infection ten years after augmentation cystoplasty after a complex pelvic fracture urethral distraction defect. on evaluation by ultrasonography, x-ray, and computed tomography of abdomen showed large burden of stones in ...

Stochastic differential equations in R with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W β 2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution p...

In this paper we prove an asymptotic estimate, up to the second order included, on the behaviour of the one-dimensional Allen-Cahn’s action functionals, around a periodic function with bounded variation and taking values in {±1}. The leading term of this estimate justifies and confirms, from a variational point of view, the results of Fusco-Hale [10] and Carr-Pego [7] on the exponentially slow ...

In 1980’s, Lee proposed an energy-preserving discrete mechanics with variable time steps by taking (discrete) time as dynamical variable [2, 3, 4]. On the other hand, motivated by the symplectic property of Lagrangian mechanics, a version of discrete Lagrangian mechanics has been devoloped and variational integrators that preserve discrete symplectic two form have been obtained [11, 12, 15, 16,...

We introduce the continuous π-calculus, a process algebra for modelling behaviour and variation in molecular systems. Key features of the language are: its expressive succinctness; support for diverse interaction between agents via a flexible network of molecular affinities; and operational semantics for a continuous space of processes. This compositional semantics also gives a modular way to g...

The Kolmogorov and total variation distance between the laws of random variables have upper bounds represented by L1-norm densities when densities. In this paper, we derive an bound, in terms such as distance, for several probabilistic distances (e.g., Wasserstein Forter–Mourier etc.) F G case where a variable follows invariant measure that admits density differentiable G, sense Malliavin calcu...

introdouction: overhang refers to the extension of restoration material from the cavity. it has an important role in decay, plaque accumulation and periodontal disease, so the aim of this study is determining the frequency of restoration overhang in patients in anzali, guilan. materials and methods: this descriptive cross-sectional study was completed using 293 patients who visited for routine ...

Let $$G=(V,E)$$ be a locally finite graph. Firstly, using calculus of variations, including direct method variation and the mountain-pass theory, we get sequences solutions to several local equations on G (the Schrödinger equation, mean field Yamabe equation). Secondly, derive uniform estimates for those solution sequences. Finally, obtain global by extracting convergent sequence solutions. Our...