We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F (t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical Itô calculus does not apply. Motivated by heuristic ideas ab...

background and aims. gingival recession (gr), a common problem in periodontium, is associated with various etiologic factors. there is controversy over the role and importance of these factors. the aim of this study was to evaluate the etiologic factors of gr in a group of subjects in northwest iran. materials and methods. in this case-control study, patients referring to a university clinic (1...

We analyze a variational time discretization of geodesic calculus on finiteand certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete parallel transport, and we prove convergence to their continuous counterparts. The presented analysis is based on th...

On a reflexive Banach space X , if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum σ(T ) ⊆ R, then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can constru...

The solutions of the dual bending energy functional on unit sphere S2 ? D3 are investigated. Dual spherical elastica is characterized by Euler-Lagrange equation using techniques calculus variation. real and parts differential solved different methods. shown to correspond elastic strip constituted planar in R3.

We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F (t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical Itô calculus does not apply. Motivated by heuristic ideas ab...

The Industrial Internet of Things (IIoT) has revolutionized businesses by changing the way data are used to make products and services more efficient, reliable, profitable. To achieve improvement goals, IIoT must guarantee real-time performance industrial applications such as motion control, providing stringent quality service (QoS) assurances for their (industrial applications) communication n...

In the modeling of a large class of problems in science and engineering, the minimization of a functional is appeared. Finding the solution of these problems needs to solve the corresponding ordinary differential equations which are generally nonlinear. In recent years, differential transform method has been attracted a lot of attention of the researchers for solving nonlinear problems. This me...

We provide in this paper the discrete equations of motion for the newtonian n-body problem deduced from the quantum calculus of variations (Q.C.V.) developed in [3, 4, 7, 8]. These equations are brought into the usual lagrangian and hamiltonian formulations of the dynamics and yield sampled functional equations involving generalized scale derivatives. We investigate especially homographic solut...