where ⌊x⌋ denotes the largest integer not greater than x. Under certain conditions, these cosine power sums can be determined exactly, without approximations [5]. If f(x) = a0 + a1x+ a2x 2 + · · ·+ anx + · · · is a finite or convergent infinite series, then for 0 ≤ r < n the sum arx r + ar+nx r+n + ar+2nx r+2n + · · · is given by the multisection formula (see [1, Ch. 16], [4, Ch. 4, S. 4.3] and...

We develop a Fourier method to solve backward stochastic differential equations (BSDEs). General theta-discretization of the time-integrands leads to an induction scheme with conditional expectations. These are approximated by using Fourier-cosine series expansions, relying on the availability of a characteristic function. The method is applied to BSDEs with jumps. Numerical experiments demonst...

In this article, we present a critical review of the swimming literature on body roll, for the purposes of summarizing and highlighting existing knowledge, identifying the gaps and limitations, and stimulating further research. The main research findings can be summarized as follows: swimmers roll their shoulders significantly more than their hips; swimmers increase hip roll but maintain should...

An Al/Stainless Steel/Al lamellar composite was produced by roll bonding of the starting sheets at 400 °C. Afterward, the roll bonded sheet was cut in half and the accumulative roll bonding (ARB) process at room temperature was applied seven times. As a result, the central steel layer fractured and distributed in the Al matrix among different layers introduced by the repetition of roll bonding ...

In order to automate the scooping task, it is desirable that the resistive force acting on the bucket be obtained before the scooping is performed. The objective of this study is to derive theoretically the resistive forces acting on the bucket during scooping of piled rock fragments. First, the changes in the shape of the rock pile due to the penetration of it by the bucket are modeled. Based ...

Analytical models for channel potential, threshold voltage, and subthreshold swing of the short-channel fin-shaped field-effect transistor (FinFET) are obtained. The analytical model results are verified against simulations and good agreements are observed. Analytical expressions for subthreshold swing, drain induced barrier lowering effect, and threshold voltage roll-off characteristics are pr...

In this paper, an analytical method based on Modified Slab Method of analysis is presented to study the asymmetrical rolling process due to difference in work rolls radii, rolls speeds and interface frictions. The shear force imposed on material along the contact region is considered to be a function of the frictional factor and the roll gap geometry. Elastic-plastic with linear work hardening ...

In this work, conditions on the coefficients {ak} are considered so that the corresponding sine sum n ∑ k=1 ak sin kθ and cosine sum a0 + n ∑ k=1 ak cos kθ are positive in the unit disc D. The monotonicity property of cosine sums is also discussed. Further a generalization of renowned Theorem of Vietoris’ for the positivity of cosine and sine sums is established. Various new results which follo...

Using a 10 nm thick molybdenum oxide (MoO3-x) layer as a transparent and low barrier contact to p-CdTe, we demonstrate nanowire CdS-CdTe solar cells with a power conversion efficiency of 11% under front side illumination. Annealing the as-deposited MoO3 film in N2 resulted in a reduction of the cell's series resistance, from 9.97 Ω/cm(2) to 7.69 Ω/cm(2), and increase in efficiency from 9.9% to ...