On Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers

Submitted to Journal of Number Theory.This paper focuses on the number of partitions of a positive integer $n$ into $k$ positive summands, where $k$ is an integer between $1$ and $n$. Recently some upper bounds were reported for this number in [Merca14]. Here, it is shown that these bounds are not as tight as an earlier upper bound proved in [Andrews76-1] for $k\le 0.42n$. A new upper bound for the number of partitions of $n$ into $k$ summands is given, and shown to be tighter than the upper bound in [Merca14] when $k$ is between $O(\frac{\sqrt{n}}{\ln n})$ and $n-O(\frac{\sqrt{n}}{\ln n})$. It is further shown that the new upper bound is also tighter than two other upper bounds previously reported in~[Andrews76-1] and [Colman82]. A generalization of this upper bound to number of partitions of $n$ into at most $k$ summands is also presented

Ordinal covering using block designs

A frequently encountered problem in peer review systems is to facilitate pairwise comparisons of a given set of documents by as few experts as possible. In [7], it was shown that, if each expert is assigned to review k documents then ⌈n(n-1)/k(k-1)⌉ experts are necessary and ⌈n(2n-k)/k 2⌉ experts are sufficient to cover all n(n-1)/2 pairs of n documents. In this paper, we show that, if √n ≤ k ≤ n/2 then the upper bound can be improved using a new assignnment method based on a particular family of balanced incomplete block designs. Specifically, the new method uses ⌈n(n+k)/k2⌉ experts where n/k is a prime power, n divides k2, and √n ≤ k ≤ n/2. When k = √n , this new method uses the minimum number of experts possible and for all other values of k, where √n < k ≤ n/2, the new upper bound is tighter than the general upper bound given in [7]. ©2010 IEEE

Thin-film ZnO charge-trapping memory cell grown in a single ALD step

Cataloged from PDF version of article.A thin-film ZnO-based single-transistor memory cell with a gate stack deposited in a single atomic layer deposition step is demonstrated. Thin-film ZnO is used as channel material and charge-trapping layer for the first time. The extracted mobility and subthreshold slope of the thin-film device are 23 cm2/V · s and 720 mV/dec, respectively. The memory effect is verified by a 2.35-V hysteresis in the Idrain–Vgate curve. Physics-based TCAD simulations show very good agreement with the experimental results providing insight to the charge-trapping physics

A plasmonic enhanced photodetector based on silicon nanocrystals obtained through laser ablation

Cataloged from PDF version of article.We present a proof-of-concept photodetector which is sensitive in the visible spectrum. Silicon nanocrystals (Si-NCs) obtained by laser ablation are used as the active absorption region. Si-NC films are formed from a polymeric dispersion. The films are sandwiched between thin insulating films to reduce the electrical leakage current. Furthermore, Ag nanoparticles are integrated with the photodetector to enhance the visible response using plasmonic effects. The measured photocurrent is resonantly enhanced, which is explained in terms of enhanced local fields caused by localized plasmons. The UV-vis spectrum of Ag nanoparticles is also measured to verify the resonance. © 2012 IOP Publishing Ltd

Dynamic Control of Photoresponse in ZnO-Based Thin-Film Transistors in the Visible Spectrum

Cataloged from PDF version of article.We present ZnO-channel thin-film transistors with actively tunable photocurrent in the visible spectrum, although ZnO band edge is in the ultraviolet. ZnO channel is deposited by atomic layer deposition technique at a low temperature (80 C), which is known to introduce deep level traps within the forbidden band of ZnO. The gate bias dynamically modifies the occupancy probability of these trap states by controlling the depletion region in the ZnO channel. Unoccupied trap states enable the absorption of the photons with lower energies than the bandgap of ZnO. Photoresponse to visible light is controlled by the applied voltage bias at the gate terminal

On The Number of Unlabeled Bipartite Graphs

This paper describes a result that has been obtained in joint work with Abdullah Atmaca of Bilkent University, Ankara, TurkeyLet $I$ and $O$ denote two sets of vertices, where $I\cap O =\Phi$, $|I| = n$, $|O| = r$, and $B_u(n,r)$ denote the set of unlabeled graphs whose edges connect vertices in $I$ and $O$. It is shown that the following two-sided equality holds. $\displaystyle \frac{\binom{r+2^{n}-1}{r}}{n!} \le |B_u(n,r)| \le 2\frac{\binom{r+2^{n}-1}{r}}{n!}

ZnO based optical modulator in the visible wavelengths

In order to demonstrate tunable absorption characteristics of ZnO, photodetection properties of ZnO based thin-film transistors are investigated. By controlling the occupancy of the trap states, the optical absorption coefficient of ZnO in the visible light spectrum is actively tuned with gate bias. An order of magnitude change of absorption coefficient is achieved. An optical modulator is proposed exploiting such tunable absorption mechanism. © 2013 SPIE