Bluetooth Accelerometer Mouse

The reason of inventing such device is to overcome problem faced in using wired mouse and also the need of a surface for its movement. It applies even for the wireless mouse too since a surface is always a priority for its usage. This could be a hassle when users are left with limited space. In order to overcome this difficulty, this particular wireless accelerometer based mouse is developed

Componentwise Linearity of Powers of Cover Ideals

Let $G$ be a finite simple graph and $J(G)$ denote its vertex cover ideal in a polynomial ring over a field. Assume that $J(G)^{(k)}$ is its $k$-th symbolic power. In this paper, we give a criteria for cover ideals of vertex decomposable graphs to have the property that all their symbolic powers are not componentwise linear. Also, we give a necessary and sufficient condition on $G$ so that $J(G)^{(k)}$ is a componentwise linear ideal for some (equivalently, for all) $k \geq 2$ when $G$ is a graph such that $G \setminus N_G[A]$ has a simplicial vertex for any independent set $A$ of $G$. Using this result, we prove that $J(G)^{(k)}$ is a componentwise linear ideal for several classes of graphs for all $k \geq 2$. In particular, if $G$ is a bipartite graph, then $J(G)$ is a componentwise linear ideal if and only if $J(G)^k$ is a componentwise linear ideal for some (equivalently, for all) $k \geq 2$.Comment: arXiv admin note: text overlap with arXiv:1908.1057

Bounds for the regularity of product of edge ideals

Let $I$ and $J$ be edge ideals in a polynomial ring $R = \mathbb{K}[x_1,\ldots,x_n]$ with $I \subseteq J$. In this paper, we obtain a general upper and lower bound for the Castelnuovo-Mumford regularity of $IJ$ in terms of certain invariants associated with $I$ and $J$. Using these results, we explicitly compute the regularity of $IJ$ for several classes of edge ideals. Let $J_1,\ldots,J_d$ be edge ideals in a polynomial ring $R$ with $J_1 \subseteq \cdots \subseteq J_d$. Finally, we compute the precise expression for the regularity of $J_1 J_2\cdots J_d$ when $d \in \{3,4\}$ and $J_d$ is the edge ideal of complete graph.Comment: Pages 11, 1 figur

On-Chip Optical Transduction Scheme for Graphene Nano-Electro-Mechanical Systems in Silicon-Photonic Platform

We present a scheme for on-chip optical transduction of strain and displacement of Graphene-based Nano-Electro-Mechanical Systems (NEMS). A detailed numerical study on the feasibility of three silicon-photonic integrated circuit configurations is presented: Mach-Zehnder Interferometer(MZI), micro-ring resonator and ring-loaded MZI. An index-sensing based technique using a Mach-Zehnder Interferometer loaded with a ring resonator with a moderate Q-factor of 2400 can yield a sensitivity of 28 fm/sqrt(Hz), and 6.5E-6 %/sqrt(Hz) for displacement and strain respectively. Though any phase sensitive integrated photonic device could be used for optical transduction, here we show that optimal sensitivity is achievable by combining resonance with phase sensitivity

Self phase modulation in Highly nonlinear hydrogenated amorphous silicon

We study self phase modulation in submicron amorphous silicon-on-insulator waveguides. We extract both the real and imaginary part of the nonlinear parameter gamma from a 1 cm long waveguide with a cross-section of 500x220nm(2). The real and imaginary part of the nonlinear parameter are found to be 767W(-1)m(-1) and -28W(-1)m(-1) respectively. The figure of merit (FOM) is found to be 3.6 times larger than the FOM in crystalline silicon (c-Si)