Abstract:
Aichholzer et al. [{\it Graphs and Combinatorics}, Vol. 23, 481-507, 2007] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number $\psi(n)$ satisfies, $\frac{3}{4}\lfloor\frac{n}{4}\rfloor\leq \psi(n)\leq\lceil\frac{n}{4}\rceil$. In this paper we prove that $\psi(13)=3$, which immediately improves the upper bound on $\psi(n)$ to $\lceil\frac{3n}{13}\rceil$, thus answering a question posed by Aichholzer et al. in the same paper.

Abstract:
Harborth [{\it Elemente der Mathematik}, Vol. 33 (5), 116--118, 1978] proved that every set of 10 points in the plane, no three on a line, contains an empty convex pentagon. From this it follows that the number of disjoint empty convex pentagons in any set of $n$ points in the plane is least $\lfloor\frac{n}{10}\rfloor$. In this paper we prove that every set of 19 points in the plane, no three on a line, contains two disjoint empty convex pentagons. We also show that any set of $2m+9$ points in the plane, where $m$ is a positive integer, can be subdivided into three disjoint convex regions, two of which contains $m$ points each, and another contains a set of 9 points containing an empty convex pentagon. Combining these two results, we obtain non-trivial lower bounds on the number of disjoint empty convex pentagons in planar points sets. We show that the number of disjoint empty convex pentagons in any set of $n$ points in the plane, no three on a line, is at least $\lfloor\frac{5n}{47}\rfloor$. This bound has been further improved to $\frac{3n-1}{28}$ for infinitely many $n$.

Abstract:
Let $E(k, \ell)$ denote the smallest integer such that any set of at least $E(k, \ell)$ points in the plane, no three on a line, contains either an empty convex polygon with $k$ vertices or an empty pseudo-triangle with $\ell$ vertices. The existence of $E(k, \ell)$ for positive integers $k, \ell\geq 3$, is the consequence of a result proved by Valtr [Discrete and Computational Geometry, Vol. 37, 565--576, 2007]. In this paper, following a series of new results about the existence of empty pseudo-triangles in point sets with triangular convex hulls, we determine the exact values of $E(k, 5)$ and $E(5, \ell)$, and prove bounds on $E(k, 6)$ and $E(6, \ell)$, for $k, \ell\geq 3$. By dropping the emptiness condition, we define another related quantity $F(k, \ell)$, which is the smallest integer such that any set of at least $F(k, \ell)$ points in the plane, no three on a line, contains a convex polygon with $k$ vertices or a pseudo-triangle with $\ell$ vertices. Extending a result of Bisztriczky and T\'oth [Discrete Geometry, Marcel Dekker, 49--58, 2003], we obtain the exact values of $F(k, 5)$ and $F(k, 6)$, and obtain non-trivial bounds on $F(k, 7)$.

Abstract:
The object of the paper is to see the effect of small stochastic parametric perturbation on a nonlinear interacting systemexhibiting Hopf bifurcation. The method is based on the technique of Markov diffusion approximation.

Abstract:
This paper analyzes the stability of carbon nanotube(CNT) and graphene nanoribbon (GNR) based interconnects forfuture VLSI technology node. We have analyzed both Bode andNyquist stability of single-wall CNT, multi-wall CNT, GNR, andcopper based interconnect systems. The stability analysis isperformed for different interconnect systems for 16nm ITRStechnology node. It is shown that densely packed single-wall CNTbundle based interconnect has highest gain margin for a widerange of interconnect length (1 m to 100 m) as compared to theother interconnect systems.

Abstract:
The work in this paper designs the basic logic circuits using the carbon nanotube field effect transistor (CNTFET). CNTFET is a novel device that is projected to outperform scaled CMOS technologies. CNTFET-based devices offer high mobility for near-ballistic transport, high carrier velocity for fast switching, as well as better electrostatic control due to the quasi one-dimensional structure of carbon nanotubes. CNTFET utilizes a semiconducting carbon nanotube (CNT) channel controlled by isolated electrostatic gates. It demonstrates p-type or n-type switching behavior depending upon the polarity-gate voltage. In this paper ambipolar CNTFETs are used to design basic logic circuits. The datapath logic blocks like half and full-adders are designed and their performances have been investigated.

Abstract:
We explore a material design strategy to optimize the thermoelectric power factor. The approach is based on screening the band structure changes upon a controlled volume change. The methodology is applied to the binary silicides and germanides. We first confirm the effect in antifluorite Mg2Si and Mg2Ge where an increased power factor by alloying with Mg2Sn is experimentally established. Within a high-throughput formalism we identify six previously unreported binaries that exhibit an improvement in their transport properties with volume. Among these, hexagonal MoSi2 and orthorhombic Ca2Si and Ca2Ge have the highest increment in zT with volume. We then perform super-cell calculations on special quasi-random structures to investigate the possibility of obtaining thermodynamically stable alloy systems which would produce the necessary volume changes. We find that for Ca2Si and Ca2Ge the solid solutions with the isostructural Ca2Sn readily forms even at low temperatures.

Abstract:
Given a set of $n$ weighted points on the $x$-$y$ plane, we want to find a step function consisting of $k$ horizontal steps such that the maximum vertical weighted distance from any point to a step is minimized. We solve this problem in $O(n)$ time when $k$ is a constant. Our approach relies on the prune-and-search technique, and can be adapted to design similar linear time algorithms to solve the line-constrained k-center problem and the size-$k$ histogram construction problem as well.

Abstract:
Considering the properties of the carbon nano tubes (CNT), their inclusion into the polymer matrix vastly increasesthe properties of the resultant composite. However, this is not the case due to the poor interfacial adhesion of the CNTand the polymer matrix. The present approach focuses on increasing the interaction between the polymer matrix andthe CNT through the chemical modification of the CNT resulting in allyl ester functionalized carbon nanotubes (ACNT)and silane functionalized carbon nano tubes (SCNT) which are capable of reacting with the polymer matrix duringthe curing reaction. The addition of ACNT/SCNT into unsaturated polyester resin (UPR) resulted in the improvementof the electrical properties of resulted nanocomposites in comparison to the CNT. The surface resistivity, volumeresistivity, dielectric strength, dry arc resistivity, and the comparative tracking index of the nanocomposites weresignificantly improved in comparison to CNT. The chemical modification of CNT was confirmed via spectroscopy.

Abstract:
Background: There are very few published reports of upper cervical spine injuries from our country and there is a heavy bias towards operative treatment of these injuries. We present below our experience of upper cervical injuries over the last four years. Materials and Methods: Twenty eight patients (20 males, 8 females) with upper cervical spine injury (including Occiput, Atlas and Axis) were treated and were followed-up for an average of 11.2 months. The data was analyzed retrospectively with regards to the location and type of injury, the treatment offered (conservative or operative) as well as the final clinical and radiological outcome. Results: The clinico-radiological outcome of treatment of these injuries is mostly very good with few complications. Other than a single case of mortality due to associated head injury there were no major complications. Conclusion: Management of these patients needs a proper evaluation to arrive at the type of injury and prompt conservative or operative treatment. Treatment is usually safe and effective with good clinical and radiological outcome.