We revisit Bjorken's model of spontaneous breakdown of Lorentz invariance. We show that the model possesses zero mass, spin zero (scalar) Nambu-Goldstone boson, in addition to the zero mass, spin one (vector) photon.

Raghunath Acharya

We present evidence that the number of string/$M$ theory vacua consistent with experiments is a finite number. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems.

Bobby S Acharya Michael R Douglas

We present a heuristic argument in support of the assertion that QCD will exhibit a mass gap, if the Callan-Symanzik function \beta(g) obeys the inequality \beta(g) < 0, for all g > 0.

Raghunath Acharya

We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$.

Raghunath Acharya

A continuum mechanical model of coupled dislocation based plasticity and fracture at finite deformation is proposed. Motivating questions and target applications of the model are sketched.

Amit Acharya

In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum distances of these codes are determined and a recursive formula for the weight of a general codeword in these codes is given.

Peter Beelen Prasant Singh

In this article, we consider the decoding problem of Grassmann codes using majority logic. We show that for two points of the Grassmannian, there exists a canonical path between these points once a complete flag is fixed. These paths are used to construct a large set of parity checks orthogonal on a coordinate of the code, resulting in a majority decoding algorithm.

Peter Beelen Prasant Singh

It is known that the region $V(s)$ of a simple polygon $P$, directly visible (illuminable) from an internal point $s$, is simply connected. Aronov et al. \cite{addpp981} established that the region $V_1(s)$ of a simple polygon visible from an internal point $s$ due to at most one diffuse reflection on the boundary of the polygon $P$, is also simply connected. In this paper we establish that the region $V_2(s)$, visible from $s$ due to at most two diffuse reflections may be multiply connected; we demonstrate the construction of an $n$-sided simple polygon with a point $s$ inside it so that and the region of $P$ visible from $s$ after at most two diffuse reflections is multiple connected.

Sudebkumar Prasant Pal Dilip Sarkar

In this paper we consider faultfree tromino tilings of rectangles and characterize rectangles that admit such tilings. We introduce the notion of {\it crossing numbers} for tilings and derive bounds on the crossing numbers of faultfree tilings. We develop an iterative scheme for generating faultfree tromino tilings for rectangles and derive the closed form expression for the exact number of faultfree tromino tilings for $4\times3t$ rectangles and the exact generating function for $5\times 3t$ rectangles, $t\geq 1$. Our iterative scheme generalizes to arbitrary rectangles; for $6\times 6t$ and $7\times 6t$ rectangles, $t\geq 1$, we derive generating functions for estimating lower bounds on the number of faultfree tilings. We also derive an upper bound on the number of tromino tilings of an $m\times n$ rectangle, where $3|mn$ and $m,n>0$.

Mridul Aanjaneya Sudebkumar Prasant Pal

We develop protocols for preparing a GHZ state and, in general,a pure multi-partite maximally entangled state in a distributed network with apriori quantum entanglement between agents using classical communication and local operations. We investigate and characterize the minimal combinatorics of the sharing of EPR pairs required amongst agents in a network for the creation of multi-partite entanglement. We also characterize the minimal combinatorics of agents in the creation of pure maximal multi-partite entanglement amongst the set $N$ of $n$ agents in a network using apriori multi-partite entanglement states amongst subsets of $N$. We propose protocols for establishing multi-partite entanglement in the above cases.

Sudhir Kumar Singh Somesh Kumar Sudebkumar Prasant Pal