Two finite words $u,v$ are 2-binomially equivalent if, for all words $x$ of length at most 2, the number of occurrences of $x$ as a (scattered) subword of $u$ is equal to the number of occurrences of $x$ in $v$. This notion is a refinement of the usual abelian equivalence. A 2-binomial square is a word $uv$ where $u$ and $v$ are 2-binomially equivalent. In this paper, considering pure morphic words, we prove that 2-binomial squares (resp. cubes) are avoidable over a 3-letter (resp. 2-letter) alphabet. The sizes of the alphabets are optimal.

M. Rao M. Rigo P. Salimov

The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose $K$ is a compact set in the complex plane and 0 belongs to the boundary $\partial K$. Let ${\cal A}(K)$ denote the space of all functions $f$ on $K$ such that $f$ is holomorphic in a neighborhood of $K$ and $f(0)=0$. Also for any given positive integer $m$, let ${\cal A}(m,K)$ denote the space of all $f$ such that $f$ is holomorphic in a neighborhood of $K$ and $f(0)=f^{\prime}(0)=...=f^{(m)}(0)=0$. Then ${\cal A}(m,K)$ is dense in ${\cal A}(K)$ under the supremum norm on $K$ provided that there exists a sector $W=\{r\hbox{\rm e}^{i\theta}; 0\leq r\leq\delta,\alpha\leq\theta\leq\beta\}$ such that $W\cap K=\{0\}$. (This is the well-known Poincare's external cone condition). We present various generalizations of this result in the context of higher dimensions replacing holomorphic with harmonic.

N. V. Rao

The electronic structure of In$_{2-x}$V$_x$O$_3$ ($x=0.08$) has been investigated using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). The V $2p$ core-level PES and XAS spectra revealed trivalent electronic state of the V ion, consistent with the substitution of the V ion for the In site. The V 3d partial density of states obtained by the resonant PES technique showed a sharp peak above the O $2p$ band. While the O $1s$ XAS spectrum of In$_{2-x}$V$_x$O$_3$ was similar to that of In$_2$O$_3$, there were differences in the In $3p$ and 3d XAS spectra between V-doped and pure In$_2$O$_3$. The observations give clear evidence for hybridization between the In conduction band and the V 3d orbitals in In$_{2-x}$V$_x$O$_3$.

M. Kobayashi Y. Ishida J. I. Hwang G. S. Song M. Takizawa A. Fujimori Y. Takeda T. Ohkochi T. Okane Y. Saitoh H. Yamagami Amita Gupta H. T. Cao K. V. Rao

Streamline tracing in conical hypersonic flows is essential for designing high-performance waverider and intake. Conventionally, the streamline equations are solved after obtaining the velocity field from the solution of the axisymmetric conical flow field. The hypersonic waverider shape is generated from the base conical flow field by repeatedly applying the streamline tracing approach along several planes. When exploring the design space for optimization of the waverider, streamline tracing can be computationally expensive. We provide a novel strategy where first the Taylor-Maccoll equations for the inviscid axisymmetric conical flowfield and the streamlines from the shock are solved for a wide range of cone angle and Mach number conditions resulting in an extensive database. The streamlines are parametrized by a third-order polynomial, and an Artificial Neural Network (ANN) is trained to predict the coefficients of the polynomial for arbitrary inputs of Mach number, cone angle, and streamline originating location on the shock . We apply this strategy to design a cone derived waverider and compare the geometry obtained with the standard conical waverider design method and the simplified waverider design method. The ANN technique is highly accurate, with a difference of 0.68% with the standard in the coordinates of the waverider. RANS computations show that the ANN derived waverider does not indicate severe flow spillage at the leading edge, which is observed in the waverider generated from the simplified method. The new ANN-based approach is 20 times faster than the conventional method.

Anagha G Rao Umesh Siddarth U S Srisha M V Rao

We have studied the magnetic properties of Ba_2FeNbO_6 and Ba_2MnNbO_6. it is seen that Ba_2FeNbO_6 is an antiferromagnet with a weak ferromagnetic behaviour at 5K while Ba_2MnNbO_6 shows two magnetic transitions one at 45 K and the other at 12K. Electron spin resonance (ESR) measurements at room temperature show that the Mn compound does not show any Jahn-Teller distortion. It is also seen that the Neel temperature of the A_2FeNbO_6 (A=Ba,Sr, BaSr) compounds do not vary significantly. However variations in the average A-site ionic radius influence the formation of short range correlations that persist above T_N.

N. Rama J. B. Philipp M. Opel K. Chandrasekaran V. Sankaranarayanan R. Gross M. S. Ramachandra Rao

We propose a computing model, the Two-Way Optical Interference Automata (2OIA), that makes use of the phenomenon of optical interference. We introduce this model to investigate the increase in power, in terms of language recognition, of a classical Deterministic Finite Automaton (DFA) when endowed with the facility of optical interference. The question is in the spirit of Two-Way Finite Automata With Quantum and Classical States (2QCFA) [A. Ambainis and J. Watrous, Two-way Finite Automata With Quantum and Classical States, Theoretical Computer Science, 287 (1), 299-311, (2002)] wherein the classical DFA is augmented with a quantum component of constant size. We test the power of 2OIA against the languages mentioned in the above paper. We give efficient 2OIA algorithms to recognize languages for which 2QCFA machines have been shown to exist, as well as languages whose status vis-a-vis 2QCFA has been posed as open questions. Finally we show the existence of a language that cannot be recognized by a 2OIA but can be recognized by an $O(n^3)$ space Turing machine.

M. V. Panduranga Rao

A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is an essential ingredient in the adiabaticity condition. In this paper we present a simple linear algebraic technique for obtaining a lower bound on the instantaneous gap even in such a situation. As an illustration, we investigate the adiabatic unordered search of van Dam et al. (How powerful is adiabatic quantum computation? Proc. IEEE FOCS, pp. 279-287, 2001) and Roland and Cerf (Physical Review A 65, 042308, 2002) when the non-zero entries of the diagonal final Hamiltonian are perturbed by a polynomial (in $\log N$, where $N$ is the length of the unordered list) amount. We use our technique to derive a bound on the running time of a local adiabatic schedule in terms of the minimum gap between the lowest two eigenvalues.

M. V. Panduranga Rao

Aperture synthesis radio telescopes generate images of celestial bodies from data obtained from several radio antennas. Placement of these antennas has always been a source of interesting problems. Often, several potentially contradictory objectives like good image quality and low infra-structural cost have to be satisfied simultaneously. In this paper, we propose a general Minimum Variance Method that focuses on obtaining good images in the presence of limiting situations. We show its versatility and goodness in three different situations: (a) Placing the antennas on the ground to get a target Gaussian UV distribution (b) Staggering the construction of a telescope in the event of staggered budgets and (c) Whenever available, using the mobility of antennas to obtain a high degree of fault tolerance.

M. V. Panduranga Rao Amrit Lal Ahuja Srinivasan Iyengar Sachin Lodha Kavita Iyer Ranu Khade Dinesh Mehta Balasz Nagy

Let $V$ be society whose members express preferences about two alternatives, indifference included. Identifying anonymous binary social choice functions with binary functions $f=f(k,m)$ defined over the integer triangular grid $G=\{(k,m)\in \mathbb{N}_0\times\mathbb{N}_0 : k+m\le |V|\} $, we show that every strategy-proof, anonymous social choice function can be described geometrically by listing, in a sequential manner, groups of segments of G, of equal (maximum possible) length, alternately horizontal and vertical, representative of preference profiles that determine the collective choice of one of the two alternatives. Indeed, we show that every function which is anonymous and strategy-proof can be described in terms of a sequence of nonnegative integers $(q_1, q_2, \cdots, q_s)$ corresponding to the cardinalities of the mentioned groups of segments. We also analyze the connections between our present representation with another of our earlier representations involving sequences of majority quotas. A Python code is available with the authors for the implementation of any such social choice function.

Achille Basile Surekha Rao K. P. S. Bhaskara Rao

Charged Particle Monitor (CPM) on-board the AstroSat satellite is an instrument designed to detect the flux of charged particles at the satellite location. A Cesium Iodide Thallium (CsI(Tl)) crystal is used with a Kapton window to detect protons with energies greater than 1 MeV. The ground calibration of CPM was done using gamma-rays from radioactive sources and protons from particle accelerators. Based on the ground calibration results, energy deposition above 1 MeV are accepted and particle counts are recorded. It is found that CPM counts are steady and the signal for the onset and exit of South Atlantic Anomaly (SAA) region are generated in a very reliable and stable manner.

A. R. Rao M. H. Patil Yash Bhargava Rakesh Khanna M. K. Hingar A. P. K. Kutty J. P. Malkar Rupal Basak S. Sreekumar Essy Samuel P. Priya P. Vinod D. Bhattacharya V. Bhalerao S. V. Vadawale N. P. S. Mithun R. Pandiyan K. Subbarao S. Seetha K. Suryanarayana Sarma