On sequences of positive integers having no pp terms in arithmetic progression

We use topological ideas to show that, assuming the conjecture of Erd\"(o)s on subsets of positive integers having no $p$ terms in arithmetic progression (A. P.), there must exist a subset $M_p$ of positive integers with no $p$ terms in A. P. with the property that among all such subsets, $M_p$ maximizes the sum of the reciprocals of its elements

High-temperature ferroelectricity in SrTiO3_{3} crystals

SrTiO$_{3}$ is known to be an incipient ferroelectric. It is thought that ferroelectric stability in SrTiO$_{3}$ is suppressed by a delicate competition with quantum fluctuation and antiferrodistortion. The ferroelectric phase can, however, be stabilized by doping, isotope manipulation and strain engineering etc. Till date ferroelectricity in SrTiO$_{3}$ thin films was observed to exist up to room temperature -- that was when the films were grown on specially engineered substrates using complex growth techniques. It was possible to write and erase ferroelectric domains on the specially engineered films at room temperature. Here, we show remarkably similar ferroelectric behavior in bulk (110) single crystals of SrTiO$_{3}$ with no special engineering well above room temperature using piezoresponse force microscopy. Hysteretic switching of local electric polarization was observed and electrically active domains could be written and erased using lithographic techniques at remarkably high temperatures up to $420K$.Comment: 10 pages, 3 figure

Comparison of Speech Activity Detection Techniques for Speaker Recognition

Speech activity detection (SAD) is an essential component for a variety of speech processing applications. It has been observed that performances of various speech based tasks are very much dependent on the efficiency of the SAD. In this paper, we have systematically reviewed some popular SAD techniques and their applications in speaker recognition. Speaker verification system using different SAD technique are experimentally evaluated on NIST speech corpora using Gaussian mixture model- universal background model (GMM-UBM) based classifier for clean and noisy conditions. It has been found that two Gaussian modeling based SAD is comparatively better than other SAD techniques for different types of noises.Comment: 7 pages, 2 figure

A complete characterization of the optimal unitary attacks in quantum cryptography with a refined optimality criteria involving the attackers Hilbert space only

Fuchs et al. [Phys. Rev. A, 1997] suggested an optimal attack on the BB84 protocol, where the necessary and sufficient condition for optimality involves the joint Hilbert space of the sender and the attacker. In this work, we propose a refined optimality criteria involving the Hilbert space of the attacker only. It reveals that the optimal (non-zero) overlaps between the attackers post-interactions states must be equal and numerically same as the difference between the fidelity and the disturbance at the receiving end. That amount turns out to be same as the reduction (factor) in Bell violation when estimated for the equivalent entanglement-based protocol. Further, a series of necessary and sufficient conditions unveil the structure of the optimal states which therefore are the only and all possible optimal interactions. We show that these optimal states are same as the outputs of an optimal phase-covariant cloner. We also demonstrate various methods to derive optimal unitary evolutions that an eavesdropper is interested to know in order to mount an optimal attack.Comment: Sequel to arXiv:1610.0714

Velocity of front propagation in the epidemic model A+B→2AA+B\to2A

We study front propagation in the irreversible epidemic model $A+B\to 2A$ in one dimension. Here, we allow the particles $A$ and $B$ to diffuse with rates $D_A$ and $D_B$, which, in general, may be different. We find analytic estimates for the front velocity by writing truncated master equation in a frame moving with the rightmost $A$ particle. The results obtained are in reasonable agreement with the simulation results and are amenable to systematic improvement. We also observe a crossover from the linear dependence of front velocity $V$ on $D_A$ for smaller values of $D_A$ to $V\propto \sqrt{D_A}$ for larger $D_A$, but numerically still significantly different from the mean field value. The deviations reflect the role of internal fluctuations which is neglected in the mean field description.Comment: 5 figure

Quantum Information splitting using a pair of GHZ states

We describe a protocol for quantum information splitting (QIS) of a restricted class of three-qubit states among three parties Alice, Bob and Charlie, using a pair of GHZ states as the quantum channel. There are two different forms of this three-qubit state that is used for QIS depending on the distribution of the particles among the three parties. There is also a special type of four-qubit state that can be used for QIS using the above channel. We explicitly construct the quantum channel, Alice's measurement basis and the analytic form of the unitary operations required by the receiver for such a purpose

On some results for meromorphic univalent functions having quasiconformal extension

We consider the class $\Sigma(p)$ of univalent meromorphic functions $f$ on \ID having simple pole at $z=p\in[0,1)$ with residue 1. Let $\Sigma_k(p)$ be the class of functions in $\Sigma(p)$ which have $k$-quasiconformal extension to the extended complex plane \sphere %with $q=\frac{1+k}{1-k}$ where $0\leq k < 1$. We first give a representation formula for functions in this class and using this formula we derive an asymptotic estimate of the Laurent coefficients for the functions in the class $\Sigma_k(p)$. Thereafter we give a sufficient condition for functions in $\Sigma(p)$ to belong in the class $\Sigma_k(p).$ Finally we obtain a sharp distortion result for functions in $\Sigma(p)$ and as a consequence, we get a distortion estimate for functions in $\Sigma_k(p).$Comment: 15 pages, This article is with a journa

Area distortion under meromorphic mappings with nonzero pole having quasiconformal extension

Let $\Sigma_k(p)$ be the class of univalent meromorphic functions defined on $\mathbb{D}$ with $k$-quasiconformal extension to the extended complex plane $\widehat{\mathbb{C}}$, where $0\leq k < 1$. Let $\Sigma_k^0(p)$ be the class of functions $f \in \Sigma_k(p)$ having expansion of the form $f(z)= 1/(z-p) + \sum_{n=1}^{\infty}b_n z^{n}$ on $\mathbb{D}$. In this article, we obtain sharp area distortion and weighted area distortion inequalities for functions in $\Sigma_k^0(p)$. As a consequence of the obtained results, we present a sharp estimate for the bounds of the Hilbert transform.Comment: 16 page

Revisiting Generalized Bertand's Postulate and Prime Gaps

It is a well-known fact that for any natural number $n$, there always exists a prime in $[n, 2n]$. Our aim in this note is to generalize this result to $[n, kn]$. A lower as well as an upper bound on the number of primes in $[n, kn]$ were conjectured by Mitra et al. [Arxiv 2009]. In 2016, Christian Axler provided a proof of the lower bound which is valid only when $n$ is greater than a very large threshold. In this paper, after almost a decade, we for the first time provide a direct proof of the lower bound that holds for all $n \geq 2$. Further, we show that the upper bound is a consequence of Firoozbakht's conjecture. Finally, we also prove a stronger version of the bounded gaps between primes

On a theorem of Eilenberg in simplicial Bredon-Illman cohomology with local coefficients

We prove simplicial version of a classical theorem of Eilenberg in the equivariant context and give an alternative description of the simplicial version of Bredon-Illman cohomology with local coefficients, as introduced in [15], to derive a spectral sequence.Comment: 16 page