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R. Balasubramanian

Publications and source records attributed to R. Balasubramanian.

At least 37 records · Page 2Linked to original sources
arXiv2013

On a Theorem of Deshouillers and Freiman

The study of `structure' on subsets of abelian groups, with small `doubling constant', has been well studied in the last fifty years, from the time Freiman initiated the subject. In \cite{DF} Deshouillers and Freiman establish a structure theorem for subsets of $\n$ with small doubling constant. In the current article we provide an alternate proof of one of the main theorem of \cite{DF}. Also our proof leads to slight improvement of the theorems in \cite{DF}.

math.CO↗
arXiv2012

Fractional Order Phase Shaper Design with Routh's Criterion for Iso-damped Control System

Phase curve of an open loop system is flat in nature if the derivative of phase with respect to frequency is zero. With a flat phase curve, the corresponding closed-loop system exhibits an iso-damped property i.e. maintains constant overshoot with the change of gain and with other parametric variations. In recent past application, fractional order (FO) phase shapers have been proposed by contemporary researchers to achieve enhanced parametric robustness. In this paper, a simple Routh tabulation based methodology is proposed to design an appropriate FO phase shaper to achieve phase flattening in a control loop, comprising a system, controlled by a classical PID controller. The method is demonstrated using MATLAB simulation of a second order DC motor plant and also a first order with time delay system.

eess.SY↗
arXiv2012

Design of a Fractional Order Phase Shaper for Iso-damped Control of a PHWR under Step-back Condition

Phase shaping using fractional order (FO) phase shapers has been proposed by many contemporary researchers as a means of producing systems with iso-damped closed loop response due to a stepped variation in input. Such systems, with the closed loop damping remaining invariant to gain changes can be used to produce dead-beat step response with only rise time varying with gain. This technique is used to achieve an active step-back in a Pressurized Heavy Water Reactor (PHWR) where it is desired to change the reactor power to a pre-determined value within a short interval keeping the power undershoot as low as possible. This paper puts forward an approach as an alternative for the present day practice of a passive step-back mechanism where the control rods are allowed to drop during a step-back action by gravity, with release of electromagnetic clutches. The reactor under a step-back condition is identified as a system using practical test data and a suitable Proportional plus Integral plus Derivative (PID) controller is designed for it. Then the combined plant is augmented with a phase shaper to achieve a dead-beat response in terms of power drop. The fact that the identified static gain of the system depends on the initial power level at which a step-back is initiated, makes this application particularly suited for using a FO phase shaper. In this paper, a model of a nuclear reactor is developed for a control rod drop scenario involving rapid power reduction in a 500MWe Canadian Deuterium Uranium (CANDU) reactor using AutoRegressive Exogenous (ARX) algorithm. The system identification and reduced order modeling are developed from practical test data. For closed loop active control of the identified reactor model, the fractional order phase shaper along with a PID controller is shown to perform better than the present Reactor Regulating System (RRS) due to its iso-damped nature.

math.OC↗
arXiv2012

Higher Residue Symbol

Given a prime number $l$ and a finite set of integers $S=\{a_1,...,a_m\}$ we find out the exact degree of the extension $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$. We give an algorithm to compute this degree and then further relate it to the study of the distribution of primes $p$ for which all of $a_i$ assume a preassigned $l^{th}$ power residue simultaneously. Also we relate this degree to rank of a matrix obtained from $S=\{a_1,...,a_m\}$. This latter arguement enable one to describe the degree $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$ in much simpler terms.

math.NT↗
arXiv2011

Zerofree region for exponenetial sums

We consider the following two closed sets in $C^n$. One is the diagonal D given by $ (z, z, z,...z_)$. The other is $A = \{(z_1,z_2,z_3,...z_n):.$ $.e^{z_1} + e^{z_2} +e^{z_3} +...+ e^{z_n}=0\}$. Clearly $D \cap A$ is empty. One can ask what is the distance between them. In this connection, Stolarsky [1] proved that the distance $d$ is given by $d^2 = (\log \ n)^2 + O (1)$. Some simple calculations will make one believe that the point $(k, 0, 0,..0)$ with $k = \log \ (n-1) + πi$ which lies on $A$ is one of the closest point to the diagaonal. We prove that this is indeed the case, atleast for sufficiently large $n$. This gives $d^2 = |k|^2 (1-1/n)$.

math.NT↗
arXiv2011

Higher residue symbols

Given a prime number $l$ and a finite set of integers $S=\{a_1,...,a_m\}$ we find out the exact degree of the extension $\mathbb{Q}(a_1^{\frac{1}{l}},...,a_m^{\frac{1}{l}})/\mathbb{Q}$. We give two different ways to compute this degree. The first method is using ramifiaction theory. The second proof follwos from our study of the distribution of primes $p$ for which all of $a_i$ are $l^{th}$ power residue simultaneously.

math.NT↗
arXiv2010

Implementation of a Cloud Data Server (CDS) for Providing Secure Service in E-Business

Cloud Data Servers is the novel approach for providing secure service to e-business .Millions of users are surfing the Cloud for various purposes, therefore they need highly safe and persistent services. Usually hackers target particular Operating Systems or a Particular Controller. Inspiteof several ongoing researches Conventional Web Servers and its Intrusion Detection System might not be able to detect such attacks. So we implement a Cloud Data Server with Session Controller Architecture using Redundancy and Disconnected Data Access Mechanism. In this paper, we generate the hash code using MD5 algorithm. With the help of which we can circumvent even the attacks, which are undefined by traditional Systems .we implement Cloud Data Sever using Java and Hash Code backup Management using My SQL. Here we Implement AES Algorithm for providing more Security for the hash Code. The CDS using the Virtual Controller controls and monitors the Connections and modifications of the page so as to prevent malicious users from hacking the website. In the proposed approach an activity analyzer takes care of intimating the administrator about possible intrusions and the counter measures required to tackle them. The efficiency ratio of our approach is 98.21% compared with similar approaches.

cs.DC↗
arXiv2008

A new Contrast Based Image Fusion using Wavelet Packets

Image Fusion, a technique which combines complimentary information from different images of the same scene so that the fused image is more suitable for segmentation, feature extraction, object recognition and Human Visual System. In this paper, a simple yet efficient algorithm is presented based on contrast using wavelet packet decomposition. First, all the source images are decomposed into low and high frequency sub-bands and then fusion of high frequency sub-bands is done by the means of Directive Contrast. Now, inverse wavelet packet transform is performed to reconstruct the fused image. The performance of the algorithm is carried out by the comparison made between proposed and existing algorithm.

cs.IT↗
arXiv2006

A template bank to search for gravitational waves from inspiralling compact binaries I: physical models

Gravitational waves from coalescing compact binaries are searched using the matched filtering technique. As the model waveform depends on a number of parameters, it is necessary to filter the data through a template bank covering the astrophysically interesting region of the parameter space. The choice of templates is defined by the maximum allowed drop in signal-to-noise ratio due to the discreteness of the template bank. In this paper we describe the template-bank algorithm that was used in the analysis of data from the Laser Interferometer Gravitational Wave Observatory (LIGO) and GEO 600 detectors to search for signals from binaries consisting of non-spinning compact objects. Using Monte-Carlo simulations, we study the efficiency of the bank and show that its performance is satisfactory for the design sensitivity curves of ground-based interferometric gravitational wave detectors GEO 600, initial LIGO, advanced LIGO and Virgo. The bank is efficient to search for various compact binaries such as binary primordial black holes, binary neutron stars, binary black holes, as well as a mixed binary consisting of a non-spinning black hole and a neutron star.

gr-qc↗
arXiv2006

Upper Bounds for the Davenport Constant

We prove that for all but a certain number of abelian groups of order n its Davenport constant is atmost n/k+k-1 for k=1,2,..,7. For groups of order three we improve on the existing bound involving the Alon-Dubiner constant.

math.NT↗
arXiv2005

Sum-free set in finite abelian groups

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. In this paper we shall characterise the largest possible sum-free subsets of G in case the order of G is only divisible by primes which are congruent to 1 modulo 3. The result is based on a recent result of Ben Green and Imre Ruzsa.

math.NT↗
arXiv2005

Asymptotic formula for sum-free sets in abelian groups

Let A be a subset of a finite abelian group G. We say that A is sum-free if there is no solution of the equation x + y = z, with x, y, z belonging to the set A. Let SF(G) denotes the set of all sum-free subets of $G$ and $σ(G)$ denotes the number $ n^{-1}(\log_2 |SF(G)|) $. In this article we shall improve the error term in the asymptotic formula of $σ(G)$ which was obtained recently by Ben Green and Ruzsa. The methods used are a slight refinement of methods developed by Ben Green and Ruzsa.

math.NT↗
arXiv2005

GEO600 Online Detector Characterization System

A world-wide network of interferometric gravitational wave detectors is currently operational. The detectors in the network are still in their commissioning phase and are expected to achieve their design sensitivity over the next year or so. Each detector is a complex instrument involving many subsystems and each subsystem is a source of noise at the output of the detector. Therefore, in addition to recording the main gravitational wave data channel at the output of the interferometer, the state of each detector subsystem is monitored and recorded. This subsidiary data is both large in volume as well as complex in nature. We require an online monitoring and analysis tool which can process all the data channels for various noise artefacts and summarize the results of the analysis in a manner that can be accessed and interpreted conveniently. In this paper we describe the GEO600 Online Detector Characterization System (GODCS), which is the tool that is being used to monitor the output of the GEO600 gravitational wave detector situated near Hannover in Germany. We describe the various algorithms that we use and how the results of several algorithms can be combined to make meaningful statements about the state of the detector. This paper will be useful to researchers in the area of gravitational wave astronomy as a record of the various analyses and checks carried out to ensure the quality and reliability of the data before searching the data for the presence of gravitational waves.

gr-qc↗
arXiv1999

Time-frequency detection of Gravitational Waves

We present a time-frequency method to detect gravitational wave signals in interferometric data. This robust method can detect signals from poorly modeled and unmodeled sources. We evaluate the method on simulated data containing noise and signal components. The noise component approximates initial LIGO interferometer noise. The signal components have the time and frequency characteristics postulated by Flanagan and Hughes for binary black hole coalescence. The signals correspond to binaries with total masses between $45 M_\odot$ to $70 M_\odot$ and with (optimal filter) signal-to-noise ratios of 7 to 12. The method is implementable in real time, and achieves a coincident false alarm rate for two detectors $\approx$ 1 per 475 years. At this false alarm rate, the single detector false dismissal rate for our signal model is as low as 5.3% at an SNR of 10. We expect to obtain similar or better detection rates with this method for any signal of similar power that satisfies certain adiabaticity criteria. Because optimal filtering requires knowledge of the signal waveform to high precision, we argue that this method is likely to detect signals that are undetectable by optimal filtering, which is at present the best developed detection method for transient sources of gravitational waves.

gr-qc↗
arXiv1997

Gravitational Waves from coalescing binaries: Estimation of parameters

The paper presents a statistical model which reproduces the results of Monte Carlo simulations to estimate the parameters of the gravitational wave signal from a coalesing binary system. The model however is quite general and would be useful in other parameter estimation problems.

gr-qc↗
arXiv1995

Estimation of parameters of gravitational waves from coalescing binaries

In this paper we deal with the measurement of the parameters of the gravitational wave signal emitted by a coalescing binary signal. We present the results of Monte Carlo simulations carried out for the case of the initial LIGO, incorporating the first post-Newtonian corrections into the waveform. Using the parameters so determined, we estimate the direction to the source. We stress the use of the time-of-coalescence rather than the time-of-arrival of the signal to determine the direction of the source. We show that this can considerably reduce the errors in the determination of the direction of the source.

gr-qc↗
arXiv1995

Gravitational waves from coalescing binaries: detection strategies and Monte Carlo estimation of parameters

The paper deals with issues pertaining the detection of gravitational waves from coalescing binaries. We introduce the application of differential geometry to the problem of optimal detection of the `chirp signal'. We have also carried out extensive Monte Carlo simulations to understand the errors in the estimation of parameters of the binary system. We find that the errors are much more than those predicted by the covariance matrix even at a high SNR of 10-15. We also introduce the idea of using the instant of coalescence rather than the time of arrival to determine the direction to the source.

gr-qc↗