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Biswaranjan Behera

Publications and source records attributed to Biswaranjan Behera.

16 recordsLinked to original sources
arXiv2023

Neutrino Phenomenology from Democratic Approach

In this article, we derive the tiny neutrino masses and mixings from the democratic and diagonal texture approach, which consistent with the recent experimental oscillation data. The unitary rotation matrices, which diagonalize the neutrino mass matrices are obtained by a specific parametrization of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix. From which, we tried to calculate all three mixing angles as well as the Dirac CP-violating phase interms of model mixing parameters. In particular, the deviation from the tribimaximal mixing is explained in this model. Along with the Jarlskog parameter in terms of model parameter and neutrino-less double beta decay (NDBD) has been discussed briefly.

hep-ph↗
arXiv2021

Uniform boundedness of the Fourier partial sum operators on the weighted spaces of local fields

Let $S_n f$ be the $n$th partial sum of the Fourier series of a function $f$ in $L^1(\D)$, where $\D$ is the ring of integers of a local field $K$. For $1<p<\infty$, we characterize all weight functions $w$ so that the partial sum operators $S_n$, $n\geq 0$, are uniformly bounded on the weighted space $L^p(\D, w)$ and that $S_n f$ converges to $f$ in $L^p(\D,w)$. This includes the case where $K$ is a $p$-adic number field or a field of formal Laurent series $\mathbb{F}_q((X))$ over a finite field $\mathbb{F}_q$, and in particular, when $\D$ is the Walsh-Paley or dyadic group $2^ω$. As an application, in a local field $K$ of positive characteristic, we provide a necessary and sufficient condition on a function $φ\in L^2(K)$ for which the collection of translates of $φ$ forms a Schauder basis for its closed linear span. Moreover, we establish sharp bounds for the Hardy-Littlewood maximal operator.

math.FA↗
arXiv2020

Pointwise Convergence of Fourier Series on the Ring of Integers of Local Fields with an Application to Gabor Systems

We construct a simple example of an integrable function on the ring of integers of the $p$-adic field $\Q_p$ having an almost everywhere divergent Fourier series. On the other hand, we prove the pointwise convergence of the Fourier series of functions in $L^p(\D,w)$, $1<p<\infty$, where $\D$ is the ring of integers of a local field $K$ and $w$ is a weight in the Muckenhoupt $A_p$ class. This result includes, as special cases, when $\D$ is the ring of integers of $\Q_p$ or the field $\mathbb{F}_q((X))$ of formal Laurent series over a finite field $\mathbb{F}_q$, and in particular, when $\D$ is the Walsh-Paley or dyadic group $2^ω$. To achieve this, we establish a weighted estimate for the maximal operator corresponding to the Fourier partial sum operators for functions in $L^p(\D,w)$. As an application, we characterize the Schauder basis property of the Gabor systems in a local field $K$ of positive characteristic in terms of the $A_2$ weights on $\D\times\D$ and the Zak transform $Zg$ of the window function $g$ that generates the Gabor system. Some examples are given to illustrate this result. In particular, we construct an example of a Gabor system which is complete and minimal, but fails to be a Schauder basis for $L^2(K)$.

math.FA↗
arXiv2017

Tracking Detector Performance and Data Quality in the NOvA Experiment

NOvA is a long-baseline neutrino oscillation experiment. It uses the NuMI beam from Fermilab and two sampling calorimeter detectors located off-axis from the beam. The NOvA experiment measures the rate of electron-neutrino appearance in the almost pure muon-neutrino NuMI beam, with the data measured at the Near Detector being used to accurately determine the expected rate at the Far Detector. It is very important to have automated and accurate monitoring of the data recorded by the detectors so any hardware, DAQ or beam issues arising in the 344k (20k) channels of the Far (Near) detector which could affect the quality of the data taking are determined. This paper will cover the techniques and detector monitoring systems in various stages of data taking.

physics.ins-det↗
arXiv2017

Status of a Deep Learning Based Measurement of the Inclusive Muon Neutrino Charged-current Cross Section in the NOvA Near Detector

NOvA is a long-baseline neutrino oscillation experiment. It uses the NuMI beam from Fermilab and two sampling calorimeter detectors placed off-axis from the beam. The 293 ton Near Detector measures the unoscillated neutrino energy spectrum, which can be used to predict the neutrino energy spectrum observed at the 14 kton Far Detector. The Near Detector also provides an excellent opportunity to measure neutrino interaction cross sections with high statistics, which will benefit current and future long-baseline neutrino oscillation experiments. This analysis implements new algorithms to identify $ν_μ$ charge-current events by using visual deep learning tools such as convolutional neural networks. We present the status of a measurement of the inclusive $ν_μ$ CC cross section in the NOvA Near Detector.

hep-ex↗
arXiv2017

Event Reconstruction in the NOvA Experiment

The NOvA experiment observes oscillations in two channels (electron-neutrino appearance and muon-neutrino disappearance) using a predominantly muon-neutrino NuMI beam. The Near Detector records multiple overlapping neutrino interactions in each event and the Far Detector has a large background of cosmic rays due to being located on the surface. The oscillation analyses rely on the accurate reconstruction of neutrino interactions in order to precisely measure the neutrino energy and identify the neutrino flavor and interaction mode. Similarly, measurements of neutrino cross sections using the Near Detector require accurate identification of the particle content of each interaction. A series of pattern recognition techniques have been developed to split event records into individual spatially and temporally separated interactions, to estimate the interaction vertex, and to isolate and classify individual particles within the event. This combination of methods to achieve full event reconstruction in the NOvA detectors has discussed.

physics.ins-det↗
arXiv2016

Affine, quasi-affine and co-affine frames on local fields of positive characteristic

The concept of quasi-affine frame in Euclidean spaces was introduced to obtain translation invariance of the discrete wavelet transform. We extend this concept to a local field $K$ of positive characteristic. We show that the affine system generated by a finite number of functions is an affine frame if and only the corresponding quasi-affine system is a quasi-affine frame. In such a case the exact frame bounds are equal. This result is obtained by using the properties of an operator associated with two such affine systems. We characterize the translation invariance of such an operator. A related concept is that of co-affine system. We show that there do not exist any co-affine frame in $L^2(K)$.

math.FA↗
arXiv2013

Characterization of wavelets and MRA wavelets on local fields of positive characteristic

We provide a characterization of wavelets on local fields of positive characteristic based on results on affine and quasi affine frames. This result generalizes the characterization of wavelets on Euclidean spaces by means of two basic equations. We also give another characterization of wavelets. Further, all wavelets which are associated with a multiresolution analysis on a such a local field are also characterized.

math.FA↗
arXiv2011

Wavelet packets and wavelet frame packets on local fields

Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this lemma we have constructed the wavelet packets associated with such MRAs. We show that these wavelet packets generate an orthonormal basis by translations only. We also prove an analogue of splitting lemma for frames and construct the wavelet frame packets in this setting.

math.FA↗
arXiv2002

Estimation of dimension functions of band-limited wavelets

The dimension function D_psi of a band-limited wavelet is bounded by n if the support of its Fourier transform is contained in the interval [-{2^(n+2)/3}pi, {2^(n+2)/3}pi]. For each positive integer n and for each epsilon > 0, we construct a wavelet psi with support of $\hat psi$ contained in [-{2^(n+2)/3}pi, {2^(n+2)/3}pi + epsilon] such that D_psi > n on a set of positive measure, which proves that [-{2^(n+2)/3}pi, {2^(n+2)/3}pi] is the largest symmetric interval for estimating the dimension function by n.

math.FA↗
arXiv2002

Large classes of minimally supported frequency wavelets of L^2(\R) and H^2(\R)

We introduce a method to construct large classes of MSF wavelets of the Hardy space H^2(\R) and symmetric MSF wavelets of L^2(\R), and discuss the classification of such sets. As application, we show that there are uncountably many wavelet sets of L^2(\R) and H^2(\R). We also enumerate all symmetric wavelets of L^2(\R) with at most three intervals in the positive axis as well as 3-interval wavelet sets of H^2(\R). Finally, we construct families of MSF wavelets of L^2(\R) whose Fourier transform does not vanish in any neighbourhood of the origin.

math.FA↗
arXiv2002

Non-MSF wavelets for the Hardy space H^2(\R)

We prove three results on wavelets for the Hardy space H^2(\R). All wavelets constructed so far for H^2(\R) are MSF wavelets. We construct a family of H^2-wavelets which are not MSF. An equivalence relation on H^2-wavelets is introduced and it is shown that the corresponding equivalence classes are non-empty. Finally, we construct a family of H^2-wavelets with Fourier transform discontinuous at the origin.

math.FA↗
arXiv2002

Multiwavelet packets and frame packets of $L^2({\mathbb R}^d)

The orthonormal basis generated by a wavelet of $L^2(\mathbb R)$ has poor frequency localization. To overcome this disadvantage Coifman, Meyer, and Wickerhauser constructed wavelet packets. We extend this concept to the higher dimensions where we consider arbitrary dilation matrices. The resulting basis of $L^2({\mathbb R}^d)$ is called the multiwavelet packet basis. The concept of wavelet frame packet is also generalized to this setting. Further, we show how to construct various orthonormal bases of $L^2({\mathbb R}^d)$ from the multiwavelet packets.

math.FA↗
arXiv2001

A Class of non-MRA Band-limited Wavelets

We give a characterization of a class of band-limited wavelets of $L^2({\mathbb R})$ and show that none of these wavelets come from a multiresolution analysis (MRA). For each $n\geq 2$, we construct a subset $S_n$ of ${\mathbb R}$ which is symmetric with respect to the origin. We give necessary and sufficient conditions on a function $ψ\in L^2({\mathbb R})$ with supp $\hatψ\subseteq S_n$ to be an orthonormal wavelet. This result generalizes the characterization of a class of wavelets of E. Hernández and G. Weiss. The dimension functions associated with these wavelets are also computed explicitly. Starting from the wavelets we have constructed, we are able to construct examples of wavelets in each of the equivalence classes of wavelets defined by E. Weber.

math.FA↗