On the best constant in fractional pp-Poincar\'e inequalities on cylindrical domains

We investigate the best constants for the regional fractional $p$-Poincar\'e inequality and the fractional $p$-Poincar\'e inequality in cylindrical domains. For the special case $p=2$, the result was already known due to Chowdhury-Csat\'{o}-Roy-Sk [Study of fractional Poincar\'{e} inequalities on unbounded domains, Discrete Contin. Dyn. Syst., 41(6), 2021]. We addressed the asymptotic behaviour of the first eigenvalue of the nonlocal Dirichlet $p$-Laplacian eigenvalue problem when the domain is becoming unbounded in several directions.Comment: To appear in Differential and Integral Equation

Bacteriological Evaluation of Drinking Water of Rajshahi City, Bangladesh

Access to pathogen free safe drinking water is one of the major challenges of the 21st century for most of the people of world. According to WHO guidelines, 100 ml sample of safe drinking must be free of total coliform, fecal coliform and E. coli. Hence, this study was designed for bacteriological evaluation of drinking water collected from different restaurant in Rajshahi city, Bangladesh. Among 10 samples, no detectable E. coli was found in 5 water samples (100 ml each) while 8-50 detectable E. coli in 100 ml water sample was found in the remaining 5 samples which exceeded the BDS and WHO standard of drinking water. Four randomly selected isolates (B1, B2, B3 and R) which were isolated from different water samples were subjected to 16S rRNA gene sequencing. It was found  that the 16S rRNA sequence of isolate B1, B2 and B3 had 98% similarity to that of Enterobacter asburiae, Escherichia coli and Acinetobacter sp respectively. Similarly, 16S rRNA sequence of isolate R had 99% similarity to that of Klebsiella pneumonia. Results of biochemical analysis revealed that all four isolates were negative to Catalase, KOH and Oxidase test while variations were found for other tests. Similarly, all four isolates were able to ferment all tested carbohydrates except cellulose. The optimum pH and temperature for the growth of the all isolates was pH 7.0 and 37ºC. It was found that all the isolates were sensitive to majority of the antibiotics used

Search for Higgs bosons of the Universal Extra Dimensions at the Large Hadron Collider

The Higgs sector of the Universal Extra Dimensions (UED) has a rather involved setup. With one extra space dimension, the main ingredients to the construct are the higher Kaluza-Klein (KK) excitations of the Standard Model Higgs boson and the fifth components of the gauge fields which on compactification appear as scalar degrees of freedom and can mix with the former thus leading to physical KK-Higgs states of the scenario. In this work, we explore in detail the phenomenology of such a Higgs sector of the UED with the Large Hadron Collider (LHC) in focus. We work out relevant decay branching fractions involving the KK-Higgs excitations. Possible production modes of the KK-Higgs bosons are then discussed with an emphasis on their associated production with the third generation KK-quarks and that under the cascade decays of strongly interacting UED excitations which turn out to be the only phenomenologically significant modes. It is pointed out that the collider searches of such Higgs bosons face generic hardship due to soft end-products which result from severe degeneracies in the masses of the involved excitations in the minimal version of the UED (MUED). Generic implications of either observing some or all of the KK-Higgs bosons at the LHC are discussed.Comment: 25 pages, 9 figures and 1 tabl

Long-Baseline Neutrino Facility (LBNF) and Deep Underground Neutrino Experiment (DUNE) Conceptual Design Report Volume 1: The LBNF and DUNE Projects

This document presents the Conceptual Design Report (CDR) put forward by an international neutrino community to pursue the Deep Underground Neutrino Experiment at the Long-Baseline Neutrino Facility (LBNF/DUNE), a groundbreaking science experiment for long-baseline neutrino oscillation studies and for neutrino astrophysics and nucleon decay searches. The DUNE far detector will be a very large modular liquid argon time-projection chamber (LArTPC) located deep underground, coupled to the LBNF multi-megawatt wide-band neutrino beam. DUNE will also have a high-resolution and high-precision near detector

The Single-Phase ProtoDUNE Technical Design Report

ProtoDUNE-SP is the single-phase DUNE Far Detector prototype that is under construction and will be operated at the CERN Neutrino Platform (NP) starting in 2018. ProtoDUNE-SP, a crucial part of the DUNE effort towards the construction of the first DUNE 10-kt fiducial mass far detector module (17 kt total LAr mass), is a significant experiment in its own right. With a total liquid argon (LAr) mass of 0.77 kt, it represents the largest monolithic single-phase LArTPC detector to be built to date. It's technical design is given in this report

The DUNE Far Detector Interim Design Report, Volume 3: Dual-Phase Module

The DUNE IDR describes the proposed physics program and technical designs of the DUNE far detector modules in preparation for the full TDR to be published in 2019. It is intended as an intermediate milestone on the path to a full TDR, justifying the technical choices that flow down from the high-level physics goals through requirements at all levels of the Project. These design choices will enable the DUNE experiment to make the ground-breaking discoveries that will help to answer fundamental physics questions. Volume 3 describes the dual-phase module's subsystems, the technical coordination required for its design, construction, installation, and integration, and its organizational structure

The DUNE Far Detector Interim Design Report, Volume 2: Single-Phase Module

The DUNE IDR describes the proposed physics program and technical designs of the DUNE far detector modules in preparation for the full TDR to be published in 2019. It is intended as an intermediate milestone on the path to a full TDR, justifying the technical choices that flow down from the high-level physics goals through requirements at all levels of the Project. These design choices will enable the DUNE experiment to make the ground-breaking discoveries that will help to answer fundamental physics questions. Volume 2 describes the single-phase module's subsystems, the technical coordination required for its design, construction, installation, and integration, and its organizational structure

The DUNE Far Detector Interim Design Report Volume 1: Physics, Technology and Strategies

The DUNE IDR describes the proposed physics program and technical designs of the DUNE Far Detector modules in preparation for the full TDR to be published in 2019. It is intended as an intermediate milestone on the path to a full TDR, justifying the technical choices that flow down from the high-level physics goals through requirements at all levels of the Project. These design choices will enable the DUNE experiment to make the ground-breaking discoveries that will help to answer fundamental physics questions. Volume 1 contains an executive summary that describes the general aims of this document. The remainder of this first volume provides a more detailed description of the DUNE physics program that drives the choice of detector technologies. It also includes concise outlines of two overarching systems that have not yet evolved to consortium structures: computing and calibration. Volumes 2 and 3 of this IDR describe, for the single-phase and dual-phase technologies, respectively, each detector module's subsystems, the technical coordination required for its design, construction, installation, and integration, and its organizational structure