The Extended Estabrook-Wahlquist Method

Variable Coefficient Korteweg de Vries (vcKdV), Modified Korteweg de Vries (vcMKdV), and nonlinear Schrodinger (NLS) equations have a long history dating from their derivation in various applications. A technique based on extended Lax Pairs has been devised recently to derive variable-coefficient generalizations of various Lax-integrable NLPDE hierarchies. The resulting Lax- or S-integrable NLPDEs have both time- AND space-dependent coefficients, and are thus more general than almost all cases considered earlier via other methods such as the Painlev\'e Test, Bell Polynomials, and various similarity methods. However, this technique, although operationally effective, has the significant disadvantage that, for any integrable system with spatiotemporally varying coefficients, one must 'guess' a generalization of the structure of the known Lax Pair for the corresponding system with constant coefficients. Motivated by the somewhat arbitrary nature of the above procedure, we embark in this paper on an attempt to systematize the derivation of Lax-integrable systems with variable coefficients. An ideal approach would be a method which does not require knowledge of the Lax pair to an associated constant coefficient system, and also involves little to no guesswork. Hence we attempt to apply the Estabrook-Wahlquist (EW) prolongation technique, a relatively self-consistent procedure requiring little prior information. The new and extended EW technique which results is illustrated by algorithmically deriving generalized Lax-integrable versions of the NLS, generalized fifth-order KdV, MKdV, and derivative nonlinear Schrodinger (DNLS) equations.Comment: arXiv admin note: substantial text overlap with arXiv:1404.460

Japan's Foreign Direct Investment Experiences in India: Lessons Learnt from Firm Level Surveys

Though economic relations between India and Korea have been strengthening, the current size of trade and investment between the two countries is relatively low compared to the size and structural complementarities of the two economies. In this context, the present paper analyses trade and investment relations and explores future areas of potential co-operation between India and Korea. We find that the increase in merchandise trade between the two countries has been mainly because of the changing demand structure and comparative advantages of both the economies in complementary sectors in recent years. The Revealed Comparative Advantage (RCA) analysis, at both the aggregated and disaggregated levels, shows that while Korea has been specialising in a few, high value-added manufacturing products, India's exports have been more diversified. The analysis also indicates that both the countries have comparative advantages in different products in the same industry, revealing the opportunity for intra-industry trade (IIT). Moreover, the increasing trade complementarity index (TCI) shows that Indian and Korean trade gradually has become more compatible over time, indicating that any agreement between the two countries is likely to enhance trade flows. The trade intensities between the two countries reveal that Korea is doing much better and there is scope for India to improve its export intensity with Korea. The study also suggests the areas where there is huge scope for increased investment and technological collaboration between the two countries. Further, there is huge potential for trade in services in areas such as information technology, science and technology, pharmaceutical industry, broadcasting, tourism, healthcare and human resource development. Removal of tariff and non-tariff barriers, especially sector specific barriers, will give a major boost to bilateral trade and investment relations.Foreign direct investment, Japanese multinational corporations, strategies,obstacles in operations.

Strong Bounds on Sum of Neutrino Masses in a 12 Parameter Extended Scenario with Non-Phantom Dynamical Dark Energy (w(z)≥−1w(z)\geq -1)

We obtained constraints on a 12 parameter extended cosmological scenario including non-phantom dynamical dark energy (NPDDE) with CPL parametrization. We also include the six $\Lambda$CDM parameters, number of relativistic neutrino species ($N_{\textrm{eff}}$) and sum over active neutrino masses ($\sum m_{\nu}$), tensor-to-scalar ratio ($r_{0.05}$), and running of the spectral index ($n_{run}$). We use CMB Data from Planck 2015; BAO Measurements from SDSS BOSS DR12, MGS, and 6dFS; SNe Ia Luminosity Distance measurements from the Pantheon Sample; CMB B-mode polarization data from BICEP2/Keck collaboration (BK14); Planck lensing data; and a prior on Hubble constant ($73.24\pm1.74$ km/sec/Mpc) from local measurements (HST). We have found strong bounds on the sum of the active neutrino masses. For instance, a strong bound of $\sum m_{\nu} <$ 0.123 eV (95\% C.L.) comes from Planck+BK14+BAO. Although we are in such an extended parameter space, this bound is stronger than a bound of $\sum m_{\nu} <$ 0.158 eV (95\% C.L.) obtained in $\Lambda \textrm{CDM}+\sum m_{\nu}$ with Planck+BAO. Varying $A_{\textrm{lens}}$ instead of $r_{0.05}$ however leads to weaker bounds on $\sum m_{\nu}$. Inclusion of the HST leads to the standard value of $N_{\textrm{eff}} = 3.045$ being discarded at more than 68\% C.L., which increases to 95\% C.L. when we vary $A_{\textrm{lens}}$ instead of $r_{0.05}$, implying a small preference for dark radiation, driven by the $H_0$ tension.Comment: 23 pages, 10 figures, matches the published versio

Searching for the reionization sources

Using a reionization model simultaneously accounting for a number of experimental data sets, we investigate the nature and properties of reionization sources. Such model predicts that hydrogen reionization starts at z \approx 15, is initially driven by metal-free (PopIII) stars, and is 90% complete by z \approx 8. We find that a fraction f_\gamma >80% of the ionizing power at z > 7 comes from haloes of mass M<10^9 M_sun predominantly harbouring PopIII stars; a turnover to a PopII-dominated phase occurs shortly after, with this population, residing in M>10^9 M_sun haloes, yielding f_\gamma \approx 60% at z=6. Using Lyman-break broadband dropout techniques, J-band detection of sources contributing to 50% (90%) of the ionizing power at z \sim 7.5 requires to reach a magnitude J_{110,AB} = 31.2 (31.7), where about 15 (30) (PopIII) sources/arcmin^2 are predicted. We conclude that z>7 sources tentatively identified in broadband surveys are relatively massive (M \approx 10^9 M_sun) and rare objects which are only marginally (\approx 1%) adding to the reionization photon budget.Comment: Extended discussions. Accepted to MNRAS Letter

Effective String Theory Inspired Potential and Meson Masses in Higher Dimension

Nambu-Goto action in classical bosonic string model for hadrons predicts quark-antiquark potential to be\cite{Nambu-Goto} $V(r)=-\frac{\gamma}{r}+\sigma r +\mu_0$. In this report we present studies of masses of heavy flavour mesons in higher dimension with our recently developed wave functions obtained following string inspired potential. We report the dimensional dependence of the masses of mesons. Our results suggest that as the meson mass increases with the number of extra spatial dimension, it will attain the Planck scale ($\sim 10^{19}GeV$) asymptotically at an astronomically large spatial dimension (we call it Planck dimension) $D_{Planck} \sim 10^{11}$, which sets the limit of applicability of Schrodinger equation in large dimension

Signatures of an invisibly decaying Higgs particles at LHC

The Higgs particle can decay dominantly into an invisible channel in the Majoron models. We have explored the prospect of detecting such a Higgs particle at LHC via its associated production with a gluon, Z or W boson. While the signal/background ratio is too small for the first process, the latter two provide viable signatures for detecting such a Higgs particle.Comment: (e-mail: [email protected]) LaTex; No. of pages 12, no. of figures 3 (available on request