Indian Institute of Technology Palakkad&nbsp;(IIT Palakkad or IIT PKD) is a public autonomous&nbsp;engineering&nbsp;and&nbsp;research&nbsp;institute located in&nbsp;Palakkad,&nbsp;Kerala. It was&nbsp;one of the five new&nbsp;IITs&nbsp;proposed in the&nbsp;2014 Union budget of India. The campus was inaugurated on 3 August 2015. The institute has 94 faculty, 978 students, and 63 non-teaching staffs.

IT Palakkad currently offers four-year Bachelor of Technology (B.Tech) and two years MS programmes in 8 different engineering disciplines including&nbsp;Computer Science, Electrical, Mechanical, Civil among others.

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IIT Palakkad

The following result is proved: Let A be a commutative real Banach algebra with unit 1. Let G denote the group of invertible elements of A and let G1 be the connected component of G containing 1. If the quotient group G/G1 contains an element of finite order other than G1, then the order of such an element must be 2. If the group G/G1 is of finite order, then its order must be 2n for some nonnegative integer n. © 2014 University of Houston.

Department of Mathematics

Houston Journal of Mathematics

The group of invertible elements of a real Banach algebra

Stream flow predictions in ungauged basins are one of the most challenging tasks in surface water hydrology because of nonavailability of data and system heterogeneity. This study proposes a method to quantify stream flow predictive uncertainty of distributed hydrologic models for ungauged basins. The method is based on the concepts of deriving probability distribution of model's sensitive parameters by using measured data from a gauged basin and transferring the distribution to hydrologically similar ungauged basins for stream flow predictions. A Monte Carlo simulation of the hydrologic model using sampled parameter sets with assumed probability distribution is conducted. The posterior probability distributions of the sensitive parameters are then computed using a Bayesian approach. In addition, preselected threshold values of likelihood measure of simulations are employed for sizing the parameter range, which helps reduce the predictive uncertainty. The proposed method is illustrated through two case studies using two hydrologically independent sub-basins in the Cedar Creek watershed located in Texas, USA, using the Soil and Water Assessment Tool (SWAT) model. The probability distribution of the SWAT parameters is derived from the data from one of the sub-basins and is applied for simulation in the other sub-basin considered as pseudo-ungauged. In order to assess the robustness of the method, the numerical exercise is repeated by reversing the gauged and pseudo-ungauged basins. The results are subsequently compared with the measured stream flow from the sub-basins. It is observed that the measured stream flow in the pseudo-ungauged basin lies well within the estimated confidence band of predicted stream flow. © 2013 John Wiley & Sons, Ltd.

World University root node

Department of Civil Engineering

Hydrological Processes

Application of distributed hydrological models for predictions in ungauged basins: A method to quantify predictive uncertainty

Journal of Indian Water Resources Society

Hydrologic Response To Climatic Change in the Baitarni River Basin

INDOROCK-2014: 5TH INDIAN ROCK CONFERENCE

Dynamic Behaviour of Socketed Single Pilein Rocks under Vertical Vibration

For 0 &lt; ε &lt; 1, the ε-condition spectrum of an element a in a complex unital Banach algebra A is defined as, (Formula Presented). This is a generalization of the idea of spectrum introduced in [5]. This is expected to be useful in dealing with operator equations. In this paper we prove a mapping theorem for condition spectrum, extending an earlier result in [5]. Let f be an analytic function in an open set Ω containing σε(a). We study the relations between the sets σε(f(a)) and f(σε (a)). In general these two sets are different. We define functions φ(ε), ψ (ε) (that take small values for small values of ε) and prove that f(σε(a)) ⊆ σφ(ε)(f(a)) and σε(f(a)) ⊆ f(σ ψ(ε)(a)). The classical Spectral Mapping Theorem is shown as a special case of this result. We give estimates for these functions in some special cases and finally illustrate the results by numerical computations. © 2014 Springer Basel.

Operator Theory: Advances and Applications

An analogue of the spectral mapping theorem for condition spectrum

It is shown that every hyperbolic rigid polynomial domain in ℂ3 of finite-type, with abelian automorphism group is equivalent to a domain that is balanced with respect to some weight. © 2014 Copyright Taylor &amp; Francis Group, LLC.

Complex Variables and Elliptic Equations

Model domains in ℂ3 with abelian automorphism group

For a closed subspace Y of a Banach space X, we define a separably determined property for Y in X. We prove that if the strong 11/ 2-ball property is separably determined for Y in X, then L 1(μ, Y) has the strong 11/2ball property in L 1(μ, X). For an M-embedded space X, we give a class of elements in L 1(μ, X having best approximations from L 1(μ, X). We also prove that some of the proximinality properties are stable under polyhedral direct sums of Banach spaces. © 2014 Copyright Taylor &amp; Francis Group, LLC.

Numerical Functional Analysis and Optimization

Proximinality properties in Lp(μ, X) and polyhedral direct sums of banach spaces

The development of spintronics devices relies on efficient generation of spin-polarized currents and their electric-field-controlled manipulation. While observation of exceptionally long spin relaxation lengths makes graphene an intriguing material for spintronics studies, electric field modulation of spin currents is almost impossible due to negligible intrinsic spin-orbit coupling of graphene. In this work, we create an artificial interface between monolayer graphene and few-layer semiconducting tungsten disulphide. In these devices, we observe that graphene acquires spin-orbit coupling up to 17 meV, three orders of magnitude higher than its intrinsic value, without modifying the structure of the graphene. The proximity spin-orbit coupling leads to the spin Hall effect even at room temperature, and opens the door to spin field effect transistors. We show that intrinsic defects in tungsten disulphide play an important role in this proximity effect and that graphene can act as a probe to detect defects in semiconducting surfaces. © 2014 Macmillan Publishers Limited. All rights reserved.

Department of Physics

Fulltext

Nature Communications

Spin-orbit proximity effect in graphene

Advances in large-area graphene synthesis via chemical vapour deposition on metals like copper were instrumental in the demonstration of graphene-based novel, wafer-scale electronic circuits and proof-of-concept applications such as flexible touch panels. Here, we show that graphene grown by chemical vapour deposition on copper is equally promising for spintronics applications. In contrast to natural graphene, our experiments demonstrate that chemically synthesized graphene has a strong spin-orbit coupling as high as 20â ‰meV giving rise to a giant spin Hall effect. The exceptionally large spin Hall angle ∼0.2 provides an important step towards graphene-based spintronics devices within existing complementary metal-oxide-semiconductor technology. Our microscopic model shows that unavoidable residual copper adatom clusters act as local spin-orbit scatterers and, in the resonant scattering limit, induce transverse spin currents with enhanced skew-scattering contribution. Our findings are confirmed independently by introducing metallic adatoms-copper, silver and gold on exfoliated graphene samples. © 2014 Macmillan Publishers Limited.

Giant spin Hall effect in graphene grown by chemical vapour deposition

Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a 'push-pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a 'critical point' for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm. © 2013 Elsevier Ltd.