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*Indian* *Statistical* *Institute*,

, 705

"... We observe that there is no clash between the works [1] and [2]. In the Comment [1] the author has shown that one can construct a Lagrangian model of a point particle with a Magueijo-Smolin (MS) form of dispersion relation in a canonical phase space provided one modifies the Lorentz generator to J µ ..."

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We observe that there is no clash between the works [1] and [2]. In the Comment [1] the author has shown that one can construct a Lagrangian model of a point particle with a Magueijo-Smolin (MS) form of dispersion relation in a canonical phase space provided one modifies the Lorentz generator to J µν DSR = (x µ − (xp) l ηµ)p ν − (x ν − (xp) l ην)p µ. (1) On the other hand in [2] I have shown that one can keep the Lorentz generator J µν = x µ p ν − x ν p µ unchanged provided a non-canonical symplectic structure is used. In my opinion the above two formalisms are complimentary and there is no reason to treat the former [1] as an improvement, but for a bias of the author of [1] against the introduction of a non-canonical phase space. Furthermore, it is crucial to keep in mind that from the point of view of DSR, the Lagrangian in (4) [1] with the chosen form of J µν DSR is fundamental and the coordinate x µ, (with its noncanonical behavior under Lorentz transformation), is the physical coordinate and p µ is the physical momentum. According to DSR, results obtained in x µ, p µ variables (and not in X µ, P µ) should be compared with experiments. Thus (4) in [1] should be considered as the starting point and (1) in [1] is obtained in a particular parameterization. This does not mean that the DSR model is trivially related to normal particle model. This is because in order to get the correct behavior of a DSR particle one has to convert the normal particle equations (in X µ, P µ) to equations involving physical DSR coordinates x µ, p µ using (2) X µ = (F −1) µ ν xν 1 as given in [1]. This will lead to new κ-DSR physics since coordinates and momenta get mixed up under Lorentz transformation. In this way one can exploit the canonical framework to generate DSR behavior. This sort of approach is discussed extensivly in [3] in a related context where it is also shown that dynamical inputs are required in order to extrapolate kinematical equations in canonical framework to equations in DSR framework.

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*Indian* *Statistical* *Institute*.

, 2006

"... Abstract: We relate the pricing policy of the firms to their size, where firm size is interpreted as the size of the clientele served by the concerned firm. We argue that a firm with a large clientele faces a more severe reputational backlash if it reneges. This allows the firm to effectively commit ..."

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Abstract: We relate the pricing policy of the firms to their size, where firm size is interpreted as the size of the clientele served by the concerned firm. We argue that a firm with a large clientele faces a more severe reputational backlash if it reneges. This allows the firm to effectively commit to its offers, leading to a unique equilibrium without delay, where the firm extracts the whole of the surplus. For smaller firms, however, the reputational effects are much less intense and, consequently, the equilibria involve reneging pos-sibilities. In this case the equilibria are non-unique, and may involve delays as well.

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*Indian* *Statistical* *Institute*—Delhi

, 2004

"... Abstract: Firm-level data have been used to estimate changes in factor efficiencies— imported inputs being one of them-- over three sub-periods, 1977-84, 1985-91 and 1992-99 respectively denoting eras before liberalization, partial liberalization of the automotive industries and economy-wide liberal ..."

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Abstract: Firm-level data have been used to estimate changes in factor efficiencies— imported inputs being one of them-- over three sub-periods, 1977-84, 1985-91 and 1992-99 respectively denoting eras before liberalization, partial liberalization of the automotive industries and economy-wide liberalization. We see that the average size of firms has increased from that in the protected regime as the degree of liberalization has advanced. We find that the substitutability among inputs changed over the three sub-periods. We also find that the marginal products of all the inputs are very heterogeneous among firms in each period. The distributions of marginal product of labour and domestic materials and has moved to the left in the later periods while that of capital has moved to the right. The distribution of marginal product of imported materials first moved to the right and then to the left as compared to the first period. Overall the smaller firms benefited more in the earlier periods and bigger ones in the last period.

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*Indian* *Statistical* *Institute*

, 2002

"... On testing dependence between time to failure and cause of failure via conditional probabilities ..."

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On testing dependence between time to failure and cause of failure via conditional probabilities

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*Indian* *Statistical* *Institute*,

"... The study presents the use of e-Resources by the faculty members and research scholars various engineering colleges of Visvesvaraya Technological University (VTU) Belgaum, Karnataka. The main aim of this study is to know the usage of e-Resources by faculty members and research scholars who have regi ..."

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The study presents the use of e-Resources by the faculty members and research scholars various engineering colleges of Visvesvaraya Technological University (VTU) Belgaum, Karnataka. The main aim of this study is to know the usage of e-Resources by faculty members and research scholars who have registered through the recognized Research Centers of Visvesvaraya Technological University (VTU), Belgaum, Karnataka. As a tool the survey method of questionnaire was distributed among the respondents of various departments. Out of 1000 questionnaires, 866 questionnaires were received from the respondents and 86.6 % of respondents have replied to the quires. It is observed that majority of senior level teachers and research scholars access the e-Resources for the research work rather than teaching. The study revealed that, 94 % of the users are depending on e-Resources which are more relevant for their study rather than print resources. The trend predicts that e-Resources has over taken the print resources and predicts that the print resources will be phased out in near future.

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*Indian* *Statistical* *Institute*,

, 802

"... In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an inhomogeneous lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us [4, 5, 6]. We show that a non-constant lattice distortion leads ..."

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In the present paper we have directly computed the Berry curvature terms relevant for Graphene in the presence of an inhomogeneous lattice distortion. We have employed the generalized Foldy Wouthuysen framework, developed by some of us [4, 5, 6]. We show that a non-constant lattice distortion leads to a valley-orbit coupling which is responsible to a valley-Hall effect. This is similar to the valley-Hall effect induced by an electric field proposed in [14] and is the analogue of the spin-Hall effect in semiconductors [16, 17]. Our general expressions for Berry curvature, for the special case of homogeneous distortion, reduce to the previously obtained results [14]. We also discuss the Berry phase in the quantization of cyclotron motion.

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*Indian* *Statistical* *Institute*,

, 2006

"... If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of P AP. As an application, we obtain a formula for the Moore-Penrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of ..."

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If A is a real symmetric matrix and P is an orthogonal projection onto a hyperplane, then we derive a formula for the Moore-Penrose inverse of P AP. As an application, we obtain a formula for the Moore-Penrose inverse of a Euclidean distance matrix (EDM) which generalizes formulae for the inverse of a EDM in the literature. To an invertible spherical EDM, we associate a Laplacian matrix (which we define as a positive semidefinite n × n matrix of rank n − 1 and with zero row sums) and prove some properties. Known results for distance matrices of trees are derived as special cases. In particular, we obtain a formula due to Graham and Lovász for the inverse of the distance marix of a tree. It is shown that if D is a nonsingular EDM and L is the associated Laplacian, then D−1 − L is nonsingular and has a nonnegative inverse. Finally, infinitely divisible matrices are constructed using EDMs. 1

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*Indian* *Statistical* *Institute*,

"... A threshold graph on n vertices is coded by a binary string of length n − 1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold graph in terms of the code of the graph. It is shown that the number of negative eigenvalues of the adjacency matrix of a threshold graph is the n ..."

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A threshold graph on n vertices is coded by a binary string of length n − 1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold graph in terms of the code of the graph. It is shown that the number of negative eigenvalues of the adjacency matrix of a threshold graph is the number of ones in the code, whereas the nullity is given by the number of zeros in the code that are preceded by either a zero or a blank. A formula for the determinant of the adjacency matrix of a generalized threshold graph and the inverse, when it exists, of the adjacency matrix of a threshold graph are obtained. Results for antiregular graphs follow as special cases. AMS Classification: 05C50