On boundedness and parallel to center dot parallel to(p) continuity of second quantisation

in this short note, we determine precisely which operators have the property that their (full, symmetric or antisymmetric) second quantisation is an operator which is bounded or belongs to one of the various Schatten ideals; we also note that in 'the interior' of the natural domain, the second quantisation is a continuous map.

A polynomial bound on the number of light cycles in an undirected graph

Let G be an undirected graph with a positive real weight on each edge. It is shown that the number of minimum-weight cycles of G is bounded above by a polynomial in the number of edges of G. A similar bound holds if we wish to count the number of cycles with weight at most a constant multiple of the minimum weight of a cycle of G.

Revisiting the earthquake sources in the Himalaya: Perspectives on past seismicity

The similar to 2500 km-long Himalaya plate boundary experienced three great earthquakes during the past century, but none of them generated any surface rupture. The segments between the 1905-1934 and the 1897-1950 sources, known as the central and Assam seismic gaps respectively, have long been considered holding potential for future great earthquakes. This paper addresses two issues concerning earthquakes along the Himalaya plate boundary. One, the absence of surface rupture associated with the great earthquakes, vis-a-vis the purported large slip observed from paleoseismological investigations and two, the current understanding of the status of the seismic gaps in the Central Himalaya and Assam, in view of the paleoseismological and historical data being gathered. We suggest that the ruptures of earthquakes nucleating on the basal detachment are likely to be restricted by the crustal ramps and thus generate no surface ruptures, whereas those originating on the faults within the wedges promote upward propagation of rupture and displacement, as observed during the 2005 Kashmir earthquake, that showed a peak offset of 7 m. The occasional reactivation of these thrust systems within the duplex zone may also be responsible for the observed temporal and spatial clustering of earthquakes in the Himalaya. Observations presented in this paper suggest that the last major earthquake in the Central Himalaya occurred during AD 1119-1292, rather than in 1505, as suggested in some previous studies and thus the gap in the plate boundary events is real. As for the Northwestern Himalaya, seismically generated sedimentary features identified in the 1950 source region are generally younger than AD 1400 and evidence for older events is sketchy. The 1897 Shillong earthquake is not a decollement event and its predecessor is probably similar to 1000 years old. Compared to the Central Himalaya, the Assam Gap is a corridor of low seismicity between two tectonically independent seismogenic source zones that cannot be considered as a seismic gap in the conventional sense. (C) 2011 Elsevier B.V. All rights reserved.

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

Solving linear programming problems exactly

A linear programming problem in an inequality form having a bounded solution is solved error-free using an algorithm that sorts the inequalities, removes the redundant ones, and uses the p-adic arithmetic. (C) Elsevier Science Inc., 1997

The complexity of certain incremental code generation problems

This paper looks at the complexity of four different incremental problems. The following are the problems considered: (1) Interval partitioning of a flow graph (2) Breadth first search (BFS) of a directed graph (3) Lexicographic depth first search (DFS) of a directed graph (4) Constructing the postorder listing of the nodes of a binary tree. The last problem arises out of the need for incrementally computing the Sethi-Ullman (SU) ordering [1] of the subtrees of a tree after it has undergone changes of a given type. These problems are among those that claimed our attention in the process of our designing algorithmic techniques for incremental code generation. BFS and DFS have certainly numerous other applications, but as far as our work is concerned, incremental code generation is the common thread linking these problems. The study of the complexity of these problems is done from two different perspectives. In [2] is given the theory of incremental relative lower bounds (IRLB). We use this theory to derive the IRLBs of the first three problems. Then we use the notion of a bounded incremental algorithm [4] to prove the unboundedness of the fourth problem with respect to the locally persistent model of computation. Possibly, the lower bound result for lexicographic DFS is the most interesting. In [5] the author considers lexicographic DFS to be a problem for which the incremental version may require the recomputation of the entire solution from scratch. In that sense, our IRLB result provides further evidence for this possibility with the proviso that the incremental DFS algorithms considered be ones that do not require too much of preprocessing.

Smart applications for energy harvested WSNs

A Wireless Sensor Network (WSN) powered using harvested energies is limited in its operation by instantaneous power. Since energy availability can be different across nodes in the network, network setup and collaboration is a non trivial task. At the same time, in the event of excess energy, exciting node collaboration possibilities exist; often not feasible with battery driven sensor networks. Operations such as sensing, computation, storage and communication are required to achieve the common goal for any sensor network. In this paper, we design and implement a smart application that uses a Decision Engine, and morphs itself into an energy matched application. The results are based on measurements using IRIS motes running on solar energy. We have done away with batteries; instead used low leakage super capacitors to store harvested energy. The Decision Engine utilizes two pieces of data to provide its recommendations. Firstly, a history based energy prediction model assists the engine with information about in-coming energy. The second input is the energy cost database for operations. The energy driven Decision Engine calculates the energy budgets and recommends the best possible set of operations. Under excess energy condition, the Decision Engine, promiscuously sniffs the neighborhood looking for all possible data from neighbors. This data includes neighbor's energy level and sensor data. Equipped with this data, nodes establish detailed data correlation and thus enhance collaboration such as filling up data gaps on behalf of nodes hibernating under low energy conditions. The results are encouraging. Node and network life time of the sensor nodes running the smart application is found to be significantly higher compared to the base application.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Robust Relay Precoder Design for MIMO-Relay Networks

In this paper, we consider a robust design of MIMO-relay precoder and receive filter for the destination nodes in a non-regenerative multiple-input multiple-output (MIMO) relay network. The network consists of multiple source-destination node pairs assisted by a single MIMO-relay node. The source and destination nodes are single antenna nodes, whereas the MIMO-relay node has multiple transmit and multiple receive antennas. The channel state information (CSI) available at the MIMO-relay node for precoding purpose is assumed to be imperfect. We assume that the norms of errors in CSI are upper-bounded, and the MIMO-relay node knows these bounds. We consider the robust design of the MIMO-relay precoder and receive filter based on the minimization of the total MIMO-relay transmit power with constraints on the mean square error (MSE) at the destination nodes. We show that this design problem can be solved by solving an alternating sequence of minimization and worst-case analysis problems. The minimization problem is formulated as a convex optimization problem that can be solved efficiently using interior-point methods. The worst-case analysis problem can be solved analytically using an approximation for the MSEs at the destination nodes. We demonstrate the robust performance of the proposed design through simulations.

Pulsed laser deposited ZnO/ZnO:Li multilayer for blue light emitting diodes

Thin films of ZnO, Li doped ZnO (ZLO) and multilayer of ZnO and ZLO (ZnO/ZLO) were grown on silicon and corning glass substrates by pulsed laser deposition technique. Single phase formation and the crystalline qualities of the films were analyzed by X-ray diffraction and Li composition in the film was investigated to be 15 wt% by X-ray photoelectron spectroscopy. Raman spectrum reveals the hexagonal wurtzite structure of ZnO, ZLO and ZnO/ZLO multilayer and confirms the single phase formation. Films grown on corning glass shows more than 80% transmittance in the visible region and the optical band gaps were calculated to be 3.245, 3.26 and 3.22 eV for ZnO, ZLO and ZnO/ZLO, respectively. An efficient blue emission was observed in all films which were grown on silicon (1 0 0) substrate by photoluminescence (PL). PL measurements at different temperatures reveal that the PL emission intensity of ZnO/ZLO multilayer was weakly dependent on temperature as compared to the single layers of ZnO and ZLO and the wavelength of emission was independent of temperature. Our results indicate that ZnO/ZLO multilayer can be used for the fabrication of blue light emitting diodes. (C) 2011 Elsevier B.V. All rights reserved.

Analysing Message Sequence Graph Specifications

We give a detailed construction of a finite-state transition system for a com-connected Message Sequence Graph. Though this result is well-known in the literature and forms the basis for the solution to several analysis and verification problems concerning MSG specifications, the constructions given in the literature are either not amenable to implementation, or imprecise, or simply incorrect. In contrast we give a detailed construction along with a proof of its correctness. Our transition system is amenable to implementation, and can also be used for a bounded analysis of general (not necessarily com-connected) MSG specifications.

An iterative auction mechanism for combinatorial exchanges

Combinatorial exchanges are double sided marketplaces with multiple sellers and multiple buyers trading with the help of combinatorial bids. The allocation and other associated problems in such exchanges are known to be among the hardest to solve among all economic mechanisms. In this paper, we develop computationally efficient iterative auction mechanisms for solving combinatorial exchanges. Our mechanisms satisfy Individual-rationality (IR) and budget-nonnegativity (BN) properties. We also show that our method is bounded and convergent. Our numerical experiments show that our algorithm produces good quality solutions and is computationally efficient.

Electrochemical tuning and mechanical resilience of single-wall carbon nanotubes

Single-wall carbon nanotubes (SWNTs) are fascinating systems exhibiting many novel physical properties. In this paper, we give a brief review of the structural, electronic, vibrational, and mechanical properties of carbon nanotubes. In situ resonance Raman scattering of SWNTs investigated under electrochemical biasing demonstrates that the intensity of the radial breathing mode varies significantly in a nonmonotonic manner as a function of the cathodic bias voltage, but does not change appreciably under anodic bias. These results can be quantitatively understood in terms of the changes in the energy gaps between the 1 D van Hove singularities in the electron density of states, arising possibly due to the alterations in the overlap integral of pi bonds between the p-orbitals of the adjacent carbon atoms. In the second part of this paper, we review our high-pressure X-ray diffraction results, which show that the triangular lattice of the carbon nanotube bundles continues to persist up to similar to10 GPa. The lattice is seen to relax just before the phase transformation, which is observed at similar to10 GPa. Further, our results display the reversibility of the 2D lattice symmetry even after compression up to 13 GPa well beyond the 5 GPa value observed recently. These experimental results explicitly validate the predicted remarkable mechanical resilience of the nanotubes.

Weakly non-linear stability of a hydrodynamic accretion disc

When the cold accretion disc coupling between neutral gas and a magnetic field is so weak that the magnetorotational instability is less effective or even stops working, it is of prime interest to investigate the pure hydrodynamic origin of turbulence and transport phenomena. As the Reynolds number increases, the relative importance of the non-linear term in the hydrodynamic equation increases. In an accretion disc where the molecular viscosity is too small, the Reynolds number is large enough for the non-linear term to have new effects. We investigate the scenario of the `weakly non-linear' evolution of the amplitude of the linear mode when the flow is bounded by two parallel walls. The unperturbed flow is similar to the plane Couette flow, but with the Coriolis force included in the hydrodynamic equation. Although there is no exponentially growing eigenmode, because of the self-interaction, the least stable eigenmode will grow in an intermediate phase. Later, this will lead to higher-order non-linearity and plausible turbulence. Although the non-linear term in the hydrodynamic equation is energy-conserving, within the weakly non-linear analysis it is possible to define a lower bound of the energy (alpha A(c)(2), where A(c) is the threshold amplitude) needed for the flow to transform to the turbulent phase. Such an unstable phase is possible only if the Reynolds number >= 10(3-4). The numerical difficulties in obtaining such a large Reynolds number might be the reason for the negative result of numerical simulations on a pure hydrodynamic Keplerian accretion disc.

Model exact low-lying states and spin dynamics in ferric wheels: Fe-6 to Fe-12

Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for ferric wheels up to Fe-12. The largest calculation involves the Fe-12 ring which spans a Hilbert space dimension of about 145x10(6) for the M-S=0 subspace. Our calculated gaps from the singlet ground state to the excited triplet state agree well with the experimentally measured values. Study of the static structure factor shows that the ground state is spontaneously dimerized for ferric wheels. The spin states of ferric wheels can be viewed as quantized states of a rigid rotor with the gap between the ground and first excited states defining the inverse of the moment of inertia. We have studied the quantum dynamics of Fe-10 as a representative of ferric wheels. We use the low-lying states of Fe-10 to solve exactly the time-dependent Schrodinger equation and find the magnetization of the molecule in the presence of an alternating magnetic field at zero temperature. We observe a nontrivial oscillation of the magnetization which is dependent on the amplitude of the ac field. We have also studied the torque response of Fe-12 as a function of a magnetic field, which clearly shows spin-state crossover.