Harmonic Analysis On Heisenberg Nilmanifolds

In these lectures we plan to present a survey of certain aspects of harmonic analysis on a Heisenberg nilmanifold Gammakslash}H-n. Using Weil-Brezin-Zak transform we obtain an explicit decomposition of L-2 (Gammakslash}H-n) into irreducible subspaces invariant under the right regular representation of the Heisenberg group. We then study the Segal-Bargmann transform associated to the Laplacian on a nilmanifold and characterise the image of L-2 (GammakslashH-n) in terms of twisted Bergman and Hermite Bergman spaces.

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes.

Space-Vector-Based Hybrid Pulsewidth Modulation Techniques for Reduced Harmonic Distortion and Switching Loss

Novel switching sequences can be employed in spacevector-based pulsewidth modulation (PWM) of voltage source inverters. Differentswitching sequences are evaluated and compared in terms of inverter switching loss. A hybrid PWM technique named minimum switching loss PWM is proposed, which reduces the inverter switching loss compared to conventional space vector PWM (CSVPWM) and discontinuous PWM techniques at a given average switching frequency. Further, four space-vector-based hybrid PWM techniques are proposed that reduce line current distortion as well as switching loss in motor drives, compared to CSVPWM. Theoretical and experimental results are presented.

Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

Identification of TGFβ signaling, p53, and actin stress fibers as targets of LKB1 tumor suppressor activity

Tumorigenesis is a consequence of inactivating mutations of tumor suppressor genes and activating mutations of proto-oncogenes. Most of the mutations compromise cell autonomous and non-autonomous restrains on cell proliferation by modulating kinase signal transduction pathways. LKB1 is a tumor suppressor kinase whose sporadic mutations are frequently found in non-small cell lung cancer and cervical cancer. Germ-line mutations in the LKB1 gene lead to Peutz-Jeghers syndrome with an increased risk of cancer and development of benign gastrointestinal hamartomatous polyps consisting of hyperproliferative epithelia and prominent stromal stalk composed of smooth muscle cell lineage cells. The tumor suppressive function of LKB1 is possibly mediated by 14 identified LKB1 substrate kinases, whose activation is dependent on the LKB1 kinase complex. The aim of my thesis was to identify cell signaling pathways crucial for tumor suppression by LKB1. Re-introduction of LKB1 expression in the melanoma cell line G361 induces cell cycle arrest. Here we demonstrated that restoring the cytoplasmic LKB1 was sufficient to induce the cell cycle arrest in a tumor suppressor p53 dependent manner. To address the role of LKB1 in gastrointestinal tumor suppression, Lkb1 was deleted specifically in SMC lineage in vivo, which was sufficient to cause Peutz-Jeghers syndrome type polyposis. Studies on primary myofibroblasts lacking Lkb1 suggest that the regulation of TGFβ signaling, actin stress fibers and smooth muscle cell lineage differentiation are candidate mechanisms for tumor suppression by LKB1 in the gastrointestinal stroma. Further studies with LKB1 substrate kinase NUAK2 in HeLa cells indicate that NUAK2 is part of a positive feedback loop by which NUAK2 expression promotes actin stress fiber formation and, reciprocally the induction of actin stress fibers promote NUAK2 expression. Findings in this thesis suggest that p53 and TGFβ signaling pathways are potential mediators of tumor suppression by LKB1. An indication of NUAK2 in the promotion of actin stress fibers suggests that NUAK2 is one possible mediator of LKB1 dependent TGFβ signaling and smooth muscle cell lineage differentiation.

Interfamilial transfer of amber suppressor gene for the isolation of amber mutants of mycobacteriophage I3

A suppressor-containing strain of Mycobacterium smegmatis SN2 was isolated by transferring an amber suppressor carried on the plasmid of Pseudomonas pseudoalcaligenes ERA through transformation. Amber mutants of mycobacteriophage I3 were isolated.

Second harmonic generation in some donor-acceptor ethylenes—I

We report the absorption spectra, oscillator strengths, ground state and excited state dipole moments, and molecular second order polarizability coefficients (βCT) due to donor—acceptor charge transfer in four trisubstituted ethylenes, namely 1,1-bisdimethylamino-2-nitroethylene, 1,1-bispyrolidino-2-nitroethylene, 1,1-bispiperidino-2-nitroethylene and 1,1-bismorpholino-2-nitroethylene. The results are compared with that of trans-N,N-dimethylamino-nitroethylene, which has a large βCT. The powder second harmonic generation (SHG) intensity of all these molecules is also measured and only 1,1-bispiperidino-2-nitroethylene is found to possess an efficiency of 20% of that of urea under the same conditions. The SHG efficiency of this compound and deficiency in the other molecules in the powdered state is discussed in terms of their arrangements in the unit cell. The crystal structure of the active molecule is also presented and the structure—property relationship is critically examined in all these molecules.

Functional regulation of the Neurofibromatosis 2 tumor suppressor merlin

Neurofibromatosis 2 (NF2) is an autosomal dominant disorder manifested by the formation of multiple benign tumors of the nervous system. Affected individuals typically develop bilateral vestibular schwannomas which lead to deafness and balance disorders. The syndrome is caused by inactivation of the NF2 tumor suppressor gene, and mutation or loss of the NF2 product, merlin, is sufficient for tumorigenesis in both hereditary and sporadic NF2-associated tumors. Merlin belongs to the band 4.1 superfamily of cytoskeletal proteins, which also contain the related ezrin, radixin, and moesin (ERM) proteins. The ERM members provide a link between the cell cytoskeleton and membrane by connecting membrane-associated proteins to actin filaments. By stabilizing complexes in the cell cortex, the ERMs modulate morphology, growth, and migration of cells. Despite their structural homology, overlapping subcellular distribution, direct molecular association, and partial overlap of molecular interactions, merlin and ezrin exert opposite effects on cell proliferation. Merlin suppresses cell proliferation, whereas ezrin expression is linked to oncogenic activity. We hypothesized that the regions which differ between the proteins might explain merlin s specificity as a tumor suppressor. We therefore analyzed the regions, which are most diverse between merlin and ezrin; the N-terminal tail and the C-terminus. To determine the properties of the C-terminal region, we studied the two most predominant merlin isoforms together with truncation variants similar to those found in patients. We also focused on the evolutionally conserved C-terminal residues, E545-E547, that harbor disease causing mutations in its corresponding DNA sequence. In addition to inhibiting cell proliferation, merlin regulates cytoskeletal organization. The morphogenic properties of merlin may play a role in tumor suppression, since patient-derived tumor cells demonstrate cytoskeletal abnormalities. We analyzed the mechanisms of merlin-induced extension formation and determined that the C-terminal region of amino acids 538-568 is particularly important for the morphogenic activity. We also characterized the role of C-terminal merlin residues in the regulation of proliferation, phosphorylation, and intramolecular associations. In contrast to previous reports, we demonstrated that both merlin isoforms are able to suppress cell proliferation, whereas C-terminally mutated merlin constructs showed reduced growth inhibition. Phosphorylation serves as a mechanism to regulate the tumor suppressive activity of merlin. The C-terminal serine 518 is phosphorylated in response to both p21-activated kinase (PAK) and protein kinase A (PKA), which inactivates the growth inhibitory function of merlin. However, at least three differentially phosphorylated forms of the protein exist. In this study we demonstrated that also the N-terminus of merlin is phosphorylated by AGC kinases, and that both PKA and Akt phosphorylate merlin at serine 10 (S10). We evaluated the impact of this N-terminal tail phosphorylation, and showed that the phosphorylation state of S10 is an important regulator of merlin s ability to modulate cytoskeletal organization but also regulates the stability of the protein. In summary, this study describes the functional effect of merlin specific regions. We demonstrate that both S10 in the N-terminal tail and residues E545-E547 in the C-terminus are essential for merlin activity and function.

Nonequilibrium stationary states of harmonic chains with bulk noises

We consider a chain composed of $N$ coupled harmonic oscillators in contact with heat baths at temperature $T_\ell$ and $T_r$ at sites 1 and $N$ respectively. The oscillators are also subjected to non-momentum conserving bulk stochastic noises. These make the heat conductivity satisfy Fourier's law. Here we describe some new results about the hydrodynamical equations for typical macroscopic energy and displacement profiles, as well as their fluctuations and large deviations, in two simple models of this type.

Second harmonic generation in poled molecularly doped polymer films : Push-pull butadienes in poly(methyl methacrylate) and polystyrene

We report second harmonic generation in a new class of organic materials, namely donor-acceptor substituted all-trans butadienes doped in poly(methyl methacrylate) or polystyrene and oriented by corona poling at elevated temperatures. Second harmonic measurements were made at room temperature. The observed d33 coefficients are greater than those of potassium dihydrogen phosphate or 4-dimethylamino-4'-nitrostilbene doped in similar polymer matrices. Rotational diffusion coefficients estimated from the decay characteristics of the second harmonic intensity in the polymer films indicate that the polymer matrix plays a major role in stabilizing the dopants in a nonlinear optics conducive environment.

Third harmonic generation through shaped superconductors

This paper describes a methodology of obtaining only third harmonic along with the fundamental using shaped superconductors. It also indicates how one can design a nonlinear superconducting resistor with the required current versus resistance variation.

Influence of poling methods on the orientational dynamics of 2-methyl-4-nitro-aniline in poly(methyl methacrylate) studied by second harmonic generation

The magnitude and stability of the induced dipolar orientation of 2-methyl-4-nitroaniline (MNA)/poly(methyl methacrylate) (PMMA) guest/host system is investigated. The chromophores are aligned using both the corona discharge and contact electrode poling techniques. The magnitude of order parameter (also an indicator for the second order nonlinear susceptibility) is measured by recording absorbances of the poled (by the two different techniques) and unpoled PMMA films at different concentrations of MNA. Under the same conditions the corona poling technique creates a higher alignment of molecules along the field direction. The time dependence of the second harmonic intensity of the MNA/PMMA film prepared by the two techniques can be described by a Kohlrausch-Williams-Watts stretched exponential. The temperature dependence of the decay time constant is found to generally follow a modified Williams-Landel-Ferry (WLF) or Vogel-Tamann-Fulcher (VTF) equation. The glass transition temperature seems to be the single most important parameter for determining the relaxation time tau(T).