J. Wolf - UC Irvine

J. Wolf
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Name
J. Wolf
Affiliation
UC Irvine
City
Irvine
Country
United States

Pubs By Year

Pub Categories

 
Physics - Optics (17)
 
Mathematics - Analysis of PDEs (12)
 
Mathematics - Differential Geometry (7)
 
Mathematics - Representation Theory (5)
 
Mathematics - Functional Analysis (4)
 
Physics - Plasma Physics (4)
 
Mathematics - Group Theory (3)
 
Physics - Atomic Physics (3)
 
Nonlinear Sciences - Pattern Formation and Solitons (2)
 
Physics - Statistical Mechanics (2)
 
Earth and Planetary Astrophysics (2)
 
Instrumentation and Methods for Astrophysics (1)
 
Mathematics - Mathematical Physics (1)
 
Mathematical Physics (1)
 
Mathematics - Symplectic Geometry (1)
 
Quantitative Biology - Cell Behavior (1)
 
Physics - Biological Physics (1)
 
Solar and Stellar Astrophysics (1)
 
Physics - Materials Science (1)
 
Astrophysics of Galaxies (1)
 
High Energy Physics - Phenomenology (1)
 
Physics - Instrumentation and Detectors (1)
 
Cosmology and Nongalactic Astrophysics (1)
 
High Energy Physics - Experiment (1)
 
Physics - Atmospheric and Oceanic Physics (1)
 
Mathematics - Algebraic Geometry (1)
 
Mathematics - Complex Variables (1)

Publications Authored By J. Wolf

State-to-state chemistry investigates chemical reactions on the most fundamental level. A primary goal of state-to-state chemistry is to determine the quantum states of the final products given the quantum state of reactants. Using the high level control for preparing reactants in the ultracold domain, we demonstrate here a method for investigating state-to-state chemistry with unprecedented resolution. Read More

While propagating in transparent media, near-infrared multi-terawatt (TW) laser beams break up in a multitude of filaments of typically 100-200 um diameter with peak intensities as high as 10 to 100~TW/cm$^{2}$. We observe a phase transition at incident beam intensities of 0.4~TW/cm$^2$, where the interaction between filaments induce solid-like 2-dimensional crystals with a 2. Read More

We spectroscopically investigate the hyperfine, rotational and Zeeman structure of the vibrational levels $\text{v}'=0$, $7$, $13$ within the electronically excited $c^3\Sigma_g^+$ state of $^{87}\text{Rb}_2$ for magnetic fields of up to $1000\,\text{G}$. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a^3\Sigma_u^+$ potential. As a byproduct, we present optical two-photon transfer of weakly bound Feshbach molecules into $a^3\Sigma_u^+$, $\text{v}=0$ levels featuring different nuclear spin quantum numbers. Read More

We experimentally demonstrate that the transmission of a 1030~nm, 1.3~ps laser beam of 100 mJ energy through fog increases when its repetition rate increases to the kHz range. Due to the efficient energy deposition by the laser filaments in the air, a shockwave ejects the fog droplets from a substantial volume of the beam, at a moderate energy cost. Read More

We study local regularity properties of a weak solution $u$ to the Cauchy problem of the incompressible Navier-Stokes equations. We present a new regularity criterion for the weak solution $u$ satisfying the condition $L^\infty(0,T;L^{3,w}(\mathbb{R}^3))$ without any smallness assumption on that scale, where $L^{3,w}(\mathbb{R}^3)$ denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time $t$. Read More

A stellar occultation by a trans-Neptunian object (TNO) provides an opportunity to probe its size and shape. Very few occultations by TNOs have been sampled simultaneously from multiple locations, while a robust estimation of shadow size has been possible for only two objects. We present the first observation of an occultation by the TNO 2007 UK126 on 15 November 2014, measured by three observers, one nearly on and two almost symmetrical to the shadow's centerline. Read More

The electric conductivity, HV discharge triggering and guiding capabilities of filaments at 3.9 micrometer in air are investigated in the perspective of lightning control applications, and compared to near-IR filaments in identical conditions Read More

In the study of local regularity of weak solutions to systems related to incompressible viscous fluids local energy estimates serve as important ingredients. However, this requires certain informations on the pressure. This fact has been used by V. Read More

We study the scenario of discretely self-similar blow-up for Navier-Stokes equations. We prove that at the possible blow-up time such solutions only one point singularity. In case of the scaling parameter $ \lambda $ near $ 1$ we remove the singularity. Read More

We examine the structure of the Levi component $MA$ in a minimal parabolic subgroup $P = MAN$ of a real reductive Lie group $G$ and work out the cases where $M$ is metabelian, equivalently where $\mathfrak{p}$ is solvable. When $G$ is a linear group we verify that $\mathfrak{p}$ is solvable if and only if $M$ is commutative. In the general case $M$ is abelian modulo the center $Z_G$, we indicate the exact structure of $M$ and $P$, and we work out the precise Plancherel Theorem and Fourier Inversion Formulae. Read More

We investigate the self-induced turbulence of high repetition rate laser filaments over a wide range of average powers (1 mW to 100 W) and its sensitivity to external atmospheric turbulence. Although both externally-imposed and self-generated turbulences can have comparable magnitudes, they act on different temporal and spatial scales. While the former drives the shot-to-shot motion at the millisecond time scale, the latter acts on the 0. Read More

We prove the existence of a forward discretely self-similar solutions to the Navier-Stokes equations in $ \Bbb R^{3}\times (0,+\infty)$ for a discretely self-similar initial velocity belonging to $ L^2_{ loc}(\Bbb R^{3})$. Read More

We prove Liouville type theorems for the self-similar solutions to the Navier-Stokes equations. One of our results generalizes the previous ones by Ne\v{c}as-R\.{u}\v{z}i\v{c}ka-\v{S}verak and Tsai. Read More

We study riemannian coverings $\varphi: \widetilde{M} \to \Gamma\backslash \widetilde{M}$ where $\widetilde{M}$ is a normal homogeneous space $G/K_1$ fibered over another normal homogeneous space $M = G/K$ and $K$ is locally isomorphic to a nontrivial product $K_1\times K_2$. The most familiar such fibrations $\pi: \widetilde{M} \to M$ are the natural fibrations of Stieffel manifolds $SO(n_1 + n_2)/SO(n_1)$ over Grassmann manifolds $SO(n_1 + n_2)/[SO(n_1)\times SO(n_2)]$ and the twistor space bundles over quaternionic symmetric spaces (= quaternion-Kaehler symmetric spaces = Wolf spaces). The most familiar of these coverings $\varphi: \widetilde{M} \to \Gamma\backslash \widetilde{M}$ are the universal riemannian coverings of spherical space forms. Read More

We investigate the pulse partitioning of a 6.3 mJ, 450 fs pulse at 1030 nm to produce plasma channels. At such moderate energies, splitting the energy into several sub-pulses reduces the ionization efficiency and thus does not extend the plasma lifetime. Read More

We study the triggering of single filaments due to turbulence in the beam path for a laser of power below the filamenting threshold. Turbulence can act as a switch between the beam not filamenting and producing single filaments. This 'positive' effect of turbulence on the filament probability, combined with our observation of off-axis filaments suggests the underlying mechanism is modulation instability caused by transverse perturbations. Read More

We study the regularity of weak solutions to the 3D valued stationary Hall magnetohydrodynamic equations on $ \Bbb R^2$. We prove that every weak solution is smooth. Furthermore, we prove a Liouville type theorem for the Hall equations. Read More

We study the partial regularity of suitable weak solutions to the three dimensional incompressible Navier--Stokes equations. There have been several attempts to refine the Caffarelli--Kohn--Nirenberg criterion (1982). We present an improved version of the CKN criterion with a direct method, which also provides the quantitative relation in Seregin's criterion (2007). Read More

In a series of recent papers we extended the notion of square integrability, for representations of nilpotent Lie groups, to that of stepwise square integrability. There we discussed a number of applications based on the fact that nilradicals of minimal parabolic subgroups of real reductive Lie groups are stepwise square integrable. Here, in Part I, we prove stepwise square integrability for nilradicals of arbitrary parabolic subgroups of real reductive Lie groups. Read More

In this paper we prove three different Liouville type theorems for the steady Navier-Stokes equations in $\Bbb R^3$. In the first theorem we improve logarithmically the well-known $L^{\frac92} (\Bbb R^3)$ result. In the second theorem we present a sufficient condition for the trivially of the solution($v=0$) in terms of the head pressure, $Q=\frac12 |v|^2 +p$. Read More

2016Mar
Authors: M. Arenz, M. Babutzka, M. Bahr, J. P. Barrett, S. Bauer, M. Beck, A. Beglarian, J. Behrens, T. Bergmann, U. Besserer, J. Blümer, L. I. Bodine, K. Bokeloh, J. Bonn, B. Bornschein, L. Bornschein, S. Büsch, T. H. Burritt, S. Chilingaryan, T. J. Corona, L. De Viveiros, P. J. Doe, O. Dragoun, G. Drexlin, S. Dyba, S. Ebenhöch, K. Eitel, E. Ellinger, S. Enomoto, M. Erhard, D. Eversheim, M. Fedkevych, A. Felden, S. Fischer, J. A. Formaggio, F. Fränkle, D. Furse, M. Ghilea, W. Gil, F. Glück, A. Gonzalez Urena, S. Görhardt, S. Groh, S. Grohmann, R. Grössle, R. Gumbsheimer, M. Hackenjos, V. Hannen, F. Harms, N. Hauÿmann, F. Heizmann, K. Helbing, W. Herz, S. Hickford, D. Hilk, B. Hillen, T. Höhn, B. Holzapfel, M. Hötzel, M. A. Howe, A. Huber, A. Jansen, N. Kernert, L. Kippenbrock, M. Kleesiek, M. Klein, A. Kopmann, A. Kosmider, A. Kovalík, B. Krasch, M. Kraus, H. Krause, M. Krause, L. Kuckert, B. Kuffner, L. La Cascio, O. Lebeda, B. Leiber, J. Letnev, V. M. Lobashev, A. Lokhov, E. Malcherek, M. Mark, E. L. Martin, S. Mertens, S. Mirz, B. Monreal, K. Müller, M. Neuberger, H. Neumann, S. Niemes, M. Noe, N. S. Oblath, A. Off, H. -W. Ortjohann, A. Osipowicz, E. Otten, D. S. Parno, P. Plischke, A. W. P. Poon, M. Prall, F. Priester, P. C. -O. Ranitzsch, J. Reich, O. Rest, R. G. H. Robertson, M. Röllig, S. Rosendahl, S. Rupp, M. Rysavy, K. Schlösser, M. Schlösser, K. Schönung, M. Schrank, J. Schwarz, W. Seiler, H. Seitz-Moskaliuk, J. Sentkerestiova, A. Skasyrskaya, M. Slezak, A. Spalek, M. Steidl, N. Steinbrink, M. Sturm, M. Suesser, H. H. Telle, T. Thümmler, N. Titov, I. Tkachev, N. Trost, A. Unru, K. Valerius, D. Venos, R. Vianden, S. Vöcking, B. L. Wall, N. Wandkowsky, M. Weber, C. Weinheimer, C. Weiss, S. Welte, J. Wendel, K. L. Wierman, J. F. Wilkerson, D. Winzen, J. Wolf, S. Wüstling, M. Zacher, S. Zadoroghny, M. Zboril

The KATRIN experiment will probe the neutrino mass by measuring the beta-electron energy spectrum near the endpoint of tritium beta-decay. An integral energy analysis will be performed by an electro-static spectrometer (Main Spectrometer), an ultra-high vacuum vessel with a length of 23.2 m, a volume of 1240 m^3, and a complex inner electrode system with about 120000 individual parts. Read More

2016Feb
Authors: R. Adhikari, M. Agostini, N. Anh Ky, T. Araki, M. Archidiacono, M. Bahr, J. Baur, J. Behrens, F. Bezrukov, P. S. Bhupal Dev, D. Borah, A. Boyarsky, A. de Gouvea, C. A. de S. Pires, H. J. de Vega, A. G. Dias, P. Di Bari, Z. Djurcic, K. Dolde, H. Dorrer, M. Durero, O. Dragoun, M. Drewes, G. Drexlin, Ch. E. Düllmann, K. Eberhardt, S. Eliseev, C. Enss, N. W. Evans, A. Faessler, P. Filianin, V. Fischer, A. Fleischmann, J. A. Formaggio, J. Franse, F. M. Fraenkle, C. S. Frenk, G. Fuller, L. Gastaldo, A. Garzilli, C. Giunti, F. Glück, M. C. Goodman, M. C. Gonzalez-Garcia, D. Gorbunov, J. Hamann, V. Hannen, S. Hannestad, S. H. Hansen, C. Hassel, J. Heeck, F. Hofmann, T. Houdy, A. Huber, D. Iakubovskyi, A. Ianni, A. Ibarra, R. Jacobsson, T. Jeltema, J. Jochum, S. Kempf, T. Kieck, M. Korzeczek, V. Kornoukhov, T. Lachenmaier, M. Laine, P. Langacker, T. Lasserre, J. Lesgourgues, D. Lhuillier, Y. F. Li, W. Liao, A. W. Long, M. Maltoni, G. Mangano, N. E. Mavromatos, N. Menci, A. Merle, S. Mertens, A. Mirizzi, B. Monreal, A. Nozik, A. Neronov, V. Niro, Y. Novikov, L. Oberauer, E. Otten, N. Palanque-Delabrouille, M. Pallavicini, V. S. Pantuev, E. Papastergis, S. Parke, S. Pascoli, S. Pastor, A. Patwardhan, A. Pilaftsis, D. C. Radford, P. C. -O. Ranitzsch, O. Rest, D. J. Robinson, P. S. Rodrigues da Silva, O. Ruchayskiy, N. G. Sanchez, M. Sasaki, N. Saviano, A. Schneider, F. Schneider, T. Schwetz, S. Schönert, S. Scholl, F. Shankar, R. Shrock, N. Steinbrink, L. Strigari, F. Suekane, B. Suerfu, R. Takahashi, N. Thi Hong Van, I. Tkachev, M. Totzauer, Y. Tsai, C. G. Tully, K. Valerius, J. W. F. Valle, D. Venos, M. Viel, M. Vivier, M. Y. Wang, C. Weinheimer, K. Wendt, L. Winslow, J. Wolf, M. Wurm, Z. Xing, S. Zhou, K. Zuber

We present a comprehensive review of keV-scale sterile neutrino Dark Matter, collecting views and insights from all disciplines involved - cosmology, astrophysics, nuclear, and particle physics - in each case viewed from both theoretical and experimental/observational perspectives. After reviewing the role of active neutrinos in particle physics, astrophysics, and cosmology, we focus on sterile neutrinos in the context of the Dark Matter puzzle. Here, we first review the physics motivation for sterile neutrino Dark Matter, based on challenges and tensions in purely cold Dark Matter scenarios. Read More

We consider the complex ind-group $G=\mathrm{SL}(\infty,\mathbb{C})$ and its real forms $G^0=\mathrm{SU}(\infty,\infty)$, $\mathrm{SU}(p,\infty)$, $\mathrm{SL}(\infty,\mathbb{R})$, $\mathrm{SL}(\infty,\mathbb{H})$. Our main objects of study are the $G^0$-orbits on an ind-variety $G/P$ for an arbitrary splitting parabolic ind-subgroup $P\subset G$. We prove that the intersection of any $G^0$-orbit on $G/P$ with a finite-dimensional flag variety $G_n/P_n$ from a given exhaustion of $G/P$ via $G_n/P_n$ for $n\to\infty$, is a single $(G^0\cap G_n)$-orbit. Read More

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on parabolic subgroups of real semisimple Lie groups, and to (infinite dimensional) locally nilpotent Lie groups. Many of these consequences are still under development. Read More

Dual-comb spectroscopy is emerging as one of the most appealing applications of mid-infrared frequency combs for high-resolution molecular spectroscopy, as it leverages on the unique coherence properties of frequency combs combined with the high sensitivities achievable by mid-infrared molecular spectroscopy. Here we present an on-chip dual-comb source based on mid-infrared quantum cascade laser frequency combs, where two frequency combs are integrated on a single chip. Control of the combs repetition and offset frequencies is obtained by integrating micro-heaters next to each laser. Read More

Quantum cascade lasers are compact sources capable of generating frequency combs. Yet key characteristics - such as optical bandwidth and power-per-mode distribution - have to be improved for better addressing spectroscopy applications. Group delay dispersion plays an important role in the comb formation. Read More

We measured the chemical composition and the size distribution of aerosols generated by femtosecond-Terawatt laser pulses in the atmosphere using an aerosol mass spectrometer (AMS). We show that nitric acid condenses in the form of ammonium nitrate, and that oxidized volatile organics also contribute to particle growth. These two components account for two thirds and one third, respectively, of the dry laser-condensed mass. Read More

Let $G$ be a complex simple direct limit group, specifically $SL(\infty;\mathbb{C})$, $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$. Let $\mathcal{F}$ be a (generalized) flag in $\mathbb{C}^\infty$. If $G$ is $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$ we suppose further that $\mathcal{F}$ is isotropic. Read More

We investigate the interaction of narrow plasma channels formed in the filamentation of ultrashort laser pulses, with a DC high voltage. The laser filaments prevent electrical arcs by triggering corona that neutralize the high-voltage electrodes. This phenomenon, due to the electric field modulation and free electron release around the filament, opens new prospects to lightning and over-voltage mitigation. Read More

Strong deformation of ultrashort laser pulse shapes is unavoidable when delivering high intensities at remote distances due to non-linear effects taking place while propagating. Relying on the reversibility of laser filamentation, we propose to explicitly design laser pulse shapes so that propagation serves as a non-linear field synthesizer at a remote target location. Such an approach allows, for instance, coherent control of molecules at a remote distance, in the context of standoff detection of pathogens or explosives. Read More

Here we report on the first successful exoplanet transit observation with the Stratospheric Observatory for Infrared Astronomy (SOFIA). We observed a single transit of the hot Jupiter HD 189733 b, obtaining two simultaneous primary transit lightcurves in the B and z' bands as a demonstration of SOFIA's capability to perform absolute transit photometry. We present a detailed description of our data reduction, in particular the correlation of photometric systematics with various in-flight parameters unique to the airborne observing environment. Read More

We study Beltrami flows in the setting of weak solution to the stationary Euler equations in $\Bbb R^3$. For this weak Beltrami flow we prove the regularity and the Liouville property. In particular, we show that if tangential part of the velocity has certain decay property at infinity, then the solution becomes trivial. Read More

We consider the Stokes problem in an exterior domain $\Omega \subset \R^n$ with an external force $\bbf \in L^s(0,T; \bW^{k,\, r}(\Omega ))\, (k\in \N, 1Read More

We show that multiple filamentation patterns in high-power laser beams, can be described by means of two statistical physics concepts, namely self-similarity of the patterns over two nested scales, and nearest-neighbor interactions of classical rotators. The resulting lattice spin model perfectly reproduces the evolution of intense laser pulses as simulated by the Non-Linear Schr\"odinger Equation, shedding a new light on multiple filamentation. As a side benefit, this approach drastically reduces the computing time by two orders of magnitude as compared to the standard simulation methods of laser filamentation. Read More

We study partial regularity of suitable weak solutions of the steady Hall magnetohydrodynamics equations in a domain $\Omega \subset \Bbb R^3$. In particular we prove that the set of possible singularities of the suitable weak solution has Hausdorff dimension at most one. Moreover, in the case $\Omega=\Bbb R^3$, we show that the set of possible singularities is compact. Read More

In this paper we develop the basic tools for a classification of Killing vector fields of constant length on pseudo--riemannian homogeneous spaces. This extends a recent paper of M. Xu and J. Read More

In this paper we give an explicit description of the bounded displacement isometries of a class of spaces that includes the Riemannian nilmanifolds. The class of spaces consists of metric spaces (and thus includes Finsler manifolds) on which an exponential solvable Lie group acts transitively by isometries. The bounded isometries are proved to be of constant displacement. Read More

We demonstrated room temperature operation of deep etched photonic crystal quantum cascade laser emitting around 8.5 micron. We fabricated buried heterostructure photonic crystals, resulting in single mode laser emission on a high order slow Bloch modes of the photonic crystal, between high symmetry points of the Brillouin. Read More

We study partial regularity of weak solutions of the 3D valued non-stationary Hall magnetohydrodynamics equations on $ \Bbb R^2$. In particular we prove the existence of a weak solution whose set of possible singularities has the space-time Hausdorff dimension at most two. Read More

A compact Riemannian homogeneous space $G/H$, with a bi--invariant orthogonal decomposition $\mathfrak{g}=\mathfrak{h}+\mathfrak{m}$ is called positively curved for commuting pairs, if the sectional curvature vanishes for any tangent plane in $T_{eH}(G/H)$ spanned by a linearly independent commuting pair in $\mathfrak{m}$. In this paper,we will prove that on the coset space $\mathrm{Sp}(2)/\mathrm{U}(1)$, in which $\mathrm{U}(1)$ corresponds to a short root, admits positively curved metrics for commuting pairs. B. Read More

We show that the onset of laser multiple filamentation can be described as a critical phenomenon that we characterize both experimentally and numerically by measuring a set of seven critical exponents. This phase transition deviates from any existing universality class, and offers a unique perspective of conducting two-dimensional experiments of statistical physics at a human scale. Read More

Killing vector fields of constant length correspond to isometries of constant displacement. Those in turn have been used to study homogeneity of Riemannian and Finsler quotient manifolds. Almost all of that work has been done for group manifolds or, more generally, for symmetric spaces. Read More

We investigate the use of Bismuth Ferrite (BFO) nanoparticles for tumor tissue labelling in combination with infrared multi-photon excitation at 1250 nm. We report the efficient and simultaneous generation of second and third harmonic by the nanoparticles. On this basis, we set up a novel imaging protocol based on the co-localization of the two harmonic signals and demonstrate its benefits in terms of increased selectivity against endogenous background sources in tissue samples. Read More

Bismuth Ferrite (BFO) nanoparticles (BFO-NP) display interesting optical (nonlinear response) and magnetic properties which make them amenable for bio-oriented applications as intra- and extra membrane contrast agents. Due to the relatively recent availability of this material in well dispersed nanometric form, its biocompatibility was not known to date. In this study, we present a thorough assessment of the effects of in vitro exposure of human adenocarcinoma (A549), lung squamous carcinoma (NCI-H520), and acute monocytic leukemia (THP-1) cell lines to uncoated and poly(ethylene glycol)-coated BFO-NP in the form of cytotoxicity, haemolytic response and biocompatibility. Read More

We present a numerical parametric study of single-cycle electromagnetic pulse generation in a DAST/SiO2 multilayer structure via collinear optical rectification of 800 nm femtosecond laser pulses. It is shown that modifications of the thicknesses of the DAST and SiO2 layers allow tuning of the average frequency of the generated THz pulses in the frequency range from 3 to 6 THz. The laser-to-THz energy conversion efficiency in the proposed structures is compared with that in a bulk DAST crystal and a quasi-phase-matching periodically poled DAST crystal and shows significant enhancement. Read More

Second Harmonic Generation (SHG) from BiFeO3 nanocrystals is investigated for the first time to determine their potential as biomarkers for multiphoton imaging. Nanocrystals are produced by an auto-combustion method with TRIS as a fuel. Stable colloidal suspensions with mean particle diameters in the range 100-120 nm are then obtained after wet-milling and sonication steps. Read More

The impact of nonadiabatic laser-induced molecular alignment on filamentation is numerically studied. Weak and strong field model of impulsive molecular alignment are compared in the context of nonlinear pulse propagation. It is shown that the widely used weak field model describing the refractive index modification induced by impulsive molecular alignment accurately reproduces the propagation dynamics providing that only a single pulse is involved during the experiment. Read More

In the classification theorems of Vinberg and Yakimova for commutative nilmanifolds, the relevant nilpotent groups have a very surprising analytic property. The manifolds are of the form $G/K = N \rtimes K/K$ where, in all but three cases, the nilpotent group $N$ has irreducible unitary representations whose coefficients are square integrable modulo the center $Z$ of $N$. Here we show that, in those three "exceptional" cases, the group $N$ is a semidirect product $N_1 \rtimes \mathbb{R}$ or $N_1 \rtimes \mathbb{C}$ where the normal subgroup $N_1$ contains the center $Z$ of $N$ and has irreducible unitary representations whose coefficients are square integrable modulo $Z$. Read More

The Stratospheric Observatory for Infrared Astronomy (SOFIA) has recently concluded a set of engineering flights for Observatory performance evaluation. These in-flight opportunities are viewed as a first comprehensive assessment of the Observatory's performance and are used to guide future development activities, as well as to identify additional Observatory upgrades. Pointing stability was evaluated, including the image motion due to rigid-body and flexible-body telescope modes as well as possible aero-optical image motion. Read More

In a recent paper we found conditions for a nilpotent Lie group $N$ to have a filtration by normal subgroups whose successive quotients have square integrable representations, and such that these square integrable representations fit together nicely to give an explicit construction of Plancherel almost all representations of $N$. That resulted in explicit character formulae, Plancherel formulae and multiplicity formulae. We also showed that nilradicals $N$ of minimal parabolic subgroups $P = MAN$ enjoy that "stepwise square integrable" property. Read More