We prove duality isomorphisms of certain representations of ${\mathcal{W}}$ -algebras which play an essential role in the quantum geometric Langlands program and some related results.

Regrasping is a manipulation to alternate between grasp configurations of an object to perform different tasks. We address a regrasping problem termed longitude regrasping to reposition a gripper along an elongated object. We propose an algorithm using the dynamics of the arm and a non-dexterous gripper to perform the manipulation. Energy control is used to toss the object up and catch it under the goal position. Clipped Linear Quadratic Regulator control approach is then applied to the gripper jaws to control the friction force on the object and to let it slide to the final goal position. The object sliding within the gripper is modeled as a semi-active linear joint where only dissipative forces can be applied to it. A set of experiments validated the feasibility of the method.

The joint effects of an insoluble surfactant and gravity on the linear stability of a two-layer Couette flow in a horizontal channel are investigated. The inertialess instability regimes are studied for arbitrary wavelengths and with no simplifying requirements on the system parameters: the ratio of thicknesses of the two fluid layers; the viscosity ratio; the base shear rate; the Marangoni number $Ma$ ; and the Bond number $Bo$ . As was established in the first part of this investigation (Frenkel, Halpern & Schweiger, J. Fluid Mech., vol. 863, 2019, pp. 150–184), a quadratic dispersion equation for the complex growth rate yields two, largely continuous, branches of the normal modes, which are responsible for the flow stability properties. This is consistent with the surfactant instability case of zero gravity studied in Halpern & Frenkel (J. Fluid Mech., vol. 485, 2003, pp. 191–220). The present paper focuses on the mid-wave regimes of instability, defined as those having a finite interval of unstable wavenumbers bounded away from zero. In particular, the location of the mid-wave instability regions in the ( $Ma$ , $Bo$ )-plane, bounded by their critical curves, depending on the other system parameters, is considered. The changes of the extremal points of these critical curves with the variation of external parameters are investigated, including the bifurcation points at which new extrema emerge. Also, it is found that for the less unstable branch of normal modes, a mid-wave interval of unstable wavenumbers may sometimes coexist with a long-wave one, defined as an interval having a zero-wavenumber endpoint.

A linear stability analysis of a two-layer plane Couette flow of two immiscible fluid layers with different densities, viscosities and thicknesses, bounded by two infinite parallel plates moving at a constant relative velocity to each other, with an insoluble surfactant monolayer along the interface and in the presence of gravity is carried out. The normal modes approach is applied to the equations governing flow disturbances in the two layers. These equations, together with boundary conditions at the plates and the interface, yield a linear eigenvalue problem. When inertia is neglected the velocity amplitudes are the linear combinations of certain hyperbolic functions, and a quadratic dispersion equation for the increment, that is the complex growth rate, is obtained, where coefficients depend on the aspect ratio, the viscosity ratio, the basic velocity shear, the Marangoni number $Ma$ that measures the effects of surfactant and the Bond number $Bo$ that measures the influence of gravity. An extensive investigation is carried out that examines the stabilizing or destabilizing influences of these parameters. Since the dispersion equation is quadratic in the growth rate, there are two continuous branches of the normal modes: a robust branch that exists even with no surfactant, and a surfactant branch that, to the contrary, vanishes when $Ma\downarrow 0$ . Regimes have been uncovered with crossings of the two dispersion curves, their reconnections at the point of crossing and separations as $Bo$ changes. Due to the availability of the explicit forms for the growth rates, in many instances the numerical results are corroborated with analytical asymptotics.

A horizontal channel flow of two immiscible fluid layers with different densities, viscosities and thicknesses, subject to vertical gravitational forces and with an insoluble surfactant monolayer present at the interface, is investigated. The base Couette flow is driven by the uniform horizontal motion of the channel walls. Linear and nonlinear stages of the (inertialess) surfactant and gravity dependent long-wave instability are studied using the lubrication approximation, which leads to a system of coupled nonlinear evolution equations for the interface and surfactant disturbances. The (inertialess) instability is a combined result of the surfactant action characterized by the Marangoni number $Ma$ and the gravitational effect corresponding to the Bond number $Bo$ that ranges from $-\infty$ to $\infty$ . The other parameters are the top-to-bottom thickness ratio $n$ , which is restricted to $n\geqslant 1$ by a reference frame choice, the top-to-bottom viscosity ratio $m$ and the base shear rate $s$ . The linear stability is determined by an eigenvalue problem for the normal modes, where the complex eigenvalues (determining growth rates and phase velocities) and eigenfunctions (the amplitudes of disturbances of the interface, surfactant, velocities and pressures) are found analytically by using the smallness of the wavenumber. For each wavenumber, there are two active normal modes, called the surfactant and the robust modes. The robust mode is unstable when $Bo/Ma$ falls below a certain value dependent on $m$ and $n$ . The surfactant branch has instability for $m<1$ , and any $Bo$ , although the range of unstable wavenumbers decreases as the stabilizing effect of gravity represented by $Bo$ increases. Thus, for certain parametric ranges, even arbitrarily strong gravity cannot completely stabilize the flow. The correlations of vorticity-thickness phase differences with instability, present when gravitational effects are neglected, are found to break down when gravity is important. The physical mechanisms of instability for the two modes are explained with vorticity playing no role in them. This is in marked contrast to the dynamical role of vorticity in the mechanism of the well-known Yih instability due to effects of inertia, and is contrary to some earlier literature. Unlike the semi-infinite case that we previously studied, a small-amplitude saturation of the surfactant instability is possible in the absence of gravity. For certain $(m,n)$ -ranges, the interface deflection is governed by a decoupled Kuramoto–Sivashinsky equation, which provides a source term for a linear convection–diffusion equation governing the surfactant concentration. When the diffusion term is negligible, this surfactant equation has an analytic solution which is consistent with the full numerics. Just like the interface, the surfactant wave is chaotic, but the ratio of the two waves turns out to be constant.

The historicity of books – their role as a force in history – has been addressed in post-war literary studies from different perspectives and across various disciplines. Nevertheless, the scholarship on the history of the book in medieval Islam is still relatively sparse, even though this society underwent a thorough process of textualization. But even authors who do consider the social and cultural role of books in medieval Islam look only at the production and consumption of Arabic books within the boundaries of Muslim society, relying on Islamic sources which reflect mainly the courtly milieu of scribes and secretariats. None discuss books produced and consumed by the religious minorities that were an indispensable part of this society, and none have made use of the abundant Genizah documents as source material. In the present programmatic article, I call attention to the many book lists found in the Cairo Genizah and to their potential as significant tools for developing a better understanding of the cultural and social history of the medieval Islamicate world.

Introduction: Point of care ultrasound has become an established tool in the initial management of patients with undifferentiated hypotension. Current established protocols (RUSH, ACES, etc) were developed by expert user opinion, rather than objective, prospective data. We wished to use reported disease incidence to develop an informed approach to PoCUS in hypotension using a “4 F’s” approach: Fluid; Form; Function; Filling. Methods: We summarized the incidence of PoCUS findings from an international multicentre RCT, and using a modified Delphi approach incorporating this data we obtained the input of 24 international experts associated with five professional organizations led by the International Federation of Emergency Medicine. The modified Delphi tool was developed to reach an international consensus on how to integrate PoCUS for hypotensive emergency department patients. Results: Rates of abnormal PoCUS findings from 151 patients with undifferentiated hypotension included left ventricular dynamic changes (43%), IVC abnormalities (27%), pericardial effusion (16%), and pleural fluid (8%). Abdominal pathology was rare (fluid 5%, AAA 2%). After two rounds of the survey, using majority consensus, agreement was reached on a SHoC-hypotension protocol comprising: A. Core: 1. Cardiac views (Sub-xiphoid and parasternal windows for pericardial fluid, cardiac form and ventricular function); 2. Lung views for pleural fluid and B-lines for filling status; and 3. IVC views for filling status; B. Supplementary: Additional cardiac views; and C. Additional views (when indicated) including peritoneal fluid, aorta, pelvic for IUP, and proximal leg veins for DVT. Conclusion: An international consensus process based on prospectively collected disease incidence has led to a proposed SHoC-hypotension PoCUS protocol comprising a stepwise clinical-indication based approach of Core, Supplementary and Additional PoCUS views.

Introduction: Point of care ultrasound (PoCUS) provides invaluable information during resuscitation efforts in cardiac arrest by determining presence/absence of cardiac activity and identifying reversible causes such as pericardial tamponade. There is no agreed guideline on how to safely and effectively incorporate PoCUS into the advanced cardiac life support (ACLS) algorithm. We consider that a consensus-based priority checklist using a “4 F’s” approach (Fluid; Form; Function; Filling), would provide a better algorithm during ACLS. Methods: The ultrasound subcommittee of the Australasian College for Emergency Medicine (ACEM) drafted a checklist incorporating PoCUS into the ACLS algorithm. This was further developed using the input of 24 international experts associated with five professional organizations led by the International Federation of Emergency Medicine. A modified Delphi tool was developed to reach an international consensus on how to integrate ultrasound into cardiac arrest algorithms for emergency department patients. Results: Consensus was reached following 3 rounds. The agreed protocol focuses on the timing of PoCUS as well as the specific clinical questions. Core cardiac windows performed during the rhythm check pause in chest compressions are the sub-xiphoid and parasternal cardiac views. Either view should be used to detect pericardial fluid, as well as examining ventricular form (e.g. right heart strain) and function, (e.g. asystole versus organized cardiac activity). Supplementary views include lung views (for absent lung sliding in pneumothorax and for pleural fluid), and IVC views for filling. Additional ultrasound applications are for endotracheal tube confirmation, proximal leg veins for DVT, or for sources of blood loss (AAA, peritoneal/pelvic fluid). Conclusion: The authors hope that this process will lead to a consensus-based SHoC-cardiac arrest guideline on incorporating PoCUS into the ACLS algorithm.

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013.

Amorphous films [BaTiO3 (BTO), SrTiO3 (STO), SrRuO3] on substrates and self-supported films (BTO and STO) were produced by controlling the film/substrate adhesion energy (level of clamping). The stress value in an as-deposited film depends on the clamping level, which defines the stress relief mode. In highly stressed films, the stress abatement is achieved via plastic transformation resulting in formation of “the strain-arranged structure of elastic domains.” Film fractures and delamination occur if the stress magnitude is too high and exceeds the elastic limit of the material. If the stress magnitude is low, the conditions favorable for nucleation and crystallization can arise. Stress in self-supported films is relieved mainly via shape change during film preparation, and the conditions favorable for nucleation and crystallization in annealed self-supported films arise more frequently.