Exterior square gamma factors for cuspidal representations of $$\mathrm {GL}_n$$ GL n : simple supercuspidal representations

We compute the local twisted exterior square gamma factors for simple supercuspidal representations, using which we prove a local converse theorem for simple supercuspidal representations.

     

THE SOLUTION PHOTODIMERIZATION OF URIDINE

Abstract— Quenching of the degradative photobleaching of FMN in anaerobic aqueous solution, and of the flavin-sensitized photo-oxidation of EDTA, alcohols, glycols, and glycerol, has been examined using flash techniques. The quenching can be produced by addition of KI, by successive flashes, and by increasing the flavin concentration (self-quenching). It is concluded that the lowest triplet is the photoreactive species in all systems, that the successive flash effect is due to triplet quenching by a reaction product, and that the concentration quenching may be due to either triplet-triplet annihilation or to reaction between a ground-state flavin and a flavin triplet.     

Dispersion measurements using time-of-flight remote detection MRI

Remote detection nuclear magnetic resonance and magnetic resonance imaging can be used to study fluid flow and dispersion in a porous medium from a purely Eulerian point of view (i.e., in a laboratory frame of reference). Information about fluid displacement is obtained on a macroscopic scale in a long-time regime, while local velocity distributions are averaged out. It is shown how these experiments can be described using the common flow propagator formalism and how experimental data can be analyzed to obtain effective porosity, flow velocity inside the porous medium, fluid dispersion and flow tracing of fluid.     

Benzimidazole tethered thioureas as a new entry to elastase inhibition and free radical scavenging: Synthesis,molecular docking,and enzyme inhibitory kinetics

The porcine pancreatic elastase inhibition and free-radical scavenging play a crucial role in age progression. All the series of 10 newly synthesized benzimidazole thioureas ( 4a-j ) were assessed for elastase inhibition and radical scavenging activity to identify the suitable anti-aging ingredient for cosmetics products. The compounds 4e , 4f , 4g , and 4h showed inhibition better than the standard, while compound 4f showed the most significant elastase inhibition with the IC₅₀ value of 1.318 ± 0.025 μM compared with oleanic acid IC₅₀ 13.451 ± 0.014 used ±1.989 and 41.563 ± 0.824, respectively, as standard. Molecular docking studies were performed and the compound 4f showed binding energy of 7.2 kcal/mol. Kinetics studies revealed inhibition of the pancreatic elastase in a competitive manner. The relative binding energy and structure activity relationship (SAR) identified compound 4f as an effective inhibitor of porcine pancreatic elastase. Compounds 4e and 4i showed remarkable free-radical scavenging activity with SC₅₀ values of 26.421.     

Network information and connected correlations

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.     

Algebraic patching over complete domains

We extend the method of algebraic patching due to Haran-Jarden-Völklein from complete absolute valued fields to complete domains. We apply the extended method to reprove a result of Lefcourt obtained by formal patching — every finite group is regularly realizable over the quotient field of a complete domain.     

A mathematical model of medial consonant identification by cochlear implant users

The multidimensional phoneme identification model is applied to consonant confusion matrices obtained from 28 postlingually deafened cochlear implant users. This model predicts consonant matrices based on these subjects' ability to discriminate a set of postulated spectral, temporal, and amplitude speech cues as presented to them by their device. The model produced confusion matrices that matched many aspects of individual subjects' consonant matrices, including information transfer for the voicing, manner, and place features, despite individual differences in age at implantation, implant experience, device and stimulation strategy used, as well as overall consonant identification level. The model was able to match the general pattern of errors between consonants, but not the full complexity of all consonant errors made by each individual. The present study represents an important first step in developing a model that can be used to test specific hypotheses about the mechanisms cochlear implant users employ to understand speech.     

Single-shot ultrabroadband two-dimensional electronic spectroscopy of the light-harvesting complex LH2

Here we present two-dimensional (2D) electronic spectra of the light-harvesting complex LH2 from purple bacteria using coherent pulses with bandwidth of over 100 nm FWHM. This broadband excitation and detection has allowed the simultaneous capture of both the B800 and B850 bands using a single light source. We demonstrate that one laser pulse is sufficient to capture the entire 2D electronic spectrum with a high signal-to-noise ratio. At a waiting time of 800 fs, we observe population transfer from the B800 to B850 band as manifested by a prominent cross peak. These results will enable observation of the dynamics of biological systems across both ultrafast (<1 ps) and slower (>1 ms) timescales simultaneously.     

Single-shot gradient-assisted photon echo electronic spectroscopy

Two-dimensional electronic spectroscopy (2D ES) maps the electronic structure of complex systems on a femtosecond time scale. While analogous to multidimensional NMR spectroscopy, 2D optical spectroscopy differs significantly in its implementation. Yet, 2D Fourier spectroscopies still require point-by-point sampling of the time delay between two pulses responsible for creating quantum coherence among states. Unlike NMR, achieving the requisite phase stability at optical frequencies between these pulse pairs remains experimentally challenging. Nonetheless, 2D optical spectroscopy has been successfully demonstrated by combining passive and active phase stabilization along with precise control of optical delays and long-term temperature stability, although the widespread adoption of 2D ES has been significantly hampered by these technical challenges. Here, we exploit an analogy to magnetic resonance imaging (MRI) to demonstrate a single-shot method capable of acquiring the entire 2D spectrum in a single laser shot using only conventional optics. Unlike point-by-point sampling protocols typically used to record 2D spectra, this method, which we call GRadient-Assisted Photon Echo (GRAPE) spectroscopy, largely eliminates phase errors while reducing the acquisition time by orders of magnitude. By incorporating a spatiotemporal encoding of the nonlinear polarization along the excitation frequency axis of the 2D spectrum, GRAPE spectroscopy achieves no loss in signal while simultaneously reducing overall noise. Here, we describe the principles of GRAPE spectroscopy and discuss associated experimental considerations.