Shock Formation and Vorticity Creation for 3d Euler

We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self-similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high-order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.     

Forest-Like Permutations

Given a permutation , construct a graph G _π on the vertex set {1, 2,..., n} by joining i to j if (i) i < j and π(i) < π(j) and (ii) there is no k such that i < k < j and π(i) < π(k) < π(j). We say that π is forest-like if G _π is a forest. We first characterize forest-like permutations in terms of pattern avoidance, and then by a certain linear map being onto. Thanks to recent results of Woo and Yong, these show that forest-like permutations characterize Schubert varieties which are locally factorial. Thus forest-like permutations generalize smooth permutations (corresponding to smooth Schubert varieties). We compute the generating function of forest-like permutations. As in the smooth case, it turns out to be algebraic. We then adapt our method to count permutations for which G _π is a tree, or a path, and recover the known generating function of smooth permutations. Received March 27, 2006     

Exponential growth of Lie algebras of finite global dimension

Let be a connected finite type graded Lie algebra. If dim and gldim , then log index . If, moreover, , then for some ,    dim where log index as

     

The strength with which a peptide group can form a hydrogen bond varies with the internal conformation of the polypeptide chain

The strength of the H-bond formed between a dipeptide and a proton acceptor molecule is assessed by correlated ab initio quantum calculations for a broad range of different conformations of the dipeptide. The H-bond energy is very sensitive to the internal (phi,psi) angles, even when the geometry of the H-bond does not vary significantly from one conformation to another. This result indicates that the peptide NH is a much less potent proton donor in certain conformations than in others. In particular, extended conformations of a polypeptide are capable of only weak H-bonds. Thus, the interstrand NH...O H-bonds in parallel and antiparallel beta-sheets are expected to be significantly weaker than those found in other conformations, such as helices, ribbons, and beta-bends, even if the H-bond geometries are similar.     

CuI-mediated cross-coupling of aryl halides with oximes: a direct access to O-aryloximes

The first Cu-catalyzed cross-coupling of aromatic oximes and haloarenes is reported. This one-step formation of the =N-O-Ar linkage gives access to a range of oxime ethers in good to moderate yields.     

Mechanism-of-action determination of GMP synthase inhibitors and target validation in Candida albicans and Aspergillus fumigatus

Mechanism-of-action (MOA) studies of bioactive compounds are fundamental to drug discovery. However, in vitro studies alone may not recapitulate a compound's MOA in whole cells. Here, we apply a chemogenomics approach in Candida albicans to evaluate compounds affecting purine metabolism. They include the IMP dehydrogenase inhibitors mycophenolic acid and mizoribine and the previously reported GMP synthase inhibitors acivicin and 6-diazo-5-oxo-L-norleucine (DON). We report important aspects of their whole-cell activity, including their primary target, off-target activity, and drug metabolism. Further, we describe ECC1385, an inhibitor of GMP synthase, and provide biochemical and genetic evidence supporting its MOA to be distinct from acivicin or DON. Importantly, GMP synthase activity is conditionally essential in C. albicans and Aspergillus fumigatus and is required for virulence of both pathogens, thus constituting an unexpected antifungal target.     

Conformationally rigid chelate rings in metal complexes of pyridyloxy-substituted 2,2'-dioxybiphenyl-cyclotetra- and cyclotriphosphazene platforms

Divalent metal halides react with pyridyloxy-substituted 2,2'-dioxybiphenyl-cyclotri- and cyclotetraphosphazene ligands to form the complexes, [MLX2] [M=Co or Cu; L=(2,2'-dioxybiphenyl)tetrakis(2-pyridyloxy)cyclotriphosphazene (L1) or (2,2'-dioxybiphenyl)tetrakis(4-methyl-2-pyridyloxy)cyclotriphosphazene (L2); X=Cl or Br], [ZnLCl2] [L=bis(2,2'-dioxybiphenyl)bis(2-pyridyloxy)cyclotriphosphazene (L3) or bis(2,2'-dioxybiphenyl)bis(4-methyl-2-pyridyloxy)cyclotriphosphazene (L4)], [MLCl2] [M=Cu or Hg; L=tris(2,2'-dioxybiphenyl)bis(2-pyridyloxy)cyclotetraphosphazene (L5)] and [Cu2LCl4] (L=trans-bis(2,2'-dioxybiphenyl)tetrakis(2-pyridyloxy)cyclotetraphosphazene (L6)]. Single-crystal X-ray structures show the L2 ligand complexes to have a N3Cl2 five-coordinate, trigonal-bipyramidal donor set with the phosphazene ring and pendant pyridyloxy nitrogens binding to the metal ions. The coordinated L2 ligand in the complex, [CoL2Cl2], slowly hydrolyses in acetonitrile with the loss of a pyridine pendant arm to form a dimetallic species, which has been characterized by crystallography as [{CoL2aCl}]2.4MeCN (L2a=[N3P3(biph)(OPy)3(O)]-, biph=2,2'-dioxybiphenyl, OPy=2-oxopyridine). The ligands, L3, L4, L5, and L6, bind to the metal halides via gem-substituted pyridyloxy nitrogens only. The resulting rigid eight-membered chelate rings all have distorted boat conformations, which force distorted-tetrahedral N2Cl2 coordination environments onto the metal ions. The spectroscopic (ESR and electronic) and magnetic properties of the complexes are reported.     

Structural characterization of modern and fossilized charcoal produced in natural fires as determined by using electron energy loss spectroscopy

Charcoal produced in natural fires is widespread, but surprisingly little is known about its structure and stability. TEM and electron energy loss spectroscopy (EELS) were used to characterize the organized graphite-like microcrystallites and amorphous nonorganized phases of modern charcoal that had been produced in natural fires. In addition, a semiordered structure was identified in two modern charcoal samples. Fossilized charcoal contains fewer graphite-like microcrystallites than modern samples. EELS spectra confirmed that the dominant structure in fossilized charcoal is amorphous carbon. EELS measurements also revealed that only the nonorganized phase contains oxygen, which indicates that the degradation of the fossilized charcoal structure occurs mainly through oxidation processes. The few graphite-like microcrystallites found in fossilized charcoal were composed of onion-like structures that are probably less prone to oxidation owing to their rounded structures.     

A novel strategy for the design of 8-hydroxyquinolinate-based lanthanide bioprobes that emit in the near infrared range

A new polydentate tripodal ligand T2soxMe was synthesized to take advantage of the chelating effect of tridentate 8-hydroxyquinolinate subunits. Potentiometric and spectrophotometric titrations reveal seven pK(a) values of between 3.7 and 10.2. In water, the use of T2soxMe leads to thermodynamically stable and soluble Ln(III) complexes at physiological pH, with conditional stability constants in the range log beta(11)=7.8-8.6. The chelates are resistant toward hydrolysis and show interesting photophysical properties, particularly in the near infrared (NIR) range. The emission lifetimes of the Nd(III) and Yb(III) complexes recorded in D(2)O and H(2)O suggest the absence of water molecules in the first coordination sphere of the metal ions. Moreover, the low energy of the triplet state allows efficient energy transfer from the ligand to the metal ions: in water at pH 7.4, the sensitization efficacy of the NIR luminescence reaches 75 and approximately 100 % for Nd(III) and Yb(III), respectively, leading to overall quantum yields of 0.027 and 0.13 %; Er(III) luminescence is also detected. According to the WST-1 test, the Yb(III) podate at concentrations of up to 250 microM does not display sizeable cytotoxicity for Jurkat cells after 24 h of incubation. Finally, the same podate is shown to couple to human serum albumin, leading to an increase of 50 % in the NIR-luminescence intensity.