Higher-order Karush–Kuhn–Tucker optimality conditions for set-valued optimization with nonsolid ordering cones

In this paper, we consider higher-order Karush–Kuhn–Tucker optimality conditions in terms of radial derivatives for set-valued optimization with nonsolid ordering cones. First, we develop sum rules and chain rules in the form of equality for radial derivatives. Then, we investigate set-valued optimization including mixed constraints with both ordering cones in the objective and constraint spaces having possibly empty interior. We obtain necessary conditions for quasi-relative efficient solutions and sufficient conditions for Pareto efficient solutions. For the special case of weak efficient solutions, we receive even necessary and sufficient conditions. Our results are new or improve recent existing ones in the literature.     

A boundary layer problem in nonflat domains with measurable viscous coefficients

We study the convergence of weak solutions of the Navier–Stokes equations with vanishing measurable viscous coefficients in domains with nonflat boundaries. Sufficient anisotropic conditions on the vanishing rates of the viscous coefficients are found to prove the convergence of Leray–Hopf weak solutions of the Navier–Stokes equations to solutions of the corresponding Euler equations. As the domains are not flat, we apply a change of variables to flatten the domains. We then construct explicit boundary layers for the system of Navier–Stokes equations in the upper-half space with measurable viscous coefficients. The result is new even when the viscous coefficients are constant, and it recovers the classical results when domains are flat and with constant viscous coefficients.     

Rational design of thioamide peptides as selective inhibitors of cysteine protease cathepsin L

Aberrant levels of cathepsin L (Cts L), a ubiquitously expressed endosomal cysteine protease, have been implicated in many diseases such as cancer and diabetes. Significantly, Cts L has been identified as a potential target for the treatment of COVID-19 due to its recently unveiled critical role in SARS-CoV-2 entry into the host cells. However, there are currently no clinically approved specific inhibitors of Cts L, as it is often challenging to obtain specificity against the many highly homologous cathepsin family cysteine proteases. Peptide-based agents are often promising protease inhibitors as they offer high selectivity and potency, but unfortunately are subject to degradation in vivo. Thioamide substitution, a single-atom O-to-S modification in the peptide backbone, has been shown to improve the proteolytic stability of peptides addressing this issue. Utilizing this approach, we demonstrate herein that good peptidyl substrates can be converted into sub-micromolar inhibitors of Cts L by a single thioamide substitution in the peptide backbone. We have designed and scanned several thioamide stabilized peptide scaffolds, in which one peptide, R^S_1A, was stabilized against proteolysis by all five cathepsins (Cts L, Cts V, Cts K, Cts S, and Cts B) while inhibiting Cts L with >25-fold specificity against the other cathepsins. We further showed that this stabilized R^S_1A peptide could inhibit Cts L in human liver carcinoma lysates (IC₅₀ = 19 μM). Our study demonstrates that one can rationally design a stabilized, specific peptidyl protease inhibitor by strategic placement of a thioamide and reaffirms the place of this single-atom modification in the toolbox of peptide-based rational drug design.

Information on the effects of sidechain and backbone modification on the activity of cathepsin (Cts) L, V, K, S, and B was used to design a thioamide peptide that is inert to all Cts and selectively inhibits Cts L.     

New isomeric states in 152,154,156Nd produced by spontaneous fission of 252Cf

Isomeric states have been observed in fission-fragments produced by spontaneous fission of ²⁵²Cf. These states are found in neutron rich nuclei of different structure and deformations. About 50 isomeric nuclei have been observed using coincidences between γ-rays identified in EUROGAM II and fission fragments detected in photovoltaic cells (SAPhIR). Lifetimes in the range from 20 ns to 2μs have been measured. Presented calculations based on HFB +D1S force on new measured isomeric states in the ^152,154,156Nd show evidence for K-isomers. Received: 3 November 1997 / Revised version: 15 December 1997     

C - axis resistivity of stages 1–7 potassium-intercalated graphite

Temperature-dependent c-axis resistivity measurements on stages 1–7 potassium-graphite compounds show a crossover from metallic to activated behaviour between stages 4 and 5, as well as the onset of a new type of anomaly for stage ≥4. KC₈ shows in addition a tendency toward a metal-insulator transition below 40K. The high-stage transport process is discussed in terms of weak depletion of the interior layers by interlayer screening. We suggest that the high stage anomalies reflect an instability in the c-axis charge distribution.     

Caesaldecan, a cassane diterpenoid from the leaves of Caesalpinia decapetala

A new cassane diterpenoid, caesaldecan, was isolated from Caesalpinia decapetala with eight known compounds, spathulenol, 4,5-epoxy-8(14)-caryophyllene, squalene, lupeol, trans-resveratrol, quercetin, astragalin, and stigmasterol. The (1)H- and (13)C-NMR spectra of the new compound were completely assigned by using a combination of 2D NMR techniques, namely, (1)H-(1)H COSY, HMQC, HMBC, and ROESY.