Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

Positive solution to semilinear parabolic equation associated with critical Sobolev exponent

We study the semilinear parabolic equation ${u_{t}- \Delta u = u^{p}, u \geq 0}$ on the whole space R ^N , ${N \geq 3}$ associated with the critical Sobolev exponent p = (N + 2)/(N ? 2). Similarly to the bounded domain case, there is threshold blowup modulus concerning the blowup in finite time. Furthermore, global in time behavior of the threshold solution is prescribed in connection with the energy level, blowup rate, and symmetry.     

Total synthesis of kehokorins A and B

The total synthesis of a dibenzofuran rhamnoside, kehokorin A, and its aglycone, kehokorin B, was achieved via a route including Suzuki-Miyaura cross-coupling followed by Ullmann ether synthesis to form a dibenzofuran, stepwise bromination at C7 of the dibenzofuran, a second Suzuki-Miyaura cross-coupling to install a 4-methoxyphenyl group at C7, and rhamnosylation.     

Chemical Interactions of Cryptic Actinomycete Metabolite 5‐Alkyl‐1,2,3,4‐tetrahydroquinolines through Aggregate Formation

Organisms often produce secondary metabolites as a mixture of biosynthetically related congeners. However, why are metabolites with minor chemical variations produced simultaneously? 5‐Alkyl‐1,2,3,4‐tetrahydroquinolines (5aTHQs) are small, lipophilic metabolites produced by Streptomyces nigrescens HEK616 when cultured with Tsukamurella pulmonis TP‐B0596. A mixture of 5aTHQs forms aggregates that show enhanced membrane affinity and biological activity. The ability to form aggregates and membrane‐binding activity is regulated by the length of the alkyl chains. Aggregates with long alkyl chains were too stable to fuse with lipid membranes. However, if inactive 5aTHQ congener was mixed with active congener, the mixture showed increased membrane affinity, enabling cellular entry and biological activity. Therefore, it is shown that sloppiness in a biosynthetic pathway, by which minor structural variations can be produced, is functionally rational, as the metabolites show synergistic action.     

Antiadhesive Nanosomes Facilitate Targeting of the Lysosomal GlcNAc Salvage Pathway through Derailed Cancer Endocytosis

Activated endocytosis of extracellular macromolecules and their intracellular trafficking to lysosomes is an essential metabolic mechanism in cancer cells during their rapid proliferation. Cancer cells reuse a vast amount of N‐acetylglucosamine (GlcNAc) supplied from the GlcNAc salvage pathway for the accelerated synthesis of a pivotal uridine diphosphate (UDP)‐GlcNAc. A method to inactivate key glycosidases in lysosomes could critically contribute to the development of potent anticancer therapy. Here we demonstrate that “nanosomes” made of core metals covered by an antiadhesive mixed self‐assembled monolayer allow for avoiding nonspecific surface protein corona and targeted molecular delivery through activated endocytosis. Nanosomes carrying suicide substrates showed that lysosomal glycosidases such as β‐hexosaminidase and β‐galactosidase in cancer cells are promising targets for novel anticancer therapeutic nanomedicine that induce apoptotic cell death through lysosomal membrane permeabilization. The advantage of this method is evident because multivalent surface loading by antiadhesive nanosomes makes it possible to highlight “weak interactions” such as carbohydrate–lectin interactions independent of surface protein corona.     

Trilinear Lp estimates with applications to the Cauchy problem for the Hartree-type equation

In this paper, $L^p$ estimates for a trilinear operator associated with the Hartree type nonlinearity are proved. Moreover, as application of these estimates, it is proved that after a linear transformation, the Cauchy problem for the Hartree-type equation becomes locally well posed in the Bessel potential and homogeneous Besov spaces under certain regularity assumptions on the initial data. This notion of well-posedness and the functional framework to solve the equation were firstly proposed by Y. Zhou.     

Investigation of Mizoroki‐Heck coupling polymerization as a catalyst‐transfer condensation polymerization for synthesis of poly(p‐phenylenevinylene)

Mizoroki‐Heck coupling polymerization of 1,4‐bis[(2‐ethylhexyl)oxy]‐2‐iodo‐5‐vinylbenzene ( 1 ) and its bromo counterpart 2 with a Pd initiator for the synthesis of poly(phenylenevinylene) (PPV) was investigated to see whether the polymerization proceeds in a chain‐growth polymerization manner. The polymerization of 1 with ^tBu₃PPd(Tolyl)Br ( 10 ) proceeded even at room temperature when 5.5 equiv of Cy₂NMe (Cy = cyclohexyl) was used as a base, but the molecular weight distribution of PPV was broad. The polymerization of 2 hardly proceeded at room temperature under the same conditions. In the polymerization of 1 , PPV with H at one end and I at the other was formed until the middle stage, and the polymer end groups were converted into tolyl and H in the final stage. The number‐average molecular weight (M_n) did not increase until about 90% monomer conversion and then sharply increased after that, indicating conventional step‐growth polymerization. The occurrence of step‐growth polymerization, not catalyst‐transfer chain‐growth polymerization, may be interpreted in terms of low coordination ability of H‐Pd(II)‐X(^tBu₃P) (X = Br or I), formed in the catalytic cycle of the Mizoroki‐Heck coupling reaction, to π‐electrons of the PPV backbone; reductive elimination of H‐X from this Pd species with base would take place after diffusion into the reaction mixture. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 543–551     

Lithium‐Ion Endohedral Fullerene (Li+@C60) Dopants in Stable Perovskite Solar Cells Induce Instant Doping and Anti‐Oxidation

Herein, we report use of [Li⁺@C₆₀]TFSI^? as a dopant for spiro‐MeOTAD in lead halide perovskite solar cells. This approach gave an air stability nearly 10‐fold that of conventional devices using Li⁺TFSI^?. Such high stability is attributed to the hydrophobic nature of [Li⁺@C₆₀]TFSI^? repelling moisture and absorbing intruding oxygen, thereby protecting the perovskite device from degradation. Furthermore, [Li⁺@C₆₀]TFSI^? could oxidize spiro‐MeOTAD without the need for oxygen. The encapsulated devices exhibited outstanding air stability for more than 1000 h while illuminated under ambient conditions.