Holonomic character and local monodromy structure of Feynman integrals

We prove that the micro-local holonomic structure controls the local monodromy structure of functions involved. This result plays an essential role in investigating hierarchical principle in perturbation theory.Supported by National Science FoundationSupported by Miller Institute for Basic Research in Science     

Finite time blow up for a solution to system of the drift–diffusion equations in higher dimensions

We discuss the existence of a blow-up solution for a multi-component parabolic–elliptic drift–diffusion model in higher space dimensions. We show that the local existence, uniqueness and well-posedness of a solution in the weighted \(L^2\) spaces. Moreover we prove that if the initial data satisfies certain conditions, then the corresponding solution blows up in a finite time. This is a system case for the blow up result of the chemotactic and drift–diffusion equation proved by Nagai (J Inequal Appl 6:37–55, 2001) and Nagai et al. (Hiroshima J Math 30:463–497, 2000) and gravitational interaction of particles by Biler (Colloq Math 68:229–239, 1995), Biler and Nadzieja (Colloq Math 66:319–334, 1994, Adv Differ Equ 3:177–197, 1998). We generalize the result in Kurokiba and Ogawa (Differ Integral Equ 16:427–452, 2003, Differ Integral Equ 28:441–472, 2015) and Kurokiba (Differ Integral Equ 27(5–6):425–446, 2014) for the multi-component problem and give a sufficient condition for the finite time blow up of the solution. The condition is different from the one obtained by Corrias et al. (Milan J Math 72:1–28, 2004).     

Symmetric quiver Hecke algebras and <Emphasis Type="Italic">R</Emphasis>-matrices of quantum affine algebras IV

Let \(U'_q(\mathfrak {g})\) be a twisted affine quantum group of type \(A_{N}^{(2)}\) or \(D_{N}^{(2)}\) and let \(\mathfrak {g}_{0}\) be the finite-dimensional simple Lie algebra of type \(A_{N}\) or \(D_{N}\). For a Dynkin quiver of type \(\mathfrak {g}_{0}\), we define a full subcategory \({\mathcal C}_{Q}^{(2)}\) of the category of finite-dimensional integrable \(U'_q(\mathfrak {g})\)-modules, a twisted version of the category \({\mathcal C}^{(1)}_{Q}\) introduced by Hernandez and Leclerc. Applying the general scheme of affine Schur–Weyl duality, we construct an exact faithful KLR-type duality functor \({\mathcal F}_{Q}^{(2)}:\mathrm{Rep}(R) \rightarrow {\mathcal C}_{Q}^{(2)}\), where \(\mathrm{Rep}(R)\) is the category of finite-dimensional modules over the quiver Hecke algebra R of type \(\mathfrak {g}_{0}\) with nilpotent actions of the generators \(x_k\). We show that \({\mathcal F}_{Q}^{(2)}\) sends any simple object to a simple object and induces a ring isomorphism Open image in new window .     

PEG-detachable polyplex micelles based on disulfide-linked block catiomers as bioresponsive nonviral gene vectors

PEG-based polyplex micelles, which can detach the surrounding PEG chains responsive to the intracellular reducing environment, were developed as nonviral gene vectors. A novel block catiomer, PEG-SS-P[Asp(DET)], was designed as follows: (i) insertion of biocleavable disulfide linkage between PEG and polycation segment to trigger PEG detachment and (ii) a cationic segment based on poly(aspartamide) with a flanking N-(2-aminoethyl)-2-aminoethyl group, P[Asp(DET)], in which the Asp(DET) unit acts as a buffering moiety inducing endosomal escape with minimal cytotoxicity. The polyplex micelles from PEG-SS-P[Asp(DET)] and plasmid DNA (pDNA) stably dispersed in an aqueous medium with a narrowly distributed size range of approximately 80 nm due to the formation of hydrophilic PEG palisades while undergoing aggregation by the addition of 10 mM dithiothreitol (DTT) at the stoichiometric charge ratio, indicating the PEG detachment from the micelles through the disulfide cleavage. The PEG-SS-P[Asp(DET)] micelles showed both a 1-3 orders of magnitude higher gene transfection efficiency and a more rapid onset of gene expression than PEG-P[Asp(DET)] micelles without disulfide linkages, due to much more effective endosomal escape based on the PEG detachment in endosome. These findings suggest that the PEG-SS-P[Asp(DET)] micelle may have promising potential as a nonviral gene vector exerting high transfection with regulated timing and minimal cytotoxicity.     

Asymmetric [2 + 2] olefin cross photoaddition in a self-assembled host with remote chiral auxiliaries

Remote chirality at the periphery of a self-assembled cage brings about the slight twist of aromatic rings, which is yet sufficient to induce considerable asymmetric induction (up to 50% ee) in the hitherto unknown [2 + 2] cross photoadditions of fluoranthenes.     

One-Handed Helical Polyacetylenes Bearing Axially-Chiral 2-Arylpyridyl-N-Oxide Units for Efficient Chromatographic Enantioseparation of Chiral Aromatic and Aliphatic Alcohols

A series of poly(biarylylacetylene)s (PBAs) bearing axially-chiral (S)-and (R)-pyridyl-N-oxide residues with a methoxy, propoxy, or acetyloxy substituent at the 3-position of the biaryl units was synthesized. All the PBAs formed a preferred-handed helix, while the helical sense preference was varied depending on the substituents despite the same twist-sense of the biaryl units. Among them, the propoxy-bound helical PBA showed an exceptionally high chiral recognition ability as a chiral stationary phase (CSP) for high-performance liquid chromatography (HPLC) and efficiently resolved not only various chiral aromatic alcohols, but also a variety of chiral aliphatic alcohols; the latter still remains difficult to resolve by commercially-available CSPs in HPLC. Such practically-useful both handed helical PBA-based CSPs can be produced from the racemic PBA composed of fully racemic monomer units through deracemization of the biaryl units with a chiral alcohol.     

Ligand-Controlled Stereoselective Synthesis and Biological Activity of 2-Exomethylene Pseudo-glycoconjugates: Discovery of Mincle-Selective Ligands

Glycoconjugate analogues in which the sp³-hybridized C2 position of the carbohydrate structure (normally bearing a hydroxy group) is converted into a compact sp²-hybridized exomethylene group are expected to have unique biological activities. We established ligand-controlled Tsuji–Trost-type glycosylation methodology to directly prepare a variety of these 2-exomethylene pseudo-glycoconjugates, including glucosylceramide analogues, in an α- or β-selective manner. Glucocerebrosidase GBA1 cleaves these synthetic pseudo-β-glucosylceramides similarly to native glucosylceramides. The pseudo-glucosylceramides exhibit selective ligand activity towards macrophage-inducible C-type lectin (Mincle), but unlike native glucosylceramides, are inactive towards CD1d.     

Palladium-catalyzed carboboration of alkynes using chloroborane and organozirconium reagents

Three-component coupling of bis(dialkylamino)chloroborane, alkynes and organozirconium reagents proceeded in the presence of palladium catalysts, leading to the formation of stereo-defined alkenylborane derivatives via cis-carboboration of carbon-carbon triple bonds.