The uncertainty principle and energy decay estimates of the fractional Klein-Gordon equation with space-dependent damping

We consider the $s$-fractional Klein-Gordon equation with space-dependent damping on $\mathbb{R}^d$. Recent studies reveal that the so-called geometric control conditions (GCC) are closely related to semigroup estimates of the equation. Particularly, in the case $d = 1$, a necessary and sufficient condition for the exponential stability in terms of GCC is known for any $s > 0$. On the other hand, in the case $d \geq 2$ and $s \geq 2$, Green-Jaye-Mitkovski (2022) proved that an `$1$-GCC' is sufficient for the exponential stability, but also conjectured that it is not necessary if $s$ is sufficiently large. In this paper, we prove the equivalence between the exponential stability and a kind of the uncertainty principle in Fourier analysis. As a consequence of the equivalence, we show that the $1$-GCC is not necessary for the exponential stability in the case $s \geq 4$. Furthermore, we also establish an extrapolation result with respect to $s$. In particular, we can obtain the polynomial stability for the non-fractional case $s = 2$ from the exponential stability for some $s > 2$.Comment: 26 pages. Added an explicit estimate of $\omega$ in Theorem 1.2 and simplified arguments in Section 3.2. Also fixed some typo

Shape transformations of lipid vesicles by insertion of bulky-head lipids

Lipid vesicles, in particular Giant Unilamellar Vesicles (GUVs), have been increasingly important as compartments of artificial cells to reconstruct living cell-like systems in a bottom-up fashion. Here, we report shape transformations of lipid vesicles induced by polyethylene glycol-lipid conjugate (PEG lipids). Statistical analysis of deformed vesicle shapes revealed that shapes vesicles tend to deform into depended on the concentration of the PEG lipids. When compared with theoretically simulated vesicle shapes, those shapes were found to be more energetically favorable, with lower membrane bending energies than other shapes. This result suggests that the vesicle shape transformations can be controlled by externally added membrane molecules, which can serve as a potential method to control the replications of artificial cells

Liposome-based liquid handling platform featuring addition, mixing, and aliquoting of femtoliter volumes

This paper describes the utilization of giant unilamellar vesicles (GUVs) as a platform for handling chemical and biochemical reagents. GUVs with diameters of 5 to 10 µm and containing chemical/biochemical reagents together with inert polymers were fused with electric pulses (electrofusion). After reagent mixing, the fused GUVs spontaneously deformed to a budding shape, separating the mixed solution into sub-volumes. We utilized a microfluidic channel and optical tweezers to select GUVs of interest, bring them into contact, and fuse them together to mix and aliquot the reaction product. We also show that, by lowering the ambient temperature close to the phase transition temperature Tm of the lipid used, daughter GUVs completely detached (fission). This process performs all the liquid-handing features used in bench-top biochemistry using the GUV, which could be advantageous for the membrane-related biochemical assays

Algorithms for Coloring Reconfiguration Under Recolorability Digraphs

In the k-Recoloring problem, we are given two (vertex-)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper k-coloring. This problem is known to be solvable in polynomial time if k ? 3, and is PSPACE-complete if k ? 4. In this paper, we consider a (directed) recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. The recolorability constraint is given in terms of a digraph R, whose vertices correspond to the colors and whose arcs represent the pairs of colors that can be recolored directly. We provide algorithms for the problem based on the structure of recolorability constraints R, showing that the problem is solvable in linear time when R is a directed cycle or is in a class of multitrees

Identification and characterization of a rhamnosyltransferase involved in rutin biosynthesis in Fagopyrum esculentum (common buckwheat)

Rutin, a 3-rutinosyl quercetin, is a representative flavonoid distributed in many plant species, and is highlighted for its therapeutic potential. In this study, we purified uridine diphosphate-rhamnose: quercetin 3-O-glucoside 6″-O-rhamnosyltransferase and isolated the corresponding cDNA (FeF3G6″RhaT) from seedlings of common buckwheat (Fagopyrum esculentum). The recombinant FeF3G6″RhaT enzyme expressed in Escherichia coli exhibited 6″-O-rhamnosylation activity against flavonol 3-O-glucoside and flavonol 3-O-galactoside as substrates, but showed only faint activity against flavonoid 7-O-glucosides. Tobacco cells expressing FeF3G6″RhaT converted the administered quercetin into rutin, suggesting that FeF3G6″RhaT can function as a rhamnosyltransferase in planta. Quantitative PCR analysis on several organs of common buckwheat revealed that accumulation of FeF3G6″RhaT began during the early developmental stages of rutin-accumulating organs, such as flowers, leaves, and cotyledons. These results suggest that FeF3G6″RhaT is involved in rutin biosynthesis in common buckwheat.Bioscience, Biotechnology, and Biochemistry. 82(10):1790–1802(2018)journal articl

Resovist-Enhanced MRI for Preoperative Assessment of Colorectal Hepatic Metastases: A Case of Multiple Bile Duct Hamartomas Associated with Colon Cancer

Extensive preoperative assessment of hepatic metastases is required in colon cancer patients. We report a case in whom the preoperative investigation by ultrasound scan and contrast-enhanced computed tomography revealed numerous cystic lesions of the liver, suspicious of von Meyenburg complex. Magnetic resonance and magnetic resonance cholangiographic images demonstrated typical features of von Meyenburg complex. Further Resovist-enhanced magnetic resonance imaging detected two hemangiomas in addition to the multiple cystic lesions. So-called Kupffer cell imaging strongly helped the detection of these hemangiomas, and a combination of various magnetic resonance pulse sequences was of great value for the differential diagnosis of cystic lesions and hemangiomas. In cases in whom conventional imaging studies fail to give a definite diagnosis, such as in the present case, superparamagnetic iron oxide-enhanced magnetic resonance imaging is meaningful for adequate preoperative staging

Magnetic transition due to the inter-singlet spin-exchange interaction and elastic softening by the interplay of electric quadrupoles in the distorted kagome lattice antiferromagnet Tb3Ru4Al12

The distorted kagome lattice antiferromagnet Tb3Ru4Al12 with a hexagonal structure has the Néel temperature TN = 22 K. To clarify the 4 f -electronic state and an influence of electric quadrupoles in Tb3Ru4Al12, ultrasonic measurements on a single-crystalline sample at zero magnetic field and under fields were carried. A characteristic elastic softening of the transverse modulus C66 originating from a quadrupole interaction was found. The crystal electric field parameters were determined to reproduce C66, magnetic susceptibilities, and magnetization curves. The obtained level scheme is that the ground and first excited states are singlets, despite the existence of both the magnetic transition and the quadrupole interaction, indicating that Tb3Ru4Al12 is a curious compound. The positive sign of the quadrupole-quadrupole coupling constant for C66 indicates a ferroquadrupolar-type interaction of the electric quadrupole Oxy or O2 2. The anisotropic magnetic field dependencies of TN in the field along [100] and [001] were also clarified.This work was supported by JSPS KAKENHI Grants No.17H06136, No. 18KK0078, and No. 19K03719. This work was also supported by CResCent (Chirality Research Center) in Hiroshima University (the MEXT program for promoting the enhancement of research universities, Japan) and by JSPS Core-to-Core Program, A. Advanced Research Networks. The work was supported by Projects No. 19-00925S and No. 19-07931Y of the Czech Science Foundation and by MGML within the Program of Czech Research Infrastructures (Project No. LM2018096)