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In this paper, we extend the results for approximation semigroups for general resolvent maps including various resolvents of maps on a general convex geodesic metric space. For our study, we introduce the notion of (general) resolvent maps which is a generalization of the resolvent maps in Lawson (J Lie Theory 33, 361–376, 2023) and then we prove several useful properties for the resolvent map and construct the approximation semigroups for resolvent maps. We also study the convergence of a proximal point like algorithm for the general resolvent map.

In this paper, by applying the intertwining properties, we introduce the fractional powers of the number operator perturbed by generalized Gross Laplacians (infinite dimensional Laplacians), which are special types of the infinitesimal generators of generalized Mehler semigroups. By applying the intertwining properties and semigroup approach, we study the Langevin type equations associated with the infinite dimensional Laplacians and with white noise distributions as forcing terms. Then we investigate the unique solution of the fractional Langevin type equations associated with the Riemann-Liouville and Caputo time fractional derivatives, and the fractional power of the infinite dimensional Laplacians, for which we apply the intertwining properties again. For our purpose, we discuss the fractional integrals and fractional derivatives of white noise distribution valued functions.

Riparian vegetation plays a fundamental role in alluvial channel evolution by modifying flow and sedimentation dynamics. To elucidate the roles of sediment supply, flow‐dependent transport capacity, and morphodynamic feedbacks on the evolution of emergent vegetation patches over a single hydrograph, we conducted two experiments with different reach‐scale sediment supplies: a high‐supply experiment (HSE) and low‐supply experiment (LSE). We measured flow velocities, bedload transport, and topographic changes around a full‐scale patch of live emergent willows in an outdoor laboratory flume. Erosion occurred in the patch‐adjacent channel areas irrespective of the sediment supply, whereas deposition within the patch interior was suppressed in the LSE and enhanced in the HSE. The magnitude of patch deposition in each experiment was controlled by the local sediment supply to the patch and local sediment mobility during each discharge in the hydrograph. The local sediment supply was affected by bed morphodynamics at the patch head, which modulated the reach‐scale sediment supply by redistributing the bedload in the channel. Sediment mobility within the patch was flow‐dependent and a function of velocity and turbulent kinetic energy. For different discharges, the velocity in the patch changed proportionally with the freestream velocity; however, the turbulent kinetic energy was more sensitive, being elevated compared with the freestream during high flows and inhibited at low flows. Therefore, deposition and erosion within vegetation patches are not simply functions of the reach‐scale sediment supply or patch flow characteristics, as is often assumed, but additionally depend on the local sediment supply to the patch interior. Riparian vegetation in rivers and deltas is considered a primary cause of sediment deposition and channel stabilization. However, in the laboratory, we identified the physical mechanisms influencing sediment deposition and erosion and their change over a natural flow regime to illustrate that the same full‐sized willow patch can either enhance or reduce sediment deposition within the patch interior relative to the same channel without vegetation. The amount of sediment deposited in the vegetation patch depended on the velocity and turbulent kinetic energy of the water, which changed as the flow decreased. Additionally, the presence of a single vegetation patch fundamentally changed the character of the channel from depositional to erosional near the patch, indicating that more erosion occurred in adjacent channels than deposition within the patch. Deposition and erosion of the bed were also influenced by the amount of sediment supplied to the channel from upstream. This reach‐scale sediment supply was modified by a sediment mound that formed at the upstream end of the patch during high sediment supply to the channel. The mound redistributed the sediment transport within the channel and vegetation patch, revealing another physical mechanism influencing the spatial and temporal variability of bedload transport in vegetated channels. Relative to the open depositional channel located upstream, a single vegetation patch caused channel erosion that lowered the median bed elevations by up to 640%The same vegetation patch can both inhibit and enhance interior sediment deposition depending on the flow‐dependent transport capacity and local sediment supplyMorphodynamic bed changes modulated the reach‐scale sediment supply in and around the patch by spatially redistributing bedload within the channel Relative to the open depositional channel located upstream, a single vegetation patch caused channel erosion that lowered the median bed elevations by up to 640% The same vegetation patch can both inhibit and enhance interior sediment deposition depending on the flow‐dependent transport capacity and local sediment supply Morphodynamic bed changes modulated the reach‐scale sediment supply in and around the patch by spatially redistributing bedload within the channel

Cell sheet engineering has attracted great attention because thin layers of tissue can be easily transplanted to defect sites. Wound-dressing materials are required to support fast re-epithelization, both with keratinocytes and fibroblasts, to enhance the prognosis and therapeutic outcomes. We prepared self-assembled cell sheets composed of adipocyte-derived stem cells (ADSCs) and surface-engineered nanofibrils (NFs). NFs were surface-engineered with multilayers of gelatin so that the cell sheets could spontaneously assemble within 3 days in cell culture plates. Dorsal wounds transplanted with the cell sheets exhibited higher wound-healing rates when a high concentration of gelatin was immobilized on the surfaces of the NFs. Histochemical staining revealed that those with gelatin-immobilized NFs showed a higher expression of cytokeratin and collagen in the re-epithelized epidermis. Keratinocytic differentiation of the epidermis was molecularly evidenced by the higher expression of keratinocyte-specific genes.

Bilayered cell sheets were fabricated with coaxial hydro-nanofibrils for three-dimensional (3D) cultivation in a biomimetic environment. Polycaprolactone (PCL) was electrospun and hydrolyzed to release fragmented nanofibrils (NF) in an alkaline condition. Methacrylated gelatin (GelMA) was adsorbed and phototethered on the surface of the fibrils to prepare coaxial NF composed of hydrophilic shells and hydrophobic cores. GelMA layers on the NF were characterized by X-ray photoemission spectroscopy, Fourier-transform infrared spectroscopy, and thermogravimetric analysis. The GelMA showed higher decoration level on NF compared to that on native gelatin. GelMA-decorated NF significantly enhanced cell proliferation rate and phenotypic expression of human dermal fibroblasts when spontaneous formation of cell sheets was observed for 7 days. HaCaT cells were layered on top of the fibroblast sheets and further cultivated in air–water interfaces to prepare bilayered skin sheets. After 21 days of incubation, the top layers of the bilayered sheets showed higher expression of pan-keratin, and the dermal cells showed higher proliferation in the GelMA-decorated NF.

We establish a noncommutative extension of the Fuk–Nagaev inequalities for random variables in a noncommutative probability space. As applications, we first obtain noncommutative versions of Bennett inequality and Rosenthal inequality, and secondly, we study the weak law of large numbers for weighted sums in a noncommutative probability space and the weak law of large numbers for weighted sums of probability measures corresponding to the free additive convolutions.

Common magnetic resonance imaging (MRI) findings in adhesive capsulitis are not often evident in rotator cuff tear concomitant with shoulder stiffness. This study aimed to determine the most predictive MRI finding of rotator cuff tear with shoulder stiffness to differentiate from that without stiffness.

The excellent conductive properties of nano-carbon fillers are difficult to realize in composites due to the aggregation of nano-carbon fillers by van der Waals forces inside the polymer matrix. To overcome this problem, a process capable of inducing uniform dispersion of the nano-carbon filler is required. In this study, a dispersion strategy was proposed to induce non-covalent functionalization of nano-carbon fillers based on phenyl glycidyl ether (PGE) including a single benzene structure as an inexpensive and effective non-covalent functionalization agent. The electrical and thermal conductivities of the composites filled with PGE-treated graphene nano-platelets (GNPs) were improved up to 296.3 and 4.4%, respectively, compared to those of the composites containing raw GNPs due to uniform dispersion of the nano-carbon fillers. In addition, the enhancements of multi-walled carbon nanotubes-filled composites using the PGE treatment were 125.8 and 11.3%, respectively. From these results, PGE was an effective non-covalent functionalization agent that can induce uniform dispersion of nano-carbon fillers and improve the conductive properties of composites.

The demand for lightweight heat-dissipating composites has increased interest in strategies to improve the thermal conductivity of polymer composites by incorporating nanocarbon fillers. In this study, composite incorporating uniformly dispersed high content (∼50 wt%) of graphene nanoplatelet was fabricated with low-viscosity polyamide 6 (PA6) resin. The measured thermal conductivity of the composite exhibited thermal percolation when GNP content exceeded 30 wt%, and the in-plane thermal conductivity improved to 19.39 W/m·K (1315% increase compared to neat PA6) at the filler content of 50 wt%. In addition, thermal conductivity of the prepared composites was in good agreement with theoretical results based on Nan's model (filler content of 0–30 wt%) considering interfacial thermal resistance and the percolation equation (filler content of 40–50 wt%) considering a connected filler network. It was confirmed that thermal percolation was generated due to contacts and network formation between fillers in the fabricated composites using an internal structure analysis. Potential insights on the design, manufacture, and application of nanocomposites exhibiting heat dissipation performance can be provided by composite systems using low-viscosity resin and theoretical evaluation methods.

The alloy design of Ni-based superalloy with high γ′ volume fraction has been studied to be suitable for additive manufacturing (AM) by using thermodynamic calculations. The design approach intended to increase AM processability while maintaining the high-temperature strength of the reference superalloy René 80. In this study, electron beam powder bed fusion also known as a selective electron beam melting (SEBM) process was utilized for alloy fabrication. All René 80 products manufactured by SEBM were cracked despite their small sizes. Using the conventional René 80 composition as a baseline, Ti reduction (5→3 wt%), 2.5 wt% Ta addition, and 1.0 wt% Hf addition successfully prevented crack formation after SEBM fabrication and considerably improved the characteristics of alloy powders, which exhibited more spherical shapes with fewer satellites. The as-SEBM modified René 80 alloy possessed a unidirectional columnar grain microstructure with a primary γ′ area fraction of 40% and size of 382 nm, which were higher than those of the conventional René 80 alloy. Atom probe tomography results indicated that the partitioning of Ti, Al, and Ta atoms into the γ′ phase was more pronounced in AM80 alloy than in René 80 alloy. This facilitated to increase the lattice misfit at the γ/γ′ interface, made it more difficult for dislocations to cut through γ′ particles, which was confirmed by the results of first-principles calculations. The SEBM products, which were subjected to a standard heat treatment demonstrated superior tensile properties at 870 °C as compared with those of the conventional cast René 80 alloy. The primary γ′ phase was sheared by a/3 < 112 > partial dislocation leaving stacking fault behind, and a high density of tangled dislocations was observed as a result of the strong interaction with fine secondary γ′ with sizes smaller than 50 nm.

In Sasang Medicine, which is a part of Eastern Traditional Medicine, human body is classified by constitutions for diagnosis and treatment. In this study, a fundamental study on the ways and means of measuring the constitutions is classified in Sasang Medicine. A method of measuring ASC (Acupuncture Spot Current) through acupuncture spots on human body is proposed, together with a way to extract characteristic points of measured signals. Based on the characteristic analysis of the measured ASC, it is able to define the measured signals of experimental targets through classification, and the defined characteristics of ASC were determined to be able to be utilized in developing systems for medical constitutional classification.

The author looks at the algebraic reasoning of several young students. The author mentions the common notion of algebra, where it is usually taught in higher levels. The author found out that several young students are capable of algebraic reasoning. Furthermore, the author also introduces the use of foreign number words in algebra.

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Symmetrically and unsymmerically substituted bis-dithiobenzil nickel complexes containing four substituted and unsubstituted methoxy groups were synthesized from a benzoin compound using phosphorous pentasulfide under the conventional thermal and microwave processing. The efficiency of microwave synthesis over the conventional thermal synthesis was illustrated by the yield of bisdithiobenzil nickel complex dyes. The samples were characterized by the means of elemental analyzer, 1HNMR, IR spectroscopy, Uv-vis spectroscopy and DSC.

Several multi-parameter transformation groups acting on the space of test white noise functionals are constructed by means of the operator theory based on white noise distribution theory. Several Lie algebras containing infinite dimensional Laplacians and their associated Lie groups are also discussed.

In this paper we shall show the heredity of a differentiable one-parameter semigroup under the second quantization and then discuss the resolvent of the differential second quantization operator and the potentials of test white noise functionals. As an application, we shall investigate the existence of solutions of the Poisson-type equations associated with differential second quantization operators as well as operators similar to differential second quantization operators.

Let (E)βand be the space of test and generalized white noise functionals, respectively. It is proved that for each positive integer kwe construct explicitly one-parameter semigroup and cosine family of operators on an appropriate (E)βspace of which infinitesimal generator is . As an application, we will prove the existence and uniqueness of solutions of the Cauchy problems for the first and second order differential equations associated with the operator . Here △ Gand Nare the Gross Laplacian and the number operator on (E)β, respectively. Also, we investigate the existence and uniqueness of solutions of the Cauchy problems associated with the operator is the adjoint operator of △ G