Search

In this paper, we study the boundedness of the fractional maximal operator and fractional integral operator on the variable exponent Morrey spaces defined over spaces $(X,d,\mu)$ of homogeneous type.

Self-oscillation is an intriguing and omnipresent phenomenon that governs a broad range of growth dynamics and formation of nanoscale periodic and delicate heterostructures. In this work, a self-oscillating growth phenomenon of catalyst droplets, consuming surface-coating a-Si/a-Ge bilayer, are exploited to accomplish a high-frequency alternating growth of ultrathin crystalline Si and Ge (c-Si/c-Ge) nano-slates, with Ge-rich layer thickness of 14-19 nm thick, embedded within a superlattice nanowire (SLNW) structure, with pre-known position and uniform channel diameter. A subsequent selective etching of the Ge-rich segments, in a simple NH3 solution dipping, leaves a chain of ultrafine standing c-Si nanosheets down to ~6 nm thick, without the use of any expensive high-resolution lithography and growth modulation control. A ternary-phase-competition model has been established to explain the underlying formation mechanism of this nanoscale self-oscillating growth dynamics. It is also suggested that these ultrathin nanosheets could help to produce ultrathin fin-channels for advanced electronics, or provide size-specified trapping sites to capture and position hetero nanoparticle for high-precision labelling or light emission.

A low temperature catalytic growth of orderly ultrathin silicon nanowires (SiNWs) is desirable for the construction of monolithic 3D stacked electronics but usually suffers a large diameter fluctuation and a low growth deployment rate (GDR). In this work, the ultra-confined growth dynamics of in-plane solid–liquid–solid SiNWs within narrow groove tracks has been systematically investigated, and a converging-guiding-track strategy is proposed and testified to accomplish 100% GDR of ultra-dense and uniform SiNW array, with diameter and spacing of only Dnw = 22.5±3.5 nm and 25 nm, respectively. Despite a low temperature growth at 350 °C, the SiNWs are found to be all monocrystalline and Si⟨100⟩ oriented, while prototype Schottky barrier tunneling field effect transistors built on the SiNW channels demonstrate a high Ion/off ratio and subthreshold swing of >105 and 197 mV dec−1. This new strategy complements a long-missing key capability of catalytic growth approach to serve a reliable integration technology of ultrafine high quality 1D c-Si channels, without the need of preexisting wafer substrate, for a wide range of 3D electronics, neuromorphic, and logic-in-memory functionalities.

Free-standing silicon nanoprobes (SiNPs) are critical tools for intracellular bioelectrical signal recording, while a scalable fabrication of these tiny SiNPs with ab initio geometry designs has not been possible. In this work, we demonstrate a novel growth shaping of slim Si nanowires (SiNWs) into SiNPs with sharp tips (curvature radii

We obtain the boundedness of some integral operators and commutators on homogeneous Herz spaces with three variable exponents $$\dot K_{p( \cdot ),q( \cdot )}^{\alpha ( \cdot )}$$ , such as some sublinear operators, the fractional integral and its commutator.

The Mekong River is the tenth largest river in the world in terms of water discharge, representing a substantial source of organic matter to the South China Sea. However, the composition and variat...

Growing high quality silicon nanowires (SiNWs) at elevated temperature on cooler polymer films seems to be contradictive but highly desirable for building high performance flexible and wearable electronics. In this work, we demonstrate a superfast (vnw > 3.5 μm·s-1) growth of high quality SiNWs on polymer/glass substrates, powered by self-selected laser at 808 nm heating of indium catalyst droplets that absorb amorphous Si layer to produce SiNWs. Because of the tiny heat capacity of the nanodroplets, the SiNW growth can be quickly heated up and frozen via rapid laser ON/OFF switching, enabling a deterministic diameter modulation in the ultralong SiNWs. Finally, prototype field effect transistors are also fabricated upon the laser-droplet-heating grown SiNWs with a high Ion/Ioff ratio of >104 and reasonable subthreshold swing of 386 mV·dec-1, opening a generic new route to integrate high-quality NW channels directly upon large area and lightweight polymer substrates for developing high-performance flexible electronics.

We establish Leibniz-type rules for bilinear and biparameter Fourier multiplier operators with limited Sobolev regularity. Applications of our result are given including the biparameter Leibniz rules, smoothing properties of bilinear-biparameter fractional integrals, and mapping properties of scattering operators for a system of PDEs.

In this article, the authors consider the Schrodinger type operator $$L:=-\mathrm{div}(A\nabla )+V$$ on $${\mathbb {R}}^n$$ with $$n\ge 3$$, where the matrix A satisfies uniformly elliptic condition and the nonnegative potential V belongs to the reverse Holder class $$RH_q({\mathbb {R}}^n)$$ with $$q\in (n/2,\,\infty )$$. Let $$p(\cdot ):\ {\mathbb {R}}^n\rightarrow (0,\,\infty )$$ be a variable exponent function satisfying the globally $$\log $$-Holder continuous condition. When $$p(\cdot ):\ {\mathbb {R}}^n\rightarrow (1,\,\infty )$$, the authors prove that the operators $$VL^{-1}$$, $$V^{1/2}\nabla L^{-1}$$ and $$\nabla ^2L^{-1}$$ are bounded on variable Lebesgue space $$L^{p(\cdot )}({\mathbb {R}}^n)$$. When $$p(\cdot ):\ {\mathbb {R}}^n\rightarrow (0,\,1]$$, the authors introduce the variable Hardy space $$H_L^{p(\cdot )}({\mathbb {R}}^n)$$, associated to L, and show that $$VL^{-1}$$, $$V^{1/2}\nabla L^{-1}$$ and $$\nabla ^2L^{-1}$$ are bounded from $$H_L^{p(\cdot )}({\mathbb {R}}^n)$$ to $$L^{p(\cdot )}({\mathbb {R}}^n)$$.

We establish Leibniz type rules for bilinear flag multipliers with limited regularity in the Lebesgue spaces with flag weights. As applications, we obtain flag fractional Leibniz rules with weights, smoothing properties of bilinear flag fractional integrals, and scattering properties for solutions to a certain system of PDEs. Our results appear to be new even in the unweighted case.

A facile strategy is needed for accurate time-space supply of suitable growth factors or drugs. Polypyrrole (PPy) was able to carry almost all kinds of negatively charged biomolecules through anodizing method, which made it an appropriate way for codeposition of multiple molecules. The difference in the conjugation between different molecules and PPy makes it possible for selective release when the redox state of PPy changes. In this work, bovine serum albumin (BSA) and heparin (Hep) were chosen to be the model molecules in view of their differences in the level of electronegativity and molecular weight. Double-layer deposition method was used to improve the biocompatibility of PPy/BSA/Hep film. It was found the content of BSA and Hep in the film can be controlled by regulating deposition current and time. BSA release was facilitated under positive voltage and then promote the proliferation of preosteoblasts, while Hep release was promoted under negative voltage and enhance cell differentiation. Our work provides a dual-molecule model in PPy for selective release and further explores the mechanism of release selectivity, this discovery has potential applications in tissue engineering and regenerative medicine.

‎In this article‎, ‎the authors consider the Schrödinger type‎ ‎operator $L:=-{\rm div}(A\nabla)+V$ on $\mathbb{R}^n$ with $n\geq 3$‎, ‎where the matrix $A$ is symmetric and satisfies‎ ‎the uniformly elliptic condition and the nonnegative potential‎ ‎$V$ belongs to the reverse Hölder class $RH_q(\mathbb{R}^n)$‎ ‎with $q\in(n/2,\,\infty)$‎. ‎Let $p(\cdot):\ \mathbb{R}^n\to(0,\,1]$ be a variable exponent function‎ ‎satisfying the globally $\log$-Hölder continuous condition‎. ‎The authors introduce the variable Hardy space $H_L^{p(\cdot)}(\mathbb{R}^n)$ associated to $L$‎ ‎and establish its atomic characterization‎. ‎The atoms here are closer to the atoms of‎ ‎variable Hardy space $H^{p(\cdot)}(\mathbb{R}^n)$ in spirit‎, ‎which further implies that $H^{p(\cdot)}(\mathbb{R}^n)$ is continuously embedded in‎ ‎$H_L^{p(\cdot)}(\mathbb{R}^n)$‎.

In this paper, the authors define the weak Herz spaces and the weak Herz-type Hardy spaces with variable exponent. As applications, the authors establish the boundedness for a large class of singular integral operators including some critical cases.

In this paper, we obtain the boundedness of commutators generated by singular integral operators and Lipschitz functions on amalgam spaces and weighted amalgam spaces.

Titanium and tantalum have been widely used for orthopedic and dental implant applications. However, how their inherent surface features regulate cellular osteogeneses still remains elusive. In this study, we engineered two distinct TiO2 and Ta2O5 nanorod films as the two model oxidized surfaces to investigate their intrinsic osteogenic behaviors. The results indicated that the distinctive gradient on zeta potential against pH, corresponding to the deprotonation rate, but not the hydroxyl amount or hydroxylation polarity played a critical role on the cellular osteogenic performance. TiO2 nanorod film with a higher deprotonation rate significantly upregulated the expression of osteogeneses-related gene and protein, comparing to that of Ta2O5 nanorod film. These results might be attributed to that surface with higher deprotonation rateprovided more Bronsted acid-base surface sites to react with protein residues, leading to a mild change in conformation of the absorbed proteins, and subsequently facilitating to trigger the integrin-focal adhesion cytoskeleton actin transduction pathway. This study, therefore, provides a new insight into the understanding the role of material surface hydroxylation on cellular osteogenic responses.

Using Calderón's reproducing formulas and almost orthogonal estimates, the $T1$ theorem for the inhomogeneous Triebel–Lizorkin and Besov spaces on RD-spaces is obtained. As an application, new characterizations for these spaces with “half” the usual conditions of the approximate to the identity are presented.

Stretchable electronics are finding widespread applications in bio-sensing, skin-mimetic electronics, and flexible displays, where high-density integration of elastic and durable interconnections is a key capability. Instead of forming a randomly crossed nanowire (NW) network, here, a large-scale and precise integration of highly conductive nickel silicide nanospring (SiNix -NS) arrays are demonstrated, which are fabricated out of an in-plane solid-liquid-solid guided growth of planar Si nanowires (SiNWs), and subsequent alloy-forming process that boosts the channel conductivity over 4 orders of magnitude (to 2 × 104 S cm-1 ). Thanks to the narrow diameter of the serpentine SiNix -NS channels, the elastic geometry engineering can be accomplished within a very short interconnection distance (down to ≈3 µm), which is crucial for integrating high-density displays or logic units in a rigid-island and elastic-interconnection configuration. Deployed over soft polydimethylsiloxane thin film substrate, the SiNix -NS array demonstrates an excellent stretchability that can sustain up to 50% stretching and for 10 000 cycles (at 15%). This approach paves the way to integrate high-density inorganic electronics and interconnections for high-performance health monitoring, displays, and on-skin electronic applications, based on the mature and rather reliable Si thin film technology.

In electrical stimulation (ES), daily stimulation time means the interacting duration with cells per day, and is a vital factor for mediating cellular function. In the present study, the effect of stimulation time on osteogenic differentiation of MC3T3-E1 cells was investigated under ES on polypyrrole (Ppy) planar interdigitated electrodes (IDE). The results demonstrated that only a suitable daily stimulation time supported to obviously upregulate the expression of ALP protein and osteogenesis-related genes (ALP, Col-I, Runx2 and OCN), while a short or long daily stimulation time showed no significant outcomes. These might be attributed to the mechanism that an ES induced transient change in intracellular calcium ion concentration, which was responsible for activating calcium ion signaling pathway to enhance cellular osteogenic differentiation. A shorter daily time could lead to insufficient duration for the transient change in intracellular calcium ion concentration, and a longer daily time could give rise to cellular fatigue with no transient change. This work therefore provides new insights into the fundamental understanding of cell responses to ES and will have an impact on further designing materials to mediate cell behaviors.