Inverse spectral problems for non-self-adjoint Sturm–Liouville operators with discontinuous boundary conditions

This paper deals with the inverse spectral problem for a non-self-adjoint Sturm–Liouville operator with discontinuous conditions inside the interval. We obtain that if the potential q is known a priori on a subinterval $$ \left[ b,\pi \right] $$ with $$b\in \left( d,\pi \right] $$ or $$b=d$$, then $$h,\,\beta ,\,\gamma $$ and q on $$\left[ 0,\pi \right] $$ can be uniquely determined by partial spectral data consisting of a sequence of eigenvalues and a subsequence of the corresponding generalized normalizing constants or a subsequence of the pairs of eigenvalues and the corresponding generalized ratios. For the case $$b\in \left( 0,d\right) $$, a similar statement holds if $$\beta ,\,\gamma $$ are also known a priori. Moreover, if q satisfies a local smoothness condition, we provide an alternative approach instead of using the high-energy asymptotic expansion of the Weyl m-function to solve the problem of missing eigenvalues and norming constants.     

Enzymatic Extraction of Bioactive and Self‐Assembling Wool Keratin for Biomedical Applications

Keratin is widely recognized as a high‐quality renewable protein resource for biomedical applications. Despite their extensive existence, keratin resources such as feathers, wool, and hair exhibit high stability and mechanical properties because of their high disulfide bond content. Consequently, keratin extraction is challenging and its application is greatly hindered. In this work, a biological extraction strategy is proposed for the preparation of bioactive keratin and the fabrication of self‐assembled keratin hydrogels (KHs). Based on moderate and controlled hydrolysis by keratinase, keratin with a high molecular weight of approximately 45 and 28 kDa that retain its intrinsic bioactivities is obtained. The keratin products show excellent ability to promote cell growth and migration and are conferred with significant antioxidant ability because of their intrinsically high cysteine content. In addition, without the presence of any cross‐linking agent, the extracted keratin can self‐assemble into injectable hydrogels. The KHs exhibit a porous network structure and 3D culture ability, showing potential in promoting wound healing. This enzyme‐driven keratin extraction strategy opens up a new approach for the preparation of keratin that can self‐assemble into injectable hydrogels for biomedical engineering.     

Visible-light-driven spirocyclization of epoxides via dual titanocene and photoredox catalysis

We describe the synergistic utilization of titanocene/photoredox dual catalysis driven by visible light for the radical opening/spirocyclization of easily accessible epoxyalkynes. This environmentally benign process uses the organic donor–acceptor fluorophore 2,4,5,6-tetra(9H-carbazol-9-yl)isophthalonitrile (4CzIPN) as a photocatalyst and Hantzsch ester (HE) as an electron donor instead of stoichiometric metallic reductants. The photocatalytic conditions showed exceptionally high reactivity for the synthesis of privileged and synthetically challenging spirocycles featuring a spiro all-carbon quaternary stereocenter. Cyclic voltammetry (CV) studies suggest that Cp₂Ti^IIICl is the catalytically active species.

We describe the synergistic utilization of titanocene/photoredox dual catalysis driven by visible light for radical opening/spirocyclization of easily accessible epoxyalkynes.

Over the last few decades, radical-based transformations have been increasingly used in organic synthesis due to their salient features, such as ease of generation, mild reaction conditions, and broad functional group compatibility.^1,2 As a mild single-electron-transfer (SET) reagent, titanocene monochloride (Cp₂Ti^IIICl) is considered a formidable tool in contemporary radical chemistry due to its ability to promote various fundamental radical-based transformations.^3–7 Cp₂Ti^IIICl was first introduced by Nugent and RajanBabu as a very mild stoichiometric reagent for the reductive opening of epoxides.^8–11 Later, the catalytic conditions developed by Gansäuer et al. (Scheme 1a)¹² employing stoichiometric amounts of active metals in combination with 2,4,6-collidine·HCl further expanded its applications and led to the discovery of a number of novel transformations.^13–16 The key to success was the formation of a stable complex A in reactions while decreasing the concentration of active Cp₂Ti^IIICl.^17,18 We were interested in the radical opening/cyclization reaction of epoxides which has attracted considerable attention from the synthetic community and has been used numerous times in the synthesis of natural products.^19,20 Nevertheless, this reaction required stoichiometric metallic reductants and proceeded slowly particularly with sterically hindered substrates even with high catalyst loading.²¹ Therefore, the development of an eco-friendly and efficient catalytic system with an expanded substrate scope is highly desirable.Open in a separate windowScheme 1Cp₂Ti^IIICl mediated radical opening/spirocyclization of epoxides; (a) generation of Ti^IIIvia a metal reduction approach; (b) dual titanocene/photoredox catalysis; (c) examples of drugs and natural products containing heterospirocycles.In recent years metallaphotoredox catalysis has been a new and rapidly growing research subject.^22–29 Photoredox processes can directly modulate the oxidation state of metals by electron transfer (ET).^30–33 Given that the generation of Ti^III is a SET process, we envisioned that the reduction could be facilitated by a photoredox-controlled process while overcoming the aforementioned limitations. On the other hand, spirocycles bearing a chiral spiro all-carbon quaternary carbon are particularly attractive synthetic targets in pharmaceutical development (Scheme 1c).^34–36 Such privileged rigid 3D structures offer the concomitant ability to project functionalities in all three-dimensional orientations and led to enhanced pharmacological activities of molecules. Thus significant attention has been paid to their synthesis.^37,38 Against this backdrop, here we describe our efforts on the synthesis of various heterospirocycles with the aid of photoredox catalysis.We chose epoxyalkyne 2a as a model substrate for optimization of reaction conditions. After a systematic variation of different reaction parameters, we were pleased to identify the optimal reaction conditions in which a mixture of Cp₂TiCl₂ (5.0 mol%), [Ir(dtbbpy)(ppy)₂]PF₆ (1a, 1.0 mol%, E^III/II_1/2 = −1.51 V vs. SCE in MeCN), HE (1.2 equiv.) and 2a (1.0 equiv.) in THF at room temperature under the irradiation of a 10 W 450 nm light emitting diode (LED) lamp for 12 hours afforded the desired product 3a in an excellent yield of 96% (13 : 1 d.r.) upon isolation (entry 1). Using a commercial 23 W compact fluorescent lamp (CFL) instead of the 10 W 450 nm LED did not compromise the overall yield of the reaction (entry 2). Notably, when the loading of Cp₂TiCl₂ was decreased to as low as only 2.0 mol%, the reaction still led to full conversion and produced 3a in 95% yield (entry 3). Further screening of other photosensitizers revealed that the cheap and readily obtained organic dye 4CzIPN 1b is a competent alternative, which led to full conversion with 94% isolated yield (entry 4). Importantly, the reaction did not proceed in the absence of Cp₂TiCl₂, HE, the photocatalyst, or visible light (entries 5–8). Various solvents, including DMF, MeOH, DMSO, and MeCN, were screened, and they all resulted in poor conversion. The use of other organic electron donors, such as triethylamine, triethanolamine, and ascorbic acid, afforded the product in poor yield.With satisfactory reaction conditions established, we then explored the scope of the cyclization reaction using 4CzIPN as the photosensitizer. Positively, the cyclization reaction worked well and afforded the desired variably heterospirocyclic products in good to excellent yield (Tables 2 and ​and3).3). The reaction allows the rapid construction of various 5/5, 5/6, 5/7 and 5/8 spiro-ring fused systems (3a–3k) bearing tetrahydrofuran or pyrrolidine motifs via the 5-exo cyclization pathway. Interesting, the diastereoselectivity of the cyclization reaction is highly correlated with the ring size in the substrates. Heterospirocycles containing a 5/5 spiro-ring fused system (3a–3f) were obtained with surprisingly high diastereoselectivity. In some cases (3b, 3c, and 3e) only a single isomer was obtained. The product 3d with a sterically hindered t-butyloxy carbonyl (Boc) protecting group on the N atom was obtained with reduced diastereoselectivity (5 : 1 d.r.). The diastereoselectivities dropped in 5/6, 5/7 and 5/8 spiro-ring fused systems. Given that enantioenriched epoxides could be easily obtained (e.g. via sharpless asymmetric epoxidation), this strategy provides access to optically active spirocycles featuring an all-carbon quaternary stereocenter with the transfer of stereochemical information from epoxides (3c, 3e and 3f). Bis-heterospirocyclic scaffolds were frequently employed in pharmaceutical chemistry. For example, bis-heterospirocyclic 3d is the core structure of DLK inhibitors³⁹ and XEN402 (ref. 40) (scheme 1c), which are used for treating neurodegeneration and congenital erythromelalgia respectively. Furthermore, 6-exo cyclization was also investigated under the standard conditions and smoothly produced a serious of drug-like 6-(trifluoromethyl)-3-pyridinesulfonyl piperidine derivatives including 6/5, 6/6 and 6/7 spiro-ring fused systems (5a–5k) in generally excellent yields. Moreover, cyclization reactions with epoxy-alkynes afforded products containing exocyclic-alkenes and free alcohols which were suitable for further functionalization. This approach provides access to a broad range of novel spirocyclic piperidine and pyrrolidine spirocycles which could be of interest to synthetic and medicinal chemists.Scope of 5-exo and 6-exo cyclization^a,b,c,d

Metal-Mediated Directional Capping of Rod-Packing Metal–Organic Frameworks

Two new rod-packing metal–organic frameworks (RPMOF) are constructed by regulating the in situ formation of the capping agent. In CPM-s7, carboxylate linkers extend 1D manganese-oxide chains in four additional directions, forming 3D RPMOF. The substitution of Mn²⁺ with a stronger Lewis acidic Co²⁺, leads to an acceleration of the hydrolysis-prone sulfonate linker, resulting in presence of sulfate ions to reduce two out of the four carboxylate-extending directions, and thus forming a new 2D rod-packing CPM-s8. Density functional theory calculations and magnetization measurements reveal ferrimagnetic ordering of CPM-s8, signifying the potential of exploring 2D RPMOF for effective low-dimensional magnetic materials.     

Amino-Acid-Induced Circular Polarized Luminescence in One-Dimensional Manganese(II) Halide Hybrid

Circular polarized luminescence (CPL)-active materials attract great attentions owing to their widely applications in 3D optical displays and encrypted transmission. Inspired by the strategies adopted in perovskite based CPL materials, herein, CPL-active hybrids (D)- and (L)-(tert-butyl prolinate)MnCl₃ were successfully prepared by assembling chiral D/L tert-butyl prolinate with manganese (II) chloride. Single crystal structures show the as-formed hybrids possess one-dimensional (1D) structure containing linear chains of face-sharing MnCl₆ octahedral surrounded by prolinate cations. The 1D Mn(II) hybrids display strong red emission peaked at 646 nm with PLQY of 67.1 % and 57.2 % for d -type and l -type, respectively, representing the highest PLQY for 1D Mn^II hybrids. Interestingly, the 1D Mn(II) hybrids exhibit prominent circular dichroism (CD) signals and remarkable CPL activity with the dissymmetry factor g of 6.1*10⁻³ and −6.3*10⁻³ from 550 to 800 nm for (D)- and (L)-(tert-butyl prolinate)MnCl₃, respectively, owing to the existence of chiral cations. It is worthy noted the obtained g represents the highest value for non-lead organic–inorganic hybrids.     

On the mean field limit of the Random Batch Method for interacting particle systems

The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.     

Terahertz Dual-Band Near-Zero Effective Index Metamaterial Based on Double-Sided Metal Microstructure

Journal of Russian Laser Research - The zero-refractive-index metamaterials have excellent electromagnetic properties, which provide new ideas and methods to realize the control of electromagnetic...     

Neuroevolution-enabled adaptation of the Jacobi method for Poisson's equation with density discontinuities

Lacking labeled examples of working numerical strategies, adapting an iterative solver to accommodate a numerical issue, e.g., density discontinuities in the pressure Poisson equation, is non-trivial and usually involves a lot of trial and error. Here, we resort to evolutionary neural network. A evolutionary neural network observes the outcome of an action and adapts its strategy accordingly. The process requires no labeled data but only a measure of a network's performance at a task. Applying neuro-evolution and adapting the Jacobi iterative method for the pressure Poisson equation with density discontinuities, we show that the adapted Jacobi method is able to accommodate density discontinuities.     

石墨烯负载的氧配位钴单原子稳定金属锂负极

Lithium (Li)-based batteries are the dominant energy source for consumer electronics, grid storage, and electrified transportation. However, the development of batteries based on graphite anodes is hindered by their limited energy density. With its ultrahigh theoretical capacity (3860 mAh∙g⁻¹), low redox potential (−3.04 V), and satisfactorily low density (0.54 g∙cm⁻³), Li metal is the most promising anode for next-generation high-energy-density batteries. Unfortunately, the limited cycling life and safety issues raised by dendrite growth, unstable solid electrolyte interphase, and "dead Li" have inhibited their practical use. An effective strategy is to develop a suitable lithiophilic matrix for regulating initial Li nucleation behavior and controlling subsequent Li growth. Herein, single-atom cobalt coordinated to oxygen sites on graphene (Co-O-G SA) is demonstrated as a Li plating substrate to efficiently regulate Li metal nucleation and growth. Owing to its dense and more uniform lithiophilic sites than single-atom cobalt coordinated to nitrogen sites on graphene (Co-N-G SA), high electronic conductivity, and high specific surface area (519 m²∙g⁻¹), Co-O-G SA could significantly reduce the local current density and promote the reversibility of Li plating and stripping. As a result, the Co-O-G SA based Li anodes exhibited a high Coulombic efficiency of 99.9% at a current density of 1 mA∙cm⁻² with a capacity of 1 mAh∙cm⁻², and excellent rate capability (high current density of 8 mA∙cm⁻²). Even at a high plating capacity of 6 mAh∙cm⁻², the Co-O-G SA electrode could stably cycle for an ultralong lifespan of 1300 h. In the symmetric battery, the Co-O-G SA based Li anode (Co-O-G SA/Li) possessed a stable voltage profile of 18 mV for 780 h at 1 mA∙cm⁻², and even at a high current density of 3 mA∙cm⁻², its overpotential maintained a small hysteresis of approximately 24 mV for > 550 h. Density functional theory calculations showed that the surface of Co-O-G SA had a stronger interaction with Li atoms with a larger binding energy, −3.1 eV, than that of Co-N-G SA (−2.5 eV), leading to a uniform distribution of metallic Li on the Co-O-G SA surface. More importantly, when matched with a sulfur cathode, the resulting Co-O-G SA/lithium sulfur full batteries exhibited a high capacity of 1002 mAh∙g⁻¹, improved kinetics with a small polarization of 191 mV, and an ultralow capacity decay rate of 0.036% per cycle for 1000 cycles at 0.5C (1C = 1675 mA∙g⁻¹) with a steady Coulombic efficiency of nearly 100%. Therefore, this work provides novel insights into the coordination environment of single atoms for the chemistry of Li metal anodes for high-energy-density batteries.     

NORMAL CONTACT STIFFNESS OF THE ELLIPTIC AREA BETWEEN TWO ASPERITIES

A new expression for contact deformation is given, and the normal contact stiffness between single asperities is derived according to Hooke’s law. A contact model between two ellipsoidal asperities is simulated by the FE method, the result compared with the theoretical solution. It is found that the curves of the normal contact stiffness versus the included angle in the principal curvature direction show similar trends and evolve as a cosine feature. The effects of the parameters on normal contact stiffness are found to show that normal contact stiffness increases and reaches the upper limit gradually with an increase in these parameters.