Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

Study of nucleon-nucleon and alphanucleon elastic scattering by the Manning-Rosen potential

Although often used in molecular dynamics, in this work the Manning–Rosen potential is parameterized to compute the scattering phase shifts for the nucleon–nucleon and the alpha-nucleon systems by exploiting the standard phase function method. We obtain excellent agreement in phase shifts with the more sophisticated calculations up to partial waves ${\ell }=2.$     

Bilayer Cylindrical Conduit Consisting of Electrospun Polycaprolactone Nanofibers and DSC Cross‐Linked Sodium Alginate Hydrogel to Bridge Peripheral Nerve Gaps

Herein, a bilayer cylindrical conduit (P‐CA) is presented consisting of electrospun polycaprolactone (PCL) nanofibers and sodium alginate hydrogel covalently cross‐linked with N,N′‐disuccinimidyl carbonate (DSC). The bilayer P‐CA conduit is developed by combining the electrospinning and outer–inner layer methods. Using DSC, as a covalent crosslinker, increases the degradation time of the sodium alginate hydrogel up to 2 months. The swelling ratio of the hydrogel is also 503% during the first 8 h. The DSC cross‐linked sodium alginate in the inner layer of the conduit promotes the adhesion and proliferation of nerve cells, while the electrospun PCL nanofibers in the outer layer provide maximum tensile strength of the conduit during surgery. P‐CA conduit promotes the migration of Schwann cells along the axon in a rat model based on functional and histological evidences. In conclusion, P‐CA conduit will be a promising construct for repairing sciatic nerves in a rat model.     

Engineering nanostructures of CuO-based photocatalysts for water treatment: Current progress and future challenges

Nowadays, increasing extortions regarding environmental problems and energy scarcity have stuck the development and endurance of human society. The issue of inorganic and organic pollutants that exist in water from agricultural, domestic, and industrial activities has directed the development of advanced technologies to address the challenges of water scarcity efficiently. To solve this major issue, various scientists and researchers are looking for novel and effective technologies that can efficiently remove pollutants from wastewater. Nanoscale metal oxide materials have been proposed due to their distinctive size, physical and chemical properties along with promising applications. Cupric Oxide (CuO) is one of the most commonly used benchmark photocatalysts in photodegradation owing to the fact that they are cost-effective, non-toxic, and more efficient in absorption across a significant fraction of solar spectrum. In this review, we have summarized synthetic strategies of CuO fabrication, modification methods with applications for water treatment purposes. Moreover, an elaborative discussion on feasible strategies includes; binary and ternary heterojunction formation, Z-scheme based photocatalytic system, incorporation of rare earth/transition metal ions as dopants, and carbonaceous materials serving as a support system. The mechanistic insight inferring photo-induced charge separation and transfer, the functional reactive radical species involved in a photocatalytic reaction, have been successfully featured and examined. Finally, a conclusive remark regarding current studies and unresolved challenges related to CuO are put forth for future perspectives.     

Synthesis of ionic liquid intercalated layered double hydroxides of magnesium and aluminum: A greener catalyst of Knoevenagel condensation

Due to their structural merits that arise from their stability and high surface area, the layered double hydroxide (LDH) materials have caused strong attention. These characteristics provided intriguing possibilities with improved efficiency for catalytic applications. In this work, the preparation of 1-butyl-3-methylimidazolium hydroxide ([BMIM]⁺OH⁻) intercalated by a facile approach in a layered double hydroxide (LDH) matrix is reported and its implementation as a greener catalyst is shown. Different physico-chemical techniques such as XRD, FTIR, TGA, and N₂-physisorption, HRTEM, and CO₂ adsorption are implemented to characterize the structure of the fabricated catalysts. The [BMIM]⁺OH⁻/LDH exhibit outstanding catalytic performance in Knoevenagel condensation, resulting from the high LDH surface area and synergistic effects between both the intercalated ionic liquid and LDHs matrix. Knoevenagel’s fabricated catalysts can be exploited to catalyze different condensations and can be reused well. This work therefore generates good opportunities in the field of catalysis for the preparing and implementation of LDH-based catalysts.     

Was Pauling Mistaken about Metals?

Pauling described metallic bonds using resonance. The maximum probability domains in the Kronig–Penney model can show a picture of it. When the walls are opaque (and the band gap is large) the maximum probability domain for an electron pair essentially corresponds to the region between the walls: the electron pairs are localized within two consecutive walls. However, when the walls become transparent (and the band gaps closes), the maximum probability domain can be moved through the system without a significant loss in probability.