Band structures of symmetrical graphene superlattice with cells of three regions

We study the electronic band structures of massless Dirac fermions in symmetrical graphene superlattice with cells of three regions. opening gaps and additional Dirac points. Finally, we inspect the potential effect on minibands, the anisotropy of group velocity and the energy bands contours near Dirac points. We also discuss the evolution of gap edges and cutoff region near the vertical Dirac points.     

Informational analysis of seismic sequences by applying the Fisher Information Measure and the Shannon entropy: An application to the 2004–2010 seismicity of Aswan area (Egypt)

The interevent-time (IET) and interevent-distance (IED) series of seismic events occurred at Aswan area (Egypt) from 2004 to 2010 were investigated by means of the Fisher Information Measure and the Shannon entropy. The analysis was performed varying the depth and the magnitude thresholds. The results point out to an increase of level of organization and order with the decrease of magnitude threshold and the increase of depth threshold for the IET series, while the IED series are characterized by a level of uncertainty approximately constant with the threshold magnitude. The complexity measure, calculated as the product of the Fisher Information Measure and the Shannon entropy power, presents very similar pattern for both the types of seismic series, indicating an increasing complexity with the decrease of the threshold magnitude and the increase of the threshold depth.     

Two-Dimensional Layered Metallic VSe2/SWCNTs/rGO Based Ternary Hybrid Materials for High Performance Energy Storage Applications

In this work, the ternary hybrid structure VSe₂/SWCNTs/rGO is reported for supercapacitor applications. The ternary composite exhibits a high specific capacitance of 450 F g⁻¹ in a symmetric cell configuration, with maximum energy density of 131.4 Wh kg⁻¹ and power density of 27.49 kW kg⁻¹. The ternary hybrid also shows a cyclic stability of 91 % after 5000 cycles. Extensive density functional theory (DFT) simulations on the structure as well as on the electronic properties of the binary hybrid structure VSe₂/SWCNTs and the ternary hybrid structure VSe₂/SWCNTs/rGO have been carried out. Due to a synergic effect, there are enhanced density of states near the Fermi level and higher quantum capacitance for the hybrid ternary structure compared to VSe₂/SWCNTs, leading to higher energy and power density for VSe₂/SWCNTs/rGO, supporting our experimental observation. Computed diffusion energy barrier of electrolyte ions (K⁺) predicts that ions move faster in the ternary structure, providing higher charge storage performance.     

Bridging the Green Gap: Metal–Organic Framework Heteromultilayers Assembled from Porphyrinic Linkers Identified by Using Computational Screening

In organic photovoltaics, porphyrins (PPs) are among the most promising compounds owing to their large absorption cross-section, wide spectral range, and stability. Nevertheless, a precise adjustment of absorption band positions to reach a full coverage of the so-called green gap has not been achieved yet. We demonstrate that a tuning of the PP Q- and Soret bands can be carried out by using a computational approach for which substitution patterns are optimized in silico. The most promising candidate structures were then synthesized. The experimental UV/Vis data for the solvated compounds were in excellent agreement with the theoretical predictions. By attaching further functionalities, which allow the use of PP chromophores as linkers for the assembly of metal-organic frameworks (MOFs), we were able to exploit packing effects resulting in pronounced redshifts, which allowed further optimization of the photophysical properties of PP assemblies. Finally, we use a layer-by-layer method to assemble the PP linkers into surface-mounted MOFs (SURMOFs), thus obtaining high optical quality, homogeneous and crystalline multilayer films. Experimental results are in full accord with the calculations, demonstrating the huge potential of computational screening methods in tailoring MOF and SURMOF photophysical properties.     

A Self-Healing Metal–Organic Hydrogel for an All-Solid Flexible Supercapacitor

A zinc containing metal–organic gel (Zn-MOG) with embedded free ions, which exhibits self-healing properties, has been synthesized for application in supercapacitors. The activated carbon-based flexible supercapacitor device with the MOG electrolyte has a broad potential window of 2.1 V, with high retention of specific capacitance compared to the traditional polyvinyl alcohol (PVA)-based gel. The Zn-MOG does not require an additional electrolyte. The sodium and sulphate ions embedded in the MOG are sufficient enough for the charge storage.     

A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations

We present a seventh order iterative method for solving systems of nonlinear equations. The algorithm is derivative free per full iteration. A comparison between the computational efficiencies of proposed technique and existing techniques of similar nature is made. It is shown that for large system the new method is more efficient. The performance is tested through numerical experimentation which also confirms the theoretical results.     

Gold-Catalyzed Oxidative Aminocyclizations of Propargyl Alcohols and Propargyl Amines to Form Two Distinct Azacyclic Products: Carbene Formation versus a 3,3-Sigmatropic Shift of an Initial Intermediate

Gold-catalyzed oxidations of propargyl alcohols with nitrones by using a P(tBu)₂(o-biphenyl)Au⁺ catalyst, afforded bicyclic annulation products from the Mannich reactions of gold enolates. The same reactions of propargyl amines with nitrones by using the same gold catalyst gave distinct oxoarylation products. Our DFT calculations indicate that oxidation of propargyl alcohols with nitrones by using electron-rich gold catalysts lead only to gold carbenes, which can generate gold enolates or oxoarylation intermediates with enolate species having a barrier smaller than that of oxoarylation species.     

Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some existence results like Bahri-Coron theorem. Furthermore, we consider the approximate subcritical problem and we construct some solutions which blow up at two different points, one of them lay on the boundary and the other one is an interior point.