Negative index fishnet with nanopillars formed by direct nano-imprint lithography

In this paper we demonstrate the ability to fabricate fishnets by nanoimprinting directly into a pre-deposited three layer metal–dielectric–metal stack, enabling us to pattern large areas in two minutes. We have designed and fabricated two different fishnet structures of varying dimensions using this method and measured their resonant wavelengths in the near-infrared at 1.45 μm and 1.88 μm. An important by-product of directly imprinting into the metal–dielectric stack, without separation from the substrate, is the formation of rectangular nanopillars that sit within the rectangular apertures between the fishnet slabs. Simulations complement our measurements and suggest a negative refractive index real part with a magnitude of 1.6. Further simulations suggest that if the fishnet were to be detached from the supporting substrate a refractive index real part of 5 and FOM of 2.74 could be obtained

A Dynamically Consistent Nonstandard Difference Scheme for a Discrete-Time Immunogenic Tumors Model

This manuscript deals with the qualitative study of certain properties of an immunogenic tumors model. Mainly, we obtain a dynamically consistent discrete-time immunogenic tumors model using a nonstandard difference scheme. The existence of fixed points and their stability are discussed. It is shown that a continuous system experiences Hopf bifurcation at one and only one positive fixed point, whereas its discrete-time counterpart experiences Neimark–Sacker bifurcation at one and only one positive fixed point. It is shown that there is no chance of period-doubling bifurcation in our discrete-time system. Additionally, numerical simulations are carried out in support of our theoretical discussion.Spanish Government and European Commission, Grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE); Basque Government, Grant IT1207-19

Antibacterial effects of cyanogenic glucoside isolated from the stem bark of Bauhinia rufescens Lam

The chemical contents and in vitro antibacterial effects of the n-butanol column fractions, stem bark methanol extracts of Bauhinia rufescens Lam. were evaluated in Gram-positive and Gram-negative bacteria using disc diffusion technique. The n-butanol soluble portion from the stem bark methanol extract was successively eluted to afford 10 pooled fractions by comparison of TLC chromatograms. The bioactive fraction (fraction D) was further chromatographed using the bioassay guided protocol to afford 4 sub-fractions from which a pure compound was isolated and characterized using spectral studies as: (4S, 6R)-(Z)-6-(â-Dglucopyranosyloxy)-4-hydroxy-2-cyclohexenyl-Ä1,á-acetonitrile–a cyclohexenyl cyano methylene known commonly as menisdaurin. Test bacteria were Bacillus subtilis, Corynaebacterium spp., Escherichia coli and Shigella dysenteriae. The diameters of inhibition zone on the Gram-positive bacteria was found in the range from11.83±0.17 (n-butanol Fraction D) to 17.33±0.67 (Fraction D2-8); while on Gram-negative organism the values ranged from  11.50±0.29 (n-butanol Fraction D) to 19.67±0.33 (Fraction D2-8). The activity index (AI) showed that Fraction D2-8 (51.18%) and Compound I [menisdaurin] (127.36%) was highly sensitive to Corynaebacterium spp. and E. coli when computed with Erythromycin and Gentamicin respectively. Highest AI was exhibited by Fraction D2-8 (93.89%) against S. dysenteriae when computed with ciprofloxacin. In continuation of our chemical studies and search for bioactive compounds from medicinal plants; this work, therefore, was aimed at characterizing and testing the antibacterial efficacy of the isolated compound in order to further confirm our earlier reports on use of this part of B. rufescens in some parts of Northern Nigeria as atreatment against diarrhoea and dysentery. This is the first report of the isolation and antibacterial activity of menisdaurin from B. rufescens.© 2013 International Formulae Group. All rights reserved.Keywords: Antibacterial, Bauhinia rufescens, cyanogenic glucoside, isolation, menisdaurin

Optimum Solutions of Systems of Differential Equations via Best Proximity Points in b-Metric Spaces

This paper deals with the existence of an optimum solution of a system of ordinary differential equations via the best proximity points. In order to obtain the optimum solution, we have developed the best proximity point results for generalized multivalued contractions of b-metric spaces. Examples are given to illustrate the main results and to show that the new results are the proper generalization of some existing results in the literature.This study is supported financially by the Basque Government through Grant IT1207-19

Higher Order Non-Planar Electrostatic Solitary Potential in a Streaming Electron-Ion Magnetoplasma: Phase Plane Analysis

We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved with the aid of the reductive perturbation (RP) technique, leading to the modified Korteweg–De Vries (mKdV) equation for the non-linear behaviour of the solitary waves in EI plasma. By employing the reduced differential transform method (RDTM), an approximate solution of the mKdV is obtained for solitary waves. Phase plane analysis reveals that these excitations exhibit periodic oscillations. The phase plane and periodic behaviour of the obtained model are studied. It is observed that the amplitude and width of the electron acoustic waves (EAWs) are affected by a slight change in the cold to hot electron temperature ratio (σc) and the number density of the cold to hot electron ratio (α). The effect of the streaming speed u(0) and superthermality index κe are investigated. This study is important for understanding the symmetric properties of cylindrical and spherical plasma, relying on the bifurcation analysis, impacted by the streaming effect in the EI plasma.Basque Government: Grant IT1555-22 Basque Government: Grant KK-2022/00090 MCIN/ AEI 269.10.13039/501100011033: Grant PID2021-1235430B-C21/C22

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

In this paper, we provide and study the concept of multi-valued generalized (α,β)-nonexpansive mappings, which is the multi-valued version of the recently developed generalized (α,β)-nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings.The authors are very grateful to the Basque Government for their support through Grant no. IT1207-19

Double Sawi Transform: Theory and Applications to Boundary Values Problems

Symmetry can play an important role in the study of boundary value problems, which are a type of problem in mathematics that involves finding the solutions to differential equations subject to given boundary conditions. Integral transforms play a crucial role in solving ordinary differential equations (ODEs), partial differential equations (PDEs), and integral equations. This article focuses on extending a single-valued Sawi transform to a double-valued ST, which we call the double Sawi (DS) transform. We derive some fundamental features and theorems for the proposed transform. Finally, we study the applications of the proposed transform by solving some boundary value problems such as the Fourier heat equation and the D’Alembert wave equation.The APC is supported by the Basque Government, Grant IT1555-22

Qualitative analysis of a discrete-time phytoplankton–zooplankton model with Holling type-II response and toxicity

[EN]The interaction among phytoplankton and zooplankton is one of the most important processes in ecology. Discrete-time mathematical models are commonly used for describing the dynamical properties of phytoplankton and zooplankton interaction with nonoverlapping generations. In such type of generations a new age group swaps the older group after regular intervals of time. Keeping in observation the dynamical reliability for continuous-time mathematical models, we convert a continuous-time phytoplankton–zooplankton model into its discrete-time counterpart by applying a dynamically consistent nonstandard difference scheme. Moreover, we discuss boundedness conditions for every solution and prove the existence of a unique positive equilibrium point. We discuss the local stability of obtained system about all its equilibrium points and show the existence of Neimark–Sacker bifurcation about unique positive equilibrium under some mathematical conditions. To control the Neimark–Sacker bifurcation, we apply a generalized hybrid control technique. For explanation of our theoretical results and to compare the dynamics of obtained discrete-time model with its continuous counterpart, we provide some motivating numerical examples. Moreover, from numerical study we can see that the obtained system and its continuous-time counterpart are stable for the same values of parameters, and they are unstable for the same parametric values. Hence the dynamical consistency of our obtained system can be seen from numerical study. Finally, we compare the modified hybrid method with old hybrid method at the end of the paper

Alternating and Rotational Losses up to Magnetic Saturation in Non-Oriented Steel Sheets

partially_open5sìpartially_openAppino, Carlo; Khan, Mahmood; de la Barrière, Olivier; Ragusa, Carlo; Fiorillo, FaustoAppino, Carlo; Khan, Mahmood; de la Barrière, Olivier; Ragusa, Carlo; Fiorillo, Faust

A simple compensation method for the accurate measurement of magnetic losses with a single strip tester

International audienceWe present a new method for the accurate characterization of soft magnetic sheets using a permeameter based on the precise compensation of the magnetomotive force (MMF) drop in the flux-closing yoke. It has been developed in order to overcome the systematic uncertainty affecting the value of the magnetic fieldstrength in single sheet testers when obtained, according to the standards, through the measurement of the magnetizing current. This phenomenon is more critical for high permeability materials, because of the reduced MMF drop across the sample. While additional sensors and auxiliary windings have been proposed in the literature, a novel approach is demonstrated here, based on the use of the permeameter upper half yoke as the MMF drop sensor and of an auxiliary winding on the lower half yoke, implementing compensation. This solution, dispensing one from dealing with the usually small signal levels of the conventional MMF drop sensors (e.g. Chattock coils), provides best results with the introduction of wedge-shaped magnetic poles, in order to accurately define the magnetic path length. The method is validated by measurements of power loss, apparent power, and hysteresis cycles on non-oriented and grain-oriented Fe-Si steel sheets, which are compared with local measurements performed on the same samples using H-coil and B-coil across a uniformly magnetized region