Congruences of multipartition functions modulo powers of primes

Let p _r (n) denote the number of r-component multipartitions of n, and let S _γ,λ be the space spanned by η(24z) ^γ ?(24z), where η(z) is the Dedekind’s eta function and ?(z) is a holomorphic modular form in \(M_{\lambda}(\mathrm{SL}_{2}(\mathbb{Z}))\) . In this paper, we show that the generating function of \(p_{r}(\frac{m^{k} n +r}{24})\) with respect to n is congruent to a function in the space S _γ,λ modulo m ^k . As special cases, this relation leads to many well known congruences including the Ramanujan congruences of p(n) modulo 5,7,11 and Gandhi’s congruences of p ₂(n) modulo 5 and p ₈(n) modulo 11. Furthermore, using the invariance property of S _γ,λ under the Hecke operator \(T_{\ell^{2}}\) , we obtain two classes of congruences pertaining to the m ^k -adic property of p _r (n).     

<Emphasis Type="Italic">Cis</Emphasis>/<Emphasis Type="Italic">trans</Emphasis> Fluorescent Recognition by Naphthalimide Dyes ⊂ CB [7] Assembly

A novel method to recognize cis/trans isomers was studied here. The naphthalimide dye as guest could bind with host cucurbit [7]uril (CB [7]) and 1:1 naphthalimide dye ? CB [7] assembly was formed. Moreover, this assembly was used as a fluorescent probe to recognized Fumaric acid (FA) and maleic acid (MA) via fluorescence titration. Two carboxyls in MA are in the same side, they could form stable interaction with the assembly and the fluorescence intensity decreased obviously when naphthalimide dye ? CB [7] was titrated by MA (nearly quenched in 1.5 equiv). But two carboxyls in FA are in opposite sides, the interaction between FA and the assembly was weak and not stable, and the fluorescence intensity changed inconspicuously when the assembly was titrated by FA.     

Tuning the Lewis acid phenol $$\varvec{}$$-prenylation as a molecular diversity tool

A diversity-oriented approach for the synthesis of various structurally different prenylated alcohols from readily accessible and common precursors was developed. With varying approaches, this article describes some successful examples of a Friedel–Crafts alkylation using methoxyphenols and different prenyl alcohols (geraniol and (E,E)-farnesol). We demonstrated that just by varying the stoichiometry of the Lewis acid used, the course of the reaction can be shifted to produce the alkylated or the cyclized product. Eighteen unique products were obtained with good isolated yields by direct alkylation with or without a consecutive \(\pi \)-cationic cyclization.     

Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials

Transformation thermodynamics as a major extension of transformation optics has recently received considerable attention. In this paper, we present two-dimensional (2D) and three-dimensional (3D) diamond-shaped transient thermal cloaks with non-singular homogeneous material parameters. The absence of singularity in the parameters results from the fact that the linear coordinate transformation is performed by expanding a line segment rather than a point into a region, while the mechanism behind the homogeneity is the homogeneous stretching and compression along orthogonal directions during the transformation. Although the derived parameters remain anisotropic, we further show that this can be circumvented by considering a layered structure composed of only four types of isotropic materials based on the effective medium theory. Numerical simulation results confirm the good performance of the proposed cloaks.     

A brief review of co-doping

Dopants and defects are important in semiconductor and magnetic devices. Strategies for controlling doping and defects have been the focus of semiconductor physics research during the past decades and remain critical even today. Co-doping is a promising strategy that can be used for effectively tuning the dopant populations, electronic properties, and magnetic properties. It can enhance the solubility of dopants and improve the stability of desired defects. During the past 20 years, significant experimental and theoretical efforts have been devoted to studying the characteristics of co-doping. In this article, we first review the historical development of co-doping. Then, we review a variety of research performed on co-doping, based on the compensating nature of co-dopants. Finally, we review the effects of contamination and surfactants that can explain the general mechanisms of co-doping.     

Ionic liquid enhanced magnesium-based polymer electrolytes for electrical double-layer capacitors

This paper describes the preparation and characterization of poly(vinyl alcohol) (PVA)-added ionic liquid-based ion conductors. The polymer electrolyte is incorporated with magnesium triflate [Mg(CF₃SO₃)₂ or MgTf] as salt and 1-butyl-3-methylimidazolium bromide (BmImBr) as ionic liquid. Differential scanning calorimetry (DSC) is carried out to investigate the glass transition temperature which is used to study the plasticizing effect of the ionic liquid. The highest conducting ionic liquid-based polymer electrolyte is used to fabricate electrical double-layer capacitors (EDLC). The electrochemical potential window is evaluated using linear sweep voltammetry (LSV). The electrochemical capacitance of the EDLC is evaluated through cyclic voltammetry (CV) and galvanostatic charge–discharge (GCD). The electrochemical potential window of ionic liquid-added polymer electrolyte is extended from 1.35 to 2.6 V. Cyclic voltammetry (CV) proves the improvement in specific capacitance of the electrical double-layer capacitors (EDLCs) containing ionic liquid-added polymer electrolyte.     

Broadband Light-Emitting Diodes with One-Dimensional Photonic Crystal Layer

In this article, a broadband gallium-nitride-based light-emitting diode with a one-dimensional photonic crystal layer is investigated. The broadband light-emitting diode using the proposed backside reflector has high reflectance (>95%) over a 270-nm bandwidth in visible light at an arbitrary incidence angle. A broadband light-emitting diode of high output power due to the high reflectivity is achieved. Also reported are the results for light-emitting diodes by the transistor outline can (TO-can) package. The proposed light-emitting diodes possess broadband high reflected spectra, high output power for light extraction, and a good view angle.     

Complete minimal hypersurfaces in quaternionic hyperbolic space

We construct new examples of embedded, complete minimal hypersurfaces in quaternionic hyperbolic space and also some minimal foliations. We introduce fans and construct analytic deformations of bisectors.     

High-field EPR Study of the Effect of Chloride on Mn2+ Ions in Frozen Aqueous Solutions

The effect of chloride concentration on Mn²⁺ (S = 5/2, I = 5/2) ions in frozen aqueous solutions is studied by high-field high-frequency electron paramagnetic resonance (HFEPR). The usually six sharp lines characteristic of Mn²⁺ ions, arising from the m _s  = ?1/2 → 1/2 transition, is modified by the addition of Cl^? anions and the six resonances become much broader and more complex. This new feature likely arises from the ligation of one Cl^? anion to a hydrated Mn²⁺ ion forming a [Mn(H₂O)₅Cl]^? complex. This complex increases linearly with Cl^? concentration with an association constant of K _{a, apparent} = 61 M^?1. The structure of the putative chloride complex was studied using density functional theory calculations and the expected zero-field interaction of such a manganese center was calculated using the superposition model. The predicted values were similar to those determined from the simulation of the spectrum of the m _s  = ?5/3 → ?3/2 transition of the chloride complex. This effect of Cl^? anions occurs at biologically relevant concentration and can be used to probe the Mn²⁺ ions in cellular and protein environments.