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Optical accordion lattices are routinely used in quantum simulation and quantum computation experiments to tune optical lattice spacings. Here, we present a technique for creating tunable optical lattices using binary-phase transmission gratings. Lattices generated using this technique have high uniformity, contrast, lattice spacing tunability, and power efficiencies. These attributes are crucial for exploring collective quantum phenomena in highly ordered atomic arrays coupled to optical waveguides for quantum networking and quantum simulation. In this paper, we demonstrate adjustable-period lattices that are ideally suited for use with optical nanofibers., Comment: 7 pages, 4 figures

We theoretically study transient electroosmotic flow of general Maxwell fluids through polyelectrolyte grafted nanochannel with a layered distribution of charges. By applying the method of Laplace transform, we semi-analytically obtain transient electroosmotic flow from Cauchy momentum equation and Maxwell constitutive equation. For nanochannels grafted with polyelectrolyte layers having different layered distribution of charges, we study the influence of dimensionless relaxation time, dimensionless polyelectrolyte layer thickness and dimensionless drag coefficient on transient electroosmotic flow. We present the results for some particular cases. Firstly, we unravel that for the case of polyzwitterionic brush that the sum of positive and negative structural charges is zero, total electroosmotic flow is non-zero. In particular, depending on charge distribution within end part of polyelectrolyte layers, the direction of electroosmotic flow can be reversed critically. Secondly, in order to quantitatively evaluate a reversal of electroosmotic flow for two polyelectrolyte layers of opposite signs, we introduce a critical number ks as the ratio between layered charge densities of two polyelectrolyte layers. Increasing ks allows electroosmotic flow to be reversed easily. We verify that adjusting charge distributions of the layer can control intentionally the direction of the flows as well as strength of electroosmotic flow.

Let $F(X)=X^{2^{2k}+2^k+1}$ be the power function over the finite field $\GF{2^{4k}}$ which is known as the Bracken-Leander function. In \cite{BCC10,BL10,CV20,Fu22,XY17}, it was proved that the number of solutions in $\GF{q^4}$ to the equation $F(X)+F(X+1)=b$ is in $\{0,2,4\}$ for any $b\in \GF{q^4}$ and the number of the $b$ giving $i$ solutions have been determined for every $i$. However, no paper provided a direct and complete method to solve such an equation, and this problem remained open. This article presents a direct technique to derive an explicit solution to that equation. The main result in \cite{BCC10,BL10,Fu22,XY17}, determining differential spectrum of $F(X)=X^{2^{2k}+2^k+1}$ over $\GF{2^{4k}}$, is re-derived simply from our results.

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance., Comment: 12 pages (main), 7 pages (supplementary), 7 figures

The uncertainty principle is the most important for the foundations of quantum mechanics but it still remains failed to reach a consensus of its interpretation, which gives rise to debates upon its physical nature. In this work, we address the problem of its foundation from a different aspect to present an alternative formulation for proving the uncertainty relations in a general way in terms of commutation relations and action function. The relationship between the de Broglie relation and the uncertainty principle is studied from a new angle. As a result, it is demonstrated that the de Broglie relation is the foundation of the uncertainty principle. Starting with the origin of the problem, we show that the de Broglie relation provides the form of the wave function and the determined form of the wave function in turn leads to the conception of operators for quantum mechanics, and thus it is possible to provide with the help of the operators and wave function a generalized proof of the uncertainty principle as the law governing ensemble of states. As a decisive solution to the problem, the interpretation of the uncertainty principle in terms of the action function is offered that gives one self-consistent explanation in agreement with the known physical phenomena. Eventually, we show the necessity and possibility of reassessing and improving the foundation and interpretation of the uncertainty principle as a leading principle of quantum mechanics., Comment: 13 pages, 0 figures

We analyze the dynamics of quantum beats in a system of two V-type three-level atoms coupled to a waveguide. We show that quantum beats can be collectively enhanced or suppressed, akin to Dicke super- and sub-radiance, depending on the interatomic separation and the initial correlations between the atoms. In particular, the interference properties of the collective beats are determined by the distance between the atoms modulo the beat wavelength. We study the collective atomic and field dynamics, illustrating a crossover from a Markovian to a non-Markovian regime as the atomic separation becomes sufficiently large to bring memory effects of the electromagnetic environment into consideration. In such a non-Markovian regime, collective quantum beats can be enhanced beyond the Markovian limit as a result of retardation effects. Our results demonstrate the rich interplay between multilevel and multiatom quantum interference effects arising in a system of distant quantum emitters., Comment: 12 pages(including appendices), 6 figures

Hybrid organic-inorganic halide perovskites for photovoltaics have attracted research interest due to their unique material properties, but suffered from poor material stability. In this work, we investigated the surface phase diagrams of PbI$_2$ and cubic CH$_3$NH$_3$PbI$_3$ (MAPbI$_3$) for a better understanding of precursor effect on perovskite synthesis via solid-gas reaction, by density functional theory calculations combined with thermodynamics. Using the devised slab models of PbI$_2$(001) and MAPbI$_3$(100), (110) and (111) surfaces with perfect and various vacant defect terminations, we calculated their formation energies and adsorption energies of CH$_3$NH$_2$ molecule on the PbI$_2$(001) surfaces under different synthesis conditions of temperature, pressure and pH via chemical potentials of species. Our calculations revealed that the adsorption can be facilitated by including HI or NH$_4$I molecule by dissociation of this additive and formation of CH$_3$NH$_3^+$ cation or NH$_3$-CH$_3$NH$_3^+$ complex, which is beneficial for conversion of PbI$_2$ to MAPbI$_3$ via solid-gas reaction. Furthermore, we found that among different perovskite MAPbI$_3$ surfaces, the MA-terminated (110) and MAI-terminated (100) surfaces are placed on the thermodynamically stable region of chemical potentials at pH values of 1 and 6, being agreed well with the experimental findings. We believe this work gives a fundamental understanding of solid-gas reaction for high-crystallinity perovskite synthesis towards perovskite solar cells with improved stability.

In this paper, we study the electroosmotic transport in a nanofluidic channel by using a mean-field theory accounting for non-uniform size effect and solvent polarization effect. We witness that in the presence of the given zeta potential, an enhancement of ion size invariably lowers the electroosmotic velocity, thereby increasing the magnitude of electrostatic potential, irrespective of considering solvent polarization. It is also proved that solvent polarization allows both the magnitude of electrostatic potential and the electroosmotic velocities to decrease. In addition, we find that increasing zeta potential augments not only ion size effect but also solvent polarization effect. Furthermore, we demonstrate that decreasing bulk ion number density causes an increase in electroosmotic velocity at the centerline. We compare the properties of aqueous electrolytes with those of the electrolytes where solvent is ethylalcohol. Finally, we study how solvent polarization and ionic size affect streaming potential and electroviscous effect. It is emphasized that the present study can provide a good way to control the nanofluidic transport for a plethora of biological and industrial applications.

The response of a suspension under a variety of static or alternating external fields strongly depends on the equilibrium electric double layer that surrounds the colloidal particles in the suspension. The theoretical models for salt-free suspensions can be improved by incorporating non-uniform size effects and orientational ordering of water dipoles neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann approach. Our model including non-uniform size effects and orientational ordering of water dipoles seems to have quite a promising effect because the model can predict the phenomena like a heavy decrease in relative permittivity of the suspension and counterion stratification near highly charged colloidal particle. In this work we numerically obtain the electric potential, the counterions concentration and the relative permittivity around a charged particle in a concentrated salt-free suspension corrected by non-uniform size effects and orientational ordering of water dipoles. The results show the worth of such corrections for medium to high particle charges at every particle volume fraction. We conclude that non-uniform size effects and orientational ordering of water dipoles are necessary for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions., Comment: arXiv admin note: text overlap with arXiv:1102.0255 by other authors

We report a theoretical study of ion size effect on various properties in a soft nanochannel with pH-dependent charge density. We develop a free energy based mean-field theory taking into account ion size as well as pH-dependence of charged polyelectrolyte layer grafted on a rigid surface in an electrolyte. The influence of ion size on properties in a soft nanochannel is evaluated by numerically calculating ion number densities and electrostatic potential. We demonstrate that unlike in point-like ions, for finite sizes of ions, a uniform distribution of chargeable sites within the polyelectrolyte layer causes unphysical discontinuities in ion number densities not only for hydrogen ion but also for other kinds of ions. It is shown that the same cubic spatial distribution of chargeable sites as for point-like ions is necessary to ensure continuity of ion number density and zero ion transport at the polyelectrolyte layer - rigid solid interface. We find that considering finite ion size causes an increase in electrostatic potential and electroosmotic velocity and a decrease in ion number densities. More importantly, we demonstrate that in polyelectrolyte layer, pH-dependence of polyelectrolyte charge density makes accumulation of hydrogen ions stronger than for the other positive ion species in the electrolyte and such a tendency is further enhanced by considering finite ion size. In addition, we discuss how consideration of finite ion size affects the role of various parameters on electrostatic and electroosmotic properties.

We study the electric double layer near a charged soft surface by using a mean-field approach including non-uniform size effect and solvent polarization. Based on a free energy model, electrostatic potential and number densities of water and ions are obtained numerically by solving coupled differential equations including the Poisson's equation. We find that the solvent polarization significantly affects electrostatic potential, ion number densities and permittivity in an electrolyte solution near a charged soft surface. We prove that the consideration of the solvent polarization increases the magnitude of Donnan potential. We also demonstrate that within the fixed charge layer the number densities of counterions and coions are slightly smaller than when the solvent polarization is not considered. An increase in the ionic size enhances the influence of solvent polarization on the electrostatic properties within the fixed charged layer of charged soft surface. In the region of high surface-charge-density, the permittivity and the number density of water dipoles considerably decrease due to water polarization.

Defect pyrochlore oxides have attracted a great interest as promising luminescent materials due to their flexible composition and high electron/hole mobility. In this work, we investigate the structural and electronic properties of lanthanide-doped (Ln) defect pyrochlore oxides \ce{KNbWO6}:0.125Ln$^{3+}$ by using first-principles calculations. We perform structural optimizations of various defect pyrochlore models and calculate their electronic structures, revealing that hydration has a significant influence on both local symmetry around Eu$^{3+}$ ion and band structures with an alteration of their luminescent behaviour. In the hydrated compounds, the electric-dipole $^5$D$_0-^7$F$_2$ transition is found to be partially suppressed by the raised local symmetry, and the water molecules in the compounds can mediate the non-radiative energy transfer between the activator Eu$^{3+}$ ions and the host, resulting in the quenching effect. It turns out that the oxygen vacancies are detrimental to luminescence as they reduce the Eu$^{3+}$ ion in its vicinity to Eu$^{2+}$ ion and also serve as traps for conduction electrons excited by incident light. Our calculations for \ce{KNbWO6}:0.125Ln$^{3+}$ (Ln = Ce, Pr, Nd, Pm, Sm) support that defect pyrochlore oxide \ce{KNbWO6} can also be used as luminescence host for Ln$^{3+}$ ion doping, giving a valuable insight into a variation trend in luminescent properties of these materials at atomic level.

All-inorganic halide perovskites have attracted a great interest as a promising light harvester of perovskite solar cells due to their enhanced chemical stability. In this work we investigate the material properties of solid solutions CsPb(I$_{1-x}$Br$_x$)$_3$ in cubic phase by applying the virtual crystal approximation approach within a density functional theory framework. First we check the validity of constructed pseudopotentials of the virtual atoms (X = I$_{1-x}$Br$_x$) by verifying that the lattice constants follow the linear function of mixing ratio. We then suggest an idea of using the hybrid HSE functional with linear increasing value of exact exchange term as increasing the Br content x, which produces the band gaps of CsPbX3 in good agreement with the available experimental data. The calculated light absorption coefficients and reflectivity show the systematic varying tendency to the Br content. We calculate the phonon dispersions of CsPbX3, CsX and PbX2 as slightly changing their volumes, revealing the phase instability of CsPbX3 and calculating the thermodynamic potential function differences. By projecting Gibbs free energy differences onto the plane of G = 0, we determine the P - T diagram for CsPbX3 to be stable against the chemical decomposition, highlighting that the area of being stable extends gradually as the Br content increases.

We study the optimal output power and efficiency of the three-terminal quantum heat engine with Coulomb-coupled quantum-dots (CCQD). It has been well known that in the weak coupling regime, two kinds of dominant transport mechanisms are sequential tunneling and cotunneling processes in CCQD. What process becomes dominant, which can be controlled by several parameters such as temperature difference, bias voltage, Coulomb interaction and tunneling parameters, is one of the key problems to determine the performance of the heat engine. We show the parametric dependence of the output power and coefficient and find the optimal performance of this CCQD heat engine through genetic algorithm.

We demonstrate collectively enhanced vacuum-induced quantum beat dynamics from a three-level V-type atomic system. Exciting a dilute atomic gas of magneto-optically trapped $^{85}$Rb atoms with a weak drive resonant on one of the transitions, we observe the forward-scattered field after a sudden shut-off of the laser. The subsequent radiative dynamics, measured for various optical depths of the atomic cloud, exhibits superradiant decay rates, as well as collectively enhanced quantum beats. Our work is also the first experimental illustration of quantum beats arising from atoms initially prepared in a single excited level as a result of the vacuum-induced coupling between excited levels., Comment: 12 pages (including Supplemental Material), 4 figures

The problem of solving explicitly the equation $P_a(X):=X^{q+1}+X+a=0$ over the finite field $\GF{Q}$, where $Q=p^n$, $q=p^k$ and $p$ is a prime, arises in many different contexts including finite geometry, the inverse Galois problem \cite{ACZ2000}, the construction of difference sets with Singer parameters \cite{DD2004}, determining cross-correlation between $m$-sequences \cite{DOBBERTIN2006} and to construct error correcting codes \cite{Bracken2009}, cryptographic APN functions \cite{BTT2014,Budaghyan-Carlet_2006}, designs \cite{Tang_2019}, as well as to speed up the index calculus method for computing discrete logarithms on finite fields \cite{GGGZ2013,GGGZ2013+} and on algebraic curves \cite{M2014}. Subsequently, in \cite{Bluher2004,HK2008,HK2010,BTT2014,Bluher2016,KM2019,CMPZ2019,MS2019,KCM19}, the $\GF{Q}$-zeros of $P_a(X)$ have been studied. In \cite{Bluher2004}, it was shown that the possible values of the number of the zeros that $P_a(X)$ has in $\GF{Q}$ is $0$, $1$, $2$ or $p^{\gcd(n, k)}+1$. Some criteria for the number of the $\GF{Q}$-zeros of $P_a(x)$ were found in \cite{HK2008,HK2010,BTT2014,KM2019,MS2019}. However, while the ultimate goal is to explicit all the $\GF{Q}$-zeros, even in the case $p=2$, it was solved only under the condition $\gcd(n, k)=1$ \cite{KM2019}. In this article, we discuss this equation without any restriction on $p$ and $\gcd(n,k)$. In \cite{KCM19}, for the cases of one or two $\GF{Q}$-zeros, explicit expressions for these rational zeros in terms of $a$ were provided, but for the case of $p^{\gcd(n, k)}+1$ $\GF{Q}-$ zeros it was remained open to explicitly compute the zeros. This paper solves the remained problem, thus now the equation $X^{p^k+1}+X+a=0$ over $\GF{p^n}$ is completely solved for any prime $p$, any integers $n$ and $k$., Comment: arXiv admin note: text overlap with arXiv:1912.12648

Motivated by recent discovery of correlated insulating and superconducting behavior in twisted bilayer graphene, we revisit graphene's honeycomb lattice doped close to the van Hove singularity, using the truncated unity functional renormalization group approach. We consider an extended Hubbard model on the honeycomb lattice including on-site and nearest-neighbor Coulomb repulsions, and nearest-neighbor ferromagnetic exchange and pair hopping interactions. By varying the strength of the nearest-neighbor exchange coupling and Coulomb repulsion as free parameters, we present rich ground-state phase diagrams which contain the spin-triplet $f$-wave and spin-singlet chiral $d$-wave superconducting phases, the commensurate and incommensurate spin- and charge-density-wave phases, and the ferromagnetic phase. In the absence of the exchange coupling and for small value of the nearest-neighbor repulsion, the four-sublattice spin-density-wave phase is generated right around the van Hove filling, while the chiral $d$-wave superconductivity emerges slightly away from it. Surprisingly, the chiral $d$-wave superconductivity is strongly suppressed by weak nearest-neighbor exchange coupling in our calculations. We argue that this suppression might be one of the reasons why the chiral superconductivity proposed for doped graphene has not yet been observed experimentally., Comment: 20 pages, 11 figures, 2 tables

Perovskite solar cells have achieved a substantial breakthrough via advanced interface engineerings. Reports have emphasized that combining the hybrid perovskites with Lewis base and graphene improve the performance; the underlying mechanisms are not yet fully understood. Here, using density functional theory, we show that upon the formation of CH3NH3PbI3 interfaces with three different Lewis base molecules and graphene, the binding strength with S-donors thiocarbamide and thioacetamide is higher than with O-donor dimethyl sulfoxide, while the interface dipole and work function reduction tend to increase from S-donors to O-donor. Furthermore, we provide evidences of deep trap states elimination in the S-donor perovskite interfaces through the analysis of defect formation on CH3NH3PbI3(110) surface, and of stability enhancement by estimating activation barriers for iodine atom migrations. These theoretical predictions are in line with the experimental observation of performance enhancement in the perovskites prepared using thiocarbamide.

The thermal conductivity of porous jennite, as the major component of cement paste, and its porosity and temperature dependences are simulated by molecular dynamics methods using ClayFF force field. The porous jennite models with different porosities are created by removing atoms within the sphere from bulk jennite model. The thermal conductivity elements of bulk jennite calculated by equilibrium Green-Kubo method are almost identical to those by non-equilibrium M\"{u}ller-Plathe (MP) method at 300 K. The volumetric thermal conductivity of porous jennite is found to decrease from 1.141 W/m$\cdot$K to 0.144 W/m$\cdot$K as increasing the porosity from 0\% to 72.22\% at 300 K, following the empirical coherent potential model when the pore is assumed to be filled with air. As increasing temperature, the thermal conductivity is observed to increase from 240 K to 560 K and gradually decrease until 1100 K for porous jennites with the porosities of 0\%, 15.99\% and 32.79\%.

Developing efficient anode materials with low electrode voltage, high specific capacity and superior rate capability is urgently required on the road to commercially viable sodium-ion batteries (SIBs). Aiming at finding a new SIB anode material, we investigate the electrochemical properties of NaxTiO2 compounds with unprecedented penta-oxygen-coordinated trigonal bipyramid (TB) structures by using the first-principles calculations. Identifying the four different TB phases, we perform the optimization of their crystal structures and calculate their energetics such as sodium binding energy, formation energy, electrode potential and activation energy for Na ion migration. The computations reveal that TB-I phase can be the best choice among the four TB phases for the SIB anode material due to relatively low volume change under 4% upon Na insertion, low electrode voltage under 1.0 V with a possibility of realizing the highest specific capacity of ~335 mAh/g from fully sodiation at x = 1, and reasonably low activation barriers under 0.35 eV at the Na content from x = 0.125 to x = 0.5. Through the analysis of electronic density of states and charge density difference upon sodiation, we find that the NaxTiO2 compounds in TB phases change from electron insulating to electron conducting material due to the electron transfer from Na atom to Ti ion, ordering the Ti 4+/Ti 3+ redox couple for SIB operation.

Molybdenum disulfide (MoS$_2$) attracts attention as a high efficient and low cost photocatalyst for hydrogen production, but suffers from low conductance and high recombination rate of photo-generated charge carriers. In this work, we investigate the MoS$_2$ heterostructures with graphene variants (GVs), including graphene, graphene oxide, and their boron- and nitrogen-doped variants, by using first-principles calculations. Systematic comparison between graphene and graphene oxide composites is performed, and contrary effect of B and N doping on interface function and hydrogen evolution is clarified. We find that upon the formation of the interfaces some amount of electronic charge transfers from the GV side to the MoS$_2$ layer, inducing the creation of interface dipole and the reduction of work function, which is more pronounced in the graphene oxide composites. Moreover, our results reveal that N doping enhances the interface functions by forming donor-type interface states, whereas B doping reduces those functions by forming acceptor-type interface states. However, the B-doped systems exhibit lower Gibbs free energy difference for hydrogen adsorption on GV side than the N-doped systems, which deserves much consideration in the design of new functional photocatalysts.

Linearized polynomials over finite fields have been intensively studied over the last several decades. Interesting new applications of linearized polynomials to coding theory and finite geometry have been also highlighted in recent years. Let $p$ be any prime. Recently, preimages of the $p-$linearized polynomials $\sum_{i=0}^{\frac kl-1} X^{p^{li}}$ and $\sum_{i=0}^{\frac kl-1} (-1)^i X^{p^{li}}$ were explicitly computed over $\GF{p^n}$ for any $n$. This paper extends that study to $p-$linearized polynomials over $\GF{p}$, i.e., polynomials of the shape $$L(X)=\sum_{i=0}^t \alpha_i X^{p^i}, \alpha_i\in\GF{p}.$$ Given a $k$ such that $L(X)$ divides $X-X^{p^k}$, the preimages of $L(X)$ can be explicitly computed over $\GF{p^n}$ for any $n$.

We investigate the post-bounce background dynamics in a certain class of single bounce scenarios studied in the literature, in which the cosmic bounce is driven by a scalar field with negative exponential potential such as the ekpyrotic potential. We show that those models can actually lead to cyclic evolutions with repeated bounces. These cyclic evolutions, however, do not account for the currently observed late-time accelerated expansion and hence are not cosmologically viable. In this respect we consider a new kind of cyclic model proposed recently and derive some cosmological constraints on this model., Comment: 26 pages, 15 figures. Significantly revised and accepted version for JHEP

Sodium-titanate \ce{Na2Ti3O7} (NTO) is regarded as a highly promising anode material with a very low voltage for Na-ion batteries and capacitors, but suffered from relatively low specific capacity and poor electron conductivity. Here we report a first-principles study of electrochemical properties of NTO and its vanadium-modified compounds, \ce{Na2Ti2VO7} and \ce{Na2TiV2O7} (NTVO), offering an insight into their detailed working mechanism and an evidence of enhancing anode performance by Ti/V cation exchange. Our calculations reveal that the specific capacity can increase from 177 mAh g$^{-1}$ in NTO to over 280 mAh g$^{-1}$ in NTVO when using \ce{NaTi_{3-$x$}V_{$x$}O7} ($x$ = 1, 2) as a starting material for Na insertion due to higher oxidation state of \ce{V^{+5}}, together with lower voltages and small volume expansion rates below 3\%. With Ti/V exchange, we obtain slightly higher activation energies for Na ion migrations along the two different pathways, but find an obvious improvement of electronic transport in NTVO.

In spite of intensive studies on the chalcogenides as conventional thermoelectrics, it remains a challenge to find a proper material with high electrical but low thermal conductivities. In this work, we introduced a new class of thermoelectrics, Ge-based inorganic halide perovskites \ce{CsGeX3} (X = I, Br, Cl), which were already known as a promising candidate for photovoltaic applications. By performing the lattice-dynamics calculations and solving the Boltzmann transport equation, we revealed that these perovskites have ultralow thermal conductivities below 0.18 W m$^{-1}$ K$^{-1}$ while very high carrier mobilities above 860 cm$^2$ V$^{-1}$ s$^{-1}$, being much superior to the conventional thermoelectrics of chalcogenides. These results highlight the way of searching high-performance and low-cost thermoelectrics based on inorganic halide perovskites.

The effect of moisture and porosity on thermal conductivity of tobermorite 14 \AA~as the major component of cement paste is studied by using molecular dynamics simulation with ClayFF potential. The calculated results show that the thermal conductivity increases monotonically as the moisture content by mass within the interior pores increases and the slope of the linear fitting function decreases as the porosity increases. Meanwhile, the normalized thermal conductivity is found to increase exponentially as increasing the moisture content by volume. Phonon density of states of porous and moist tobermorite 14 \AA~is used to explain the contribution of individual atoms and molecules to the thermal properties. The results can be potentially used to design higher thermal insulating materials with cement and concrete for energy saving buildings.

Let $l$ and $k$ be two integers such that $l|k$. Define $T_l^k(X):=X+X^{p^l}+\cdots+X^{p^{l(k/l-2)}}+X^{p^{l(k/l-1)}}$ and $S_l^k(X):=X-X^{p^l}+\cdots+(-1)^{(k/l-1)}X^{p^{l(k/l-1)}}$, where $p$ is any prime. This paper gives explicit representations of all solutions in $\GF{p^n}$ to the affine equations $T_l^{k}(X)=a$ and $S_l^{k}(X)=a$, $a\in \GF{p^n}$. For the case $p=2$ that was solved very recently in \cite{MKCL2019}, the result of this paper reveals another solution.

Enhancement of thermal performance of concrete wall is nowadays of great importance in reducing the operational energy demand of buildings. We developed a new kind of inorganic coating material based on \ce{SiO2}-\ce{Al2O3}-rich minerals and Portland cement (PC) powder. The finely pulverized mineral powder with the particle size distribution (PSD) of 0.4-40 $\mu$m was mixed with the vehicle solvent containing some agents, cement powder with PSD of 2-100 $\mu$m, and water in the certain weight ratio, producing the colloid solution. After application within 2 hours to the plaster layer of concrete wall and sufficient long hardening period of over three months, the coating layer of 0.6-1.0 mm thickness was observed to become a densified ceramic. Powder X-ray diffraction (XRD) experiments were performed to identify the crystalline components of minerals, cement and ceramic coating powders. Three- and two-dimensional surface morphologies and chemical compositions of coating material were obtained with the optical interferometer and scanning electron microscope (SEM) equipped with an energy dispersive X-ray analyzer (EDX). These XRD and SEM/EDX analyses demonstrated obviously that the coating layer is mainly composed of the calcium-silicate-hydrate (C-S-H) and the calcium-aluminate-hydrate (C-A-H) ceramics with the relatively small number of closed pores (10\% porosity) compared with the cement mortar and concrete layers. Two-step hydrations of cement and subsequently \ce{SiO2}-\ce{Al2O3} promoted by the alkali product \ce{Ca(OH)2} were proposed as the main mechanism of ceramic formation.

Calcium fluoride has been widely used for light up-/down-conversion luminescence by accommodating lanthanide ions as sensitizers or activators. Especially, Yb-doped \ce{CaF2} exhibits unique defect physics, causing various effects on the luminescence. This makes it vital for high efficiency of devices to control the defect-clustering, but theoretically principal guidelines for this are rarely provided. Here we perform the first-principles study on defect physics in Yb-doped \ce{CaF2} to reveal the thermodynamic transition levels and formation energies of possible defects. We suggest that the fluorine rich growth condition can play a key role in enhancing the luminescence efficiency by facilitating the Yb-clustering and suppressing the defect quenchers in bulk. Detailed energetics of defect aggregation not only well explains the experimentally favored Yb-clustering but also presents $n$- or $p$-type doping method for the cluster control.

Vacancy-ordered double perovskites K2SnX6 (X = I, Br, Cl) attract significant research interest due to their potential application as light-absorbing materials in perovskite solar cells. However, a deep insight into their material properties at the atomic scale is yet scarce. Here we present a systematic investigation on their structural, electronic, optical properties and phase stabilities in cubic, tetragonal, and monoclinic phases based on density functional theory calculations. Quantitatively reliable prediction of lattice constants, band gaps, effective masses of charge carriers, exciton binding energies is provided in comparison with the available experimental data, revealing the increasing tendency of band gap and exciton binding energy as lowering the crystallographic symmetry from cubic to monoclinic and going from I to Cl. We highlight that cubic K2SnBr6 and monoclinic K2SnI6 are suitable for the application as a light-absorber for solar cell devices due to their proper band gaps of 1.65 and 1.16 eV and low exciton binding energies of 59.4 and 15.3 meV, respectively. The constant-volume Helmholtz free energies are determined through phonon calculations, giving a prediction of their phase transition temperatures as 449, 433 and 281 K for cubic-tetragonal and 345, 301 and 210 K for tetragonal-monoclinic transitions for X = I, Br and Cl. Our calculations provide an understanding of material properties of vacancy-ordered double perovskite K2SnX6, helping to devise a low-cost and high performance perovskite solar cell.

Though it is well known that the roots of any affine polynomial over a finite field can be computed by a system of linear equations by using a normal base of the field, such solving approach appears to be difficult to apply when the field is fairly large. Thus, it may be of great interest to find an explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over a binary finite field. This paper gives an explicit representation of solutions for a much wider class of affine polynomials over a binary prime field.

We proposed an experimentally feasible scheme of nano-plamonic switch and quantum router via the single self-assembled InGaAs/GaAs semiconductor quantum dot (SQD) with a V type three-level energy structure located between two silver metallic waveguides. We studied theoretically transmission and transfer rates of single plasmons in such a multi-ports system via the real-space approach, where our results showed that single plasmons from the input port could be switchable and redirected by controlling parameters, such as the intensity of the classical field, the detunings, and the interaction between the SQD and the waveguides. Our proposed scheme could be used not only in the design of quantum routers and quantum switches for the construction of quantum network, but also in quantum photonic integrated circuits.

The cointercalation of sodium with the solvent organic molecule into graphite can resolve difficulty of forming the stage-I Na-graphite intercalation compound, which is a predominant anode of Na-ion battery. To clarify the mechanism of such cointercalation, we investigate the atomistic structure, energetics, electrochemical properties, ion and electron conductance, and charge transferring upon de/intercalation of the solvated Na-diglyme ion into graphite with {\it ab initio} calculations. It is found that the Na(digl)$_2$C$_n$ compound has the negatively lowest intercalation energy at $n\approx$21, the solvated Na(digl)$_2$ ion diffuses fast in the interlayer space, and their electronic conductance can be enhanced compared to graphite. The calculations reveal that the diglyme molecules as well as Na atom donates electrons to the graphene layer, resulting in the formation of ionic bonding between the graphene layer and the moiety of diglyme molecule. This work will contribute to the development of innovative anode materials for alkali-ion battery applications.

In this paper, we propose a new fuzzy reasoning principle, so called Movement and Transformation Principle(MTP). This Principle is to obtain a new fuzzy reasoning result by Movement and Transformation the consequent fuzzy set in response to the Movement, Transformation, and Movement-Transformation operations between the antecedent fuzzy set and fuzzificated observation information. And then we presented fuzzy modus ponens and fuzzy modus tollens based on MTP. We compare proposed method with Mamdani fuzzy system, Sugeno fuzzy system, Wang distance type fuzzy reasoning method and Hellendoorn functional type method. And then we applied to the learning experiments of the fuzzy neural network based on MTP and compared it with the Sugeno method. Through prediction experiments of fuzzy neural network on the precipitation data and security situation data, learning accuracy and time performance are clearly improved. Consequently we show that our method based on MTP is computationally simple and does not involve nonlinear operations, so it is easy to handle mathematically.

Among the recent achievements of sodium-ion battery (SIB) electrode materials, hybridization of two-dimentional (2D) materials is one of the most interesting appointments. In this work, we propose to use the 2D hybrid composites of SnS2 with graphene or graphene oxide (GO) layers as SIB anode, based on the first-principles calculations of their atomic structures, sodium intercalation energetics and electronic properties. The calculations reveal that graphene or GO film can effectively support not only the stable formation of hetero-interface with the SnS2 layer but also the easy intercalation of sodium atom with low migration energy and acceptable low volume change. The electronic charge density differences and the local density of state indicate that the electrons are transferred from the graphene or GO layer to the SnS2 layer, facilitating the formation of hetero-interface and improving the electronic conductance of the semiconducting SnS2 layer. These 2D hybrid composites of SnS2/G or GO are concluded to be more promising candidates for SIB anodes compared with the individual monolayers.

We study the thermoelectric transport through a single-level quantum dot (QD) coupled to two normal metallic leads and side-coupled to Majorana bound state (MBS). The Coulomb interaction in QD is considered. To investigate only the influence of MBS on thermoelectric transport, we focus on the relatively high temperature region ($T\gg T_K$), where Kondo effect does not appear. The electric and thermal conductance and thermopower as a function of gate voltage (i.e. QD level) are completely different whether the coupling between MBSs is zero or not. When the coupling between MBSs is finite, all thermoelectric characteristics are similar to the transport without MBS. However, for zero MBSs' coupling, the electric and thermal conductance peaks are reduced by 3/4. Especially, in the case of QD without MBS, the sign of thermopower changes three times, however, in the case of QD strongly side-coupled to ideal and isolated MBS, the sign of thermopower changes 9 or 5 times. It can be used for detecting of the signature of MBS. It has actual possibilities when the nanowire is long enough and pure without any defects., Comment: 9 pages, 7 figures, accepted to be published in Eur. Phys. J. B

We predict the structural, electronic and optic properties of the inorganic Ge-based halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl) by using first-principles method. In particular, absolute electronic energy band levels are calculated using two different surface terminations of each compound, reproducing the experimental band alignment.

Firstly in this paper we propose a new criterion function for evaluation of the reductive property about the fuzzy reasoning result for fuzzy modus ponens and fuzzy modus tollens. Secondly unlike fuzzy reasoning methods based on the similarity measure, we propose a new fuzzy reasoning method based on distance measure. Thirdly the reductive property for 5 fuzzy reasoning methods are checked with respect to fuzzy modus ponens and fuzzy modus tollens. Through the experiment, we show that proposed method is better than the previous methods in accordance with human thinking.

In this paper we calculate ab initially the phonon dispersion relationship of the superconductor LaFeAsO and investigate a main property in the superconductor, the oxygen isotope effect. Based on this phonon dispersion relationship, we find the fact that an important reason of the oxygen isotope effect is connected with the phonon. This result agrees well with the experimental data where the power index of the oxygen isotope effect in the superconductor LaFeAsO is small., Comment: 10 pages, 2 figures, accepted to be published in Int. J. Mod. Phys. B

Inorganic halide perovskite \ce{Cs(Rb)PbI3} has attracted significant research interest in the application of light-absorbing material of perovskite solar cells (PSCs). Although there have been extensive studies on structural and electronic properties of inorganic halide perovskites, the investigation on their thermodynamic stability is lack. Thus, we investigate the effect of substituting Rb for Cs in \ce{CsPbI3} on the chemical decomposition and thermodynamic stability using first-principles thermodynamics. By calculating the formation energies of solid solutions \ce{Cs$_{1-x}$Rb$_x$PbI3} from their ingredients \ce{Cs$_{1-x}$Rb$_x$I} and \ce{PbI2}, we find that the best match between efficiency and stability can be achieved at the Rb content $x\approx$ 0.7. The calculated Helmholtz free energy of solid solutions indicates that \ce{Cs$_{1-x}$Rb$_x$PbI3} has a good thermodynamic stability at room temperature due to a good miscibility of \ce{CsPbI3} and \ce{RbPbI3}. Through lattice-dynamics calculations, we further highlight that \ce{RbPbI3} never stabilize in cubic phase at any temperature and pressure due to the chemical decomposition into its ingredients \ce{RbI} and \ce{PbI2}, while \ce{CsPbI3} can be stabilized in the cubic phase at the temperature range of 0$-$600 K and the pressure range of 0$-$4 GPa. Our work reasonably explains the experimental observations, and paves the way for understanding material stability of the inorganic halide perovskites and designing efficient inorganic halide PSCs.

The mechanism of superstability of nanobubbles in liquid confirmed by many experimental studies is still in debate since the classical diffusion predicts their lifetime on the order of a few microseconds. In this work, we study the requirement for bulk nanobubbles to be stable by using molecular dynamics simulations. Periodic cubic cells with different cell sizes and different initial radii are treated to simulate the nanobubble cluster, providing the equilibrium bubble radius and the interbubble distance. We find out that for nanobubble with a certain radius $R$ to be stable, the interbubble distance should be smaller than the maximum interbubble distance $L^*$ being proportional to $R^{4/3}$.

Recently, replacing or mixing organic molecules in the hybrid halide perovskites with the inorganic Cs or Rb cations has been reported to increase the material stability with the comparable solar cell performance. In this work, we systematically investigate the electronic and optical properties of all-inorganic alkali iodide perovskites Rb1-xCsxPbI3 using the first-principles virtual crystal approximation calculations. Our calculations show that as increasing the Cs content x, lattice constants, band gaps, exciton binding energies, and effective masses of charge carriers decrease following the quadratic (linear for effective masses) functions, while static dielectric constants increase following the quadratic function, indicating an enhancement of solar cell performance upon the Rb addition to CsPbI3. When including the many-body interaction within the GW approximation and incorporating the spin-orbit coupling (SOC), we obtain more reliable band gap compared with experiment for CsPbI3, highlighting the importance of using GW+SOC approach for the all-inorganic as well as organic-inorganic hybrid halide perovskite materials.

This paper reports the analytical method for gamma-amino butyric acid in the germinated brown rice by liquid chromatography. GABA was derivatized by pre-column derivatization with 2, 4-dinitrofluorobenzene. To separate GABA in the germinated brown rice extracts containing various amino acids, we reviewed the influence of the kind of separation columns and the gradient of mobile phase of ultra performance liquid chromatography. GABA was extracted with distilled water from the germinated brown rice with the optimum extraction time of 12 h. To validate this method the precision and the recovery were discussed. In the concentration range from 5 to 50 microgram per mililiter, the calibration curve for GABA was linear and the regression equation was obtained with correlation coefficient of 0.999. GABA was analyzed by amino acid analyzer in comparison with this method and the results of F-test and t-test indicated that there were no significant differences in accuracy and precision between two methods.

Discovering new electrodes for sodium-ion battery requires clear understanding of the material process during battery operation. Using first-principles calculations, we identify mechanisms of ionic diffusion and electronic transfer in newly developed cathode material, eldfellite Na$_x$Fe(SO$_4$)$_2$, reproducing the electrochemical properties in good agreement with experiment. The inserted sodium atom is suggested to diffuse along the two-dimensional pathway with preceding movement of the host sodium atom, and the activation energy is calculated to be reasonable for fast insertion. We calculate the electronic properties, showing the band insulating at low composition of inserted sodium, for which the electron polaron formation and hoping are also suggested. Our results may contribute to opening a new way of developing innovative cathode materials based on iron and sulfate ion.

Using density functional theory calculations, we have investigated the interlayer cation exchange phenomena in muscovite mica, which is motivated by a necessity to develop flexible high-insulating covering materials. The crystalline structures, chemical bonding properties, energetics, and electronic properties of muscovites before and after exchange of interlayer K$^+$ cation with ammonium (NH$_4^+$) or methylammonium (CH$_3$NH$_3^+$) ion were calculated. It was found that the unit cell volume changes are negligibly small upon exchange with NH$_4^+$ ion, while the unit cells are expanded with about 4 \% relative rate when replacing the interlayer K$^+$ cation with CH$_3$NH$_3^+$ ion. The energy band gap of pre-exchanged muscovite was calculated to be about 5 eV, which hardly changes upon interlayer cation exchange with either NH$_4^+$ or CH$_3$NH$_3^+$ ion, indicating the preservation of high insulating property of muscovite. The exchange energies were found to be about -100 kJ/mol for NH$_4^+$ and about -50 kJ/mol for CH$_3$NH$_3^+$ exchange, indicating that the exchange reactions are exothermic. A detailed analysis of atomic resolved density of states and electron density redistribution was provided.

This paper describes the algorithm for translating English negative sentences into Korean in English-Korean Machine Translation (EKMT). The proposed algorithm is based on the comparative study of English and Korean negative sentences. The earlier translation software cannot translate English negative sentences into accurate Korean equivalents. We established a new algorithm for the negative sentence translation and evaluated it., Comment: 9 pages, 1 figure, 2 tables

We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase space using statistical methodology. The adopted perspective leads to obtaining within the framework of its theory the master quantum-mechanical equation without recourse to the other formalisms of quantum mechanics, and gives the idea of operators pertaining to dynamical quantities. The derivation of this equation starts with the ensemble in phase space. We have explained with the help of this equation the structure of quantum mechanics in phase space and the approximation to the Schrodinger equation. Furthermore, we have shown that this formalism provides reasonable results of quantization by dealing with some simple cases, which confirm the validity of this formalism. In particular, we have demonstrated that this formalism can easily give the relativistic wave equation without treating the problem of linearizing the Hamiltonian operator by making the most of the point that the master equation is a first-order partial differential equation with respect to time, position and momentum variables, and makes use of the phase velocity. The ultimate outcome this formalism produces is that primary and general matters of quantum mechanics can be studied reasonably within the framework of statistical mechanics., Comment: 19 pages

We present an alternative one-electron equation for resolving many-electron problem to one-electron approximation and including the exchange and correlation effects in an analytical way, thereby fulfilling the requirements for ab initio calculation. To derive one-electron equation, we accept a new notion of equivalent function suggestive of the pseudo wavefunction. As a result, we reduce many-electron equation to one-electron including the exchange effect in an analytical method. Moreover we accept the notion of phase norm for two electrons to resolve the electronic correlation problem. The phase norm is used to specify the electron-approachable limit between particles. We take into consideration the electronic correlation with the help of a correlation-hole function in terms of the phase norm, by which multiplying the integrand of the operator term representing the interaction between electrons. Using the phase norm leads to analytical consideration of the electronic correlation without employing in a factitious way the additional term pertaining to correlation, so it embodies the physical essence of electronic correlation. The derived equation becomes an one-electron equation which does not include an additional term pertaining to the exchange and correlation, but takes into consideration the exchange and correlation effects in a rigorous ab initio way., Comment: 12 pages

Natural abundance of sodium and its similar behavior to lithium triggered recent extensive studies of cost-effective sodium-ion batteries (SIBs) for large-scale energy storage systems. A challenge is to develop electrode materials with a high electrode potential, specific capacity and a good rate capability. In this work we propose mixed eldfellite compounds \ce{Na_x(Fe_{1/2}M_{1/2})(SO4)2} (M = Mn, Co, Ni) as a new family of high electrode potential cathodes of SIBs and present their material properties predicted by first-principles calculations. The structural optimizations show that these materials have significantly small volume expansion rates below 5\% upon Na insertion/desertion with negative Na binding energies. Through the electronic structure calculations, we find band insulating properties and hole (and/or electron) polaron hoping as a possible mechanism for the charge transfer. Especially we confirm the high electrode voltages over 4 V with reasonably high specific capacities. We also investigate the sodium ion mobility by estimating plausible diffusion pathways and calculating the corresponding activation barriers, demonstrating the reasonably fast migrations of sodium ions during the operation. Our calculation results indicate that these mixed eldfellite compounds can be suitable materials for high performance SIB cathodes.

The chemical stability of methylammonium lead iodide (\ce{MAPbI3}) under humid conditions remains the primary challenge facing halide perovskite solar cells. We investigate defect processes in the water-intercalated iodide perovskite (\ce{MAPbI3}\_\ce{H2O}) and monohydrated phase (\ce{MAPbI3}$\cdot$\ce{H2O}) within a first-principles thermodynamic framework. We consider the formation energies of isolated and aggregated vacancy defects with different charge states under I-rich and I-poor conditions. It is found that a \ce{PbI2} (partial Schottky) vacancy complex can be formed readily, while the \ce{MAI} vacancy complex is difficult to form in the hydrous compounds. Vacancies in the hydrous phases create deep charge transition levels, indicating the degradation of halide perovskite upon exposure to moisture. Electronic structure analysis supports a novel mechanism of water-mediated vacancy-pair formation.