An integer-valued multiplicative function
f
is said to be polynomially-defined if there is a nonconstant separable polynomial
F
(
T
)
∈
Z
T
with
f
(
p
)
=
F
(
p
)
for all primes
p
. We study the ...distribution in coprime residue classes of polynomially-defined multiplicative functions, establishing equidistribution results allowing a wide range of uniformity in the modulus
q
. For example, we show that the values
ϕ
(
n
)
, sampled over integers
n
≤
x
with
ϕ
(
n
)
coprime to
q
, are asymptotically equidistributed among the coprime classes modulo
q
, uniformly for moduli
q
coprime to 6 that are bounded by a fixed power of
log
x
.
Abstract
Our study suggested a new distribution through the use of the cum. dis. function for the exp. dis., as well as the cum. dis. function for the uni. dis. in addition to the quantitative ...function of the unified generalization using the quantitative function. Therefore it is covered different mathematical and statistical properties .of this distribution.
Uncontrolled Li plating in graphite electrodes endangers battery life and safety, driving tremendous efforts aiming to eliminate Li plating. Herein we systematically investigate the boundary of Li ...plating in graphite electrode for safe lithium‐ion batteries. The cell exhibits superior safety performance than that with Li dendrites by defining the endurable amount of uniform Li plating in graphite anode. The presence of “dead Li” can be eliminated owing to the uniform distribution of Li plating, and the average Coulombic efficiency for deposited Li during reversible plating/stripping process is decoupled as high as about 99.5 %. Attributing to the limited Li plating with superior Coulombic efficiency, the LiNi0.5Mn0.3Co0.2O2 | graphite cell achieves a high capacity retention of 80.2 % over 500 cycles. This work sheds a different light on further improving the fast‐charging capability, low‐temperature performance, and energy density of practical lithium‐ion batteries.
The boundary of Li plating in a graphite electrode for safe lithium‐ion batteries is defined. The cell with regulated Li plating exhibits highly reversible Li plating/stripping Coulombic efficiency >99.5 % with superior safety performance, offering a strategy to achieve safe high‐energy fast‐charging lithium‐ion batteries.
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•The homogeneous Ru0.5Ir0.5 alloy was fabricated by a facile reduction method.•Ru0.5Ir0.5||Ru0.5Ir0.5 shows outstanding electrocatalytic activity and stability.•The leaching of Ru ...produces protective skeleton to prevent its further dissolution.•The origin of excellent catalytic activity and stability of the alloy was proposed.
Developing bifunctional electrocatalysts with high activity and long-term stability over the whole pH range is still a great challenge. Herein, the unsupported RuIr alloys are reported as robust electrocatalysts for pH-universal overall water splitting. The as-synthesized Ru0.5Ir0.5 alloy exhibits unexpected low overpotentials of 4, 28, 16 mV for hydrogen evolution reaction (HER) and 160, 176, 248 mV for oxygen evolution reaction (OER) at 10 mA cm−2 in 0.5 M H2SO4, 1.0 M KOH and 1.0 M PBS solutions, respectively. Especially, the Ru0.5Ir0.5||Ru0.5Ir0.5 cell only needs voltages of 1.44, 1.48 and 1.51 V in the three environments to reach the same current density for overall water splitting and can continuously operate for more than 400, 100 and 100 h. Comprehensive studies verify that the excellent electrocatalytic performance of Ru0.5Ir0.5 originates from the uniform arrangement of Ru and Ir atoms in the alloy, which leads to the leaching of an appropriate amount of Ru atoms and thus produces a protective skeleton composed of high valence Ir (IV) to prevent further dissolution of Ru. In addition, the weak coupling between Ru and Ir makes electron transfer from Ir to adjacent Ru as active sites, resulting in optimal adsorption strength for key intermediates.
•A novel class of functionally graded GPL/polymer composite beam is proposed.•Nonlinear free vibration of functionally graded GPL/polymer beam is studied.•Larger sized GPLs with fewer layers have ...better reinforcing effects.•Placing more GPLs near sides of the beam is preferred to increase stiffness.
This paper studies the nonlinear free vibration of a multi-layer polymer nanocomposite beam reinforced by graphene platelets (GPLs) non-uniformly distributed along the thickness direction. Theoretical formulations are based on Hamilton’s principle, Timoshenko beam theory, and von Kármán nonlinear strain-displacement relationship. The effective Young’s modulus of the GPL/polymer composites is estimated by Halpin-Tsai micromechanics model to account for the effects of GPL geometry and dimensions. The vibration frequencies and amplitude of the beam are obtained numerically by employing Ritz method. The influences of the distribution pattern, weight fraction, geometry and size of GPL nanofillers, the total number of layers together with the vibration amplitude and boundary conditions on the nonlinear free vibration behavior are investigated. The results show that adding a very small amount of GPLs into polymer matrix as reinforcements significantly increases the natural frequencies of the beam. Using larger sized GPLs with fewer single graphene layers and placing more GPLs near the top and bottom surfaces of the beam are the most effective ways to strengthen the beam stiffness and increase the linear and nonlinear natural frequencies.
Controllable synthesis of atomically ordered intermetallic nanoparticles (NPs) is crucial to obtain superior electrocatalytic performance for fuel cell reactions, but still remains arduous. Herein, ...we demonstrate a novel and general hydrogel‐freeze drying strategy for the synthesis of reduced graphene oxide (rGO) supported Pt3M (M=Mn, Cr, Fe, Co, etc.) intermetallic NPs (Pt3M/rGO‐HF) with ultrasmall particle size (about 3 nm) and dramatic monodispersity. The formation of hydrogel prevents the aggregation of graphene oxide and significantly promotes their excellent dispersion, while a freeze‐drying can retain the hydrogel derived three‐dimensionally (3D) porous structure and immobilize the metal precursors with defined atomic ratio on GO support during solvent sublimation, which is not afforded by traditional oven drying. The subsequent annealing process produces rGO supported ultrasmall ordered Pt3M intermetallic NPs (≈3 nm) due to confinement effect of 3D porous structure. Such Pt3M intermetallic NPs exhibit the smallest particle size among the reported ordered Pt‐based intermetallic catalysts. A detailed study of the synthesis of ordered intermetallic Pt3Mn/rGO catalyst is provided as an example of a generally applicable method. This study provides an economical and scalable route for the controlled synthesis of Pt‐based intermetallic catalysts, which can pave a way for the commercialization of fuel cell technologies.
A novel and general strategy for the synthesis of reduced graphene oxide (rGO) supported atomically ordered Pt3M (M=Mn, Cr, Fe, Co, etc.) intermetallic nanoparticles is reported under the aid of freeze‐drying technology. This synthetic strategy is demonstrated to be effective for the preparation and handling of nanoparticles with controlled particle size and ordered phase.
The tax gap can be considered as the criterion and principle of the effectiveness and efficiency of the tax system. Inadequate collection of taxes as well as non-realization of tax revenues is called ...tax gap, which is one of the factors that aggravate the budget deficit. In this paper, the issue of tax gap is investigated with two approaches. The first approach is a situation where two groups of investigators who are willing and unwilling to collude with two groups of taxpayers who are willing and unwilling to collude with a uniform distribution are placed in the game. The second approach also shows a situation where the probability of not discovering a taxpayer's violation is shown by a mathematical function and the quality of investigating groups for taxpayers who are uniformly distributed is unknown. The results of the first approach show that with the increase in the number of taxpayers unwilling to collude and the increase in the number of groups willing to collude with taxpayers, the tax gap decreases. Also, with the reduction of the tax rate and the increase in the number of groups unwilling to collude, the tax gap increases. The results of the second approach show that the tax gap increases with the increase in the number of investigators and also the increase in the probability of dishonesty of the taxpayer.
In this paper, a downlink single-cell non-orthogonal multiple access (NOMA) network with uniformly deployed users is considered and an analytical framework to evaluate its performance is developed. ...Particularly, the performance of NOMA is studied by assuming two types of partial channel state information (CSI). For the first one, which is based on imperfect CSI , we present a simple closed-form approximation for the outage probability and the average sum rate, as well as their high signal-to-noise ratio (SNR) expressions. For the second type of CSI, which is based on second order statistics (SOS) , we derive a closed-form expression for the outage probability and an approximate expression for the average sum rate for the special case two users. For the addressed scenario with the two types of partial CSI, the results demonstrate that NOMA can achieve superior performance compared to the traditional orthogonal multiple access (OMA). Moreover, SOS-based NOMA always achieves better performance than that with imperfect CSI, while it can achieve similar performance to the NOMA with perfect CSI at the low SNR region. The provided numerical results confirm that the derived expressions for the outage probability and the average sum rate match well with the Monte Carlo simulations.
•A new model was proposed to predict hydrate deposition in gas-dominated systems with free water.•Hydrates formed in liquid film and liquid droplets were both considered in the model.•The effective ...deposition ratio was introduced to estimate the deposition of hydrate particles.•The accuracy of the model was verified by literature experimental data.•The most vulnerable position of hydrate deposition can be analyzed by the model.
Hydrate deposition is an important issue for flow assurance in subsea pipelines. Current models for hydrate deposition in gas-dominated systems with free water mainly consider hydrate formation in liquid films on pipe walls. However, hydrate particles formed from water droplets in the gas phase may also play a significant role in hydrate deposition. In this work, a new model for predicting hydrate deposition is proposed. This model considers hydrate formation from both liquid film and liquid droplets. In the model, an effective deposition ratio is introduced to calculate the deposition of hydrate particles from the gas phase by considering the influence of liquid film atomization. The simulation results agree well with the experimental data. It is indicated that the deposition of hydrate particles formed by liquid droplets in the gas phase has a significant influence on the reduction of the flow passage in the pipeline. By using the new model, the non-uniform distribution of the flow passage at different times and locations can be obtained, and the most vulnerable position for hydrate deposition can be predicted. The model predicts the risk of hydrate deposition more reliably than current methods and provides helpful advice for the prevention of hydrate deposition in the field.
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