Pseudo Almost Periodic Functions And Their Applications

The space of pseudo almost periodic functions on {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}{dollar} (denoted by {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} when they are vector-valued and {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}){dollar} when they are scalar-valued, {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\lbrack a,\infty){dollar} for {dollar}a\in\IR{dollar} and {dollar}{lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}=\IR{dollar} for {dollar}a={lcub}-\infty{rcub}{dollar}, X is a Banach space) is defined and its properties are studied. A decomposition theorem is given showing that a function is in {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} if and only if it is the sum of an almost periodic function and an ergodic perturbation. The relation between a pseudo almost periodic function and its almost periodic component is discussed. It is shown that {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar} is a Banach space, and in the case of scalar-valued functions, is a {dollar}C\sp*{dollar}-algebra. Fourier analysis is carried out on {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar}.;As applications of the general theory of {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub}){dollar}, the solutions for three types of differential equations--ordinary, nonlinear parabolic and boundary value problems for harmonic functions--are investigated.;A necessary and sufficient condition is given for the pseudo almost periodicity of the primitive of a function in {dollar}{lcub}\cal PAP{rcub}({lcub}\rm J\!I{rcub}\sb{lcub}a{rcub},X){dollar}. As a corollary of this, an open question is answered: a necessary and sufficient condition is given for the weak almost periodicity of the primitive of a weakly almost periodic function.;The theory of vector-valued means is developed. A formula is set up between a vector-valued mean and a scalar-valued mean. As an application of the theory of vector-valued means, a theorem is given to show that the space of vector-valued weakly almost periodic functions is admissible

Existence of Almost Periodic Solutions for Impulsive Neutral Functional Differential Equations

The existence of piecewise almost periodic solutions for impulsive neutral functional differential equations in Banach space is investigated. Our results are based on Krasnoselskii’s fixed-point theorem combined with an exponentially stable strongly continuous operator semigroup. An example is given to illustrate the theory

Evaluation of WIC Online Ordering During the COVID-19 Pandemic: Evidence From an Oklahoma Grocery Store Chain

The COVID-19 pandemic is worsening the disparities in food access in the United States. As consumers have been increasingly using grocery online ordering services to limit their exposure to the COVID-19 virus, participants of federal nutrition assistance programs lack the online benefit redemption option. With the support of the US Department of Agriculture (USDA), retailers are pilot-testing online food benefit ordering in the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC). By combining the Oklahoma WIC administrative data, the online ordering data from a grocery store chain in Oklahoma, and the COVID-19 data in Oklahoma, this study examines how WIC participants responded to the online food benefit ordering option and how their adoption of online ordering was associated with the COVID-19 incidence. Results show that from July to December 2020, 15,171 WIC households redeemed WIC benefits at an Oklahoma chain store, but only 819 of them adopted online ordering. They together completed 102,227 online orders, which accounted for 2.7% of the store visits and 2.6% of the monetary value of WIC redemptions at these stores. There was no significant relationship between WIC online ordering adoption and COVID-19 incidence in Oklahoma

Vector-valued means and weakly almost periodic functions

A formula is set up between vector-valued mean and scalar-valued means that enables us translate many important results about scalar-valued means developed in [1] to vector-valued means. As applications of the theory of vector-valued means, we show that the definitions of a mean in [2] and [3] are equivalent and the space of vector-valued weakly almost periodic functions is admissible

Carbon Monoxide Oxidation Promoted by Surface Polarization Charges in a CuO/Ag Hybrid Catalyst.

Composite structures have been widely utilized to improve material performance. Here we report a semiconductor-metal hybrid structure (CuO/Ag) for CO oxidation that possesses very promising activity. Our first-principles calculations demonstrate that the significant improvement in this system's catalytic performance mainly comes from the polarized charge injection that results from the Schottky barrier formed at the CuO/Ag interface due to the work function differential there. Moreover, we propose a synergistic mechanism underlying the recovery process of this catalyst, which could significantly promote the recovery of oxygen vacancy created via the M-vK mechanism. These findings provide a new strategy for designing high performance heterogeneous catalysts

Association Between Usage of an App to Redeem Prescribed Food Benefits and Redemption Behaviors Among the Special Supplemental Nutrition Program for Women, Infants, and Children Participants: Cross-Sectional Study

BACKGROUND: The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) is one of the most important food assistance programs in the United States, serving 6.4 million low-income, eligible women, infants, and children under 5 years of age in 2019. In the program, participants are prescribed a list of food benefits, which can be redeemed in WIC-authorized stores. However, there are multiple behavioral barriers in the program and the stores that prevent participants from redeeming the benefits fully. OBJECTIVE: This study aims to examine the relationship between the use of a widely used mobile phone app, WICShopper, and the redemption of the prescribed food packages. METHODS: WIC administrative data were obtained from West Virginia for the period January 2019 to January 2020 and included 30,440 WIC households that had received food benefits in that period. The redemption rates of 18 WIC food benefits were compared between app users and nonapp users, that is, those who never used the app in the study period. The use behaviors were defined for the app users, including the number of active use benefit cycles, active benefit cycle rates, number of active use days in the cycle, and proportion rates of daytime use. Panel linear regressions were applied to examine how the redemption rates were related to these behaviors over time. RESULTS: App users consistently had higher average redemption rates than nonapp users; the difference ranged from 3.6% (4.8% relative) for infant formula to 14.3% (40.7% relative) for fish. After controlling for sociodemographics, the coefficients of app use were significantly positive for all benefit categories except for WIC-eligible nutritionals. More active cycles and active days in the cycle were significantly related to redemption rates for all categories, except for frozen juice (coefficient=-0.002, P=.09). Daytime app access was positively associated with redemption rates for most food benefits except only a few, such as infant formula (coefficient=-0.03, P\u3c.001). CONCLUSIONS: Use of the WIC app was significantly related to higher redemption rates across food benefits, although the association varied across benefit categories. More active days were positively related to benefit redemptions across food categories, and the app\u27s daytime use was positively associated with the redemption of most benefit categories. These findings suggest that the WIC app can be an important tool for the promotion of benefit redemption among WIC participants

The Online Ordering Behaviors among Participants in the Oklahoma Women, Infants, and Children Program: A Cross-Sectional Analysis

The Special Supplemental Nutrition Program for Women, Infants, and Children (WIC) is a nutrition assistance program in the United States (U.S.). Participants in the program redeem their prescribed food benefits in WIC-authorized grocery stores. Online ordering is an innovative method being pilot-tested in some stores to facilitate WIC participants\u27 food benefit redemption, which has become especially important in the COVID-19 pandemic. The present research aimed to examine the online ordering (OO) behaviors among 726 WIC households who adopted WIC OO in a grocery chain, XYZ (anonymous) store, in Oklahoma (OK). These households represented approximately 5% of WIC households who redeemed WIC benefits in XYZ stores during the study period, which was 1 July to 31 December 2020. This period was during the COVID-19 pandemic but after the temporary lockdown in Oklahoma had been lifted. Descriptive statistics were estimated for WIC OO households\u27 adoption behaviors and their orders. The Cox proportional hazard model and zero-truncated negative binomial regression were applied to examine the relationship between participants\u27 socio-demographics and the length of time between 1 July 2020, and their first OO, as well as the number of WIC online orders. About 80% of these online orders were picked up without any changes. Minority households had a significantly longer time before adopting their first OO (hazard ratio (HR) \u3c 1, p \u3c 0.001), while households with a child or a woman participant, or more participants, had a shorter time before adopting OO (HR \u3e 1, p \u3c 0.05). Non-Hispanic black households had a fewer number of OOs than non-Hispanic white households (B = -0.374, p = 0.007). OO adoption varied across socio-demographics. More efforts are needed to ensure equal access and adoption of WIC OO

Occurrence Rates and Heating Effects of Tangential and Rotational Discontinuities as Obtained from Three-dimensional Simulation of Magnetohydrodynamic Turbulence

In solar wind, magnetohydrodynamic (MHD) discontinuities are ubiquitous and often found to be at the origin of turbulence intermittency. They may also play a key role in the turbulence dissipation and heating of the solar wind. The tangential (TD) and rotational (RD) discontinuities are the two most important types of discontinuities. Recently, the connection between turbulence intermittency and proton thermodynamics has been being investigated observationally. Here we present numerical results from three-dimensional MHD simulation with pressure anisotropy and define new methods to identify and to distinguish TDs and RDs. Three statistical results obtained about the relative occurrence rates and heating effects are highlighted: (1) RDs tend to take up the majority of the discontinuities along with time; (2) the thermal states embedding TDs tend to be associated with extreme plasma parameters or instabilities, while RDs do not; (3) TDs have a higher average T as well as perpendicular temperature $T_\perp$. The simulation shows that TDs and RDs evolve and contribute to solar wind heating differently. These results will inspire our understanding of the mechanisms that generate discontinuities and cause plasma heating.Comment: 5 Figures, Submitted to Astrophys. J. Lett., in the process of refereein

Formation of Rotational Discontinuities in Compressive three-dimensional MHD Turbulence

Measurements of solar wind turbulence reveal the ubiquity of discontinuities. In this study, we investigate how the discontinuities, especially rotational discontinuities (RDs), are formed in magnetohydrodynamic (MHD) turbulence. In a simulation of the decaying compressive three-dimensional (3-D) MHD turbulence with an imposed uniform background magnetic field, we detect RDs with sharp field rotations and little variations of magnetic field intensity as well as mass density. At the same time, in the de Hoffman-Teller (HT) frame, the plasma velocity is nearly in agreement with the Alfv\'{e}n speed, and is field-aligned on both sides of the discontinuity. We take one of the identified RDs to analyze in details its 3-D structure and temporal evolution. By checking the magnetic field and plasma parameters, we find that the identified RD evolves from the steepening of the Alfv\'{e}n wave with moderate amplitude, and that steepening is caused by the nonuniformity of the Alfv\'{e}n speed in the ambient turbulence.Comment: Five figures enclosed. Submitted to Astrophys. J., Under referrin

On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument

The spectrum containment of almost periodic solution of second-order neutral delay differential equations with piecewise constant of argument (EPCA, for short) of the form (x(t)+px(t-1))′′=qx(2[(t+1)/2])+f(t) is considered. The main result obtained in this paper is different from that given by some authors for ordinary differential equations (ODE, for short) and clearly shows the differences between ODE and EPCA. Moreover, it is also different from that given for equation (x(t)+px(t-1))′′=qx([t])+f(t) because of the difference between [t] and 2[(t+1)/2]