Continuous Distribution Research Articles

Experimental Study on Calcination of Portland Cement Clinker Using Different Contents of Stainless Steel Slag

In order to increase the utilization rate of stainless steel slag, reduce storage needs, and mitigate environmental impacts, this study replaces a portion of limestone with varying amounts of stainless steel slag in the calcination of Portland cement clinker. The study primarily examines the influence of stainless steel slag on the phase composition, microstructure, compressive strength, and free calcium oxide (ƒ-CaO) content of Portland cement clinker. The results show the following: (1) Using stainless steel slag to calcine Portland cement clinker can lower the calcination temperature, reducing industrial production costs and energy consumption. (2) With an increase in the amount of stainless steel slag, the dicalcium silicate (C2S) and tricalcium silicate (C3S) phases in Portland cement clinker initially increase and then decrease; the C3S crystals gradually transform into continuous hexagonal plate-shaped distributions, while the tricalcium aluminate (C3A) and tetracalcium aluminoferrite (C4AF) crystal structures become denser. When the stainless steel slag content is 15%, the dicalcium silicate and tricalcium silicate phases are at their peak; the C3S crystals are continuously distributed with a relatively dense structure, and C3A and C4AF crystals melt and sinter together, becoming distributed around C3S. (3) As stainless steel slag content increases, the compressive strength of Portland cement clinker at 3 days, 7 days, and 28 days increases and then decreases, while ƒ-CaO content decreases and then increases. When the stainless steel slag content is 15%, the compressive strength at 28 days is at its highest, 64.4 MPa, with the lowest ƒ-CaO content, 0.78%. The test results provide a basis for the utilization of stainless steel slag in the calcination of Portland cement clinker.

Low-complexity continuous-variable quantum key distribution with true local oscillator using pilot-assisted frequency locking

In the domain of continuous variable quantum key distribution (CV-QKD), a significant challenge arises in achieving precise frequency synchronization, an issue commonly termed as frequency locking. This involves matching the optical frequencies of both the quantum signal laser and the local oscillator laser for accurate symbol demodulation during the exchange of quantum keys. As such, implementations today still grapple with maintaining precise synchronization between sender and receiver frequencies, occasionally hindering the efficiency and reliability of the information exchange. Addressing this challenge, we present and empirically validate a novel approach to CV-QKD by incorporating a pilot tone-assisted frequency locking algorithm to enhance stability when using a locally generated local oscillator (LLO) at the receiver. The proposed design leverages software-based optimization techniques, thereby eliminating the need for high-speed electronic stabilization devices and achieving efficient performance at typical repetition rates. Specifically, the introduction of the pilot tone algorithm allows us to effectively mitigate phase fluctuations and preserve the integrity of the quantum signals during transmission without resorting to time-multiplexed reference pulses or fast-locking electronics in the lasers. Our results suggest the potential for achieving secure key rates of up to 1 Mb/s over a 50 km single-mode fiber when using these techniques, offering promising insights into the feasibility of high-rate, low-complexity CV-QKD implementations under realistic conditions.

The reflective measurement model of adherence to non-pharmaceutical interventions (NPIs) in accordance with normalization process theory (NPT) in coherent and convenient social subgroups: PLS-SEM analysis.

Non-pharmaceutical interventions (NPIs) decrease COVID-19 transmission. Reliability and validity of adherence to NPIs in accordance with normalization process theory (NPT) in coherent and convenient social subgroups using reflective measurement model assessment has not been evaluated. In February 2021, a sample of medical students and people with substance use disorders in treatment as coherent (based on continuous probability distribution) vs. convenient groups (based on convenience, not equal probability) composed of travellers and COVID-19 suspected persons from Split-Dalmatia County (SDC) (n = 656) in the Mediterranean completed self-administered surveys. Partial least squares structural equation modelling (PLS-SEM) was used to measure reflective model assessment of adherence to NPIs according to NPT. PLS-SEM reflective model assessment provided two-group specific factors in inverse relationships which determined adherence to NPIs with excellent goodness-of-fit [χ2 = 1.292, df = 1; P = 0.297, CFI = 1, TLI = 0.997, RMSEA = 0.011 (90% CI 0-0.105), RMSEA P = 0.604, SRMR = 0.008, Hoelter CN (α = 0.05) = 2322.757]. Significant negative factors covariance estimate (-0.716) revealed an inverse relationship between first (adherence to NPIs and internal locus of control (LoC) (0.640)) and second factor; young adulthood age (≤25) and highest level of education (1362). As the first factor increased the second tended to decrease. LoC is expected potential mechanism by which sex (MLsex = -0.017, SE = 0.007, P < 0.016) and belonging to coherent subgroups (MLgroup = -0.008, SE = 0.003, P = 0.015) can produce indirect effect of adherence to NPIs. Coherent subgroups had a more pronounced tendency toward integration of NPIs in everyday life. Group factors that facilitate the normalization were higher educated younger adults with a tendency toward external LoC.

Partial differential equation modelling of the solid–liquid phase process in iron sintering and interface control with backstepping method

Due to the highly continuous temporal and spatial distribution characteristics of the sintering process, the solid–liquid phase interface during sintering is uneven and discontinuous, which seriously affects the quality of sintered ore. In order to achieve real-time and effective control of the solid–liquid interface in the sintering system, this study proposes a spatiotemporally distributed partial differential equation (PDE) thermal system with Stefan interface boundaries. Slice the 3D sintering mixing space and establish a discrete 1D space multi-distributed system to achieve distributed control of the sintering thermal system. Based on this system, a distributed boundary controller is designed using the backstepping method to drive the solid–liquid phase interface to the desired position. This method fully adapts to the nonlinear problems of the sintering thermal system and can quickly respond to system changes. Based on real data from the sintering site, a multi-physics simulation model was designed to verify the correctness of the theoretical research. Comparing the simulation results with the actual sintering state shows that this control method can effectively control the position of the sintering solid–liquid interface, which plays a vital role in improving the quality of sinter and sintering efficiency.

A qualitative look at bed net access and use in Burkina Faso, Mozambique, Nigeria, and Rwanda following piloted distributions of dual-active ingredient insecticide-treated nets

BackgroundUniversal coverage with insecticide-treated nets (ITNs) is important for malaria control and elimination. The emergence and intensification of insecticide resistance threatens progress made through the deployment of these interventions and has required the development of newer, more expensive ITN types. Understanding malaria prevention behaviour, including barriers and facilitators to net access and use, can support effective decision-making for the promotion and distribution of ITNs.MethodsIn-depth interviews and focus group discussions were conducted in 3 to 4 villages per district, in 13 districts across Burkina Faso, Mozambique, Nigeria and Rwanda from 2019 to 2022. Interviews were conducted in the local language, translated and transcribed in English, French or Portuguese. Transcripts were coded and analysed using Nvivo and ATLAS.ti.ResultsITNs were obtained from mass distribution campaigns, antenatal care and immunization visits, and purchased on the private market in some locations. While there were divergent perspectives in whether the number of distributed nets were adequate, participants consistently expressed concerns of bias, discrimination, and a lack of transparency with the distribution process. ITNs were frequently used alongside other malaria prevention methods. The primary motivation for use was malaria prevention. While some participants reported using nets nightly throughout the year, other participants reported seasonal use, both due to the perceived higher density of mosquitoes and discomfort of sleeping under a net in the increased heat. Other barriers to consistent net use included activities that take place away from the home, sleeping patterns and arrangements, and sensitivity to the insecticides on the nets.ConclusionsITNs remain an important malaria control intervention. To ensure adequate and increased net access, distribution campaigns should consider family structures, available sleeping spaces, and other bed sharing preferences when identifying the number of nets needed for distribution. In addition, campaigns should allow for multiple options for net distribution points and timing to accommodate households remote to health services. Continuous distribution channels and complimentary distribution through the private sector could help fill gaps in coverage. Solutions are needed for outdoor malaria transmission, including alternative designs for ITNs, and improving access to complementary personal protective measures.

The isosbestic point in the Raman spectra of the hydration shell

Isosbestic point is often observed in a series of spectra, but their interpretation is still controversial, such as whether the continuum model can produce an isosbestic point. In order to answer this question, the Raman spectra of hydration shell with continuous distribution structure in different ionic aqueous solutions were separated by Raman ratio spectra, and an isosbestic point was successfully observed. Our experimental results show that the continuum model can indeed produce the isosbestic point. In order to deepen the understanding of the isosbestic point, we calculate the first moment of the Raman spectra and conduct molecular dynamics (MD) simulations. Both experimental and theoretical findings indicate that elevated temperatures lead to increased disorder among water molecules within the hydration shell.

Rainstorm erosion difference and topographical changes induced by heavy rainfall between afforestation and grassland restoration catchments on the Chinese Loess Plateau

The frequency and intensity of heavy rainfall on the Chinese Loess Plateau (CLP) are increasing due to global climate change, which has caused severe soil erosion. However, precise evaluation of heavy rainfall-induced soil erosion, deposition, and related topographical changes at the catchment scale is lacking, and there is uncertainty as to how effectively trees can inhibit erosion, especially during heavy rainfall. In this study, we selected a pair of catchments with afforestation and natural grassland restoration on the CLP. Precise evaluation of erosion and topographic changes induced by heavy rainfall was conducted based on airborne light detection and ranging (LiDAR) data. In the grassland catchment, the gully bed area increased by 17.6 %, the gully slope and inter-gully land area decreased by 1.4 %, and the length of the gully shoulder line decreased by 4.4 %. Conversely, the forestland catchment experienced a decrease in gully bed area of 8.8 %, an increase in gully slope area of 5.3 %, a decrease in inter-gully land area of 9.9 %, and a decrease in the length of the gully shoulder line of 11.4 %. Following heavy rainfall, both catchments experienced a substantial increase in terrain relief. Soil erosion in the gully slope accounted for >90 % of the total erosion in both catchments, while deposition in the same area contributed to >75 % of the total deposition. The grassland catchment experienced a unit area erosion of 233,908 m3 km−2, which was 4.7 times greater than that of the forestland catchment (49,768 m3 km−2). In both catchments, erosion predominantly transpired in the steep slope region adjacent to the gully shoulder line, accounting for >15 % of the gully slope erosion area. The grassland catchment exhibited a continuous distribution pattern of erosion and deposition, whereas the forestland catchment exhibited a scattered and intertwined distribution pattern. This study is essential for further research on erosion and topographic changes induced by extreme weather events and to determine appropriate measures.

Data-driven traffic signal adaptive control algorithm integrating vehicle perception and traffic flow data

Due to the equipment error, environmental interference and data transmission delay of vehicle flow detection, the accuracy and real-time performance of vehicle perception and traffic flow data will be affected to some extent, resulting in poor traffic signal control effect. Therefore, a data-driven traffic signal adaptive control algorithm is designed by integrating vehicle perception and traffic flow data. To complete the modeling of urban traffic, the discrete distribution and continuous distribution of traffic are obtained. Based on this research environment, the DV-hop localization algorithm is improved to sense the vehicle position. Based on the phase space reconstruction of traffic flow time series and vehicle location information, traffic flow data is predicted. Based on the driving of traffic data, the vehicle types are divided into small, medium and large three categories, and the impact weights are assigned respectively, and the weight values affecting the final allocation of green time are obtained to realize the allocation of green time. The experimental results show that: The research algorithm can not only predict the traffic flow intensity effectively, but also the predicted results are highly coincident with the actual traffic flow intensity. Vehicle arrival rates are higher, vehicle delays are shorter, and vehicles stop fewer times on average.

The estimation of b-value of the frequency-magnitude distribution and of its one-sigma intervals from binned magnitude data

Summary The estimation of the slope (b-value) of the frequency magnitude distribution of earthquakes is based on a formula derived by Aki decades ago, assuming a continuous exponential distribution. However, as the magnitude is usually provided with a limited resolution, its distribution is not continuous but discrete. In the literature, this problem was initially solved by an empirical correction (due to Utsu) to the minimum magnitude, and later by providing an exact formula such as that by Tinti and Mulargia, based on the geometric distribution theory. A recent paper by van der Elst showed that the b-value can be estimated also by considering the magnitude differences (which are proven to follow an exponential discrete Laplace distribution) and that in this case the estimator is more resilient to the incompleteness of the magnitude dataset. In this work we provide the complete theoretical formulation including i) the derivation of the means and standard deviations of the discrete exponential and Laplace distributions; ii) the estimators of the decay parameter of the discrete exponential and trimmed Laplace distributions; and iii) the corresponding formulas for the parameter b. We deduce iv) the standard one-sigma intervals for the estimated b. Moreover, we are able v) to quantify the error associated with the Utsu minimum-magnitude correction. Furthermore, we have discussed the formulas to produce statistically independent magnitude differences. We tested extensively the b-value estimators on simulated synthetic datasets including complete catalogues as well as catalogues affected by a strong incompleteness degree such as aftershock sequences where the incompleteness is made to vary from one event to the next. We have also analysed the real aftershock sequence of the 30/10/2016 Norcia (central Italy) to integrate the finding of the simulations. To judge the performance of the various estimators we have introduced an index p that can be seen as a non-parametric extension of the Student's t index. The main outcomes of this paper are that 1) the b-value estimators devised for continuous magnitude data are not adequate for binned magnitudes, 2) for complete datasets, estimators based on magnitudes and on magnitude differences provide substantially equivalent results, 3) for incomplete magnitude datasets, estimators based on magnitude differences provide better results, 4) for incomplete aftershock sequences there is no evidence that methods based on positive magnitude differences are superior than other methods using differences. This conclusion is further confirmed by our analysis of the above-mentioned Norcia seismic sequence. This last finding contrasts with the van der Elst's claim that the so called ${b}_ + $ method is the most adequate to treat real aftershock sequences.

Effect of volume ratios on the novel Solanum lycopersicum leaf extract-mediated production of ZnO and Co3O4 nanoparticles for potential antifungal applications

ABSTRACT Antimicrobial infectious disease has become a major problem in the world. It has been found as its continual distribution is at extremely frightening rate. The most curable technique is the design and synthesis of effective nano-based drugs as green alternative. In this study, ZnO and Co3O4 nanoparticles (NPs) were produced from their precursor salts in the volume ratios of 1:3, 1:1, and 3:1 with Solanum lycopersicum leaf as a capping and reducing agent. Characterizations were performed using TGA/DTA, XRD, SEM, TEM, HRTEM, SAED, UV-Vis, and FTIR techniques. After 450°C and 500°C, ZnO and Co3O4 NPs were found to be thermally stable, respectively. For the ZnO and Co3O4 NPs in 1:3, 1:1, and 3:1 volume ratios, respectively, their average crystalline sizes were 51, 20, 29 and 26, 21 and 28 nm. The degree of crystallinity is confirmed by SEM in conjunction with TEM-HRTEM, and SAED. Among the numerous volume ratios, Co3O4 (1:3) and Co3O4 (1:1) showed 100% promised activity against Alternaria solani pathogen. Antimicrobial infectious disease has become a major serious problem in the modern world. It has been found as its continual distribution is at an extremely frightening rate. The most curable technique for this worldwide issue is the design and synthesis of effective nano-based drugs as green alternative solutions. In this study, ZnO and Co3O4 nanoparticles (NPs) were produced from their respective precursor salts in the volume ratios of 1:3, 1:1, and 3:1 with Solanum lycopersicum leaf as a capping and reducing agent. Characterizations were performed using TGA/DTA, XRD, SEM, TEM, HRTEM, SAED, UV-Vis, and FTIR techniques. After 450°C and 500°C, greenly synthesized ZnO and Co3O4 NPs were found to be thermally stable, respectively. For the ZnO and Co3O4 synthesized in 1:3, 1:1, and 3:1 volume ratios, respectively, their average crystalline sizes were 51, 20, 29 and 26, 21 and 28 nm. The degree of crystallinity is confirmed by SEM examination in conjunction with TEM-HRTEM, and SAED. Among the numerous volume ratios, Co3O4 (1:3) and Co3O4 (1:1) showed 100% promised activity against Alternaria solani pathogen.

Shape-dependent size polydispersity: DEM investigation of mixing behavior in a vibrating packed bed system

The Discrete element method is applied to examine the influence of shape-dependent size polydispersity on mixing behavior in a vibrating packed bed system. A series of tests for optimized simulation settings for evaluation of mixing are performed. The influence of size polydispersity (standard deviation to mean particle diameter ratio) and the particle shape on mixing is assessed using the overall mixing index. The mixtures are differentiated between homogeneous and heterogeneous mixtures. In homogeneous mixtures, continuous (Gaussian) distribution outperforms discrete (binary and ternary). Mixing decreases with size polydispersity transitioning from narrow to wide distributions in homogeneous Gaussian mixtures. For heterogeneous Gaussian mixtures, the mixing trends for fine particle shapes are ellipsoid > sphere > cylinder > cube, while the mixing trends for coarse particle shapes are cylinder > sphere > ellipsoid > cube. Changing intermediate particle shapes in heterogeneous ternary mixtures impacts mixing; the cube shows worst performance.

Error correction based artificial neural network in multi-modes CV-QKD with simultaneous type-I and type-II parametric-down conversion entangled photon source

We model simultaneous type-I and type-II phase matching in a single non-linear crystal (NLC), based on a double periodically poled lithium niobate crystal. We also discuss entanglement based continuous variable quantum key distribution (CV-QKD), and the security of such scheme is analyzed considering an eavesdropper being capable of individual attacks. We further demonstrate efficiency of the artificial neural network (ANN) algorithm during post-processing or errors correction in such CV-QKD protocols. Results show that employing simultaneous type-I and type-II SPDC process in single NLC is a potential source to generate high dimensional (or hyper-entangled) states, strongly required for quantum information processing tasks, an example of CV-QKD. Security analysis of such a CV-QKD protocol shows a strong advantage of employing the above entangled photon state source, given that it provides a higher secure key rate and thus a secure communication within a larger distance. In addition, the suggested error correction algorithm is less time consuming and highly efficient, since full synchronization is achieved just after a few number of updates of trusted parties’ tree-parity-machines. Our results sufficiently demonstrate that the suggested CV-QKD is able to distribute secure keys in nearby inter-city areas, and therefore allows lower-cost secure communication networks.

Two-dimensional shielded vortices in a shear current

The interaction of shielded vortices, with a continuous vorticity distribution, and a shear current of weak vorticity amplitude but similar velocity compared to the vortex amplitude is numerically investigated in two-dimensional isochoric flows. Different types of axisymmetric shielded vortices, namely, a neutral unstable vortex, a neutral robust vortex, and a non-neutral vortex are considered. The vortices are linear combinations of vorticity layer-modes, which consist of conveniently normalized cylindrical Bessel functions of order 0, truncated by a zero of the Bessel function of order 1. The vortex–current interaction is investigated by superposing initially the vortices at different initial locations along the cross-flow axis in the shear current. The numerical results show that some shielded vortices, as well as the shear current, remain robust while the vortices cross the shear current and reach a stable equilibrium location, which is of the same sign vorticity as its amount of circulation. There exist two unstable equilibrium locations where most of the vortices persist during a relatively short time interval before heading to their stable equilibrium region in the shear current.

Influence of soundboard modelling approaches on piano string vibration.

This work explores the influence of the dynamics of the piano soundboard on string vibration and on the force acting between the vibrating string and the bridge. Four different soundboard representations of different complexities are considered: (i) a finite element model that considers the complete dynamic behavior of the soundboard at the connection point with the string within the frequency range of interest, (ii) a reduced modal model containing only five modes, (iii) a Kelvin-Voigt system characterized by an equivalent stiffness and damping, and (iv) a rigid soundboard represented by a simply supported boundary condition. The connection between the string and the soundboard is modelled by coupling a simply supported stiff string model with the different representations of the soundboard through a contact stiffness. As well as directly accounting for the string-soundboard coupling, this approach also includes the duplex scaling segment. The latter can be left to vibrate freely or muted with a continuous distribution of dampers. Although the simplest soundboard representation is not dissimilar from the other more complex models, the dynamics of the soundboard affect the decay time of the note, the force transmitted to it, and the vibration of the radiating surface of the soundboard.

Practical Security of Continuous Variable Quantum Key Distribution Ascribable to Imperfect Modulator for Fiber Channel

An amplitude modulator plays an essential role in the implementation of continuous-variable quantum key distribution (CVQKD), whereas it may bring about a potential security loophole in the practical system. The high-frequency modulation of the actual transmitter usually results in the high rate of the system. However, an imperfect amplitude modulator (AM) can give birth to a potential information leakage from the modulation of the transmitter. To reveal a potential security loophole from the high-frequency AM embedded in the transmitter, we demonstrate an influence on the practical security of the system in terms of the secret key rate and maximal transmission distance. The results indicate the risk of this security loophole in the imperfect AM-embedded transmitter. Fortunately, the legal participants can trace back the potential information leakage that has been produced from the imperfect transmitter at high frequencies, which can be used for defeating the leakage attack in CVQKD. We find the limitations of the imperfect AM-embedded transmitter of the high-frequency quantum system, and hence, we have to trade off the practical security and the modulation frequency of the AM-embedded transmitter while considering its implementation in a practical environment.

Spatial–temporal evolution and driving factors of ecosystem services trade‐offs and synergies in karst areas from a geospatial perspective

AbstractNowadays, studies of ecosystem services (ESs) trade‐offs and synergies in karst areas are limited to a single region. In particular, the quantification of the nature and intensity of the relationships between ESs in continuous karst distribution areas (CKDAs) and non‐karst areas (NKAs), and a full understanding of the drivers behind this change remains a challenge. In this study, the province of Guizhou in China was used as study area and a framework was developed to analyze the spatial variation of trade‐offs and synergies between ESs. The framework utilized Spearman, geographical detector, and multi‐scale geographically weighted regression (MGWR) to establish connections between four key ESs: habitat quality (HQ), water yield (WY), soil conservation (SC), and net primary productivity (NPP). Through the examination of these relationships, this article has revealed the influence of the driving forces on this ecological process. The study indicated that: (1) During this period, ESs in study area increased steadily, with the average value of HQ always above 0.6, and WY, SC, and NPP increased by 2.32%, 6.07%, and 15.18%, respectively. (2) WY had a trade‐off relationship with other ESs, and SC, HQ, and NPP were synergistic with each other. (3) In the CKDA, topography and precipitation dominated the relationship between SC and other ESs. In contrast, in the NKA, ecological processes involving HQ were more prominent in human/natural interactions. Therefore, proposing ecological measures at different spatial scales to promote synergistic development between ESs is of great importance for ecological governance and sustainability of karst areas.

Ключевые особенности протоколов квантового распределения ключей на непрерывных переменных

The key features of continuous variables quantum key distribution protocols are considered in the paper. The motivation for studying and developing methods of quantum cryptography is substantiated. The main aspects inherent to continuous-variable protocols are highlighted, and they are classified based on various characteristics, peculiarities, and implementation variants. A detailed examination of a protocol example with discrete modulation and signal registration through balanced homodyne detection is provided. A classification of attacks on the quantum protocol is presented. A general overview of post-processing methods is given. The role of noise is indicated, and approaches to assessing the level of security applicable to continuous-variable protocols are discussed. In conclusion, the main conclusions regarding the current status of this problem are presented, and aspects requiring further study are identified.

On probabilistic mean value theorem and covariance identities

In this paper, further results for a probabilistic analogue of the mean value theorem proposed by Di Crescenzo (1999) are studied, focused on Normal and Poisson distributions. By applying this theorem for two normally distributed random variables with the same variance, a new symmetric unimodal distribution is obtained, and statistical measures of it are provided. By introducing a family of real valued continuous distributions, covariance identities are also investigated. Covariance identities are also explored for a Poisson distributed random variable. Some illustrative examples are finally given.

Deformation of power law in the double Pareto distribution using uniformly distributed observation time

The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the exponential distribution of the observation time is replaced with a continuous uniform distribution. The probability density, complementary cumulative distribution, and moments of this model are exactly calculated. Furthermore, the validity of the analytical calculations is discussed in comparison with numerical simulations of stochastic processes.

Longer Term Follow-up on Acuity Circle Allocation Strategies in Liver Transplantation

Abstract Purpose of Review This review summarizes longer term follow-up of acuity circle–based distribution for livers, which was implemented on February 4, 2020. Recent Findings After 2 years of policy implementation, the likelihood of transplant increased, while removals for death or being too sick decreased. The median transplant score was unchanged, and the variance in the median MELD at transplant decreased for OPTN regions, DSA, and state. Concurrently, median distance from donor to transplant hospital and cold ischemia times increased. A slight increase in liver non-use rate and decrease in liver utilization rate has been observed. Summary Acuity circle–based distribution improved access to liver transplantation for the sickest patients through broader sharing, at the cost of increased travel and logistics. The continuous distribution framework may be an opportunity for the liver transplant community to further address geographic disparities in access to transplant in the United States.