Potential Kernel Research Articles

On sharp heat kernel estimates in the context of Fourier–Dini expansions

We prove sharp estimates of the heat kernel associated with Fourier–Dini expansions on (0,1) equipped with Lebesgue measure and the Neumann condition imposed on the right endpoint. Then we give several applications of this result including sharp bounds for the corresponding Poisson and potential kernels, sharp mapping properties of the maximal heat semigroup and potential operators and boundary convergence of the Fourier–Dini semigroup.

The invariant measure of a walking droplet in hydrodynamic pilot–wave theory

We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.

Molecular pentaquarks with hidden charm and double strangeness

We analyze theoretically the coupled-channel meson-baryon interaction with global flavor c¯cssn and c¯csss, where mesons are pseudoscalars or vectors, and baryons have JP=1/2+ or 3/2+. The aim is to explore whether the nonlinear dynamics inherent in the unitarization process within coupled channels can dynamically generate double- and triple-strange pentaquark-type states (Pcss and Pcsss, respectively), for which there is no experimental evidence to date. We evaluate the s-wave scattering matrix by implementing unitarity in coupled channels, using potential kernels obtained from t-channel vector meson exchange. The required PPV and VVV vertices are obtained from Lagrangians derived through appropriate extensions of the local hidden gauge symmetry approach to the charm sector, while capitalizing on the symmetry of the spin and flavor wave function to evaluate the BBV vertex. We find four different poles in the double strange sector, some of them degenerate in spin. For the triple-strange channel, we find the meson-baryon interaction insufficient to generate a bound or resonance state through the unitary coupled-channel dynamics. Published by the American Physical Society 2024

Combining mBJ exchange potential and bootstrap kernel of TDDFT to compute optical spectra of solids

One of the fundamental challenges in calculating the optical properties of crystalline materials is the accurate description of exciton effects so as to make it computationally viable for studying large systems. We combine the modified Becke-Johnson (mBJ) exchange potential and bootstrap kernel (BSK) of time-dependent density functional theory (TDDFT) to compute the imaginary part of the dielectric function of a variety of semiconductors and insulators (Si, GaAs, NiO, TiO2, LiF, LiCl, SrTiO3 and NaMgF3). The results are compared with the experimental data available in the literature. We also compute their dielectric functions using the random phase approximations (RPA) to verify the effect of the BSK method on the optical spectra of these compounds. We conclude that TDDFT+BSK+mBJ calculations can determine the optical spectra of the solids in good agreement with the experimental data (except for small-energy gap materials such as Si and GaAs) with low computational cost, and using a fully ab initio procedure.

Positivity conditions on the annulus via the double-layer potential kernel

Positivity conditions on the annulus via the double-layer potential kernel

Solution Representations for Poisson’s Equation, Martingale Structure, and the Markov Chain Central Limit Theorem

The solution of Poisson’s equation plays a key role in constructing the martingale through which sums of Markov correlated random variables can be analyzed. In this paper, we study three different representations for the solution for countable state space irreducible Markov chains, two based on entry time expectations, and the other based on a potential kernel. Our consideration of null recurrent chains allows us to extend our theory to positive recurrent nonexplosive Markov jump processes. We also develop the martingale structure induced by these solutions to Poisson’s equation, under minimal conditions, and establish verifiable Lyapunov conditions to support our theory. Finally, we provide a central limit theorem for Markov dependent sums, under conditions weaker than have previously appeared in the literature.

Yield response of maize hybrids with different ear flex to nitrogen rate and plant density

AbstractMaize (Zea mays L.) hybrids are frequently labeled as fixed or flex hybrid ear types by seed companies based on pre‐commercial trials or field observations during commercialization. However, the underlying physiological cause and the associated management with each hybrid ear type remains a question for growers. Experiments were conducted at multiple locations across 3 years to determine the yield and yield component response to combinations of plant density (4, 6, 8, 10, and 12 plant m−2) and nitrogen (N) rate (0, 78, 159, 235, and 314 kg N ha−1) for three fixed and four flex hybrid ear types. Optimal plant density (OPD) to reach maximum yield was 1.7 plant m−2 greater for fixed hybrid ear type compared to the flex hybrid ear type for N rates greater than 78 kg N ha−1. Flex hybrid ear type achieved similar yield at lower OPD through increased kernel weight (KW) without reduced kernels per square meter. Potential kernel number at silk appearance and established kernels 15 days after silk appearance were similar between hybrid ear types, indicating that the flex component was driven by KW. Fixed hybrid ear type displayed a lower threshold value of total aboveground biomass per plant at physiological maturity to set kernels compared to a flex hybrid ear type. Selection of a flex hybrid ear type provides opportunity for reduced planting density with similar yield potential and N management practices.

Harnack inequality and one-endedness of UST on reversible random graphs.

We prove that for recurrent, reversible graphs, the following conditions are equivalent: (a) existence and uniqueness of the potential kernel, (b) existence and uniqueness of harmonic measure from infinity, (c) a new anchored Harnack inequality, and (d) one-endedness of the wired uniform spanning tree. In particular this gives a proof of the anchored (and in fact also elliptic) Harnack inequality on the UIPT. This also complements and strengthens some results of Benjamini et al.(Ann Probab 29(1):1-65, 2001). Furthermore, we make progress towards a conjecture of Aldous and Lyons by proving that these conditions are fulfilled for strictly subdiffusive recurrent unimodular graphs. Finally, we discuss the behaviour of the random walk conditioned to never return to the origin, which is well defined as a consequence of our results.

Metal Artifact Reduction in Photon-Counting Detector CT: Quantitative Evaluation of Artifact Reduction Techniques.

With the introduction of clinical photon-counting detector computed tomography (PCD-CT) and its novel reconstruction techniques, a quantitative investigation of different acquisition and reconstruction settings is necessary to optimize clinical acquisition protocols for metal artifact reduction. A multienergy phantom was scanned on a clinical dual-source PCD-CT (NAEOTOM Alpha; Siemens Healthcare GmbH) with 4 different central inserts: water-equivalent plastic, aluminum, steel, and titanium. Acquisitions were performed at 120 kVp and 140 kVp (CTDI vol 10 mGy) and reconstructed as virtual monoenergetic images (VMIs; 110-150 keV), as T3D, and with the standard reconstruction "none" (70 keV VMI) using different reconstruction kernels (Br36, Br56) and with as well as without iterative metal artifact reduction (iMAR). Metal artifacts were quantified, calculating relative percentages of metal artifacts. Mean CT numbers of an adjacent water-equivalent insert and different tissue-equivalent inserts were evaluated, and eccentricity of metal rods was measured. Repeated-measures analysis of variance was performed for statistical analysis. Metal artifacts were most prevalent for the steel insert (12.6% average artifacts), followed by titanium (4.2%) and aluminum (1.0%). The strongest metal artifact reduction was noted for iMAR (with iMAR: 1.4%, without iMAR: 10.5%; P < 0.001) or VMI (VMI: 110 keV 2.6% to 150 keV 3.3%, T3D: 11.0%, and none: 16.0%; P < 0.001) individually, with best results when combining iMAR and VMI at 110 keV (1.2%). Changing acquisition tube potential (120 kV: 6.6%, 140 kV: 5.2%; P = 0.33) or reconstruction kernel (Br36: 5.5%, Br56: 6.4%; P = 0.17) was less effective. Mean CT numbers and standard deviations were significantly affected by iMAR (with iMAR: -3.0 ± 21.5 HU, without iMAR: -8.5 ± 24.3 HU; P < 0.001), VMI (VMI: 110 keV -3.6 ± 21.6 HU to 150 keV -1.4 ± 21.2 HU, T3D: -11.7 ± 23.8 HU, and none: -16.9 ± 29.8 HU; P < 0.001), tube potential (120 kV: -4.7 ± 22.8 HU, 140 kV: -6.8 ± 23.0 HU; P = 0.03), and reconstruction kernel (Br36: -5.5 ± 14.2 HU, Br56: -6.8 ± 23.0 HU; P < 0.001). Both iMAR and VMI improved quantitative CT number accuracy and metal rod eccentricity for the steel rod, but iMAR was of limited effectiveness for the aluminum rod. For metal artifact reduction in PCD-CT, a combination of iMAR and VMI at 110 keV demonstrated the strongest artifact reduction of the evaluated options, whereas the impact of reconstruction kernel and tube potential was limited.

Combined analysis on nature of X(3960), chi _{c0}(3930), and X_0(4140)

In this work, a study of the D_s{bar{D}}_s interaction and its couplings to the channels D{bar{D}} and J/psi phi is performed in a quasipotential Bethe–Salpeter equation approach. The D_s^+{D}_s^- and D^+{D}^- invariant mass spectra in three-body B decays are investigated in order to understand the origin of X(3960), chi _{c0}(3930), and X_0(4140) structures reported at LHCb. With the help of effective Lagrangians, the potential kernel can be constructed with meson exchanges, from which the scattering amplitudes can be obtained. By inserting it into the three-body decay processes, the invariant mass spectra can be calculated with an additional Breit–Wigner resonance introduced. The D_s^+{D}_s^- invariant mass spectrum in the decay process B^+rightarrow D^+_sD^-_sK^+ is well reproduced, and the X(3960) structure can be explained as a molecular state from the D_s{bar{D}}_s interaction. The state also exhibits as a peak in the D^+{D}^- invariant mass spectrum in the decay B^+rightarrow D^+D^-K^+, however, it is too narrow to reproduce the experimental structure around 3930 MeV. The dip around 4140 MeV in the D_s^+{D}_s^- invariant mass spectrum can be reproduced by the additional resonance with interference effect. However, a small bump instead of a dip is produced from the D_s{bar{D}}_s-J/psi phi coupled-channel effect, which suggests that the X_0(4140) cannot be interpreted as the D_s{bar{D}}_s-J/psi phi coupling in the current model.

Possible molecular states from interactions of charmed strange baryons* *Supported by the National Natural Science Foundation of China (11675228)

In this study, we investigate possible molecular states composed of two charmed strange baryons from the interaction and their hidden-charm hidden-strange partners from the interaction. With the aid of heavy quark chiral effective Lagrangians, the interactions of charmed strange baryons are described with light meson exchanges. The potential kernels are constructed and inserted into the quasipotential Bethe–Salpeter equation. The bound states are produced from most interactions considered, which suggests that strong attractions exist widely between the charmed strange baryons. Experimental search for these types of molecular states is suggested in future high-precision measurements.

Physiological Mechanism of Waterlogging Stress on Yield of Waxy Maize at the Jointing Stage.

In the main agricultural area for waxy maize production in China, waterlogging occurs frequently during the waxy maize jointing stage, and this causes significant yield reduction. It is very important to understand the physiological mechanism of waterlogging stress in waxy maize during the jointing stage to develop strategies against waterlogging stress. Therefore, this study set waterlogging treatments in the field for 0, 2, 4, 6, 8, and 10 days during the waxy maize jointing stage, and were labelled CK, WS2, WS4, WS6, WS8 and WS10, respectively. By analyzing the effect of waterlogging on the source, sink, and transport of photoassimilates, the physiological mechanism of waterlogging stress in the jointing stage was clarified. The results show that PEPC and POD activities and Pro content decreased significantly under WS2 compared to CK. Except for these three indicators, the Pn, GS, leaf area, kernel number, yield, and puncture strength of stems were significantly decreased under the WS4. Under the WS6, the content of MDA began to increase significantly, while almost all other physiological indices decreased significantly. Moreover, the structure of stem epidermal cells and the vascular bundle were deformed after 6 days of waterlogging. Therefore, the threshold value of waterlogging stress occured at 4 to 6 days in the jointing stage of waxy maize. Moreover, waterlogging stress at the jointing stage mainly reduces the yield by reducing the number of kernels; specifically, the kernel number decreased by 6.7-15.5% in 4-10 days of waterlogging, resulting in a decrease of 9.9-20.2% in the final yield. Thus, we have shown that waterlogging stress at the jointing stage results in the decrease of potential waxy maize kernel numbers and yield when the synthesis of sources was limited and the transport of photoassimilates was restricted.

Integral operators in Hölder spaces on upper Ahlfors regular sets

Volume and layer potentials are integrals on a subset Y of the Euclidean space {\mathbb{R}}^n that depend on a variable in a subset X of {\mathbb{R}}^n . Here we present a unified approach to some results by assuming that X and Y are subsets of a metric space M and that Y is equipped with a measure \nu that satisfies upper Ahlfors growth conditions that include non-doubling measures. We prove continuity statements in the frame of (generalized) Hölder spaces upon variation both of the density functions on Y and of the off-diagonal potential kernel and T1 theorems that generalize corresponding results of J. García-Cuerva and A. E. Gatto in case X=Y for kernels that include the standard ones.

Possible molecular dibaryons with csssqq quarks and their baryon–antibaryon partners

In this work, we systematically investigate the charmed–strange dibaryon systems with csssqq quarks and their baryon–antibaryon partners from the interactions varXi ^{(',*)}_{c}varXi ^{(*)}, varOmega ^{(*)}_cvarLambda , varOmega ^{(*)}_cvarSigma ^{(*)}, varLambda _cvarOmega and varSigma ^{(*)}_cvarOmega and their baryon–antibaryon partners from interactions varXi ^{(',*)}_{c}bar{varXi }^{(*)}, varOmega ^{(*)}_cbar{varLambda }, varOmega ^{(*)}_cbar{varSigma }^{(*)}, varLambda _cbar{varOmega } and varSigma ^{(*)}_cbar{varOmega }. The potential kernels are constructed with the help of effective Lagrangians under SU(3), heavy quark, and chiral symmetries to describe these interactions. To search for possible molecular states, the kernels are inserted into the quasipotential Bethe–Salpeter equation, which is solved to find poles from scattering amplitude. The results suggest that 36 and 24 bound states can be found in the baryon–baryon and baryon–antibaryon interactions, respectively. However, much large values of parameter alpha are required to produce the bound states from the baryon–antibaryon interactions, which questions the existence of these bound states. Possible coupled-channel effect are considered in the current work to estimate the couplings of the molecular states to the channels considered.

Hydrodynamic Limit of the Incompressible Navier–Stokes–Fourier–Maxwell System with Ohm’s Law from the Vlasov–Maxwell–Boltzmann System: Hilbert Expansion Approach

We prove a global-in-time limit from the two-species Vlasov–Maxwell–Boltzmann system with a cutoff hard potential collision kernel to the two-fluid incompressible Navier–Stokes–Fourier–Maxwell system with Ohm’s law. Besides the techniques developed for the classical solutions to the Vlasov–Maxwell–Boltzmann equations in the past years, such as the nonlinear energy method and micro–macro decomposition are employed, in this paper, key roles are played by the decay properties of both the electric field and the wave equation with linear damping of the divergence free magnetic field. This is a companion paper of Jiang and Luo (Ann PDE, 8(1), Paper No. 4, 126, 2022) in which Hilbert expansion was not employed but only the hard sphere case was considered.

Numerical simulation of contact problem with potential kernel

Numerical simulation of contact problem with potential kernel

The Boltzmann equation with an external force on the torus : incompressible Navier–Stokes–Fourier hydrodynamical limit

We study the Boltzmann equation with external forces, not necessarily deriving from a potential, in the incompressible Navier-Stokes perturbative regime. On the torus, we establish local-in-time, for any time, Cauchy theories that are independent of the Knudsen number in Sobolev spaces. The existence is proved around a time-dependent Maxwellian that behaves like the global equilibrium both as time grows and as the Knudsen number decreases. We combine hypocoercive properties of linearized Boltzmann operators with linearization around a time-dependent Maxwellian that catches the fluctuations of the characteristics trajec-tories due to the presence of the force. This uniform theory is sufficiently robust to derive the incompressible Navier-Stokes-Fourier system with an external force from the Boltzmann equation. Neither smallness, nor time-decaying assumption is required for the external force, nor a gradient form, and we deal with general hard potential and cutoff Boltzmann kernels. As a by-product the latest general theories for unit Knudsen number when the force is sufficiently small and decays in time are recovered.

Possible molecular states from interactions of charmed baryons

In this work, we perform a systematic study of possible molecular states composed of two charmed baryons including hidden-charm systems $\Lambda_c\bar{\Lambda}_c$, $\Sigma_c^{(*)}\bar{\Sigma}_c^{(*)}$, and $\Lambda_c\bar{\Sigma}_c^{(*)}$, and corresponding double-charm systems $\Lambda_c\Lambda_c$, $\Sigma_c^{(*)}\Sigma_c^{(*)}$, and $\Lambda_c\Sigma_c^{(*)}$. With the help of the heavy quark chiral effective Lagrangians, the interactions are described with $\pi$, $\rho$, $\eta$, $\omega$, $\phi$, and $\sigma$ exchanges. The potential kernels are constructed, and inserted into the quasipotential Bethe-Salpeter equation. The bound states from the interactions considered is studied by searching for the poles of the scattering amplitude. The results suggest that strong attractions exist in both hidden-charm and double-charm systems considered in the current work, and bound states can be produced in most of the systems. More experiment studies about these molecular states are suggested though the nucleon-nucleon collison at LHC and nucleon-antinucleon collison at $\rm \bar{P}ANDA$.

Exotic molecular meson states of B^{(*)} K^{(*)} nature

We evaluate theoretically the interaction of the open bottom and strange systems {{bar{B}}}{{bar{K}}}, {{bar{B}}^*}{{bar{K}}}, {{bar{B}}}{{bar{K}}^*} and {{bar{B}}^*}{{bar{K}}^*} to look for possible bound states which could correspond to exotic non-quark–antiquark mesons since they would contain at least one b and one s quarks. The s-wave scattering matrix is evaluated implementing unitarity by means of the Bethe–Salpeter equation, with the potential kernels obtained from contact and vector meson exchange mechanisms. The vertices needed are supplied from Lagrangians derived from suitable extensions of the hidden gauge symmetry approach to the bottom sector. We find poles below the respective thresholds for isospin 0 interaction and evaluate the widths of the different obtained states by including the main sources of imaginary part, which are the B^*rightarrow Bgamma decay in the {{bar{B}}^*}{{bar{K}}} channels, the K^*rightarrow K pi in the channels involving a K^*, plus the box diagrams with {{bar{B}}}{{bar{K}}} and {{bar{B}}^*}{{bar{K}}} intermediate states for the {{bar{B}}^*}{{bar{K}}^*} channels.

Mitigating the effect of dataset shift in clustering

Dataset shift is a relevant topic in unsupervised learning since many applications face evolving environments, causing an important loss of generalization and performance. Most techniques that deal with this issue are designed for data stream clustering, whose goal is to process sequences of data efficiently under Big Data. In this study, we claim dataset shift is an issue for static clustering tasks in which data is collected over a long period. To mitigate it, we propose Time-weighted kernel k-means, a k-means variant that includes a time-dependent weighting process. We do this via the induced ordered weighted average (IOWA) operator. The weighting process acts as a gradual forgetting mechanism, prioritizing recent examples over outdated ones in the clustering algorithm. The computational experiments show the potential Time-weighted kernel k-means has in evolving environments.