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We prove that a globally hyperbolic smooth spacetime endowed with a C1-Lorentzian metric whose Ricci tensor is bounded from below in all timelike directions, in a distributional sense, obeys the timelike measure-contraction property. This result includes a class of spacetimes with borderline regularity for which local existence results for the vacuum Einstein equation are known in the setting of spaces with timelike Ricci bounds in a synthetic sense. In particular, these spacetimes satisfy timelike Brunn-Minkowski, Bonnet-Myers, and Bishop-Gromov inequalities in sharp form, without any timelike nonbranching assumption. If the metric is even C1,1, in fact the stronger timelike curvature-dimension condition holds. In this regularity, we also obtain uniqueness of chronological optimal couplings and chronological geodesics. [ABSTRACT FROM AUTHOR]

In this work, we mainly focus on testing the spacetime properties around black holes surrounded by a dark fluid, which are potential candidates for dark energy described by the Chaplygin-like equation of state through its shadow. To do this, we first study the black hole's horizon structure and shadow for the non-rotating case. Then, we obtain a rotating black hole solution in the presence of a dark fluid using the generalized Newman–Janis algorithm and study the effects of the black hole spin and the fluid parameters on the black hole horizons. Also, we obtained the shadow cast of the rotating black hole using celestial coordinates and showed that the presence of the dark fluid causes an increase in shadow size. Moreover, we use the shadow size of supermassive black holes Sagittarius A* and M87* from Event Horizon Telescope observations to obtain constraints on the spin, black hole charge, and dark fluid parameters. Lastly, we investigate the energy emission rate of a charged black hole surrounded by a Chaplygin-like dark fluid, comparing it to both rotating and non-rotating cases. [ABSTRACT FROM AUTHOR]

There are two metaphysical pictures of spacetime: The evolutionary picture and the all-at-once picture. According to the evolutionary picture, spacetime is nothing but the evolution of space over time. In contrast, the all-at-once picture considers spacetime as ‘a global, four-dimensional boundary value problem’ that can be solved only in an all-at-once manner, i.e. as a whole which is fundamentally four-dimensional and non-decomposable into spatial and temporal parts. The two most-known formulations of general theory of relativity, i.e. the Hamiltonian (or the canonical) and the Lagrangian (or the standard) formulations, enjoy the evolutionary and all-at-once pictures of spacetime respectively. Here, we have argued that (1) the all-at-once picture is more aligned with the philosophy of relativity theory, i.e. uniting space and time into spacetime, (2) the evolutionary picture is not as general as the all-at-once, since only in special cases, such as globally hyperbolic spacetimes, is it possible to deal with spacetime as the evolution of a spatial slice over time, and (3) the all-at-once picture paves the way to better understanding four-dimensional physical entities, like event horizons, which cannot be explained within an evolutionary picture without raising a paradox. Therefore, the evolutionary picture is neither the fundamentally-true nor the naturally-chosen picture of spacetime. Rather, we choose the evolutionary picture for practical and computational reasons. While the all-at-once picture seems a more appropriate description of the quantum and cosmological reality, the evolutionary picture can be applied occasionally and locally, or quasi-locally, and is not the proper metaphysical picture of spacetime at the fundamental level of reality. [ABSTRACT FROM AUTHOR]

We study the sharp interface limit of the stochastic Cahn-Hilliard equation with cubic double-well potential and additive space-time white noise ε σ W, where ε>0 is an interfacial width parameter. We prove that, for a sufficiently large scaling constant σ>0, the stochastic Cahn-Hilliard equation converges to the deterministic Mullins-Sekerka/Hele-Shaw problem for ε→0. The convergence is shown in suitable fractional Sobolev norms as well as in the L p -norm for p∈(2,4] in spatial dimension d=2,3. This generalizes the existing result for the space-time white noise to dimension d=3 and improves the existing results for smooth noise, which were so far limited to p∈(2, d+2 2d+8) in spatial dimension d=2,3. As a byproduct of the analysis of the stochastic problem with space-time white noise, we identify minimal regularity requirements on the noise which allow convergence to the sharp interface limit in the H¹-norm and also provide improved convergence estimates for the sharp interface limit of the deterministic problem. [ABSTRACT FROM AUTHOR]

We study reflected diffusion on uniform domains where the underlying space admits a symmetric diffusion that satisfies sub-Gaussian heat kernel estimates. A celebrated theorem of Jones (Acta Math 147(1-2):71–88, 1981) states that uniform domains in Euclidean space are extension domains for Sobolev spaces. In this work, we obtain a similar extension property for metric spaces equipped with a Dirichlet form whose heat kernel satisfies a sub-Gaussian estimate. We introduce a scale-invariant version of this extension property and apply it to show that the reflected diffusion process on such a uniform domain inherits various properties from the ambient space, such as Harnack inequalities, cutoff energy inequality, and sub-Gaussian heat kernel bounds. In particular, our work extends Neumann heat kernel estimates of Gyrya and Saloff-Coste (Astérisque 336:145, 2011) beyond the Gaussian space-time scaling. Furthermore, our estimates on the extension operator imply that the energy measure of the boundary of a uniform domain is always zero. This property of the energy measure is a broad generalization of Hino's result (Probab Theory Relat Fields 156:739–793, 2013) that proves the vanishing of the energy measure on the outer square boundary of the standard Sierpiński carpet equipped with the self-similar Dirichlet form. [ABSTRACT FROM AUTHOR]

We consider the following stochastic heat equation ∂ t u (t , x) = 1 2 ∂ x 2 u (t , x) + b (u (t , x)) + σ (u (t , x)) W ˙ (t , x) , defined for (t , x) ∈ (0 , ∞) × R , where W ˙ denotes space-time white noise. The function σ is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly away from the origin, and the function b is assumed to be positive, locally Lipschitz and nondecreasing. We prove that the Osgood condition ∫ 1 ∞ d y b (y) < ∞ implies that the solution almost surely blows up everywhere and instantaneously, In other words, the Osgood condition ensures that P { u (t , x) = ∞ for all t > 0 and x ∈ R } = 1. The main ingredients of the proof involve a hitting-time bound for a class of differential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincaré inequalities that were developed in Chen et al. (Electron J Probab 26:1–37, 2021, J Funct Anal 282(2):109290, 2022). [ABSTRACT FROM AUTHOR]

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons. [ABSTRACT FROM AUTHOR]

The concept of wormholes is still hypothetical in physics but attractive among researchers. In this work, motivated by the important effect of f (R , T) gravity theory, we seek the existence of wormhole solutions. We consider the field equations that can be derived from two different choices of matter Lagrangian density and utilize them to find the possibility of having some wormhole geometry. This procedure is based on the specific choice of an equation-of-state that obeys a certain physical requirement on the matter stress-energy [S. Kar and D. Sahdev, Restricted class of traversable wormholes with traceless matter, Phys. Rev. D 52 (1995) 2030]. For this purpose, the functional form of the redshift function is taken into consideration, and the possible existence of wormhole solutions is proven. Finally, the work examines the energy conditions and shows that violations of null energy conditions hold throughout spacetime. [ABSTRACT FROM AUTHOR]

Exploring spatial-temporal interactions among group members is crucial for group activity recognition. However, most existing approaches cannot jointly consider it from multi-level cross-relations, which results in an incomplete representation. To address this issue, we propose a relational complementary module that comprehensively learns the interactions among members from both time-space and space-time perspectives. To suppress the information redundancy caused by this all-view interaction description, we introduce NH-Softmax to impose sparsity on the few relevant attention weights to generate robust and differentiated feature representations. In addition, to fully explore individual contextual interaction information, relaxed attention (RAT) is designed to enhance the feature information of each individual in a relaxed manner. It fleshes out individual representations by highlighting the most salient features and eases the computational burden. Our experiments on Volleyball dataset and Collective Activity dataset show significant improvements over previous state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the discrete inf-sup condition and related error estimates for a modified Hilbert transformation as used in the space-time discretization of time-dependent partial differential equations. It turns out that the stability constant c S depends linearly on the finite element mesh size h. While the ratio c S / h decreases as 1 / T for T → ∞ , numerical results indicate a decay of c S / h ≃ ν − α for some α ∈ [ 1 4 , 1 3 ] in the polynomial degree ν of the finite element basis functions. However, in most cases, we can show optimal convergence. We present a series of numerical experiments which illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper we study long time dynamics (i.e., scattering and blow-up) of solutions for the focusing NLS with a repulsive inverse-power potential and with initial data lying exactly at the mass-energy threshold, namely, when $ E_{V}(u_{0})M(u_{0}) = E_{0}(Q)M(Q) $. Moreover, we prove failure of the uniform space-time bounds at the mass-energy threshold. [ABSTRACT FROM AUTHOR]

The article presents a method of planning the flight trajectory of a swarm of drones using a modified RRT (Rapidly-exploring Random Tree) algorithm. The version of the RRT algorithm presented in the article is called Multiplatform Spacetime RRT*. The proposed modifications make it possible to determine the flight trajectory of UAVs taking into account time constraints related to the area occupied by each platform. Additionally, the proposed algorithm ensures the avoidance of potential collisions of platforms in the air by using a collision avoidance algorithm used in practice based on geometric methods. Two designed and tested modifications of RRT were presented, based on the basic RRT* and Informed RRT* algorithms. The algorithm used in both tested versions guarantees the determination of the optimal flight path for unmanned platforms in a finite, small number of steps, which solely depends on the number of UAVs involved. This algorithm takes into account the dynamic model of the fixed-wing UAV. The simulation results presented by planning the flight trajectory of a swarm, consisting of three and four UAVs using the Multiplatform Spacetime RRT* algorithm, are significantly better than the algorithms that were compared to achieve these results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the well-posedness of weak solutions to the time-fractional Fokker–Planck equation. Its dynamics is governed by anomalous diffusion, and we consider the most general case of space-time dependent forces. Consequently, the fractional derivatives appear on the right-hand side of the equation, and they cannot be brought to the left-hand side, which would have been preferable from an analytical perspective. For showing the model's well-posedness, we derive an energy inequality by considering nonstandard and novel testing methods that involve a series of convolutions and integrations. We close the estimate by a Henry–Gronwall-type inequality. Lastly, we propose a numerical algorithm based on a nonuniform L1 scheme and present some simulation results for various forces. [ABSTRACT FROM AUTHOR]

The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach’s principle. We discuss Mach’s principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach’s principle holds and that there is a fundamental relation between the gravitational constant G and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven.

In this work, a two-dimensional Coupled Map Lattice (CML) method is applied to a continuous Reaction–Diffusion (RD) SIRS epidemic model. The model involves a complex, nonlinear incidence rate and the spatially heterogeneous self- and cross-diffusion coefficients. The CML method applied here results in a space–time discrete counterpart of the model. The basic reproduction number is derived, and the local stability of the fixed points of the discrete model is established. The two typical bifurcations of codimension 1, such as the flip and the Neimark–Sacker (NS) bifurcations, are investigated by utilizing the center manifold theory and the normal form theorem. Furthermore, the codimension-2 fold–flip bifurcation about the endemic fixed point is discussed in detail. Turing instability criterion of the cross-diffusion epidemic model is established by utilizing the CML method under periodic boundary conditions. Finally, the numerical simulations clarify both the effectiveness of all theoretical findings and the effects of time step size and cross-diffusion on the spatiotemporal patterns. The main contribution of this work is the discovery of some interesting Turing and non-Turing patterns which may be induced by flip–Turing instability, NS–Turing instability or fold–flip–Turing instability. Concretely speaking, spiral patterns are observed near the flip bifurcation threshold value and ultimately evolve into an irregular defect pattern. Stripe pattern, labyrinth pattern and circular pattern are observed near the NS bifurcation threshold value. The disorderly interwoven ribbon pattern, mosaic pattern and some irregular oscillatory patterns are observed near the fold–flip bifurcation point. Our results greatly help in predicting the long-term behavior of the space–time discrete SIRS epidemic model under study. [ABSTRACT FROM AUTHOR]

This paper examines the viable characteristics of anisotropic compact stars in f(ℜ,T2) theory (ℜ is the Ricci scalar and T2 = T αβTαβ). In this perspective, we use Tolman–Kuchowicz solutions (μ = wr2 + 2ln z and ν =ln(1 + xr2 + yr4)) to examine the configurations of static spherically symmetric structures. The unknown constants are found by the first fundamental form of Darmois junction conditions. We analyze the behavior of fluid parameters in the interior of 4U 1538-52, PSRJ 1614-220, EXO 1785-248 and SAXJ 1808.4-3658 compact stars correspond to different models of this theory. Furthermore, the stability of the proposed compact stellar objects is examined through sound speed and adiabatic index methods. The satisfaction of requisite conditions ensures that stable compact objects exist in this framework. [ABSTRACT FROM AUTHOR]

This study reveals the implication of charge within the framework of f(G) gravity models by considering the Tolman–Kuchowicz space–time. The use of the Bardeen model to describe the fundamental characteristics of the external geometry is an important aspect of current findings. Moreover, for the qualitative analysis, we compare all the parameters involved in the selected metric potentials with Bardeen’s model. We apply this analysis to the stars PSR1903 + 327, PSR1937 + 21, PSRJ1614 − 2230, 4U608 − 52, VelaX − 1, LMYX − 4, CenX − 3, HERX − 1, SMXJ1808 − 3658 and 4U1820 − 30. We study all the necessary characteristics of stellar structures, such as energy density and pressure progression, equation of state parameters, equilibrium conditions, mass–radius ratio, adiabatic index, and energy conditions. A thorough graphical analysis is provided to establish the viability of the considered f(G) models. It is important to emphasize that our acquired solutions are physically acceptable. [ABSTRACT FROM AUTHOR]

In this paper, we investigate conformal η-Ricci–Yamabe soliton on semiconformally flat Kählerian Norden spacetime in conjunction with the Kählerian Norden torse-forming vector field. Furthermore, we examine various physical aspects of such soliton on special fluid spacetime, such as dust fluid, dark fluid, radiation era, viscous fluid, and heat flux. In addition, we light up the harmonic features of conformal η-Ricci-Yamabe soliton on semiconformally flat Kählerian Norden spacetime. Finally, we also deduce the necessary and sufficient conditions for a 1-form η, which is the g-dual of the vector field ξ on such a spacetime, to be a solution of the Schrödinger-Ricci equation. [ABSTRACT FROM AUTHOR]

This research work discusses the energy bounds in f(R,T) gravity with an anisotropic background, where R is the Ricci scalar and T is the trace of the energy–momentum tensor. For our study, we consider the locally rotationally symmetric Bianchi Type-I space-time. Moreover, we calculate the field equations and find exact solutions by considering different f(R,T) gravity models. We investigate the graphical behavior of energy density and pressure components by considering these distinct gravity models. We further use Hubble, deceleration, jerk, and snap parameters to evaluate the viability of our models. We also perform the graphical analysis to observe the behavior of energy conditions especially null energy conditions, weak energy conditions, strong energy conditions, and dominant energy conditions. It can be noticed that all considered f(R,T) gravity models support the idea of the presence of exotic matter, which justifies the phenomenon of expansion of the universe. [ABSTRACT FROM AUTHOR]

Objectives: In Canada, substance-related accidental acute toxicity deaths (AATDs) continue to rise at the national and sub-national levels. However, it is unknown if, where, when, and to what degree AATDs cluster in space, time, and space–time across the country. The objectives of this study were to 1) assess for clusters of AATDs that occurred in Canada during 2016 and 2017 at the national and provincial/territorial (P/T) levels, and 2) examine the substance types detected in AATD cases within each cluster. Methods: Two years of person-level data on AATDs were abstracted from coroner and medical examiner files using a standardized data collection tool, including the decedent's postal code and municipality information on the places of residence, acute toxicity (AT) event, and death, and the substances detected in the death. Data were combined with Canadian census information to create choropleth maps depicting AATD rates by census division. Spatial scan statistics were used to build Poisson models to identify clusters of high rates (p < 0.05) of AATDs at the national and P/T levels in space, time, and space–time over the study period. AATD cases within clusters were further examined for substance types most present in each cluster. Results: Eight clusters in five regions of Canada at the national level and 24 clusters in 15 regions at the P/T level were identified, highlighting where AATDs occurred at far higher rates than the rest of the country. The risk ratios of identified clusters ranged from 1.28 to 9.62. Substances detected in clusters varied by region and time, however, opioids, stimulants, and alcohol were typically the most commonly detected substances within clusters. Conclusion: Our findings are the first in Canada to reveal the geographic disparities in AATDs at national and P/T levels using spatial scan statistics. Rates associated with substance types within each cluster highlight which substance types were most detected in the identified regions. Findings may be used to guide intervention/program planning and provide a picture of the 2016 and 2017 context that can be used for comparisons of the geographic distribution of AATDs and substances with different time periods. [ABSTRACT FROM AUTHOR]

The Barrow’s Holographic Dark Energy (BHDE) Model is proposed in an axially symmetric anisotropic spacetime which is employing Hubble horizon as an infrared cutoff (IR cutoff). The transition of the universe from a matter dominated era to a dark energy dominated era is investigated in this model. Furthermore, the Equation of State (EoS) parameter explains how the universe evolves with non-extensive term or Barrow parameter Δ for both phase (i) phantom era (ωB ≤−1) and (ii) quintessence era (ωB ≥−1). In order to reconcile the dark energy, the reconstruction of scalar field potential is considered. Some of the physical properties of the model are also described. [ABSTRACT FROM AUTHOR]

Background: Malaria, a prominent vector borne disease causing over a million annual cases worldwide, predominantly affects vulnerable populations in the least developed regions. Despite their preventable and treatable nature, malaria remains a global public health concern. In the last decade, India has faced a significant decline in malaria morbidity and mortality. As India pledged to eliminate malaria by 2030, this study examined a decade of surveillance data to uncover space–time clustering and seasonal trends of Plasmodium vivax and Plasmodium falciparum malaria cases in West Bengal. Methods: Seasonal and trend decomposition using Loess (STL) was applied to detect seasonal trend and anomaly of the time series. Univariate and multivariate space–time cluster analysis of both malaria cases were performed at block level using Kulldorff's space–time scan statistics from April 2011 to March 2021 to detect statistically significant space–time clusters. Results: From the time series decomposition, a clear seasonal pattern is visible for both malaria cases. Statistical analysis indicated considerable high-risk P. vivax clusters, particularly in the northern, central, and lower Gangetic areas. Whereas, P. falciparum was concentrated in the western region with a significant recent transmission towards the lower Gangetic plain. From the multivariate space–time scan statistics, the co-occurrence of both cases were detected with four significant clusters, which signifies the regions experiencing a greater burden of malaria cases. Conclusions: Seasonal trends from the time series decomposition analysis show a gradual decline for both P. vivax and P. falciparum cases in West Bengal. The space–time scan statistics identified high-risk blocks for P. vivax and P. falciparum malaria and its co-occurrence. Both malaria types exhibit significant spatiotemporal variations over the study area. Identifying emerging high-risk areas of P. falciparum malaria over the Gangetic belt indicates the need for more research for its spatial shifting. Addressing the drivers of malaria transmission in these diverse clusters demands regional cooperation and strategic strategies, crucial steps towards overcoming the final obstacles in malaria eradication. [ABSTRACT FROM AUTHOR]

In space-time adaptive processing (STAP), the coprime sampling structure can obtain better clutter suppression capabilities at a lower hardware cost than the uniform linear sampling structure. However, in practical applications, the performance of the algorithm is often limited by the number of training samples. To solve this problem, this paper proposes a fast iterative coprime STAP algorithm based on truncated kernel norm minimization (TKNM). This method establishes a virtual clutter covariance matrix (CCM), introduces truncated kernel norm regularization technology to ensure the low rank of the CCM, and transforms the non-convex problem into a convex optimization problem. Finally, a fast iterative solution method based on the alternating direction method is presented. The effectiveness and accuracy of the proposed algorithm are verified through simulation experiments. [ABSTRACT FROM AUTHOR]

Plagued by heterogeneous clutter, it is a serious challenge for airborne radars to detect low-altitude, weak targets. To overcome this problem, a novel matrix information geometry detector for airborne multi-channel radar is proposed in this paper. The proposed detector applies the given steering vector and array structure information to the matrix information geometry detection method so that it can be used for space–time adaptive detection. While improving the detection performance, the matrix information geometry detector's original anti-clutter advantage is enhanced as well. The simulation experiment results indicate that the proposed detector has advantages in several of the properties related to space–time adaptive detection, while its computational complexity does not increase significantly. Moreover, experiment results based on the measured data verify the superior performance of the proposed method. Sea-detecting data-sharing-program data, mountaintop data, and phased-array radar data are employed to verify the performance advantage of the proposed method in heterogeneous clutter and the ability for weak target detection. [ABSTRACT FROM AUTHOR]

In this paper, the fractional space-time nonlinear Chen-Lee-Liu equation has been considered using various methods. The investigation of the transition from periodic to quasi-periodic behavior has been conducted using a saddle-node bifurcation approach. The paper reports the conditions of multi-dimensional bifurcations of dynamical solutions. Additionally, a direct algebraic method has been used to calculate various 2D and 3D solitonic structures of the equation, and an analysis of their accuracy and effectiveness has been conducted. Furthermore, the Galilean transformation has been used to convert the equation into a planar dynamical system, which is further utilized to obtain bifurcations and chaotic structures. Chaotic structures of perturbed dynamical system are observed and detected through chaos detecting tools such as 2D-phase portrait, 3D-phase portrait, time series analysis, multistability and Lyapunov exponents over time. Further, sensitivity behavior for a range of initial conditions, both perturbed and unperturbed. The results suggest that the investigated equation exhibits a higher degree of multi-stability. [ABSTRACT FROM AUTHOR]

We prove that the time of classical existence of smooth solutions to the relativistic Euler equations can be bounded from below in terms of norms that measure the "(sound) wave-part" of the data in Sobolev space and "transport-part" in higher regularity Sobolev space and Hölder spaces. The solutions are allowed to have nontrivial vorticity and entropy. We use the geometric framework from [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré20(7) (2019) 2173–2270], where the relativistic Euler flow is decomposed into a "wave-part", that is, geometric wave equations for the velocity components, density and enthalpy, and a "transport-part", that is, transport-div-curl systems for the vorticity and entropy gradient. Our main result is that the Sobolev norm H 2 + of the variables in the "wave-part" and the Hölder norm C 0 , 0 + of the variables in the "transport-part" can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption H 2 + is the optimal result for the variables in the "wave-part". Compared to low-regularity results for quasilinear wave equations and the three-dimensional (3D) non-relativistic compressible Euler equations, the main new challenge of the paper is that when controlling the acoustic geometry and bounding the wave equation energies, we must deal with the difficulty that the vorticity and entropy gradient are four-dimensional space-time vectors satisfying a space-time div-curl-transport system, where the space-time div-curl part is not elliptic. Due to lack of ellipticity, one cannot immediately rely on the approach taken in [M. M. Disconzi and J. Speck, The relativistic Euler equations: Remarkable null structures and regularity properties, Ann. Henri Poincaré20(7) (2019) 2173–2270] to control these terms. To overcome this difficulty, we show that the space-time div-curl systems imply elliptic div-curl-transport systems on constant-time hypersurfaces plus error terms that involve favorable differentiations and contractions with respect to the four-velocity. By using these structures, we are able to adequately control the vorticity and entropy gradient with the help of energy estimates for transport equations, elliptic estimates, Schauder estimates and Littlewood–Paley theory. [ABSTRACT FROM AUTHOR]

This paper investigates the space-time residual-based a posteriori error bounds of the mixed finite element method for the optimal control problem governed by the parabolic equation in a bounded convex domain. For the spatial discretization of the state and co-state variables, the lowest-order Raviart-Thomas spaces are utilized, although for the control variable, variational discretization technique is used. The backward-Euler implicit method is applied for temporal discretization. To provide a posteriori error estimates for the state and control variables in the L ∞ (L 2) -norm, an elliptic reconstruction approach paired with an energy strategy is utilized. The reliability and efficiency of the a posteriori error estimators are discussed. The effectiveness of the estimators is finally confirmed through the numerical tests. [ABSTRACT FROM AUTHOR]

Empirical science has traditionally deemed itself unqualified to address the topic of immortality, viewing it as beyond its purview. However, in recent times, numerous proponents of the transhumanism movement have posited the potential for fostering a form of immortality within the confines of space-time. The most prevalent proposition involves adopting an algorithmic understanding of the human mind and attempting to substitute the conventional biological substrate with an electronic one. Other endeavors focus on combating the typical causes of aging and death through the advancements of scientific progress. An objective scrutiny of these methodologies reveals them to be implausible. [ABSTRACT FROM AUTHOR]

Beginning from the standard Arnowitt–Deser–Misner (ADM) formulation of general relativity we construct a tentative model of quantum gravity from the point of view of an observer with constant proper acceleration, just outside of a horizon of spacetime. In addition of producing the standard results of black-hole thermodynamics, our model makes an entirely new prediction that there is a certain upper bound for the energies of massive particles. For protons, for instance, this upper bound is around 1.1 × 10 21 eV. The result is interesting, because this energy is roughly of the same order of magnitude as are the highest energies ever measured for protons in cosmic rays. [ABSTRACT FROM AUTHOR]

According to studies by the Intergovernmental Panel on Climate Change (IPCC), tropical mountainous areas are experiencing increasingly unfavorable climatic conditions regarding geohazards due to a heightened occurrence of intense rainfall events. These climatic shifts contribute to heightened geological risks, notably an elevated frequency of landslides, exacerbating the challenges faced by these regions. There is an urgent need to understand and measure how rainfall variability affects geo-hydrological hazards, which remain difficult to determine and predict. The complex and non-linear space-time relationships and dynamics of rainfall, El Niño-Southern Oscillation (ENSO), and landslides in the Tropical Andean Mountain region in Colombia require an adequate analysis and understanding of their link in terms of its spatial and temporal component at different scales. By evaluation in annual, seasonal, and monthly scales, additional insights on the relationships using a wavelet spectral analysis and a space-time permutation scan statistics method using SaTScan™ are provided. In this study, a space-time and frequency analysis of landslides using a 42-year (1981–2022) rainfall and Multivariate ENSO Index v2.0 time series is presented. According to the results, landslides closely aligned with rainfall patterns, exhibiting a bimodal annual cycle. The ENSO added complexity, with La Niña years leading to more frequent landslides throughout the year and El Niño years showing concentrated occurrences in specific months. This study highlights the influence of rainfall patterns and antecedent rainfall on landslide occurrence, the impact of ENSO phases on rainfall and landslides, and the increasing trend of landslides in Colombia. [ABSTRACT FROM AUTHOR]

The determination of transport schemes represents a critical facet of operational management in express freight logistics and constitutes a significant scientific challenge within the domain of freight transportation. Globally, there is an escalating focus on adopting low-carbon transit strategies, and it has been established that multimodal transport methods can significantly diminish carbon emissions associated with freight transportation. Moreover, the scheduled arrival and departure times for railway and aviation are pivotal in shaping the selection of transport schemes. Regrettably, these critical considerations are frequently neglected in the prevailing body of research. This paper endeavors to bridge this research gap by advocating for a lowcarbon transport scheme for express freight through the utilization of an integrated transportation system. It undertakes a collaborative optimization study concerning transportation modes and routes. This document proposes an optimization framework for the selection of express freight transport schemes that incorporates considerations for carbon emissions and fixed timetables. A three-layer service network is developed, integrating the fixed schedules of railway and aviation to formulate a space-time shortest path problem aimed at minimizing the generalized transportation cost. Three models are formulated to reduce the transportation costs and carbon emissions of logistics enterprises, taking into account diverse carbon emission policies. Subsequently, a two-stage heuristic algorithm is introduced to address this complex problem. The findings reveal that by accounting for customers' transportation time constraints and judiciously selecting transportation modes and routes, it is feasible to effectively minimize transportation costs and carbon emissions. [ABSTRACT FROM AUTHOR]

While (2+1)$(2+1)$‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment k$k$ is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher k$k$ resembles that in four‐dimensional spacetime with the corresponding asymptotic. While (2 + 1)‐dimensional black holes in the Einstein theory allow for only the anti‐de Sitter (AdS) asymptotic, when the higher curvature correction is tuned on, the asymptotically flat, de Sitter, and AdS cases are included. Here, a detailed study of the stability and quasinormal spectra of the scalar field perturbations around such black holes with all three asymptotics is proposed. Calculations of the frequencies are fulfilled with the help of the 6th order Wentzel–Kramers–Brillouin (WKB) method with Pade approximants, Bernstein polynomial method, and time‐domain integration. Results obtained by all three methods are in a very good agreement in their common range of applicability. When the multipole moment k is equal to zero, the purely imaginary, i.e., non‐oscillatory, modes dominate in the spectrum for all types of the asymptotic behavior, while the spectrum at higher k resembles that in four‐dimensional spacetime with the corresponding asymptotic. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime within the Lambda Cold Dark Matter (Λ CDM) model. Using the radial free motion solutions, we provide two methods for characterizing the geodesics and defines a general formula that encapsulates all possible solutions, determined by two initial conditions. We show that the past light cone, event horizon, and particle horizon, can be considered as special cases of this overarching formula. Furthermore, the paper explores the free geodesics within the currently accepted cosmological model based on the recent Planck results, thoroughly examining the various possible geodesic scenarios. [ABSTRACT FROM AUTHOR]

Differentiation of the scalar Feynman propagator with respect to the spacetime coordinates yields the metric on the background spacetime that the scalar particle propagates in. Now Feynman propagators can be modified in order to include quantum-gravity corrections as induced by a zero-point length L > 0. These corrections cause the length element s 2 to be replaced with s 2 + 4 L 2 within the Feynman propagator. In this paper, we compute the metrics derived from both the quantum-gravity free propagators and from their quantum-gravity corrected counterparts. We verify that the latter propagators yield the same spacetime metrics as the former, provided one measures distances greater than the quantum of length L. We perform this analysis in the case of the background spacetime ℝ D in the Euclidean sector. [ABSTRACT FROM AUTHOR]

It is generally assumed that compatibility with special relativity is guaranteed by the invariance of the fundamental equations of quantum physics under Lorentz transformations and the impossibility of transferring energy or information faster than the speed of light. Despite this, various contradictions persist, which make us suspect the solidity of that compatibility. This paper focuses on collapse theories—although they are not the only way of interpreting quantum theory—in order to examine what seems to be insurmountable difficulties we encounter when trying to construct a space–time picture of such typically quantum processes as state vector reduction or the non-separability of entangled systems. The inescapable nature of such difficulties suggests the need to go further in the search for new formulations that surpass our current conceptions of matter and space–time. [ABSTRACT FROM AUTHOR]

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, r → r − e H t a , where H is the Hubble parameter. For H → 0 , this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations r → r − a . Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature T = H / π , which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature T = H / π determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, S hor = 4 π K A , where K = 1 / (16 π G) . This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the f (R) gravity. In this thermodynamics, the Ricci scalar curvature R and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling K = d f / d R . Such a connection takes place only in the 3 + 1 spacetime, where there is a special symmetry due to which the variables K and R have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes. [ABSTRACT FROM AUTHOR]

We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as Z ∼ T 3 2 e S 0 + c log S 0 , with S0 the classical degeneracy and c a numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficient c. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify. [ABSTRACT FROM AUTHOR]

Space and time, which should properly be taken conjointly, are both communicatively produced and created with certain contextual perspectives—they are not independent physical entities. The standpoint of production makes the relationship between space and time comprehensible. They can either be mental-subjective, physical-objective, or social-intersubjective. Social and intersubjective (or E-series) spacetime might shed new light on biological thinking. For general readers, this paper provides a clue regarding an alternative conceptualization of spacetime based on biology. [ABSTRACT FROM AUTHOR]

We describe laboratory experiments in a 2D wave tank that aim at building up and monitor 2D shallow water soliton gas. The water surface elevation is obtained over a large ( ∼ 100 m 2 ) domain, with centimeter-resolution, by stereoscopic vision using two cameras. Floating particles are seeded to get surface texture and determine the wave field by image correlation. With this setup, soliton propagation and multiple interactions can be measured with a previously unreachable level of detail. The propagation of an oblique soliton is analyzed, and the amplitude decay and local incidence are compared to analytical predictions. We further present two cases of 2D soliton gas, emerging from multiple line solitons with random incidence ( | θ | < 30 ∘ ) and from irregular random waves forced with a JONSWAP spectrum ( | θ | < 45 ∘ ). To our knowledge, those are the first observations of random 2D soliton gas for gravity waves. In both cases, Mach reflections and Mach expansions result in solitons that mainly propagate in directions perpendicular to the wavemakers. [ABSTRACT FROM AUTHOR]

In the present paper, it has been obtained that the fundamental group of n -dimensional Minkowski space with the time topology contains uncountably many copies of the additive group of integers and is not abelian. The result has been first proved for n = 2. Thereafter, it is extended to n > 2 by proving that loops nonhomotopic in M 2 continue to be nonhomotopic in Mn using embedding of M 2 in Mn as a retract through the projection map. [ABSTRACT FROM AUTHOR]

The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some certain conditions. We have gone on to refine the classification of the potential function with respect to gradient h-almost conformal η-Ricci-Bourguignon soliton in a perfect uid spacetime with torse-forming vector field ξ. Finally, we have developed an example of h-almost conformal η-Ricci-Bourguignon soliton. [ABSTRACT FROM AUTHOR]

Liberal theories of property assume a linear and serialized temporal orientation facilitated by title registries, recording systems, and the exaltation of land archives. These assumptions, what I call 'property-time', can be productively put into relation with dominant geographic theories of space in two ways. First, I argue that distinguishing liberal notions of property-time from geographic space–time allows us to observe a key dialectic involving the attachment of value (and capital) to space, a process that tracks alongside contradictions of capitalist desire: the desire to continually reshape space (becoming) and to extract enduring and permanent, individuated value from it (being). Second, liberal temporalities of property struggle to apply in illiberal global contexts. Here, states enact urban accumulation regimes that deviate from linear, individuated and sequential notions of property by manipulating records and surgically erasing past ownership. These acts are often characterized as forms of state variegation and provisionality. They are also endemic to how both capital and value are created and/or arbitraged by states through the land regime. These formations remain difficult to connect to traditional theories about the production of value under capital because assumed time logics of property limit our theoretical capacity to describe illiberal urban accumulation regimes. [ABSTRACT FROM AUTHOR]

We investigate the geometry of space-time prisms and their associated potential path areas (for movement that takes place in the plane) in the setting where the prism anchors have a spatial uncertainty area attached to them. Our main result is a characterisation of such space-time prisms and their potential path areas in terms of a generalised distance function between closed subsets of the ambient space. Since the case where this spatial anchor uncertainty takes the form of a closed disk has already been addressed by Kuijpers and Othman (2017), we focus on the more realistic case where the uncertainty areas are ellipses and we apply our general characterisation to this example to obtain explicit descriptions of the uncertain prisms and their potential path areas. [ABSTRACT FROM AUTHOR]

In this article, we consider the nonlinear stochastic partial differential equation of fractional order in both space and time variables with constant initial condition: \begin{equation*} \left (\partial ^{\beta }_t+\dfrac {\nu }{2}\left (-\Delta \right)^{\alpha / 2}\right) u(t, x) = \: I_{t}^{\gamma }\left [\lambda u(t, x) \dot {W}(t, x)\right ] \quad t>0,\: x\in \mathbb {R}^d, \end{equation*} with constants \lambda \ne 0 and \nu >0, where \partial ^{\beta }_t is the Caputo fractional derivative of order \beta \in (0,2], I_{t}^{\gamma } refers to the Riemann-Liouville integral of order \gamma \ge 0, and \left (-\Delta \right)^{\alpha /2} is the standard fractional/power of Laplacian with \alpha >0. We concentrate on the scenario where the noise \dot {W} is the space-time white noise. The existence and uniqueness of solution in the Itô-Skorohod sense is obtained under Dalang's condition. We obtain explicit formulas for both the second moment and the second moment Lyapunov exponent. We derive the p-th moment upper bounds and find the matching lower bounds. Our results solve a large class of conjectures regarding the order of the p-th moment Lyapunov exponents. In particular, by letting \beta = 2, \alpha = 2, \gamma = 0, and d = 1, we confirm the following standing conjecture for the stochastic wave equation: \begin{align*} \frac {1}{t}\log \mathbb {E}[|u(t,x)|^p ] \asymp p^{3/2}, \quad \text {for p\ge 2 as t\to \infty.} \end{align*} The method for the lower bounds is inspired by a recent work of Hu and Wang, where the authors focus on the space-time colored Gaussian noise case. [ABSTRACT FROM AUTHOR]

In this article, new traveling wave solutions are retrieved for two space-time fractional models: the resonant nonlinear Schrödinger equation and the Biswas–Milovic equation which illustrates the dynamics of optical soliton promulgation in optical fibers, both featuring Kerr law nonlinearity. These equations are explored via an efficient method namely, the extended simple equation method. The fractional derivative is used in the conformable sense to accomplish this analysis. The extracted solutions show dark, periodic, singular, and singular-periodic solitons behaviors, which are depicted graphically by using line, surface, and contour plots. The reported solutions are unique and novel. The proposed method distinguishes itself by its simplicity, reliability, and ability to generate novel soliton solutions for nonlinear Schrödinger equations within the realm of mathematical physics. [ABSTRACT FROM AUTHOR]

Female domestic workers (FDWs) experience space–time constraints and mobility challenges corresponding to their demanding daily work responsibilities. Studies have shown that FDWs' mobility and activities are primarily dictated by their employers through work tasks. It is unclear, though, how FDWs' activity and mobility patterns outside their employers' homes are shaped by individual and contextual factors, including government policies that mandate that FDWs be granted a rest day. Using an activity space approach combined with multilevel modeling, I evaluated mobility and activity patterns on work and rest days for a sample of Indonesian FDWs in Hong Kong. Data were collected using innovative online activity diaries and were triangulated with qualitative data from WhatsApp follow-up conversations. This research uncovers that FDWs' activity patterns differ significantly between work and rest days. FDWs rarely go outside on workdays except to perform work-related tasks. On the rest day, FDWs' activity spaces are much more expansive as they conduct social and personal activities that are essential for maintaining their well-being. By comparing work and rest days, this research deepens our understanding of geographical, social, and temporal aspects of FDWs' space–time constraints and (im)mobility experiences that encompass and go beyond employer-assigned tasks. Furthermore, the findings demonstrate the benefits of rest day policies for enhancing the visibility of marginalized women in public spaces, particularly in the context of FDWs' restrictive space–time constraints. [ABSTRACT FROM AUTHOR]

We investigate the response of Casimir energies to fluctuations in a scalar field in the background of a weak gravitational field in κ -deformed space-time. We model the Casimir plates in a gravitational field by κ -deformed Rindler coordinates and calculate the Casimir energy using the κ -deformed scalar field. We show that the Casimir energy accelerates in a weak gravitational field like a mass. Thus, our calculations show that the mass–energy equivalence principle holds in κ -deformed space-time even though a length scale is introduced through space-time non-commutativity. [ABSTRACT FROM AUTHOR]

For active volcanoes, knowledge of the architecture of the plumbing system and the conditions of magma storage prior to an eruption are highly important, given their influence on the eruptive style and, thus, the management of future volcanic crises. Here, chlorine is used as a geobarometer for potassic alkaline magmas at the Campi Flegrei volcanic complex, revealing the shallowest depth of fluid-melt equilibration with respect to Cl. The results for representative fallout deposits of selected explosive eruptions show the existence of a multi-depth equilibration zone through time, including shallow magma storage. We describe evidence for the shallowest zone located at a depth equivalent to 65 MPa for the Agnano Monte Spina eruption (4482–4625 cal. yrs BP), at ~100 MPa for the Pomici Principali (11 915–12 158 cal. yrs BP), and the Astroni 6 (4098–4297 cal. yrs BP) eruptions, and close to 115 MPa for the last explosive eruption of Monte Nuovo (AD 1538). For comparison, the pressure estimated for a possible reservoir feeding the Cretaio eruption of Ischia island (AD 430), the only studied eruption on Ischia, is ~140 MPa. The pressure estimates for the two largest magnitude eruptions, the Campanian Ignimbrite (40 ka) and the Neapolitan Yellow Tuff (14.9 ka), are also discussed with respect to available magma withdrawal models. The pressures estimated using the Cl geobarometer for the magma leading to the fallout phases of these two eruptions provide evidence for a low-volume, shallow domain (~40 MPa) for the Plinian phase of the Campanian Ignimbrite eruption and a main, deeper reservoir (~130–165 MPa) for the Neapolitan Yellow Tuff eruption. The inferred shallowest equilibration pressures are interpreted here as corresponding to transitory, short-lived magma apophyses, whose eruption may have been facilitated by optimum tectonic stresses, rheological behavior of the crust, and efficiency of volatile exsolution. Alternatively, these magma apophyses may represent an evolved, crystal-rich ponded magma into which a volatile-rich magma ascending from depth was injected. The transient nature of such very shallow reservoirs is suggested by the short timescales inferred from diffusion modeling on crystals available in the literature for the studied Campi Flegrei eruptions. The influence of sulfur (S) on Cl solubility is assessed through Cl solubility modeling and applied to different eruptions. In addition, the pressure at which magmatic fluids and melts equilibrated with respect to Cl is shallower for the Campi Flegrei volcanic complex than the Somma-Vesuvio volcanic complex, erupting more homogeneous differentiated magma, of trachytic or phonolitic composition. This approach of using Cl to investigate the architecture of the plumbing system can be extended to all alkali-rich magma systems. [ABSTRACT FROM AUTHOR]

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