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Lack of data on the population size of chimpanzees (Pan troglodytes) in the Yoko Council Forest (YCF), located in the Centre region of Cameroon has hindered the ability to develop conservation measures. The sustainable management of this species requires reliable knowledge of their ecology, habits and resource needs. This study was conducted from February–July 2022 to assess nesting ecology and to use nest decay rates to estimate population size. The retrospective method for studying the degradation of animal indices was used. The mean nest decay rate was 77.5 days and density was estimated at 69.3 [54.9 86.7] nests/ km2 to 113 chimpanzees per km2. We also found a high preference for nests in specific forest types, with 92% of nests in marantaceous forests, and a preference for nests to be on Khaya grandifolia (Meliaceae) (28.24%) or Uapaca guinensis (Euphorbiaceae) (27.06%) trees. The preferential position for construction of chimpanzee nests was on a branch (58.82%) as opposed to in a branch fork (40.39%), which is interesting since one would assume a fork would offer more nest stability. Our study offers crucial insights that can guide policymakers in formulating targeted conservation strategies for the substantial chimpanzee population in the YCF. [ABSTRACT FROM AUTHOR]

In this paper, we prove an interpolation inequality on Riemann–Liouville fractional integrals and then use it to study the strong stability and semi-uniform stability of fractional resolvent families of order 0 < α < 2 . Let A denote the generator of a bounded fractional resolvent family. We show that if σ (A) ∩ (i R) α is countable and σ r (A) ∩ (i R) α = ∅ , then the bounded fractional resolvent family is strongly stable. And the semi-uniform stability of the fractional resolvent family is equivalent to σ (A) ∩ (i R) α = ∅ . Moreover, the relation between decay rates of semi-uniform stability and growth of the resolvent of A along (i R) α is given. [ABSTRACT FROM AUTHOR]

In this study, our primary emphasis lies in examining and exploring the decay rate of solutions of a Lord‐Shulman thermoelastic Timoshenko model with microtemperature impact. Through the application of the energy method within the Fourier space and subject to appropriate assumptions, we prove that the decay rate of the solution is of the form (1+t)−18$$ {\left(1&#x0002B;t\right)}&#x0005E;{-\frac{1}{8}} $$ in the case of absence of mechanical damping term. [ABSTRACT FROM AUTHOR]

The standard model Higgs boson has various decay modes, some of which have been measured in the CMS and ATLAS experiments, located at the Large Hadron Collider at CERN. This paper, calculates the decay of the standard model Higgs boson into D ∗ ± meson through the mechanism direct fragmentation. In this approach, the Higgs boson, first decays into c c ¯ and b b ¯ pairs, and then the heavy quarks fragment directly into D ∗ ± meson. The branching ratios of the SM Higgs boson into D ∗ ± meson have been calculated by considering NLO and NNLO corrections in the fragmentation functions of D ∗ ± . [ABSTRACT FROM AUTHOR]

This paper investigates the stability problem and large time behavior of solutions to the three‐dimensional magnetohydrodynamic equations with horizontal velocity dissipation and magnetic diffusion only in the x2$x_2$ direction. By applying the structure of the system, time‐weighted methods, and the method of bootstrapping argument, we prove that any perturbation near the background magnetic field (1, 0, 0) is globally stable in the Sobolev space H3(R3)$H^3(\mathbb {R}^3)$. Furthermore, explicit decay rates in H2(R3)$H^2(\mathbb {R}^3)$ are obtained. Motivated by the stability of the three‐dimensional Navier–Stokes equations with horizontal dissipation, this paper aims to understand the stability of perturbations near a magnetic background field and reveal the mechanism of how the magnetic field generates enhanced dissipation and helps stabilize the fluid. [ABSTRACT FROM AUTHOR]

This paper studies the problems of stability analysis and stabilisation synthesis for a class of impulsive switched stochastic systems. By constructing a novel impulsive switching condition, the sufficient conditions of globally asymptotic stability in probability and stochastic input-to-state stability for the considered systems are presented. Furthermore, the stabilising controller design method can be presented for the corresponding closed-loop systems. Two examples are given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this article, we aim to establish the optimal time decay rates of strong solutions to a two-phase flow model derived from a type of coupled fluid-kinetic equation. It is proved that the strong solutions converge to the given constant states with algebraic time decay rates under some additional assumptions on the initial data.

The generalized three dimensional Navier–Stokes equations with damping are considered. Firstly, existence and uniqueness of strong solutions in the periodic domain T 3 are proved for 1 2 < α < 1 , β + 1 ≥ 6 α 2 α - 1 ∈ (6 , + ∞) . Then, in the whole space R 3 , if the critical situation β + 1 = 6 α 2 α - 1 and if u 0 ∈ H 1 (R 3) ⋂ H ˙ - s (R 3) with s ∈ [ 0 , 1 / 2 ] , the decay rate of solution has been established. We give proofs of these two results, based on energy estimates and a series of interpolation inequalities, the key of this paper is to give an explanation for that on the premise of increasing damping term, the well-posedness and decay can still preserve at low dissipation α < 1 , and the relationship between dissipation and damping is given. [ABSTRACT FROM AUTHOR]

In this work, we prove a nonlocal Halanay inequality with an exact decay rate. This enables us to analyze behavior of solutions to some classes of nonlocal ODEs and PDEs involving unbounded delays. The obtained results extend and improve the previous ones proved for fractional differential equations and other nonlocal subdiffusion equations. [ABSTRACT FROM AUTHOR]

The present study examines the effect of storage conditions on the characteristics of cryogenic hydrogen jets released into the atmosphere, relevant to an accidental leakage scenario during storage or transportation. The compressible Reynolds-Averaged Navier–Stokes equations, coupled with the Peng–Robinson equation of state for hydrogen-air mixtures, are solved for a range of operating conditions (storage pressures from 3 – 7 bar and storage temperatures of 50 – 70 K). Flow structures in the near-orifice and self-similar regions are analysed, showing that the presence of shock waves creates conditions favourable for possible condensation of hydrogen and air. In the self-similar region, decay laws based on the shock exit conditions are proposed, demonstrating a slower decay of centreline temperature in comparison to hydrogen concentration and velocity. Additionally, a universal relationship between the centreline mole fraction of hydrogen and temperature is observed, explained using an adiabatic mixing model. [Display omitted] • Numerical simulations of cryogenic hydrogen jet dispersion are performed. • Shock waves in the near-orifice region create conditions conducive to condensation of air. • Scaling of far-field flow quantities using shock exit conditions is more appropriate than using orifice exit conditions. • A universal relationship between the centreline mole fraction of hydrogen and temperature is found. • The found universal relationship can be explained by considering adiabatic mixing between hydrogen and air. [ABSTRACT FROM AUTHOR]

Persistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersion ∂tu+(−1)j+1∂x2j+1u=∂xu2k+1,$$\begin{equation*} \partial _{t} u+(-1)^{j+1}\partial _{x}^{2j+1} u= \partial _x{\left(u^{2k+1} \right)}, \end{equation*}$$where j≥2$j\ge 2$, k≥1$k\ge 1$ are integers. For a class of analytic initial data with a fixed radius of analyticity σ0$\sigma _0$, we show that the uniform radius of spatial analyticity σ(t)$\sigma (t)$ of solutions at time t$t$ cannot decay faster than 1t$\frac{1}{\sqrt t}$ as t→∞$t\rightarrow \infty$. In particular, this improves a recent result due to Petronilho and Silva [Math. Nachr. 292 (2019), no. 9, 2032–2047] for the modified Kawahara equation (j=2$j=2$, k=1$k=1$), where they obtained a decay rate of order t−4+$ t^{-4 +}$. Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates. [ABSTRACT FROM AUTHOR]

On 6 February 2023, Türkiye experienced a pair of consecutive earthquakes with magnitudes of Mw 7.8 and 7.5, and accompanied by an intense aftershock sequence. These seismic events were particularly impactful on the segments of the East Anatolian Fault Zone (EAFZ), causing extensive damage to both human life and urban centers in Türkiye and Syria. This study explores the analysis of a dataset spanning almost one year following the Turkiye mainshocks, including 471 events with a magnitude of completeness (Mc) ≥ 4.4. We employed the maximum likelihood approach to estimate the b-value and Omori-Utsu parameters (K, c, and p-values). The estimated b-value is 1.21 ± 0.1, indicating that the mainshocks occurred in a region characterized by elevated stress levels, leading to a sequence of aftershocks of larger magnitudes due to notable irregularities in the rupture zone. The aftershock decay rate (p-value = 1.1 ± 0.04) indicates a rapid decrease in stress levels following the main shocks. However, the c-value of 0.204 ± 0.058 would indicate a relatively moderate or low initial productivity of aftershocks. Furthermore, the k-value of 76.75 ± 8.84 suggests that the decay of aftershock activity commenced within a range of approximately 68 to 86 days following the mainshocks. The fractal dimension (Dc) was assessed using the correlation integral method, yielding a value of 0.99 ± 0.03. This implies a tendency toward clustering in the aftershock seismicity and a linear configuration of the epicenters. The slip ratio during the aftershock activity was determined to be 0.75, signifying that 75% of the total slip occurred in the primary rupture, with the remaining fraction distributed among secondary faults. The methodologies and insights acquired in this research can be extended to assist in forecasting aftershock occurrences for future earthquakes, thus offering crucial data for future risk assessment. [ABSTRACT FROM AUTHOR]

AbstractPatterns created by buckling of thin films on substrates have important applications in many fields such as functional devices and surface engineering. Introducing hierarchy to such patterns may further enhance their functionalities. However, unpredictable geometrical and material defects may disturb the formation of patterns. It is thus attractive to construct robust hierarchical buckling patterns that are insensitive to defects. Here, inspired by the construction of topologically protected localized states insensitive to defects in wave mechanics, a thin film of finite length bonded on a simple Winkler substrate is quantitatively designed by just varying its width continuously. Under the action of specific compressive stresses within such a continuous thin film owing to thermal mismatch between the film and substrate, there really exists a hierarchical film-buckling mode generated by topologically protected localization. Conditions under which the topologically protected localization exists are given explicitly, and the underlying mechanism is intuitively demonstrated from the mechanical point of view. Moreover, an analytical solution for the decay rate of localization is obtained as a satisfactory second-order approximation, from which the associated influencing factors are clearly identified. This work is expected to provide a theoretical guidance for the design and optimization of hierarchical patterns in film/substrate systems via the concept of topology. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability of planar viscous shock wave for the 3-dimensional compressible Navier-Stokes-Poisson (NSP) system in the domain Ω : = R × T 2 with T 2 = (R / Z) 2. The stability problem of viscous shock under small 1-dimensional perturbations was solved in Duan-Liu-Zhang [7]. In this paper, we prove the viscous shock is still stable under small 3-d perturbations. Firstly, we decompose the perturbation into the zero mode and non-zero mode. Then we can show that both the perturbation and zero-mode time-asymptotically tend to zero by the anti-derivative technique and crucial estimates on the zero-mode. Moreover, we can further prove that the non-zero mode tends to zero with exponential decay rate. The key point is to estimate the non-zero mode of nonlinear terms involving electronic potential, see Lemma 6.1 below. [ABSTRACT FROM AUTHOR]

Gelatinous zooplankton (GZ) biomass is an important, yet often overlooked, vector of the particulate organic matter downward export and a nutritional prey source for the mesopelagic and benthic communities. To better quantify the potential impact of their blooms on biogeochemistry and food webs, we performed decomposition and sinking experiments under two different temperature regimes, 6 and 12 °C using 260 Salpa aspera, sampled in the Northeast Pacific (48.39°–50.40°N, 126.40°–145.00°W) during May 2021. Salps sank 1312 and 1424 m day−1 on average in 6 and 12 °C, respectively. The fast sinking is common among other salp species. Salp decay was exponential and occurred ~ 1.5 times faster under warmer conditions. Comparison of the published GZ decay rates supported their strong temperature dependence (Q10 = 3.46) and revealed that S. aspera decayed slower than most GZ taxa. Carcass sinking rates were higher than previously reported for this species and slowed after a prolonged decay. Biochemical (proteins, carbohydrates, lipids) and elemental (C: carbon, N: nitrogen) compositions were determined for salps at various decomposition stages. The high water content (~ 97%) and low organic content (27.8 ± 7.1% dry weight) were typical of other thaliaceans. The high C:N ratio (6.61 ± 1.14) of S. aspera, compared to many thaliaceans, suggested that their carcasses are valuable sources of carbon beyond the euphotic zone. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the nonlinear MGT plate equation in the unbounded domain. By using semigroup theory, we first establish the well-posedness result for the Cauchy problem related to the linear MGT plate equation. By using the energy method in the Fourier space, we then prove the optimal decay estimate results for the non-critical case, in which the optimality is analyzed by considering the asymptotic expansion of the eigenvalues. By using the contraction mapping, we also show the local existence for the Cauchy problem of the nonlinear plate in appropriate function spaces, based on which we prove a global existence result for small data by using a priori energy estimates. Finally, based on the decay estimation of linear problems, the decay results of nonlinear problems are obtained. [ABSTRACT FROM AUTHOR]

We investigate the local-in-time existence results of classical solutions to the 3D (Hall-)MHD equations with power-law type nonlinear viscous fluid when magnetic resistance is vanished and also show the global-in-time existence of classical solutions under small initial data. Moreover, we prove the space-time decay property for these solutions. [ABSTRACT FROM AUTHOR]

In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Timoshenko system with Lord-Shulman’s heat conduction is sufficiently robust to stabilize the system, albeit with a gradual decay rate. To support our findings, we convert the system into a first-order form and, utilizing the energy method in Fourier space, and derive point wise estimates for the Fourier transform of the solution. These estimates, in turn, provide evidence for the slow decay of the solution.

Abstract The significance of water in public health cannot be overemphasized. In Nigeria, many people living along the courses of water bodies still source and drink from the rivers and streams. There is, therefore, the need to determine the load of contamination and effect of pH and salinity on the decay rate of enteric bacteria in water samples from River Owena, Owena, Nigeria, in order to develop adequate water quality management. Water samples from River Owena were collected from three sampling points (inflow, middle course and the outflow) along the River Owena, Nigeria. The load of enteric bacteria in the water samples was enumerated using membrane filtration technique. The physicochemical parameters of the water samples were determined using standard methods. The incidence and prevalence of gastroenteritis in the community around River Owena was determined using a structured questionnaire. Microcosm studies were used to determine the decay rate of enteric bacteria at varying salinity and pH. Canonical correlation analysis was used to describe the relationship between the load of enteric bacteria and the incidence and prevalence of gastroenteritis in the community around River Owena. The incidence and prevalence of gastroenteritis in the community around River Owena were estimated to be 0.75 and 0.51, respectively. Escherichia coli had positive relationships with incidence (r = 0.76) and prevalence (r = 0.65). Similarly, faecal coliforms had positive relationships with incidence (r = 0.82) and prevalence of gastroenteritis (r = 0.67), while enterococci showed positive relationship with incidence (r = 0.59) and prevalence of gastroenteritis (r = 0.87). Increase in pH and salinity increased the decay rate of enteric bacteria thereby reducing the growth of enteric bacteria, the optimum pH for the growth and survival of enteric bacteria ranged between pH 5.0 and pH 7.0. The optimum salinity for the growth of enteric bacteria isolated in water samples from River Owena ranged between 10 and 50% salinity. Findings revealed high levels of faecal contamination at the different representative monitoring points on River Owena, pH and salinity influenced the load and decay rate of enteric bacteria in water from River Owena.

The study of non-circular jet flows has become important due to their various applications, such as aircraft exhaust, combustion chambers and injectors. The present paper examines the impact of elliptical, square, and triangular-shaped orifices on the mixing characteristics of a free jet with Mach number 0.8. Numerical simulations using an SST K-1 two-equation turbulence model were conducted with a Reynolds number of 3.46×105 for all cases. The mean velocity, decay rate, half-velocity width, spread rate, and turbulence intensity of the jet were analysed. The results showed that the triangular orifice provided the best mixing efficiency, with a shorter jet core length. The decay rate was found to be lowest for the square jet and highest for the triangular jet, which matches the previous research. The asymmetric jets experienced two axis-switching points, while the square jet experienced a 450 rotation of its axes but no axis-switching. The core region had lower turbulence levels, while the highest turbulence levels were in the shear layer. [ABSTRACT FROM AUTHOR]

We consider the Cauchy problem of the compressible quantum Navier–Stokes–Maxwell equations with the linear damping in the isentropic case under the small perturbation of the constant equilibrium state in three dimensions. Based on the refined energy method, we establish the classical solution globally in time in Sobolev space. By the combination of the energy estimates with the interpolation between the positive Sobolev norms and the negative Sobolev norms ∥·∥Ḣ−s$\Vert \cdot \Vert _{\dot{H}^{-s}}$ with 0⩽s<3/2$0\leqslant s<3/2$ , we also obtain the algebraic decay rates of the classical solution. What is more, the Lp$L^p$–L2(1

In this paper, the authors establish the stability and the explicit decay estimates of the 2D incompressible magneto-micropolar fluid equations without magnetic diffusion and zero spin viscosity on a flat strip Ω : = T × [ 0 , 1 ] under the assumption that Navier type condition being imposed. The results are obtained heavily based on some time-weight energy estimates and a bootstrap argument. [ABSTRACT FROM AUTHOR]

The Inverted Pendulum On a Cart (IPOC) system poses a challenge in control engineering due to its inherent instability, nonlinearity, and underactuation. This addresses the fundamental issues arising from its underactuated nature and introduces an approach that combines Takagi-Sugeno (T-S) fuzzy control with an awareness of real-world constraints to create a control system ensuring both stability and practicality. By aligning theoretical insights with extended considerations, the Linear Matrix Inequality (LMI)-based control design is demonstrated in a comprehensive framework. Theorems are introduced and validated, leading to the derivation of LMI conditions. The simulation results are assessed with accompanying comments to demonstrate the effectiveness of the theorems. Through this integration of T-S fuzzy control with additional considerations, the paper aims to bridge the gap between theory and practical applications, advancing the field of control engineering. [ABSTRACT FROM AUTHOR]

The decomposition of deadwood plays a key role in forest carbon emissions. Most pieces of downed deadwood are partially suspended above the forest floor, but how this suspension affects decomposition rates is typically ignored and remains largely unexplored. Here, we combine field observations and experimental manipulations to explore how partial suspension of downed wood (that is, wood debris in contact with the ground) influences decomposer communities and patterns of decomposition in a lowland tropical forest. Experimental manipulations of wood sticks showed that small-scale suspension above the forest floor (ca. 5 cm) slowed decomposition and altered microbial community assembly, regardless of whether the suspended section was connected to a piece of downed wood. Across a 41-year chronosequence of dead trees, the average percent of wood volume suspended above the forest floor decreased during the initial 10 years post-death, but this trend reversed after 10 years, with the oldest logs being the most suspended. Among downed woody pieces sampled in situ, sections suspended above the forest floor had less moisture, fewer macrofungi, and more photosynthetic growth (for example, moss, algae, and so on) than downed sections of the same bole. Surprisingly, wood density, termite presence, and mass-specific respiration did not differ with ground contact. Combined, these data suggest that suspension within downed wood reduces moisture content, influences decomposer community assembly, and contributes to the strong variability in decomposition rates. The strong effect of partial suspension within downed wood pieces heightens concerns about the accuracy and applicability of experiments and surveys focused on down deadwood, which are the foundation of our understanding of wood decomposition and associated carbon losses. [ABSTRACT FROM AUTHOR]

In this paper, we consider the initial boundary value problem of the generalized pseudo‐parabolic equation containing viscoelastic terms and associated with Robin conditions. We establish first the local existence of solutions by the standard Galerkin method. Then, we prove blow‐up results for solutions when the initial energy is negative or nonnegative but small enough or positive arbitrary high initial energy, respectively. We also establish the lifespan and the blow‐up rate for the weak solution by finding the upper bound and the lower bound for the blow‐up times and the upper bound and the lower bound for the blow‐up rate. For negative energy, we introduce a new method to prove blow‐up results with a sharper estimate for the upper bound for the blow‐up times. Finally, we prove both the global existence of the solution and the general decay of the energy functions under some restrictions on the initial data. [ABSTRACT FROM AUTHOR]

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density, velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞. [ABSTRACT FROM AUTHOR]

On April 25 of 2015, earthquake of 7.6 ML struck the central Himalayan region having epicenter at Barpak village in the Gorkha district of Nepal. The event was followed by 7.0 ML earthquake known as Dolakha earthquake, epicenter on the border of Dolakha and Sindhupalchowk. In this study, the b-value, aftershock decay rate p-value, and correlation fractal dimension were estimated for the aftershock sequences. The data used were obtained from the National Earthquake Monitoring and Research Centre (NEMRC), Nepal. The b–values 0.89 ± 0.05 and 0.90 ± 0.07 were computed for aftershocks after Gorkha and Dolakha event, respectively. A significant increase in b-values were reported following the Gorkha earthquake and Dolakha earthquake. The slip procured in the primary fault is respectively 60 % and 56 % after the events. The aftershocks sequences after both events were modelled by the Omori-Utsu law with p = 1.2 ± 0.11 and p = 0.76 ± 0.04. The observed b and p values after the earthquake sequences may correlate well with the large slip experienced by the seismogenic fault. This study sheds light on the mechanism behind the preparation of the significant earthquakes in the tectonic regions of the Himalaya.

Background Escherichia coli is a commonly used faecal indicator bacterium to assess the level of faecal contamination in aquatic habitats. However, extensive studies have reported that sediment acts as a natural reservoir of E. coli in the extraintestinal environment. E. coli can be released from the sediment, and this may lead to overestimating the level of faecal contamination during water quality surveillance. Thus, we aimed to investigate the effects of E. coli habitat transition from sediment to water on its abundance in the water column. Methods This study enumerated the abundance of E. coli in the water and sediment at five urban lakes in the Kuala Lumpur-Petaling Jaya area, state of Selangor, Malaysia. We developed a novel method for measuring habitat transition rate of sediment E. coli to the water column, and evaluated the effects of habitat transition on E. coli abundance in the water column after accounting for its decay in the water column. Results The abundance of E. coli in the sediment ranged from below detection to 12,000 cfu g–1, and was about one order higher than in the water column (1 to 2,300 cfu mL–1). The habitat transition rates ranged from 0.03 to 0.41 h–1. In contrast, the E. coli decay rates ranged from 0.02 to 0.16 h−1. In most cases (>80%), the habitat transition rates were higher than the decay rates in our study. Discussion Our study provided a possible explanation for the persistence of E. coli in tropical lakes. To the best of our knowledge, this is the first quantitative study on habitat transition of E. coli from sediments to water column.

On 6 February 2023, Türkiye experienced a pair of consecutive earthquakes with magnitudes of Mw 7.8 and 7.5, and accompanied by an intense aftershock sequence. These seismic events were particularly impactful on the segments of the East Anatolian Fault Zone (EAFZ), causing extensive damage to both human life and urban centers in Türkiye and Syria. This study explores the analysis of a dataset spanning almost one year following the Turkiye mainshocks, including 471 events with a magnitude of completeness (Mc) ≥ 4.4. We employed the maximum likelihood approach to estimate the b-value and Omori-Utsu parameters (K, c, and p-values). The estimated b-value is 1.21 ± 0.1, indicating that the mainshocks occurred in a region characterized by elevated stress levels, leading to a sequence of aftershocks of larger magnitudes due to notable irregularities in the rupture zone. The aftershock decay rate (p-value = 1.1 ± 0.04) indicates a rapid decrease in stress levels following the main shocks. However, the c-value of 0.204 ± 0.058 would indicate a relatively moderate or low initial productivity of aftershocks. Furthermore, the k-value of 76.75 ± 8.84 suggests that the decay of aftershock activity commenced within a range of approximately 68 to 86 days following the mainshocks. The fractal dimension (Dc) was assessed using the correlation integral method, yielding a value of 0.99 ± 0.03. This implies a tendency toward clustering in the aftershock seismicity and a linear configuration of the epicenters. The slip ratio during the aftershock activity was determined to be 0.75, signifying that 75% of the total slip occurred in the primary rupture, with the remaining fraction distributed among secondary faults. The methodologies and insights acquired in this research can be extended to assist in forecasting aftershock occurrences for future earthquakes, thus offering crucial data for future risk assessment.

Deadwood decomposition modulates habitat structure and enhances resource availability within forest ecosystems. Deadwood decomposition is influenced by a combination of abiotic and biotic factors, wherein climatic variables, tree species, and wood characteristics play fundamental roles. However, the scarcity of studies conducted in dry and semiarid regions restricts our understanding of deadwood decomposition dynamics. Here, we studied the decomposition of logs in four plots across an elevation gradient spanning approximately 1000 m (from 1477 to 2317 m a.s.l.). The site was a burnt reforestation of different pine species in a Mediterranean mountain (Sierra Nevada, SE Spain). Logs of a range of diameters were cut to a similar length (75 cm), and their density loss was monitored over 15 years. We fitted three different types of functions (linear, negative exponential and negative sigmoidal) to evaluate the temporal trajectory of decomposition across the elevation gradient. Average wood density loss through the 15-year period ranged from 30.4 % to 63.3 % depending on the elevation plot, and it was highest at an intermediate elevation. The negative sigmoidal equation showed the best fit, but all functions rendered similar half-life values, which ranged between 12.8 and 29.4 years depending on the elevation plot. Contrary to most studies, larger-diameter logs experienced a quicker decomposition process, which could be linked to increased moisture retention and greater activity of large invertebrates in the larger-diameter logs. The variations observed across the elevation gradient are consistent with expectations on how the interaction between precipitation and temperature influences decomposition rates. The observed decomposition patterns in these mountain forests indicate a relatively rapid process, and underline the vital contribution of deadwood biological legacies to the preservation of soil fertility in the Mediterranean region. • We studied wood decomposition for 15 y in a Mediterranean mountain at 1477 – 2317 m elevation. • Trunks lost 30.4 % – 63.3 % of density, peaking at intermediate elevation. • A negative sigmoidal curve explained the process better than a linear or negative exponential. • Modelled half-life of wood ranged from 12.8 to 29.4 y across elevations. • Thicker logs decomposed faster, challenging findings from other regions. [ABSTRACT FROM AUTHOR]

The asymptotic stability and long time decay rates of solutions to linear Caputo time-fractional ordinary differential equations are known to be completely determined by the eigenvalues of the coefficient matrices. Very different from the exponential decay of solutions to classical ordinary differential equations, solutions of time-fractional ordinary differential equations decay only polynomially, leading to the so-called Mittag-Leffler stability, which were already extended to linear fractional delay differential equations (FDDEs) with real constants by Čermák et al. (2017) [17]. This paper is devoted to the asymptotical stability and long time decay rates of the solutions for a class of fractional delay abstract evolution equations with complex-valued coefficients. By applying the spectral decomposition method, we reformulate the fractional delay abstract evolution equations to an infinite-dimensional FDDEs. Through the root locus technique, we develop a necessary and sufficient stability condition in a coefficient criterion for FDDEs. At the same time, we are able to deal with the awful singularities caused by delay and fractional exponent by introducing a novel integral path, and hence to give an accurate estimation for the fractional resolvent operators. We show that the long time decay rates of the solutions for both linear FDDEs and fractional delay abstract evolution equations with complex-valued coefficients are O (t − α). Finally, several application models including both time and time-space fractional Schrödinger equations are presented to illustrate the effectiveness of our proposed criteria. • A stability criterion is established for complex-valued fractional delay abstract evolution equations. • A novel integral path is introduced to give an accurate estimation for the fractional resolvent operators. • The long-time decay rate is proved to be polynomial. • Our results provide stability criteria for various models such as time and time-space fractional Schrodinger equations. [ABSTRACT FROM AUTHOR]

Background: Escherichia coli is a commonly used faecal indicator bacterium to assess the level of faecal contamination in aquatic habitats. However, extensive studies have reported that sediment acts as a natural reservoir of E. coli in the extraintestinal environment. E. coli can be released from the sediment, and this may lead to overestimating the level of faecal contamination during water quality surveillance. Thus, we aimed to investigate the effects of E. coli habitat transition from sediment to water on its abundance in the water column., Methods: This study enumerated the abundance of E. coli in the water and sediment at five urban lakes in the Kuala Lumpur-Petaling Jaya area, state of Selangor, Malaysia. We developed a novel method for measuring habitat transition rate of sediment E. coli to the water column, and evaluated the effects of habitat transition on E. coli abundance in the water column after accounting for its decay in the water column., Results: The abundance of E. coli in the sediment ranged from below detection to 12,000 cfu g -1 , and was about one order higher than in the water column (1 to 2,300 cfu mL -1 ). The habitat transition rates ranged from 0.03 to 0.41 h -1 . In contrast, the E. coli decay rates ranged from 0.02 to 0.16 h -1 . In most cases (>80%), the habitat transition rates were higher than the decay rates in our study., Discussion: Our study provided a possible explanation for the persistence of E. coli in tropical lakes. To the best of our knowledge, this is the first quantitative study on habitat transition of E. coli from sediments to water column., Competing Interests: The authors declare there are no competing interests., (©2024 Liu et al.)

On April 25 of 2015, earthquake of 7.6 M L struck the central Himalayan region having epicenter at Barpak village in the Gorkha district of Nepal. The event was followed by 7.0 M L earthquake known as Dolakha earthquake, epicenter on the border of Dolakha and Sindhupalchowk. In this study, the b-value, aftershock decay rate p-value, and correlation fractal dimension were estimated for the aftershock sequences. The data used were obtained from the National Earthquake Monitoring and Research Centre (NEMRC), Nepal. The b-values 0.89 ± 0.05 and 0.90 ± 0.07 were computed for aftershocks after Gorkha and Dolakha event, respectively. A significant increase in b-values were reported following the Gorkha earthquake and Dolakha earthquake. The slip procured in the primary fault is respectively 60 % and 56 % after the events. The aftershocks sequences after both events were modelled by the Omori-Utsu law with p = 1.2 ± 0.11 and p = 0.76 ± 0.04. The observed b and p values after the earthquake sequences may correlate well with the large slip experienced by the seismogenic fault. This study sheds light on the mechanism behind the preparation of the significant earthquakes in the tectonic regions of the Himalaya., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2024 The Authors.)