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We prove that multiplicative chaos measures can be constructed from extreme level sets or thick points of the underlying logarithmically correlated field. We develop a method which covers the whole subcritical phase and only requires asymptotics of suitable exponential moments for the field. As an application, we establish that these estimates hold for the logarithm of the absolute value of the characteristic polynomial of a Haar distributed random unitary matrix (CUE), using known asymptotics for Toeplitz determinant with (merging) Fisher–Hartwig singularities. Hence, this proves a conjecture of Fyodorov and Keating concerning the fluctuations of the volume of thick points of the CUE characteristic polynomial. [ABSTRACT FROM AUTHOR]

Ditylenchus gigas Vovlas is the dominant species of Ditylenchus nematode on faba bean in the UK. It is normally reported with Botrytis fabae Sardiña, which causes chocolate spot of faba bean. The aim of the work reported here was to estimate how fast isolated infections of D. gigas may spread spatially and how background infection of the host with B. fabae alters multiplication of D. gigas. Spatial spread in field conditions was measured in plants growing in square grids. After establishment, single plants at the centre of each grid were spray inoculated with D. gigas. In summer 2017, D. gigas spread to a distance of at least 1 m, the edge of each 2 m × 2 m plot. Incidence on shoots decreased very slowly with distance beyond 0.4 m. In a repeat experiment harvested in autumn 2018, D. gigas was detected at distances of up to 160 cm in 4 m × 4 m plots. The yield effect and reproduction rate of D. gigas were measured in glasshouse experiments, alone and following brush inoculation with low (103) or high (106 conidia/mL) doses of B. fabae. At low doses of D. gigas inoculum multiplied by approximately 75‐fold, with lower rates of multiplication as the inoculum dose increased. The reproduction rate of D. gigas was reduced in plants inoculated with B. fabae, especially at high doses of D. gigas. The reduction was approximately proportional to log (B. fabae dose). Seed yield from inoculated plants decreased approximately in proportion to the logarithms of the initial dose of D. gigas and of B. fabae. [ABSTRACT FROM AUTHOR]

We obtain almost sure bounds for the weighted sum ∑n⩽tf(n)n$\sum _{n \leqslant t} \frac{f(n)}{\sqrt {n}}$, where f(n)$f(n)$ is a Steinhaus random multiplicative function. Specifically, we obtain the bounds predicted by exponentiating the law of the iterated logarithm, giving sharp upper and lower bounds. [ABSTRACT FROM AUTHOR]

Let E/Q$E/\mathbb {Q}$ be an elliptic curve without complex multiplication. By Serre's open image theorem, the mod ℓ$\ell$ Galois representation ρ¯E,ℓ$\overline{\rho }_{E, \ell }$ of E$E$ is surjective for each prime number ℓ$\ell$ that is sufficiently large. Under the generalized Riemann hypothesis, we give an explicit upper bound on the largest prime ℓ$\ell$, linear in the logarithm of the conductor of E$E$, such that ρ¯E,ℓ$\overline{\rho }_{E, \ell }$ is nonsurjective. [ABSTRACT FROM AUTHOR]

In this paper, we study the nonlinear weighted elliptic problem −∇.(w(x)|∇u|N−2∇u)=f(x,u),u∈W01,N(B,w),$$\begin{equation*}\hskip5pc -\nabla.(w(x)|\nabla u|^{N-2} \nabla u) = f(x,u),\nobreakspace \nobreakspace u\in W_{0}^{1,N}(B,w),\hskip-5pc \end{equation*}$$where B is the unit ball of RN$\mathbb {R^{N}}$, N≥2$N\ge 2$, and w(x)=log1|x|β(N−1)$ w(x)=\left(\log \frac{1}{|x|}\right)^{\beta (N-1)}$ the singular logarithm weight with the limiting exponent N−1$N-1$ in the Trudinger–Moser embedding. The nonlinearities are critical or subcritical growth in view of Trudinger–Moser inequalities. We prove the existence of nontrivial solutions via the critical point theory. In the critical case, the associated energy functional does not satisfy the compactness condition. We give a new growth condition and we point out its importance for checking the Palais–Smale compactness condition. [ABSTRACT FROM AUTHOR]

We aim at nonlinear model order reduction (MOR) in hybrid mechanical systems by means of Principal Geodesic Analysis (PGA) on the Riemannian manifolds S2 (the sphere) and SO(3) (the rotation group). MOR requires highly accurate and efficient implementations of the logarithm maps and the resulting lifts across multiple branches. However, in our cases these maps have singularities due to periodicity. In this work we focus on the logarithm and lift maps for the sphere S2. We conduct detailed numerical experiments on mechanical systems to achieve maximal accuracy in spite of the singularities. [ABSTRACT FROM AUTHOR]

We study the spectral heat content for a class of open sets with fractal boundaries determined by similitudes in Rd${\mathbb {R}}^{d}$, d≥1$d\ge 1$, with respect to subordinate killed Brownian motions via α/2$\alpha /2$‐stable subordinators and establish the asymptotic behavior of the spectral heat content as t→0$t\rightarrow 0$ for the full range of α∈(0,2)$\alpha \in (0,2)$. Our main theorems show that these asymptotic behaviors depend on whether the sequence of logarithms of the coefficients of the similitudes is arithmetic when α∈[d−b,2)$\alpha \in [d-\mathfrak {b},2)$, where b$\mathfrak {b}$ is the interior Minkowski dimension of the boundary of the open set. The main tools for proving the theorems are the previous results on the spectral heat content for Brownian motions and the renewal theorem. [ABSTRACT FROM AUTHOR]

Background and purpose: Aneurysmal subarachnoid hemorrhage (ASAH) is a complex disease with higher incidence in women compared to men and in Japan compared to other countries. It was hypothesized that ASAH is consistent with a multistep model of disease. The following assessments were made: (1) the number of steps needed for the disease to occur and (2) whether this number may be different in female versus male and in Japanese versus non‐Japanese patients. Methods: Incidence data were generated from a meta‐analysis on ASAH incidence until 2017, which was supplemented with a literature search from 2017 to April 2023. Age‐ and sex‐adjusted incidences per 10‐year age groups were calculated and the logarithm of age‐specific incidence against the logarithm of age was regressed with least‐squares regression. Results: In 2317 ASAH patients a linear relationship between logarithm of incidence and logarithm of age was found with a slope estimate of 3.13 (95% confidence interval 2.60–3.65), consistent with a four‐step process. Similar estimates were found for female, male, Japanese and non‐Japanese patients. Conclusions: Our results suggest that ASAH is a four‐step process, also in subgroups with higher ASAH incidence. Elucidation of the exact nature of these steps can provide important clues for identification of disease mechanisms underlying ASAH. [ABSTRACT FROM AUTHOR]

The logarithm of n‐octanol–water partition coefficient (logP) is frequently used as an indicator of lipophilicity in drug discovery, which has substantial impacts on the absorption, distribution, metabolism, excretion, and toxicity of a drug candidate. Considering that the experimental measurement of the property is costly and time‐consuming, it is of great importance to develop reliable prediction models for logP. In this study, we developed a transfer free energy‐based logP prediction model‐FElogP. FElogP is based on the simple principle that logP is determined by the free energy change of transferring a molecule from water to n‐octanol. The underlying physical method to calculate transfer free energy is the molecular mechanics‐Poisson Boltzmann surface area (MM‐PBSA), thus this method is named as free energy‐based logP (FElogP). The superiority of FElogP model was validated by a large set of 707 structurally diverse molecules in the ZINC database for which the measurement was of high quality. Encouragingly, FElogP outperformed several commonly‐used QSPR or machine learning‐based logP models, as well as some continuum solvation model‐based methods. The root‐mean‐square error (RMSE) and Pearson correlation coefficient (R) between the predicted and measured values are 0.91 log units and 0.71, respectively, while the runner‐up, the logP model implemented in OpenBabel had an RMSE of 1.13 log units and R of 0.67. Given the fact that FElogP was not parameterized against experimental logP directly, its excellent performance is likely to be expanded to arbitrary organic molecules covered by the general AMBER force fields. [ABSTRACT FROM AUTHOR]

This paper is dedicated to obtaining closed‐form solutions of linear difference equations which are asymptotically close to the self‐adjoint Euler‐type difference equation. In this sense, the equation is related to the Euler–Cauchy differential equation y′′+λ/t2y=0$$ {y}^{\prime \prime }+\lambda /{t}^2y=0 $$. Throughout the paper, we consider a system of sequences which behave asymptotically as an iterated logarithm. [ABSTRACT FROM AUTHOR]

In this paper, we show how the chemotactic model ∂tρ=d1Δxρ−∇x·(ρ∇xc)∂tc=d2Δxc+F(ρ,c,∇xρ,∇xc,Δxρ)$$ \left\{\begin{array}{l}{\partial}_t\rho ={d}_1{\Delta}_x\rho -{\nabla}_x\cdotp \left(\rho {\nabla}_xc\right)\\ {}{\partial}_tc={d}_2{\Delta}_xc+F\left(\rho, c,{\nabla}_x\rho, {\nabla}_xc,{\Delta}_x\rho \right)\end{array}\right. $$introduced in Alejo and López (2021), which accounts for a chemical production–degradation operator of Hamilton–Jacobi type involving first‐ and second‐order derivatives of the logarithm of the cell concentration, namely, F=μ+τc−σρ+AΔxρρ+B|∇xρ|2ρ2+C|∇xc|2,$$ F=\mu +\tau c-\sigma \rho +A\frac{\Delta_x\rho }{\rho }+B\frac{{\left|{\nabla}_x\rho \right|}^2}{\rho^2}+C{\left|{\nabla}_xc\right|}^2, $$with μ,τ,σ,A,B,C∈ℝ$$ \mu, \tau, \sigma, A,B,C\in \mathbb{R} $$, can be formally reduced to a repulsive Keller–Segel model with logarithmic sensitivity ∂tρ=D1Δxρ+χ∇x·(ρ∇xlog(c))∂tc=D2Δxc+λρc−βc,χ,λ,β>0,$$ \left\{\begin{array}{l}{\partial}_t\rho ={D}_1{\Delta}_x\rho +\chi {\nabla}_x\cdotp \left(\rho {\nabla}_x\log (c)\right)\\ {}{\partial}_tc={D}_2{\Delta}_xc+\lambda \rho c-\beta c\end{array}\right.,\kern0.30em \chi, \lambda, \beta >0, $$whenever the chemotactic parameters are appropriately chosen and the cell concentration keeps strictly positive. In this way, some explicit solutions (namely, traveling waves and stationary cell density profiles) of the former system can be transferred to a number of variants of the the latter by means of an adequate change of variables. [ABSTRACT FROM AUTHOR]

We obtained an expression for the Coulomb logarithm for a dense semiclassical plasma based on momentum transport cross sections using an effective interaction potential. It was shown that for densities and temperatures corresponding to the dense semiclassical plasma our results are in good agreement with MD simulations. We applied the Coulomb logarithm for the calculation of the Dreicer field. The case of dense non‐thermal Lorentzian semiclassical plasma was considered, too. [ABSTRACT FROM AUTHOR]

This paper describes magnetospheric waves of very long wavelength in thin magnetic filaments. We consider an average magnetospheric configuration with zero ionospheric conductance and calculate waves using two different formulations: classic interchange theory and ideal magnetohydrodynamic (MHD) ballooning. Classic interchange theory, which is developed in detail in this paper, is basically analytic and is relatively straightforward to determine computationally, but it cannot offer very high accuracy. The eigenfrequencies from the two formulations cover a range of a factor of seven and generally agree with a root-mean-square difference between the common logarithms of interchange and MHD frequencies to be ∼0.054. The pressure perturbations in the classic interchange theory are assumed constant along each field line, but the MHD computed pressure perturbations along the field line vary in a range ∼30% in the plasma sheet but are larger in the inner magnetosphere. The parallel and perpendicular displacements, which are very different in the plasma sheet and inner magnetosphere, show good qualitative agreement between the two approaches. In the plasma sheet, the perpendicular displacements are strongly concentrated in the equatorial plane, whereas the parallel displacements are spread through most of the plasma sheet away from the equatorial plane; and can be regarded as buoyancy waves. In the inner magnetosphere, the displacements are more sinusoidal and are more like conventional slow modes. The different forms of the waves are best characterized by the flux tube entropy PVγ. [ABSTRACT FROM AUTHOR]

Consider a graph G with an assignment of costs to vertices. Even if G and all its subgraphs admit balanced separators of sublinear size, G may only admit a balanced separator of sublinear cost after deleting a small set Z of exceptional vertices. We improve the bound on ∣Z∣ from O(log∣V(G)∣) to O(loglog...log∣V(G)∣), for any fixed number of iterations of the logarithm. [ABSTRACT FROM AUTHOR]

This document is a section from the journal "School Science & Mathematics" that allows readers to share and solve mathematical problems. It provides contact information for submitting problems and solutions, as well as a website for accessing solutions to previously published problems. The document features three mathematical problems proposed by different authors. The first problem involves finding positive integers that satisfy a given equation with natural logarithms. The second problem asks to prove that 3 is the largest value of a constant that satisfies a certain inequality. The third problem seeks to find all continuous functions that satisfy a specific equation involving integrals. These problems are presented as challenges for mathematicians to solve. [Extracted from the article]

In finite deformation inelasticity, one often has to deal with the incompressibility constraint. In the past, this was dealt with using, for example, an exponential mapping approach, which yields exact volume preservation in plastic deformations. In this article however, the special‐linear update approach by Hurtado et al. The special‐linear update: An application of differential manifold theory to the update of isochoric plasticity flow rules, Int J Numer Methods Eng. 2014;97(4):298‐312, which utilizes a projection method to fulfill the incompressibility constraint is used. The model is applied to isotropic plasticity by a novel approximation of the logarithm and treats kinematic hardening without losing the symmetry of the internal variables. The model results are compared to models utilizing an exponential mapping approach in numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we derive a variant of the classical Keller–Segel model of chemotaxis incorporating a growth term of logistic type for the cell population n(t,x), say νn(1−n) with ν>0, and a nonstandard chemical production–degradation mechanism involving first‐ and second‐order derivatives of the logarithm of the cell density, say fλab(n,nx,nxx)=λn+anxxn+bnx2n2 with λ,a,b∈R, via the (n,S)‐hydrodynamical system associated with a modified Ginzburg–Landau equation governing the evolution of the complex wavefunction ψ=neiS. In a chemotactic context, S(t,x) will play the role of the concentration of chemical substance. Then, after carrying out a detailed analysis of the modulational stability of uniform‐in‐space plane waves, dark soliton‐shaped traveling wave densities of the former system are constructed from solitary wave solutions of the latter. [ABSTRACT FROM AUTHOR]

Alan Baker, Fields Medallist, died on 4 February 2018 in Cambridge, England, after a severe stroke a few days earlier. In 1970 he was awarded the Fields Medal at the International Congress in Nice on the basis of his outstanding work on linear forms in logarithms and its consequences. Since then he received many honours, including the prestigious Adams Prize of Cambridge University, the election to the Royal Society (1973) and the Academia Europeae; and he was made an honorary fellow of University College London, a foreign fellow of the Indian Academy of Science, a foreign fellow of the National Academy of Sciences, India, an honorary member of the Hungarian Academy of Sciences, and a fellow of the American Mathematical Society. [ABSTRACT FROM AUTHOR]

The compression depth of explosives is obtained on the basis of Lee penetration equation and the upper bound method to analyze the critical initiation threshold of finite thickness explosives. According to the pop curve, a theoretical model that reflects the relationship between critical initiation threshold and explosive thickness is established. Numerical simulation was carried out to simulate the initiation process and initiation threshold of explosives with different cover plate thicknesses. At the same time, we combine with the experimental data, to compare with the theoretical results. The calculations are in good agreement with data. Results show that the height of the bulge on the back of the cover plate and the compression depth of the explosive gradually increase with the thickness of the cover plate. When the cover plate reaches a certain thickness, there is no significant change on the final height of the bulge and the compression depth of the explosive. The decrease in explosive thickness increases the critical initiation threshold value, and the logarithm of the critical initiation threshold of the finite thickness explosive is approximately linearly related to the logarithm of the explosive thickness minus the compression depth. Therefore, this study can provide a reference for the initiation and simple calculation of the critical threshold of finite thickness explosives. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyse the effects of quality competitiveness based on technological innovation on the bilateral trade of goods. Our approach is based on the estimation of an import demand model that uses the data for 19 manufacturing sectors across 28 OECD countries over the period of 1998–2012. In the first step, to identify quality from prices, the logarithm of unit value (a proxy of price) is regressed on the logarithm of private R&D expenditure (a proxy for quality). The quality‐adjusted prices are derived from the difference between the unit value and its predicted value. In the second step, an import demand function is used to distinguish the effects of quality (private R&D expenditure) from the effects of other factors, such as production costs, which are approximated by the quality‐adjusted prices. The results of the first step indicate a significant positive effect of quality on the prices of imported goods in 7 out of 19 sectors. The results of the second step emphasise significant nonlinear effects of prices and quality on the import demand of goods: when the quality of imported goods is higher, the marginal effect of an increase in quality on the import demand is greater. [ABSTRACT FROM AUTHOR]

Frequency diverse array (FDA), by virtue of its range‐angle‐dependent beam pattern, has drawn a substantial attention in recent years. However, as far as the time‐variant range‐angle‐coupled beam pattern is concerned, such inherent flaw has become a bottleneck of its further development. To address this issue, herein, a logarithm‐based optimised static non‐linear frequency offset (LOSNFO) for FDA is proposed, which can successfully alleviate its inherent flaw, thus producing a short‐time range‐angle‐decoupled beam pattern with low sidelobe levels (SLLs) and narrow half‐power beam widths (HPBWs). Moreover, for practical applications, the proposed LOSNFO considers the propagation effect, which is always neglected in its counterpart. Numerical results are reported to demonstrate the effectiveness and superiority of the proposed LOSNFO‐FDA. [ABSTRACT FROM AUTHOR]

The purpose of this article is proving the equality of two natural L‐invariants attached to the adjoint representation of a weight one cusp form, each defined by purely analytic, respectively, algebraic means. The proof departs from Greenberg's definition of the algebraic L‐invariant as a universal norm of a canonical Zp‐extension of Qp associated to the representation. We relate it to a certain 2×2 regulator of p‐adic logarithms of global units by means of class field theory, which we then show to be equal to the analytic L‐invariant computed in Rivero and Rotger [J. Eur. Math. Soc., to appear]. [ABSTRACT FROM AUTHOR]

We investigate a variant of the Beurling–Ahlfors extension of quasisymmetric homeomorphisms of the real line that is given by the convolution of the heat kernel, and prove that the complex dilatation of such a quasiconformal extension of a strongly symmetric homeomorphism (that is, its derivative is an A∞‐weight whose logarithm is in VMO) induces a vanishing Carleson measure on the upper half‐plane. [ABSTRACT FROM AUTHOR]

Chemotaxis is an important biological mechanism in the nature. We prove the existence of spiky steady states of the one‐dimensional continuous chemotaxis model with logarithm sensitivity in a more general case by using global bifurcation theory with chemotactic coefficient being the bifurcating parameter and by studying the asymptotic behavior of the steady states as the chemotactic coefficient goes to infinity. One can use spiky steady states to model the cell aggregation, which is one of the most important phenomenon in chemotaxis. [ABSTRACT FROM AUTHOR]

In this article, we introduce an agent‐based model for a Limit Order Book (LOB) market with a price limit and simulate and estimate its parameters. In this framework, we have reached a linear relation between the percentage of the sellers in the market and the changes in the logarithm of the price. Moreover, we demonstrate that in this model if the supply and demand are equal and naturally if the demand is more than the supply, on the average, logarithm of the price strictly increases and this occurs while in the model argued, the inflation is assumed to be zero, no real factor exists in order to increase the value of stocks and no factor‐like rumors enters. This conclusion implies that merely the normal activities of the dealers to gain profit causes a false increase in the stock price. This fact, as being demonstrated in the simulation, has also been proved analytically. We call this phenomenon "the intrinsic bubble". Finally, we show that if the rules of the market change in the way that the daily price of the stock is calculated by the median of the prices traded, instead of their mean, this intrinsic bubble will more or less disappear. [ABSTRACT FROM AUTHOR]

Hemodialysis (HD) is a method used to remove biogenic substances or blood components that cause disease and some drugs used by patients to treat their diseases. Therefore, dosing schedule must be planned according to HD clearance (CLHD) when medical treatment is provided to patients receiving HD. We aimed to clarify the physical properties (eg, octanol‐water partition coefficient and molecular electronegativity) or pharmacokinetic parameters (eg, volume of distribution) of compounds affecting CLHD and to construct a mathematical model to predict CLHD. The analysis covered individual CLHD data for nine compounds from the literature. The molecular descriptors which are physical properties or pharmacokinetic parameters were calculated using the structural formula of each compound, and searched for factors related to CLHD among the calculated 148 molecular descriptors. Nonlinear mixed‐effects model analysis with CLHD as objective variable and molecular descriptors as explanatory variable was conducted to examine the factor affecting CLHD and develop a model for predicting CLHD. The logarithm of the brain/blood partition coefficient was detected as a factor affecting CLHD. The predictive accuracy of CLHD using the constructed mathematical model with the logarithm of the brain/blood partition coefficient as explanatory variable was adequate. [ABSTRACT FROM AUTHOR]

Background and Purpose: Airway hyperresponsiveness (AHR) is a central abnormality in asthma. IL‐5 may modulate AHR in animal models of asthma, but the available data is inconsistent on the impact of targeting IL‐5 pathway against AHR. The difference between targeting IL‐5 or the IL‐5 receptor, α subunit (IL‐5Rα) in modulating AHR remains to be investigated in human airways. The aim of this study was to compare the role of the anti‐IL‐5Rα benralizumab and the anti‐IL‐5 mepolizumab against AHR and to assess whether these agents influence the levels of cAMP. Experimental Approach Passively sensitized human airways were treated with benralizumab and mepolizumab. The primary endpoint was the inhibition of AHR to histamine. The secondary endpoints were the protective effect against AHR to parasympathetic activation and mechanical stress, and the tissue modulation of cAMP. Key Results: Benralizumab and mepolizumab significantly inhibited the AHR to histamine (maximal effect −134.14 ± 14.93% and −108.29 ± 32.16%, respectively), with benralizumab being 0.73 ± 0.10 logarithm significantly more potent than mepolizumab. Benralizumab and mepolizumab significantly inhibited the AHR to transmural stimulation and mechanical stress. Benralizumab was 0.45 ± 0.16 logarithm significantly more potent than mepolizumab against AHR to parasympathetic activation. The effect of these agents was significantly correlated with increased levels of cAMP. Conclusion and Implications: Targeting the IL‐5/IL‐5Rα axis is an effective strategy to prevent the AHR. Benralizumab was more potent than the mepolizumab and the concentration‐dependent beneficial effects of both these monoclonal antibodies were related to improved levels of cAMP in hyperresponsive airways. [ABSTRACT FROM AUTHOR]

The transfer coefficient (or, equivalently, the Tafel slope) is an experimentally measurable parameter defined as the change in the logarithm of the current density as a function of the applied potential, where the current density has been corrected (jcorr) for changes in the concentration of the reagent at the interface. For some electrode geometries (such as the rotating disc or a micro hemispherical electrode) where the electroactive interface is uniformly accessible and the mass‐transport is at steady‐state, these changes in concentration can be corrected for analytically. Correcting for the depletion of the reagent significantly increases the range over which Tafel analysis can be used to accurately yield information regarding the electron‐transfer process. The important question arises, therefore, for non‐uniformly accessible electrodes or for a system not at steady state, such as often encountered with disc electrodes, how can the experimentally measured electrochemical flux be rigorously corrected for to account for the changes in the surface concentration of the reagent? This work presents a simple simulation technique that allows the voltammetry of a disc to be "mass‐transport"‐corrected without recourse to the use of analytical approximations. [ABSTRACT FROM AUTHOR]

The Nash‐Sutcliffe efficiency (NSE) and the Kling‐Gupta efficiency (KGE) are now the most widely used indices in hydrology for evaluation of the goodness of fit between model simulations S and observations O. We introduce two theoretical (probabilistic) definitions of efficiency, E and E′, based on the estimators NSE and KGE, respectively, which enable controlled Monte Carlo experiments at 447 watersheds to evaluate their performance. Although NSE is generally unbiased, it exhibits enormous variability from one sample to another, due to the remarkable skewness and periodicity of daily streamflow data. However, use of NSE with logarithms of daily streamflow leads to estimates of E with almost no variability from one sample to the next, though with high upward bias. We introduce improved estimators of E and E′ based on a bivariate lognormal monthly mixture model that are shown to yield considerable improvements over NSE and slight improvements over KGE in controlled Monte Carlo experiments. Our new estimators of E should avoid most previous criticisms of NSE implied by the literature. Improved estimators of E that account for skewness and periodicity are needed for daily and subdaily streamflow series because NSE is not suited to such applications. [ABSTRACT FROM AUTHOR]

The magnitudes of earthquakes are known to follow a power law distribution referred to as the Gutenberg‐Richter empirical law. Seismological observations and laboratory experiments suggest a decrease of the decay exponent (b value) with differential stress. The physical mechanism controlling this decrease, however, remains unclear. The present study is dedicated to the origin of relative b value variations with stress obtained in a 2‐D rate‐and‐state planar fault model considering a population of asperities with size‐dependent fracture energy. The simulations show that both b value in the intermediate magnitude range and mainshock magnitude increase with normal stress. Analytical relationships are derived, showing that the increase of b value is related to the decrease of critical nucleation length with normal stress, enhancing the productivity of small‐magnitude events and partial ruptures. The theoretical formulas also show how the increase of mainshock magnitude is a consequence of normal stress dependence of stress drop. Plain Language Summary: One of the most documented observations about earthquakes is the Gutenberg‐Richter law, stating that the number of earthquakes decreases with the magnitude. Such a decay is characterized by the b value, ranging from 0.5 to 2. As the b value increases, the probability of large events decreases. Typical observations report a slight decrease of the b value with stress acting on the faults at the origin of earthquakes, but no clear physical mechanism could account for this feature. This study shows an attempt to understand b value relative variations with stress observed in a mechanical model of fault, consisting in a heterogeneous frictional interface between elastic slabs. It is shown theoretically and through numerical simulations that both b value in the intermediate magnitude range and maximum magnitude increase as the logarithm of normal stress. Key Points: The b value varies with normal stress in a planar and heterogeneous rate‐and‐state fault model with scale‐dependent fracture energyThe b value for intermediate magnitudes and mainshock magnitude both increase as the logarithm of normal stressThe b value variations and maximum magnitude are controlled in this model by the normal stress dependence of nucleation length and mainshock stress drop [ABSTRACT FROM AUTHOR]

In this article, we give, under the Riemann hypothesis, an upper bound for the exponential moments of the imaginary part of the logarithm of the Riemann zeta function on the critical line. Our result, which gives information on the fluctuations of the distribution of the zeros of ζ, has the same accuracy as the result obtained by Soundararajan (Ann. of Math. (2)170(2) (2009), 981–993) for the moments of |ζ|. [ABSTRACT FROM AUTHOR]

Background and purpose: Contingent negative variation (CNV) is a negative cortical wave that precedes a pre‐cued imperative stimulus requiring a quick motor response. It has been related to motor preparation and anticipatory attention. The aim was to ascertain whether the clinical improvement of functional movement disorders after physiotherapy would be associated with faster reaction times and modulation of CNV. Methods: Motor performance and CNV were analysed during a pre‐cued choice reaction time task with varying cue validity. Twenty‐one patients with functional movement disorders and 13 healthy controls at baseline were compared. Patients then underwent physiotherapy. At follow‐up after physiotherapy, patients were categorized as clinically improved (responders) or not improved (non‐responders) and retested. Results: At baseline, patients did not generate CNV, contrary to controls [mean amplitude (µV) at the end of preparation to move: patients −0.47 (95% CI −1.94, 1.00) versus controls −2.59 (95% CI −4.46, −0.72)]. Responders performed faster after physiotherapy [mean natural logarithm (ln) reaction time (RT) (ms): follow‐up 6.112 (95% CI 5.923, 6.301) versus baseline 6.206 (95% CI 6.019, 6.394), P = 0.010], contrary to non‐responders. Simultaneously, responders showed a recovery of CNV after physiotherapy [follow‐up −1.95 (95% CI −3.49, −0.41) versus baseline −0.19 (95% CI −1.73, 1.35), P < 0.001], contrary to non‐responders [follow‐up −0.32 (95% CI −1.79, 1.14) versus baseline −0.72 (95% CI −2.19, 0.75), P = 0.381]. Conclusions: Clinical improvement of functional movement disorders after physiotherapy was associated with faster reaction times and normalization of CNV, which was absent at baseline. These findings suggest that CNV may constitute a useful neurophysiological biomarker related to abnormal attention in functional movement disorders. [ABSTRACT FROM AUTHOR]

Evolving factor analysis (EFA) investigates the evolution of the singular values of matrices formed by a series of measured spectra, typically, resulting from the spectral observation of an ongoing chemical process. In the original EFA, the logarithms of the singular values are plotted for submatrices that include an increasing number of spectra. A typical observation in these plots is that pairs of trajectories of the singular values are on a collision course, but finally, the curves seem to repel each other and then run in different directions. For parameter‐dependent square matrices, such a behaviour is known for the eigenvalues under the keyword of an avoidance of crossing. Here, we adjust the explanation of this avoidance of crossing to the curves of singular values of EFA. Further, a condition is studied that breaks this avoidance of crossing. We demonstrate that the understanding of this noncrossing allows us to design model data sets with a predictable crossing behaviour. The curves of singular values as considered in the evolving factor analysis are well known to show an avoidance of crossing behavior. This phenomenon is analyzed and a mathematical explanation is given. [ABSTRACT FROM AUTHOR]

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with (p,q)‐growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a new synthesis procedure for nonrational driving‐point functions by defining and using the G operator. The operator is defined, and its properties are explored. Applying the Stieltjes transform on the G operator, the Padé approximant or the continued fraction form of the nonrational network function can be achieved with reduced computational complexity. Thus, the classical Foster and Cauer form or other techniques may be applied to synthesize network functions. The application of this work is demonstrated by considering certain functions such as the square root, inverse tangent, logarithm, and Lambert's W function. A set of conditions called synthesis criteria is proposed, which should be satisfied by a nonrational function to be realizable. [ABSTRACT FROM AUTHOR]

Logarithms are notorious for being a difficult concept to understand and teach. Research suggests that learners can be supported in understanding logarithms by making connections between mathematics and science concepts such as pH. This study investigated how an integrated chemistry and mathematics lesson impacted 29 teachers' understanding of the logarithmic relationship and pH. Pre‐ and post‐test data indicated 23 teachers improved their understanding of logarithms and 28 improved their understanding of pH, suggesting that teacher educators in both science and mathematics context can use this approach to foster better understanding with their teachers and ultimately school students. Our analysis also identified professional development components and teacher characteristics associated with gains in understanding of pH and logarithms, which mathematics and science teacher educators can use to strategically adapt and implement the lesson within other teacher education settings. [ABSTRACT FROM AUTHOR]

The spectral factorization mapping F→F+ puts a positive definite integrable matrix function F having an integrable logarithm of the determinant in correspondence with an outer analytic matrix function F+ such that F=F+(F+)∗ almost everywhere. The main question addressed here is to what extent ∥F+−G+∥H2 is controlled by ∥F−G∥L1 and ∥logdetF−logdetG∥L1. [ABSTRACT FROM AUTHOR]

Applied econometricians frequently apply the inverse hyperbolic sine (or arcsinh) transformation to a variable because it approximates the natural logarithm of that variable and allows retaining zero‐valued observations. We provide derivations of elasticities in common applications of the inverse hyperbolic sine transformation and show empirically that the difference in elasticities driven by ad hoc transformations can be substantial. We conclude by offering practical guidance for applied researchers. [ABSTRACT FROM AUTHOR]

The permutation flow shop problems with truncated exponential sum of logarithm processing times based and position‐based learning effects are considered in this study. The objective is to minimize makespan and total weighted completion time, respectively. Several heuristics and a branch‐and‐bound algorithm are proposed in this paper. The tight worst‐case bounds of some simple heuristics are also given. Numerical experiments are tested to evaluate the performance of the heuristics and branch‐and‐bound algorithm. [ABSTRACT FROM AUTHOR]

Near‐surface velocity structures are generally inverted by ray‐based traveltime tomography in which the objective function is usually constructed using raypath traveltime residuals. However, inversion accuracy in these situations remains low due to the asymptotic assumption. On the contrary, phase and instantaneous traveltime tomographies invert frequency‐dependent traveltime rather than the asymptotic raypath version that is contained in the first‐arrival waveform for near‐surface velocities. They also take the finite‐frequency effect of the seismic wave propagation into account by using wavepaths instead of raypaths as sensitivity kernels. In this context, we firstly compare synthetic results between raypath traveltime, phase traveltime and instantaneous traveltime in this study before comparing their corresponding sensitivity kernels. We then analyse three sets of inversion results to prove that it is still an acceptable way to construct the objective function using raypath traveltime for tomography within the seismic exploration frequency band. In this way, time‐domain wave‐equation forward simulation can be avoided and therefore the computational cost can be dramatically reduced. We also demonstrate that a sensitivity kernel that takes the finite‐frequency effect into account is more important for inversion accuracy than traveltime used in tomography. [ABSTRACT FROM AUTHOR]

This paper is concerned with the compressible Cahn‐Hilliard‐Navier‐Stokes system. We establish a sufficient regularity condition such that every weak solution conserves its energy equality for every t > 0. Our approach is based on the commutator and mollification approximation. [ABSTRACT FROM AUTHOR]

Size structure of organisms at logarithmic scale (i.e. size spectrum) can often be described by a linear function with a negative slope; however, substantial deviations from linearity have often been found in natural systems. Theoretical studies suggest that greater nonlinearity in community size spectrum is associated with high predator–prey size ratios but low predator–prey abundance ratios; however, empirical evaluation of the effects of predator–prey interactions on nonlinear structures remains scarce. Here, we aim to empirically explore the pattern of the size‐specific residuals (i.e. deviations from the linear regression between the logarithmic fish abundance and the logarithmic mean fish size) by using size spectra of fish communities in 74 German lakes. We found that nonlinearity was strong in lakes with high predator–prey abundance ratios but at low predator–prey size ratios. More specifically, our results suggest that only large predators, even if occurring in low abundances, can control the density of prey fishes in a broad range of size classes in a community and thus promote linearity in the size spectrum. In turn, the lack of large predator fishes may cause high abundances of fish in intermediate size classes, resulting in nonlinear size spectra in these lakes. Moreover, these lakes were characterized by a more intense human use including high fishing pressure and high total phosphorus concentrations, which have negative impacts on the abundance of large, predatory fish. Our findings indicate that nonlinear size spectra may reflect dynamical processes potentially caused by predator–prey interactions. This opens a new perspective in the research on size spectrum, and can be relevant to further quantify the efficiency of energy transfer in aquatic food webs. [ABSTRACT FROM AUTHOR]

In this paper we characterize the equilibrium measure for a nonlocal and anisotropic weighted energy describing the interaction of positive dislocations in the plane. We prove that the minimum value of the energy is attained by a measure supported on the vertical axis and distributed according to the semicircle law, a well‐known measure that also arises as the minimizer of purely logarithmic interactions in one dimension. In this way we give a positive answer to the conjecture that positive dislocations tend to form vertical walls. This result is one of the few examples where the minimizer of a nonlocal energy is explicitly computed and the only one in the case of anisotropic kernels. © 2018 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Tests are conducted for the presence of unit roots in the autoregressive representations of the logarithms of spot and forward exchange rates. The results from these tests provide one explanation for some of the conflicting conclusions which emerge from recent empirical papers on the foreign exchange market. [ABSTRACT FROM AUTHOR]

In this paper, we present evidence that local trends do exist in the Standard and Poor's Index. We begin by assuming that the logarithm of the price at time t[sub 1], say log P(t[sub 1]), has an expected value which is a linear function of time. That is, E log P(t[sub 1]) = at[sub 1] + b where a and b are arbitrary but fixed constants. Then we use the techniques of the analysis of variance to test whether any constants in the expression above satisfy the data. The tests show that these data are not explained by such an expected value. We conclude that the mean is different (certainly more complicated than at[sub 1] + b) over different intervals of time. The changes in expected value over these intervals are referred to as local trends. Finally, by repetition of the tests for different interval sizes, we find that the tests are significant for interval sizes up to approximately one year but not longer. Thus the evidence suggests that the local trends, when they occur, do not last longer than this period of time. [ABSTRACT FROM AUTHOR]

Abstract: The first part of the paper studies the expression for, and the properties of, the logarithm map on an orthant space, which is a simple stratified space, with the aim of analysing Fréchet means of probability measures on such a space. In the second part, we use these results to characterise Fréchet means and to derive various of their properties, including the limiting distribution of sample Fréchet means. [ABSTRACT FROM AUTHOR]

We consider the inverse problem of detecting an inclusion in conductor through electrostatic measurements taken on the boundary. We analyze in particular the stability issue showing that the solution depends from the available data with a rate of continuity of logarithmic type. [ABSTRACT FROM AUTHOR]

Abstract: Let p ⩾ 5 and N be prime numbers such that p divides N − 1. We estimate the p‐rank of the class group of Q ( N 1 / p ) in terms of the discrete logarithm, with values in Z / p Z, of certain units. Using the Gross–Koblitz formula and identities on the N‐adic Gamma function, we explicitly compute these logarithms. In particular, we give a new proof which does not use modular forms of a result of Calegari and Emerton. Using the same method, we prove a special case of a twisted form of a conjecture of Gross about the relation between some Stickelberger element and the Galois structure of the class group of the cyclotomic field Q ( ζ p , ζ N ). A special case of our formulae, for which we do not have an elementary proof, is the following: Assume there are some integers a, b such that N = ( a p + b p ) / ( a + b ). Then ( a + b ) · ( ∏ k = 1 ( N − 1 ) / 2 k 8 k ) is a pth power modulo N. [ABSTRACT FROM AUTHOR]

Abstract: We define and study infinite root stacks of fine and saturated logarithmic schemes, a limit version of the root stacks introduced by Niels Borne and the second author in Adv. Math. (231 (2012) 1327–1363). We show in particular that the infinite root stack determines the logarithmic structure and recovers the Kummer‐flat topos of the logarithmic scheme. We also extend the correspondence between parabolic sheaves and quasi‐coherent sheaves on root stacks to this new setting. [ABSTRACT FROM AUTHOR]

The latency and reliability of single-relay and multi-relay systems are investigated in this study. In a single-relay system with the amplify-and-forward protocol, a new approximation analytical method is proposed for the outage probability, which can also be extended to be used in the multi-relay system. The latency-reliability trade-off degree (LRTD) of single- and multi-relay systems, i.e. the slope of the latency-outage probability curve with logarithmic scales, is analysed and proved to be the same as the number of relay nodes. In the multi-relay system, the relationship between the system LRTD and the channel state information overhead is investigated. The optimum number of relay nodes can be derived according to the approximate expression of the outage probability. A simple iterative method is proposed to obtain the optimum number of relay nodes. The convergence of the iterative method is also proved. [ABSTRACT FROM AUTHOR]