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Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

The concept of "approximate reasoning" is central to Zadeh's contributions in logic. Standard fuzzy logic as we use today is only one potential interpretation of Zadeh's concept. I discuss various meanings for the syntagme "approximate reasoning" as intuitively presented in the paper Zadeh dedicated to the memory of Grigore C. Moisil in 1975. [ABSTRACT FROM AUTHOR]

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state. [ABSTRACT FROM AUTHOR]

In his famous paper [15] Ibragim Ibishievich Ibragimov has given asymptotic valucs of the best uniform approximation of functions of the form (a - χ)s lnm(a - χ), (a ≥ 1). These results have led to the developmcnt of a series of new directions in approximation theory, including the following ones, to which we devote this paper. • Constructive characterization of approximation of functions on a closed interval. • Babenko spaces. • Ditzian-Totik moduli of smoothness. • Constructive characterization of approximation of functions on the sets of complex plane. • Shape preserving approximation. In particular, we will show how we have used the results by I. I. Ibragimov in our recent paper in Constructive Approximation. [ABSTRACT FROM AUTHOR]

Abstract: A physical model of a continuous paper pulp digester is simplified and two subprocesses selected from the digester are modelled by coupled linear partial differential equations. This study focuses on the parameter identification of the simplified linear models. Finite-dimensional approximation of the model is made and a software package developed for identification of distributed parameter processes is applied. This identification system is developed for flexibility to allow identification for different choices of subprocesses and process variables. Unknown parameters of the subprocess models are estimated and the results are illustrated by process simulation and model validation. [Copyright &y& Elsevier]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

Abstract: Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in -norm equals the best weighted Euclidean approximation of the Bernstein–Bézier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181–191. In this note, we point out an error in their paper and give the correct result. [Copyright &y& Elsevier]

In this paper, we explore the numerical analysis of the microscale heat equation. We present the characteristics of numerical solutions obtained through both semi- and fully-discrete linear finite element methods. We establish a priori estimates and error bounds for both semi-discrete and fully-discrete finite element approximations. Additionally, the existence and uniqueness of the semi-discrete and fully-discrete finite element approximations have been confirmed. The study explores error bounds in various spaces, comparing the semi-discrete to the exact solutions, the semidiscrete against the fully-discrete solutions, and the fully-discrete solutions with the exact ones. A practical algorithm is introduced to address the system emerging from the fully-discrete finite element approximation at every time step. Additionally, the paper presents numerical error calculations to further demonstrate and validate the results. [ABSTRACT FROM AUTHOR]

In this paper, a special system of non-linear Abel integral equations (SNAIEs) is studied, which arises in astrophysics. Here, the well-known collocation method is extended to obtain an approximate solution of the SNAIEs. The existence and uniqueness conditions of the solution are investigated. Finally, some examples are solved to illustrate the accuracy and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

We shall give an elementary proof for Lemma 2.4 and correct some errors in Table 1 of the author's paper of the title. Moreover, we shall extend this table up to integers below 232. [ABSTRACT FROM AUTHOR]

The aim of the paper is to develop some representation formulae for strongly continuous operator semigroups on Banach spaces, in terms of limits of integrated means with respect to some given family of probability Borel measures and other parameters. The cases where these limits hold true pointwise or uniformly on compact subintervals are discussed separately. In order to face them different methods have been required: the former case has been studied by using purely functional-analytic methods, the latter one by involving methods arising from Approximation Theory. The paper also contains some estimates of the rate of convergence in terms of the rectified modulus of continuity and the second modulus of continuity. In a final section some illustrative examples and applications are provided. [ABSTRACT FROM AUTHOR]

Oil spill models are used to forecast the transport and fate of oil after it has been released. CranSLIK is a model that predicts the movement and spread of a surface oil spill at sea via a stochastic approach. The aim of this work is to identify parameters that can further improve the forecasting algorithms and expand the functionality of CranSLIK, while maintaining the run time efficiency of the method. The results from multiple simulations performed using the operational, validated oil spill model, MEDSLIK-II, were analysed using multiple regression in order to identify improvements which could be incorporated into CranSLIK. This has led to a revised model, namely CranSLIK v2.0, which was validated against MEDSLIK-II forecasts for real oil spill cases. The new version of CranSLIK demonstrated significant forecasting improvements by capturing the oil spill accurately in real validation cases and also proved capable of simulating a broader range of oil spill scenarios. [ABSTRACT FROM AUTHOR]

This paper presents a novel deep-learning network designed to detect intervals of jump discontinuities in single-variable piecewise smooth functions from their noisy samples. Enhancing the accuracy of jump discontinuity estimations can be used to find a more precise overall approximation of the function, as traditional approximation methods often produce significant errors near discontinuities. Detecting intervals of discontinuities is relatively straightforward when working with exact function data, as finite differences in the data can serve as indicators of smoothness. However, these smoothness indicators become unreliable when dealing with highly noisy data. In this paper, we propose a deep-learning network to pinpoint the location of a jump discontinuity even in the presence of substantial noise. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new iterative scheme to approximate the fixed point of generalized α-nonexpansive mappings. we first prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. Using the example presented in [R. Pant and R. Shukla, Approximating fixed point of generalized α-nonexpansive mappings in Banach spaces, J. Numer. Funct. Anal. Optim. 38(2017) 248-266.], we compare the convergence behavior of the new iterative process with other iterative processes. [ABSTRACT FROM AUTHOR]

In this paper, a high order accuracy method is developed for finding the approximate solution of two-point boundary value problems. The present approach is based on a special algorithm, taken from Pascal’s triangle, for obtaining a generalized form of the parametric splines of degree (2k + 1), k = 1, 2, . . ., which has a lower computational cost and gives the better approximation. Some appropriate band matrices are used to obtain a matrix form for this algorithm. The approximate solution converges to the exact solution of order O(h4k ), where k is a quantity related to the degree of parametric splines and the number of matrix bands that are applied in this paper. Some examples are given to illustrate the applicability of the method, and we compare the computed results with other existing known methods. It is observed that our approach produced better results. [ABSTRACT FROM AUTHOR]

Structural reliability is an important method to measure the safety performance of structures under the influence of uncertain factors. Traditional structural reliability analysis methods often convert the limit state function to the polynomial form to measure whether the structure is invalid. The uncertain parameters mainly exist in the form of intervals. This method requires a lot of calculation and is often difficult to achieve efficiently. In order to solve this problem, this paper proposes an interval variable multivariate polynomial algorithm based on Bernstein polynomials and evidence theory to solve the structural reliability problem with cognitive uncertainty. Based on the non-probabilistic reliability index method, the extreme value of the limit state function is obtained using the properties of Bernstein polynomials, thus avoiding the need for a lot of sampling to solve the reliability analysis problem. The method is applied to numerical examples and engineering applications such as experiments, and the results show that the method has higher computational efficiency and accuracy than the traditional linear approximation method, especially for some reliability problems with higher nonlinearity. Moreover, this method can effectively improve the reliability of results and reduce the cost of calculation in practical engineering problems. [ABSTRACT FROM AUTHOR]

This paper discusses the linear fractional Fredholm-Volterra integro-differential equations (IDEs) considered in the Caputo sense. For this purpose, Laguerre polynomials have been used to construct an approximation method to obtain the solutions of the linear fractional Fredholm-Volterra IDEs. By this approximation method, the IDE has been transformed into a linear algebraic equation system using appropriate collocation points. In addition, a novel and exact matrix expression for the Caputo fractional derivatives of Laguerre polynomials and an associated explicit matrix formulation has been established for the first time in the literature. Furthermore, a comparison between the results of the proposed method and those of methods in the literature has been provided by implementing the method in numerous examples. [ABSTRACT FROM AUTHOR]

In this paper, a computational method based on parameterizing state and control variables is presented for solving Stochastic Optimal Control (SOC) problems. By using Chebyshev wavelets with unknown coefficients, state and control variables are parameterized, and then a stochastic optimal control problem is converted to a stochastic optimization problem. The expected cost functional of the resulting stochastic optimization problem is approximated by sample average approximation thereby the problem can be solved by optimization methods more easily. For facilitating and guaranteeing convergence of the presented method, a new theorem is proved. Finally, the proposed method is implemented based on a newly designed algorithm for solving one of the well-known problems in mathematical finance, the Merton portfolio allocation problem in finite horizon. The simulation results illustrate the improvement of the constructed portfolio return. [ABSTRACT FROM AUTHOR]

In the air combat process, confrontation position is the critical factor to determine the confrontation situation, attack effect and escape probability of UAVs. Therefore, selecting the optimal confrontation position becomes the primary goal of maneuver decision-making. By taking the position as the UAV's maneuver strategy, this paper constructs the optimal confrontation position selecting games (OCPSGs) model. In the OCPSGs model, the payoff function of each UAV is defined by the difference between the comprehensive advantages of both sides, and the strategy space of each UAV at every step is defined by its accessible space determined by the maneuverability. Then we design the limit approximation of mixed strategy Nash equilibrium (LAMSNQ) algorithm, which provides a method to determine the optimal probability distribution of positions in the strategy space. In the simulation phase, we assume the motions on three directions are independent and the strategy space is a cuboid to simplify the model. Several simulations are performed to verify the feasibility, effectiveness and stability of the algorithm. [ABSTRACT FROM AUTHOR]

Analytic approximations of the binary collision rates of hydrometeors are derived for use in bulk microphysical parameterizations. Special attention is given to non-spherical hydrometeors like raindrops and snowflakes. The terminal fall velocity of these particles cannot be sufficiently well approximated by power law relations which are used in most microphysical parameterizations and therefore an improved formulation is needed. The analytic approximations of the bulk collision rates given in this paper are an alternative to look-up tables and can replace the Wisner approximation which is used in many atmospheric models. [ABSTRACT FROM AUTHOR]

This paper describes an integrated assessment modelling framework for uncertainty studies in global and regional climate change. In this framework, the Massachusetts Institute of Technology (MIT) Integrated Global System Model (IGSM), an integrated assessment model that couples an earth system model of intermediate complexity to a human activity model, is linked to the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM). Since the MIT IGSM-CAM framework (version 1.0) incorporates a human activity model, it is possible to analyse uncertainties in emissions resulting from both uncertainties in the economic model parameters and uncertainty in future climate policies. Another major feature is the flexibility to vary key climate parameters controlling the climate system response: climate sensitivity, net aerosol forcing and ocean heat uptake rate. Thus, the IGSM-CAM is a computationally efficient framework to explore the uncertainty in future global and regional climate change associated with uncertainty in the climate response and projected emissions. This study presents 21st century simulations based on two emissions scenarios (unconstrained scenario and stabilization scenario at 660 ppm CO2-equivalent) and three sets of climate parameters. The chosen climate parameters provide a good approximation for the median, and the 5th and 95th percentiles of the probability distribution of 21st century global climate change. As such, this study presents new estimates of the 90% probability interval of regional climate change for different emissions scenarios. These results underscore the large uncertainty in regional climate change resulting from uncertainty in climate parameters and emissions, especially when it comes to changes in precipitation. [ABSTRACT FROM AUTHOR]

The article presents a study which looks into an approach for profiling atmospheric temperature through Doppler-Radio Acoustic Sounding System (RASS). The study describes the application of RASS and antenna configurations and introduces the Kon's approximation-based relationship between Doppler shift and phase velocity. It also proposes the empirical correction of the Kon's approximation and presents results from several measurement campaigns.

This paper deals with global well-posedness of the solution to the complex short pulse equation. We first use regularized technology and the approximation argument to prove the local existence and uniqueness of this equation. Then, based on conserved quantities and energy analysis, we show that the solution can be extended globally in time for suitably small initial data. [ABSTRACT FROM AUTHOR]

Today, the Radio frequency identification system is widely used in various applications on a large scale. The readers must be densely deployed in order to cover their entire work area. If the number of readers is not optimal, some readers will be redundant, which will reduce the efficiency of the whole system. In more detail, redundant readers increase system overhead, unnecessary tag-reader communication, tag collision, and reader collision, and also, decrease the lifetime of RFID networks. The redundant reader elimination problem is a process that finds the least number of readers to cover all system tags. It is proved that the redundant reader elimination problem is NP hard. One of the useful tasks in eliminating redundant readers is improving the performance of existing approximation algorithms. In this paper, we propose a distributed algorithm, the LWFO algorithm, which combines the count base algorithm (CBA) and a weighting algorithm. The simulation results show that the proposed algorithm reduces reader redundancy compared to existing algorithms also processing time is reasonable. [ABSTRACT FROM AUTHOR]

Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space L p , w , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function f ∈ L p , w . We use the modulus of continuity of the functions to measure the rate of convergence. [ABSTRACT FROM AUTHOR]

This research paper deals with the numerical method for the solution of high-order Fredholm integro-differential difference equations using Legendre polynomials. We obtain the integral form of the problem, which is transformed into a system of algebraic equations using the collocation method. We then solve the algebraic equation using Newton's method. We establish the uniqueness and convergence of the solution. Numerical problems are considered to test the efficiency of the method, which shows that the method competes favorably with the existing methods and, in some cases, approximates the exact solution. [ABSTRACT FROM AUTHOR]

This paper discusses the large deviations for stochastic predator–prey model driven by multiplicative Lévy noise. Using Galerkin approximation, we initially prove the existence and uniqueness of solution. Due to the equivalence between Laplace principle and large deviation principle under a Polish space, the method of weak convergence has been followed in order to establish our results for this coupled system of equations. [ABSTRACT FROM AUTHOR]

In this paper, Computing the eigenvalues of the Conformable Sturm-Liouville Problem (CSLP) of order 2α, 1/2 < α; ≤ 1, and dirichlet boundary conditions is considered. For this aim, CSLP is discretized to obtain a matrix eigenvalue problem (MEP) using finite element method with fractional shape functions. Then by a method based on the asymptotic form of the eigenvalues, we correct the eigenvalues of MEP to obtain efficient approximations for the eigenvalues of CSLP. Finally, some numerical examples to show the efficiency of the proposed method are given. Numerical results show that for the nth eigenvalue, the correction technique reduces the error order from O(n4h²) to O(n²h²). [ABSTRACT FROM AUTHOR]

The increase in anthropogenic CO2 emissions largely followed an exponential path between 1850 and 2010, and the corresponding increases in atmospheric CO2 concentration were almost constantly proportional to the emissions by the so-called "airborne fraction". These observations suggest that the dynamics of atmospheric CO2 concentration through this time period may be properly approximated as a linear system. We demonstrate this hypothesis by deriving a linear box-model to describe carbon exchanges between the atmosphere and the surface reservoirs under the influence of disturbances such as anthropogenic CO2 emissions and global temperature changes. We show that the box model accurately simulates the observed atmospheric CO2 concentrations and growth rates across interannual to multi-decadal time scales. The model also allows us to analytically examine the dynamics of such changes/variations, linking its characteristic disturbance-response functions to bio-geophysically meaningful parameters. In particular, our results suggest that the elevated atmospheric CO2 concentrations have significantly promoted the gross carbon uptake by the terrestrial biosphere. However, such "fertilization" effects are partially offset by enhanced carbon release from surface reservoirs promoted by warmer temperatures. The result of these interactions appears to be a decline in net efficiency in sequestering atmospheric CO2 by ~ 30% since 1960s. We believe that the linear modeling framework outlined in this paper provides a convenient tool to diagnose the observed atmospheric CO2 dynamics and monitor their future changes. [ABSTRACT FROM AUTHOR]

Abstract: A comment on a recent paper about the combined effects of radiation and viscous dissipation on the convection in an annular porous enclosure has raised the problem of the role played by the viscous dissipation and the pressure work contributions in buoyant flows. The aim of this further comment is to show that the criticism expressed by Costa on the model of the viscous dissipation effect employed in the paper by Badruddin and co-workers is unjustified. [ABSTRACT FROM AUTHOR]

The paper is devoted to the investigation of problem of approximation of continuous periodic functions by trigonometric polynomials, which are generated by linear methods of summation of Fourier series. The simplest example of a linear approximation of periodic functions is the approximation of functions by partial sums of their Fourier series. However, the sequences of partial Fourier sums are not uniformly convergent over the class of continuous periodic functions. Therefore, many studies devoted to the research of the approximative properties of approximation methods, which are generated by transformations of the partial sums of Fourier series and allow us to construct sequences of trigonometrical polynomials that would be uniformly convergent for the whole class of continuous functions. Particularly, Fej'er sums have been widely studied recently. One of the important problems in this area is the study of asymptotic behavior of the sharp upper bounds over a given class of functions of deviations of the trigonometric polynomials. In the paper, we study upper asymptotic estimates for deviations between a function and the Fej'er means for the Fourier series of the function. The asymptotic behavior is considered for the functions represented by the Poisson integrals of periodic functions of a real variable. The mentioned classes consist of analytic functions of a real variable. These functions can be regularly extended into the corresponding strip of the complex plane. An asymptotic equality for the upper bounds of Fej'er means deviations on classes of Poisson integrals was obtained. [ABSTRACT FROM AUTHOR]

We monitored CO2 and CH4 fluxes using eddy covariance from 19 May to 27 September 2011 in a poor fen located in northern Michigan. The objectives of this paper are to: (1) quantify the flux of CH4 from a sub-boreal peatland, and (2) determine which abiotic and biotic factors were the most correlated to the flux of CHv over the measurement period. Net daily CH4 fluxes increased from 70 mgm-2 d-1 to 220mgm-2 d-1 from mid May to mid July. After July, CH4 losses steadily declined to approximately 50 mgm-2 d-1 in late September. During the study period, the peatland lost 17.4 g CH4 m-2. Both abiotic and biotic variables were correlated with changes in CH4 flux. When the different variables were analyzed together, the preferred model included mean daily soil temperature at 20cm, daily net ecosystem exchange (NEE) and the interaction between mean daily soil temperature at 20 cm and NEE (R² = 0.47, p value < 0.001). The interaction was important because the relationship between daily NEE and mean daily soil temperature with CH4 flux changed in conjunction with changes in daily NEE. On days when daily NEE was negative, 25% of the CH4 flux could be explained by changes in NEE, however on days when daily NEE was positive, there was no correlation between daily NEE and the CH4 flux. In contrast, daily mean soil temperature at 20 cm was poorly correlated to changes in CH4 when NEE was negative (17%), but the correlation increased to 34% when NEE was positive. The interaction between daily NEE and mean daily soil temperature at 20 cm indicates shifting environmental controls on the CH4 flux throughout the growing season. [ABSTRACT FROM AUTHOR]

In this paper, we extend the notion of approximate convexity to setvalued maps and obtain some relations between approximate convexity and approximate monotonicity of their normal subdifferential. [ABSTRACT FROM AUTHOR]

In this paper, we study the Ulam stability and hyperstability of two general functional equations in several variables in 2-Banach spaces. Multi-additive and multi-Jensen functions are particular cases of these functional equations. We also improve the main results of Theorem 3 and Theorem 4 of [Ciepli'nski, K. Ulam stability of functional equations in 2-Banach spaces via the fixed point method. J. Fixed Point Theory Appl. 23 (2021), no. 3, Paper No. 33, 14 pp.] and their consequences. [ABSTRACT FROM AUTHOR]

This paper proposes a dead-reckoning (DR) method for vehicles using Lie theory. This approach treats the pose (position and attitude) and velocity of the vehicle as elements of the Lie group SE 2 (3) and follows the computations based on Lie theory. Previously employed DR methods, which have been widely used, suffer from cumulative errors over time due to inaccuracies in the calculated changes from velocity during the motion of the vehicle or small errors in modeling assumptions. Consequently, this results in significant discrepancies between the estimated and actual positions over time. However, by treating the pose and velocity of the vehicle as elements of the Lie group, the proposed method allows for accurate solutions without the errors introduced by linearization. The incremental updates for pose and velocity in the DR computation are represented in the Lie algebra. Experimental results confirm that the proposed method improves the accuracy of DR. In particular, as the motion prediction time interval of the vehicle increases, the proposed method demonstrates a more pronounced improvement in positional accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a one-step block of optimized hybrid schemes for the numerical integration of second-order initial value problems (IVP) of ordinary differential equations (ODE) is constructed via collocation techniques. The developed scheme is obtained by considering two intra-step nodal points as hybrid points, which are chosen in order to achieve optimized errors of the main formulae approximating the solution such that 0 < v1 < v2 < 1 where v1 and v2 are defined as hybrid points. The characteristics of the developed scheme are analyzed. Application of the new scheme on some second-order IVPs shows the accuracy and effectiveness of the scheme compared with some existing methods. [ABSTRACT FROM AUTHOR]

The classical synthetic aperture radar (SAR) imaging techniques based on matched filters are limited by data bandwidth, resulting in limited imaging performance with side lobes and speckles present. To address the high-resolution SAR imaging problem, sparse reconstruction has been extensively investigated. However, the state-of-the-art sparse recovery methods seldom consider the complex-valued reflectivity of the scene and only recover an approximated real-valued scene instead. Furthermore, iterative schemes associated with the sparse recovery methods demand a high computational cost, which limits the practical applications of these methods. In this paper, we establish a sphere-constrained magnitude-sparsity SAR imaging model, aiming at enhancing the SAR imaging quality with high efficiency. We propose a non-convex non-smooth optimization method, which can be accelerated by stochastic average gradient acceleration to be scalable with large-scale problems. Numerical experiments are conducted with point-target and extended-target simulations. On the one hand, the point-target simulation showcases the superiority of our proposed method over the classical methods in terms of resolution. On the other hand, the extended-target simulation with random phases is considered to be in line with the practical scenario, and the results demonstrate that our method outperforms the classical SAR imaging methods and sparse recovery without phase prior in terms of PSNR. Meanwhile, owing to the stochastic acceleration, our method is faster than the existing sparse recovery methods by orders of magnitude. [ABSTRACT FROM AUTHOR]

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This paper mainly focuses on the development of a learning-based controller for a class of uncertain mechanical systems modeled by the Euler-Lagrange formulation. The considered system can depict the behavior of a large class of engineering systems, such as vehicular systems, robot manipulators and satellites. All these systems are often characterized by highly nonlinear characteristics, heavy modeling uncertainties and unknown perturbations, therefore, accurate-model-based nonlinear control approaches become unavailable. Motivated by the challenge, a reinforcement learning (RL) adaptive control methodology based on the actor-critic framework is investigated to compensate the uncertain mechanical dynamics. The approximation inaccuracies caused by RL and the exogenous unknown disturbances are circumvented via a continuous robust integral of the sign of the error (RISE) control approach. Different from a classical RISE control law, a tanh($) function is utilized instead of a sign($) function to acquire a more smooth control signal. The developed controller requires very little prior knowledge of the dynamic model, is robust to unknown dynamics and exogenous disturbances, and can achieve asymptotic output tracking. Eventually, co-simulations through ADAMS and MATLAB/Simulink on a three degrees-of-freedom (3-DOF) manipulator and experiments on a real-time electromechanical servo system are performed to verify the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

For energetic particle measurements whose spectra follow a power law, it is often challenging to define a characteristic ("effective") energy of an energy channel. In order to avoid time-consuming calculations, the geometric mean is often used as an approximation for the effective energy. This approximation is considered to be pretty good. It is, however, potentially inadequate in cases with wide energy channels and soft spectral slopes. In order to determine the limits of the goodness of the approximation, we derive formulas to calculate the deviation of the effective energy, phase space density and energy density based on the geometric mean approximation from those based on the power law. The results show that the geometric mean approximation is usually adequate and that corrections are needed only in extraordinary cases. [ABSTRACT FROM AUTHOR]

Radio Occultation (RO) sensing is used to probe the Earth's atmosphere in order to obtain information about its physical properties. With a main interest in the parameters of the neutral atmosphere, there is the need to perform a correction of the ionospheric contribution to the bending angle. Since this correction is an approximation to first order, there exists an ionospheric residual, which can be expected to be larger when the ionization is high (day versus night, high versus low solar activity). The ionospheric residual systematically affects the accuracy of the atmospheric parameters at low altitudes, at high altitudes (above 25km to 30km) it even is an important error source. In climate applications this could lead to a time dependent bias which induces wrong trends in atmospheric parameters at high altitudes. The first goal of our work was to study and characterize this systematic residual error. In a second step we developed a simple correction method, based purely on observational data, to reduce this residual for large ensembles of RO profiles. In order to tackle this problem we analyzed the bending angle bias of CHAMP and COSMIC RO data from 2001 to 2011. We could observe that the night time bending angle bias stays constant over the whole period of 11 yr, while the day time bias increases from low to high solar activity. As a result, the difference between night and day time bias increases from about -0.05μrad to -0.4μrad. This behavior paves the way to correct the solar cycle dependent bias of day time RO profiles. In order to test the newly developed correction method we performed a simulation study, which allowed to separate the influence of the ionosphere and the neutral atmosphere. Also in the simulated data we observed a similar increase in the bias in times from low to high solar activity. In this model world we performed the climatological ionospheric correction of the bending angle data, by using the bending angle bias characteristics of a solar cycle as a correction factor. After the climatological ionospheric correction the bias of the simulated data improved significantly, not only in the bending angle but also in the retrieved temperature profiles. [ABSTRACT FROM AUTHOR]

The comment by Nicholson (2011 a) questions the "consistency" of the "definition" of the "biological end-member" used by Kaiser (2011 a) in the calculation of oxygen gross production. "Biological end-member" refers to the relative oxygen isotope ratio difference between photosynthetic oxygen and Air-O2 (abbreviated 17δP and 18δP for 17O/16O and 18O/16O, respectively). This comment has no merit for the following reasons: (a) the isotopic composition of photosynthetic oxygen cannot be "defined", it can only be measured, modelled or calculated based on other data; (b) the isotopic composition of photosynthetic oxygen was not "defined" in Kaiser (2011a), but derived from published measurements; (c) the published measurements themselves were inconsistent and no single result could be identified as best; (d) since no best value could be identified, a hypothetical base case was constructed in a way that was consistent with previous publications; (e) the values of 17δP = -11.646‰ and 18δP = -22.835‰ assumed for the base case are compatible with the experimental evidence published before the paper of Kaiser (2011a); (f) even if the "biological end-member" was based on a definition, there could be no argument about the "consistency" of this definition - as per its nature, a definition is arbitrary. The qualification of base case gross production values as being "30% too high" must therefore also be rejected. Even though recently revised measurements of the relative 17O/16O isotope ratio difference between VSMOW and Air-O2, 17δVSMOW (Barkan and Luz, 2011), do support lower estimates of gross production, our own measurements disagree with these revised 17δVSMOW values. If scaled for differences in 18δVSMOW, they are actually in good agreement with the original data (Barkan and Luz, 2005). Moreover, species-dependent differences in photosynthetic isotope fractionation (Eisenstadt et al., 2010) correspond to an uncertainty of at least 15% around the central estimate for the inferred gross production. Nicholson (2011a) also suggests that approximated calculations of gross production should be performed with a triple isotope excess defined as 17Δ# ≡ ln(1 + 17δ) - λln(1 + 18δ), with λ = θR = ln(1 + 17εR)/ln(1 + 18εR). However, this only improves the approximation for certain 17δP and 18δP values, for certain net to gross production ratios (f) and for certain ratios of gross production to gross Air-O2 invasion (g). In other cases, the approximated calculation based on 17Δ† ≡ 17 δ - κ 18 δ with κ = γR = 17εR/18εR gives better results. [ABSTRACT FROM AUTHOR]

We study the existence and approximation of fixed points for the recently introduced class of mappings called enriched Suzuki nonexpansive mappings in the setting of Banach spaces. We use the modified K-iteration process to establish the main results of the paper. The class of enriched Suzuki nonexpansive operators is an important class of nonlinear operators that includes properly the class of Suzuki nonexpansive operators as well as enriched nonexpansive operators. Various assumptions are imposed on the domain or on the operator to establish the main convergence theorems. Eventually, a numerical example of enriched Suzuki nonexpansive operators is used to show the effectiveness of the studied iteration scheme. The main outcome of the paper is new and essentially suggests a new direction for researchers who are working on fixed point problems in a Banach space setting. Our results improve and extend some main results due to Hussain et al. [ABSTRACT FROM AUTHOR]

Several tools have been put forth to handle the problem of uncertain knowledge. Pawlak (1982) initiated the concept of rough set theory, which is a completely new tool for solving imprecision and vagueness (uncertainty). The main notions in this theory are the upper and lower approximations. One of the most important aims of this theory is to reduce the vagueness of a concept to uncertainty areas at their borders by decreasing the upper approximations and increasing the lower approximations. So, the object of this study is to propose four types of approximation spaces in rough set theory utilizing ideals and a new type of neighborhoods called "the intersection of maximal right and left neighborhoods". We investigate the master properties of the proposed approximation spaces and demonstrate that these spaces reduce boundary regions and improve accuracy measures. A comparative study of the present methods and the previous ones is given and shown that the current study is more general and accurate. The importance of the current paper is not only that it is introducing new kinds of approximation spaces relying mainly on ideals and a new type of neighborhoods which increases the accuracy measure and reduces the boundary region of subsets, but also that these approximation spaces are monotonic, which means that it can be successfully used to evaluate the uncertainty in the data. In the end of this paper, we provide a medical example of the heart attacks problem to show the efficiency of the current techniques in terms of approximation operators, accuracy measures, and monotonic property. [ABSTRACT FROM AUTHOR]

Theoretical model identifiability and universality are opposites. Only the strongest and most basic forces and models are universal enough to permit reasonable extrapolation above and beyond their specific historical contexts. Unfortunately, papers that admit to these limits are rarely considered interesting. Instead, researchers search for and find ever-more unlikely explanations and ever-more unlikely evidence in a competitive quest to be surprising, clever and published. The review processes have also incentiviced lack of care, private and social failure to correct errors, and even outright misconduct. The discipline is veering towards a theater of the absurd. To help correct the problem, I suggest dedicating a third of every journal to independent replications and critique of prior papers. [ABSTRACT FROM AUTHOR]

Aircraft observations of meteorological, trace gas, and aerosol properties were made during May-September 2013 in the southeastern United States (US) under fair-weather, afternoon conditions with well-defined planetary boundary layer structure. Optical extinction at 532 nm was directly measured at three relative humidities and compared with extinction calculated from measurements of aerosol composition and size distribution using the κ-Köhler approximation for hygroscopic growth. Using this approach, the hygroscopicity parameter κ for the organic fraction of the aerosol must have been < 0.10 to be consistent with 75 % of the observations within uncertainties. This subsaturated κ value for the organic aerosol in the southeastern US is consistent with several field studies in rural environments. We present a new parameterization of the change in aerosol extinction as a function of relative humidity that better describes the observations than does the widely used power-law (gamma, γ) parameterization. This new single-parameter κext formulation is based upon κ-Köhler and Mie theories and relies upon the well-known approximately linear relationship between particle volume (or mass) and optical extinction (Charlson et al., 1967). The fitted parameter, κext, is nonlinearly related to the chemically derived κ parameter used in κ-Köhler theory. The values of κext we determined from airborne measurements are consistent with independent observations at a nearby ground site. [ABSTRACT FROM AUTHOR]

Cultivation of the terrestrial land surface can create either a source or sink of atmospheric CO2, depending on land management practices. The Community Land Model (CLM) provides a useful tool to explore how land use and management impact the soil carbon pool at regional to global scales. CLM was recently updated to include representation of managed lands growing maize, soybean, and spring wheat. In this study, CLM-Crop is used to investigate the impacts of various management practices, including fertilizer use and differential rates of crop residue removal, on the soil organic carbon (SOC) storage of croplands in the continental United States over approximately a 170 year period. Results indicate that total US SOC stocks have already lost over 8PgC (10%) due to land cultivation practices (e.g., fertilizer application, cultivar choice, and residue removal), compared to a land surface composed of native vegetation (i.e., grasslands). After long periods of cultivation, individual plots growing maize and soybean lost up to 65 % of the carbon stored, compared to a grassland site. Crop residue management showed the greatest effect on soil carbon storage, with low and medium residue returns resulting in additional losses of 5% and 3.5%, respectively, in US carbon storage, while plots with high residue returns stored 2% more carbon. Nitrogenous fertilizer can alter the amount of soil carbon stocks significantly. Under current levels of crop residue return, not applying fertilizer resulted in a 5% loss of soil carbon. Our simulations indicate that disturbance through cultivation will always result in a loss of soil carbon, and management practices will have a large influence on the magnitude of SOC loss. [ABSTRACT FROM AUTHOR]