Search

The moving asymptotes function is widely applied as sequential explicit convex approximation in topology optimization, due to the controllable conservatism and convergence. In virtue of these advantages, it is supposed that the efficiency of optimality criteria method will become higher if constraint functions are approximated by moving asymptotes function instead of linear function. This work presents an optimality criteria method for topology optimization under multiple constraints where the constraint functions are approximated by moving asymptotes function. The dual feasibility condition is customarily adopted to establish explicit update scheme of topological variable, where hypothesis of active topological variable set is avoided, in the case that gradient of objective function is positive. The complementary slackness condition and primal feasibility condition are combined into a simplified dual programming to solve for the Lagrange multipliers, where hypothesis of active constraint set is avoided. Three benchmark examples under multiple displacement, stress, compliance or eigenfrequency constraints are solved by the presented optimality criteria method, the results are compared to the method of moving asymptotes and the optimality criteria method with linear constraint approximation.

In this paper, in the scope of a non-extensive statistical model for the nucleon’s structure function, the volume of the gluons in the nucleons and the relations among the temperature, T, the parameter “q” of Tsallis statistics, and the scattering energies, Q2, are studied. A system of equations with the usual sum rules are solved for the valence quarks, the experimental results for the polarized structure function, and the estimated carried moments for gluons and quarks. Each state of T and q leads to a set of chemical potentials and different radii for gluons and quarks. We conclude that gluons must occupy a larger volume than the quarks to fit the fraction of the total momentum. A linear function of the temperature with Q2 is obtained as an approach. The obtained range of temperatures is different from the previous models.

Analysis of transient recovery voltage is essential to develop high-voltage direct current circuit breakers with active current injection technology. This study presents a theoretical analysis of the transient recovery voltage using the Laplace transform, thereafter the value of the transient recovery voltage obtained using this analytical equation is compared to measured reference values. It is found that the analytical transient recovery voltage is given by the sum of a linear function and a damped oscillation function. The amplitude of the damped oscillation is reduced by the resistance of post-arc plasma; therefore, it is necessary to consider the resistance owing to post-arc plasma to evaluate the transient recovery voltage accurately.

This paper is devoted to solving inverse problems of simulation modeling, which are presented in the form of an optimization problem. The article discusses the use of direct search methods taking into account the specifics of the problem under consideration. Due to the fact that these methods require a lot of computational experiments, two algorithms based on approximation were proposed for solving the problem. The first algorithm consists in determining and evaluating the parameters of the function of dependence (which can be linear or non-linear) of the output variable on the input variables and solving the inverse problem by minimizing increments of the arguments. In the second algorithm a linear function of dependence is iteratively constructed using the data set generated by changing the input variables in given increments, and the inverse problem is solved by minimizing increments of the arguments. The classical inventory management model with a threshold strategy is considered as an example. The inverse problem was solved using direct search and approximation-based methods.

The speed of short-term memory scanning is thought to be captured in the slope of the linear function of mean reaction times (RTs) regressed on set size in the Sternberg memory scanning task (SMST). Individual differences in the slope parameter have been hypothesized to correlate with general intelligence ('g'). However, this correlation can usually not be found. This present study chose a fixed-links model (FLM) approach to re-evaluate the RT slope parameter on a latent level in a sample of 102 participants aged 18 to 61 years who completed the SMST with set sizes 1, 3, and 5. The same was tried for P3 latencies to investigate whether or not both parameters measure the same cognitive processes in the SMST, and to assess the usability of both slopes to predict 'g'. For RTs, a linear increase with set size was found. The slope of mean RTs correlated with 'g' on a manifest level already. The FLM approach could better reveal this relationship with the correlation between the slope and 'g' being substantially higher. For P3 latencies, we found no evidence for a linear increase, but a general increase from the smallest set size to the two larger ones. This indicates that RTs and P3 latencies do not measure the same cognitive processes in the SMST. The FLM proved suitable to investigate the association between the speed of short-term memory scanning and intelligence.

Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a surprising lack of work on computing the non-linearity of a function. The non-linearity is related to the Walsh coefficient with the largest absolute value; however, the naive attempt of picking the maximum after constructing a Walsh spectrum requires $\Theta(2^n)$ queries to an $n$-bit function. We improve the scenario by designing highly efficient quantum and randomised algorithms to approximate the non-linearity allowing additive error, denoted $\lambda$, with query complexities that depend polynomially on $\lambda$. We prove lower bounds to show that these are not very far from the optimal ones. The number of queries made by our randomised algorithm is linear in $n$, already an exponential improvement, and the number of queries made by our quantum algorithm is surprisingly independent of $n$. Our randomised algorithm uses a Goldreich-Levin style of navigating all Walsh coefficients and our quantum algorithm uses a clever combination of Deutsch-Jozsa, amplitude amplification and amplitude estimation to improve upon the existing quantum versions of the Goldreich-Levin technique., Comment: Accepted in ACM Transactions on Quantum Computing

We consider the quantity P ( G ) associated with a graph G that is defined as the probability that a randomly chosen subtree of G is spanning. Motivated by conjectures due to Chin, Gordon, MacPhee and Vincent on the behaviour of this graph invariant depending on the edge density, we establish first that P ( G ) is bounded below by a positive constant provided that the minimum degree is bounded below by a linear function in the number of vertices. Thereafter, the focus is shifted to the classical Erdos-Renyi random graph model G ( n , p ). It is shown that P ( G ) converges in probability to e - 1 / ( e p infinity ) if p -> p infinity > 0 and to 0 if p -> 0. As side results, we find in the dense case that the total number of subtrees satisfies a log-normal limit law, and that the number of vertices missing in a random subtree asymptotically follows a Poisson distribution.

Coefficient of restitution is regarded as a dominating parameter in rockfall research. Generally, small-scale experiments were developed without considering interactions between boulder and slope. However, preimpact moving statuses are essential to evaluate rockfall behaviors. To reveal the effect of preimpact interactions on coefficient of restitution, energy dissipation considering initial velocity, surface type, and slope angle is executed based on medium-scale tests. The results show that (1) as the inclination of initial velocity, higher rebound height, and the declining normal coefficient of restitution occur, a determinable linear function could demonstrate relationships among energy dissipation and all coefficient of restitution; when initial velocity exceeds 5 m/s, the recovery ability shows and produces an increasing trend with respect to the variation of kinematic coefficient of restitution and kinetic energy coefficient of restitution. (2) As the surface material varies, slope hardness and rebound ability influence normal coefficient of restitution, and the surface roughness and rotation feature dominate tangential coefficient of restitution; considering preimpact slope and boulder interactions, four types of coefficient of restitution follow declining trend with different material sequence. (3) Slope angle affects normal coefficient of restitution, and tangential coefficient of restitution relatively descends 18% and inclines 10% when the angle ranges from 30° to 75°; regarding preimpact moving status, it differs from bounce times. The correlation between preimpact energy dissipation and four coefficients of restitution can be represented by the same decreasing linear function, when increasing the slope angle.

We propose a multithreshold change plane regression model which naturally partitions the observed subjects into subgroups with different covariate effects. The underlying grouping variable is a linear function of observed covariates and thus multiple thresholds produce change planes in the covariate space. We contribute a novel two-stage estimation approach to determine the number of subgroups, the location of thresholds, and all other regression parameters. In the first stage we adopt a group selection principle to consistently identify the number of subgroups, while in the second stage change point locations and model parameter estimates are refined by a penalized induced smoothing technique. Our procedure allows sparse solutions for relatively moderate- or high-dimensional covariates. We further establish the asymptotic properties of our proposed estimators under appropriate technical conditions. We evaluate the performance of the proposed methods by simulation studies and provide illustrations using two medical data examples. Our proposal for subgroup identification may lead to an immediate application in personalized medicine.

The article provides analytical expressions for the electromagnetic fields generated by a lightning return stroke characterized by a channel-base current with arbitrary time waveform, in presence of either a perfectly conducting or a lossy ground, assuming the transmission line model for the current along the channel. In this second case, a time-domain analytical expression for the Cooray–Rubinstein formula is presented. The main idea that leads to the derivation of analytical formulas consists of dividing the channel into intervals in which the distance between the field source point and the observation point can be approximated with a linear function of the time, and of the spatial coordinates of both points. In the companion aticle, a detailed comparison is proposed with the classical (numerical) approach highlighting an excellent agreement both at close and far distances, considering all the values of practical interest for the ground conductivity. Moreover, the method guarantees a meaningful improvement in computational performance.

In this paper, we study the optimal execution problem by considering the trading signal and the transaction risk simultaneously. We propose an optimal execution problem by taking into account the trading signal and the execution risk with the associated decay kernel function and the transient price impact function being of generalized forms. In particular, we solve the stochastic optimal control problems under the assumptions that the decay kernel function is the Dirac function and the transient price function is a linear function. We give the optimal executing strategies in state-feedback form and the Hamilton‐Jacobi‐Bellman equations that the corresponding value functions satisfy in the cases of a constant execution risk and a linear execution risk. We also demonstrate that our results can recover previous results when the process of the trading signal degenerates.

The Khrapchenko method of finding a lower bound for the complexity of binary formulas is extended to formulas in $$k$$ -ary bases. The resulting extension makes it possible to evaluate the complexity of linear Boolean functions and a majority function of $$n$$ variables when realized by formulas in the basis of all $$k$$ -ary monotone functions and negation as $$\Omega(n^{g(k)})$$ , where $$g (k)=1+\Theta(1/\ln k)$$ . For a linear function, the complexity bound in this form is unimprovable. For $$k=3$$ , the sharper lower bound $$\Omega(n^{1.53})$$ is proved.

The generalized variable step-size diffusion continuous mixed p-norm (GVSS-DCMPN) algorithm is proposed in this paper, which is derived based on the improved continuous mixed p-norm (CMPN) strategy. In detail, a linear function is designed for the CMPN strategy. The proposed GVSS-DCMPN algorithm capable of exploiting various error norms to obtain performance improvement in non-Gaussian noise environment can be viewed as the generalization of the traditional p-norm-based algorithms in the sense of continuous errors. In particular, the GVSS-DCMPN algorithm transforms into the VSS-DCMPN algorithm when the slope of the linear function is set to 0. The computational complexity as well as the mean convergence is analyzed in the paper. Simulation results over the diffusion network show that the proposed algorithm achieves performance gain over some existing diffusion algorithms.

In this paper, we consider data driven control of Hammerstein systems. For such systems a common control structure is a transfer function followed by a static output nonlinearity that tries to cancel the input nonlinearity of the system, which is modeled as a polynomial or piece-wise linear function. The linear part of the controller is used to achieve desired disturbance rejection and tracking properties. To design a linear part of the controller, we propose a weighted average risk criterion with the risk being the average of the squared L2 tracking error. Here the average is with respect to the observations used in the controller and the weighting is with respect to how important it is to have good control for different impulse responses. This criterion corresponds to the average risk criterion leading to the Bayes estimator and we therefore call this approach Bayes control. By parametrizing the weighting function and estimating the corresponding hyperparameters we tune the weighting function to the information regarding the true impulse response contained in the data set available to the user for the control design. The numerical results show that the proposed methods result in stable controllers with performance comparable to the optimal controller, designed using the true input nonlinearity and true plant.

In this work, we prove that the ratio of torsion and curvature of any dual rectifying curve is a non-constant linear function of its dual arc length parameter. Thereafter, a dual differential equation of third order is constructed for every dual curve. Then, several well-known characterizations of dual spherical, normal and rectifying curves are consequences of this differential equation. Finally, we prove a simple new characterization of dual spherical curves in terms of the Darboux vector.

When using the Cobb-Douglas (C-D) production function to measure the contribution rate of agricultural technological progress (ATP), it is necessary to estimate the output elasticity coefficient (OEC) of each input factor in C-D production function. For this purpose, it is usually necessary to take logarithm at both sides of C-D production function and convert it into a linear function, and then use regression analysis method to estimate the OECs of input factors. However, there are some problems in this method remains unsolved: first, the OECs estimated by taking logarithm of C-D production function are not the optimal estimation of the original C-D production function; second, the regression results sometimes fail to pass statistical test; third, some OECs cannot be guaranteed to be non-negative. Aiming at resolving these problems, a method for estimating OECs in C-D production function based on the Hybrid Improved Bat Optimization Algorithm (HIBA) was proposed. This method solves the problems existing in the OEC estimation methods in the existing literatures. To verify the effectiveness of the proposed method in this study, the OECs of input factors in China’ Sichuan Province from 1996 to 2018 was estimated. The estimation results show that, compared with other estimation methods in the existing literatures, the proposed method can not only guarantee that it is the optimal estimation of the OECs in the original C-D production function, but also ensure that the OECs are non-negative and with high precision and good fitting effect. Finally, based on the estimation results, this study measured and analyzed the contribution rate of agricultural input factors and ATP of Sichuan Province and puts forward corresponding suggestions for the agricultural development in this region.

Problems of differential equations construction of equilibrium of a geometrically and physically nonlinear continuous medium under conditions of one-dimensional plane deformation are considered, when the diagrams of volumetric and shear deformation are approximated by quadratic functions. The construction of physical dependencies is based on calculating the secant moduli of volumetric and shear deformation. When approximating the graphs of the volumetric and shear deformation diagrams using two segments of parabolas, the secant shear modulus in the first segment is a linear function of the intensity of shear deformations, the secant modulus of volumetric expansion - contraction is a linear function of the first invariant of the strain tensor. In the second section of the diagrams of both volumetric and shear deformation, the secant shear modulus is a fractional (rational) function of the shear strain intensity, the secant modulus of volumetric expansion - compression is a fractional (rational) function of the first invariant of the strain tensor. Based on the assumption of independence, generally speaking, from each other of the volumetric and shear deformation diagrams, six main cases of physical dependences are considered, depending on the relative position of the break points of the graphs of the diagrams volumetric and shear deformation, each approximated by two parabolas. The differential equations of equilibrium in displacements constructed in the article can be applied in determining the stressed and deformed state of a continuous medium under conditions of one-dimensional plane deformation, the closing equations of physical relations for which, constructed on the basis of experimental data, are approximated by biquadratic functions.

This paper is concerned with global stabilization of discrete-time multiple integrators with bounded controls by utilizing the energy function based approach. First, a discrete-time double integrators system subject to input additive disturbances is stabilized by a bounded feedback whose formula involves a linear function of the state and a saturation function only. Next, this result is used to stabilize a discrete-time multiple integrators of arbitrary length by bounded control with the aid of a special canonical form. Compared with the existing results, the proposed controllers require fewer saturation functions, which allow a better use of the control energy. Moreover, some free parameters that are introduced into these controllers can help improve the transient performance of the closed-loop systems significantly. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

A study has been made of the pressure field in filtration of a weakly compressible fluid in a homogeneous isotropic compressible medium at high-amplitude perturbations. The equation used in formulating the problem is nonlinear: the densities of a porous medium and of a saturating fluid are assumed to be dependent on the function sought. Use is made of the fact that the dependences of the densities of the fluid and the skeleton material on pressure are approximated with a high degree of accuracy by the linear function. Consideration is given to one-dimensional plane horizontal filtration. The porosity and permeability of a porous medium, and also the viscosity of a filtering medium, are considered to be constant. A solution to the problem has been found with asymptotic expansions where a cofactor of the compressibility factor of the liquid acts as a small parameter. Analytical expressions have been found for the zero and first expansion factors. It has been shown that the zero expansion factor may be used to investigate the evolution of the pressure field of an incompressible liquid, whereas the expression for the first factor contains information on the contribution of nonlinearity due to the fluid’s compressibility. Values of the zero and first residual terms have been determined. It has been proved that the zero and first residual terms contain terms of only higher orders as far as the asymptotic-expansion parameter is concerned, i.e., the corresponding requirement of asymptoticity of expressions of the zero and first factors is met. On the basis of a computational experiment, the regularities of the dependence of the contribution of the nonlinearity under study on time and on the spatial coordinate have been established.

Ping’ou hybrid hazelnut is produced by cross cultivation and is widely cultivated in northern China with good development prospects. Based on a field experiment of fertilizer efficiency, the leaf spectral reflectance and leaf potassium (K) concentration were measured with different quantities of K fertilizer applied at four fruit growth stages (fruit setting stage, fruit rapid growth stage, fruit fat-change stage, and fruit near-maturity stage) of Ping’ou hybrid hazelnut in 2019. Spectral parameters that were significantly correlated with leaf K concentration were selected using Pearson correlation analysis, and spectral parameter estimation models of leaf K concentration were established by employing six different modelling methods (exponential function, power function, logarithmic function, linear function, quadratic function, and cubic function). The results indicated that at the fruit setting period, leaf K concentration was significantly correlated with Dy (spectra slope of yellow edge), Rg (reflectance of the green peak position), λo (red valley position), SDb (blue edge area), SDr/SDb (where SDr represents red edge area), and (SDr−SDb)/(SDr+SDb) (P

In this paper, weighted sum energy efficiency (WSEE) in uplink and downlink of a multi-user non-orthogonal multiple access (NOMA) system is considered. we adopt a more realistic power consumption model where signal processing power is modeled as a linear function of transmit power. Rather than the well-known network-centric global energy efficiency (GEE) metric, which is a pseudo-concave (PC) function, the weighted sum energy efficiency metric is considered, which is not PC in general. To find the optimum user power allocation Dinkelbach-like algorithm is adopted, by which each individual fractional EE function is converted to a parametric function where under some conditions on the weights falls into a class of convex optimization problems and it is solved in the dual domain. The dual variables are updated using a sub-gradient and cutting plane-based algorithm, which here ellipsoid method is used. Since the optimum solution restricts user weights, a low complexity suboptimum algorithm that does not consider any condition on user's weights is proposed. The problem is non-convex in general; hence, epigraph form followed by successive convex approximation (SCA) is used to deal with that problem. Results demonstrate that with the user-oriented metric, one can provide different priorities to users, and by choosing proper weights entail fairness among users.

Surgical invasion activates nociception, while anesthesia suppresses it. Under general anesthesia, stimulation, which is the balance between nociception and anti-nociception, induces responses, including activation of the autonomic nervous system. To evaluate the associations between stimulation (S) and the resultant responses (R), we examined R values, which were calculated using mathematical models of Stevens’ power law, Gompertz function and logistic function. The previously developed Nociceptive Response (NR) formula was applied as a modified logistic model. S values were calculated using a linear function in the NR formula. In a retrospective study, we developed an exponential model of Stevens’ power law and a sigmoidal model of Gompertz function using differential equations, by adjusting R values to correspond to NR values, in consecutive patients undergoing surgery under general anesthesia (n = 4,395). In a subsequent prospective study, we validated the superiority of R values of Gompertz function and the NR formula in an exponential model in adult patients undergoing tympanoplasty (n = 141) and laparoscopic cholecystectomy (n = 86). In conclusion, both modified logistic function and Gompertz function are likely appropriate mathematical models for representing responses to stimulation resulting from the balance between nociception/anti-nociception during surgical procedures under general anesthesia.

The paper deals with estimating the r -colorability threshold for a random k -uniform hypergraph in the binomial model H ( n , k , p ) . We consider the sparse case, when the expected number of edges is a linear function of n , p n k = c n , and c > 0 , k ⩾ 4 , r ⩾ 3 are some fixed constants. We show that if c r k − 1 ln r − 1 2 ln r − r − 1 r + O ( k 2 r 1 − k ∕ 3 ln r ) then H ( n , k , c n ∕ n k ) is r -colorable with probability tending to 1 as n → ∞ .

Combinatorial optimization problems and methods of their solution have been a subject of numerous studies, since a large number of practical problems are described by combinatorial optimization models. Many studies consider approaches to and describe methods of solution for combinatorial optimization problems with linear or fractionally linear target functions on combinatorial sets such as permutations and arrangements. Studies consider solving combinatorial problems by means of well-known methods, as well as developing new methods and algorithms of searching a solution. We describe a method of solving a problem of a linear target function localization on a permutation set. The task is to find those locally admissible permutations on the permutation set, for which the linear function possesses a given value. In a general case, this problem may have no solutions at all. In the article, we propose a newly developed method that allows us to obtain a solution of such a problem (in the case that such solution exists) by the goal-oriented seeking for locally admissible permutations with a minimal enumeration that is much less than the number of all possible variants. Searching for the solution comes down to generating various permutations and evaluating them. Evaluation of each permutation includes two steps. The first step consists of function decreasing by transposing the numbers in the first n – 3 positions, and the second step is evaluation of the permutations for the remaining three numbers. Then we analyze the correlation (which is called balance) to define whether the considered permutation is the solution or not. In our article, we illustrate the localization method by solving the problem for n = 5. Keywords: localization, linear function, permutation, transposition, balance, position.

We consider n-bit permutations with differential uniformity of 4 and null nonlinearity. We first show that the inverses of Gold functions have the interesting property that one component can be replaced by a linear function such that it still remains a permutation. This directly yields a construction of 4-uniform permutations with trivial nonlinearity in odd dimension. We further show their existence for all n = 3 and n ≥ 5 based on a construction in Alsalami (Cryptogr. Commun. 10(4): 611–628, 2018). In this context, we also show that 4-uniform 2-1 functions obtained from admissible sequences, as defined by Idrisova in (Cryptogr. Commun. 11(1): 21–39, 2019), exist in every dimension n = 3 and n ≥ 5. Such functions fulfill some necessary properties for being subfunctions of APN permutations. Finally, we use the 4-uniform permutations with null nonlinearity to construct some 4-uniform 2-1 functions from $\mathbb {F}_{2}^{n}$ F 2 n to $\mathbb {F}_{2}^{n-1}$ F 2 n − 1 which are not obtained from admissible sequences. This disproves a conjecture raised by Idrisova.

Based on the method for establishing a global plasmaspheric model using observations from COSMIC and MetOp-A orbit determination GNSS receivers, Chen et al. (2017) obtained a global plasmaspheric total electron content product with a spatial resolution of 2.5° × 5° and a time resolution of 4 h. In this paper, we use those global plasmaspheric electron content product in 2008, 2010, 2011, 2012, 2014 for 1446 days to establish a global plasmaspheric empirical model based on empirical orthogonal function (EOF). The model can well characterize the spatiotemporal variation of plasmaspheric electron content (PEC) and the influence of solar radiation on it. Only the first four orders of EOF sequences can characterize the 98.43% features of the original PEC dataset. The principal component coefficient Pk is decomposed twice during modeling, and the combination of trigonometric function and linear function is used to model Pk to characterize the solar cycle, annual cycle, semi-annual cycle and quarter-cycle variation. We compare the PEC model values with the actual observation data, the results show that the empirical PEC model values are highly correlated with the actual observations. The correlation between the two is above 0.96, and the RMS maximum of the difference between the PEC model values and the observed values are 0.70 TECU, and the average of the difference between the PEC model values and the observed values are −0.18 TECU, respectively. In addition, we validate the reliability of the global plasmaspheric model established by two empirical orthogonal function decomposition method using actual observation data, according to the global distribution of the differences between the PEC model values and the observed values in low solar activity and high solar activity, it can be seen that under low solar activity and high solar activity conditions, the model has good adaptability.

Comparative analyze of the methods of interpolation of dependence of electron beam radius on position of cutting plane by the longitudinal coordinate with using three basic point have been provided in the article. It is shown, that main particularity of analytical functions, which are described such dependences, is that they have one global minimum, and outside the minimum region the character of such dependences is similar to linear. Two different approaches to interpolation of such dependences are considered. First method is based on the assumption, that in the region of beam focus the parabolical interpolation is used, and outside the focal region used the linear function. For describing of such dependences, the apparat of mathematical logic and arithmetic-logic expressions have been used. The main disadvantage of such describing of boundary trajectories of electron beams, propagated in the ionized gas, is that it is usually difficult to find the basic point, where the transfer from linear to parabolical dependence have to be realized. Another method of interpolation is based on the use of class of special functions, which are defined as the roots of n power from the polynomials of the same power. It is shown with using the method of computer simulation, that the behavior of such functions is generally corresponded to the ravine dependence, which described the trajectories of electron beams, propagated in the ionized gas. It is shown, that with using of such interpolation functions the difference between the simulation results, which are interpolated, and the values of interpolation function, always isn’t grater, than few percent, but in the most cases it consist the part of percent. Therefore, it is proved on the base of testing computer experiments, that using as the interpolation functions the roots of n power from the polynomial’s of the same power is the effective instrument for describing the boundary trajectories of short-focus electron beams in ionized gas. The obtained results are very important for the solution the practical task of defining the focal parameters of electron beams, generated by the electron sources, based on the high voltage glow discharge.

This research aims to determine the mathematical connection ability of junior high school students in Bandung. This research uses descriptive qualitative method with data triangulation. The instrument used in the form is test description as many as three questions that have been consulted with experts and refers to indicators of mathematical connection ability. The results of this research describe 1) the ability of students to connect between mathematical concepts with a percentage of 58.33%, 2) the ability of students to connect and apply mathematical concepts in other disciplines of sciences with a percentage of 50%, 3) the ability of students to apply mathematical concepts to solving problems in daily life with a percentage of 66.67%. The results showed that the mathematical connection ability of junior high school students in Bandung on the topic of linear function was good enough.

The present investigation examined the influence of heat source on a variable viscosity reactive Couette fluid flow. The upper plate moves with constant velocity while the lower plate is kept fixed. The heat source is considered to be a linear function of temperature while the fluid viscosity depends on temperature. The coupled set of differential equations regulating the fluid regime are obtained using the technique of Adomian Decomposition Method (ADM). Graphical and tabular representations showed the impacts of heat source parameter by increasing the fluid motion and temperature. Finally, the outcome of the solutions compared with previously obtained results without the influence of internal energy parameter significantly showed the effects.

BACKGROUNDAn altered balance of neuronal excitation and inhibition (E-I balance) might be implicated in the co-occurrence of autism and intellectual disability, but this hypothesis has never been tested. E-I balance changes can be estimated from the spectral slope of the aperiodic 1/f neural activity. Herein, we used magnetoencephalography (MEG) to test whether the 1/f slope would differentiate ASD children with and without intellectual disability.METHODSMEG was recorded at rest with eyes open/closed in 49 boys with ASD aged 6-15 years with a broad range of IQs, and in 49 age-matched typically developing (TD) boys. The cortical source activity was estimated using the LCMV beamformer approach. We then extracted the 1/f slope by fitting a linear function in to the log-log-scale power spectra in the high-frequency range.RESULTSThe grand averaged 1/f slope was steeper in the eyes closed than in the eyes open condition, but had high rank-order stability between them. In line with the previous research, the slope flattened with age. Children with ASD and below-average (CONCLUSIONSThe atypically flattened spectral slope of aperiodic activity in children with ASD and below-average IQ suggests a shift of the global E-I balance toward hyper-excitation. The spectral slope can provide an accessible non-invasive biomarker of the E-I ratio for translational research and making objective judgments about treatment effectiveness.

The Cox proportional hazards model is used extensively in clinical and epidemiological research. A key assumption of this model is that of proportional hazards. A variable satisfies the proportional hazards assumption if the effect of that variable on the hazard function is constant over time. When the proportional hazards assumption is violated for a given variable, a common approach is to modify the model so that the regression coefficient associated with the given variable is assumed to be a linear function of time (or of log-time), rather than being constant or fixed. However, this is an unnecessarily restrictive assumption. We describe two different methods to allow a regression coefficient, and thus the hazard ratio, in a Cox model to vary as a flexible function of time. These methods use either fractional polynomials or restricted cubic splines to model the log-hazard ratio as a function of time. We illustrate the utility of these methods using data on 12 705 patients who presented to a hospital emergency department with a primary diagnosis of heart failure. We used a Cox model to assess the association between elevated cardiac troponin at presentation and the hazard of death after adjustment for an extensive set of covariates. SAS code for implementing the restricted cubic spline approach is provided, while an existing Stata function allows for the use of fractional polynomials.

The weighted mean temperature (Tm) is a crucial parameter for determining the tropospheric delay in transforming precipitable water vapor. We used the reanalysis data provided by European Centre for Medium-Range Weather Forecasts (ECMWF) to analyze the distribution characteristics of Tm in the vertical direction in China. To address the problem that the precision of the traditional linear function model is limited in fitting the Tm profile, a scheme using the linear and Fourier functions to fit the Tm profile was constructed. Based on the least squares principle (LSQ) to fit the change in its coefficients over time, a Tm model for China with nonlinear elevation correction (CTm-h) was constructed. The experimental results show that, using ECMWF and radiosonde data to evaluate the precision of the CTm-h model, the RMS is 3.43 K and 4.64 K, respectively. Compared to GPT2w, the precision of the CTm-h model in China is increased by about 26.8%. The CTm-h model provides a significant improvement in the correction effect of Tm in the vertical direction, and the Tm profile calculated by the model is closer to the reference value.

The ratio of the B s 0 and B 0 fragmentation fractions, f s / f d , in proton-proton collisions at the LHC, is obtained as a function of B -meson transverse momentum and collision center-of-mass energy from the combined analysis of different B -decay channels measured by the LHCb experiment. The results are described by a linear function of the meson transverse momentum or with a function inspired by Tsallis statistics. Precise measurements of the branching fractions of the B s 0 → J / ψ ϕ and B s 0 → D s - π + decays are performed, reducing their uncertainty by about a factor of 2 with respect to previous world averages. Numerous B s 0 decay branching fractions, measured at the LHCb experiment, are also updated using the new values of f s / f d and branching fractions of normalization channels. These results reduce a major source of systematic uncertainty in several searches for new physics performed through measurements of B s 0 branching fractions.

The estimation of the rate at which value declines with delay requires identifying the correct discounting model, applying the appropriate parameter estimation method, and choosing the dependent measure from which parameters are estimated. The simplest adequate discounting model is the hyperbolic model; the simplest method to estimate its sole free parameter, K, is the method of least squares. Estimates of K based on relative subjective values (RSV), although typical, are not necessarily more reliable than those obtained through other measures. We consider an alternative measure termed immediacy premium (IP): the ratio of value lost over value preserved due to outcome delay. According to hyperbolic discounting, IP is a linear function of delay. As a result, estimates of K obtained from IP circumvent the divergence between individual and aggregate estimates obtained with the RSV method. Moreover, published data suggests that estimates of K based on RSV and IP differ systematically in humans and in pigeons. Regardless of the dependent measure adopted, estimates of K obtained from nonhuman animals, but not from humans, yield residuals that conform with error-distribution assumptions of the method of least squares. Although residuals obtained using the IP method in human data diverged more from normality than those obtained using the RSV method, the sequential dependence over delays of the former was weaker than that of the latter. We therefore recommend adopting both RSV and IP when estimating hyperbolic K using the method of least squares, resorting to more elaborate estimation methods when inferences drawn from these estimates are inconsistent.

In this paper, we consider the condition number theory for a linear function of the solution to the constrained and weighted least squares problem. We first present two explicit expressions without Kronecker product of normwise condition number using the classical method for condition numbers. Then, we derive the explicit expression of mixed and componentwise condition numbers by the dual techniques. To estimate these condition numbers with high reliability, we choose the probabilistic spectral norm estimator and the small-sample statistical condition estimation method and devise three algorithms. Numerical experiments are provided to illustrate the obtained results.

Stochastic $$R_0$$ matrix, which is a generalization of $$R_0$$ matrix, is instrumental in the study of the stochastic linear complementarity problem (SLCP). In this paper, we focus on the expected residual minimization (ERM) of the SLCP via the Fischer–Burmeister (FB) function, which enjoys better properties of the continuity and differentiability than the min-function-based ERM when the involved matrix is a stochastic $$R_0$$ matrix. First, we prove that the solution set of the FB-function-based ERM is nonempty and bounded if and only if the involved matrix is a stochastic $$R_0$$ matrix. Second, we show that its objective function is continuously differentiable in $${\mathbb {R}}^n$$ , which makes it possible for us to design the gradient-type algorithm. Finally, we implement the numerical experiments generated randomly via sample average approximation, and the numerical results indicate that the optimal solutions of the FB-function-based ERM are better than that of the min-function-based ERM in terms of preserving the nonnegativity of the involved linear function, especially when the involved matrix is a constant matrix.

This paper addresses a version of the single-facility Maximal Covering Location Problem on a network where the demand is: (i) distributed along the edges and (ii) uncertain with only a known interval estimation. To deal with this problem, we propose a minmax regret model where the service facility can be located anywhere along the network. This problem is called Minmax Regret Maximal Covering Location Problem with demand distributed along the edges (MMR-EMCLP). Furthermore, we present two polynomial algorithms for finding the location that minimises the maximal regret assuming that the demand realisation is an unknown constant or linear function on each edge. We also include two illustrative examples as well as a computational study for the unknown constant demand case to illustrate the potential and limits of the proposed methodology.

International audience; We consider combinatorial semi-bandits over a set X ⊂ {0, 1} d where rewards are uncorrelated across items. For this problem, the algorithm ESCB yields the smallest known regret bound R(T) = O d (ln m) 2 (ln T) ∆ min after T rounds, where m = max x ∈X 1 ⊤ x. However, ESCB has computational complexity O(|X|), which is typically exponential in d, and cannot be used in large dimensions. We propose the first algorithm that is both computationally and statistically efficient for this problem with regret R(T) = O d (ln m) 2 (ln T) ∆ min and computational asymptotic complexity O(δ −1 T poly(d)), where δ T is a function which vanishes arbitrarily slowly. Our approach involves carefully designing AESCB, an approximate version of ESCB with the same regret guarantees. We show that, whenever budgeted linear maximization over X can be solved up to a given approximation ratio, AESCB is implementable in polynomial time O(δ −1 T poly(d)) by repeatedly maximizing a linear function over X subject to a linear budget constraint, and showing how to solve these maximization problems efficiently. Additional algorithms, proofs and numerical experiments are given in the complete version of this work.

In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail.

In this paper we study a certain differential subordination related to the harmonic mean and its symmetry properties, in the case where a dominant is a linear function. In addition to the known general results for the differential subordinations of the harmonic mean in which the dominant was any convex function, one can study such differential subordinations for the selected convex function. In this case, a reasonable and difficult issue is to look for the best dominant or one that is close to it. This paper is devoted to this issue, in which the dominant is a linear function, and the differential subordination of the harmonic mean is a generalization of the Briot–Bouquet differential subordination.

Maximum parsimony distance is a measure used to quantify the dissimilarity of two unrooted phylogenetic trees. It is NP-hard to compute, and very few positive algorithmic results are known due to its complex combinatorial structure. Here we address this shortcoming by showing that the problem is fixed parameter tractable. We do this by establishing a linear kernel i.e., that after applying certain reduction rules the resulting instance has size that is bounded by a linear function of the distance. As powerful corollaries to this result we prove that the problem permits a polynomial-time constant factor approximation algorithm; that the treewidth of a natural auxiliary graph structure encountered in phylogenetics is bounded by a function of the distance; and that the distance is within a constant factor of the size of a maximum agreement forest of the two trees, a well studied object in phylogenetics. (C) 2020 The Author(s). Published by Elsevier Inc.

Our present study involves the strange stars model in the framework of $f(R,T)$ theory of gravitation. We have taken a linear function of the Ricci scalar $R$ and the trace $T$ of the stress-energy tensor $T_{\mu \nu}$ for the expression of $f(R,T)$, i.e., $f(R,T)=R+ 2 \gamma T $ to obtain the proposed model, where $\gamma$ is a coupling constant. Moreover, to solve the hydrostatic equilibrium equations, we consider a linear equation of state between the radial pressure $p_r$ and matter density $\rho$ as $p_r=\alpha \rho-\beta$, where $\alpha$ and $\beta$ are some positive constants, Both $\alpha,\,\beta$ depend on coupling constant $\gamma$ which have been also depicted in this paper. By employing the Krori-Barua {\em ansatz} already reported in the literature [J. Phys. A, Math. Gen. 8:508, 1975] we have found the solutions of the field equations in $f (R, T )$ gravity. The effect of coupling constant $\gamma$ have been studied on the model parameters like density, pressures, anisotropic factor, compactness, surface redshift, etc. both numerically and graphically. A suitable range for $\gamma$ is also obtained. The physical acceptability and stability of the stellar system have been tested by different physical tests, e.g., the causality condition, Herrera cracking concept, relativistic adiabatic index, energy conditions, etc. One can regain the solutions in Einstein gravity when $\gamma\rightarrow 0$, Comment: 26 Pages, 10 Figures

Let $M$ be a compact constant mean curvature surface either in $\mathbb{S}^3$ or $\mathbb{R}^3$. In this paper we prove that the stability index of $M$ is bounded below by a linear function of the genus. As a by product we obtain a comparison theorem between the spectrum of the Jacobi operator of $M$ and those of Hodge Laplacian of $1$-forms on $M$., Minor revision + references added

In this paper, we address an online knapsack problem under concave function f(x), i.e., an item with size x has its profit f(x). We first obtain a simple lower bound \(\max \{q, \frac{f'(0)}{f(1)}\}\), where \(q \approx 1.618\), then show that this bound is not tight, and give an improved lower bound. Finally, we find the online algorithm for linear function [8] can be employed to the concave case, and prove its competitive ratio is \(\frac{f'(0)}{f(1/q)}\), then we give a refined online algorithm with a competitive ratio \(\frac{f'(0)}{f(1)} +1\). And we also give optimal algorithms for some piecewise linear functions.

Searching for targets among similar distractors requires more time as the number of items increases, with search efficiency measured by the slope of the reaction-time (RT)/set-size function. Horowitz and Wolfe (Nature, 394(6693), 575-577, 1998) found that the target-present RT slopes were as similar for "dynamic" as for standard static search, even though the items were randomly reshuffled every 110 ms in dynamic search. Somewhat surprisingly, attempts to understand dynamic search have ignored that the target-absent RT slope was as low (or "flat") as the target-present slope-so that the mechanisms driving search performance under dynamic conditions remain unclear. Here, we report three experiments that further explored search in dynamic versus static displays. Experiment 1 confirmed that the target-absent:target-present slope ratio was close to or smaller than 1 in dynamic search, as compared with being close to or above 2 in static search. This pattern did not change when reward was assigned to either correct target-absent or correct target-present responses (Experiment 2), or when the search difficulty was increased (Experiment 3). Combining analysis of search sensitivity and response criteria, we developed a multiple-decisions model that successfully accounts for the differential slope patterns in dynamic versus static search. Two factors in the model turned out to be critical for generating the 1:1 slope ratio in dynamic search: the "quit-the-search" decision variable accumulated based upon the likelihood of "target absence" within each individual sample in the multiple-decisions process, whilst the stopping threshold was a linear function of the set size and reward manipulation.

Low-cost accurate digital realization of the spiking neural networks is crucial to investigate the behaviors of human brain performance. This paper presents a multiplierless burst-mode Fitz–Hugh Nagumo (MBM-FHN) model, which is used for generating the burst-mode of the FHN neuron model. Using extra parameters (time-varying function) in neuron equations and estimating it by linear function, efficient low-cost and high-speed implementation is achieved. The simulation results show that the MBM-FHN model generates the similar bursting patterns of the original FHN neuron. The comparison shows that the MBM-FHN model has a better performance and best cost reduction related to the original neuron model especially in overall saving and speed-up parameters.

In the paper Euclidean problems of lexicographic combinatorial; optimization are discussed. These problems are to find lexicographically minimal (for minimization problems) or lexicographically maximal (for maximization problems) points among those that give the extremum of the objective function on a given Euclidean combinatorial set. The properties of linear and linear-fractional problems of lexicographic combinatorial optimization on a general set of arrangements are substantiated. The results obtained in the work are based on the previously known criteria of extremals of linear and linear-fractional functions on arrangements: any extremal is an element of certain set of polyarrangements (for linear problems the form of the extremal set is established explicitly, for linear-fractional problems the polyarrangement set is formed on the basis of some known extremal). In the paper we substantiate the form of points that are an lexicographic minimal and lexicographic maximal of linear function on the general set of arrangements. In particular if elements of multiset are in nondecreasing order, coefficients of objective function are in nonincreasing order and s is the least index such that corresponding coefficient of objective function is negative, tehn lexicographic minimal if formed as s – 1 first and k – s + 1 ( k is the dimension of space) last elements of multiset which are in nondecreasing order. For problems with linear-fractional function we obtain the method of forming solution of lexicographic combinatorial problem on arrangements, if any minimal (for minimization problems) or any maximal (for maximization problems) of objective function on given set of arrangements is known. In this case ordering of components of the extremal is carried out taking into account ordering for nonincreasing of coefficients of special linear function

This paper extends the approach based on bargaining for computing DEA targets. Thus, for each inefficient Decision Making Unit (DMU), a bargaining problem is defined where the players are the input and output variables that can be improved. In the case of the output players, their utility is an increasing linear function of the corresponding variable. The utility of input players is a decreasing linear function of the input. The disagreement point corresponds to the input and output utilities of the DMU being projected. We show how various well-known bargaining solutions, such as Nash bargaining solution, lexicographic Kalai–Smorodinsky solution, lexicographic egalitarian solution and normalized utilitarian solution, lead to corresponding DEA bargaining models. Some properties of the DEA bargaining models are derived as a consequence of those of the corresponding bargaining solutions. The proposed approach is validated using a container shipping lines application.

An abelian processor is an automaton whose output is independent of the order of its inputs. Bond and Levine have proved that a network of abelian processors performs the same computation regardless of processing order (subject only to a halting condition). We prove that any finite abelian processor can be emulated by a network of certain very simple abelian processors, which we call gates. The most fundamental gate is a "toppler", which absorbs input particles until their number exceeds some given threshold, at which point it topples, emitting one particle and returning to its initial state. With the exception of an adder gate, which simply combines two streams of particles, each of our gates has only one input wire. Our results can be reformulated in terms of the functions computed by processors, and one consequence is that any increasing function from N^k to N^l that is the sum of a linear function and a periodic function can be expressed in terms of (possibly nested) sums of floors of quotients by integers., Comment: 35 pages, many figures. v2 revised for referee comments, to appear in Combinatorics, Probability and Computing

L-menthol is an essential oil produced from Mentha arvensis. An experimental L-menthol solid-liquid equilibrium in menthol oil constituents was determined in the temperature range between 271 K and 300 K, by the method of creating a saturated solution at a given temperature by using an excess of crystals in the suspension. The mole fraction of the experimental data, on a logarithmic basis, were fitted against T by the Apelblat equation and by a linear equation with good results. The equations were: ln(x) =#091;- 52.45 + 1,170.70/T + 8.48.ln(T) #093; and ln(x) = 3.98 -1,249.65/T with T in K. Both equations give a good correlation with the experimental data. From the Apelblat equation the enthalpy of solution was also calculated as a linear function of temperature and has an average value of 150.31 J/mol in the temperature interval studied.