## We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations.

Simple equations method (SEsM) and its connection with the inverse scattering transform method

## We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations.

Homogeneous balance method and auxiliary equation method as particular cases of simple equations method (SEsM)

## Although the model’s essence is encapsulated in only two simple equations, it can simulate well the experimentally observed volume change accumulation with freeze-thaw cycles under different stress levels and densities (or over-consolidation ratios).

A model for freeze-thaw-induced plastic volume changes in saturated clays

## In this article, two simple equations are developed for percolation onset and electrical conductivity of multiphase polymer systems containing carbon nanotubes (CNTs) and nanoclay.

Percolation onset and electrical conductivity for a multiphase system containing carbon nanotubes and nanoclay

## We further provide simple equations to calculate the global optimal solution for our nonlinear programme allocation models.

A DEA-based incentive approach for allocating common revenues or fixed costs

## The model provides simple equations, fed with data from literature on materials, production and their tribological combination to provide initial insight on the sustainability of these types of bearings and future designs.

An eco-impact design metric for water lubricated bearings based on anticipatory Life Cycle Assessment

## In this paper, we derive simple equations to qualitatively explain the tail profile under a horizontal wind.

Kite festival: the physics behind the oscillations of a kite’s long tail

## Our model of the electric charge and its field (this paper) enables us (in additional papers), for the first time, to derive simple equations for the radii and masses of the electron/positron muon/anti-muon and quarks/anti-quarks.

Electric Charge and Its Field as Deformed Space

## Based on our previous work on generalising Bianchi identities for this kind of theories, we show how this search of solutions can be reduced to the study of two relatively simple equations.

Approaches to Spherically Symmetric Solutions in f(T) Gravity

## The database obtained from the parametric study was then used in a sophisticated artificial intelligence/machine learning analysis via evolutionary polynomial regression (EPR) technique to return a standalone design tool in the form of relatively simple equations for predicting the RBB pile capacity.

Design of Ram-Compacted Bearing Base Piling Foundations by Simple Numerical Modelling Approach and Artificial Intelligence Technique

## We present simple equations to facilitate the comparison of different fabrication methods based on the density and location of NITs and give some information about their origin.

A method for characterizing near-interface traps in SiC metal–oxide–semiconductor capacitors from conductance–temperature spectroscopy measurements

## In order to help workers develop appropriate sampling approaches that produce the desired level of precision, we present simple equations that approximate the proportional uncertainty associated with the 50th and 84th percentiles of the distribution as a function of sample size and sorting coefficient; the true uncertainty in any sample depends on the shape of the sample distribution and can only be accurately estimated once the sample has been collected.

Percentile-based grain size distribution analysis tools (GSDtools) – estimating confidence limits and hypothesis tests for comparing two samples

## We derive new simple equations, which explain how the ideal Hawkes reconstruction is linked to the covariance between the observed neurons.

Towards a mathematical definition of functional connectivity

## Numerical simulations have shown a good accuracy of the new simple equations when these are used within their limits of application.

Numerical Investigation of Analytical Models of Drug Flux Through Microporated Skin.

## Instead of replacing the previous SNI (The Indonesian National Standard) 6389:2011, this paper will introduce several simple equations as empirical formulas covering solar factor (SF), effective shading coefficient (SCeff), and OTTV.

Practical-Empirical Modeling on Envelope Design towards Sustainability in Tropical Architecture

## However, PET and WET can be easily calculated using several simple equations based on available climate data.

Combining generalized complementary relationship models with the Bayesian Model Averaging method to estimate actual evapotranspiration over China

## Three simple equations were developed for the three soils to predict frozen soil hydraulic conductivity.

Hydraulic Conductivity Measurement for Three Frozen and Unfrozen Soils in the Red River of the North Basin

## From these results, we provide three simple equations for CRT, AGT, and SGT correction for future research use under warm-hot and clear conditions.

Improved methods for estimating mean radiant temperature in hot and sunny outdoor settings

## In case of a single interface in the fracture, numerical experimentation yields simple equations for recommended timestep in Newtonian/Newtonian displacement based on the fluid mobility ratio and the maximum allowed error in the breakthrough time.

Fluid Displacement in a 2D DFN Fracture: Time Integration of the Interface Position

## The framework yields simple equations that can be arranged in a layered structure that we call the evo-devo process, whereby five elementary components generate all equations including those describing genetic covariation and the evo-devo dynamics.

A mathematical framework for evo-devo dynamics

## In this study, data-driven methods (DDMs) including different kinds of group method of data handling (GMDH) hybrid models with particle swarm optimization (PSO) and Henry gas solubility optimization (HGSO) methods, and simple equations methods were applied to simulate the maximum hydro-suction dredging depth (hs).

Prediction of hydro-suction dredging depth using data-driven methods

## We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities.

On the Use of Composite Functions in the Simple Equations Method to Obtain Exact Solutions of Nonlinear Differential Equations

## The comparison reveals that these simple equations would not be able to estimate the impact force well, even though parameter setting is required for applying the equations.

Dynamic centrifuge model tests and material point method analysis of the impact force of a sliding soil mass caused by earthquake-induced slope failure

## Simple equations would fail since a living being or an idea may face different conditions after every step in diffusion.

The Invasions of Genes and Plants

10.1016/j.jmmm.2020.167368

## Together with data provided from the ferrite manufacturers, offered set of simple equations can qualitatively estimate quiescent and operating power consumption, and help in avoidance of design solutions that lead to unnecessary power losses.

Low-power self-oscillating fluxgate current sensor based on Mn-Zn ferrite cores

10.1016/J.ISTRUC.2021.01.084

## Simple equations for the determination of structural lateral stiffness, critical loads, and natural frequencies are presented and verified against the linear elastic analysis results or numerical models developed by ANSYS.

Relations between buckling & vibrational characteristics of coupled shear walls

10.1016/J.JCSR.2021.106702

## The strength equations developed in this study are expressed as simple equations and provide reliable strength predictions without any inherent subjectivity.

Compressive strength equations for box-girder flanges stiffened with U-ribs in cable-supported bridges

## Additionally, the quantitative method offers a strictly cartesian perspective for determining future scenarios, while the sustainable vector model, based on a fractalized vision of reality, manages to capture a plurality of perspectives, as well as the interrelationships between the determining parameters, thus being a complex system of simple equations, as opposed to the quantitative method which is defined as a simple system of complex equations.

Analysing the Stock Market as an Economic Lever, Using a Qualitative and a Quantitative Model

## Here, an analytical model is suggested which allows for both the simplified fitting of the parameters required for predicting boron transport coefficients and also the simple equations that can be used for the design of combined seawater and boron removal systems.

Analytical Models for Seawater and Boron Removal through Reverse Osmosis

10.1007/s11709-021-0719-7

## In this study, data-driven methods (DDMs) including different kinds of group method of data handling (GMDH) hybrid models with particle swarm optimization (PSO) and Henry gas solubility optimization (HGSO) methods, and simple equations methods were applied to simulate the maximum hydro-suction dredging depth (hs).

Prediction of hydro-suction dredging depth using data-driven methods

## In the limit of high oxygen consumption in the catalyst layer, simple equations for the static point of zeta impedance are derived.

Analytical Model for Pem Fuel Cell Concentration Impedance

## This includes obtaining a set of analytical solutions related to the steady motion in wind and analysis of wind-tunnel data which resulted in simple equations for conservative generalized envelopes for the aerodynamic forces which are especially convenient for standardizing purposes.

Review on Ship Manoeuvrability Criteria and Standards

## The low Young’s modulus and large fracture energy of SR gels are expressed by simple equations as a function of the degree of sliding movement.

Softness, Elasticity, and Toughness of Polymer Networks with Slide-Ring Cross-Links

10.1016/j.jenvman.2021.113031

## A control-oriented quality modeling approach is proposed for sewer networks, which can represent quality dynamics using simple equations in order to optimize pollution load from combined sewer overflows in large scale sewer network in real time.

Control-oriented quality modelling approach of sewer networks.

10.4230/LIPIcs.MFCS.2021.78

## The NP certificates are solutions of simple equations involving relations over the syntactic monoid.

Syntactic Minimization of Nondeterministic Finite Automata

10.3390/computation9100104

## We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities.

On the Use of Composite Functions in the Simple Equations Method to Obtain Exact Solutions of Nonlinear Differential Equations

10.1016/J.HEALUN.2021.01.988

## This study compared bedside prediction of EER using simple equations with a more complex technology based EER using a multisensor device (Sensewear v8.

Comparison of Estimated Energy Requirements in Lung Transplant Candidates

10.1016/j.jelechem.2021.115672

## In the limit of high oxygen consumption in the catalyst layer, simple equations for the static point of zeta impedance are derived.

Analytical model for PEM fuel cell concentration impedance

10.1021/acs.nanolett.0c04702

## Surprisingly, simple equations describe this intensity sensitivity very accurately and allow us to distinguish the various contributions: Rayleigh scattering, dielectric contrast, plasmon shift, and frequency-dependent plasmon bulk damping.

Intensity-Based Single Particle Plasmon Sensing.

10.1523/JNEUROSCI.0269-21.2021

## Short sentences and simple equations were presented diotically at fixed and distinct word/symbol and sentence/equation rates.

Cortical Processing of Arithmetic and Simple Sentences in an Auditory Attention Task

10.1016/J.OCEANENG.2021.108717

## Simple equations are used for estimating the overwash height and energy fluxes, which are found to be in fair agreement with the present CFD simulations.

Wave energy attenuation by drifting and non-drifting floating rigid plates

10.1109/TAP.2021.3070719

## Simple equations describing the beam steering angle and overall size for a minimum radar cross-sectional area (RCS) are presented that aid the system designer.

Linearly Polarized Reconfigurable Reflectarray Surface

10.1016/J.IJHYDENE.2021.06.230

## Based on parametric study, the relationships among the average dehydriding rate, the heat transfer coefficient, the heating water temperature and the outlet pressure have been found and fitted as simple equations.

Hydrogen release from a metal hydride tank with phase change material jacket and coiled-tube heat exchanger

## By processing using simple equations, the stiffness of each spring can be obtained.

Pengujian Kekakuan Gas Spring 80 N

10.5459/bnzsee.54.3.211-227

## A clear trend was observed regarding the influence of these parameters on the initiation of OOP displacement, based on which simple equations are proposed for prediction of OOP instability in rectangular walls.

Design recommendations to prevent global out-of-plane instability of rectangular reinforced concrete ductile walls

10.1016/J.COLSURFA.2021.127330

## The moduli and volume portions of networked HNT and nearby interphase section are expressed by simple equations and meaningful factors.

An applicable model for the modulus of polymer halloysite nanotubes samples by the characteristics of halloysite nanotubes, interphase zone and filler/interphase network

10.1016/J.RSMA.2021.101713

## A set of simple equations were derived, which link the salt-wedge intrusion length, salt-wedge volume, and salt-wedge spread to the river flow rate.

Salt-wedge dynamics in microtidal Neretva River estuary

10.1134/s0010508221040110

## A description of the obtained experimental data using simple equations of state is proposed.

Shock Compression of Titanium Hydride and Titanium, Tantalum, and Zirconium Deuterides

10.1109/NEWCAS50681.2021.9462789

## An approach with simple equations aided with look up tables is used to obtain a theoretical prediction of the minimum voltage and current required for operation.

Minimum Supply Voltage of 2.45 GHz LC Oscillator in 28 nm FD-SOI Process

10.1016/j.ifacol.2021.08.210

## A nonlinear model predictive controller with an internal model structure is designed from these simple equations, showing the simplicity of tuning and implementation.

Simple Model and Predictive Control of a Pharmaceutical Batch Fluidized Bed Dryer

10.3389/fpsyt.2021.595124

## It firstly describes how complex patterns can emerge from simple equations.

Health and Disease Are Dynamic Complex-Adaptive States Implications for Practice and Research

10.1101/2021.01.31.429030

## Short sentences and simple equations were presented diotically at fixed and distinct word/symbol and sentence/equation rates.

Cortical Processing of Arithmetic and Simple Sentences in an Auditory Attention Task

## Using particular case of the recently developed SEsM (Simple Equations Method) namely the Modified method of Simplest Equation – and one of its extended versions [8, 9], we obtain a new traveling wave solution of the model system.

Nonlinear travelling waves in a generalized model of interacting dense populations

## RESULTS A correlation was found between the determined CFR from simple equations and from a steady flow simulation (r = 0.

Simplified coronary flow reserve calculations based on three-dimensional coronary reconstruction and intracoronary pressure data.

## The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times.

Global Tree Taper Modelling: A Review of Applications, Methods, Functions, and Their Parameters

10.47363/jpsos/2021(3)137

## The conclusion reached in this article is that Time Dilation and Length Contraction cannot be characterized by simple equations due to repulsion gravity.

Relativity Tied to Repulsion Gravity

## By using simple equations for how the traveltime will change if a thin sand layer is charged by gas in a localized and constrained region, we show that such variations can be used to map and quantify the thickness of the gas layer.

Using diving waves for detecting shallow overburden gas layers

10.22541/au.162779065.53682371/v1

## Simple equations are proposed to account for SCE in fatigue crack growth.

Significance of Stable Crack Extension to Fatigue Crack Growth

10.3934/matersci.2021043

## Simple equations, which can be used to calculate the length and amount of SMA bars required to retrofit a RC BCJ, are then developed.

Numerical investigation of reinforced-concrete beam-column joints retrofitted using external superelastic shape memory alloy bars

## With the objective of providing a simple, but empowering, tool for these forest owners, simple equations based only on diameter were developed to estimate individual tree volume for the Orbigo River basin.

Empowering Forest Owners with Simple Volume Equations for Poplar Plantations in the Órbigo River Basin (NW Spain)