## What is/are Simple Equations?

Simple Equations - 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.^{[1]}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.

^{[2]}The strength equations developed in this study are expressed as simple equations and provide reliable strength predictions without any inherent subjectivity.

^{[3]}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.

^{[4]}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.

^{[5]}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).

^{[6]}In the limit of high oxygen consumption in the catalyst layer, simple equations for the static point of zeta impedance are derived.

^{[7]}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.

^{[8]}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.

^{[9]}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.

^{[10]}The NP certificates are solutions of simple equations involving relations over the syntactic monoid.

^{[11]}We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of a class of nonlinear differential equations containing polynomial nonlinearities.

^{[12]}This study compared bedside prediction of EER using simple equations with a more complex technology based EER using a multisensor device (Sensewear v8.

^{[13]}In the limit of high oxygen consumption in the catalyst layer, simple equations for the static point of zeta impedance are derived.

^{[14]}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.

^{[15]}Short sentences and simple equations were presented diotically at fixed and distinct word/symbol and sentence/equation rates.

^{[16]}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.

^{[17]}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.

^{[18]}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.

^{[19]}By processing using simple equations, the stiffness of each spring can be obtained.

^{[20]}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.

^{[21]}The moduli and volume portions of networked HNT and nearby interphase section are expressed by simple equations and meaningful factors.

^{[22]}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.

^{[23]}A description of the obtained experimental data using simple equations of state is proposed.

^{[24]}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.

^{[25]}A nonlinear model predictive controller with an internal model structure is designed from these simple equations, showing the simplicity of tuning and implementation.

^{[26]}It firstly describes how complex patterns can emerge from simple equations.

^{[27]}Short sentences and simple equations were presented diotically at fixed and distinct word/symbol and sentence/equation rates.

^{[28]}Using particular case of the recently developed SEsM (Simple Equations Method) namely the Modified method of Simplest Equation [5]–[8] and one of its extended versions [8, 9], we obtain a new traveling wave solution of the model system.

^{[29]}RESULTS A correlation was found between the determined CFR from simple equations and from a steady flow simulation (r = 0.

^{[30]}The reviewed studies also show that taper functions have been developed from simple equations in the early 1900s to complex functions in modern times.

^{[31]}The conclusion reached in this article is that Time Dilation and Length Contraction cannot be characterized by simple equations due to repulsion gravity.

^{[32]}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.

^{[33]}Simple equations are proposed to account for SCE in fatigue crack growth.

^{[34]}Simple equations, which can be used to calculate the length and amount of SMA bars required to retrofit a RC BCJ, are then developed.

^{[35]}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.

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## nonlinear partial differential

We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations.^{[1]}We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations.

^{[2]}The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM.

^{[3]}In order to study these waves we use a method for obtaining exact solutions of nonlinear partial differential equations called Simple Equations method (SEsM).

^{[4]}We discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations.

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## Two Simple Equations

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).^{[1]}In this article, two simple equations are developed for percolation onset and electrical conductivity of multiphase polymer systems containing carbon nanotubes (CNTs) and nanoclay.

^{[2]}As we are fine just the profile of domain wall it is beneficial for us to consider the wall at rest (static) and by the aid of Euler equation we obtain two simple equations; using the equilibrium conditions, the differential equation is obtained and solved by the quadratic method and separation variables method.

^{[3]}The obtained solutions are generalized as two simple equations valid for laminar and turbulent flows, respectively.

^{[4]}To determine FMR proportionality status, we used a novel approach where two simple equations establish an individual cut-off of regurgitant volume/effective regurgitant orifice area, categorizing the study population into non-severe, proportionate and disproportionate FMR (Figure 1).

^{[5]}We also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time.

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## Provide Simple Equations

We further provide simple equations to calculate the global optimal solution for our nonlinear programme allocation models.^{[1]}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.

^{[2]}We provide simple equations to estimate the effect of channeling quantitatively and demonstrate that proximity can have a more pronounced effect under crowding conditions in vivo, particularly that crowding can enhance the overall rates of channeled cascade reactions.

^{[3]}Finally, this paper provides simple equations that are useful to provide first estimates of intrusion length and vertical average salinity in the Sebou estuary, which can be obtained by a simple desk study without the use of every measurements day.

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## Derive Simple Equations

In this paper, we derive simple equations to qualitatively explain the tail profile under a horizontal wind.^{[1]}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.

^{[2]}Here, we derive simple equations based on chemical kinetic principles to measure the translation-initiation rate, transcriptome-wide elongation rate, and individual codon translation rates from ribosome profiling experiments.

^{[3]}Here, we derive simple equations based on chemical kinetic principles to measure the translation-initiation rate, transcriptome-wide elongation rate, and individual codon translation rates from ribosome profiling experiments.

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## Relatively Simple Equations

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.^{[1]}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.

^{[2]}Analytical calculations give relatively simple equations that provide qualitative assessment of the paramagnetic particles separation process.

^{[3]}In the important special case of periodically driven systems at stroboscopic times, we find relatively simple equations for the coupling constants of the Floquet Hamiltonian, where a straightforward truncation of the couplings leads to a powerful class of approximations.

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