## What is/are First Kind?

First Kind - Finally, an application from our results using the modified Bessel function of the first kind is established as well.^{[1]}Herein, spinel Zn3V3O8 is presented as the first kind of vanadium-based material as zinc supplied cathode for AZIBs.

^{[2]}This research investigates two methods which use accelerating of Al Tememe’s inverse triangular acceleration of the first kind [1], by using “inverse sine triangular acceleration rule for Al-Tememe of the first kind” in the first method, and “inverse tangent triangular acceleration rule for Al-Tememe of the first kind” in the second method ; both of them have a major error of the first kind and these are beneficial to find double integrations with the continuous integrands specified numerically by the midpoint rule on both internal and external dimensions x and t respectively by above methods.

^{[3]}We give some relationships between degenerate poly-Frobenius-Euler polynomials and degenerate Whitney numbers and Stirling numbers of the first kind.

^{[4]}The latter provides evidence about further generalizations of coherent states, built from the Susskind-Glogower ones by extending the indexes of the Bessel functions of the first kind and, alternatively, by employing the modified Bessel functions of the second kind.

^{[5]}The given conditions and criteria, the fulfillment of which reduces the problem of heat transfer under boundary conditions of the third kind to a problem under boundary conditions of the first kind.

^{[6]}The resulting excitation force is expressed as a series of Bessel functions of the first kind.

^{[7]}Then, some useful relations including the Stirling numbers of the second and the first kinds, the usual Fubini polynomials, and the higher-order Bernoulli polynomials are derived.

^{[8]}The purpose of the present paper is to give sufficient conditions for the families of integral operators, which involve the normalized forms of the generalized Lommel functions of the first kind to be univalent in the open unit disk.

^{[9]}The relations among individuals are divided into three categories: strong links (SLs), the first kind of weak links (FWLs) and the second kind of weak links (SWLs).

^{[10]}A convolution integral equation of the first kind and integro-differential equation of the second kind with the kernel $e^{-\gamma |y-\eta|}$ on a finite and semi-infinite interval are analyzed.

^{[11]}Also, we study the necessary conditions for finding the optimal strategies for each government to fight terrorism; we discuss the existence of the solution of the formulated problem and the stability set of the first kind of the optimal strategies.

^{[12]}The first kind of method modifies the baseline method by adding the road centerline extraction task branch based on ordinal regression.

^{[13]}The second comparison is of the first kind where NO2 products from Brewer MK IV and Pandora were compared over a year-long time period.

^{[14]}High-temperature gas-cooled reactor (HTGR) is the first kind of power plant with fourth-generation features in the world, and a large amount of graphite and carbon material is adopted as structural material and fuel matrix material, including boron-containing carbon (BC) and isostatic pressure graphite (IG-110).

^{[15]}Base Isolation (BI) systems represent the first kind of control devices applied to civil structures.

^{[16]}Moreover, the closer the point of application of the pulsed force to the middle of the elastic body under boundary conditions of the first kind is greater (for boundary conditions of the second kind closer to the end).

^{[17]}A method is proposed for constructing a spline function, which has on the indicated lines the same discontinuities of the first kind as the approximated discontinuous function, and a method for finding the Fourier coefficients of the indicated continuous or differentiable function.

^{[18]}Consequently, this new procedure is especially useful for solving non-homogeneous Fredholm integral equations of the first kind.

^{[19]}Numerical schemes for nonlinear weakly singular Volterra and Fredholm integral equations of the first kind are rarely investigated in the literature.

^{[20]}This system of boundary integral equations consists of singular integral equations of the first kind and integral equations of the second kind with a logarithmic singularity.

^{[21]}To deal with the spatial discretization of the displacement field, the displacements of plate are expressed as the expansions of Chebyshev polynomials of the first kind (CPOFK).

^{[22]}On the bottom of the boundary, the Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at a point.

^{[23]}According to Wagner and Schmalzried, one has to distinguish between rate constants of the first kind (“practical” Tammann constant), in the case of simultanous and coupled growth of multiple product phases, and rate constants of the second kind (“true” Tammann constant), in the case of the uncoupled and only growth of one product phase in equilibrium with the adjacent phases.

^{[24]}Here we use a fast and simple L-curve method to estimate the TR parameter (λ) for regularization of the Fredholm integral equations of first kind in impedance.

^{[25]}Based on the three-phase model of simple matter reviewed to the appearance and disappearance of the S-loop of a phase transition (PT) of the first kind on isotherme of state equation in the range of PT crystal-liquid (C-L).

^{[26]}Since in this model of friction there are no discontinuities of the first kind in velocity, the problem is mathematically simpler than problems with one-dimensional (according to Coulomb) dry friction.

^{[27]}We then discuss some modern methods for screening through the analysis of online data streams, either through active or passive data collection, the difference being that in the first kind, the subject is active in the data collection process; in the second kind, secondary data streams are used, such as Twitter tweets, Facebook posts, or Google searches.

^{[28]}As a rule, it is the product of a smooth function of bounded variation by a Bessel function of the first kind.

^{[29]}Originality/valueThis is first kind of study to identify CSFs for implementing environmentally sustainable practices in the utilities sector.

^{[30]}For the first kind of scenario, OS-ELM is inserted an alternative output node which can be extended whenever the new class instances are received.

^{[31]}Here, we address the theory of photophoresis for a more general class of on-axis axisymmetric beams of the first kind.

^{[32]}The first kind is obtained by imposing the $\ell_{2,1}$ constraint on the projection matrix in order to perform feature ranking.

^{[33]}The Sturm-Liouville method was used to solve this problem by reduce it to the integral equation for first kind.

^{[34]}For the elastic modulus of the first kind, the excess varies from 1.

^{[35]}5) in the limiting current density due to electroconvection, which occurs according to the mechanism of electroosmosis of the first kind.

^{[36]}We review some structural details of Promise Theory, applied to Promises of the First Kind, to assist in the comparison of Promise Theory with other forms of physical and mathematical modelling, including Category Theory and Dynamical Systems.

^{[37]}Subsequently, a combination of the nonnegative least squares (NNLS) algorithm and post facto smoothing method has been employed to derive the discretized solution of the Fredholm integral equation of the first kind.

^{[38]}It is the first kind of study to analyze the facial expressions and behavioural measures (coughing, sneezing, flu and hand movements).

^{[39]}The method used in the code is based on the Bessel function of the first kind of order zero.

^{[40]}Finally, to validate the superiority of the obtained results, an application is provided to solve a first kind of Fredholm type integral equations.

^{[41]}We consider the Dirichlet condition at the left end of the rod (at x = 0) corresponding to the heating of this end and the homogeneous condition of the first kind at the right end (at x = 1) corresponding to cooling during interaction with the environment as boundary conditions.

^{[42]}On the lateral surface of a cylidrical region, the homogeneous boundary conditions of the first kind are given.

^{[43]}A method is presented for computing exponential spectro-temporal modulation, showing that it can be expressed analytically as a sum over linearly offset sidebands with component amplitudes equal to the values of the modified Bessel function of the first kind.

^{[44]}We give sufficient conditions so that the ground states of a given Hamiltonian are stable under perturbations of the first kind in terms of order preservation.

^{[45]}In this paper, we obtained a simple rational approximation for $${\mathcal {K}}_{a}(r)$$ K a ( r ) : $$\begin{aligned} \frac{2}{\pi }{\mathcal {K}}_{a}(r) \, \mathbf {>}\frac{\left( 1-3a+3a^{2}\right) r\mathbf {^{\prime }}+\left( 1+3a-3a^{2}\right) }{\left( 1+a-a^{2}\right) r\mathbf {^{\prime }}+\left( 1-a+a^{2}\right) }\; \end{aligned}$$ 2 π K a ( r ) > 1 - 3 a + 3 a 2 r ′ + 1 + 3 a - 3 a 2 1 + a - a 2 r ′ + 1 - a + a 2 holds for all $$r\in (0,1),$$ r ∈ ( 0 , 1 ) , where $${\mathcal {K}}_{a}(r)=$$ K a ( r ) = $$\frac{\pi }{2}F\left( a,1-a;1;r^{2}\right) =\frac{\pi }{2}\sum _{n=0}^{\infty }\frac{ \left( a\right) _{n}\left( 1-a\right) _{n}}{(n!)^{2}}r^{2n}$$ π 2 F a , 1 - a ; 1 ; r 2 = π 2 ∑ n = 0 ∞ a n 1 - a n ( n ! ) 2 r 2 n is the generalized elliptic integral of the first kind, and $$r\mathbf {^{\prime }=} \sqrt{1-r^{2}}$$ r ′ = 1 - r 2.

^{[46]}In the article, the conditions for the existence of limit cycles of the first kind are obtained for self-tuning systems with delay, which, in turn, determine the conditions for the occurrence of hidden synchronization modes in such systems.

^{[47]}

## boundary value problem

The boundary-value problem is reduced to a Fredholm integral equation of the first kind in the velocity magnitude on the free surface.^{[1]}We study how a boundary value problem with a nonlocal integral condition of the first kind for a mixed type equation with a singular coefficient in a rectangular domain depends on a numerical parameter occurring in the equation.

^{[2]}The boundary-value problem for the Laplace's equation in the prolate spheroidal coordinates with the boundary conditions of the first kind is solved.

^{[3]}The boundary value problem can be represented as an integral equation of the first kind by using the separation of variables method.

^{[4]}One of the problems is a system which contains the boundary value problem of the first kind and the equation for a time dependence of the sought source function.

^{[5]}

## ill posed problem

As it is well known the problem of solving the Fredholm integral equation of the first kind belongs to the class of ill-posed problems.^{[1]}Since the solution of the equation obtained by the ultrasonic attenuation model produces a Fredholm integral equation of the first kind, an inversion algorithm combining simulated annealing with genetic algorithm based on ultrasonic attenuation mechanism is proposed to solve the ill-posed problem in the inversion calculation of particle concentration.

^{[2]}This is theoretical study of the ill-posed problem on localization (determination of position) of discontinuities of the first kind of a function of one variable.

^{[3]}We consider a linear ill-posed problem for the Fredholm equation of the first kind.

^{[4]}

## heat conduction problem

The heat conduction problem can be formulated as Fredholm integral first kind equations.^{[1]}This paper presents an approximate analytical solution of the heat conduction problem for a two-layer plate under symmetric boundary conditions of the first kind.

^{[2]}Based on the integral heat balance method and additional boundary conditions (characteristics) use, a numerical - analytical solution of the heat conduction problem for an infinite plate under symmetric first kind border conditions with constant power internal sources is obtained.

^{[3]}

## right hand side

In the space H, a nonlinear operator equation of the first kind is studied, when the linear, nonlinear operator and the right-hand side of the equation are given approximately.^{[1]}We consider solving a system of semi-discrete first kind integral equations with a right-hand-side being a finite dimensional vector of sampling values and propose a regularization method for the system in a functional reproducing kernel Hilbert space (FRKHS), where the linear functionals that define the semi-discrete integral operator are continuous.

^{[2]}This paper focuses on the numerical solution for Volterra integral equations of the first kind with highly oscillatory Bessel kernel and highly oscillatory triangle function on the right-hand side.

^{[3]}

## power grid strength

The results show that: for the first kind of subsynchronous oscillation, the dominant influencing factors are the power grid strength and the current inner loop control parameters; with the decrease of the power grid strength, the current inner loop control parameters decrease, weakening the system damping, and the oscillation frequency gradually decreases; for the second kind of subsynchronous oscillation, the dominant influencing factors are the current inner loop control parameters, with the decrease of the power grid strength The damping of the system is weakened and the oscillation frequency increases slightly.^{[1]}

## 1 − x

In this paper, we present Padé approximations of some functions involving complete elliptic integrals of the first kind K ( x ) $K(x)$ , and motivated by these approximations we also present the following double inequality: 1 − x 2 1 − x 2 + x 4 62 < 2 e 2 π K ( x ) − 1 ( 1 + 1 1 − x 2 ) < 1 − 96 100 x 2 1 − 96 100 x 2 + x 4 64 , x ∈ ( 0 , 1 ).^{[1]}

## first kind integral

We consider solving a system of semi-discrete first kind integral equations with a right-hand-side being a finite dimensional vector of sampling values and propose a regularization method for the system in a functional reproducing kernel Hilbert space (FRKHS), where the linear functionals that define the semi-discrete integral operator are continuous.^{[1]}Finally, some numerical experiments with a Fredholm first kind integral equation are carried out to demonstrate the performance of our designed hypothesis testing statistics in an ill-posed model.

^{[2]}It is formulated in terms of two first kind integral equations, one involving the difference of potential across the wetted part of the wall and the other involving the horizontal component of velocity across the gap.

^{[3]}

## first kind equation

The heat conduction problem can be formulated as Fredholm integral first kind equations.^{[1]}However, there are no relations binding the values of all components of the stress-strain state at the half-plane boundary This paper shows that arbitrary formulation of the boundary conditions considerably simplifies integral equations and transfers them to the class of Fredholm’s first kind equations.

^{[2]}

## first kind involving

For each configuration of the barrier, the problem is reduced to solving an integral equation or a coupled integral equation of first kind involving horizontal component of velocity below or above the barrier and above the step.^{[1]}For each position of the barrier, the problem is reduced to solving three weakly singular integral equations of first kind involving horizontal component of velocity above the two edges of the trench and below the barrier.

^{[2]}

## first kind fredholm

The RRA-algorithm is a variation of the Tikhonov method and it is suggested as a regularization method for first kind Fredholm integral equation.^{[1]}The downward continuation (DWC) of airborne gravity data usually adopts the Poisson integral equation, which is the first kind Fredholm integral equation.

^{[2]}

## first kind boundary

In specific cases the Legendre wavelet Galerkin method is used for the numerical solution when surface is subjected to the first kind boundary condition with constant latent heat and thus the results obtained are compared with Turkyilmazoglu (2018) results and found in good compliance.^{[1]}In both cases our numerical simulation strategy involves approximating the fractal screen $\Gamma$ by a sequence of smoother "prefractal" screens, for which we compute the scattered field using boundary element methods that discretise the associated first kind boundary integral equations.

^{[2]}

## first kind abel

In this paper, under certain assumptions and transformations, the spacecraft relative equations of motion, in terms of orbital element differences, is approximated into the nonlinear first kind Abel-type and Riccati-type differential equations.^{[1]}Of the integral equations considered here are first kind Abel integral equation and integral equation with log kernel and hypersingular integral equations of first and second kind.

^{[2]}