In [16], the uniqueness theorems of inverse spectral problems have been proved for the higher-order differential operators with distribution coefficients of the Mirzoev–Shkalikov class [1,2] on a finite interval. In [18], differential operators on the half-line with singular coefficients of ...
Adapting the notations in advanced calculus, a point x = (x1, x2, ··· , xn) ∈ Rn is sometimes called a vector and we use |x| instead of x 2 to denote its Euclidean norm. All is about linearization. Recall that a real-valued function on an open interval I is di?erentiable...
In fact, if we add up the heights of the function values in the two graphs above, we can get \pi/2 for any value of x. \sin ^{-1}(x)+\cos ^{-1}(x)=\frac{\pi}{2} \\ for any x in the interval [−1, 1]. This can be proved by calculus.(How?) But we can also...
Although we did not differentiate them by notations, we ensured that there was no confusion. The water retention curve in the Peters-Durner-Iden model is described by the sum of capillary and adsorbed film water: (10)θ(ψ)=(θs−θr)Sc(ψ)+θrSf(ψ),where Sc is the capillary ...
Recursive frame inverse on the interval The data is now only given on a ?nite interval [K? , K+ ]. The lower scale (e.g., (7) hj ↑ [p ? n]? aj +1 [n] 1) in problem (8) is allowed to vary with n∈Z value j in order to ?nd a scale recursive solution. At scale ...
Comparing the two first exploration mechanisms (ACTUATOR-RANDOM and ACTUATOR-RIAC) we cannot distinguish any notable difference, the space explored appears similar and the extent of explored space on the (u, v) axis is comprised in the interval [−5; 5] for u and [−2.5; 2.5] for v ...
2 Preliminary Notes The aim of this section is to present some notations, notions and results which are of useful in our further considerations. 2.1 Comparing Interval Numbers Sengupta and Pal [2] proposed a simple and efficient index for comparing any two intervals on IR through decision maker...
In Section 5, we provide the main conclusions. 2. Preliminaries and Notations This section introduces some properties of the shifted Jacobi polynomials. The Jacobi polynomials are defined as follows: G k + 1 ( σ 1 , ϱ 1 ) ( y ) = ( a k ( σ 1 , ϱ 1 ) y − b k ( ...
In Section 4, Monte Carlo simulations are carried out to investigate the performances of different point estimates and interval estimates. In Section 5, a real data set has been analyzed for illustrative purposes. The conclusions are given in Section 6. 2. Maximum Likelihood Estimation In this ...
The common scenario consists in truncating the cdf a flexible distribution (inverse or not, generally with support on (0,+∞) or ℝ) over the interval (0,1) and compounding it by a simple baseline cdf. Current developments include the truncated Fréchet-G (TF-G) family by [17], ...