ing the programming with respect to list length norm :filter match(list,dynamic). :filter match1(list,dynamic,list,dynamic). bin_solve_atom__0(match(B,_),unfold(match1(B,_,B,_))). bin_solve_atom__1(match1(1+C,_,F,_),unfold(match1(F,_,F,_))). bin_solve_atom__1(match1(1+C,_,E,_),unfold(match1(C,_,E,_))). For each binary clause of the form: bin solve atom(p(--),unfold(p(--)): bin_solve_atom__1(mat...

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Let m,n, p be positive integers such that m ≥ n + p. Suppose (A,B) ∈ Cm×n ×Cm×p, and let P(A,B) = {(E,F ) ∈ Cm×n ×Cm×p : there is X ∈ Cn×p such that (A− E)X = B − F}. The total least square problem concerns the determination of the existence of (E,F ) in P(A,B) having the smallest Frobenius norm. In this paper, we characterize elements of the set P(A,B) and derive a formula for ρ(A,B) = inf {‖[...

and Applied Analysis 3 Proof. Let p(z) be given by (11), which clearly belongs to the class A(n). Now differentiating (11), we have p 󸀠 (z) = ( f (z) ∗ g (z) z ) 1/(p+b−1) × 1 p + b − 1 { z(f (z) ∗ g (z)) 󸀠 f (z) ∗ g (z) + b − 1} (20) which gives 󵄨󵄨󵄨󵄨 arg p (z)󵄨󵄨󵄨󵄨 = 󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨 arg( f (z) ∗ g (z) z ) 1/(p+b−1) + arg{ 1 p+b−1 ( z(f (z) ∗ g (z)) 󸀠 f (z) ∗ g (z) +b−1)} 󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨󵄨 . (21) Thus using (...

f(T, B) teleparallel gravity is a recently proposed straightforward generalization of the popular f(T) by incorporation boundary term B=2e∂i(eTi)=▽iTi where T denote torsion scalar (Bahamonde et al., 2015). In this work, I investigate viability some well motivated models forms f=αBn+βTm, f=αBnTm and f=αlog(B)+βT α, β, n m are free parameters from inequalities imposed weak energy condition. use ...

Given a graph $G$ and an odd prime $p$, for mapping $f: E(G) \to {\mathbb Z}_p\setminus\{0\}$ ${\mathbb Z}_p$-boundary $b$ of $G$, orientation $\tau$ is called $(f,b;p)$-orientation if the net out $f$-flow same as $b(v)$ in Z}_p$ at each vertex $v\in V(G)$ under $D$. This concept was introduced by Esperet et al. (2018), generalizing mod $p$-orientations closely related to Tutte's nowhere zero 3...