In this paper, the reliability of a system is discussed when the strength of the system and the stress imposed on it are independent, non identical exponentiated Pareto (EP) distributed random variables with doubly Type-II censored scheme. Different point estimations and interval estimations are proposed. The point estimators obtained are uniformly minimum variance unbiased estimators (UMVUE) and maximum likelihood estimators (MLE). The interval estimations obtained are the exact, approximate and bootstrap confidence intervals. An extensive computer simulation is used to compare the performances of the proposed estimators. One data analysis has been performed for illustrative purpose.
We study the following fractional Schrödinger-Kirchhoff equations with sign-changing potential function:
where s ∈ (0,1), p ∈[2, ∞), q ∈ (1, p), a, b > 0, λ, μ > 0 are positive constants, and by some appropriate assumptions on V, f, g, we use the fountain theorem to obtain the existence of infinitely many high energy solutions for the above system.
Let U=Tri(A, M, B) be a triangular algebra, and {φn}n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φn}n∈N satisfies φn([U, V]ξ)=Σi+j=n φi(U)φj(V)-ξφi(V)φj(U) for any U, V ∈ U with U?V=P being the standard idempotent, then {φn}n∈N is a higher derivation, where φ0=id is the identity map, U?V=UV+VU is the Jordan product and[U, V]ξ=UV-ξVU is the ξ-Lie product.
We discuss the fundamental solution for m-th powers of the sub-Laplacian on the quaternionic Heisenberg group, This result is the extension of the conclusion on the Heisenberg group. We use the representation theory of nilpotent Lie groups of step two to analyze the associated m-th powers of the sub-Laplacian on the quaternionic Heisenberg group and to construct its fundamental solution.
The representation category of a dihedral group is a symmetric semisimple monoidal category, so the Grothendieck ring of such a category is a commutative ring generated by finitely many elements. In this paper, the minimal generators of the Grothendieck ring are determined. Moreover, it is shown that the Grothendieck ring is isomorphic to a quotient of a polynomial ring.
p-adic hypergeometric functions are hypergeometric functions over finite fields analogous to the classical Gaussian hypergeometric functions, which have been found applications in diverse number theory problems. Let Fq be the finite field of q elements, λ ∈ Fq and n be a positive integer. This paper investigates the Fq-rational points on the Dwork hypersurface Xλn:x1n+x2n+…+xnn=nλx1x2…xn as well as its generalized form, and provides the formula for the number of the Fq-rational points in terms of a p-adic hypergeometric function when n and q(q-1) are coprime, which revises and improves the results given by Barman and Goodson et al.
The main purpose of this paper is using the properties of the trigonometric sums and the number of the congruence equation to study the computational problem of the one kind fourth power mean involving the four-term exponential sums, and give two interesting computational formulae for it.
In this paper, we perform a further investigation for a finite trigonometric sum considered by Hardy and Littlewood. By making use of some properties for the Chebyshev polynomials and M¨ obius function, we establish an interesting identity for the finite trigonometric sum of Hardy and Littlewood, by virtue of which an explicit asymptotic formula is also derived.
In this note, a structure of the Coleman automorphism group of a finite solvable group is given by using the projection limit property of the group. As an application, it is proved that the Coleman outer automorphism group of a dihedral group is either 1 or an elementary abelian 2-group.
