In this paper, we establish improved upper bounds on the size of integral solutions to hyper- and super-elliptic equations under the conditions of LeVeque ( Acta. Arith. IX (1964), 209- 219). The proof follows the classical argument of Siegel ( J. London Math. Soc. 1 (1926), 66-68...
摘要: The purpose of this study is the problem of finding an upper bound and a lower bound of integral operators defined by $ (Bf)(x) = \int\limits_0^\infty {b(x,y)f(y)dy,}$ (Bf)(x) = \int\limits_0^\infty {b(x,y)f(y)dy,}...
The purpose of this study is the problem of finding an upper bound and a lower bound of integral operators defined by $$ (Bf)(x) = \\\int\\\limits_0^\\\infty {b(x,y)f(y)dy,} $$ on weighted spaces. In fact, we consider certain integral operators such as Averaging, Copson...
We prove explicit upper bounds of the function $S_m(T)$, defined by the repeated integration of the argument of the Riemann zeta-function. The explicit upper bound of $S(T)$ and $S_1(T)$ have already been obtained by A. Fujii. Our result is a generalization of Fujii's results....
1)integral upper limit function积分上限函数 1.This paper applies an integral upper limit functions to giving a method for the solution of the problems similar to those as the proven mean value theorem.本文利用积分上限函数给出证明中值定理及类似问题的一种方法。 2.What is discussed in this paper...
As far as the types of improper integrals with infinite intervals go, there are three kinds to consider: First, one may find an integral without an upper bound like this: ∫1∞1x2dx=limt→+∞∫1t1x2dx Examining the graph in figure 2, one can observe the the area of each element un...
Improper Integral: The integral which contains the upper bound and the lower bound as definite integral whose one and both limits should be infinite or a real number then it is called improper integral. It has two types: Convergent:...
An integral controller (also called reset controller) can eliminate the steady-state error that occurs with a proportional controller. Integral control action is expressed as follows: (8.3)fIt=Ki∫otevdv fI(t) is the integral control action and Ki is the integral constant. Because of the contin...
We also obtain a uniform upper bound for a related expression, which allows us, as a consequence, to prove our upper bound (2.12) for the integral (1.4), which is valid for all x>0, ν>−12, 0<γ<1. We complement our upper bounds with lower bounds for the supremum over all x...
The order of integration in the iterated integral can be changed—that is, integration may be performed first with respect toxand then with respect toy—if certain conditions are imposed onf(x, y)andS. The iterated integral is defined in a similar manner for functions of more than two ...