The usual way to determine the asymptotic behavior of the Chebyshev coefficients for a function is to apply the method of steepest descent to the integral representation of the coefficients. However, the procedure is usually laborious. We prove an asymptotic upper bound on the Chebyshev coefficients for the kth integral of a function. The tightness of this upper bound is then analyzed for the c...

rupture and wrinkling are two prevalent phenomena that happen in hydro-forming process. many efforts have been made to achieve the upper and lower bounds for the pressure related to rupture and wrinkling of sheet, respectively. the aim of this investigation is to improve the upper bound of fluid pressure in hydro-forming process by hemispherical punch. in this article, analytical study of the u...

From the Paley–Wiener 1/4-theorem, the finite energy signal f(t) can be reconstructed from its irregularly sampled values f(k+ k) if f(t) is band-limited and supk j kj < 1=4. We consider the signals in wavelet subspaces and wish to recover the signals from its irregular samples by using scaling functions. Then the way to estimate the upper bound of sup k j kj such that the irregularly sampled s...

The Upper Bound Conjecture is verified for a class of odd-dimensional simplicial complexes that in particular includes all Eulerian simplicial complexes with isolated singularities. The proof relies on a new invariant of simplicial complexes—a short simplicial h-vector.

For an absolutely continuous probability measure on Rd and a nonnegative integer k, let ~ sk( ;0) denote the probability that the convex hull of k + d + 1 random points which are i.i.d. according to contains the origin 0. For d and k given, we determine a tight upper bound on ~ sk( ;0), and we characterize the measures in Rd which attain this bound. As we will see, this result can be considered...

Let S(n, d) and C(n, d) denote, respectively, the stacked and the cyclic d-dimensional polytopes on n vertices. Furthermore, fi(P ) denotes the number of i-dimensional faces of a polytope P . Theorem 1. Let P be a d-dimensional simplicial polytope. Suppose that fr(S(n1, d)) ≤ fr(P ) ≤ fr(C(n2, d)) for some integers n1, n2 and r ≤ d − 2. Then, fs(S(n1, d)) ≤ fs(P ) ≤ fs(C(n2, d)) for all s such ...

‎In this paper we give an upper bound for Noetherian dimension of all injective modules with Krull dimension on arbitrary rings‎. ‎In particular‎, ‎we also give an upper bound for Noetherian dimension of all Artinian modules on Noetherian duo rings.

We show that the recently discovered universal upper bound on the thermal conductance of a single channel comprising particles obeying arbitrary fractional statistics is in fact a consequence of a more general universal upper bound, involving the averaged entropy and energy currents of a single channel connecting heat reservoirs with arbitrary temperatures and chemical potentials. The latter up...