The long-term listening range was defined as extending, at any frequency, from the threshold of audibility to the upper limit of the comfortable loudness range. The relationship between the aided preferred listening level and the long-term listening range was investigated by analyzing data obtained from 16 hearing impaired subjects. Results support a tentative conclusion that the aided preferre...

We compute classical trajectories of Ultracold neutrons (UCNs) in a superconducting Ioffe-type magnetic trap using a symplectic integration method. We find that the computed escape time for a particular set of initial conditions (momentum and position) does not generally stabilize as the time step parameter is reduced unless the escape time is short (less than approximately 10 s). For energy in...

where h >  is a stepsize. It is known that if f :RN →RN is Lipschitz continuous and sufficiently smooth, then the sequence {xn} generated by (.) converges to the exact solution of (.) as h→  uniformly over t ∈ [, t̄] for any fixed t̄ > . If we write the function f in the form f (t) = g(t) – t, then differential equation (.) becomes x′ = g(t)– t. Then the equilibrium problem associated w...

The paper deals with expressions for the midpoint and the radius of the product of two intervals. Based on these expressions two applications are considered: One leads to an explicit representation of the fixed point of the function [A][x]+ [b] if zero is contained in the interval vector [b] but not in the interior of the entries of the interval matrix [A]. The second application proves the sem...

The midpoint potentials of the mitochondrial respiratory chain cytochromes of the protozoan Crithidia fasciculata at pH 7.2, Em7.2, show great similarity to those measured in higher organisms. Values of Em7.2 for cytochromes a and a3 are +165 and +340 mV. Both c cytochromes have Em7.2 = +230 mV. There are two b cytochromes with the same spectral characteristics with Em7.2 = -20 and -135 mV. The...

We propose a new version of potentially optimal intervals for the DIRECT algorithm. A two-points based sampling method is presented. The method starts from a distingished point (the peak point) by forming an initial triangle. The idea is to sample the midpoint of a specific interval: the basis of the resulting triangle. This specific interval is obtained by translating the initial interval towa...

We investigate the equilibrium unfolding of Zn-cytochrome c in guanidine hydrochloride by three-pulse photon echo peak shift (3PEPS) spectroscopy. Unexpectedly, the measurements reveal that inhomogeneous broadening of the sample at the midpoint of the denaturation is larger than that of either native or unfolded states. To interpret this finding, we present simulations of the peak shift for bot...

Second proof. Let O be the circumcenter of ABC and let ω be the circle centered at D with radius DB. Let lines AB and AC meet ω at P and Q, respectively. Since ∠PBQ = ∠DQC + ∠BAC = 1 2(∠BDC + ∠DOC) = 90 ◦, we see that PQ is a diameter of ω and hence passes through D. Since ∠ABC = ∠AQP and ∠ACB = ∠APQ, we see that triangles ABC and AQP are similar. If M is the midpoint of BC, noting that D is th...

Second proof. Let O be the circumcenter of ABC and let ω be the circle centered at D with radius DB. Let lines AB and AC meet ω at P and Q, respectively. Since ∠PBQ = ∠BQC+∠BAC = 1 2 (∠BDC + ∠DOC) = 90, we see that PQ is a diameter of ω and hence passes through D. Since ∠ABC = ∠AQP and ∠ACB = ∠APQ, we see that triangles ABC and AQP are similar. If M is the midpoint of BC, noting that D is the m...

One of the main problems of interval computations is to compute the range of a given function over given intervals. In general, this problem is computationally intractable (NP-hard) – that is why we usually compute an enclosure and not the exact range. However, there are cases when it is possible to feasibly compute the exact range; one of these cases is when the function is monotonic with resp...