At first glance, it seems to make sense to conclude that when a 1 dollar reward tomorrow is equivalent to a D < 1 dollar reward today, the day-after-tomorrow’s 1 dollar reward would be equivalent to D ·D = D dollars today, and, in general, a reward after time t is equivalent to D(t) = D dollars today. This exponential discounting function D(t) was indeed proposed by the economists, but it does ...

The logic construction of a double-edge-triggered (DET) flip-flop, which can receive input signal at two levels of the clock, is analyzed and a new circuit design of CMOS DET flip-flop is proposed. Simulation using SPICE and a 1μ technology shows that this DET flip-flop has ideal logic functionality, a simpler structure, lower delay time, and higher maximum data rate compared to other existing ...

In this paper, we study the following delay dynamic equation xΔ(t)+ p(t)x(τ(t)) = 0 for t ∈ [t0,∞)T , where t0 ∈ T , supT = ∞ , p ∈ Crd([t0,∞)T,R) alternates in sign infinitely many times and τ ∈ Crd([t0,∞)T,T) is a strictly increasing unbounded function satisfying τ(t) t for all t ∈ [t0,∞)T . Our results extend recent results for arbitrary time scales. Mathematics subject classification (2010)...

The purpose of this study was to examine the effect of an 18-wk weight-training program on average daily metabolic rate (ADMR). Before the intervention and in weeks 8 and 18 (T0, T8, and T18, respectively) data on body composition, sleeping metabolic rate (SMR), food intake, energy cost of the weight-training program (EEex), and nontraining physical activity (accelerometer) were collected in th...

and Applied Analysis 3 For 0 < q ≤ 1 we have t0D q t x t 1 Γ ( 1 − q d dt (∫ t t0 x s t − s q ds ) , ( 0 < q ≤ 1, c t0D q t x t 1 Γ ( 1 − q ∫ t t0 x′ s t − s q ds, ( 0 < q ≤ 1. 2.2 Some properties of Riemann-Liouville and Caputo derivatives are recalled below 1–3 . Property 1. When 0 < q ≤ 1, we have c t0D q t x t t0D q t x t − x t0 Γ ( 1 − q t − t0 −q. 2.3 In particular, if x t0 0, we have c t...

BACKGROUND AND OBJECTIVES Robotic cystectomy is rapidly becoming a part of the standard surgical repertoire for the treatment of prostate cancer. Our aim was to describe respiratory and hemodynamic challenges and the complications observed in robotic cystectomy patients. PATIENTS Sixteen patients who underwent robotic surgery between December 2009 and January 2011 were prospectively enrolled....

subject to (tf , x(tf )) ∈ S = [t0,∞)× S1 where S1 is a k dimensional manifold in Rn S1 = {x ∈ R : h1(x) = h2(x) = · · · = hn−k(x) = 0} where hi are C1 functions from Rn to R subject to ẋ = f(x, u), x(t0) = x0 for u ∈ C[t0, T ] and u(t) ∈ U ⊂ Rm with f and L being C1 functions. Let u∗ : [t0, tf ] → R be an optimal control with state trajectory x∗ : [t0, tf ] → Rn and a constant. Then there exis...

and Applied Analysis 3 Thus, we have E sup t∈[t0 ,T] 󵄨󵄨󵄨󵄨xn+1 (t) − xn (t) 󵄨󵄨󵄨󵄨 2 ≤ 3(L 2 1 E sup t∈[t0,T] 󵄨󵄨󵄨󵄨xn (t) − xn−1 (t) 󵄨󵄨󵄨󵄨 2 + (T − t0) 2 L 2 E sup t∈[t0 ,T] 󵄨󵄨󵄨󵄨xn (t) − xn−1 (t) 󵄨󵄨󵄨󵄨 2