In the Fixed Effects Model, a different

constant term is used for each section while the slope coefficient remains the same.

Basically, the tool chooses the values for the

constant term (a) and the slope coefficient (b) so as to minimize ESS.

Equation (37) may be assumed as second-order partial differential equation near the event horizon in general nonstationary black hole since all the coefficients [L.sub.1], [L.sub.2], [L.sub.3], and [L.sub.4] are

constant terms when r [right arrow] [r.sub.h]([u.sub.0], [d.sub.0], [[theta].sub.0]), u [right arrow] [u.sub.0], [theta] [right arrow] [[theta].sub.0], and [phi] [right arrow] [[phi].sub.0].

An average inactive participant aged 28 shows a HS score of 1.12 (

constant term) indicating that the samples average participant in early adulthood shows rarely any lifestyle impacting health limitations.

The computation overhead Scheme GKD Each group member GKMP [19] t enc 1 dec AGKTP [4] 1 Gen_[f.sub.t](x) + 1 hash 1 Gen_[f.sub.t](0) + 1 hash SAKDA [20] 2 inv + 1 hash 1 inv + 1 exp +x + 1 hash Our Scheme t Gen_[f.sub.1](x) + 1 hash or 1 Gen_[f.sub.1](0) + 1 hash or 1 Gen_[f.sub.1](x) + 1 hash + 1 enc 1 dec + 1 hash t: the number of group members Gen_[f.sub.d](x): generate a polynomial of degree d [4] Gen_[f.sub.d](0): restore the

constant term of [f.sub.d](x) [4] inv: modular multiplicative inverse exp: modular exponentiation enc/dec: symmetric encryption/decryption

Evaluation parameters 250 frames 500 frames SSE 3.86 35.27 R-square 0.9989 0.9907 Adjusted R-square 0.9978 0.9815 RMSE 0.1279 0.2656 TABLE 3: Effect of evaluation parameter values of 500-frame thermal image data fitted by model with or without

constant term. Evaluation parameters Initial model Improved model (w/o

constant term) (w

constant term) SSE 35.27 0.89 R-square 0.9907 0.9998 Adjusted R-square 0.9815 0.9995 RMSE 0.2656 0.0422

Clearly, (3) has no

constant term because it is a homogeneous exponential equation.

The set of instruments for the GMM estimation includes [z.sub.t], [[??].sup.+.sub.t] and [[??].sup.-.sub.t] with 1 and 2 lags and a

constant term. Similar to the above case, the discount factor [delta] is set to 0.999, 0.950, and 0.900 to check the robustness of our estimation results.

[[beta].sub.0] is the

constant term while [[epsilon].sub.it] is the error term.

US $ Period

Constant term Regression t=Values R2 = Values (a) coefficient (b) 1 2 3 4 5 Industrial Countries (ICs) 1981-91 148.03 767.86 * 5.72 0.86 * 1991-99 179.19 2298.59 * 17.78 0.90 * 1981-99 167.41 666.18 * 7.06 0.96 * Developing Countries (DCs) 1981-91 39.62 518.13 * 9.70 0.74 * 1991-99 120.92 910.66 * 10.90 0.91 * 1981-99 79.85 302.73 * 4.04 0.90 * World 1981-91 187.64 1286.04 * 7.35 0.86 * 1991-99 305.12 3195.38 * 15.73 0.91 * 1981-99 248.66 960.16 * 6.17 0.95 * India 1981-91 1.01 5.18 * 5.64 0.83 * 1991-99 2.47 15.61 * 10.33 0.92 * 1981-99 1.71 21.07 *** 1.54 0.93 * Y = Export in bill.

This can be explained by the fact that the even leading terms do not have a

constant term but only sinusoidal functions which converge faster than the

constant term.

Our specific interest is predicates of the form P(x) = [[1 + sign(Q(x))]/2] where Q: [R.sup.k] [right arrow] R is a quadratic polynomial with no

constant term, i.e., Q(x) = [[summation].sup.k.sub.i=1] [[alpha].sub.i][x.sub.i] + [[summation].sub.i[not equal to]j] [b.sub.ij][x.sub.i][x.sub.j] for some set of coefficients [a.sub.1],..., [a.sub.n] and [b.sub.11],..., [b.sub.nn].