### Table 5: The Laplace transforms

"... In PAGE 56: ...Inverse Laplace transforms Here, the inverse Laplace transforms are derived for functions used in the trans- mission line model implemented. Table5 lists the essential Laplace transforms where I0 and I1 are the modi ed Bessel functions of order 0 and 1, and quot;(t)is the Heaviside function or unit-step function. Table 5: The Laplace transforms... ..."

### Table 1: A List of Laplace and Inverse Laplace Transforms Related to Fractional Order Calculus

2001

### Table 2: A List of Laplace and Inverse Laplace Transforms Related to Fractional Order Calculus (Continued)

2001

### Table 3. Laplace transforms of probabilities associated to some major geometric

in The Formal Theory of Birth-and-Death Processes, Lattice Path Combinatorics, and Continued Fractions

"... In PAGE 19: ...#29 The corresponding condition is speci#0Ced by#28H #5B#15h#5D h;h b h #29, whichby #283.6#29 and Entry 3 of Table3 leads to e #12 h #28s#29=#1F s #28H #5B#15h#5D h;h b h #29= Q h #28,s#29 e P 0;0 #28s#29 ,P h #28,s#29 Q h,1 #28,s#29 e P 0;0 ,P h,1 #28,s#29 : #283.13#29 In this case, one has #1F 0 #28H #5B#15h#5D h;h b h #29 = 1, which is consistent with ergodicity.... In PAGE 20: ...19#29 and that can be identi#0Ced in some important cases; see #5B19,20#5D and Section 5. Formul#1A entirely parallel to those derived for the standard probabilistic morphism #28Theorems 3, 4 and Table3 #29 can then be easily developed. The morphism #1F s is susceptible to enrichmentinvarious other ways.... In PAGE 22: ... Let #5Bs ,m #5Df#28s#29 denote the coe#0Ecientofs ,m in the expansion of some function f#28s#29 at in#0Cnity. Theorem 4 and Entry 8 of Table3 provide an expression for e P k;l #28s#29 that implies #28,1#29 n #5Bs ,n,1 #5D 1 #19 l e P k;l #28s#29 = #28,1#29 n #5Bs ,n,1 #5DQ k #28,s#29Q l #28,s#29 e P 0;0 #28s#29 #284.8#29 = Z 1 0 Q k #28x#29Q l #28x#29x n d#20#28x#29; #284.... ..."

### Table 3: A List of Laplace and Inverse Laplace Transforms Related to Fractional Order Calculus (Mittag-Le er function type)

2001

### Table 7.1: Loss probabilities for uniform deadlines, derived from numeric convolution (C), numeric inversion of the Laplace transform (L), closed-form expression (F) or closed-form inversion of the Laplace transform (I)

1990

Cited by 10

### Table 3 Laplace Transform of the Exit Time of Brownian Motion from [0; 1] as a Function of

"... In PAGE 11: ... to xn 0 = 0nq(0) + q(1) + (n) ? n(n ? 1) 2 (n ? 2); n 0 k X i=0 k i (?1)i (i + j) 0; j = 0; 1; 2; : : : ; k = 0; 1; 2; : : : q(0) ; q(1) 0: We provide two displays of results from solving the linear program. Table3 displays the Laplace transform of the exit time distribution for various values of . The exact values are based on the formula (see, for instance, [10, p.... In PAGE 11: ...100]) Ex0 e? = cosh ?x0 ? 1 2 p2 cosh 12 p2 : (4.2) Note that when x0 = 1=2, as it does for Table3 , this reduces to... ..."

Cited by 1

### Table 1 An initial approach to defining a quality framework for transformations

"... In PAGE 12: ... It may be important for maintainability and evolution not to overwrite the source model. The above discussion is summarized in Table1 . Table 1 is by no means a complete set of quality goals for transformations but it shows to some degree the state of work and the need to evaluate the impact of transformation approaches on quality goals.... ..."

### Table 2: Numerical results for the domain transformation technique for solving the 2D Laplace equation with prescribed surface shapes 1, 2 and 3. 3.2.2 Numerical results for the PCG method Now we want to study the number of CG-iterations needed to solve the linear system associated with the two-dimensional test problem described above. A vector 0 with

"... In PAGE 11: ... Gaussian elimination is used as the equation solver, and linear elements (triangles with three nodes) are used for the discretization. The numerical results are shown in Table2 , where nite element solutions are denoted by b apos;. Clearly, second order convergence is obtained for all test problems.... ..."