### Table 1. Integrity transforms

2007

"... In PAGE 6: ... in Table 6.10.1.a of RFC 3830 with the addition of the values found in Table1 above.... In PAGE 10: ... IANA Considerations According to Section 10 of RFC 3830, IETF consensus is required to register values in the range 0-240 in the SRTP auth alg namespace and the SRTP Type namespace. The value 2 for RCCm1, the value 3 for RCCm2, and the value 4 for RCCm3 have been registered in the SRTP auth alg namespace as specified in Table1 in Section 4. The value 13 for ROC transmission rate has been registered in the SRTP Type namespace as specified in Table 2 in Section 4.... ..."

### Table 1: Canonical integral transform: main theorems

"... In PAGE 4: ... The fractional FT and the Fresnel transform are usually applied in optical information processing due to their simple analog realizations. Since both of them belong to the class of canonical integral transforms, we summarize the main the- orems for the canonical transform in Table1 . For simplic- ity, we consider only the one-dimensional case, and we will do the same in the rest of the paper if the generalization to the two-dimensional case is straightforward.... ..."

### Table 3.4: Comparison of the LPP algorithm followed by transformations (Separate) to integrating transformations into the LPP algorithm (Integrated) for heuristic scheduling.

2007

### Table 1: The PERFECT Club Benchmark Suite terminations of molecular electronic structure. The two-electron integral transformation transforms the electron repul- sion integrals from the atomic orbital (AO) basis set to the molecular orbital (MO) basis set according to a fourth-order tensor transformation equation. The evaluation of the integral transformation is formulated as a series of matrix multiplications.

1989

"... In PAGE 18: ... The Fortran 77 language standard that was adopted by the PERFECT Club (after a few porting iterations) can be classi ed into ve categories: syntax, documentation, declarations, In- put/Output (I/O), and general programming techniques. The modi cation of the original Fortran 77 program in Table1 according to the following guidelines insured a successful run on the machines in Table 2. We note that many of the requirements re ect well-known ANSI Fortran 77 standards1.... In PAGE 22: ... is the maximum allowable relative error. Since the outputs of a few of the benchmark programs in Table1 are quite sensitive to machine round-o errors2, a large relative error (e.... In PAGE 22: ... 4.3 Performance Measures The fundamental measurements that were recorded for each of the programs in Table1 on the machines in Table 2 were the CPU time and wall-clock times. Initially, these measures were taken on the original (or baseline) code without any manual optimization by the programmer using 64-bit arithmetic3.... In PAGE 25: ... Identifying di erences in the type and the impact of software transformations used in these diaries should lead to a better understanding of the performance behavior of supercomputers, in general. 5 Results In this section, we present the baseline (compiler-optimized only) and hand- optimized measurements for the PERFECT benchmark suite ( Table1 ) on the machines listed in Table 2. Figures 1 through 6 illustrate the range of performance obtained when the PERFECT Club benchmarks are simply ported and compiler-optimized on each machine.... In PAGE 42: ... 5.3 MDG Although many of the diaries recorded for a particular benchmark program in Table1 were unique to the respective machines in Table 2, the molecu- lar dynamics benchmark, MDG, provides one example in which practically the same transformations were chosen for optimization on the Alliant FX/8, CRAY X-MP/416, IBM 3090-600S, and NEC SX-2. Diaries for MDG on the iPSC/1, MARK III, and NCUBE/10 machines are not included in our comparison.... In PAGE 44: ... Redundant array operations removed. (CSHIFT, INTERF, POTENG) 2 1 Microtask (parallelize) outermost loops and (INTERF, POTENG) Table1 1: Diary entries for MDG on the Alliant FX/8 and CRAY X-MP/416.... In PAGE 45: ... (INTERF) 3 4,11,14 Unrolled inner-most loop and expanded scalar variables for vector operations. (POTENG) Table1 2: Diary entries for MDG on IBM 3090-600S and NEC SX-2.... In PAGE 54: ...3.0 Table1 3: Machines used by PERFECT Club Members . Descriptor Machine NEC SX-2 NCUBE/10 iPSC/1 Mark III Location HARC Cal.... In PAGE 54: ...20A V2.4 Table1 4: Machines used by PERFECT Club Members .... ..."

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### TABLE 4 Distributions of One-Day-Ahead Probability Integral Transforms Density Forecasts From Long-Memory Lognormal-Normal Mixture Model

### Table IV. Free energy per particle f at temperature T and density 0 computed by the thermodynamic integration technique that transforms the system into an Einstein crystal.

### Table 4: Relationship of memory con icts, strides, and algorithms for the Perfect Club Bench- marks. G/S = gather/scatter. The algorithms are: 1) Sparse linear systems solvers, 2) Non- linear algebraic system solvers, 3) Fast Fourier transform, 4) Rapid elliptic problem solvers, 5) Multigrid schemes, 6) Ordinary di erential equation solvers, 7) Monte Carlo schemes, 8) Integral transforms, 9) Convolution.

"... In PAGE 8: ... Stride information is not available from the hardware performance monitor, but this infor- mation can be extracted from the sim traces. Table4 shows the percentage of some selected strides for the Perfect Club Benchmarks. The strides have been taken modulo 32 since only strides which are multiples of eight (0, 8, 16, and 24) cause internal memory con icts.... In PAGE 22: ... All counts are in millions. Table4 : Relationship of memory con icts, strides, and algorithms for the Perfect Club Bench- marks. G/S = gather/scatter.... ..."

### Table 1: A list of three-dimensional Fourier transforms of various integrable functions used in meshless methods. with the exception of that of the Gaussian, the inverse multiquadric, and the Sobolev spline [28, Theorems 6.10, 6.13, and Page 133], the Fourier transform of each function was computed using (6).

"... In PAGE 6: ...Examples of integrable radial basis functions are given in Table1 . Non-integrable radial basis functions and polynomial terms are sometimes used, examples of which include the multiquadric and the thin-plate spline.... ..."