### Table 1: Mathematical Notation for AKE

1998

"... In PAGE 5: ...Table 1: Mathematical Notation for AKE Table1 summarizes the notation used in this section. We make no assumptions at this point about the domain, range, or input/output types of the functions save for the following: (8w; x; y; z) S(R(P(w); P(x)); Q(y; z)) = S(R(P(y); P(z)); Q(w; x)) (1) Equation 1 must be satis ed for AKE to work properly.... ..."

Cited by 141

### Table 1: Mathematical Notation for AKE

1998

"... In PAGE 5: ...Table 1: Mathematical Notation for AKE Table1 summarizes the notation used in this section. We make no assumptions at this point about the domain, range, or input#2Foutput types of the functions save for the following: #288w; x; y; z#29 S#28R#28P#28w#29;P#28x#29#29;Q#28y;z#29#29 = S#28R#28P#28y#29;P#28z#29#29;Q#28w;x#29#29 #281#29 Equation 1 must be satis#0Ced for AKE to work properly.... ..."

Cited by 141

### Table 1: Mathematical Notation for AKE

"... In PAGE 4: ...uch an application, the user apos;s secret #28i.e. the pass- word#29 never has to leave the local host during the ini- tial password setup and password change procedures; only the veri#0Cer needs to be sent, greatly improving the overall security of the system. Table1 summarizes the notation used in this sec- tion. We make no assumptions at this point about the domain, range, or input#2Foutput types of the func- tions save for the following: #288w; x; y; z#29 S#28R#28P#28w#29;P#28x#29#29;Q#28y;z#29#29 = S#28R#28P#28y#29;P#28z#29#29;Q#28w;x#29#29 #281#29 Equation 1 must be satis#0Ced for AKE to work prop- erly.... ..."

### Table 2 Notations used in mathematical analysis Notation Description

2005

"... In PAGE 9: ...1. Theoretical analysis Table2 describes the notation that will be used in this section. The analysis in the section is based on the follow- ing assumptions: Assumption 1.... ..."

### Table 2. Mathematical Functions Currently Provided

"... In PAGE 6: ... 3.0 Functions Provided The functions provided by Intel are listed in Table2 . Note that this does not provide the full complement of functions that are usually available to programmers, e.... In PAGE 7: ... Numbers in lighter font represent functions that could be made significantly faster, and perhaps will be in the future. hypotf hypot hypotl ilogbf ilogb ilogbl invsqrtf invsqrt invsqrtl isnanf isnan isnanl ldexpf ldexp ldexpl logf log logl log10f log10 log10l log1pf log1p log1pl log2f log2 log2l logbf logb logbl modff modf modfl nearbyintf nearbyint nearbyintl nextafterf nextafter nextafterl powf pow powl remainderf remainder remainderl remquof remquo remquol rintf rint rintl roundf round roundl scalbf scalb scalbl scalbnf scalbn scalbnl significandf significand significandl sinf sin sinl sinhf sinh sinhl sqrtf sqrt sqrtl tanf tan tanl tanhf tanh tanhl truncf trunc truncl Table2 . Mathematical Functions Currently Provided (Continued) Single Double Double-Extended... ..."

### Table 2. Mathematical Functions Currently Provided (Continued)

"... In PAGE 6: ... 3.0 Functions Provided The functions provided by Intel are listed in Table2 . Note that this does not provide the full complement of functions that are usually available to programmers, e.... In PAGE 6: ... However, it is felt that this list contains most of the functions whose performance is normally important, and portable C versions can be used for the functions that are missing. Table2 . Mathematical Functions Currently Provided Single Double Double-Extended acosf acos acosl acoshf acosh asinf asin asinl asinhf asinh atanf atan atanl atan2f atan2 atan2l atanhf atanh cabsf cabs cabsl cbrtf cbrt cbrtl ceilf ceil ceill copysignf copysign copysignl cosf cos cosl coshf cosh coshl expf exp expl exp10f exp10 exp10l exp2f exp2 exp2l expm1f expm1 expm1l fabsf fabs fabsl fdimf fdim fdiml finitef finite finitel floorf floor floorl fmaf fma fmal fmaxf fmax fmaxl fminf fmin fminl fmodf fmod fmodl frexpf frexp frexpl... ..."

### Table 1. Assumptions to be met for the use of parametric tests

"... In PAGE 1: ... These techniques are termed parametric because they focus on specif_ic parameters of the population, usually the mean and variance (1). In order to utilize these techniques, a number of assumptions regarding the nature of population from which the data are drawn must be met ( Table1 ). One might note that typical health science research often violates one, if not all of these parametric assumptions.... ..."

### Table 11-1 When we fit a particular regression model to our data, our assumptions about its stochastic component (usually the assumptions about the distributional properties and about the independence or particular type of cross-dependence between

### Table 7-4. Mathematical Formula Expressions Needed to Solve Design Problems.

"... In PAGE 72: ...). Table7 -1. Data Collection Design Determination.... In PAGE 72: ...ype of non-statistical design is appropriate (e.g., haphazard or judgmental). If the design is non-statistical, fill in the following table and skip to worksheet activity 5; if the design is statistical, proceed to the next table in this worksheet activity. Table7 -2. Data Collection Design Alternatives.... In PAGE 73: ...Rev. 1 A-37 Table7 -3. Statistical Design Determination.... In PAGE 73: ... For example, if a mean concentration of a COPC will be measured by a field screening instrument rather than through laboratory analyses, the model that relates the field screening results to the concentration results must be specified, along with any assumptions upon which the model is based. Table7 -5. Relationships and Assumptions Between True and Measured Values.... In PAGE 74: ... Vary the Type I and Type II error rates (and other inputs in the equations) to examine the relationship between the number of samples and the inputs. Table7 -6. Calculation of Number of Samples for Each Design Alternative.... In PAGE 74: ...e.g., spatial and temporal boundaries or scope of the project). Table7 -7. Results of Trade-Off Analysis.... In PAGE 75: ... The results of the trade-off analyses should lead to one of two outcomes: (a) either the selection of a design that most efficiently meets all of the DQO constraints, or (b) the modification of one or more outputs from DQO process Steps 1 through 6 and the selection of a design that meets the new constraints. Table7 -8. Selection of Appropriate Data Collection Design.... In PAGE 75: ... The most efficient way to deal with uncertainties about the conceptual site model, historical data, or unforeseen implementation problems is to plan an alternative course of action that may be appropriate. Table7 -9. Outline of Alternative Strategies.... In PAGE 76: ...Rev. 1 A-40 Table7 -10. Key Features of Selected Design.... In PAGE 76: ...istribution of the parameter of interest (e.g., the mean concentration is assumed Gaussian) y Statistical independence y Distribution of the population of interest y Model that shows the relationship between the variable being measured and the variable of interest. Table7 -11. Documentation on Theoretical Assumptions.... ..."

### Table 7-5. Relationships and Assumptions Between True and Measured Values.

"... In PAGE 72: ...). Table7 -1. Data Collection Design Determination.... In PAGE 72: ...ype of non-statistical design is appropriate (e.g., haphazard or judgmental). If the design is non-statistical, fill in the following table and skip to worksheet activity 5; if the design is statistical, proceed to the next table in this worksheet activity. Table7 -2. Data Collection Design Alternatives.... In PAGE 73: ...Rev. 1 A-37 Table7 -3. Statistical Design Determination.... In PAGE 73: ... Define a suggested method for testing the statistical hypothesis defined above and define a sample size formula that corresponds to the method, if one exists. Table7 -4. Mathematical Formula Expressions Needed to Solve Design Problems.... In PAGE 74: ... Vary the Type I and Type II error rates (and other inputs in the equations) to examine the relationship between the number of samples and the inputs. Table7 -6. Calculation of Number of Samples for Each Design Alternative.... In PAGE 74: ...e.g., spatial and temporal boundaries or scope of the project). Table7 -7. Results of Trade-Off Analysis.... In PAGE 75: ... The results of the trade-off analyses should lead to one of two outcomes: (a) either the selection of a design that most efficiently meets all of the DQO constraints, or (b) the modification of one or more outputs from DQO process Steps 1 through 6 and the selection of a design that meets the new constraints. Table7 -8. Selection of Appropriate Data Collection Design.... In PAGE 75: ... The most efficient way to deal with uncertainties about the conceptual site model, historical data, or unforeseen implementation problems is to plan an alternative course of action that may be appropriate. Table7 -9. Outline of Alternative Strategies.... In PAGE 76: ...Rev. 1 A-40 Table7 -10. Key Features of Selected Design.... In PAGE 76: ...istribution of the parameter of interest (e.g., the mean concentration is assumed Gaussian) y Statistical independence y Distribution of the population of interest y Model that shows the relationship between the variable being measured and the variable of interest. Table7 -11. Documentation on Theoretical Assumptions.... ..."