a—derivation of equations for nominal strength p 307r 9

... 150(3sg)/130(fm) 1.054 0 .97 3 0 .94 0 1.058 0 .97 6 0 .94 4 1.062 0 .98 0 0 .94 7 1.065 0 .98 3 0 .95 0 1.0 69 0 .98 8 0 .95 5 1.072 0 .99 1 0 .95 8 1.073 0 .99 3 0 .96 0 1.074 0 .99 3 0 .96 0 1.0 79 0 .99 8 0 .96 5 10 1.082 1.00 0 .96 7 11 1.084 ... wind speeds Per ACI 307-88 Vcr, mph V(zcr), mph 78 .9 76.2 106.4 54.0 101.1 72.0 71.8 39. 7 Chimney 13 12 93 .9 84.0 84.8 96 .0 86.4 92 .3 87.2 91 .1 VI, mph 85.0 76.8 74 .9 85.6 74 .9 74 .9 85.6 85.6 Per ... response spectrum, normalized for a peak horizontal ground acceleration of 1.00 with percent of critical damping It represents a spectrum of 50 percent shapebound probability level that the response...

Ngày tải lên: 24/10/2014, 15:45

... [ À 1.5 695 , 0 .93 91] 1, ; yn ˆ filter(b,a,xn) ; plot(n,xn,`:' n,yn,`À') , ; 464 APPENDIX B: INTRODUCTION OF MATLAB FOR DSP APPLICATIONS Figure B.3 shows the MATLAB plots of input and output signals ... window for the current plot The windows are numbered from left to right, top to bottom For example, subplot(2,1,1), plot(n), subplot(2,1,2), plot(xn) ; will split the graph window into a top plot for ... form variable ˆ expression 458 APPENDIX B: INTRODUCTION OF MATLAB FOR DSP APPLICATIONS or simply expression Since MATLAB supports long variable names (up to 19 characters, start with a letter,...

Ngày tải lên: 25/01/2014, 19:20

... Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light 6th corr ed 199 7, Oxford; New York: Cambridge University Press c 199 7 xxviii, 808 Sheppard, ... microscopy Optics Letters, 199 4 19( 3): p 222–224 10 Schrader, M., et al., Optical transfer functions of 4Pi confocal microscopes: theory and experiment Optics Letters, 199 7 22(7): p 436–438 22 I Optical ... Optics, 199 7 36(34): p 892 9– 893 2 16 Schrader, M., S W Hell, and H T M van der Voort, Potential of confocal microscopes to resolve in the 50–100 nm range Applied Physics Letters, 199 6 69( 24): p 3644–3646...

Ngày tải lên: 04/06/2014, 14:24

... have equal length Both pairs of opposite angles are equal Two opposite sides are parallel and have equal length The diagonals meet and bisect each other Properties of parallelograms: The diagonals ... altitude of a trapezoid Properties of trapezoids: A trapezoid is circumscribed if and only if a + b = c + d A trapezoid is inscribed if and only if it is isosceles The area of a trapezoid is ... connecting the midpoints of the diagonals is parallel to the bases and has the length (b – a) Example Consider an application of plane geometry to measuring distances in geodesy Suppose that the...

Ngày tải lên: 02/07/2014, 13:20

... Rochester, 195 7 Pipkin, A C., A Course on Integral Equations, Springer-Verlag, New York, 199 1 Polyanin, A D and Manzhirov, A V., A Handbook of Integral Equations, CRC Press, Boca Raton, 199 8 Porter, ... Boundary Problems of Function Theory and Their Applications to Mathematical Physics, Dover Publications, New York, 199 2 Petrovskii, I G., Lectures on the Theory of Integral Equations, Graylock Press, ... graph of the function f (y) at the point P1 = (y1 , y2 ) with y2 = f (y1 ) Repeating the operations of steps and 2, we obtain the following sequence on the graph of f (y): P0 = (y0 , f (y0 )), P1 ...

Ngày tải lên: 02/07/2014, 13:20

... general solution of the corresponding homogeneous equation is constructed with the help of the formulas from Paragraph 17.1.5-1, and a particular solution of the nonhomogeneous equation for an arbitrary ... With regard to the solution of this equation see Paragraph 17.1.1-2 (1) (2) 3◦ Superposition principle Let yn and yn be solutions of two nonhomogeneous linear difference equations with the same ... with the help of the formulas from Paragraph 17.1.6-2 2◦ If the roots λ1 , λ2 , , λm of the characteristic equation (17.1.5.2) are mutually distinct, the particular solution of the nonhomogeneous...

Ngày tải lên: 02/07/2014, 13:20

... help of formulas from Paragraph 17.2.1-3 8 89 17.2 LINEAR DIFFERENCE EQUATIONS WITH A SINGLE CONTINUOUS VARIABLE 17.2.1-3 Homogeneous linear difference equations Cauchy’s problem 1◦ Cauchy’s problem: ... coefficients 7◦ The particular solutions from Items 1◦ – 6◦ allow us to obtain solutions of more intricate linear difference equations with the help of formulas from Paragraph 17.2.1-1 Example Consider ... y(x + 1) – exp[Pn (x)]y(x) = 0, n Pn (x) = bk xk , k=1 has a particular solution of the form n+1 y(x) = exp[Qn+1 (x)], Qn+1 (x) = ck xk , k=1 where ck can be found by the method of indefinite...

Ngày tải lên: 02/07/2014, 13:20

... arbitrary 1-periodic functions, Θ1,2 (x) = Θ1,2 (x + 1) * Condition (17.2.2.10) may be violated at singular points of equation (17.2.2 .9) ; for details see Paragraph 17.2.3-3  896 DIFFERENCE EQUATIONS ... (17.2.2.22) considered in detail in Paragraphs 17.2.1-4–17.2.1-7 4◦ The structure of particular solutions of second-order difference equations with specific (polynomial, exponential, sinusoidal, etc.) ... over the empty index set (for [x] = 0) are assumed equal to and 0, respectively  894 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS If a nontrivial particular solution y1 (x) of the homogeneous...

Ngày tải lên: 02/07/2014, 13:20

... (multiplicity r) [P +r (x) cos βx + Qν+r (x) sin βx]eαx Notation: Pm (x) and Qn (x) are polynomials of degrees m and n with given coefficients; Pm (x), P (x), and Qν (x) are polynomials of degrees ... entire complex plane (except, possibly, the infinite point) Any such function can be expanded in power series, f (x) = plane, i.e., lim |bk |1/k = k→∞ ∞ k=0 bk xk , convergent on the entire complex ... characterizes the order of their growth for large values of the argument The class of functions of exponential growth of finite degree σ is denoted by [1, σ] and is defined as the set of all entire functions*...

Ngày tải lên: 02/07/2014, 13:20

... EQUATIONS 17.3.1-3 Asymptotic properties of iterations in a neighborhood of a fixed point 1◦ Let f (0) = 0, < f (x) < x for < x < x0 , and suppose that in a neighborhood of the fixed point the function ... 17.3.1-2 Fixed points of a function Some classes of functions A point ξ is called a fixed point of the function f (x) if f (ξ) = ξ A point ξ is called an attractive fixed point of the function ... < x0 17.3.1-4 Representation of iterations by power series Let f (x) be a function with a fixed point ξ = f (ξ) and suppose that in a neighborhood of that point f (x) can be represented by the...

Ngày tải lên: 02/07/2014, 13:20

... admits particular solutions of the form y(x) = C| ln x |p , where C is an arbitrary constant and p is a root of the transcendental equation am |nm |p + am–1 |nm–1 |p + · · · + a1 |n1 |p + a0 |n0 |p ... help of the replacement u(x) = sy(x)/c ; see equation (17.3.2.5) 91 6 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS 17.3.4 Linear Functional Equations Reducible to Linear Difference Equations ... solution of equation (17.3.4.7) has the form y(x) ≡ x 91 8 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS 3◦ Solution in parametric form: t+1 t , y=Θ , 2 where Θ(t) = Θ(t + 1) is an arbitrary periodic...

Ngày tải lên: 02/07/2014, 13:20

... substituting particular values of independent arguments This procedure is aimed at reducing the problem for a functional equation with several independent variables to a problem for a system of algebraic ... functional equations with one independent variable 17.5 Functional Equations with Several Variables 17.5.1 Method of Differentiation in a Parameter 17.5.1-1 Classes of equations Description of the ... FUNCTIONAL EQUATIONS 17.5.3 Method of Substituting Particular Values of Independent Arguments In order to solve functional equations with several independent variables, one often uses the method of substituting...

Ngày tải lên: 02/07/2014, 13:20

... The method of splitting will be used in Paragraph 17.5.5-3 for the construction of solutions of some nonlinear functional equations 93 2 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS 17.5.5-3 ... The method of elimination of an argument is much simpler than that of differentiation in a parameter, since the former only requires to solve algebraic (transcendental) equations of the form (17.5.4.3) ... with respect to ξ and does not require solutions of the corresponding first-order partial differential equations (see Subsection 17.5.1) 93 0 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS...

Ngày tải lên: 02/07/2014, 13:20

... functional equations [in Russian], Uspekhi Mat Nauk, Vol 11, No ( 69) , pp 3–68, 195 6 Acz´ l, J and Dhombres, J., Functional Equations in Several Variables, Cambridge University Press, Came bridge, 198 9 ... Mathematical Geophysics, Novosibirsk, 199 7 93 6 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS Pelyukh, G P and Sharkovskii, O M., Introduction to the Theory of Functional Equations [in Russian], ... V., Handbook of Integral Equations: Exact Solutions (Supplement Some Functional Equations) [in Russian], Faktorial, Moscow, 199 8 Polyanin, A D and Zaitsev, V F., Handbook of Nonlinear Partial Differential...

Ngày tải lên: 02/07/2014, 13:20

... A., Interior Point Polynomial Methods in Convex Programming, SIAM Studies in Applied Mathematics 13, Philadelphia, PA, 199 4 Sturm, J.F., Using SeDuMi 1.02, A Matlab toolbox for optimization over ... http://www.mosis.org/Technical/Testdata/tsmc-018-prm.html 11 Wolkowicz, H., Saigal, R., and Vandenberghe, L., Handbook of Semidefinite Programming: Theory, Algorithms and Applications, Kluwer Academic Press, pp 163–188, 199 9 Alpert/Handbook ... of some other well-known convex optimization problems can also be reformulated in a finite way as a conic optimization problem, often as an SOCP or SDP Next we consider a robust formulation of...

Ngày tải lên: 03/07/2014, 20:20

... p+ < θµ Then E satisfies condition (P. S)c for any c = Proof By (a4 ), for u large enough, p+ J(u) = p+ a( ≥ p+ a ≥ a Ω | u |p( x) + |u |p( x) dx) Ω p( x) 1 | u |p( x) + |u |p( x) dx | u |p( x) + |u |p( x) ... −1 )p( x) N p( x) , ∞ (Ω) the closure of C0 (Ω) when p( x) < N , and p = p = ∞, when p( x) > N Proposition 2.1 [22, 41] (1) If p ∈ C+ (Ω), the space (Lp(x) (Ω), | · |p( x) ) is a separable, uniform ... The operator p( x) u = div(| u |p( x)−2 u) is called p( x)-Laplacian, which becomes p- Laplacian when p( x) ≡ p (a constant) The p( x)-Laplacian possesses more complicated nonlinearities than p- Laplacian...

Ngày tải lên: 20/06/2014, 21:20

... important in the study of the oscillation of the solutions of p- Laplacian equations There are many papers about the oscillation problem of p- Laplacian equations (see [7– 10]) On the typical p- Laplacian ... Analysis and Applications, vol 312, no 1, pp 24–32, 2005 [5] Q H Zhang, “The asymptotic behavior of solutions for p( x)-laplace equations, ” to appear in Journal of Zhengzhou University of Light [6] ... of p- Laplacian problems It is well known that, there exists Picone-type identity for p- Laplacian equations, and then it is easy to obtain Sturmian comparison theorems for p- Laplacian equations, ...

Ngày tải lên: 22/06/2014, 18:20

... p/ 2 λ p C2 p p p p x x p p −2 − p/ 2−2 p/ 2 C1 λ p C2 p qm C1 C2 p qm C1 C2 p p p/ 2 − 2− p/ 2−2 λmin p p/2 x p − 2− p/ 2−2 λmin x p − p/ 2 C1 λ 2p C2 p p/2 max xn+1 p , xn p n =1 p/ 2 xn+1 p + xn p n ... n =1 C1 p/ 2+1 x p x p = p p 1 2p C2 p p/2 λmin x p (3.13) p/ 2 Take σ = 1/ 2p( 1/C2 ) p λmin δ p , then J(x) ≥ σ > 0, ∀x ∈ Y ∩ ∂Bδ (3.14) So c0 = sup J(x) ≥ σ > 0, x∈Eqm (3.15) which implies that ... λmin p C2 p, ∀ρ ≤ δ (3.12) Therefore, for any x = (x1 ,x2 , ,xqm )T with x ≤ δ, x ∈ Y , we have J(x) ≥ 1 p C2 p xT Ax qm F n,xn+1 ,xn − n =1 p/ 2 ≥ λmin p C2 ≥ p/ 2 p/ 2 λ p C2 = p/ 2 λ p C2 ≥ p/ 2...

Ngày tải lên: 22/06/2014, 19:20

... identically of Ω, it is positive everywhere in Ω (2.15) A class of superlinear p- Laplacian equations Proof of the theorems Proof of Theorem 1.3 It is well known that to seek a nontrivial weak solution of ... and the Poincare inequality, we have Ω a(x) p dx ≤ λ1 Ω p dx ≤ Ω ∇vn p dx = p = (2.7) J Wang and C.-L Tang Therefore, we obtain 1− ≤ n Ω p a(x) dx ≤ λ1 Ω p dx ≤ 1 ,p Ω ∇vn p dx = (2.8) 1 ,p For {vn ... (3.8) that F x,tϕ1 ≥ p p t ϕ1 − c(ε)tϕ1 p (3 .9) Dividing by t p , one has F x,tϕ1 p c(ε)ϕ1 ≥ ϕ − p −1 , p t p t (3.10) thus we have F x,tϕ1 dx ≥ Ω Ω p c(ε)ϕ1 ϕ − p 1 dx p t (3.11) Let t →...

Ngày tải lên: 22/06/2014, 22:20

... (72%) PPV = 75%, 95 % CI 62, 86% NPV = 90 %, 95 % CI 84, 94 % 56 (28%) 141 (72%) 197 (100%) Sn = 75% Sp = 90 % 95 % CI 62, 95 % CI 84, 86% 94 % CI: Confidence Interval; NPV: Negative Predictive Value; PPV: ... 19 79( 26%) No 23 203 226 (74%) Total 83(27%) Sn = 72% 222 (73%) Sp = 91 % 305(100%) PPV = 76%, 95 % CI71, 81% NPV = 90 %, 95 % CI88, 92 % 95 % CI 67, 95 % CI 89, 77% 93 % CI: Confidence Interval; NPV: ... specificity, unlike PPV and NPV, should be less dependent on the prevalence in the population, and more reflective of the test itself, lessening the impact of any unique features of the VA population Moreover,...

Ngày tải lên: 25/10/2012, 10:45