b—derivation of equations for temperature stresses p 307r 13

... 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 ... mean Eq (4-6) is a simple empirical fit to values of Gw′ computed as before for a structural damping of 1.5 percent of critical Except for referencing V as the 3-sec gust speed, no revisions have ... results of a full dynamic analysis employing accepted approaches and recognizing the flow profile and turbulence levels at a specific site may be used in place of the standard provisions The approximate...

Ngày tải lên: 24/10/2014, 15:45

... 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 ... will be discussed in Chapter There are many other specialized graphics functions for 2D plotting For example, the command stem(n,xn) ; produces the `lollipop' presentation of the same data In addition, ... search for information is provided by lookfor 455 ELEMENTARY OPERATIONS B.1.2 Graphics MATLAB provides a variety of sophisticated techniques for presenting and visualizing data as 2D and 3D graphs...

Ngày tải lên: 25/01/2014, 19:20

... Michael Introduction Historical Development of EBSD Origin of EBSD Patterns Resolution of EBSD Sample Preparation of Nano-materials for EBSD Applications of EBSD to Nano-materials Summary Acknowledgements ... nano-photoluminescence: Principle and applications Journal of Applied Physics, 2003 93(10): p 6265–6272 26 Bae, J H., et al., High resolution confocal detection of nanometric displacement by use of a × optical ... Microstrip Line Phase Shifter for Room -Temperature Communications Applications Microwave and Optical Technology Letters, 1999 20(1): p 53–56 49 Hubert, C and J Levy, New optical probe of GHz polarization...

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

... 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 ... and Their Applications to Mathematical Physics, Dover Publications, New York, 1992 Petrovskii, I G., Lectures on the Theory of Integral Equations, Graylock Press, Rochester, 1957 Pipkin, A C., ... constructing the points P0 , P1 , P2 , on the graph of the function z = f (y) with the abscissas y0 , y1 , y2 , determined by equation (17.1.2.8) z P z=y z = f (y) P y2 y1 P * P Q1 Q0 y O y0...

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

... coefficients Pn (x)y(x + 1) – Qm (x)y(x) = 0, where Pn (x) and Qm (x) are given polynomials of degrees n and m, respectively Suppose that these polynomials are represented in the form Pn (x) = a(x ... 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 ... help of formulas from Paragraph 17.2.1-3 889 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:...

Ngày tải lên: 02/07/2014, 13:20

... (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 ... 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...

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 ... (17.2.3 .13) where a0 (x)am (x) This equation admits the trivial solution y(x) ≡ The set E of all singular points of equation (17.2.3 .13) consists of points of three classes: 1) zeroes of the function ... 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...

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 ... (Cyclic) Functional Equations 17.4.2-1 Reciprocal functional equations depending on y(x) and y(a – x) 1◦ Consider a reciprocal equation of the form F x, y(x), y(a – x) = Replacing x by a – x, ... special case of (17.3.4.4) with a = 0, b = –1 The corresponding characteristic equation (17.3.3.5) has the roots λ1,2 = The parametric representation of solution (17.3.4.6) contains the complex...

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 932 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) ... EQUATIONS AND OTHER FUNCTIONAL EQUATIONS 17.5.4 Method of Argument Elimination by Test Functions 17.5.4-1 Classes of equations Description of the method Consider linear functional equations of...

Ngày tải lên: 02/07/2014, 13:20

... World of Mathematical Equations, http://eqworld.ipmnet.ru/en/solutions/fe.htm Polyanin, A D and Manzhirov, A V., Handbook of Integral Equations: Exact Solutions (Supplement Some Functional Equations) ... et – dt t for x < 0, for x > for x > 0, for x < 0, for x > 0, for x > 0, where C = 0.5772 is the Euler constant 18.2.2-2 Expansions as x → and x → ∞ Expansion into series in powers of x as x ... 940 SPECIAL FUNCTIONS AND THEIR PROPERTIES 18.2.1-2 Expansions as x → and x → ∞ Definite integral Expansion of erf x into series in powers of x as x → 0: erf x = √ π ∞ (–1)k k=0 ∞ x2k+1 = √ exp –x2...

Ngày tải lên: 02/07/2014, 13:20

... 127 128 130 130 130 131 132 132 132 132 Modern standard cell placement techniques must handle huge and ever-increasing design sizes It is computationally infeasible to place flattened representations ... 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 ... robust posynomial constraint of Equation 6.38 to a set of posynomial constraints of Equations 6.46 through 6.48 For a general circuit, the procedure described for the example circuit of Figure...

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 ... has limsup n→∞ Ω m F x,wn dx = limsup n→∞ Ω + F x,(2pm)1/ p wn dx p ≤ limsup Ω n→∞ + 2m λ1 + ε wn dx + + = limsup C1 wn n→∞ = C1 w + p p p p q q + A(2pm)q/ p (wn )q dx q q + + C2 wn + C2 w+ Ω...

Ngày tải lên: 22/06/2014, 22:20

... 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, ... although not perfect, performance of our effectiveness algorithm applied to administrative claims data By way of comparison, the corresponding performance characteristics in administrative data for a ... a proxy for the effectiveness of medications for RA patients Materials and methods Eligible patient population After Institutional Review Board (IRB) approval, we used data from a cohort of patients...

Ngày tải lên: 25/10/2012, 10:45