4—service loads and general design criteria

... splicing and concrete placement CHAPTER 4—SERVICE LOADS AND GENERAL DESIGN CRITERIA 4.1 General The 1995 Committee re-evaluated the previous exemptions regarding two-face reinforcement and minimum ... The material in the standard was reorganized, charts were added, and the methods for determining loads due to wind and earthquakes were revised The information on design and construction of various ... strength design and encouraged experiments in this area Shortly after the 1979 edition was issued, the Committee decided to incorporate strength design provisions and update the wind and earthquake design...

Ngày tải lên: 24/10/2014, 15:45

... data as 2D and 3D graphs and annotating these graphs The most useful command for generating a simple 2D plot is plot(x, y, `options' ; ) where x and y are vectors containing the x- and y-coordinates ... by using the MATLAB command save This command saves all variables in the file matlab.mat These variables can be restored to the workspace using the load command The command save file_name xn yn ... the following statement at the command prompt: help save The help command will return the text information on how to use save in the command window The help command with no arguments will display...

Ngày tải lên: 25/01/2014, 19:20

... nanoscale-designed material that has superior and unique performance? Microscopy is essential to the development of nanotechnology, serving as its eyes and hands The rationale for editing this Handbook ... discovery and fundamental understanding of nanoscale phenomena and structures This Handbook comprehensively covers the state-of-the-art in techniques to observe, characterize, measure and manipulate ... June, July and August 1827 on the Particles Contained in the Pollen of Plants; and on the General Existence of Active Molecules in Organic and Inorganic Bodies 1828, London: Taylor Born, M and E Wolf,...

Ngày tải lên: 04/06/2014, 14:24

... are parallel and have equal length The diagonals meet and bisect each other Properties of parallelograms: The diagonals meet and bisect each other Opposite sides have equal length, and opposite ... (ϕ – ψ) and, substituting ϕ = ε1 + ε2 and ψ = ε1 – ε2 into (3.1.2.5), obtain the Example Suppose that the mutual position of three points A, B, and C is determined by the segments AC = a and BC ... auxiliary angle We find the angles ϕ and ψ from (3.1.2.6) and (3.1.2.8), substitute them into (3.1.2.7) to determine z, and finally apply the law of sines to obtain x and y 3.1.2-5 Regular polygons...

Ngày tải lên: 02/07/2014, 13:20

... V., and Monastyrnyi, P I., Introduction to the Theory of Numerical Methods Integral Equations, Problems, and Improvement of Convergence [in Russian], Nauka i Tekhnika, Minsk, 1984 Kythe, P K and ... Boston, a 2002 Ladopoulos, E G., Singular Integral Equations: Linear and Non-Linear Theory and Its Applications in Science and Engineering, Springer-Verlag, Berlin, 2000 Lavrentiev, M M., Some ... Mikhlin, S G and Pr¨ ssdorf, S., Singular Integral Operators, Springer-Verlag, Berlin, 1986 o Mikhlin, S G and Smolitskiy, K L., Approximate Methods for Solution of Differential and Integral...

Ngày tải lên: 02/07/2014, 13:20

... 3◦ Superposition principle Let yn and yn be solutions of two nonhomogeneous linear difference equations with the same left-hand sides and different right-hand sides: an yn+2 + bn yn+1 + cn yn ... 2◦ Superposition principle Let yn and yn be solutions of two nonhomogeneous linear difference equations with the same left-hand side and different right-hand sides: am (n)yn+m + am–1 (n)yn+m–1 ... constants 2◦ There are k equal real roots λ1 = λ2 = · · · = λk (k ≤ m), and the other roots are real and distinct In this case, the general solution is given by yn = (C1 + C2 n + · · · + Ck nk–1 )λn...

Ngày tải lên: 02/07/2014, 13:20

... with rational and exponential functions Their general solutions can be obtained as a product of a particular solution and an arbitrary 1-periodic function; see (17.2.1.2) 1◦ The general solution ... 1-periodic functions, since tan(πx) and cot(πx) have period Therefore, without the loss of generality, we can take Θ1 (x) ≡ in (17.2.1.6b) (or Θ2 (x) ≡ 0) And we should consider bounded, as well ... 886 DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS Remark The general solution of a difference equation may be represented by quite different formulas Thus, the general solution of equation...

Ngày tải lên: 02/07/2014, 13:20

... integer and the fractional parts of x (x = [x] + {x}); the product and the sum over the empty index set (for [x] = 0) are assumed equal to and 0, respectively 894 DIFFERENCE EQUATIONS AND OTHER ... 1, 2, , and this leads us to the condition ϕ(1) = ϕ(0) + g(0) (17.2.1.23) The solution is continuously differentiable if the functions g(x) and ϕ(x) are continuously differentiable and, together ... (17.2.1.18) and the boundary condition (17.2.1.10); on the interval ≤ x < 3, one uses equation (17.2.1.18) and the solution obtained for ≤ x < 2; on the interval ≤ x < 4, one uses equation (17.2.1.18) and...

Ngày tải lên: 02/07/2014, 13:20

... (x) sin βx]eαx Notation: Pm (x) and Qn (x) are polynomials of degrees m and n with given coefficients; Pm (x), Pν (x), and Qν (x) are polynomials of degrees m and ν whose coefficients are determined ... particular solution into the basic equation; ν = max(m, n); and α and β are real numbers, i2 = –1 Example Taking F (λ) = aλb , b ≥ 0, and L = {0 ≤ x ≤ 1} in (17.2.3.7), we have a x+b Therefore, ... DIFFERENCE EQUATIONS AND OTHER FUNCTIONAL EQUATIONS THEOREM (CASORATTI) Formula (17.2.3.15) gives the general solution of the linear homogeneous difference equation (17.2.3.13) if and only if for...

Ngày tải lên: 02/07/2014, 13:20

... of general form Possible cases 1◦ Consider a linear nonhomogeneous functional equation of the general form y(f (x)) = g(x)y(x) + F (x) (17.3.3.1) Let x I and ξ I, f (x) Rξ Suppose that g(x) and ... place, the following simple criteria can be used (i) This case takes place if ξ is a strongly attractive fixed point of f (x) and there exist positive constants δ, μ, and M such that |g(x) – 1| ... 17.3.2-1 Equations of general form Possible cases A linear homogeneous functional equation has the form y f (x) = g(x)y(x), (17.3.2.1) where f (x) and g(x) ≠ are known functions and the function y(x)...

Ngày tải lên: 02/07/2014, 13:20

... (t)λt+1 , where Θ1 (t) and Θ2 (t) are arbitrary 1-periodic functions, Θk (t) = Θk (t + 1) Taking Θ1 (t) = C1 and Θ2 (t) = C2 in (17.3.4.6), where C1 and C2 are arbitrary constants, and eliminating the ... [0, a], and the following conditions hold: f (0) = and f (x) < x ≤ a for x ≠ We define a function ϕ(y) on the semiaxis [0, ∞) by ϕ(y) = f [n] ϕ0 ({y}) , n = [y], (17.3.3.8) where [y] and {y} are, ... (y – n) , n ≤ y < n + 1, (17.3.3.9) and therefore is continuous and strictly decreasing, being a superposition of continuous strictly increasing functions and a continuous strictly decreasing...

Ngày tải lên: 02/07/2014, 13:20

... exist a and b such that ϕ(a) = a, F (a, b) = b; 2) the function ϕ(x) is analytic in a neighborhood of a and |ϕ (a)| < 1; 3) the function F is analytic in a neighborhood of the point (a, b) and | ... VARIABLES Let us expand (17.5.1.1) in powers of the small parameter a in a neighborhood of a0 , taking into account (17.5.1.2), and then divide the resulting equation by a – a0 and pass to the limit ... equation in x and y, we get (17.5.2.5) fzz (z) = afx (x)fy (y), where z = x + y Taking the logarithm of both sides of equation (17.5.2.5) and differentiating the resulting relation in x and y, we...

Ngày tải lên: 02/07/2014, 13:20

... functions f (t) and ψ(t) is prescribed and the other is assumed unknown; also one of the functions g(x) and ϕ(x) is prescribed and the other is unknown, and the functions h(x), Q(z), and R(z) are ... functions fn (and gn ) are linearly dependent Remark The bilinear functional equation (17.5.5.8) and its solutions (17.5.5.9) play an important role in the methods of generalized and functional ... = ϕp (x) and ψq = ψq (y) depending on different variables Here, for simplicity, we consider an equation that contains only second-order derivatives; in the general case, the right-hand sides...

Ngày tải lên: 02/07/2014, 13:20

... Verlag, Boston, 2003 a Castillo, E and Ruiz-Cobo, M R., Functional Equations and Modelling in Science and Engineering, Marcel Dekker, New York, 1992 Castillo, E and Ruiz-Cobo, R., Functional Equations ... Polyanin, A D and Manzhirov, A V., Handbook of Integral Equations: Exact Solutions (Supplement Some Functional Equations) [in Russian], Faktorial, Moscow, 1998 Polyanin, A D and Zaitsev, V F., Handbook ... Berlin, 2007 Smital, J and Dravecky, J., On Functions and Functional Equations, Adam Hilger, Bristol-Philadelphia, 1988 Zwillinger, D., CRC Standard Mathematical Tables and Formulae, 31st Edition,...

Ngày tải lên: 02/07/2014, 13:20

... Saigal, R., and Vandenberghe, L., Handbook of Semidefinite Programming: Theory, Algorithms and Applications, Kluwer Academic Press, pp 163–188, 1999 Alpert/Handbook of Algorithms for Physical Design ... of inverters and two and three input NAND and NOR gates We use a TSMC 180 nm technology parameter [10] to estimate the constants for the on resistance and the source, drain, and gate capacitances ... 2005 IEEE Design and Automation Conference, Anaheim, California, 2005.) Alpert/Handbook of Algorithms for Physical Design Automation AU7242_C006 108 Finals Page 108 23-9-2008 #21 Handbook of...

Ngày tải lên: 03/07/2014, 20:20

... ), (H2 ) and the following conditions hold true: (b+ ) b(t) ≥ for t ≥ (f+ ) f (x, t) ≥ for x ∈ Ω and t ≥ (g+ ) g(x, t) ≥ for x ∈ ∂Ω and t ≥ (f2 )+ There exist an open subset Ω0 of Ω and r1 > ... M > and Mε ≥ M > such that (µ − ε) F (x, u)dx ≤ θ(µ − ε) G(x, u)dσ C1 µ F (x, u)dx ≥ Mε and ∂Ω g(x, u)udσ, if ∂Ω We may assume Mε > Mε and Ω ≤ ∂Ω Ω F (x, u)dx ≥ Mε , f (x, u)udx, if Ω Ω and Mε ... (f1 ) and (f5 ) we have|Φ(u)| ≤ C2 u from(g1 ) and (g5 ) we have |Ψ(u)| ≤ C2 u r2− β3 r1− α3 p+ , , and in the similar way Thus by (H4 ), we conclude that there exist positive constants ρ and...

Ngày tải lên: 20/06/2014, 21:20

... (H) if it is continuous and satisfies limt→∞ f (t) = f∞ , and t | f (t)− f∞ | ≤ M ∗ for t > Throughout the paper, we always assume that (A1 ) θ ∈ C(R+ , R), p ∈ C (R,(1, ∞)) and satisfies < inf p(x) ... limt→+∞ p(t) and q(t) possesses property (H), then all the solutions of (1.1) are oscillatory Proofs of main results In the following, we denote −(ϕ(t,u )) = −(|u | p(t)−2 u ) , and use Ci and ci to ... contradiction to (2.10) Thus < θ1 < p− , and we have − u (t) ≥ ϕ−1 t, (C1 )(q −1) , θ1 − t θ1 −1 ∀t > T2 , (2.19) then, there exists T3 > T2 and positive constant c3 and C2 such that u (t) ≥ c3 1/(p−...

Ngày tải lên: 22/06/2014, 18:20

... dimensional Hilbert space and linearly homeomorphic to Rqm On the other hand, we define the norm · p on Eqm as follows: qm x xi p= p 1/ p , (2.5) i=1 for all x ∈ Eqm and p > Clearly, x = x Since ... Since · exist constants C1 , C2 , such that C2 ≥ C1 > 0, and C1 x p ≤ x ≤ C2 x p, p and · ∀x ∈ Eqm are equivalent, there (2.6) P Chen and H Fang Define the functional J on Eqm as follows: qm J(x) ... X for which {I(un )} is bounded and I (un ) → 0, as n → ∞, possesses a convergent subsequence in X Let Bρ be the open ball in X with radius ρ and centered at and let ∂Bρ denote its boundary Lemma...

Ngày tải lên: 22/06/2014, 19:20

... [6] for p = 2, and recently by Liu and Li in [9] for general p > We can easily prove that Assumption 1.2 is equivalent to Assumption 1.1 when θ = and Assumption 1.2 gives some general sense of ... satisfies Assumption 1.2 and the following conditions hold: (f1) f (x,t) ≥ for all t ≥ 0, x ∈ Ω and f (x,t) ≡ for all t ≤ 0, x ∈ Ω; (f2) limsupt→0+ ( f (x,t)/t p−1 ) = a(x) and limt→+∞ ( f (x,t)/t ... x ∈ Ω and a(x) < λ1 on some Ω ⊂ Ω with |Ω | > 0, λ1 is the first eigenvalue of −Δ p and |Ω | is the measure of Ω Then problem (1.1) has at least one solution u > If we consider a more general...

Ngày tải lên: 22/06/2014, 22:20

... All authors made substantial contributions to conception and design, and to the analysis and interpretation of the data TRM and GWC handled acquisition of data All authors contributed to the ... diseases (DMARD) and with registry follow-up at one year, VARA and administrative data were used to create a gold standard and claims-based effectiveness algorithm The gold standard outcome was ... offdiagonal (discordant) cells of Table and are shown in Table For the 19 treatment episodes where the effectiveness algorithm criteria were satisfied but the gold standard criteria were not, the most common...

Ngày tải lên: 25/10/2012, 10:45