In this paper, a procedure has been introduced to the multi-objective optimal design of semi-active tuned mass dampers (SATMDs) with variable stiffness for nonlinear structures considering soil-structure interaction under multiple earthquakes. Three bi-objective optimization problems have been defined by considering the mean of maximum inter-story drift as safety criterion of structural compone...

We consider the problem of approximating xed points of non smooth con tractive functions with using of the absolute error criterion In we proved that the upper bound on the number of function evaluations to compute approximations is O n ln ln q ln n in the worst case where q is the contraction factor and n is the dimension of the problem This upper bound is achieved by the circumscribed ellipso...

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

In a recent paper Xian-Jin Li showed that the Riemann Hypothesis holds if and only if n = P 1?(1?1==) n has n > 0 for n = 1; 2; 3; : : : where runs over the complex zeros of the Riemann zeta function. We show that Li's criterion follows as a consequence of a general set of inequalities for an arbitrary multiset of complex numbers and therefore is not speciic to zeta functions. We also give an a...

We characterize decomposition over C of polynomials f (a,B) n (x) defined by the generalized Dickson-type recursive relation (n ≥ 1), f (a,B) 0 (x) = B, f (a,B) 1 (x) = x, f (a,B) n+1 (x) = xf (a,B) n (x)− af (a,B) n−1 (x), where B, a ∈ Q or R. As a direct application of the uniform decomposition result, we fully settle the finiteness problem for the Diophantine equation f (a,B) n (x) = f (â,B̂)...

Since numerical error is the source of non-robustness, it is natural to try to improve upon the standard floating point arithmetic. Can we improve on the conventional floating point arithmetic, which has already reached a highly optimal design under the IEEE Standard? More generally, what techniques are available in the FP mode of computation? In conventional floating point systems, the number ...

A bipartite spin-1/2 system having the probabilities 1+3x 4 of being in the Einstein-Podolsky-Rosen entangled state |Ψ−>≡ 1 √ 2 (|↑>A |↓>B−|↓>A |↑>B) and 3(1−x) 4 of being orthogonal, is known to admit a local realistic description if and only if x < 1/3 (Peres criterion). We consider here a more general case where the probabilities of being in the entangled states |Φ±>≡ 1 √ 2 (|↑>A |↑>B ±|↓>A ...