Let C(A) denote the multiplicative complexity of a finite dimensional associative k-algebra A. For algebras A with nonzero radical radA, we exhibit several lower bound techniques for C(A) that yield bounds significantly above the Alder–Strassen bound. In particular, we prove that the multiplicative complexity of the multiplication in the algebras k[X1; : : : ; Xn]= Id+1 (X1; : : : ; Xn) is boun...

In decision making, consistency in fuzzy preference relations is associated with the study of transitivity property. While using additive consistency property to complete incomplete preference relations, the preference values found may lie outside the interval [0, 1] or the resultant relation may itself be inconsistent. This paper proposes a method that avoids inconsistency and completes an inc...

We consider the joint source-channel coding problem of sending a Gaussian source over a K-user Gaussian broadcast channel with bandwidth mismatch. A new outer bound to the achievable distortion region is derived using the technique of introducing more than one additional auxiliary random variable, which was previously used to derive sum-rate lower bound for the symmetric Gaussian multiple descr...

Consider the problem of learning a kernel for use in SVM classification. We bound the estimation error of a large margin classifier when the kernel, relative to which this margin is defined, is chosen from a family of kernels based on the training sample. For a kernel family with pseudodimension dφ, we present a bound of √ Õ(dφ + 1/γ2)/n on the estimation error for SVMs with margin γ. This is t...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollaries of ...

In this paper, we discuss the perturbation analysis of extended vertical linear complementarity problem (EVLCP). Under assumption row $${\mathcal {W}}$$ -property, derive several absolute and relative bounds EVLCP, which extend some existing results. Several numerical examples are given to show proposed bounds.

By constructing a coupling with unbounded time-dependent drift, lower bound estimate of dimension-free Harnack inequality power is obtained for large class stochastic differential equation multiplicative noise. The key an application the inverse Hölder inequality. Combining this well-known upper bound, bilateral established. As dual inequality, shift-Harnack inequalities are also investigated a...