This paper describes a new firstand second-order delta-sigma modulator concept where the first integrator is extracted and implemented by a frequency modulator with the modulating signal as the input. The result is a simple delta-sigma modulator with no need for digital-to-analog converters, allowing straight-forward multi-bit quantization. Without the frequency modulator, the circuit becomes a...

For the first-order language the compactness theorem was proved by K. Gödel and A. I. Mal’cev in 1936. In 1955, it was proved by J. Łoś (1955) by means of the method of ultraproducts. Unfortunately, for the usual second-order language the compactness theorem does not hold. Moreover, the method of ultraproducts is also inapplicable to second-order models. A possible way out of this situation is ...

The generalized second-order partial derivatives of 1/r , where r is the radial distance in three dimensions (3D), are obtained using a result of the potential theory of classical analysis. Some non-spherical-regularization alternatives to the standard spherical-regularization expression for the derivatives are derived. The utility of a spheroidal-regularization expression is illustrated on an ...

This paper deals with generalized semi-infinite optimization problems where the (infinite) index set of inequality constraints depends on the state variables and all involved functions are twice continuously differentiable. Necessary and sufficient second order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is seco...

A generalized semi-Markou scheme models the structure of a discrete event system, such as a network of queues. By studying combinatorial and geometric representations of schemes we find conditions for second-order properties-convexity/concavity, sub/supermodularity-of their event epochs and event counting processes. A scheme generates a language of feasible strings of events. We show that monot...

The impulse response of a generalized fractional second order filter of the form ( s2α +asα +b )−γ is derived, where 0 < α ≤ 1, γ > 0. The asymptotic properties of the impulse responses are obtained for two cases, and similar properties are shown for these two cases when we change the value of γ . It is shown that only when ( s2α +asα +b )−1 has the critical stability, the generalized fractiona...

and Applied Analysis 3 It can be easily seen that for a compact convex set C, y is in NC x if and only if S y | C xy, or equivalently, x is in ∂S y | C . Definition 2.2. A functional F : X × X × R → R where X ⊆ R is sublinear with respect to the third variable if for all x, u ∈ X ×X, i F x, u; a1 a2 ≤ F x, u; a1 F x, u; a2 for all a1, a2 ∈ R, ii F x, u;αa αF x, u; a , for all α ∈ R and for all ...

The purpose of this paper is concerned with a class of multi objective programming problems in which the objective functions and constrained functions are twice differentiable and containing the support functions of a compact convex set. For such mathematic programming, to deal with its dual problem, first, the concept of second order ( , ) B p r   invexity is introduced. Further, the Mangasa...

The deployment of power electronic devices has become a big concern for quality in these days. voltage stabilization distribution networks interconnected with Photo Voltaic (PV) is very critical promoting the smooth operation all linked system. Voltage profile maintenance one challenges PV integration into grid. Conventional such as passive filters, series and shunt synchronous condensers, etc....

In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the phase space of the elastic pendulum at higher order resonance, a numerical integrator which preserves qualitative features after long integration times is neede...