An extensive study of two current ion mobility resolving power theories ("conditional" and "semi-empirical") was undertaken using a recently developed drift tube ion mobility-mass spectrometer. The current study investigates the quantitative agreement between experiment and theory at reduced pressure (4 Torr) for a wide range of initial ion gate widths (100 to 500 μs), and ion mobility values (...

Motivated by the work of Angeli and Sontag [1] and Enciso and Sontag [7] in control theory, we show that certain finite and infinite dimensional semi-dynamical systems with “negative feedback” can be decomposed into a monotone “open loop” system with “inputs” and a decreasing “output” function. The original system is reconstituted by “plugging the output into the input”. Employing a technique o...

Each lower semi-continuous proper convex function f on a Banach space E defines a certain multivalued mapping of from E to E* called the subdifferential of f. It is shown here that the mappings arising this way are precisely the ones whose graphs are maximal "cyclically monotone" relations on Ex E*, and that each of these is also a maximal monotone relation. Furthermore, it is proved that of de...

In this paper we discuss some basic properties of computable real functions of bounded variation (CBV-functions for short). Especially, it is shown that the image set of semi-computable real numbers under CBV-functions is a proper subset of the class of weakly computable real numbers; Two applications of CBV-functions to semi-computable real numbers produce the whole closure of semi-computable ...

In this paper we discuss some basic properties of computable real functions which have bounded variations (CBV-functions for short). Especially, it is shown that the image set of semi-computable real numbers under CBV-functions is a proper subset of weakly computable real number class; Two applications of CBV-functions to semi-computable real numbers produce the whole closure of semi-computable...

We consider the problem of semi-supervised bootstrap learning for scene categorization. Existing semi-supervised approaches are typically unreliable and face semantic drift because the learning task is under-constrained. This is primarily because they ignore the strong interactions that often exist between scene categories, such as the common attributes shared across categories as well as the a...

In this paper, we focus on error estimates to smooth solutions of semi-discrete discontinuous Galerkin (DG) methods with quadrature rules for scalar conservation laws. The main techniques we use are energy estimate and Taylor expansion first introduced by Zhang and Shu in [24]. We show that, with P k (piecewise polynomials of degree k) finite elements in 1D problems, if the quadrature over elem...

The concept of a monotone operator — which covers both linear positive semi-definite operators and subdifferentials of convex functions — is fundamental in various branches of mathematics. Over the last few decades, several stronger notions of monotonicity have been introduced: Gossez’s maximal monotonicity of dense type, Fitzpatrick and Phelps’s local maximal monotonicity, and Simons’s monoton...

In this paper we explore the existence of periodic solutions of a nonautonomous semi-ratio-dependent predator-prey dynamical system with functional responses on time scales. To illustrate the utility of this work, we should mention that, in our results this system with a large class of monotone functional responses, always has at least one periodic solution. For instance, this system with some ...