Recent (scale-free) quantitative unique continuation estimates for spectral subspaces of Schrödinger operators are extended to allow singular potentials such as certain Lp-functions. The proof is based on accordingly adapted Carleman estimates. Applications include Wegner and initial length scale random control theory the controlled heat equation with generation term.

Businesses have changed dramatically in recent decades, with continuous advancements new technology business-oriented strategies. Research has shown that the phenomenon started basic programming now expanded to smart software tools affect nearly all functions. Auditing is one of functions affected by newly emerging technologies. This paper based on a literature review pros and cons applying bus...

so far various methods for optimization presented and one of most popular of them are optimization algorithms based on swarm intelligence and also one of most successful of them is particle swarm optimization (pso). prior some efforts by applying fuzzy logic for improving defects of pso such as trapping in local optimums and early convergence has been done. moreover to overcome the problem of i...

in this paper we present a new method for solving fractional optimal control problems with delays in state and control. this method is based upon bernstein polynomial basis and using feedback control. the main advantage of using feedback or closed-loop controls is that they can monitor their effect on the system and modify the output accordingly. in this work, we use bernstein polynomials to tr...

A partial differential equation (PDE) is a mathematical relation which involves functions of multiple variables and their partial derivatives. PDEs are used to formulate (and hence to aid in the solution of) problems involving functions of several variables, and they arise in a variety of important fields. For example, in physics, they are used to describe the propagation of sound or heat, elec...

Recently, Gómez-Ullate et al. [1] have studied a particular N -particle quantum problem with an elliptic function potential supplemented by an external field. They have shown that the Hamiltonian operator preserves a finite dimensional space of functions and as such is quasi exactly solvable (QES). In this paper we show that other types of invariant function spaces exist, which are in close rel...

Evidence theory extends Bayesian probability theory by allowing for a more expressive model of subjective uncertainty. Besides standard interpretation of belief functions, where uncertainty corresponds to probability masses which might refer to whole subsets of the possibility space, credal semantics can be also considered. Accordingly, a belief function can be identified with the whole set of ...

This paper deals with contextual aspects of locative preposition processing. Firstly, accordingly to a study on the referential behavior of the pronominal adverb ”y” in its locative uses, we show that static locative prepositions are functions, not only at the conceptual level (as shown in previous studies), but also from a contextual point of view. Such functions introduce new objects in the d...

We present a technique to compress data de ned as functions in high dimensional spaces. The objects in the spaces are represented by manifolds. Traditionally, data compression methods have been applied to functions de ned on simple manifolds such as the real line (e.g., audio), a rectangle (e.g., images), or a three{dimensional open{ended box (e.g., video). However, many conventional data compr...

The Fbw7 tumor suppressor targets a broad network of proteins for ubiquitylation. Here we show critical functions for Fbw7 dimerization in regulating the specificity and robustness of degradation. Dimerization enables Fbw7 to target substrates through concerted binding to two suboptimal and independent recognition sites. Accordingly, an endogenous dimerization-deficient Fbw7 mutation stabilizes...