A Brief Story about the Operators of the Generalized Fractional Calculus

2000 Mathematics Subject Classification: 26A33, 33C60, 44A20

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1operator from a modular space X ρs(ϕ) to the generalized Orlicz sequence space lϕ.

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

Generalized Backscattering and the Lax-Phillips Transform

2000 Mathematics Subject Classification: 35P25, 35R30, 58J50.

Generalized Derivations and Norm Equality in Normed Ideals

2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.

Formalizing operator task analysis

Human operators are unique in their decision making capability, judgment and nondeterminism. Their sense of judgment, unpredictable decision procedures, susceptibility to environmental elements can cause them to erroneously execute a given task description to operate a computer system. Usually, a computer system is protected against some erroneous human behaviors by having necessary safeguard mechanisms in place. But some erroneous human operator behaviors can lead to severe or even fatal consequences especially in safety critical systems. A generalized methodology that can allow modeling and analyzing the interactions between computer systems and human operators where the operators are allowed to deviate from their prescribed behaviors will provide a formal understanding of the robustness of a computer system against possible aberrant behaviors by its human operators. We provide several methodology for assisting in modeling and analyzing human behaviors exhibited while operating computer systems. Every human operator is usually given a specific recommended set of guidelines for operating a system. We first present process algebraic methodology for modeling and verifying recommended human task execution behavior. We present how one can perform runtime monitoring of a computer system being operated by a human operator for checking violation of temporal safety properties. We consider the concept of a protection envelope giving a wider class of behaviors than those strictly prescribed by a human task that can be tolerated by a system. We then provide a framework for determining whether a computer system can maintain its guarantees if the human operators operate within their protection envelopes. This framework also helps to determine the robustness of the computer system under weakening of the protection envelopes. In this regard, we present a tool called Tutela that assists in implementing the framework. We then examine the ability of a system to remain safe under broad classes of variations of the prescribed human task. We develop a framework for addressing two issues. The first issue is: given a human task specification and a protection envelope, will the protection envelope properties still hold under standard erroneous executions of that task by the human operators? In other words how robust is the protection envelope? The second issue is: in the absence of a protection envelope, can we approximate a protection envelope encompassing those standard erroneous human behaviors that can be safely endured by the system? We present an extension of Tutela that implements this framework. The two frameworks mentioned above use Concurrent Game Structures (CGS) as models for both computer systems and their human operators. However, there are some shortcomings of this formalism for our uses. We add incomplete information concepts in CGSs to achieve better modularity for the players. We introduce nondeterminism in both the transition system and strategies of players and in the modeling of human operators and computer systems. Nondeterministic action strategies for players in \emph{i}ncomplete information \emph{N}ondeterministic CGS (iNCGS) is a more precise formalism for modeling human behaviors exhibited while operating a computer system. We show how we can reason about a human behavior satisfying a guarantee by providing a semantics of Alternating Time Temporal Logic based on iNCGS player strategies. In a nutshell this dissertation provides formal methodology for modeling and analyzing system robustness against both expected and erroneous human operator behaviors.

Dependence of the crossover exponent with the diffusion rate in the generalized contact process model

We study how the crossover exponent, phi, between the directed percolation (DP) and compact directed percolation (CDP) behaves as a function of the diffusion rate in a model that generalizes the contact process. Our conclusions are based in results pointed by perturbative series expansions and numerical simulations, and are consistent with a value phi = 2 for finite diffusion rates and phi = 1 in the limit of infinite diffusion rate.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Generalized connectivity between any two nodes in a complex network

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how these paths can be used for characterization of topological properties of theoretical and real-world complex networks. This analysis revealed that the number of paths can provide a better discrimination of network models than traditional network measurements. In addition, the analysis of real-world networks suggests that the long-range connectivity tends to be limited in these networks and may be strongly related to network growth and organization.

Study of the influence of indium segregation on the optical properties of InGaAs/GaAs quantum wells via split-operator method

In the case of quantum wells, the indium segregation leads to complex potential profiles that are hardly considered in the majority of the theoretical models. The authors demonstrated that the split-operator method is useful tool for obtaining the electronic properties in these cases. Particularly, they studied the influence of the indium surface segregation in optical properties of InGaAs/GaAs quantum wells. Photoluminescence measurements were carried out for a set of InGaAs/GaAs quantum wells and compared to the results obtained theoretically via split-operator method, showing a good agreement.

Generalized Sznajd model for opinion propagation

In the last decade the Sznajd model has been successfully employed in modeling some properties and scale features of both proportional and majority elections. We propose a version of the Sznajd model with a generalized bounded confidence rule-a rule that limits the convincing capability of agents and that is essential to allow coexistence of opinions in the stationary state. With an appropriate choice of parameters it can be reduced to previous models. We solved this model both in a mean-field approach (for an arbitrary number of opinions) and numerically in a Barabaacutesi-Albert network (for three and four opinions), studying the transient and the possible stationary states. We built the phase portrait for the special cases of three and four opinions, defining the attractors and their basins of attraction. Through this analysis, we were able to understand and explain discrepancies between mean-field and simulation results obtained in previous works for the usual Sznajd model with bounded confidence and three opinions. Both the dynamical system approach and our generalized bounded confidence rule are quite general and we think it can be useful to the understanding of other similar models.

Coexistence of interacting opinions in a generalized Sznajd model

The Sznajd model is a sociophysics model that mimics the propagation of opinions in a closed society, where the interactions favor groups of agreeing people. It is based in the Ising and Potts ferromagnetic models and, although the original model used only linear chains, it has since been adapted to general networks. This model has a very rich transient, which has been used to model several aspects of elections, but its stationary states are always consensus states. In order to model more complex behaviors, we have, in a recent work, introduced the idea of biases and prejudices to the Sznajd model by generalizing the bounded confidence rule, which is common to many continuous opinion models, to what we called confidence rules. In that work we have found that the mean field version of this model (corresponding to a complete network) allows for stationary states where noninteracting opinions survive, but never for the coexistence of interacting opinions. In the present work, we provide networks that allow for the coexistence of interacting opinions for certain confidence rules. Moreover, we show that the model does not become inactive; that is, the opinions keep changing, even in the stationary regime. This is an important result in the context of understanding how a rule that breeds local conformity is still able to sustain global diversity while avoiding a frozen stationary state. We also provide results that give some insights on how this behavior approaches the mean field behavior as the networks are changed.

Estimating losses in teleportation schemes using the phenomenological operator approach to dissipation in cavity quantum electrodynamics

In this paper, we estimate the losses during teleportation processes requiring either two high-Q cavities or a single bimodal cavity. The estimates were carried out using the phenomenological operator approach introduced by de Almeida et al. [Phys. Rev. A 62, 033815 (2000)].

Nonempirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound

A simple and completely general representation of the exact exchange-correlation functional of density-functional theory is derived from the universal Lieb-Oxford bound, which holds for any Coulomb-interacting system. This representation leads to an alternative point of view on popular hybrid functionals, providing a rationale for why they work and how they can be constructed. A similar representation of the exact correlation functional allows to construct fully nonempirical hyper-generalized-gradient approximations (HGGAs), radically departing from established paradigms of functional construction. Numerical tests of these HGGAs for atomic and molecular correlation energies and molecular atomization energies show that even simple HGGAs match or outperform state-of-the-art correlation functionals currently used in solid-state physics and quantum chemistry.