Ultrafast all-optical integrator based on a fiber Bragg grating:proposal and design

We demonstrate a simple technique for the implementation of an all-optical integrator based on a uniform-period fiber Bragg grating (FBG) in reflection that is designed to present a decreasing exponential impulse response. The proposed FBG integrator is readily feasible and can perform close to ideal integration of few-picosecond and subpicosecond pulses.

CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Exponential Rates of Convergence in the Ergodic Theorem: A Constructive Approach

We prove that, once an algorithm of perfect simulation for a stationary and ergodic random field F taking values in S(Zd), S a bounded subset of R(n), is provided, the speed of convergence in the mean ergodic theorem occurs exponentially fast for F. Applications from (non-equilibrium) statistical mechanics and interacting particle systems are presented.

Conception of a flexible integrator and lean model for integrated management systems

Management systems standards (MSSs) have developed in an unprecedented manner in the last few years. These MSS cover a wide array of different disciplines, aims and activities of organisations. Also, organisations are populated with an enormous diversity of independent management systems (MSs). An integrated management system (IMS) tends to integrate some or all components of the business. Maximising their integration in one coherent and efficient MS is increasingly a strategic priority and constitutes an opportunity for businesses to be more competitive and consequently, promote its sustainable success. Those organisations that are quicker and more efficient in their integration and continuous improvement will have a competitive advantage in obtaining sustainable value in our global and competitive business world. Several scholars have proposed various theoretical approaches regarding the integration of management sub-systems, leading to the conclusion that there is no common practice for all organisations as they encompass different characteristics. One other author shows that several tangible and intangible gains for organisations, as well as to their internal and external stakeholders, are achieved with the integration of the individual standardised MSs. The purpose of this work was to conceive a model, Flexible, Integrator and Lean for IMSs, according to ISO 9001 for quality; ISO 14001 for environment and OHSAS 18001 for occupational health and safety (IMS–QES), that can be adapted and progressively assimilate other MSs, such as, SA 8000/ISO 26000 for social accountability, ISO 31000 for risk management and ISO/IEC 27001 for information security management, among others. The IMS–QES model was designed in the real environment of an industrial Portuguese small and medium enterprise, that over the years has been adopting, gradually, in whole or in part, individual MSSs. The developed model is based on a preliminary investigation conducted through a questionnaire. The strategy and research methods have taken into consideration the case study. Among the main findings of the survey we highlight: the creation of added value for the business through the elimination of several organisational wastes; the integrated management of the sustainability components; the elimination of conflicts between independent MS; dialogue with the main stakeholders and commitment to their ongoing satisfaction and increased contribution to the company’s competitiveness; and greater valorisation and motivation of employees as a result of the expansion of their skill base, actions and responsibilities, with their consequent empowerment. A set of key performance indicators (KPIs) constitute the support, in a perspective of business excellence, to the follow up of the organisation’s progress towards the vision and achievement of the defined objectives in the context of each component of the IMS model. The conceived model had many phases and the one presented in this work is the last required for the integration of quality, environment, safety and others individual standardised MSs. Globally, the investigation results, by themselves, justified and prioritised the conception of an IMS–QES model, to be implemented at the company where the investigation was conducted, but also a generic model of an IMS, which may be more flexible, integrator and lean as possible, potentiating the efficiency, added value both in the present and, fundamentally, for future.

Error bounds for low-rank approximations of the first exponential integral kernel

A hierarchical matrix is an efficient data-sparse representation of a matrix, especially useful for large dimensional problems. It consists of low-rank subblocks leading to low memory requirements as well as inexpensive computational costs. In this work, we discuss the use of the hierarchical matrix technique in the numerical solution of a large scale eigenvalue problem arising from a finite rank discretization of an integral operator. The operator is of convolution type, it is defined through the first exponential-integral function and, hence, it is weakly singular. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Some computational results illustrating the efficiency and robustness of the approach are presented.

Financing exponential growth at H3

H3 is a fast-food chain that introduced the concept of gourmet hamburgers in the Portuguese market. This case-study illustrates its financing strategy that supported an exponential growth represented by opening 33 restaurants within approximately 3 years of its inception. H3 is now faced with the challenge of structuring its foreign ventures and change its financial approach. The main covered topics are the options an entrepreneur has for financing a new venture and how it evolves along the life cycle and different business approaches, namely franchising. It aims to be used as a learning tool in courses such as entrepreneurial finance.

Double-Exponential Model of a Photovoltaic Cell with Temperature Dependence

The purpose of the research is the creation of mathematical models in MATLAB based on the double exponential model of the photovoltaic cell. The developed model allows for different physical and environmental parameters. An equivalent circuit of the model includes a photocurrent source, two diodes, and a series and parallel resistance. The paper presents the simulation results for each parameter. The simulation data are displayed graphically and numerical results are saved in a file.

Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities

This paper shows that certain quotients of entire functions are characteristic functions. Under some conditions, we provide expressions for the densities of such characteristic functions which turn out to be generalized Dirichlet series which in turn can be expressed as an infinite linear combination of exponential or Laplace densities. We apply these results to several examples.

Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Repression of flagellar genes in exponential phase by CsgD and CpxR, two crucial modulators of Escherichia coli biofilm formation.

Escherichia coli adapts its lifestyle to the variations of environmental growth conditions, swapping between swimming motility or biofilm formation. The stationary-phase sigma factor RpoS is an important regulator of this switch, since it stimulates adhesion and represses flagellar biosynthesis. By measuring the dynamics of gene expression, we show that RpoS inhibits the transcription of the flagellar sigma factor, FliA, in exponential growth phase. RpoS also partially controls the expression of CsgD and CpxR, two transcription factors important for bacterial adhesion. We demonstrate that these two regulators repress the transcription of fliA, flgM, and tar and that this regulation is dependent on the growth medium. CsgD binds to the flgM and fliA promoters around their -10 promoter element, strongly suggesting direct repression. We show that CsgD and CpxR also affect the expression of other known modulators of cell motility. We propose an updated structure of the regulatory network controlling the choice between adhesion and motility.

On the connectivity of the escaping set for complex exponential Misiurewicz parameters

Let $ E_{\lambda}(z)=\lambda {\rm exp}(z), \lambda\in \mathbb{C}$, be the complex exponential family. For all functions in the family there is a unique asymptotic value at 0 (and no critical values). For a fixed $ \lambda$, the set of points in $ \mathbb{C}$ with orbit tending to infinity is called the escaping set. We prove that the escaping set of $ E_{\lambda}$ with $ \lambda$ Misiurewicz (that is, a parameter for which the orbit of the singular value is strictly preperiodic) is a connected set.

Intravoxel incoherent motion diffusion-weighted imaging in the liver: comparison of mono-, bi- and tri-exponential modelling at 3.0-T.

PURPOSE: To determine whether a mono-, bi- or tri-exponential model best fits the intravoxel incoherent motion (IVIM) diffusion-weighted imaging (DWI) signal of normal livers. MATERIALS AND METHODS: The pilot and validation studies were conducted in 38 and 36 patients with normal livers, respectively. The DWI sequence was performed using single-shot echoplanar imaging with 11 (pilot study) and 16 (validation study) b values. In each study, data from all patients were used to model the IVIM signal of normal liver. Diffusion coefficients (Di ± standard deviations) and their fractions (fi ± standard deviations) were determined from each model. The models were compared using the extra sum-of-squares test and information criteria. RESULTS: The tri-exponential model provided a better fit than both the bi- and mono-exponential models. The tri-exponential IVIM model determined three diffusion compartments: a slow (D1 = 1.35 ± 0.03 × 10(-3) mm(2)/s; f1 = 72.7 ± 0.9 %), a fast (D2 = 26.50 ± 2.49 × 10(-3) mm(2)/s; f2 = 13.7 ± 0.6 %) and a very fast (D3 = 404.00 ± 43.7 × 10(-3) mm(2)/s; f3 = 13.5 ± 0.8 %) diffusion compartment [results from the validation study]. The very fast compartment contributed to the IVIM signal only for b values ≤15 s/mm(2) CONCLUSION: The tri-exponential model provided the best fit for IVIM signal decay in the liver over the 0-800 s/mm(2) range. In IVIM analysis of normal liver, a third very fast (pseudo)diffusion component might be relevant. KEY POINTS: ? For normal liver, tri-exponential IVIM model might be superior to bi-exponential ? A very fast compartment (D = 404.00 ± 43.7 × 10 (-3)  mm (2) /s; f = 13.5 ± 0.8 %) is determined from the tri-exponential model ? The compartment contributes to the IVIM signal only for b ≤ 15 s/mm (2.)