On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation

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On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.

Effect of fractional urea clearance on survival of hemodialysis patients in relation to gender

Many studies have demonstrated the relationship between dialysis dose and survival. Global mortality is similar among men and women; however, the influence of dialysis dose in the survival could be more intensive between women. Therefore, we conduct an observational study to evaluate the gender-related impact of single pool Kt/V (spKt/V) on the survival of patients submitted to hemodialysis in a university hospital. We found that survival was lower in groups with spKt/V smaller than 1.2 than in those with Kt/V between 1.2 and 1.4. Among female patients, spKt/V smaller than 1.2 had a more adverse effect in survival than among men with a comparable Kt/V. Otherwise, among women, the dialysis dose had an impact in survival even with Kt/V greater than 1.4. Thus, fractional urea clearance more heavily influenced the survival of females than males in hemodialysis patients.

On the entropy operator for the general SU(1,1) TFD formulation

In this Letter, an entropy operator for the general unitary SU(1, 1) TFD formulation is proposed and used to lead a bosonic system from zero to finite temperature. Namely, considering the closed bosonic string as the target system, the entropy operator is used to construct the thermal vacuum. The behaviour of such a state under the breve conjugation rules is analyzed and it was shown that the breve conjugation does not affect the thermal effects. From this thermal vacuum the thermal energy, the entropy and the free energy of the closed bosonic string are calculated and the appropriated thermal distribution for the system is found after the free energy minimization. (C) 2004 Elsevier B.V. All rights reserved.

Massive superstring vertex operator in D=10 superspace

Using the pure spinor formalism for the superstring, the vertex operator for the first massive states of the open superstring is constructed in a manifestly super-Poincare covariant manner. This vertex operator describes a massive spin-two multiplet in terms of ten-dimensional superfields.

Entanglement and entropy operator for strings in pp-wave time dependent background

In this Letter new aspects of string theory propagating in a pp-wave time dependent background with a null singularity are explored. It is shown the appearance of a 2d entanglement entropy dynamically generated by the background. For asymptotically flat observers, the vacuum close to the singularity is unitarily inequivalent to the vacuum at tau = -infinity and it is shown that the 2d entanglement entropy diverges close to this point. As a consequence. The positive time region is inaccessible for observers in tau = -infinity. For a stationary measure, the vacuum at finite time is seen by those observers as a thermal state and the information loss is encoded as a heat bath of string states. (c) 2006 Elsevier B.V. All rights reserved.

Tunneling time through a barrier using the local value of a time operator

A time for a quantum particle to traverse a barrier is obtained for stationary states by setting the local value of a time operator equal to a constant. This time operator, called the tempus operator because it is distinct from the time of evolution, is defined as the operator canonically conjugate to the energy operator. The local value of the tempus operator gives a complex time for a particle to traverse a barrier. The method is applied to a particle with a semiclassical wave function, which gives, in the classical limit, the correct classical traversal time. It is also applied to a quantum particle tunneling through a rectangular barrier. The resulting complex tunneling time is compared with complex tunneling times from other methods.

On the N=2 superstring BRST operator

We show that the BRST charge for the N = 2 superstring system can be written as Q = e(-R)(phi dz/2 pi ib gamma(+)gamma(-))e(R), when b and gamma(+/-) are super-reparametrizations ghosts. This provides a trivial proof of the nilpotence of this operator. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Operator ordering in quantum radiative processes

In this work we reexamine quantum electrodynamics of atomic electrons in the Coulomb gauge in the dipole approximation and calculate the shift of atomic energy levels in the context of Dalibard, Dupont-Roc and Cohen-Tannoudji formalism by considering the variation rates of physical observable. We then analyze the physical interpretation of the ordering of operators in the dipole approximation interaction Hamiltonian in terms of field fluctuations and self-reaction of atomic electrons, discussing the arbitrariness in the statistical functions in second-order bound-state perturbation theory. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Statements on chaos control designs, including a fractional order dynamical system, applied to a MEMS comb-drive actuator

In this work, we deal with a micro electromechanical system (MEMS), represented by a micro-accelerometer. Through numerical simulations, it was found that for certain parameters, the system has a chaotic behavior. The chaotic behaviors in a fractional order are also studied numerically, by historical time and phase portraits, and the results are validated by the existence of positive maximal Lyapunov exponent. Three control strategies are used for controlling the trajectory of the system: State Dependent Riccati Equation (SDRE) Control, Optimal Linear Feedback Control, and Fuzzy Sliding Mode Control. The controls proved effective in controlling the trajectory of the system studied and robust in the presence of parametric errors.

Optimization of an amperometric biosensor for the detection of hepatitis C virus using fractional factorial designs

Fractional factorial design and factorial with center point design were applied to the development of an amperometric biosensor for the detection of the hepatitis C virus. Biomolecules were immobilized by adsorption on graphite electrodes modified with siloxane-poly(propyleneoxide) hybrid matrix prepared using the sol-gel method. Several parameters were optimized, such as the streptavidin concentration at 0.01 mg mL(-1) and 1.0% bovine serum albumin, the incubation time of the electrodes in the complementary DNA solution for 30 minutes and a 1: 1500 dilution of the avidin-peroxidase conjugate, among others. The application of chemometric studies has been efficient, since the best conditions have been established with a restricted number of experiments, indicating the influence of different factors on the system.

Spectrophotometric Determination of Captopril Through Charge Transfer Complex Formation Using Fractional Factorial and Central Composite Design

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PHENOMENOLOGICAL APPLICATION OF THE PROJECTION-OPERATOR METHOD AND ITS CONNECTION WITH CRITICAL-DYNAMICS

We consider the dynamics of a system of interacting spins described by the Ginzburg-Landau Hamiltonian. The method used is Zwanzig's version of the projection-operator method, in contrast to previous derivations in which we used Mori's version of this method. It is proved that both methods produce the same answer for the Green's function. We also make contact between the projection-operator method and critical dynamics.

PATH INTEGRAL AND OPERATOR APPROACH FOR THE PODOLSKY-SCHWINGER MODEL

We study the role of the thachyonic excitation which emerges from the quantum electrodynamics in two dimensions with Podolsky term. The quantization is performed by using path integral framework and the operator approach.

Operator formulation of q-deformed dual string model

We present an operator formulation of the q-deformed dual string model amplitude using an infinite set of q-harmonic oscillators. The formalism attains the crossing symmetry and factorization and allows to express the general n-point function as a factorized product of vertices and propagators.