We experimentally demonstrate a wavelength-spacing tunable multiwavelength erbium-doped fiber las... more We experimentally demonstrate a wavelength-spacing tunable multiwavelength erbium-doped fiber laser based on degenerate four-wave mixing in a dispersion-shifted fiber incorporating multiple-fiber Bragg gratings. We have achieved stable operation of the multiwavelength erbium-doped fiber laser, which has 0.8 nm spacing ten-channel lasing wavelengths and a high extinction ratio of more than approximately 45 dB, at room temperature. The output power of the multiwavelength erbium-doped fiber laser is stable, so the peak fluctuation is less than approximately 0.2 dB. By changing the properties such as loss and polarization state of multiple fiber Bragg grating cavities, we can exercise flexible control of the wavelength spacing of the multiwavelength output. We can also obtain switchable multiwavelength lasing operation by elimination of the effects of alternate single-fiber Bragg gratings.
... Let m I 1 be chosen arbitrary. Then j= (ovg(t)dB(t))ej 2z E ,=E, 2 nI = EZ gi(Bh(ti+&#x27... more ... Let m I 1 be chosen arbitrary. Then j= (ovg(t)dB(t))ej 2z E ,=E, 2 nI = EZ gi(Bh(ti+' ) Bh(ti)) i=0 m n1 nI K2Z ZZ g(()(ti+l)Bh(ti))(B)(tl+l) B)('I))) j=li=0 =lm nI )2 =K2ZE(i=o(Bh(ti+l)B(ti)) j=lmj=lo = K2 T2h #jj=l for all m. Consequently, r dBh(t) ez for (t)ej2z Ef O(t) = E 9(t)dB K2T2h . ...
As e-commerce becomes common a large number of Internet-based systems has been developed to assis... more As e-commerce becomes common a large number of Internet-based systems has been developed to assist users in different aspects of electronic trading. In particular systems that use software agent
Instability and fragmentation of a core melt jet in water have been actively studied during the p... more Instability and fragmentation of a core melt jet in water have been actively studied during the past 10 years. Several models, and a few computer codes, have been developed. However, there are, still, large uncertainties, both, in interpreting experimental results and in predicting reactor-scale processes. Steam explosion and debris coolability, as reactor safety issues, are related to the jet fragmentation process. A better understanding of the physics of jet instability and fragmentation is crucial for assessments of fuel-coolant interactions (FCIs). This paper presents research, conducted at the Division of Nuclear Power Safety, Royal Institute of Technology (RIT/NPS), Stockholm, concerning molten jet-coolant interactions, as a precursor for premixing. First, observations were obtained from scoping experiments with simulant fluids. Second, the linear perturbation method was extended and applied to analyze the interfacial-instability characteristics. Third, two innovative approaches to computational fluid dynamics (CFD) modeling of jet fragmentation were developed and employed for analysis. The focus of the studies was placed on (a) identifying potential factors, which may affect the jet instability, (b) determining the scaling laws, and (c) predicting the jet behavior for severe accident conditions. In particular, the effects of melt physical properties, and the thermal hydraulics of the mixing zone, on jet fragmentation were investigated. Finally, with the insights gained from a synthesis of the experimental results and analysis results, a new phenomenological concept, named 'macrointeractions concept of jet fragmentation' is proposed.
Study objective: To test the ability of a locally designed priority dispatch system to safely exc... more Study objective: To test the ability of a locally designed priority dispatch system to safely exclude the need for advanced life support (ALS).
Background: Thymic stromal lymphopoietin (TSLP) endows human CD11c 1 dendritic cells (DCs) from p... more Background: Thymic stromal lymphopoietin (TSLP) endows human CD11c 1 dendritic cells (DCs) from peripheral blood with the capacity to induce proallergic T cells. TSLP is present at high levels in the epidermis of atopic dermatitis where it appears to trigger emigration of epidermal Langerhans cells (LCs); however, nothing else is known about the influence of TSLP on LCs. Objective: Effects of TSLP on human epidermal LCs were investigated. Methods: LCs were isolated by trypsinization from healthy human skin, highly enriched by immunomagnetic techniques (via CD1a) and cultured for 2 days. Additionally, migratory LCs were obtained by emigration from epidermal sheets for 3 days.
Eurasip Journal on Wireless Communications and Networking, 2007
We present the results of multiple-input multiple-output orthogonal frequency-division multiplexi... more We present the results of multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) channel measurements. The measurements were performed in indoor environments using four transmitters and four receivers with 40 MHz bandwidth at 5.25 GHz. Our measurements reveal two-dimensional small-scale fading, and correlation between MIMO subchannels. In the line-of-sight (LoS) case, the MIMO-OFDM channel capacity is found to be strongly dependent on the local scattering environment; and much less dependent in the non-LoS (NLoS) case. Also, MIMO channel capacity is found to be largely uncorrelated over 20 MHz in NLoS, while a strong correlation is found over 40 MHz in some LoS environments. The validity of the conventional Kronecker correlation channel model is tested, along with a recently proposed joint correlation model. The effects of varying antenna element spacing are also investigated, taking into account such effects as mutual coupling, radiation efficiency, and radiation pattern.
Interleukin-10 (IL-10) has been used in the treatment of viral hepatitis in interferon-alpha (IFN... more Interleukin-10 (IL-10) has been used in the treatment of viral hepatitis in interferon-alpha (IFN-alpha) non-responders while patients who have high levels of IL-10 are poorly responsive to IFN-alpha. The mechanism underlying such controversial functions of IL-10 remains unknown. Here we demonstrated that injection of IL-10 into mice attenuated IFN-alpha-induced signal transducer and activator transcription factor (STAT)1 tyrosine phosphorylation in the liver. Reverse transcriptase-polymerase chain reaction assay demonstrated that mouse liver expressed high levels of IL-10 receptor 2 (IL-10R2) but low levels of IL-10R1. Injection of IL-10 into mice activated STAT3 but not STAT1 tyrosine phosphorylation and induced suppressor of cytokine signal 2 (SOCS2), SOCS3, and cytokine-inducible SH2 protein (CIS) mRNA expression in the liver. Furthermore, overexpression of SOCS2 or SOCS3 inhibited IFN-alpha-induced reporter activity in hepatic cells. These findings suggest that IL-10 inhibits IFN-alpha-activated STAT1 in the liver, at least in part, by inducing SOCS2, SOCS3, and CIS expression, which may be responsible for the resistance of IFN-alpha therapy in patients who have high levels of IL-10 and recommends that IL-10 treatment for viral hepatitis should be cautious.
Biochemical and Biophysical Research Communications, 2000
Liver regeneration is controlled by multiple signaling pathways induced by a variety of growth fa... more Liver regeneration is controlled by multiple signaling pathways induced by a variety of growth factors, hormones, and cytokines. Here we report that protein kinase B (PKB)/Akt, part of a key cell survival signaling pathway, is markedly activated after partial hepatectomy (PHX). The antiapoptotic protein Bad, a downstream target of PKB/Akt, is also phosphorylated. This cascade can be activated by various factors in primary hepatocytes, with the strongest activation by insulin and the ␣ 1 -adrenergic agonist phenylephrine (PE), followed by IL-6, epidermal growth factor (EGF), and hepatocyte growth factor (HGF). Pretreatment of cells with the specific PI3 kinase inhibitor LY294002 abolished insulin-or PE-activation of PKB/ Akt, suggesting that activation of PKB/Akt is mediated by a PI3 kinase-dependent mechanism. In vivo administration of PE, insulin, IL-6, HGF, or EGF to mice markedly stimulated PKB/Akt in the liver, with the strongest stimulation induced by insulin and PE. Moreover, HGF and insulin were able to attenuate transforming growth factor -induced apoptosis in hepatic cells, and these effects were antagonized by LY294002. Taken together, these findings suggest that rapid activation of PKB/Akt is a key antiapoptotic signaling pathway involved in liver regeneration.
Journal of Statistical Planning and Inference, 1999
Many existing stochastic models have been developed for description and analysis of Markov di usi... more Many existing stochastic models have been developed for description and analysis of Markov di usion. This paper outlines the new concept of -duality which lays the foundation for an extension of Markov di usion to fractional di usion. The theory of Riesz and Bessel potentials and the corresponding potential spaces play a key role in this new approach. We establish the existence of an important subclass of fractional random ÿelds, namely that of fractional Riesz-Bessel motions, which extends the class of fractional Brownian motions. As a result, the scope of Markov di usion is widened to cover random ÿelds with long-range dependence.
Negotiation typically involves a number of parties with different criteria, constraints and prefe... more Negotiation typically involves a number of parties with different criteria, constraints and preferences that determine the individual areas of interest, i.e. the range and order of the preferred solutions of each party. The parties usually have a limited common knowledge of each other’s areas of interest. Therefore a range of possible agreements, i.e. the common area of interest is typically not known to the parties a priori. In order to find a mutual agreement the parties explore possible agreements by the process of exchanging information in the form of offers. During the negotiation process the range of possible offers of each party changes according to the current information available. As negotiation progresses and more information become available the ranges reduce until an agreement can be found or the parties withdraw from negotiation. This interpretation allows one to consider the negotiation problem as a constraint satisfaction problem and the negotiation process as constraint-based reasoning. This paper presents some aspects of that interpretation. In particular it outlines the constraint-based representation and constraint propagation mechanisms used in an experimental system of e-Negotiation Agents (eNAs). The eNAs can autonomously negotiate the multi-issue terms of transactions in an e-commerce environment tested with the used car trading problem.
Journal of Applied Mathematics and Computing, 2003
A time fractional advection-dispersion equation is obtained from the standard advection-dispersio... more A time fractional advection-dispersion equation is obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0
The time fractional diffusion equation (tfde) is obtained from the standard diffusion equation by... more The time fractional diffusion equation (tfde) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order in (0,1). In this work, an explicit finite-difference scheme for tfde is presented. Discrete models of a non-...
In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is consi... more In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.
In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion... more In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grü nwald-Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.
In this paper, we consider a space-time fractional advection dispersion equation (STFADE) on a fi... more In this paper, we consider a space-time fractional advection dispersion equation (STFADE) on a finite domain. The STFADE is obtained from the standard advection dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order a 2 (0, 1], and the first-order and second-order space derivatives by the Riemman-Liouville fractional derivatives of order b 2 (0, 1] and of order c 2 (1, 2], respectively. For the space fractional derivatives D b
Journal of Computational and Applied Mathematics, 2004
The traditional second-order Fokker-Planck equation may not adequately describe the movement of s... more The traditional second-order Fokker-Planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of Brownian motion. Densities of α-stable type have been used to describe the probability distribution of these motions. The resulting governing equation of these motions is similar to the traditional Fokker-Planck equation except that the order α of the highest derivative is fractional.
This is the first of two papers in which we consider a stock with price process defined by a stoc... more This is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y (·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y (·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show that the process Y (·) has a good MA(∞)-type representation. The existence of such simultaneous good AR(∞) and MA(∞) representations enables us to apply a new method for the calculation of relevant conditional expectations, whence to obtain various explicit results for problems such as portfolio optimization. The financial market defined by the above stock price process is complete, and if the coefficients are constant, then the prices of European calls and puts are given by the Black-Scholes formulas as in the Black-Scholes model. Unlike the latter, however, the model allows for differences between the historical and implied volatilities. The model includes a special case in which only two additional parameters are introduced to describe the memory of the market, compared with the Black-Scholes model. Analysis based on real market data shows that this simple model with two additional parameters is more realistic in capturing the memory effect of the market, while retaining the simplicity and usefulness of the Black-Scholes model.
This paper introduces the notion of measure representation of DNA sequences. Spectral analysis an... more This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the D q spectra and related C q curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations, considered as time series, exhibit strong long-range correlation. Here the long-range correlation is for the K-strings with dictionary ordering, and it is different from the base pair correlations introduced by other people. For substrings with length Kϭ8, the D q spectra of all organisms studied are multifractal-like and sufficiently smooth for the C q curves to be meaningful. With the decreasing value of K, the multifractality lessens. The C q curves of all bacteria resemble a classical phase transition at a critical point. But the ''analogous'' phase transitions of chromosomes of nonbacteria organisms are different. Apart from chromosome 1 of C. elegans, they exhibit the shape of double-peaked specific heat function. A classification of genomes of bacteria by assigning to each sequence a point in two-dimensional space (D Ϫ1 ,D 1 ) and in three-dimensional space (D Ϫ1 ,D 1 ,D Ϫ2 ) was given. Bacteria that are close phylogenetically are almost close in the spaces (D Ϫ1 ,D 1 ) and (D Ϫ1 ,D 1 ,D Ϫ2 ).
We experimentally demonstrate a wavelength-spacing tunable multiwavelength erbium-doped fiber las... more We experimentally demonstrate a wavelength-spacing tunable multiwavelength erbium-doped fiber laser based on degenerate four-wave mixing in a dispersion-shifted fiber incorporating multiple-fiber Bragg gratings. We have achieved stable operation of the multiwavelength erbium-doped fiber laser, which has 0.8 nm spacing ten-channel lasing wavelengths and a high extinction ratio of more than approximately 45 dB, at room temperature. The output power of the multiwavelength erbium-doped fiber laser is stable, so the peak fluctuation is less than approximately 0.2 dB. By changing the properties such as loss and polarization state of multiple fiber Bragg grating cavities, we can exercise flexible control of the wavelength spacing of the multiwavelength output. We can also obtain switchable multiwavelength lasing operation by elimination of the effects of alternate single-fiber Bragg gratings.
... Let m I 1 be chosen arbitrary. Then j= (ovg(t)dB(t))ej 2z E ,=E, 2 nI = EZ gi(Bh(ti+&#x27... more ... Let m I 1 be chosen arbitrary. Then j= (ovg(t)dB(t))ej 2z E ,=E, 2 nI = EZ gi(Bh(ti+' ) Bh(ti)) i=0 m n1 nI K2Z ZZ g(()(ti+l)Bh(ti))(B)(tl+l) B)('I))) j=li=0 =lm nI )2 =K2ZE(i=o(Bh(ti+l)B(ti)) j=lmj=lo = K2 T2h #jj=l for all m. Consequently, r dBh(t) ez for (t)ej2z Ef O(t) = E 9(t)dB K2T2h . ...
As e-commerce becomes common a large number of Internet-based systems has been developed to assis... more As e-commerce becomes common a large number of Internet-based systems has been developed to assist users in different aspects of electronic trading. In particular systems that use software agent
Instability and fragmentation of a core melt jet in water have been actively studied during the p... more Instability and fragmentation of a core melt jet in water have been actively studied during the past 10 years. Several models, and a few computer codes, have been developed. However, there are, still, large uncertainties, both, in interpreting experimental results and in predicting reactor-scale processes. Steam explosion and debris coolability, as reactor safety issues, are related to the jet fragmentation process. A better understanding of the physics of jet instability and fragmentation is crucial for assessments of fuel-coolant interactions (FCIs). This paper presents research, conducted at the Division of Nuclear Power Safety, Royal Institute of Technology (RIT/NPS), Stockholm, concerning molten jet-coolant interactions, as a precursor for premixing. First, observations were obtained from scoping experiments with simulant fluids. Second, the linear perturbation method was extended and applied to analyze the interfacial-instability characteristics. Third, two innovative approaches to computational fluid dynamics (CFD) modeling of jet fragmentation were developed and employed for analysis. The focus of the studies was placed on (a) identifying potential factors, which may affect the jet instability, (b) determining the scaling laws, and (c) predicting the jet behavior for severe accident conditions. In particular, the effects of melt physical properties, and the thermal hydraulics of the mixing zone, on jet fragmentation were investigated. Finally, with the insights gained from a synthesis of the experimental results and analysis results, a new phenomenological concept, named 'macrointeractions concept of jet fragmentation' is proposed.
Study objective: To test the ability of a locally designed priority dispatch system to safely exc... more Study objective: To test the ability of a locally designed priority dispatch system to safely exclude the need for advanced life support (ALS).
Background: Thymic stromal lymphopoietin (TSLP) endows human CD11c 1 dendritic cells (DCs) from p... more Background: Thymic stromal lymphopoietin (TSLP) endows human CD11c 1 dendritic cells (DCs) from peripheral blood with the capacity to induce proallergic T cells. TSLP is present at high levels in the epidermis of atopic dermatitis where it appears to trigger emigration of epidermal Langerhans cells (LCs); however, nothing else is known about the influence of TSLP on LCs. Objective: Effects of TSLP on human epidermal LCs were investigated. Methods: LCs were isolated by trypsinization from healthy human skin, highly enriched by immunomagnetic techniques (via CD1a) and cultured for 2 days. Additionally, migratory LCs were obtained by emigration from epidermal sheets for 3 days.
Eurasip Journal on Wireless Communications and Networking, 2007
We present the results of multiple-input multiple-output orthogonal frequency-division multiplexi... more We present the results of multiple-input multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) channel measurements. The measurements were performed in indoor environments using four transmitters and four receivers with 40 MHz bandwidth at 5.25 GHz. Our measurements reveal two-dimensional small-scale fading, and correlation between MIMO subchannels. In the line-of-sight (LoS) case, the MIMO-OFDM channel capacity is found to be strongly dependent on the local scattering environment; and much less dependent in the non-LoS (NLoS) case. Also, MIMO channel capacity is found to be largely uncorrelated over 20 MHz in NLoS, while a strong correlation is found over 40 MHz in some LoS environments. The validity of the conventional Kronecker correlation channel model is tested, along with a recently proposed joint correlation model. The effects of varying antenna element spacing are also investigated, taking into account such effects as mutual coupling, radiation efficiency, and radiation pattern.
Interleukin-10 (IL-10) has been used in the treatment of viral hepatitis in interferon-alpha (IFN... more Interleukin-10 (IL-10) has been used in the treatment of viral hepatitis in interferon-alpha (IFN-alpha) non-responders while patients who have high levels of IL-10 are poorly responsive to IFN-alpha. The mechanism underlying such controversial functions of IL-10 remains unknown. Here we demonstrated that injection of IL-10 into mice attenuated IFN-alpha-induced signal transducer and activator transcription factor (STAT)1 tyrosine phosphorylation in the liver. Reverse transcriptase-polymerase chain reaction assay demonstrated that mouse liver expressed high levels of IL-10 receptor 2 (IL-10R2) but low levels of IL-10R1. Injection of IL-10 into mice activated STAT3 but not STAT1 tyrosine phosphorylation and induced suppressor of cytokine signal 2 (SOCS2), SOCS3, and cytokine-inducible SH2 protein (CIS) mRNA expression in the liver. Furthermore, overexpression of SOCS2 or SOCS3 inhibited IFN-alpha-induced reporter activity in hepatic cells. These findings suggest that IL-10 inhibits IFN-alpha-activated STAT1 in the liver, at least in part, by inducing SOCS2, SOCS3, and CIS expression, which may be responsible for the resistance of IFN-alpha therapy in patients who have high levels of IL-10 and recommends that IL-10 treatment for viral hepatitis should be cautious.
Biochemical and Biophysical Research Communications, 2000
Liver regeneration is controlled by multiple signaling pathways induced by a variety of growth fa... more Liver regeneration is controlled by multiple signaling pathways induced by a variety of growth factors, hormones, and cytokines. Here we report that protein kinase B (PKB)/Akt, part of a key cell survival signaling pathway, is markedly activated after partial hepatectomy (PHX). The antiapoptotic protein Bad, a downstream target of PKB/Akt, is also phosphorylated. This cascade can be activated by various factors in primary hepatocytes, with the strongest activation by insulin and the ␣ 1 -adrenergic agonist phenylephrine (PE), followed by IL-6, epidermal growth factor (EGF), and hepatocyte growth factor (HGF). Pretreatment of cells with the specific PI3 kinase inhibitor LY294002 abolished insulin-or PE-activation of PKB/ Akt, suggesting that activation of PKB/Akt is mediated by a PI3 kinase-dependent mechanism. In vivo administration of PE, insulin, IL-6, HGF, or EGF to mice markedly stimulated PKB/Akt in the liver, with the strongest stimulation induced by insulin and PE. Moreover, HGF and insulin were able to attenuate transforming growth factor -induced apoptosis in hepatic cells, and these effects were antagonized by LY294002. Taken together, these findings suggest that rapid activation of PKB/Akt is a key antiapoptotic signaling pathway involved in liver regeneration.
Journal of Statistical Planning and Inference, 1999
Many existing stochastic models have been developed for description and analysis of Markov di usi... more Many existing stochastic models have been developed for description and analysis of Markov di usion. This paper outlines the new concept of -duality which lays the foundation for an extension of Markov di usion to fractional di usion. The theory of Riesz and Bessel potentials and the corresponding potential spaces play a key role in this new approach. We establish the existence of an important subclass of fractional random ÿelds, namely that of fractional Riesz-Bessel motions, which extends the class of fractional Brownian motions. As a result, the scope of Markov di usion is widened to cover random ÿelds with long-range dependence.
Negotiation typically involves a number of parties with different criteria, constraints and prefe... more Negotiation typically involves a number of parties with different criteria, constraints and preferences that determine the individual areas of interest, i.e. the range and order of the preferred solutions of each party. The parties usually have a limited common knowledge of each other’s areas of interest. Therefore a range of possible agreements, i.e. the common area of interest is typically not known to the parties a priori. In order to find a mutual agreement the parties explore possible agreements by the process of exchanging information in the form of offers. During the negotiation process the range of possible offers of each party changes according to the current information available. As negotiation progresses and more information become available the ranges reduce until an agreement can be found or the parties withdraw from negotiation. This interpretation allows one to consider the negotiation problem as a constraint satisfaction problem and the negotiation process as constraint-based reasoning. This paper presents some aspects of that interpretation. In particular it outlines the constraint-based representation and constraint propagation mechanisms used in an experimental system of e-Negotiation Agents (eNAs). The eNAs can autonomously negotiate the multi-issue terms of transactions in an e-commerce environment tested with the used car trading problem.
Journal of Applied Mathematics and Computing, 2003
A time fractional advection-dispersion equation is obtained from the standard advection-dispersio... more A time fractional advection-dispersion equation is obtained from the standard advection-dispersion equation by replacing the firstorder derivative in time by a fractional derivative in time of order α(0
The time fractional diffusion equation (tfde) is obtained from the standard diffusion equation by... more The time fractional diffusion equation (tfde) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order in (0,1). In this work, an explicit finite-difference scheme for tfde is presented. Discrete models of a non-...
In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is consi... more In this paper, a fractional partial differential equation (FPDE) describing subdiffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.
In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion... more In this paper we present a random walk model for approximating a Lévy-Feller advection-dispersion process, governed by the Lévy-Feller advection-dispersion differential equation (LFADE). We show that the random walk model converges to LFADE by use of a properly scaled transition to vanishing space and time steps. We propose an explicit finite difference approximation (EFDA) for LFADE, resulting from the Grü nwald-Letnikov discretization of fractional derivatives. As a result of the interpretation of the random walk model, the stability and convergence of EFDA for LFADE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.
In this paper, we consider a space-time fractional advection dispersion equation (STFADE) on a fi... more In this paper, we consider a space-time fractional advection dispersion equation (STFADE) on a finite domain. The STFADE is obtained from the standard advection dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order a 2 (0, 1], and the first-order and second-order space derivatives by the Riemman-Liouville fractional derivatives of order b 2 (0, 1] and of order c 2 (1, 2], respectively. For the space fractional derivatives D b
Journal of Computational and Applied Mathematics, 2004
The traditional second-order Fokker-Planck equation may not adequately describe the movement of s... more The traditional second-order Fokker-Planck equation may not adequately describe the movement of solute in an aquifer because of large deviation from the dynamics of Brownian motion. Densities of α-stable type have been used to describe the probability distribution of these motions. The resulting governing equation of these motions is similar to the traditional Fokker-Planck equation except that the order α of the highest derivative is fractional.
This is the first of two papers in which we consider a stock with price process defined by a stoc... more This is the first of two papers in which we consider a stock with price process defined by a stochastic differential equation driven by a process Y (·) different from Brownian motion. The adoption of such a colored noise input is motivated by an analysis of real market data. The process Y (·) is defined by a continuous-time AR(∞)-type equation and may have either short or long memory. We show that the process Y (·) has a good MA(∞)-type representation. The existence of such simultaneous good AR(∞) and MA(∞) representations enables us to apply a new method for the calculation of relevant conditional expectations, whence to obtain various explicit results for problems such as portfolio optimization. The financial market defined by the above stock price process is complete, and if the coefficients are constant, then the prices of European calls and puts are given by the Black-Scholes formulas as in the Black-Scholes model. Unlike the latter, however, the model allows for differences between the historical and implied volatilities. The model includes a special case in which only two additional parameters are introduced to describe the memory of the market, compared with the Black-Scholes model. Analysis based on real market data shows that this simple model with two additional parameters is more realistic in capturing the memory effect of the market, while retaining the simplicity and usefulness of the Black-Scholes model.
This paper introduces the notion of measure representation of DNA sequences. Spectral analysis an... more This paper introduces the notion of measure representation of DNA sequences. Spectral analysis and multifractal analysis are then performed on the measure representations of a large number of complete genomes. The main aim of this paper is to discuss the multifractal property of the measure representation and the classification of bacteria. From the measure representations and the values of the D q spectra and related C q curves, it is concluded that these complete genomes are not random sequences. In fact, spectral analyses performed indicate that these measure representations, considered as time series, exhibit strong long-range correlation. Here the long-range correlation is for the K-strings with dictionary ordering, and it is different from the base pair correlations introduced by other people. For substrings with length Kϭ8, the D q spectra of all organisms studied are multifractal-like and sufficiently smooth for the C q curves to be meaningful. With the decreasing value of K, the multifractality lessens. The C q curves of all bacteria resemble a classical phase transition at a critical point. But the ''analogous'' phase transitions of chromosomes of nonbacteria organisms are different. Apart from chromosome 1 of C. elegans, they exhibit the shape of double-peaked specific heat function. A classification of genomes of bacteria by assigning to each sequence a point in two-dimensional space (D Ϫ1 ,D 1 ) and in three-dimensional space (D Ϫ1 ,D 1 ,D Ϫ2 ) was given. Bacteria that are close phylogenetically are almost close in the spaces (D Ϫ1 ,D 1 ) and (D Ϫ1 ,D 1 ,D Ϫ2 ).
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