Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations

Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12

On a Class of Elliptic Equations for the N-Laplacian in R^n with One-Sided Exponential Growth

2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30

PREFACE

The Conference on Partial Differential Equations and Applications, Sofia, September 14–16, 2011 (In honor of 65-th Anniversary of Professor Petar Popivanov) took place in the premises of the Institute of Mathematics and Informatics (IMI) of the Bulgarian Academy of Sciences (BAS). The conference was organized by the Section “Differential Equations and Mathematical Physics” of IMI with the participation of research groups on PDE from Universit`a di Cagliari and Universit`a di Torino (Italy), with the organizing committee – N. Kutev (IMI–BAS) – chair, G. Boyadzhiev (IMI–BAS) – secretary, T. Gramchev (Univ. Cagliari) and A. Oliaro (Univ. Torino) – members, and thefollowing program/scientific committee: T. Gramchev (chair), N. Kutev (IMI–BAS), L. Rodino (Universit`a di Torino), M. Ruzhansky (Imperial College London), A. Slavova (IMI–BAS), C. Van Der Mee (Universit`a di Cagliari).

Monte Carlo Algorithm for Solving Integral Equations with Polynomial Non-Linearity. Parallel Implementation

An iterative Monte Carlo algorithm for evaluating linear functionals of the solution of integral equations with polynomial non-linearity is proposed and studied. The method uses a simulation of branching stochastic processes. It is proved that the mathematical expectation of the introduced random variable is equal to a linear functional of the solution. The algorithm uses the so-called almost optimal density function. Numerical examples are considered. Parallel implementation of the algorithm is also realized using the package ATHAPASCAN as an environment for parallel realization.The computational results demonstrate high parallel efficiency of the presented algorithm and give a good solution when almost optimal density function is used as a transition density.

Branching Particle Representation of a Class of Semilinear Equations

2000 Mathematics Subject Classification: 60J80, 60J85

Symbolic Solving of Partial Differential Equation Systems and Compatibility Conditions

An algorithm is produced for the symbolic solving of systems of partial differential equations by means of multivariate Laplace–Carson transform. A system of K equations with M as the greatest order of partial derivatives and right-hand parts of a special type is considered. Initial conditions are input. As a result of a Laplace–Carson transform of the system according to initial condition we obtain an algebraic system of equations. A method to obtain compatibility conditions is discussed.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Stochastic calculations for fibre Raman amplifiers with randomly varying birefringence

For the first time for the model of real-world forward-pumped fibre Raman amplifier with the randomly varying birefringence, the stochastic calculations have been done numerically based on the Kloeden-Platen-Schurz algorithm. The results obtained for the averaged gain and gain fluctuations as a function of polarization mode dispersion (PMD) parameter agree quantitatively with the results of previously developed analytical model. Simultaneously, the direct numerical simulations demonstrate an increased stochastisation (maximum in averaged gain variation) within the region of the polarization mode dispersion parameter of 0.1÷0.3 ps/km1/2. The results give an insight into margins of applicability of a generic multi-scale technique widely used to derive coupled Manakov equations and allow generalizing analytic model with accounting for pump depletion, group-delay dispersion and Kerr-nonlinearity that is of great interest for development of the high-transmission-rates optical networks.

Stochastic anti-resonance in a fibre Raman amplifier

Stochastic anti-resonance, that is resonant enhancement of randomness caused by polarization mode beatings, is analyzed both numerically and analytically on an example of fibre Raman amplifier with randomly varying birefringence. As a result of such anti-resonance, the polarization mode dispersion growth causes an escape of the signal state of polarization from a metastable state corresponding to the pulling of the signal to the pump state of polarization.This phenomenon reveals itself in abrupt growth of gain fluctuations as well as in dropping of Hurst parameter and Kramers length characterizing long memory in a system and noise induced escape from the polarization pulling state. The results based on analytical multiscale averaging technique agree perfectly with the numerical data obtained by direct numerical simulations of underlying stochastic differential equations. This challenging outcome would allow replacing the cumbersome numerical simulations for real-world extra-long high-speed communication systems.

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Revisiting the Late Jurassic-Early Cretaceous of the NW South Iberian Basin: new ages and sedimentary environments

The study of the Upper Jurassic-Lower Cretaceous deposits (Higueruelas, Villar del Arzobispo and Aldea de Cortés Formations) of the South Iberian Basin (NW Valencia, Spain) reveals new stratigraphic and sedimentological data, which have significant implications on the stratigraphic framework, depositional environments and age of these units. The Higueruelas Fm was deposited in a mid-inner carbonate platform where oncolitic bars migrated by the action of storms and where oncoid production progressively decreased towards the uppermost part of the unit. The overlying Villar del Arzobispo Fm has been traditionally interpreted as an inner platform-lagoon evolving into a tidal-flat. Here it is interpreted as an inner-carbonate platform affected by storms, where oolitic shoals protected a lagoon, which had siliciclastic inputs from the continent. The Aldea de Cortés Fm has been previously interpreted as a lagoon surrounded by tidal-flats and fluvial-deltaic plains. Here it is reinterpreted as a coastal wetland where siliciclastic muddy deposits interacted with shallow fresh to marine water bodies, aeolian dunes and continental siliciclastic inputs. The contact between the Higueruelas and Villar del Arzobispo Fms, classically defined as gradual, is also interpreted here as rapid. More importantly, the contact between the Villar del Arzobispo and Aldea de Cortés Fms, previously considered as unconformable, is here interpreted as gradual. The presence of Alveosepta in the Villar del Arzobispo Fm suggests that at least part of this unit is Kimmeridgian, unlike the previously assigned Late Tithonian-Middle Berriasian age. Consequently, the underlying Higueruelas Fm, previously considered Tithonian, should not be younger than Kimmeridgian. Accordingly, sedimentation of the Aldea de Cortés Fm, previously considered Valangian-Hauterivian, probably started during the Tithonian and it may be considered part of the regressive trend of the Late Jurassic-Early Cretaceous cycle. This is consistent with the dinosaur faunas, typically Jurassic, described in the Villar del Arzobispo and Aldea de Cortés Fms.

Censura preventiva o repressiva? Note di Pasquale Galluppi sulla legge del 26 luglio 1820 del Regno di Sicilia

Se examina en el presente trabajo la difusión y reacciones provocadas por un escrito aparecido en los convulsos años 1820-1821 para el Reino de las Dos Sicilias, en donde se pone de manifiesto la necesidad de la libertad de prensa (el Opuscolo de P. Galluppi es el hilo conductor del trabajo), texto elaborado a propósito de la ley reguladora de esa libertad indispensable para la construcción del Estado liberal y para el surgimiento de la opinión pública al mismo tiempo que dicho escrito activa la labor de la censura en su doble papel de represión y punición, en unos tiempos en donde el Liberalismo no había acabado de asentarse y el Absolutismo se negaba a desaparecer.

Uguaglianza e differenza di genere nella riforma del diritto di famiglia: una lettura luhmanniana

La igualdad ante la ley es uno de los derechos fundamentales de las Constituciones modernas. Sin embargo, hay algo más. De hecho podría decirse que los modernos sistemas jurídicos se han ido formando alrededor de la idea de igualdad. El valor de la igualdad parece expresar una manera común de entender las relaciones humanas, especialmente en el caso de la igualdad de género, expresamente mencionado por el artículo de las Constituciones democráticas modernas que se refiere al principio de igualdad ante la ley. El presente estudio trata esa forma específica de igualdad que se caracteriza por la paradoja de querer tratar como igual lo que es diferente, o sea, de hacer distinciones sin discriminar. Con este fin nos referimos al enfoque jurídico y al enfoque político del tema como se encuentran en la reforma del derecho de familia. No es un problema de una específica legislación nacional, sino más bien una versión específica de un problema de nivel general. Se trata de la imposibilidad de construir como indistinguible lo que es diferente. El intento político de reformar el derecho de familia para implementar el principio constitucional de igualdad no consigue resolver el problema. Éste vuelve a aparecer por la imposibilidad que el derecho funcione sin crear diferencias. Al mismo tiempo, surgen problemas nuevos relacionado con formas nuevas de organizar la vida familiar.