Liviu Popescu - Academia.edu (original) (raw)

Papers by Liviu Popescu

Research paper thumbnail of Dual Structures on the Prolongations of a Lie Algebroid

Annals of the Alexandru Ioan Cuza University - Mathematics, 2013

In the present paper we study the properties of dual structures on the prolongations of a Lie alg... more In the present paper we study the properties of dual structures on the prolongations of a Lie algebroid. We introduce the dynamical covariant derivative on Lie algebroids and prove that the nonlinear connection induced by a regular Lagrangian is compatible with the metric and symplectic structures. The notions of mechanical structure and semi-Hamiltonian section are introduced on the prolongation of the Lie algebroid to its dual bundle and their properties are investigated. Finally, we prove the equivalence between the metric nonlinear connection and semi-Hamiltonian section, using the Legendre transformation induced by a regular Hamiltonian.

Research paper thumbnail of Metric Non-Linear Connections on the Prolongation of a Lie Algebroid to its Dual Bundle

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011

In the present paper the problem of compatibility between a nonlinear connection and other geomet... more In the present paper the problem of compatibility between a nonlinear connection and other geometric structures on Lie algebroids is studied. The notion of dynamical covariant derivative is introduced and a metric nonlinear connection is found. We prove that the nonlinear connection induced by a regular Hamiltonian on a Lie algebroid is the unique connection which is compatible with the metric and symplectic structures.

Research paper thumbnail of Pathway Tools version 13.0: integrated software for pathway/genome informatics and systems biology

Briefings in bioinformatics, 2010

Pathway Tools is a production-quality software environment for creating a type of model-organism ... more Pathway Tools is a production-quality software environment for creating a type of model-organism database called a Pathway/Genome Database (PGDB). A PGDB such as EcoCyc integrates the evolving understanding of the genes, proteins, metabolic network and regulatory network of an organism. This article provides an overview of Pathway Tools capabilities. The software performs multiple computational inferences including prediction of metabolic pathways, prediction of metabolic pathway hole fillers and prediction of operons. It enables interactive editing of PGDBs by DB curators. It supports web publishing of PGDBs, and provides a large number of query and visualization tools. The software also supports comparative analyses of PGDBs, and provides several systems biology analyses of PGDBs including reachability analysis of metabolic networks, and interactive tracing of metabolites through a metabolic network. More than 800 PGDBs have been created using Pathway Tools by scientists around the world, many of which are curated DBs for important model organisms. Those PGDBs can be exchanged using a peerto-peer DB sharing system called the PGDB Registry.

Research paper thumbnail of The MetaCyc database of metabolic pathways and enzymes and the BioCyc collection of pathway/genome databases

Nucleic Acids Research, 2010

The MetaCyc database (MetaCyc.org) is a comprehensive and freely accessible database describing m... more The MetaCyc database (MetaCyc.org) is a comprehensive and freely accessible database describing metabolic pathways and enzymes from all domains of life. MetaCyc pathways are experimentally determined, mostly small-molecule metabolic pathways and are curated from the primary scientific literature. MetaCyc contains >2100 pathways derived from >37 000 publications, and is the largest curated collection of metabolic pathways currently available. BioCyc (BioCyc.org) is a collection of >3000 organism-specific Pathway/Genome Databases (PGDBs), each containing the full genome and predicted metabolic network of one organism, including metabolites, enzymes, reactions, metabolic pathways, predicted operons, transport systems and pathway-hole fillers. Additions to BioCyc over the past 2 years include YeastCyc, a PGDB for Saccharomyces cerevisiae, and 891 new genomes from the Human Microbiome Project. The BioCyc Web site offers a variety of tools for querying and analysis of PGDBs, including Omics Viewers and tools for comparative analysis. New developments include atom mappings in reactions, a new representation of glycan degradation pathways, improved compound structure display, better coverage of enzyme kinetic data, enhancements of the Web Groups functionality, improvements to the Omics viewers, a new representation of the Enzyme Commission system and, for the desktop version of the software, the ability to save display states.

Research paper thumbnail of Machine learning methods for metabolic pathway prediction

BMC Bioinformatics, 2010

A key challenge in systems biology is the reconstruction of an organism's metabolic network from ... more A key challenge in systems biology is the reconstruction of an organism's metabolic network from its genome sequence. One strategy for addressing this problem is to predict which metabolic pathways, from a reference database of known pathways, are present in the organism, based on the annotated genome of the organism.

Research paper thumbnail of Cheap SEO Services

Research paper thumbnail of London SEO Company

Research paper thumbnail of Cost of SEO in the UK

Research paper thumbnail of Exponential dichotomy roughness and structural stability for evolution families without bounded growth and decay

Nonlinear Analysis: Theory, Methods & Applications, 2009

We show that if U (t, s) is an exponentially dichotomic evolution operator, then the unique solut... more We show that if U (t, s) is an exponentially dichotomic evolution operator, then the unique solution of the Volterra equation

Research paper thumbnail of Exponential dichotomy roughness on Banach spaces

Journal of Mathematical Analysis and Applications, 2006

In the present paper we extend existing results on exponential dichotomy roughness for linear ODE... more In the present paper we extend existing results on exponential dichotomy roughness for linear ODE systems to infinite dimensional Banach space. We give new conditions for the existence of exponential dichotomy roughness in infinite dimensional space and in the finite interval case. We also improve previous results by indicating the exact values of the dichotomic constants of the perturbed equation.

Research paper thumbnail of On admissible perturbations for exponential dichotomy

Journal of Mathematical Analysis and Applications, 2008

In this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite-dim... more In this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite-dimensional Banach spaces. Unlike some previous works, we do not assume bounded growth. We consider linear, non-autonomous ordinary differential equations with ...

Research paper thumbnail of A topological classification of linear differential equations on Banach spaces

Journal of Differential Equations, 2004

In the present work, we give necessary and sufficient conditions for linear differential non-auto... more In the present work, we give necessary and sufficient conditions for linear differential non-autonomous equations on a Banach space, that satisfy exponential dichotomy, to be topologically equivalent. We shall also prove that such equations are structurally stable.

Research paper thumbnail of Topological Classification and Structural Stability of Strongly Continuous Groups

Integral Equations and Operator Theory, 2014

ABSTRACT

Research paper thumbnail of MANAGEMENT OF RURAL TOURISM IN MOUNTAIN AREA OF ARGEŞ COUNTY

Management of rural tourism in the mountain area of Arges County is the leading anticipation, org... more Management of rural tourism in the mountain area of Arges County is the leading anticipation, organization, coordination, control process of all tourism resources to achieve maximum efficiency, without prejudice to the environment and to ensure at the same time the relaxation of the tourist.

Research paper thumbnail of Dual Structures on the Prolongations of a Lie Algebroid

Annals of the Alexandru Ioan Cuza University - Mathematics, 2013

In the present paper we study the properties of dual structures on the prolongations of a Lie alg... more In the present paper we study the properties of dual structures on the prolongations of a Lie algebroid. We introduce the dynamical covariant derivative on Lie algebroids and prove that the nonlinear connection induced by a regular Lagrangian is compatible with the metric and symplectic structures. The notions of mechanical structure and semi-Hamiltonian section are introduced on the prolongation of the Lie algebroid to its dual bundle and their properties are investigated. Finally, we prove the equivalence between the metric nonlinear connection and semi-Hamiltonian section, using the Legendre transformation induced by a regular Hamiltonian.

Research paper thumbnail of Metric Non-Linear Connections on the Prolongation of a Lie Algebroid to its Dual Bundle

Annals of the Alexandru Ioan Cuza University - Mathematics, 2011

In the present paper the problem of compatibility between a nonlinear connection and other geomet... more In the present paper the problem of compatibility between a nonlinear connection and other geometric structures on Lie algebroids is studied. The notion of dynamical covariant derivative is introduced and a metric nonlinear connection is found. We prove that the nonlinear connection induced by a regular Hamiltonian on a Lie algebroid is the unique connection which is compatible with the metric and symplectic structures.

Research paper thumbnail of Pathway Tools version 13.0: integrated software for pathway/genome informatics and systems biology

Briefings in bioinformatics, 2010

Pathway Tools is a production-quality software environment for creating a type of model-organism ... more Pathway Tools is a production-quality software environment for creating a type of model-organism database called a Pathway/Genome Database (PGDB). A PGDB such as EcoCyc integrates the evolving understanding of the genes, proteins, metabolic network and regulatory network of an organism. This article provides an overview of Pathway Tools capabilities. The software performs multiple computational inferences including prediction of metabolic pathways, prediction of metabolic pathway hole fillers and prediction of operons. It enables interactive editing of PGDBs by DB curators. It supports web publishing of PGDBs, and provides a large number of query and visualization tools. The software also supports comparative analyses of PGDBs, and provides several systems biology analyses of PGDBs including reachability analysis of metabolic networks, and interactive tracing of metabolites through a metabolic network. More than 800 PGDBs have been created using Pathway Tools by scientists around the world, many of which are curated DBs for important model organisms. Those PGDBs can be exchanged using a peerto-peer DB sharing system called the PGDB Registry.

Research paper thumbnail of The MetaCyc database of metabolic pathways and enzymes and the BioCyc collection of pathway/genome databases

Nucleic Acids Research, 2010

The MetaCyc database (MetaCyc.org) is a comprehensive and freely accessible database describing m... more The MetaCyc database (MetaCyc.org) is a comprehensive and freely accessible database describing metabolic pathways and enzymes from all domains of life. MetaCyc pathways are experimentally determined, mostly small-molecule metabolic pathways and are curated from the primary scientific literature. MetaCyc contains >2100 pathways derived from >37 000 publications, and is the largest curated collection of metabolic pathways currently available. BioCyc (BioCyc.org) is a collection of >3000 organism-specific Pathway/Genome Databases (PGDBs), each containing the full genome and predicted metabolic network of one organism, including metabolites, enzymes, reactions, metabolic pathways, predicted operons, transport systems and pathway-hole fillers. Additions to BioCyc over the past 2 years include YeastCyc, a PGDB for Saccharomyces cerevisiae, and 891 new genomes from the Human Microbiome Project. The BioCyc Web site offers a variety of tools for querying and analysis of PGDBs, including Omics Viewers and tools for comparative analysis. New developments include atom mappings in reactions, a new representation of glycan degradation pathways, improved compound structure display, better coverage of enzyme kinetic data, enhancements of the Web Groups functionality, improvements to the Omics viewers, a new representation of the Enzyme Commission system and, for the desktop version of the software, the ability to save display states.

Research paper thumbnail of Machine learning methods for metabolic pathway prediction

BMC Bioinformatics, 2010

A key challenge in systems biology is the reconstruction of an organism's metabolic network from ... more A key challenge in systems biology is the reconstruction of an organism's metabolic network from its genome sequence. One strategy for addressing this problem is to predict which metabolic pathways, from a reference database of known pathways, are present in the organism, based on the annotated genome of the organism.

Research paper thumbnail of Cheap SEO Services

Research paper thumbnail of London SEO Company

Research paper thumbnail of Cost of SEO in the UK

Research paper thumbnail of Exponential dichotomy roughness and structural stability for evolution families without bounded growth and decay

Nonlinear Analysis: Theory, Methods & Applications, 2009

We show that if U (t, s) is an exponentially dichotomic evolution operator, then the unique solut... more We show that if U (t, s) is an exponentially dichotomic evolution operator, then the unique solution of the Volterra equation

Research paper thumbnail of Exponential dichotomy roughness on Banach spaces

Journal of Mathematical Analysis and Applications, 2006

In the present paper we extend existing results on exponential dichotomy roughness for linear ODE... more In the present paper we extend existing results on exponential dichotomy roughness for linear ODE systems to infinite dimensional Banach space. We give new conditions for the existence of exponential dichotomy roughness in infinite dimensional space and in the finite interval case. We also improve previous results by indicating the exact values of the dichotomic constants of the perturbed equation.

Research paper thumbnail of On admissible perturbations for exponential dichotomy

Journal of Mathematical Analysis and Applications, 2008

In this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite-dim... more In this work we obtain an optimal upper bound for exponential dichotomy roughness in infinite-dimensional Banach spaces. Unlike some previous works, we do not assume bounded growth. We consider linear, non-autonomous ordinary differential equations with ...

Research paper thumbnail of A topological classification of linear differential equations on Banach spaces

Journal of Differential Equations, 2004

In the present work, we give necessary and sufficient conditions for linear differential non-auto... more In the present work, we give necessary and sufficient conditions for linear differential non-autonomous equations on a Banach space, that satisfy exponential dichotomy, to be topologically equivalent. We shall also prove that such equations are structurally stable.

Research paper thumbnail of Topological Classification and Structural Stability of Strongly Continuous Groups

Integral Equations and Operator Theory, 2014

ABSTRACT

Research paper thumbnail of MANAGEMENT OF RURAL TOURISM IN MOUNTAIN AREA OF ARGEŞ COUNTY

Management of rural tourism in the mountain area of Arges County is the leading anticipation, org... more Management of rural tourism in the mountain area of Arges County is the leading anticipation, organization, coordination, control process of all tourism resources to achieve maximum efficiency, without prejudice to the environment and to ensure at the same time the relaxation of the tourist.