1,811 research outputs found
The Lagrangian and Hamiltonian Aspects of the Electrodynamic Vacuum-Field Theory Models
We review the modern classical electrodynamics problems and present the
related main fundamental principles characterizing the electrodynamical
vacuum-field structure. We analyze the models of the vacuum field medium and
charged point particle dynamics using the developed field theory concepts.
There is also described a new approach to the classical Maxwell theory based on
the derived and newly interpreted basic equations making use of the vacuum
field theory approach. In particular, there are obtained the main classical
special relativity theory relations and their new explanations. The well known
Feynman approach to Maxwell electromagnetic equations and the Lorentz type
force derivation is also discussed in detail. A related charged point particle
dynamics and a hadronic string model analysis is also presented. We also
revisited and reanalyzed the classical Lorentz force expression in arbitrary
non-inertial reference frames and present some new interpretations of the
relations between special relativity theory and its quantum mechanical aspects.
Some results related with the charge particle radiation problem and the
magnetic potential topological aspects are discussed. The electromagnetic
Dirac-Fock-Podolsky problem of the Maxwell and Yang-Mills type dynamical
systems is analyzed within the classical Dirac-Marsden-Weinstein symplectic
reduction theory. The problem of constructing Fock type representations and
retrieving their creation-annihilation operator structure is analyzed. An
application of the suitable current algebra representation to describing the
non-relativistic Aharonov-Bohm paradox is presented. The current algebra
coherent functional representations are constructed and their importance
subject to the linearization problem of nonlinear dynamical systems in Hilbert
spaces is demonstrated.Comment: 70 p, revie
The Tumor Suppressor HHEX Inhibits Axon Growth when Prematurely Expressed in Developing Central Nervous System Neurons
Neurons in the embryonic and peripheral nervoussystem respond to injury by activating transcriptional programs supportive of axon growth, ultimately resulting in functional recovery. In contrast, neurons in the adult central nervous system (CNS) possess a limited capacity to regenerate axons after injury, fundamentally constraining repair. Activating pro-regenerative gene expression in CNS neurons is a promising therapeutic approach, but progress is hampered by incomplete knowledge of the relevant transcription factors. An emerging hypothesis is that factors implicated in cellular growth and motility outside the nervous system may also control axon growth in neurons. We therefore tested sixty-nine transcription factors, previously identified as possessing tumor suppressive or oncogenic properties in non-neuronal cells, in assays of neurite outgrowth. This screen identified YAP1 and E2F1 as enhancers of neurite outgrowth, and PITX1, RBM14, ZBTB16, and HHEX as inhibitors. Follow-up experiments are focused on the tumor suppressor HHEX, one of the strongest growth inhibitors. HHEX is widely expressed in adult CNS neurons, including corticospinal tract neurons after spinal injury, but is present only in trace amounts in immature cortical neurons and adult peripheral neurons. HHEX overexpression in early postnatal cortical neurons reduced both initial axonogenesis and the rate of axon elongation, and domain deletion analysis strongly implicated transcriptional repression as the underlying mechanism. These findings suggest a role for HHEX in restricting axon growth in the developing CNS, and substantiate the hypothesis that previously identified oncogenes and tumor suppressors can play conserved roles in axon extension
A vertex operator representation of solutions to the Gurevich-Zybin hydrodynamical equation
An approach based on the spectral and Lie - algebraic techniques for
constructing vertex operator representation for solutions to a Riemann type
Gurevicz-Zybin hydrodynamical hierarchy is devised. A functional representation
generating an infinite hirerachy of dispersive Lax type integrable flows is
obtaned.Comment: 6 page
Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators
The Lie algebraic scheme for constructing Hamiltonian operators is differential-algebraically recast and an effective approach is devised for classifying the underlying algebraic structures of integrable Hamiltonian systems. Lie–Poisson analysis on the adjoint space to toroidal loop Lie algebras is employed to construct new reduced pre-Lie algebraic structures in which the corresponding Hamiltonian operators exist and generate integrable dynamical systems. It is also shown that the Balinsky–Novikov type algebraic structures, obtained as a Hamiltonicity condition, are derivations on the Lie algebras naturally associated with differential toroidal loop algebras. We study nonassociative and noncommutive algebras and the related Lie-algebraic symmetry structures on the multidimensional torus, generating via the Adler–Kostant–Symes scheme multi-component and multi-dimensional Hamiltonian operators. In the case of multidimensional torus, we have constructed a new weak Balinsky–Novikov type algebra, which is instrumental for describing integrable multidimensional and multicomponent heavenly type equations. We have also studied the current algebra symmetry structures, related with a new weakly deformed Balinsky–Novikov type algebra on the axis, which is instrumental for describing integrable multicomponent dynamical systems on functional manifolds. Moreover, using the non-associative and associative left-symmetric pre-Lie algebra theory of Zelmanov, we also explicate Balinsky–Novikov algebras, including their fermionic version and related multiplicative and Lie structures
List Decoding of Matrix-Product Codes from nested codes: an application to Quasi-Cyclic codes
A list decoding algorithm for matrix-product codes is provided when are nested linear codes and is a non-singular by columns matrix. We
estimate the probability of getting more than one codeword as output when the
constituent codes are Reed-Solomon codes. We extend this list decoding
algorithm for matrix-product codes with polynomial units, which are
quasi-cyclic codes. Furthermore, it allows us to consider unique decoding for
matrix-product codes with polynomial units
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