1,823 research outputs found
Minimality and irreducibility of symplectic four-manifolds
We prove that all minimal symplectic four-manifolds are essentially
irreducible. We also clarify the relationship between holomorphic and
symplectic minimality of K\"ahler surfaces. This leads to a new proof of the
deformation-invariance of holomorphic minimality for complex surfaces with even
first Betti number which are not Hirzebruch surfaces.Comment: final version; cosmetic changes only; to appear in International
Mathematics Research Notice
Minimum dissipation principle in stationary non equilibrium states
We generalize to non equilibrium states Onsager's minimum dissipation
principle. We also interpret this principle and some previous results in terms
of optimal control theory. Entropy production plays the role of the cost
necessary to drive the system to a prescribed macroscopic configuration
Non-Newtonian Mechanics
The classical motion of spinning particles can be described without employing
Grassmann variables or Clifford algebras, but simply by generalizing the usual
spinless theory. We only assume the invariance with respect to the Poincare'
group; and only requiring the conservation of the linear and angular momenta we
derive the zitterbewegung: namely the decomposition of the 4-velocity in the
newtonian constant term p/m and in a non-newtonian time-oscillating spacelike
term. Consequently, free classical particles do not obey, in general, the
Principle of Inertia. Superluminal motions are also allowed, without violating
Special Relativity, provided that the energy-momentum moves along the worldline
of the center-of-mass. Moreover, a non-linear, non-constant relation holds
between the time durations measured in different reference frames. Newtonian
Mechanics is re-obtained as a particular case of the present theory: namely for
spinless systems with no zitterbewegung. Introducing a Lagrangian containing
also derivatives of the 4-velocity we get a new equation of the motion,
actually a generalization of the Newton Law a=F/m. Requiring the rotational
symmetry and the reparametrization invariance we derive the classical spin
vector and the conserved scalar Hamiltonian, respectively. We derive also the
classical Dirac spin and analyze the general solution of the Eulero-Lagrange
equation for Dirac particles. The interesting case of spinning systems with
zero intrinsic angular momentum is also studied.Comment: LaTeX; 27 page
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Productive stagnation and unproductive accumulation: an econometric analysis of the United States
In this paper I evaluate the dynamic interactions between productive and unproductive forms of capital accumulation in the United States economy from 1947 to 2011. I employ time series econometrics to formally assess two questions that other scholars have hitherto considered mostly through verbal or descriptive approaches. First, I check whether unproductive accumulation hinders or fosters productive accumulation. Second, I check whether or not productive stagnation leads to faster unproductive accumulation. I introduce different measures of productive and unproductive forms of capital accumulation using a new methodology to estimate Marxist categories from conventional input-output matrices, national income and product accounts, and fixed assets accounts. A core feature of my methodology is the notion that the production of knowledge and information is also a form of unproductive activity. Results indicate two-way positive effects between productive and unproductive activities in the short run but no self-correcting mechanism that would bring productive and unproductive forms of accumulation back to a stable equilibrium path over the long run
Self-similar solutions for a superdiffusive heat equation with gradient nonlinearity
This paper is devoted to global well-posedness, self-similarity and
symmetries of solutions for a superdiffusive heat equation with superlinear and
gradient nonlinear terms with initial data in new homogeneous Besov-Morrey type
spaces. Unlike the heat equation, we need to develop an appropriate
decomposition of the two-parametric Mittag-Leffler function in order to obtain
Mikhlin-type estimates get our well-posedness theorem. To the best of our
knowledge, the present work is the first one concerned with a well-posedness
theory for a time-fractional partial differential equations of order
with non null initial velocity
Spaces of solutions of relativistic field theory with constraints
In this paper I shall explain how the reduction results of Marsden and Weinstein [38] can be used to study the space of solutions of relativistic field theories. Two of the main examples that will be discussed are the Einstein equations and the Yang-Mills equations. The basic paper on spaces of solutions is that of Segal [49]. That paper deals with unconstrained systems and is primarily motivated by semilinear wave equations. We are mainly concerned here with systems with constraints in the sense of Dirac. Roughly speaking, these are systems whose four dimensional Euler-Lagrange equations are not all hyperbolic but rather split into hyperbolic evolution equations and elliptic constraint equations
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