Abstract:
If we consider the finite actions of electromagnetic fields in Hamiltonian regime and use vector bundles of geodesic in movement of the charges with a shape operator (connection) that measures the curvature of a geometrical space on these geodesic (using the light caused from these points (charges) acting with the infinite null of gravitational field (background)) we can establish a model of the curvature through gauges inside the electromagnetic context. In partular this point of view is useful when it is about to go on in a quantized version from the curvature where the space is distorted by the interactions between particles. This demonstrates that curvature and torsion effect in the space-time are caused in the quantum dimension as back-reaction effects in photon propagation. Also this permits the observational verification and encodes of the gravity through of light fields deformations. The much theoretical information obtained using the observable effects like distortions is used to establish inside this Lagrangian context a classification of useful spaces of electro-dynamic configuration for the description of different interactions of field in the Universe related with gravity. We propose and design one detector of curvature using a cosmic censor of the space-time developed through distortional 3-dimensional sphere. Some technological applications of the used methods are exhibited.

Abstract:
We consider a generalization of the Radon-Schmid transform on coherent D-modules of sheaves of holomorphic complex bundles inside a moduli space, with the purpose of establishing the equivalences among geometric objects (vector bundles) and algebraic objects as they are the coherent D-modules, these last with the goal of obtaining conformal classes of connections of the holomorphic complex bundles. The class of these equivalences conforms a moduli space on coherent sheaves that define solutions in field theory. Also by this way, and using one generalization of the Penrose transform in the context of coherent D-modules we find conformal classes of the space-time that include the heterotic strings and branes geometry.

We consider generalizations of the Radon-Schmid transform on coherent D_{G/H}-Modules, with the intention of obtaining the equivalence between geometric objects (vector bundles) and algebraic objects (D-Modules) characterizing conformal classes in the space-time that determine a space moduli [1] on coherent sheaves for the securing solutions in field theory [2]. In a major context, elements of derived categories like D-branes and heterotic strings are considered, and using the geometric Langlands program, a moduli space is obtained of equivalence between certain geometrical pictures (non-conformal world sheets [3]) and physical stacks (derived sheaves), that establishes equivalence between certain theories of super symmetries of field of a Penrose transform that generalizes the implications given by the Langlands program. With it we obtain extensions of a cohomology of integrals for a major class of field equations to corresponding Hecke category.

Considering the finite actions of a field on the matter
and the space which
used to infiltrate their quantum reality at level particle,
methods are developed to serve to base the concept of “intentional action” of a
field and their ordered and supported effects (synergy) that must be realized for the “organized
transformation” of the space and matter. Using path integrals, these transformations
are decoded and their quantum principles are shown.

Some derived categories
and their deformed versions are used to develop a theory of the ramifications of
field studied in the geometrical Langlands program to obtain the correspondences
between moduli stacks and solution classes represented cohomologically under the
study of the kernels of the differential operators studied in their classification
of the corresponding field equations. The corresponding D-modules in this case may be viewed as sheaves of conformal blocks
(or co-invariants) (images under a version of the Penrose transform) naturally arising
in the framework of conformal field theory. Inside the geometrical Langlands correspondence
and in their cohomological context of strings can be established a framework of
the space-time through the different versions of the Penrose transforms and their
relation between them by intertwining operators (integral transforms that are isomorphisms
between cohomological spaces of orbital spaces of the space-time), obtaining the
functors that give equivalences of their corresponding categories.(For more
information,please refer to the PDF version.)

Administrative
law is the body of law which provides the mechanisms for challenging and
regulating government decision making. There are two fundamental elements in
Australian administrative law—judicial review and merits review. Judicial
review is concerned with the legality of administrative decisions, and
is the sole province of the courts. Merits review is concerned with the
substance of a decision and is carried out by various review bodies. Reasons
for decisions lie at the heart of administrative decision-making. A statement
of reasons should provide fairness by enabling decisions to be properly
explained and defended and will assist the person affected by a decision to
decide whether to exercise rights of review or appeal. Australian law does not
yet recognize a general duty to give reasons for administrative decisions.
However, there are legislative provisions which encapsulate an obligation to
provide reasons. It is all part and parcel of procedural fairness—Findings on
Material Questions of Fact; Reference to Evidence on which Findings of Fact are
Based; Dealing with Inadequate Statements of Reasons; Requests for Further and
Better Particulars.

Abstract:
Considering the different versions of the Penrose transform on D-modules and their applications to different levels of DM-modules in coherent sheaves, we obtain a geometrical re-construction of the electrodynamical carpet of the space-time, which is a direct consequence of the equivalence between the moduli spaces, that have been demonstrated in a before work. In this case, the equivalence is given by the Penrose transform on the quasi coherent Dλ-modules given by the generalized Verma modules diagram established in the Recillas conjecture to the group SO(1, n + 1), and consigned in the Dp-modules on which have been obtained solutions in field theory of electromagnetic type.

Abstract:
Technological change is a distinctive characteristic of modern labor
markets. New technologies change the demand for different skills in the labor
market and thus introduce uncertainty in the wage structure that agents will
face in the future. In this way, technological change affects agents decisions
about which skills to invest in. In this paper, I study how labor market
uncertainty arising from technological change influences the private incentives
for specialization. I show that in a world populated by risk-averse agents,
technologies that generate a positive covariance of wages across sectors or
tasks within sectors will strengthen the incentives for specialization, whereas
technological progress that generates a negative covariance of wages will generate
strong private incentives for agents to become generalists. Therefore, there is
no unique relationship between technological progress and specialization. The
nature of the new technologies introduced in the labor market is what matters.

It’s created a canonical Lie algebra in
electrodynamics with all the “nice” algebraic and geometrical properties of
an universal enveloping algebra with the goal of can to obtain generalizations
in quantum electrodynamics theory of the TQFT, and the Universe based in lines
and twistor bundles to the obtaining of irreducible unitary representations of
the Lie groups SO(4)？andO(3,1), based in admissible representations of U(1), and SU(n)？

Abstract:
Discrete dynamical systems are given by the pair (X,f) where X is a compact metric space and f: X→X is a continuous map. During years, a long list of results have appeared to precise and understand what is the complexity of the systems. Among them, one of the most popular is that of topological entropy. In modern applications, other conditions on X and f have been considered. For example, X can be non-compact or f can be discontinuous (only in a finite number of points and with bounded jumps on the values of f or even non-bounded jumps). Such systems are interesting from theoretical point of view in Topological Dynamics and appear frequently in applied sciences such as Electronics and Control Theory. In this paper, we are reviewing the origins of the notion of entropy and studying some developing of it leading to modern notions of entropies. At the same time, we will incorporate some mathematical foundations of such old and new ideas until the appearance of Shannon entropy. To this end, we start with the introduction for the first time of the notion of entropy in thermodynamics by R. Clausius and its evolution by L. Boltzmann until the appearing in the twenty century of Shannon and Kolmogorov-Sinai entropies and the subsequent topological entropy. In turn, such notions have evolved to other recent situations where it is necessary to give some extended versions of them adapted to new problems. Of special interest is to appreciate the connexions of the notions of entropy from Boltzmann and Shannon. Since this history is long, we will not deal with the Kolmogorov-Sinai entropy or with topological entropy and modern approaches.