Autonomous and Mobile Prototype of Curvature Sensor with Remote Reliable Communication of Spectral Curvature

Through the creation and construction of a curvature sensor of accelerometer type, using the spectral curvature concept or curvature energy that measures curvature in Volts/m3, an autonomous and mobile censorship of curvature sensing with reliable data transmission/reception in real time and remote position is designed and constructed considering the spectra of curvature of the measured curvature energy during the advance of the prototype as the normed measure by with β , a constant rationalized parameter according with the required advance of the mobile device in the control scale of their velocity. Likewise, the sensed curvature data are digitalized through wireless interconnectivity using a HC-05 Module with a programmable device that includes logic blocks whose interconnection and functionality can be configured according to the sensor measure in situs. Also an application is planted to the obtaining of an energy plus due to the curvature that could be used in the displacement of a vehicle.

Mathematical Nanotechnology: Quantum Field Intentionality

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.

Design and Development of Impeller Synergic Systems of Electromagnetic Type to Levitation/Suspension Flight of Symmetrical Bodies

Using certain models of twistor surfaces for fields of force and the mathematical relationships that lie among fields, lines, surfaces and flows of energy, it has been designed and developed a flight electromagnetic type system based on the synergic study of their electromagnetic field geodesics to generate vehicle levitation, suspension and movement without being in contact with the surface. The idea of such work is to obtain a new flight and impulse patent of an electromagnetic vehicle by principles of super-conduction and some laws of the current like Eddy currents and principles which are very similar to mechanics of sidereal objects like galaxies or stars under models of twistor surfaces. This vehicle will be controlled by one microchip that will be programmed by conscience operators algebra of electromagnetic type that leads to the flow of Eddy currents, the iso-rotations and suspension of the special geometrical characteristics vehicle, generating also on the vehicle structure certain “magnetic conscience” that provokes all movements like succeeding to the sidereal objects in the universe.

Design and Development of an Electronic Sensor to Detect and Measure Curvature of Spaces Using Curvature Energy

Using fine electromagnetic signals to measure observables of other fields like curvature and torsion of a space, and the corresponding value of their integrals of the action of perception of curvature through electronic signals that detect curvature on a curved surface, it is designed and constructed a sensor of curvature of accelerometer type that detects and curvature measures in 2 and 3-dimensional spaces using the programming of shape operators on spheres and the value of their integrals along the curves and geodesics in their principal directions.

Geometrical Langlands Ramifications and Differential Operators Classification by Coherent D-Modules in Field Theory

Spaces of equivalence modulo a relation of congruence are constructed on field solutions to establish a theory of the universe that includes the theory QFT （Quantum Field theory）, the SUSY （Super-symmetry theory） and HST （heterotic string theory） using the sheaves correspondence of differential operators of the field equations and sheaves of coherent D - Modules [1]. The above mentioned correspondence use a Zuckerman functor that is a factor of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry [2, 3]. The obtained development includes complexes of D - modules of infinite dimension, generalizing for this way, the BRST-cohomology in this context. With it, the class of the integrable systems is extended in mathematical physics and the possibility of obtaining a general theory of integral transforms for the space - time （integral operator cohomology [4]）, and with it the measurement of many of their observables [5]. Also tends a bridge to complete a classification of the differential operators for the different field equations using on the base of Verma modules that are classification spaces of SO（l, n ＋ 1）, where elements of the Lie algebra al（1, n ＋ 1）, are differential operators, of the equations in mathematical physics [1]. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field （Verma modules） and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic L G - bundles category with a special connection （Deligne connection）. The corresponding D - modules may be viewed as sheaves of conformal blocks （or co-invariants） （images under a version of the Penrose transform [1, 6]） naturally arising in the framework of conformal field theory.

Heat Flux Analysis in Electrical Transformers through Integral Operators of Mechanics

Considering the continuous functioning of a power transformer under charge of high capacity of 50 MVA, predicted studies are proposed to be performed of their thermal behavior under perma nent and variable regimens of flow of charge, using noninvasive methods based in integral trans forms that measure and determine parameters of geometrical, analytical and physical type of the transformer. In before works, we have studied a basic geometry of a winding composed of high and low voltage sections with a uniform heat generation and heat convection boundary conditions. The heat conduction equation representing the phenomena of heat generation in a cylindrical structure was solved by using an integral transform. In this sense, this new study considers the basic geometry composed of a three cylindrical windings (high and low voltage turns) and a rec tangular core. Thus it is proposed to solve magnetic flow equations using integral transforms (Han kel transforms and Bessel integrals) in order to obtain the heat source distribution in the core due to the magnetization currents which are developed in function of the magnetic field flow equations. Based on this, it is proposed as a second step to use this heat source distribution to obtain the corresponding temperature distribution in the core by solving the cylindrical heat conduction equation for the core (cylindrical). Bearing this in mind, it is proposed finally to solve the 3D cylindrical heat conduction equation for the one winding using the calculated heat convection coefficients, the conductivity of the winding, behavior of the mineral oil and the non uniform winding heat generation predicted in recent researches. This equation will be solved by using integral methods (Radon, Hankel and Fourier transforms). This methodology will be useful to establish a new design of a power transformer based on the values of their integrals and the results that throw the inverse methods for this case. Finally if possible we will use the programs of Fluent and/or Phoenics for the validation of functional proposed models of prediction and prevention of heat flow and charge based on the obtained results.

Derived Categories in Langlands Geometrical Ramifications: Approaching by Penrose Transforms

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.)

Electromagnetic Gauges and Maxwell Lagrangians Applied to the Determination of Curvature in the Space-Time and their Applications

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.

Penrose Transform on <i>D</i>-Modules, Moduli Spaces and Field Theory

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.

Framework of Penrose Transforms on DP-Modules to the Electromagnetic Carpet of the Space-Time from the Moduli Stacks Perspective

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.

Homological Electromagnetism and Electromagnetic Demonstrations on the Existence of Superconducting Effects Necessaries to Magnetic Levitation/Suspension

Considering results obtained in magnetic levitation and suspension of the symmetrical bodies are designed and developed several experiments of the electromagnetism that demonstrate the effects of a superconductor necessary to the magnetic levitation/suspension. This generates bases to the development of a reactor to impulse and anti-gravitational magnetic displacement of a vehicle considering the production and transference of Eddy currents on their structure to microscopic level and the effect of auto-levitation/auto-suspension that is obtained with the iso-rotations of the impulse magnetic ring of the proper vehicle.

Penrose Transform on Induced <i>D_G/H</i>-Modules and Their Moduli Stacks in the Field Theory

We consider generalizations of the Radon-Schmid transform on coherent DG/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.

QED-Lie Algebra and Their &pound;-Modules in Superconductivity

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)? . The obtained object haves the advantages to be an algebraic or geometrical space at the same time. This same space of ￡-modules can explain and model different electromagnetic phenomena in superconductor and quantum processes where is necessary an organized transformation of the electromagnetic nature of the space- time and obtain nanotechnologies of the space-time and their elements.

Curvature Energy and Their Spectrum in the Spinor-Twistor Framework: Torsion as Indicium of Gravitational Waves

The twistor kinematic-energy model of the space-time and the kinematic-energy tensor as the energy-matter tensor in relativity are considered to demonstrate the possible behavior of gravity as gravitational waves that derive of mass-energy source in the space-time and whose contorted image is the spectrum of the torsion field acting in the space-time. The energy of this field is the energy of their second curvature. Likewise, it is assumed that the curvature energy as spectral curvature in the twistor kinematic frame is the curvature in twistor-spinor framework, which is the mean result of this work. This demonstrates the lawfulness of the torsion as the indicium of the gravitational waves in the space-time. A censorship to detect gravitational waves in the space-time is designed using the curvature energy.

Quasi-Relaxation Transforms, Meromorphic Curves and Hereditary Integrals of the Stress-Deformation Tensor to Metallic Specimens

Into the study of quasi-relaxation, in the past researches it has been concluded that the condition of meta-stability in the metallic specimen is given by the plasticity explained by the plastic energy in the process of the quasi-relaxation. It is calculated through quasi-relaxation functional of this energy to obtain a spectra in the space D(σ – ε;t), that induces the existence of functions φ(t), and Ψ(t), related with the fundamental curves of quasi-relaxation given by σ(t), with their poles in , which is got in the maximum of stress given by σ0 = σ1. Also the tensor of plastic deformation that represents the plastic load during the application of specimen machine, cannot be obtained without poles in the space D(σ;t), corresponding the curves calculated into the space D(σ – ε;t), by curves that in the kinetic process of quasi-relaxation are represented by experimental curves in coordinates log σ – t. This situation cannot be eluded, since in this phenomena exist dislocations that go conform fatigue in the nano-crystalline structure of metals. From this point of view, is necessary to obtain a spectral study related to the energy using functions that permits the modeling and compute the states of quasi-relaxation included in the poles in the deformation problem to complete the solutions in the space D(σ – ε;t), and try a new method of solution of the differential equations of the quasi-relaxation analysis. In a nearly future development, the information obtained by this spectral study (by our integral transforms), will be able to give place to the programming through the spectral encoding of the materials in the meta-stability state, which is propitious to a nano-technological transformation of materials, concrete case, some metals.

Water Manipulation through Curvature Energy on Humidity Microparticles

The electric field created in a curvature energy sensor on air microparticles is used to obtain a temperature-humidity map G:M→SO(2)∪F,by stereo-radially of the sensor design to detect and measure the temperature and humidity of certain local region of the environment space.Likewise,considering the curvature energy as the deviation of any field interaction,even the obstruction to its proper flow,is designed and created a humidity-resistor sensor to the control and optimization of humidity in a space with different gradients of humidity,pressure and temperature in a radial detection and measuring.Then the sensing problem is a problem of free boundary conditions where is satisfied an energy functional of norm ||ξ||_(2),to curvature functions κ,that satisfy in the temperature and humidity function ξ,the change limit condition ξ|_(∂Ω)≤2πξ(r).This carries to that the temperature-humidity sensor must be designed on a length gauge to measure the changes of humidity and temperature in the space.

The Development and Creation of Intelligent Systems in the Next One Hundred Years

Today the intelligent systems are technological imple­mented as advanced machines[1]which have high percep­tion,interaction and response to the real world being in much cases an extension of the reality,anticipating events,intertwining remote events,saving life and predicting preferences of human been[2,3]through of robust pro­gramming and electronic systems with high performance,optimization and design in operations where are required machines with an strong and complete interacting with the environment[2];environment which also goes increasing until;in the very near future,to the ends of the Universe.