THE GRAVITATIONAL FIELD OF A BODY WITH ROTATIONAL SYMMETRY IN EINSTEIN'S THEORY OF GRAVITATION ABSTRACT Einstein's set of field equations in vaccuo is reduced to such a form tbat simp~e [r]

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Abstract: In order to unite **gravitational** **field** with other fields, we must find the common material foundation of the **gravitation** **theory** and quantum **theory**. For the end, I propose the duality framework of the universe. The universe is composed of continuous universal continuum and separate p net; Universal energy Eu and various special energies Es that transform into one another at high frequency; Basic forces that dominate the universe are the universal compressive force and quantum dispersive force. The above duality framework, can explain naturally the wave-particle duality, probabilistic nature, uncertainty relation and quantum entanglement; no using Einstein’s **theory**, can obtain the mass-energy relation, Einstein’s equations, Friedmann’s equation and the proportions of dark energy, dark matter and ordinary matter; includes, links and foreruns both the **gravitation** **theory** and quantum **theory**; is their common material foundation to give their unified harmonious image; and can solve the puzzlers about the singularity, non-locality, uncertainty of energy, et al . Daring predictions: The electromagnetic wave must have an adjoint strain wave. The **gravitational** wave must have an adjoint wave of matching **field**. It is in the wrong direction to find the particle of the “dark matter”.

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The modern **theory** of **gravitation**—the **theory** general relativity of **Einstein**—is a basis for calculation of the astrophysics phenomena. It is generalization Newto- nian dynamics, including the law of universal **gravitation**. As well as Newtonian dynamics the **theory** general relativity is not the quantum **theory**. The Einstein’s equation for a **gravitational** **field** does not have stochastic nature. It contradicts modern physics. For example, for an electron cooperating with a **gravitational** **field** with help of the Einstein’s equation, it is possible to calculate position ab- solutely precisely that contradicts a principle of Heisenberg’s uncertainty.

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The development of Physics—whether we realize it or not—is in large driven by it’s mathematical representation. It is based on **Einstein** General Relativity, that we arrive to such constructions as: Event Horizon, Black Holes, Open and Close Universe, Big Bang, Black Energy, etc. If this Eddington Unification **theory** with accumulating **Gravitational** **field** G is correct, it is not clear which of these phenomena survive. Or what their mathematical description would be if they still exist. For example, we might learn that “black holes” that don’t allow light to escape do exist (which would not be a big surprise to Astronomers), but those “black hole” have no event horizon. In fact, if the “event horizon” did ex- ist, would we see a ring of a bright glow around each black hole, due to the “stacked” light (from outsider point of view) of all the stars that fell into that “hole” over millions and millions year of its history?

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In the present paper, by means of Lagrange dynamical **theory** and Eulor’s equation for a **rotational** rigid **body**, the Lagrangian and dynamic equations of a **rotational** charged rigid **body** under a uniform magnetic ﬁeld has been successfully derived; Also two symmetric simple cases have been solved and analyzed under conditions of slow rotation and no **gravitation**. We limit our research object to the dielectric rigid **body** under conditions of slow rotation and no **gravitation** so that the damping eﬀect of electromagnetic radiation and the relativistic eﬀects caused by rotation can all be ignorable. 2. FUNDAMENTAL CONCEPTS OF CHARGE

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The ascent and descent of the air carry along the positive ions resulting in a change of the EFE strength and produce the difference in the potentials along the surface of the Earth leading to the appearance of telluric currents. The at- mosphere contains the ions of both signs formed as a result of the ionizing caused by the ultraviolet and cosmic rays as well as by the natural radioactivity, etc. These ions are affected by the Lorentz force when they move with an air current, for instance, with wind or under convection in the magnetic **field** of the Earth, there appears an electromotive force and an electric current. The direc- tion of the current is determined by the mutual orientation of the vector of the magnetic **field** strength and that of the speed of the air, and it can have both the vertical and the horizontal components. On the one hand, this current results in the potential difference along the surface of the Earth and is one more source of telluric currents. On the other hand, it can lead to the separation of the charges in the atmosphere both along the vertical and the horizontal as well as to the formation of lightnings. Charges of large values are not formed at a small height above the surface of the Earth due to the Earth proximity. Its high electrical conductivity produces a shunting effect suppressing the separation of charges. Regions charged up to high values of the potential can form in the atmosphere only at a rather large height.

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In this paper, we show how to realise a quantum simulation of the generation of parti- cles by **gravitational** waves in a BEC. We exploit the fact that the Bogoliubov modes of a trapped BEC satisfy a Klein-Gordon equation on a curved background metric. The met- ric has two terms [, –], one corresponding to the real spacetime metric and a second term, corresponding to what we call the analogue gravity metric, which depends on BEC parameters such as velocity ﬂows and energy density. While in [] we analyse the eﬀect of changes in the real spacetime metric, in this case we consider the manipulation of the ana- logue gravity [–] metric, assuming that the real spacetime is ﬂat. Since in this case the experimentalist is able to manipulate artiﬁcially the parameters of the condensate, we are able to simulate spacetime distortions with a much larger amplitude, as if the laboratory were closer to the source of the **gravitational** ripples. We show that with realistic experi- mental parameters, a physically meaningful model of **gravitational** wave can be simulated with current technology.

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Many Steganography methods have been introduced on different cover media such as images [5, 10, 13], video files [14,15] and audio files [16]. Due lack of large scale repeated information in a text file when compared with images, audio and video files. Text Steganography seems to be most complicated kind of Steganography [17]. This paper presents a novel approach for text Steganography by generating the summery of a text file that contains English language text. The proposed method takes as input a widely available text and the secret message. The secret message is hidden in the summery by following the **rotational** **symmetry** properties of the characters of English alphabets along the axis of rotation. As result of the system, a review is generated from the chosen input text and that review is our cover text. That review is to be sent to the receiving end. At the other end depending on the same properties of the alphabets, relevant secret bits from the cover text are generated to get back the Input message.

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the imaginary energy, which energy must be proportional to the electric charge ot the system.. If the total mass.[r]

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Abstract. We construct a covariant closed string **field** **theory** by extending recent works on the covariant open string **field** **theory** in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string **field** **theory** in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string ver- tices. We show that the Fock space representations of the closed string **field** **theory** may be completely factorized into those of the open string **field** **theory**. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string **theory** may be promoted to the second quantized closed string **theory**. We explicitly calculate the scatter- ing amplitudes of three gravitons by using the closed string **field** **theory** in the proper-time gauge.

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Understanding the nature of mass is crucial in fundamental re- search. Since attempts to detect the Higgs boson, and therefore to verify the Higgs **field** as the mass-generating mechanism of the Stan- dard Model, have been unsuccessful, paper proposes a very simple model of **gravitation** that use the Descartes’ void (holes in space- time). The advantage of the present approach is that it can easily explain the curvature of space-time using the properties of Descartes’ vacuum only. **Gravitation** is a phenomenon by which all objects with mass attract each other. Hole **theory** of **gravitation** explains why ob- ject have mass, how all objects with mass attract each other. Matter interacts with space-time that and radiates a flux of holes that is the cause of the **gravitation**. Thus for explanation of **gravitation** the present **theory** use the hole structure of space-time only.

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Initially the paqft framework was developed for scalar fields, but recently there has been a lot of progress in constructing more complicated models. In particular, quantum electrodynamics (QED) was discussed in [23] and Yang-Mills **theory** was discussed in [12, 43]. A general framework which deals with arbitrary theories with local symmetries was subsequently proposed in [37, 38, 55]. This setting makes use of the Batalin-Vilkovisky formalism, which relies on homological algebra methods. In [37, 38] these algebraic tools are refined by introducing functional-analytic aspects and generalizing the BV formalism to infinite dimensional spaces. In [38] a general quantization scheme for gauge theories is proposed and some comparison with the approach of [43] is made. In the present work we want to continue this line. We discuss various aspects of local gauge invariance in p aqft , pointing out differences and common features of existing approaches. The framework proposed in [37, 38] is a very convenient tool for such analysis, since it is general and flexible enough. We focus our discussion on two problems: general formulation of consistency conditions that have to be satisfied by the deformed ⋆-product in order to be compatible with structures appearing in the BV formalism, and the definition and intrinsic meaning of the free and the interacting BRST charge. Our main result is the proof that the interacting BRST charge R V (Q) (R V denotes the derivative of the relative **S**-matrix)

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Thus, one may say in summary that if the Gauss’ theorem is valid for the **gravitational** **field** R , and the continuity equation is satisfied for ρ and J , then, there must exist a **gravitational** vector **field** W such that W and R satisfy inhomogeneous wave equations which propagate with an unknown speed “ λ ”. One must mention that there has not been a direct measurement of the speed of **gravitational** waves, but it is assume that gravity also travel to the speed of light [6]. In addition, none experiment has been so far trying to find the **gravitational** **field** W , and general controversy about Maxwell equations for **gravitational** **field** can be found in reference [34].

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, taking into account their own **gravitational** **field**. Equations with power and polynomial nonlinearities are studied in detail. It is shown that the initial set of the **Einstein** and spinor **field** equations with a power nonlinearity has regular solutions with spinor **field** localized energy and charge densities. The total energy and charge are finite. Besides, exact solutions, including soliton-like solutions, to the spinor **field** equations are also obtained in flat space-time. Keywords: Lagrangian; Static Spherical Symmetric Metric; **Field** Equations; **Einstein** Equations; Dirac Equation;

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The authors thank the tens of thousands of volunteers who have supported the **Einstein**@Home project by donat- ing their computer time and expertise for this analysis. Without their contributions, this work would not have been possible. The authors gratefully acknowledge the support of the United States National Science Foundation for the construction and operation of the LIGO Laboratory and the Science and Technology Facilities Council of the United Kingdom, the Max-Planck-Society, and the State of Niedersachsen/Germany for support of the construction and operation of the GEO600 detector. The authors also gratefully acknowledge the support of the research by these agencies and by the Australian Research Council, the Council of Scientific and Industrial Research of India, the Istituto Nazionale di Fisica Nucleare of Italy, the Spanish Ministerio de Educacio´n y Ciencia, the Conselleria d’Economia, Hisenda i Innovacio´ of the Govern de les Illes Balears, the Scottish Funding Council, the Scottish Universities Physics Alliance, the National Aeronautics and Space Administration, the Carnegie Trust, the Leverhulme Trust, the David and TABLE VIII. Post-processing candidates that have 9 or more coincidences and that are not excluded by the veto. The frequency f cand

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GFA is derived from the point of view of the hypoth- esis **theory** described above. To start with, all the solu- tions, which are the dusts in the algorithm model, are initialized randomly, or based on the prior knowledge; what’s more, we assign every dust (solution) a weight, we call it mass, whose values are based on the mass function generated from the space of the problem solu- tion; finally, the GFA begins. The power of attraction, which belongs to a certain dust and exists between every two dusts, pulls other dusts, which have the same influence to other dusts. Hence, the dusts assemble together, and the planets come out in the end – they are the optima. If you want to find global optimal solution, the planets assemble again, and the biggest planets will come out. To give a penalty of that the highest mass dust rules the whole space of solution, we propose a dis- tance which can reduce the effect of **gravitation** **field**. Methods

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Rectangle packing problems have attracted considerable inter- est in constraint programming [27] owing to their application in scheduling and layout design. This paper considers the consecutive squares packing problem [17], the problem of placing squares of size 1 × 1,2 × 2,...,n × n into a rectangle of given dimensions. It is argued in [27] that this problem is a good test of search meth- ods for constraint problems. The problem has a natural model as boolean combinations of integer difference constraints, and the disjunctive nature of the model suggests that the problem might be tackled using an SMT solver over the **theory** of integer difference constraints (often called integer difference logic). This **theory** has been supported by SMT solvers since their first development [23]. This paper details developments of a declarative SMT solver motivated by tackling this class of problems as a strength test. The solver is coded in Prolog and has at its heart the SAT solver from [12–14], whilst using constraint reification [25] as a mechanism to realise **theory** propagation. In [26] integer difference logic was integrated into the solver using an incremental variation of the Floyd-Warshall algorithm, together with a structure called a watch matrix that improves propagation from the **theory** decision pro- cedure into the boolean component of the problem. The solver works with the natural declarative model of the problem, and this paper details enhancements to the solver. In particular, the Floyd- Warshall matrix can be adapted to build unsatisfiable cores, that is, certificates of unsatisfiability, and these can be used to add **theory** learning (the learning of new boolean constraints from **theory** fail- ure) to the solver. Most significantly, **theory** learning is enhanced by exploiting **symmetry**, so that a single failure can be used to learn multiple clauses. Whilst this specialisation of learning is applica- tion specific in its detail, the tactic of specialising learning using problem structure is more generally applicable and promises to be a powerful tactic for SMT solving in general.

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But let us go back to the generalized **theory** of **gravitation**. We note that, as shown in [3], within the framework of the generalized **theory** of **gravitation**, one can obtain formulas according to which the perihelion precession for all planets is a necessary consequence of this **theory**. However, these formulas hardly can prove anything. The fact is that according to the generalized **theory** of gravita- tion, all celestial mechanics and its results should be revised. As it was shown above (see Figure 1), the action of the Sun on planets is expressed not by one force, but by five forces, and the action of each planet on each other planet is ex- pressed not by one force, but by five forces. Therefore, as a matter of fact, all the information about our solar system, obtained on the basis of Newton’s conven- tional **theory**, should be considered only approximately correct. So, from the point of view of the generalized **theory**, there is no point in trying to explain the 43’’rd residue in the displacement of the perihelion of Mercury. After all, if we take into account all the forces that act on Mercury, including the forces asso- ciated with the movement of the Sun in relation to the Galaxy, the rotation of the Sun around its axis, the dependence of the forces acting on Mercury on the speed and acceleration of the planets, on the speed of Mercury itself, and , finally, the retardation in the action of **gravitational** and cogravitational forces, will we get this discrepancy at all in the displacement of the perihelion of Mercury, es- pecially the discrepancy exactly in 43 seconds? It is clear that until all these cal- culations are performed, until the necessary corrections in celestial mechanics are amended, it is pointless to speak of testing the generalized **theory** of gravita- tion by analyzing the motion of Mercury.

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When the twin 0’ in the rocket thinks that he is at vest about the stars and the Earth flies away in the opposite direction from him, this system is not real but imaginary and unrelated to the existing situation: no matter what he thinks, his rocket flies faster than the Earth and the proc- esses are slowed down or him as before. Thus, neither acceleration nor the inclusion of **gravitational** affects (Einstein’s equivalence principle) are related to this pa- radox. To solve this paradox we have to go beyond the existing paradigm and to accept absolute material space de facto.

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With regard to a time variable-G (i.e., the Newtonian **gravitational** constant), recent research has shown that, at least for the last 9 billion of the Universe’s assumed 13.8-billion-year history, the Newtonian **gravitational** constant G has not varied more than (at most) one part in a billion. This result is obtained after an exhaustive study of about 580 observed supernovae events by Professor Jeremy Mould and his Ph.D. student Syed Uddin at the Swinburne Centre for Astrophysics and Supercomputing and the ARC Centre of Excellence for All-Sky As- trophysics. Their research findings show that the Newtonian constant G has not changed appreciably over cos- mic time. This research which focused on Type 1a supernovae, demonstrated a constant G within an upper bound of G G − 10 − 10 yr − 1 [65]. If as suggested here that G G ≡ 0 , then experiments such as those of Pro- fessor Jeremy Mould [65], these experiments; as is the case with the issue of whether or not a photon has mass (see e.g. [66]), they will not yield any conclusive answers as one experiment to the other, researchers will only push the measurements to the next decimal place.

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