Graviton in condensed photon sea

The ground-based device simulates the graviton explosion between gravity and magnetic seas. Trapped graviton was set to behave as free relativistic quantum particles, making it possible to induce magnetic fields as a function of time in the space Hieut (H). Our result is grounded on rigorous proof based on the photon sea for different initial superpositions of positive- negative-graviton spinor states. This explains that the interactive inducing protocol can be used to test the ability of the magnetic field not to communicate but to explode with relativistic quantum gravity.

Polynomial time solution to NP-complete problem Hamiltonian cycle (P=NP Proof)

P vs NP is one of the open and most important mathematics/computer science questions that has not been answered since it was raised in 1971 despite its importance and a quest for a solution since 2000. P vs NP is a class of problems that no polynomial time algorithm exists for any. If any of the problems in the class gets solved in polynomial time, all can be solved as the problems are translatable to each other. One of the famous problems of this kind is Hamiltonian cycle. Here we propose a polynomial time algorithm with rigorous proof that it always finds a solution if there exists one. It is expected that this solution would address all problems in the class and have a major impact in diverse fields including computer science, engineering, biology, and cryptography.

On the state independency and log-linearity of error propagation for discrete group affine systems with application to attitude estimation

Purpose This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems. Design/methodology/approach The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems. Findings The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis. Practical implications An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results. Originality/value The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

Peregrine Soliton as a Limiting Behavior of the Kuznetsov-Ma and Akhmediev Breathers

This article discusses a limiting behavior of breather solutions of the focusing nonlinear Schrödinger equation. These breathers belong to the family of solitons on a non-vanishing and constant background, where the continuous-wave envelope serves as a pedestal. The rational Peregrine soliton acts as a limiting behavior of the other two breather solitons, i.e., the Kuznetsov-Ma breather and Akhmediev soliton. Albeit with a phase shift, the latter becomes a nonlinear extension of the homoclinic orbit waveform corresponding to an unstable mode in the modulational instability phenomenon. All breathers are prototypes for rogue waves in nonlinear and dispersive media. We present a rigorous proof using the ϵ-δ argument and show the corresponding visualization for this limiting behavior.

Eventual Convergence of the Reputation-Based Algorithm in IoT Sensor Networks

Uncertainty in dense heterogeneous IoT sensor networks can be decreased by applying reputation-inspired algorithms, such as the EWMA (Exponentially Weighted Moving Average) algorithm, which is widely used in social networks. Despite its popularity, the eventual convergence of this algorithm for the purpose of IoT networks has not been widely studied, and results of simulations are often taken in lieu of the more rigorous proof. Therefore the question remains, whether under stable conditions, in realistic situations found in IoT networks, this algorithm indeed converges. This paper demonstrates proof of the eventual convergence of the EWMA algorithm. The proof consists of two steps: it models the sensor network as the UOG (Uniform Opinion Graph) that enables the analytical approach to the problem, and then offers the mathematical proof of eventual convergence, using formalizations identified in the previous step. The paper demonstrates that the EWMA algorithm converges under all realistic conditions.

Constraint-following servo control for an underactuated mobile robot under hard constraints

This article formulates the control problem of underactuated mobile robot as servo constraint-following, and develops a novel constraint-following servo control approach for underactuated mobile robot under both servo soft and hard constraints. Servo soft constraints are expressed as equalities, which may be holonomic or non-holonomic. Servo hard constraints are expressed as inequalities. It is required that the underactuated mobile robot motion eventually converges to servo soft constraints, and satisfies servo hard constraints at all times. Diffeomorphism is employed to incorporate hard constraints into soft constraints, yielding new soft constraints to relax hard constraints. By this, we design a constraint-following servo control based on the new servo soft constraints, which drives the system to strictly follow the original servo soft and hard constraints. The effectiveness of the proposed approach is proved by rigorous proof and simulations.

A Rigorous Proof of Fundamental Theorem of Uncertain Calculus

This paper revises the definition of the general Liu process via requiring its drift and diffusion to be sample-continuous. Then it is verified that almost all sample paths of the general Liu process are locally Lipschitz continuous. At last, a rigorous proof of fundamental theorem of uncertain calculus is given.

Experiment Regarding Magnetic Fields with Gravity

The ground-based device simulates the potential energy (voltages) between gravity and magnetic seas. The gravity generator (GG) generated currents and voltages on the mesoscopic scale in the vacuum. Gravity interacts to generate electricity in the Earth's direction or the opposite direction by the repulsive magnetic force. A trapped gravity was set to behave as free relativistic quantum particles or fluids, which made it possible to measure the particle position as a function of time. Our result is grounded on a rigorous proof based on numerical and analytic computations, which took it accessible to study the magnetic sea for different initial superposition of positive- negative-gravity spinor state. It might explain the relativistic quantum gravity and the heating mechanism of the Sun.

Discipline for the Masses

Chapter 5 explores how state and Church finally reached their goal of enforcing confession among the Russian masses. Enforcement of confession over the Orthodox population became more extensive and more rigorous. Proof of having gone to confession became a routine component of getting married, getting divorced, or filing one’s business paperwork. Being caught shirking the sacraments itself called for penance. There were more attempts to use police to enforce confession and penances in the 1850s and early 1860s in the Russian empire than at any other time—and they worked. In the middle of the nineteenth century Church and state came far closer to getting the Orthodox Christian masses to reach the same baseline level of Christian performance as the elites had a century earlier.

New Newtonian Mechanics and New Laws of Motion

Newton’s third law has been proved to be wrong, there are experimental evidence of the video, there are rigorous proof of a strong paper. Further obtained based on this, that is, Newton’s second law to prove is wrong. Therefore, the Newton law of correcting wrong, there are new second law of motion and new third law of motion, to be produces. So including Newton’s first law the New three laws of motion, will become more accurate, more efficient mechanical principles, guiding the new mechanical system is derived and the establishment. No one would doubt that Newton’s second law and Newton’s third law would be wrong. But a surprising discovery was produced in a simple mechanic’s experiment. The earliest experiments showed that two objects interact, acting force and reaction force, Is not the same size. Therefore, Newton’s third law seems to be wrong. Using conventional methods, considering objects with different masses, the inertia is also different. It can also provide a reasonable explanation for the unequal force and reaction force. But when It was further discovered that when Newton’s second law was also wrong, the introduction of the new second law made the establishment of the new third law also perfect. A series of extremely important new discoveries were successively produced and realized.