The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the k...The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.展开更多
Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the eff...Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.展开更多
We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists betw...We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.展开更多
Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision mod...Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.展开更多
Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the ...Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the gradient method is linearly convergent while Newton's method has second order convergence rate. The fast computing algorithm of Hesse matrix of the cost function of NN is proposed and it is the theory basis of the improvement of Newton's learning algorithm. Simulation results show that the convergence rate of Newton's learning algorithm is high and apparently faster than the traditional BP method's, and the robustness of Newton's learning algorithm is also better than BP method' s.展开更多
A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is g...A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.展开更多
On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form...On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.展开更多
Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presen...Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.展开更多
The ring-opening polymerization of e-caprolactone (CL) initiated by novel single lanthanide tris(4-tert-butylphenolate)s [Ln(OTBP)3] is reported. Single-component La(OTBP)3 can effectively prepare polycaprolactone (PC...The ring-opening polymerization of e-caprolactone (CL) initiated by novel single lanthanide tris(4-tert-butylphenolate)s [Ln(OTBP)3] is reported. Single-component La(OTBP)3 can effectively prepare polycaprolactone (PCL) with over 90% yield and viscosity average molecular weight about 60 x 10 under quite mild conditions: molar ratio of CL to initiator is 1000, 60 C, 2 h in toluene. Mechanism study indicates that the monomer inserts into the growing chain via the break of acyl-oxygen bond of CL.展开更多
Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, <i>q<...Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, <i>q<sub>pl</sub></i>, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, <img src="Edit_770c2a48-039c-4cc9-8f66-406c0cfc565c.png" width="90" height="15" alt="" />, where <i>ζ</i>(3) equals Apery’s constant, 1.202 …, and, <i>n</i><sub>+</sub>(0)=<i>n</i>_(0), is the relaxed, <i>i.e.</i>, <img src="Edit_813d5a6f-b79a-49ba-bdf7-5042541b58a0.png" width="25" height="12" alt="" />, number density of the positive and negative mass planckions. In the present epoch, we estimate that, <i>n</i><sub>+</sub>(0) equals, 7.848E54 m<sup>-3</sup>, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, <i>l</i><sub>+</sub>(0)=<i>l</i><sub>_</sub>(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, <img src="Edit_efc8003d-5297-4345-adac-4ac95536934d.png" width="80" height="15" alt="" />, due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, <i>g</i>=9.81m/s<sup>2</sup>, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.展开更多
Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and...Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is, to some degree, well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is when we first combine Newton’s assumptionn, that matter and light ultimately consist of hard indivisible particles, with new insight in atomism that we can truly begin to understand gravity at a deeper level. This leads to a quantum gravity theory that is unified with quantum mechanics and in which there is no need for G and not even a need for the Planck constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant as almost holy and untouchable. Thus, we have neglected to see an important aspect of mass;namely, the indivisible particle that Newton also held in high regard. Second, standard physics have built their quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength, the true matter wavelength.展开更多
The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has...The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.展开更多
In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two...In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.展开更多
In order to calculate the electronic structure of correlated materials, we propose implementation of the LDA+Gutzwiller method with Newton's method. The self-consistence process, efficiency and convergence of calcul...In order to calculate the electronic structure of correlated materials, we propose implementation of the LDA+Gutzwiller method with Newton's method. The self-consistence process, efficiency and convergence of calculation are improved dramatically by using Newton's method with golden section search and other improvement approaches.We compare the calculated results by applying the previous linear mix method and Newton's method. We have applied our code to study the electronic structure of several typical strong correlated materials, including SrVO3, LaCoO3, and La2O3Fe2Se2. Our results fit quite well with the previous studies.展开更多
In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are ...In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given.展开更多
Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology...Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology of hepatitis C virus(HCV)infection.On the other hand,Kemeny’s constant(Ω)is a beneficial quantifier characterizing the universal average activities of a Markov chain.This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state si.Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues.Motivated by Levene and Loizou,we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial.Based on the achieved results,entirely results are obtained for the M鯾ius hexagonal ring network.展开更多
文摘The Newton gravitational constant is considered a cornerstone of modern gravity theory. Newton did not invent or use the gravity constant;it was invented in 1873, about the same time as it became standard to use the kilogram mass definition. We will claim that G is just a term needed to correct the incomplete kilogram definition so to be able to make gravity predictions. But there is another way;namely, to directly use a more complete mass definition, something that in recent years has been introduced as collision-time and a corresponding energy called collision-length. The collision-length is quantum gravitational energy. We will clearly demonstrate that by working with mass and energy based on these new concepts, rather than kilogram and the gravitational constant, one can significantly reduce the uncertainty in most gravity predictions.
文摘Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.
文摘We compare Newton’s force law of universal gravitation with a corrected simple approach based on Bhandari’s recently presented work, where the gravitation constant G is maintained. A reciprocity relation exists between both alternative gravity formulas with respect to the distances between mass centers. We conclude a one-to-one mapping of the two gravitational formulas. We don’t need Einstein’s construct of spacetime bending by matter.
文摘Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx<sub>1</sub>, and slow-jet, vx<sub>2</sub>. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.
文摘Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the gradient method is linearly convergent while Newton's method has second order convergence rate. The fast computing algorithm of Hesse matrix of the cost function of NN is proposed and it is the theory basis of the improvement of Newton's learning algorithm. Simulation results show that the convergence rate of Newton's learning algorithm is high and apparently faster than the traditional BP method's, and the robustness of Newton's learning algorithm is also better than BP method' s.
基金supported by National Foundation of Natural Science(11471092,11326231)Zhejiang Provincial Natural Science Foundation of China(LZ13A010003)
文摘A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h = H2. Both theoretical analysis and numerical experiments illustrate the efficiency of the algorithm for solving the coupled problem.
文摘On the basis of the vector formula of the Newton’s law for a viscous liquid and the integrated vector form of the equation of an impulse for a viscous liquid for resistance and carrying power of a profile of any form and the big length dependences are found in a stream. Application of the found dependences at a circulating flow of the cylinder located across a stream is showed. The analysis of a tensor of viscosity for laminar and turbulent flow is carried out.
文摘Gain based predistorter (PD) is a highly effective and simple digital baseband predistorter which compensates for the nonlinear distortion of PAs. Lookup table (LUT) is the core of the gain based PD. This paper presents a discrete Newton’s method based adaptive technique to modify LUT. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on athematics. And we deduce discrete Newton’s method based adaptive iterative formula used for updating LUT. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify gain based PD using discrete Newton’s method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times and less runtime than secant method.
基金supported by the National Natural Science Foundation of China.(Grant No.20174033 and 20254001)the Special Found for Major State Basic Research Project(Grant No.G1999064801)the Committee of Science and Technology of Zhejiang Province.
文摘The ring-opening polymerization of e-caprolactone (CL) initiated by novel single lanthanide tris(4-tert-butylphenolate)s [Ln(OTBP)3] is reported. Single-component La(OTBP)3 can effectively prepare polycaprolactone (PCL) with over 90% yield and viscosity average molecular weight about 60 x 10 under quite mild conditions: molar ratio of CL to initiator is 1000, 60 C, 2 h in toluene. Mechanism study indicates that the monomer inserts into the growing chain via the break of acyl-oxygen bond of CL.
文摘Assuming a Winterberg model for space where the vacuum consists of a very stiff two-component superfluid made up of positive and negative mass planckions, Q theory is the hypothesis, that Planck charge, <i>q<sub>pl</sub></i>, was created at the same time as Planck mass. Moreover, the repulsive force that like-mass planckions experience is, in reality, due to the electrostatic force of repulsion between like charges. These forces also give rise to what appears to be a gravitational force of attraction between two like planckions, but this is an illusion. In reality, gravity is electrostatic in origin if our model is correct. We determine the spring constant associated with planckion masses, and find that, <img src="Edit_770c2a48-039c-4cc9-8f66-406c0cfc565c.png" width="90" height="15" alt="" />, where <i>ζ</i>(3) equals Apery’s constant, 1.202 …, and, <i>n</i><sub>+</sub>(0)=<i>n</i>_(0), is the relaxed, <i>i.e.</i>, <img src="Edit_813d5a6f-b79a-49ba-bdf7-5042541b58a0.png" width="25" height="12" alt="" />, number density of the positive and negative mass planckions. In the present epoch, we estimate that, <i>n</i><sub>+</sub>(0) equals, 7.848E54 m<sup>-3</sup>, and the relaxed distance of separation between nearest neighbor positive, or negative, planckion pairs is, <i>l</i><sub>+</sub>(0)=<i>l</i><sub>_</sub>(0)=5.032E-19 meters. These values were determined using box quantization for the positive and negative mass planckions, and considering transitions between energy states, much like as in the hydrogen atom. For the cosmos as a whole, given a net smeared macroscopic gravitational field of, <img src="Edit_efc8003d-5297-4345-adac-4ac95536934d.png" width="80" height="15" alt="" />, due to all the ordinary, and bound, matter contained within the observable universe, an average displacement from equilibrium for the planckion masses is a mere 7.566E-48 meters, within the vacuum made up of these particles. On the surface of the earth, where, <i>g</i>=9.81m/s<sup>2</sup>, the displacement amounts to, 7.824E-38 meters. All of these displacements are due to increased gravitational pressure within the vacuum, which in turn is caused by applied gravitational fields. The gravitational potential is also derived and directly related to gravitational pressure.
文摘Newton did not invent or use the so-called Newton’s gravitational constant G. Newton’s original gravity formula was and not . In this paper, we will show how a series of major gravity phenomena can be calculated and predicted without the gravitational constant. This is, to some degree, well known, at least for those that have studied a significant amount of the older literature on gravity. However, to understand gravity at a deeper level, still without G, one needs to trust Newton’s formula. It is when we first combine Newton’s assumptionn, that matter and light ultimately consist of hard indivisible particles, with new insight in atomism that we can truly begin to understand gravity at a deeper level. This leads to a quantum gravity theory that is unified with quantum mechanics and in which there is no need for G and not even a need for the Planck constant. We claim that two mistakes have been made in physics, which have held back progress towards a unified quantum gravity theory. First, it has been common practice to consider Newton’s gravitational constant as almost holy and untouchable. Thus, we have neglected to see an important aspect of mass;namely, the indivisible particle that Newton also held in high regard. Second, standard physics have built their quantum mechanics around the de Broglie wavelength, rather than the Compton wavelength. We claim the de Broglie wavelength is merely a mathematical derivative of the Compton wavelength, the true matter wavelength.
文摘The article is devoted to hitherto never undertaken applying an almost unknown logically formalized axiomatic epistemology-and-axiology system called “Sigma-V” to the Third Newton’s Law of mechanics. The author has continued investigating the extraordinary (paradigm-breaking) hypothesis of formal-axiological interpreting Newton’s mathematical principles of natural philosophy and, thus, has arrived to discrete mathematical modeling a system of formal axiology of nature by extracting and systematical studying its proper algebraic aspect. Along with the proper algebraic machinery, the axiomatic (hypothetic-deductive) method is exploited in this investigation systematically. The research results are the followings. 1) The Third Newton’s Law of mechanics has been modeled by a formal-axiological equation of two-valued algebraic system of metaphysics as formal axiology. (Precise defining the algebraic system is provided.) The formal-axiological equation has been established (and examined) in this algebraic system by accurate computing compositions of relevant evaluation-functions. Precise tabular definitions of the evaluation-functions are given. 2) The wonderful formula representing the Third Newton’s Law (in the relevant physical interpretation of the formal theory Sigma-V) has been derived logically in Sigma-V from the presumption of a-priori-ness of knowledge. A precise axiomatic definition of the nontrivial notion “a-priori-ness of knowledge” is given. The formal derivation is implemented in strict accordance with the rigor standard of D. Hilbert’s formalism;hence, checking the formal derivation submitted in this article is not a difficult task. With respect to proper theoretical physics, the formal inference is a nontrivial scientific novelty which has not been discussed and published elsewhere yet.
基金Jointly supported by China Major Key Project for Basic Researcher and Provincial Natrural Science Foundation.
文摘In this paper we discuss the convergence of a modified Newton’s method presented by A. Ostrowski [1] and J.F. Traub [2], which has quadratic convergence order but reduces one evaluation of the derivative at every two steps compared with Newton’s method. A convergence theorem is established by using a weak condition a≤3-2(2<sup>1/2</sup>) and a sharp error estimate is given about the iterative sequence.
基金supported by the National Natural Science Foundation of China(Grant No.2011CBA00108)the National Basic Research Program of China(Grant No.2013CB921700)the Foundation of LCP
文摘In order to calculate the electronic structure of correlated materials, we propose implementation of the LDA+Gutzwiller method with Newton's method. The self-consistence process, efficiency and convergence of calculation are improved dramatically by using Newton's method with golden section search and other improvement approaches.We compare the calculated results by applying the previous linear mix method and Newton's method. We have applied our code to study the electronic structure of several typical strong correlated materials, including SrVO3, LaCoO3, and La2O3Fe2Se2. Our results fit quite well with the previous studies.
文摘In this paper, we propose an inexact damped Newtonmethod for solving nonlinear complementarity problems based on the equivalent B differentiable equations.Global convergence and locally quadratic convergence are obtained,and numerical results are given.
文摘Spanning tree(τ)has an enormous application in computer science and chemistry to determine the geometric and dynamics analysis of compact polymers.In the field of medicines,it is helpful to recognize the epidemiology of hepatitis C virus(HCV)infection.On the other hand,Kemeny’s constant(Ω)is a beneficial quantifier characterizing the universal average activities of a Markov chain.This network invariant infers the expressions of the expected number of time-steps required to trace a randomly selected terminus state since a fixed beginning state si.Levene and Loizou determined that the Kemeny’s constant can also be obtained through eigenvalues.Motivated by Levene and Loizou,we deduced the Kemeny’s constant and the number of spanning trees of hexagonal ring network by their normalized Laplacian eigenvalues and the coefficients of the characteristic polynomial.Based on the achieved results,entirely results are obtained for the M鯾ius hexagonal ring network.