Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new pr...Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.展开更多
We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth ad...We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.展开更多
It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in t...It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.展开更多
The aim of this work is to show that the currently widely accepted geometrical model of space and time based on the works of Einstein and Minkowski is not unique. The work presents an alternative geometrical model of ...The aim of this work is to show that the currently widely accepted geometrical model of space and time based on the works of Einstein and Minkowski is not unique. The work presents an alternative geometrical model of space and time, a model which, unlike the current one, is based solely on Euclidean geometry. In the new model, the pseudo-Euclidean spacetime is replaced with a specific subset of four-dimensional Euclidean space. The work shows that four-dimensional Euclidean space allows explanation of known relativistic effects that are now explained in pseudo-Euclidean spacetime by Einstein’s Special Theory of Relativity (STR). It also shows simple geometric-kinematical nature of known relativistic phenomena and among others explains why we cannot travel backward in time. The new solution is named the Euclidean Model of Space and Time (EMST).展开更多
In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the...In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.展开更多
In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of al...In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to <em>T</em><em>c</em> in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition <em>T</em><em>c</em> upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schr<span style="white-space:nowrap;">ö</span>dinger to most recently Geesink.展开更多
In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contracti...In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.展开更多
Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the...Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.展开更多
A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condit...A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.展开更多
文摘Let χ= be a metric space and let ε be a positive real number. Then a function f: X→Y is defined to be an ε-map if and only if for all y∈Y, the diameter of f-1(y)?is at most ε. In Theorem 10 we will give a new proof for the following well known fact: if χ is totally bounded, then for all ε there exists a finite number n and a continuous ε-map fε: X→Rn (here Rn is the usual n-dimensional Euclidean space endowed with the Euclidean metric). If ε is “small”, then fε is “almost injective”;and still exists even if χ has infinite covering dimension (in this case, n depends on ε, of course). Contrary to the known proofs, our proof technique is effective in the sense, that it allows establishing estimations for n in terms of ε and structural properties of χ.
文摘We propose the generalization of Einstein’s special theory of relativity (STR). In our model, we use the (1 + 4)-dimensional space G, which is the extension of the (1 + 3)-dimensional Minkowski space M. As a fifth additional coordinate, the interval S is used. This value is constant under the usual Lorentz transformations in M, but it changes when the transformations in the extended space G are used. We call this model the Extended space model (ESM). From a physical point of view, our expansion means that processes in which the rest mass of the particles changes are acceptable now. In the ESM, gravity and electromagnetism are combined in one field. In the ESM, a photon can have a nonzero mass and this mass can be either positive or negative. It is also possible to establish in the frame of ESM connection between mass of a particle and its size.
文摘It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.
文摘The aim of this work is to show that the currently widely accepted geometrical model of space and time based on the works of Einstein and Minkowski is not unique. The work presents an alternative geometrical model of space and time, a model which, unlike the current one, is based solely on Euclidean geometry. In the new model, the pseudo-Euclidean spacetime is replaced with a specific subset of four-dimensional Euclidean space. The work shows that four-dimensional Euclidean space allows explanation of known relativistic effects that are now explained in pseudo-Euclidean spacetime by Einstein’s Special Theory of Relativity (STR). It also shows simple geometric-kinematical nature of known relativistic phenomena and among others explains why we cannot travel backward in time. The new solution is named the Euclidean Model of Space and Time (EMST).
基金Supported by the Technological Project of Jiangxi Province Education Department(GJJ 08389)
文摘In this paper, the concept of the equidistant conjugate points of a triangle to the n-dimensional Euclidean space is extended. The concept of equidistant conjugate point in high dimensional simplex is defined, and the property of the equidistant conjugate points of a triangle is generalized to high dimensional simplex.
文摘In this paper, we briefly go over the homogeneous 5D model field theory: from the 5D space-time inception, to its quantum field solutions given in terms of Higgs vacuum, filled with magnetic monopole bose fields of all energies. Then through the space dimension reduction projections, the Gell-Mann standard model was obtained as well as a quantum to Classical connection was made via introducing Bose distribution to the monopoles to obtain the Perelman entropy and Ricci Flow mappings. This provided us a picture to the creation of Astronomical objects, from galaxies to stars and planets. This method of splitting the monopole energy into ranges is extended to show that below the basic rest mass range of the electron and Quark, it still can be applied to explaining for the creation of the chemical elements periodic table. But perhaps the most interesting is in the lowest hundreds of Hz energy range, obtained from yet another 3 fold space symmetry breaking, into 2D × 1D, producing bio nitrogenous bases composed of 3 Carbon 12 in hexagon structures, due to preservation of the 1D monopole standing waves of this low frequencies. From that by imposing gauge changes the monopole states into DNA spectra. Since such spectra states retain the DLRO, it induces formation of charge carriers periodicity in a spherical bio cell.. It was then argued that due to cell’s surface proteins, the structure must contain partial filled VB, with “p” state hole density, and empty CB, separated from VB by a positive band gap. Such band structures resemble known HTC Cuprate ceramics. Since the HTC goes through a Superconductivity transition via the simultaneous bose exciton condensation, providing a Coulomb pressure, which reduces the band gap substantially, and induces the ODLRO transition of the hole density. The same obviously applies to the bio cells. Because of the near continuous exciton levels generated, a matching to the DNA spectra then can always occur by selective choices of proteins on the cell surface. Judging from a numerical study, we did years ago on YBCO, with doping. We found with a large enough VB hole density, the exciton induced superconducting gap can easily lead to <em>T</em><em>c</em> in the room temperature range. In fact by EMF excitation can increase the exciton pressure and trigger the ODLRO transition <em>T</em><em>c</em> upward. In fact, numerical results then suggest there do exist coherent EMF spectra from three key elements: Water, Carbon and Hydrogen, together with Oxygen, as studied over the years by numerous people, starting from Schr<span style="white-space:nowrap;">ö</span>dinger to most recently Geesink.
文摘In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.
文摘Class of 5-dimensional functions Φ was introduced and a convergent sequence determined by non-self mappings satisfying certain Φi-contractive condition was constructed, and then that the limit of the sequence is the unique com-mon fixed point of the mappings was proved. Finally, several more general forms were given. Our main results gener-alize and unify many same type fixed point theorems in references.
基金supported by the National Natural Science Foundation of China(No.11361064)
文摘A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.
