Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I ex...Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.展开更多
At the point of death,a human being only has had the experience of nonexistence before birth and the experience of having lived his/her life after they were born.In the final analysis from the perspective of strict em...At the point of death,a human being only has had the experience of nonexistence before birth and the experience of having lived his/her life after they were born.In the final analysis from the perspective of strict empiricism,the individual only has two options:the nonexistence before birth or the eventual reliving of one’s life.The return of one’s life is supported by the paradigm of a multiverse and an antimatter universe.This is atheism’s logical certainty.展开更多
Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal ...Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.展开更多
Finite volumes of magma moving in confinement, store hydraulic potential energy for the generation,control and transmission of power. The Pascal's principle in a hydraulic jack arrangement is used to model the ver...Finite volumes of magma moving in confinement, store hydraulic potential energy for the generation,control and transmission of power. The Pascal's principle in a hydraulic jack arrangement is used to model the vertical and lateral growth of sills. The small input piston of the hydraulic jack is equivalent to the feeder dike, the upper large expansible piston equivalent to the magmatic chamber and the inertial force of the magma in the dike is the input force. This arrangement is particularly relevant to the case of sills expanding with blunt tips, for which rapid fracture propagation is inhibited. Hydraulic models concur with experimental data that show that lateral expansion of magma into a sill is promoted when the vertical ascent of magma through a feeder dike reaches the bottom contact with an overlying, flat rigid-layer. At this point, the magma is forced to decelerate, triggering a pressure wave through the conduit caused by the continued ascent of magma further down(fluid-hammer effect). This pressure wave can provide overpressure enough to trigger the initial hydraulic lateral expansion of magma into an incipient sill, and still have enough input inertial force left to continue feeding the hydraulic system. The lateral expansion underneath the strong impeding layer, causes an area increase and thus, further hydraulic amplification of the input inertial force on the sides and roof of the incipient sill, triggering further expansion in a self-reinforcing process. Initially, the lateral pressure increase is larger than that in the roof allowing the sill to expand. However, expansion eventually increases the total integrated force on the roof allowing its uplift into either a laccolith, if the roof preserves continuity, or into a piston bounded by a circular set of fractures. Hydraulic models for shallow magmatic chambers, also suggest that laccolith-like intrusions require the existence of a self-supported chamber roof. In contrast, if the roof of magmatic chambers loses the self-supporting capacity, lopoliths and calderas should be expected for more or less dense magmas, respectively, owing to the growing influence of the density contrast between the host rock and the magma.展开更多
We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid...We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid’s “Elements”. According to “Proclus hypothesis”, the main goal of Euclid was to create a full geometric theory of Platonic solids, associated with the ancient conception of the “Universe Harmony”. We consider the main periods in the development of the “Mathematics of Harmony” and its main mathematical results: algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions, following from Binet’s formulas, and the hyperbolic Fibonacci l-functions (l = 1, 2, 3, …), following from Gazale’s formulas, and their applications for hyperbolic geometry, in particular, for the solution of Hilbert’s Fourth Problem.展开更多
After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first...After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.展开更多
We demonstrate how to extract the Planck length from hydrostatic pressure without relying on any knowledge of Newton’s gravitational constant, G. By measuring the pressure from a water column, we can determine the Pl...We demonstrate how to extract the Planck length from hydrostatic pressure without relying on any knowledge of Newton’s gravitational constant, G. By measuring the pressure from a water column, we can determine the Planck length without requiring knowledge of either G or the Planck constant. This experiment is simple to perform and cost-effective, making it not only of interest to researchers studying gravity but also suitable for low-budget educational settings. Despite its simplicity, this has never been demonstrated to be possible before, and it is achievable due to new theoretical insights into gravity and its connection to quantum gravity and the Planck scale. This provides new insights into fluid mechanics and the Planck scale. We are also exploring initial concepts related to what we are calling “Planck fluid”, which could potentially play a central role in quantum gravity and quantum fluid mechanics.展开更多
This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixin...This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixing and their exact concentrations,which,when applied correctly,gives the desired color.The objective function and all constraints of the model are expressed linearly according to the solution variables.Carpet design has become an emerging technological field known for its creativity,science and technology.Many carpet design concepts have been analyzed in terms of color,contrast,brightness,as well as other mathematical concepts such as geometric changes and formulas.These concepts represent a common process in the carpet industry.This article discusses the use of complex fractal images in carpet design and simplex optimization in color selection.展开更多
文摘Generally Fibonacci series and Lucas series are the same, they converge to golden ratio. After I read Fibonacci series, I thought, is there or are there any series which converges to golden ratio. Because of that I explored the inter relations of Fibonacci series when I was intent on Fibonacci series in my difference parallelogram. In which, I found there is no degeneration on Fibonacci series. In my thought, Pascal triangle seemed like a lower triangular matrix, so I tried to find the inverse for that. In inverse form, there is no change against original form of Pascal elements matrix. One day I played with ring magnets, which forms hexagonal shapes. Number of rings which forms Hexagonal shape gives Hex series. In this paper, I give the general formula for generating various types of Fibonacci series and its non-degeneration, how Pascal elements maintain its identities and which shapes formed by hex numbers by difference and matrices.
文摘At the point of death,a human being only has had the experience of nonexistence before birth and the experience of having lived his/her life after they were born.In the final analysis from the perspective of strict empiricism,the individual only has two options:the nonexistence before birth or the eventual reliving of one’s life.The return of one’s life is supported by the paradigm of a multiverse and an antimatter universe.This is atheism’s logical certainty.
文摘Summetor is an operator used in the mathematics to calculate the special numbers like binomial coefficients and combinations of group elements. It has many applications in algebra, matrices like calculation of pascal triangle elements and pascal matrix formation, etc. This paper explains about its functions and properties of N-Summet-k. The result of variation between N and k is shown in tabulation.
基金projects UNLP 11N/689 and 790, CONICET PID 00688:Agencia Nacional PICT 0910/13 and PICT 1754/16the GIU17/033 (UPV/EHU) and CGL201782976-P (AEI/FEDER, UE) projects
文摘Finite volumes of magma moving in confinement, store hydraulic potential energy for the generation,control and transmission of power. The Pascal's principle in a hydraulic jack arrangement is used to model the vertical and lateral growth of sills. The small input piston of the hydraulic jack is equivalent to the feeder dike, the upper large expansible piston equivalent to the magmatic chamber and the inertial force of the magma in the dike is the input force. This arrangement is particularly relevant to the case of sills expanding with blunt tips, for which rapid fracture propagation is inhibited. Hydraulic models concur with experimental data that show that lateral expansion of magma into a sill is promoted when the vertical ascent of magma through a feeder dike reaches the bottom contact with an overlying, flat rigid-layer. At this point, the magma is forced to decelerate, triggering a pressure wave through the conduit caused by the continued ascent of magma further down(fluid-hammer effect). This pressure wave can provide overpressure enough to trigger the initial hydraulic lateral expansion of magma into an incipient sill, and still have enough input inertial force left to continue feeding the hydraulic system. The lateral expansion underneath the strong impeding layer, causes an area increase and thus, further hydraulic amplification of the input inertial force on the sides and roof of the incipient sill, triggering further expansion in a self-reinforcing process. Initially, the lateral pressure increase is larger than that in the roof allowing the sill to expand. However, expansion eventually increases the total integrated force on the roof allowing its uplift into either a laccolith, if the roof preserves continuity, or into a piston bounded by a circular set of fractures. Hydraulic models for shallow magmatic chambers, also suggest that laccolith-like intrusions require the existence of a self-supported chamber roof. In contrast, if the roof of magmatic chambers loses the self-supporting capacity, lopoliths and calderas should be expected for more or less dense magmas, respectively, owing to the growing influence of the density contrast between the host rock and the magma.
文摘We give a survey on the history, the main mathematical results and applications of the Mathematics of Harmony as a new interdisciplinary direction of modern science. In its origins, this direction goes back to Euclid’s “Elements”. According to “Proclus hypothesis”, the main goal of Euclid was to create a full geometric theory of Platonic solids, associated with the ancient conception of the “Universe Harmony”. We consider the main periods in the development of the “Mathematics of Harmony” and its main mathematical results: algorithmic measurement theory, number systems with irrational bases and their applications in computer science, the hyperbolic Fibonacci functions, following from Binet’s formulas, and the hyperbolic Fibonacci l-functions (l = 1, 2, 3, …), following from Gazale’s formulas, and their applications for hyperbolic geometry, in particular, for the solution of Hilbert’s Fourth Problem.
文摘After posing the axiom of linear algebra, the author develops how this allows the calculation of arbitrary base powers, which provides an instantaneous calculation of powers in a particular base such as base ten;first of all by developing the any base calculation of these powers, then by calculating triangles following the example of the “arithmetical” triangle of Pascal and showing how the formula of the binomial of Newton is driving the construction. The author also develops the consequences of the axiom of linear algebra for the decimal writing of numbers and the result that this provides for the calculation of infinite sums of the inverse of integers to successive powers. Then the implications of these new forms of calculation on calculator technologies, with in particular the storage of triangles which calculate powers in any base and the use of a multiplication table in a very large canonical base are discussed.
文摘We demonstrate how to extract the Planck length from hydrostatic pressure without relying on any knowledge of Newton’s gravitational constant, G. By measuring the pressure from a water column, we can determine the Planck length without requiring knowledge of either G or the Planck constant. This experiment is simple to perform and cost-effective, making it not only of interest to researchers studying gravity but also suitable for low-budget educational settings. Despite its simplicity, this has never been demonstrated to be possible before, and it is achievable due to new theoretical insights into gravity and its connection to quantum gravity and the Planck scale. This provides new insights into fluid mechanics and the Planck scale. We are also exploring initial concepts related to what we are calling “Planck fluid”, which could potentially play a central role in quantum gravity and quantum fluid mechanics.
文摘This article proposes a new approach based on linear programming optimization to solve the problem of determining the color of a complex fractal carpet pattern.The principle is aimed at finding suitable dyes for mixing and their exact concentrations,which,when applied correctly,gives the desired color.The objective function and all constraints of the model are expressed linearly according to the solution variables.Carpet design has become an emerging technological field known for its creativity,science and technology.Many carpet design concepts have been analyzed in terms of color,contrast,brightness,as well as other mathematical concepts such as geometric changes and formulas.These concepts represent a common process in the carpet industry.This article discusses the use of complex fractal images in carpet design and simplex optimization in color selection.
