Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-value...Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.展开更多
There has been protracted historical evidence of a relative paucity in the distribution frequency of global earthquakes within the M = 3.5 to 4.0 range. We observed a similar phenomenon for all recently recorded earth...There has been protracted historical evidence of a relative paucity in the distribution frequency of global earthquakes within the M = 3.5 to 4.0 range. We observed a similar phenomenon for all recently recorded earthquakes from January 2009 through August 2013. Frequency distributions with increments of M = 0.1 verified the trough of the diminished incidence to be between M = 3.6 and 3.7 with an abrupt increase between M = 3.9 and 4.0. The calculated equivalent photon wavelength for the energies associated with M = 3.6 approaches Planck’s Length while the related time increment is the cutoff frequency for the Zero Point Fluctuation force coupled to gravity. The conspicuous congruence between Planck’s time and length and the lower than expected frequency based upon Gaussian assumptions of distribution for the discrete band of energy associated with this magnitude range of earthquakes suggests a conduit may exist between intrinsic features of Planck space-time and geophysical processes. The existence of such a connection would encourage alternative explanations for sun-seismic activities as due to solar instabilities. Instead, it may reflect influence upon both from alterations in the structure of space being traversed by the solar system as it moves through the galaxy.展开更多
In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings fo...In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.展开更多
Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in ...Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.展开更多
We establish that ordinary energy, Casimir energy and dark energy are not only interlinked but are basically the same thing separated merely by scale and topology. Casimir energy is essentially a nano scale spacetime ...We establish that ordinary energy, Casimir energy and dark energy are not only interlinked but are basically the same thing separated merely by scale and topology. Casimir energy is essentially a nano scale spacetime phenomenon produced by the boundary condition of the two Casimir plates constituting the Casimir experimental set up for measuring the Casimir force. By contrast dark energy is the result of the cosmic boundary condition, i.e. the boundary of the universe. This one sided M?bius-like boundary located at vast cosmic distance and was comparable only to the Hubble radius scales of the universe. All the Casimir energy spreads out until the majority of it reaches the vicinity of the edge of the cosmos. According to a famous theorem due to the Ukrainian-Israeli scientist I. Dvoretzky, almost 96% of the total energy will be concentrated at the boundary of the universe, too far away to be measured directly. The rest of the accumulated Casimir energy density is consequently the nearly 4% to 4.5%, the existence of which is confirmed by various sophisticated cosmic measurements and observations. When all is said and done, the work is essentially yet another confirmation of Witten’s T-duality and mirror symmetry bringing nano scale and Hubble scale together in an unexpected magical yet mathematically rigorous way.展开更多
The pristine point of zero charge(p.p.z.c)and zeta potential as a function of pH of boehmite oxide/hydroxide(α-Al_(2)O_(3)·H_(2)O)have been determined for three filter media.The active component in the first two...The pristine point of zero charge(p.p.z.c)and zeta potential as a function of pH of boehmite oxide/hydroxide(α-Al_(2)O_(3)·H_(2)O)have been determined for three filter media.The active component in the first two filter media is boehmite nanofibers,only 2 nm in diameter and about 300 nm long.Boehmite nanofibers create high zeta potential(ζtrue≥46 mV)in aqueous solutions in the pH range of 3–8.The p.p.z.c.values were determined to be 11.60±0.15 for nanofibers grafted onto microglass fibers and 11.40±0.15 for agglomerated nanofibers.In the third filter media,a boehmite nanolayer in the form of monocrystalline oxide/hydroxide with a thickness of approximately 1.2 nm is electroadhesively deposited onto siliceous support material with large surface area of about 50 m^(2)/g,therefore forming a highly electropositive composite of boehmite nanolayer on the second highly electronegative solid.Boehmite’s oxide-hydroxide nanolayer surface creates high zeta potential(ζtrue≥50 mV)in aqueous solutions in the pH range of 3–8.The p.p.z.c.value was determined to be 11.38±0.15.The reported values are within accuracy,but they are much higher than the values reported in the literature.X-ray powder diffraction data were supplemented by microscopy,infrared spectroscopy in order to characterize fully synthetic boehmite surfaces.展开更多
文摘Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.
文摘There has been protracted historical evidence of a relative paucity in the distribution frequency of global earthquakes within the M = 3.5 to 4.0 range. We observed a similar phenomenon for all recently recorded earthquakes from January 2009 through August 2013. Frequency distributions with increments of M = 0.1 verified the trough of the diminished incidence to be between M = 3.6 and 3.7 with an abrupt increase between M = 3.9 and 4.0. The calculated equivalent photon wavelength for the energies associated with M = 3.6 approaches Planck’s Length while the related time increment is the cutoff frequency for the Zero Point Fluctuation force coupled to gravity. The conspicuous congruence between Planck’s time and length and the lower than expected frequency based upon Gaussian assumptions of distribution for the discrete band of energy associated with this magnitude range of earthquakes suggests a conduit may exist between intrinsic features of Planck space-time and geophysical processes. The existence of such a connection would encourage alternative explanations for sun-seismic activities as due to solar instabilities. Instead, it may reflect influence upon both from alterations in the structure of space being traversed by the solar system as it moves through the galaxy.
文摘In this paper, a new viewpoint of the division by zero z/0 = 0 in matrices is introduced and the results will show that the division by zero is our elementary and fundamental mathematics. New and practical meanings for many mathematical and physical formulas for the denominator zero cases may be given. Furthermore, a new space idea for the point at infinity for the Eucleadian plane is also introduced.
文摘Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.
文摘We establish that ordinary energy, Casimir energy and dark energy are not only interlinked but are basically the same thing separated merely by scale and topology. Casimir energy is essentially a nano scale spacetime phenomenon produced by the boundary condition of the two Casimir plates constituting the Casimir experimental set up for measuring the Casimir force. By contrast dark energy is the result of the cosmic boundary condition, i.e. the boundary of the universe. This one sided M?bius-like boundary located at vast cosmic distance and was comparable only to the Hubble radius scales of the universe. All the Casimir energy spreads out until the majority of it reaches the vicinity of the edge of the cosmos. According to a famous theorem due to the Ukrainian-Israeli scientist I. Dvoretzky, almost 96% of the total energy will be concentrated at the boundary of the universe, too far away to be measured directly. The rest of the accumulated Casimir energy density is consequently the nearly 4% to 4.5%, the existence of which is confirmed by various sophisticated cosmic measurements and observations. When all is said and done, the work is essentially yet another confirmation of Witten’s T-duality and mirror symmetry bringing nano scale and Hubble scale together in an unexpected magical yet mathematically rigorous way.
文摘The pristine point of zero charge(p.p.z.c)and zeta potential as a function of pH of boehmite oxide/hydroxide(α-Al_(2)O_(3)·H_(2)O)have been determined for three filter media.The active component in the first two filter media is boehmite nanofibers,only 2 nm in diameter and about 300 nm long.Boehmite nanofibers create high zeta potential(ζtrue≥46 mV)in aqueous solutions in the pH range of 3–8.The p.p.z.c.values were determined to be 11.60±0.15 for nanofibers grafted onto microglass fibers and 11.40±0.15 for agglomerated nanofibers.In the third filter media,a boehmite nanolayer in the form of monocrystalline oxide/hydroxide with a thickness of approximately 1.2 nm is electroadhesively deposited onto siliceous support material with large surface area of about 50 m^(2)/g,therefore forming a highly electropositive composite of boehmite nanolayer on the second highly electronegative solid.Boehmite’s oxide-hydroxide nanolayer surface creates high zeta potential(ζtrue≥50 mV)in aqueous solutions in the pH range of 3–8.The p.p.z.c.value was determined to be 11.38±0.15.The reported values are within accuracy,but they are much higher than the values reported in the literature.X-ray powder diffraction data were supplemented by microscopy,infrared spectroscopy in order to characterize fully synthetic boehmite surfaces.
