In this article, we prove certain isoperimetric inequalities for eigenvalues of Riesz potentials and show some applications of the results to a non-local boundary value problem of the Laplace operator.
Here the biquaternionic model of electro-gravimagnetic field (EGM-field) has been considered, which describes the change of EGM-fields, charges and currents in their interaction. The invariance of these equations with...Here the biquaternionic model of electro-gravimagnetic field (EGM-field) has been considered, which describes the change of EGM-fields, charges and currents in their interaction. The invariance of these equations with respect to the group of Poincare-Lorentz transformations has been proved. The relativistic formulae of transformation for density of electric and gravity-magnetic charges and currents, active power and forces have been obtained.展开更多
One the base of differential algebra of biquaternions, the one model of electro-gravimagnetic interactions of electric and gravimagnetic charges and currents has been constructed. For this, three Newton laws analogues...One the base of differential algebra of biquaternions, the one model of electro-gravimagnetic interactions of electric and gravimagnetic charges and currents has been constructed. For this, three Newton laws analogues are used. The closed system of biquaternionic wave equations is constructed for determination of the charges-currents and electro-gravimagnetic fields and united field of interactions. The equation of charge-current transformation is like the generalization of biquaternionic presentation of Dirac equation. The properties of its solutions are described, depending on properties of external EGM field. The biquaternions of energy-pulse of EGM-field and charges-currents are considered. The energy-pulse of EGM-interactions is calculated.展开更多
One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free...One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.展开更多
In the paper we study questions about solvability of some boundary value prob- lems for a non-homogenous poly-harmonic equation. As a boundary operator we consider differentiation operator of fractional order in Mille...In the paper we study questions about solvability of some boundary value prob- lems for a non-homogenous poly-harmonic equation. As a boundary operator we consider differentiation operator of fractional order in Miller-Ross sense. The considered problem is a generalization of well-known Dirichlet and Neumann problems.展开更多
On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the di...On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the direction of the unknown point. The requirement must be fulfilled: the distance from each point to an unknown point must be equal to the sum of the length of the segment outgoing from this point, and some increment, the same for all three segments. In the article, the conditions for the solvability of a geometric problem are established by the methods of spherical trigonometry and vector algebra. It is proved that when they are fulfilled, the problem is always solvable. The number of solutions is two, except in rare cases where there is only one solution. A solution method is presented. One of the practical applications is the problem of determining the time and location of a cloud-to-ground lightning discharge, which is directly reduced to this problem.展开更多
Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing el...Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing electro-gravimagnetic waves. The two classes of solutions of this biquaternionic wave equation have been investigated, generated by scalar potentials (pulsars) and vectorial potentials (spinors). Their asymptotic properties are considered, on the base of which they are classified into heavy (boson) and light (lepton) elementary particles. The biquaternion representation of the hydrogen atom is given. The periodic system of elements is produced, which is built on the principle of the musical structure of a simple gamma.展开更多
文摘In this article, we prove certain isoperimetric inequalities for eigenvalues of Riesz potentials and show some applications of the results to a non-local boundary value problem of the Laplace operator.
文摘Here the biquaternionic model of electro-gravimagnetic field (EGM-field) has been considered, which describes the change of EGM-fields, charges and currents in their interaction. The invariance of these equations with respect to the group of Poincare-Lorentz transformations has been proved. The relativistic formulae of transformation for density of electric and gravity-magnetic charges and currents, active power and forces have been obtained.
文摘One the base of differential algebra of biquaternions, the one model of electro-gravimagnetic interactions of electric and gravimagnetic charges and currents has been constructed. For this, three Newton laws analogues are used. The closed system of biquaternionic wave equations is constructed for determination of the charges-currents and electro-gravimagnetic fields and united field of interactions. The equation of charge-current transformation is like the generalization of biquaternionic presentation of Dirac equation. The properties of its solutions are described, depending on properties of external EGM field. The biquaternions of energy-pulse of EGM-field and charges-currents are considered. The energy-pulse of EGM-interactions is calculated.
文摘One the base of Maxwell and Dirac equations the one biquaternionic model of electro-gravimagnetic (EGM) fields is considered. The closed system of biquaternionic wave equations is constructed for determination of free system of electric and gravimagnetic charges and currents and generated by them EGM-field. By using generalized functions theory the fundamental and regular solutions of this system are determined and some of them are considered (spinors, plane waves, shock EGM-waves and others). The properties of these solutions are investigated.
基金financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan(0819/GF4)
文摘In the paper we study questions about solvability of some boundary value prob- lems for a non-homogenous poly-harmonic equation. As a boundary operator we consider differentiation operator of fractional order in Miller-Ross sense. The considered problem is a generalization of well-known Dirichlet and Neumann problems.
文摘On the unit sphere, the geometric problem of calculating the position of a point relative to three given points is considered. We know the length of three spherical segments that go out from the given points in the direction of the unknown point. The requirement must be fulfilled: the distance from each point to an unknown point must be equal to the sum of the length of the segment outgoing from this point, and some increment, the same for all three segments. In the article, the conditions for the solvability of a geometric problem are established by the methods of spherical trigonometry and vector algebra. It is proved that when they are fulfilled, the problem is always solvable. The number of solutions is two, except in rare cases where there is only one solution. A solution method is presented. One of the practical applications is the problem of determining the time and location of a cloud-to-ground lightning discharge, which is directly reduced to this problem.
文摘Private monochromatic solutions of the free-field equation of electro-gravimagnetic charges and currents are constructed in the differential algebra of biquaternions, which describe elementary particles as standing electro-gravimagnetic waves. The two classes of solutions of this biquaternionic wave equation have been investigated, generated by scalar potentials (pulsars) and vectorial potentials (spinors). Their asymptotic properties are considered, on the base of which they are classified into heavy (boson) and light (lepton) elementary particles. The biquaternion representation of the hydrogen atom is given. The periodic system of elements is produced, which is built on the principle of the musical structure of a simple gamma.
基金supported by FAPESP 2019/03655-4,CNPq 302980/2019-9,RFBR 20-01-00030,MTM2016-79661-P,AP08052405 of MES RK,FPU scholarship(Spain)FCT UIDB/00212/2020 and UIDP/00212/2020+1 种基金supported by the Austrian Science Foundation FWF,grant P 33811-N,by Agencia Estatal de Investigación(Spain),grant PID2020-115155GB-I00(European FEDER support included,UE)by Xunta de Galicia,grant ED431C 2019/10(European FEDER support included,UE).
文摘We give a classification of 5-and 6-dimensional complex one-generated nilpotent bicommutative algebras.
