Мурат Мамчуев - Academia.edu (original) (raw)

Papers by Мурат Мамчуев

Vestnik of Samara University. Natural Science Series, 2018

A study model of the drift-diffusion transport of charge carriers in the layers of fractal struct... more A study model of the drift-diffusion transport of charge carriers in the layers of fractal structure taking into account the process of recombination of charge carriers. In the closed form solutions are found model equations.

In this article, diffusion-wave equation with fractional derivative in Rieman- n-Liouville sense i... more In this article, diffusion-wave equation with fractional derivative in Rieman- n-Liouville sense is investigated. Integral operators with the Write function in the kernel associated with the investigational equation are introduced. In terms of these operators necessary non-local conditions binding traces of solution and its derivatives on the boundary of a rectangular domain are found. Necessary non-local conditions for the wave are obtained by using the limiting properties of Write function. By using the integral operator’s properties the theorem of existence and uniqueness of solution of the problem with integral Samarski’s condition for the diffusion-wave equation is proved. The solution is obtained in explicit form.

Дифференциальные уравнения, 2016

Дифференциальные уравнения, 2015

Дифференциальные уравнения, 2015

Дифференциальные уравнения, 2016

Differential Equations, 2016

Agradeço, em primeiro lugar, a Deus por ter sido meu companheiro incondicional e confidente em to... more Agradeço, em primeiro lugar, a Deus por ter sido meu companheiro incondicional e confidente em todos os momentos da minha vida. À minha esposa Naira, por seu amor e carinho, permanecendo ao meu lado durante todo esse tempo, sendo incontestavelmente minha companheira, aturandome e compreendendo meus defeitos, minhas faltas e, de qualquer forma, incondicionalmente acreditando em mim. À minha mãe, Amélia Augusta, por seu amor absoluto, por sua dedicação e seu carinho. Mulher batalhadora, de fibra e sempre de coração aberto para ajudar. Por mais que eu escreva, não vou conseguir traduzir em palavras tudo que sinto pela senhora. Muito obrigado. Ao meu pai, Douglas, que me ensinou a correr atrás da vida e procurar ser alguém. Sem dúvida seu exemplo, como homem, cidadão e pai, sempre será ímpar. Como o senhor sempre me disse: "Um homem de verdade nunca poderá morrer sem dizer que ao menos tentou alcançar seus objetivos, mesmo que falhe! Isso é ser homem de verdade!" Pois então, obrigado! À Duda (Maria Eduarda), minha amada filha que veio ao mundo no meio desta jornada. Não foi fácil deixar de acompanhar seus primeiros passos para me dedicar a este trabalho. Ao Lucas, meu enteado que incondicionalmente vive no meu coração. Espero que tenha lhe dado exemplos para seguir e construir um futuro maravilhoso. Ao meu orientador e amigo, Helvécio Rocha, profissional e pessoa que confiou em mim para o desenvolvimento deste trabalho. Suportou minhas ausências, minhas falhas, mas também soube me orientar para o êxito. Sem dúvida tinha que ser o Helvécio. À Lívia Prado, à Thaís Durli, ao Thiago Bandini pelo apoio e ajuda em todas as análises realizadas. Vocês foram excelentes. Aos amigos Vitor Luiz e Daniel Lacerda, que me ajudaram no início do trabalho. À Juliana Medeiros, chefe do Laboratório de Tecnologia Farmacêutica de Farmanguinhos, onde trabalho e tive a liberação para realizar todo o estudo.

Differential Equations, 2015

We study a second-order partial differential equation containing fractional derivatives with resp... more We study a second-order partial differential equation containing fractional derivatives with respect to one of the two independent variables. We construct a fundamental solution of this equation, analyze its properties, and derive a general representation of solutions in a rectangular domain. It follows from this representation that the presence of a lower fractional derivative in the equation may affect the well-posedness of initial and initial–boundary value problems.

Differential Equations, 2016

We study a mixed boundary value problem in the general setting for a system of Riemann–Liouville ... more We study a mixed boundary value problem in the general setting for a system of Riemann–Liouville fractional partial differential equations with constant matrix coefficients. By using a system of Volterra integral equations of the second kind, we reduce the problem to a special case for which the solution was earlier constructed in terms of the Green matrix. Existence and uniqueness theorems are proved for the problem in question.

Differential Equations, 2015

We give a well-posed statement of the initial value problem for a second-order parabolic equation... more We give a well-posed statement of the initial value problem for a second-order parabolic equation containing Riemann–Liouville fractional partial derivatives in one of the two independent variables. We prove existence and uniqueness theorems for the solution of this problem.

Differential Equations, 2010

Differential Equations, 2008

The relative importance of north-south migrations of the intertropical convergence zone (ITCZ) ve... more The relative importance of north-south migrations of the intertropical convergence zone (ITCZ) versus El niño-southern oscillation and its associated Pacific Walker Circulation (PWC) variability for past hydrological change in the western tropical Pacific is unclear. Here we show that north-south ITCZ migration was not the only mechanism of tropical Pacific hydrologic variability during the last millennium, and that PWC variability profoundly influenced tropical Pacific hydrology. We present hydrological reconstructions from Cattle Pond, Dongdao Island of the south China sea, where multi-decadal rainfall and downcore grain size variations are correlated to the southern oscillation Index during the instrumental era. our downcore grain size reconstructions indicate that this site received less precipitation during relatively warm periods, AD 1000-1400 and AD 1850-2000, compared with the cool period (AD 1400-1850). Including our new reconstructions in a synthesis of tropical Pacific records results in a spatial pattern of hydrologic variability that implicates the PWC.

Mathematical Notes, 2015

A system of two Riemann-Liouville partial differential equations with constant coefficients is st... more A system of two Riemann-Liouville partial differential equations with constant coefficients is studied. The existence and uniqueness theorem for the solution of the mixed problem is proved and its Green function is constructed.

Geometry & Graphics

It is known that squaring the circle (the problem consisting in construction of a square with the... more It is known that squaring the circle (the problem consisting in construction of a square with the same area as a given circle), together with duplication of cube and angle trisection, is one of the most famous unsolv able problems of constructive geometry for construction with compass and straightedge. The solution of squaring the circle problem is reduced to the straightening of the circle, that is, to the construction of a segment equal in length to the circle, and its insolvability is connected with the pi character transcendence. In this paper, the limiting case of one of Christian Huygens theorems, which establishes an estimate for length of circumference of a circle through perimeters of regular polygons inscribed in circle and circumscribed about it, is proved. On this basis has been proposed and justified an approximate method for squaring the circle problem solving, which allows consistently construct arbitrarily exact solutions of the problem. We will approximate an arc of...

Математические заметки, 2015

Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с произво... more Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с производными Римана-Лиувилля

Математические заметки, 2015

Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с произво... more Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с производными Римана-Лиувилля

— We give well-posed statements of the main initial–boundary value problems in a rectangular doma... more — We give well-posed statements of the main initial–boundary value problems in a rectangular domain and in a half-strip for a second-order parabolic equation that contains partial Riemann–Liouville fractional derivatives with respect to one of the two independent variables. We construct Green functions and representations of solutions of these problems. We prove existence and uniqueness theorems for the first boundary value problem and the problem in the half-strip with the boundary condition of the first kind.

— We study a mixed boundary value problem in the general setting for a system of Riemann–Liouvill... more — We study a mixed boundary value problem in the general setting for a system of Riemann–Liouville fractional partial differential equations with constant matrix coefficients. By using a system of Volterra integral equations of the second kind, we reduce the problem to a special case for which the solution was earlier constructed in terms of the Green matrix. Existence and uniqueness theorems are proved for the problem in question.

—We consider a system of Riemann–Liouville fractional partial differential equations with constan... more —We consider a system of Riemann–Liouville fractional partial differential equations with constant coefficients and obtain a general representation of solutions in a rectangular domain. The asymptotic behavior and other properties of the fundamental solution are studied.

Vestnik of Samara University. Natural Science Series, 2018

A study model of the drift-diffusion transport of charge carriers in the layers of fractal struct... more A study model of the drift-diffusion transport of charge carriers in the layers of fractal structure taking into account the process of recombination of charge carriers. In the closed form solutions are found model equations.

In this article, diffusion-wave equation with fractional derivative in Rieman- n-Liouville sense i... more In this article, diffusion-wave equation with fractional derivative in Rieman- n-Liouville sense is investigated. Integral operators with the Write function in the kernel associated with the investigational equation are introduced. In terms of these operators necessary non-local conditions binding traces of solution and its derivatives on the boundary of a rectangular domain are found. Necessary non-local conditions for the wave are obtained by using the limiting properties of Write function. By using the integral operator’s properties the theorem of existence and uniqueness of solution of the problem with integral Samarski’s condition for the diffusion-wave equation is proved. The solution is obtained in explicit form.

Дифференциальные уравнения, 2016

Дифференциальные уравнения, 2015

Дифференциальные уравнения, 2015

Дифференциальные уравнения, 2016

Differential Equations, 2016

Agradeço, em primeiro lugar, a Deus por ter sido meu companheiro incondicional e confidente em to... more Agradeço, em primeiro lugar, a Deus por ter sido meu companheiro incondicional e confidente em todos os momentos da minha vida. À minha esposa Naira, por seu amor e carinho, permanecendo ao meu lado durante todo esse tempo, sendo incontestavelmente minha companheira, aturandome e compreendendo meus defeitos, minhas faltas e, de qualquer forma, incondicionalmente acreditando em mim. À minha mãe, Amélia Augusta, por seu amor absoluto, por sua dedicação e seu carinho. Mulher batalhadora, de fibra e sempre de coração aberto para ajudar. Por mais que eu escreva, não vou conseguir traduzir em palavras tudo que sinto pela senhora. Muito obrigado. Ao meu pai, Douglas, que me ensinou a correr atrás da vida e procurar ser alguém. Sem dúvida seu exemplo, como homem, cidadão e pai, sempre será ímpar. Como o senhor sempre me disse: "Um homem de verdade nunca poderá morrer sem dizer que ao menos tentou alcançar seus objetivos, mesmo que falhe! Isso é ser homem de verdade!" Pois então, obrigado! À Duda (Maria Eduarda), minha amada filha que veio ao mundo no meio desta jornada. Não foi fácil deixar de acompanhar seus primeiros passos para me dedicar a este trabalho. Ao Lucas, meu enteado que incondicionalmente vive no meu coração. Espero que tenha lhe dado exemplos para seguir e construir um futuro maravilhoso. Ao meu orientador e amigo, Helvécio Rocha, profissional e pessoa que confiou em mim para o desenvolvimento deste trabalho. Suportou minhas ausências, minhas falhas, mas também soube me orientar para o êxito. Sem dúvida tinha que ser o Helvécio. À Lívia Prado, à Thaís Durli, ao Thiago Bandini pelo apoio e ajuda em todas as análises realizadas. Vocês foram excelentes. Aos amigos Vitor Luiz e Daniel Lacerda, que me ajudaram no início do trabalho. À Juliana Medeiros, chefe do Laboratório de Tecnologia Farmacêutica de Farmanguinhos, onde trabalho e tive a liberação para realizar todo o estudo.

Differential Equations, 2015

We study a second-order partial differential equation containing fractional derivatives with resp... more We study a second-order partial differential equation containing fractional derivatives with respect to one of the two independent variables. We construct a fundamental solution of this equation, analyze its properties, and derive a general representation of solutions in a rectangular domain. It follows from this representation that the presence of a lower fractional derivative in the equation may affect the well-posedness of initial and initial–boundary value problems.

Differential Equations, 2016

We study a mixed boundary value problem in the general setting for a system of Riemann–Liouville ... more We study a mixed boundary value problem in the general setting for a system of Riemann–Liouville fractional partial differential equations with constant matrix coefficients. By using a system of Volterra integral equations of the second kind, we reduce the problem to a special case for which the solution was earlier constructed in terms of the Green matrix. Existence and uniqueness theorems are proved for the problem in question.

Differential Equations, 2015

We give a well-posed statement of the initial value problem for a second-order parabolic equation... more We give a well-posed statement of the initial value problem for a second-order parabolic equation containing Riemann–Liouville fractional partial derivatives in one of the two independent variables. We prove existence and uniqueness theorems for the solution of this problem.

Differential Equations, 2010

Differential Equations, 2008

The relative importance of north-south migrations of the intertropical convergence zone (ITCZ) ve... more The relative importance of north-south migrations of the intertropical convergence zone (ITCZ) versus El niño-southern oscillation and its associated Pacific Walker Circulation (PWC) variability for past hydrological change in the western tropical Pacific is unclear. Here we show that north-south ITCZ migration was not the only mechanism of tropical Pacific hydrologic variability during the last millennium, and that PWC variability profoundly influenced tropical Pacific hydrology. We present hydrological reconstructions from Cattle Pond, Dongdao Island of the south China sea, where multi-decadal rainfall and downcore grain size variations are correlated to the southern oscillation Index during the instrumental era. our downcore grain size reconstructions indicate that this site received less precipitation during relatively warm periods, AD 1000-1400 and AD 1850-2000, compared with the cool period (AD 1400-1850). Including our new reconstructions in a synthesis of tropical Pacific records results in a spatial pattern of hydrologic variability that implicates the PWC.

Mathematical Notes, 2015

A system of two Riemann-Liouville partial differential equations with constant coefficients is st... more A system of two Riemann-Liouville partial differential equations with constant coefficients is studied. The existence and uniqueness theorem for the solution of the mixed problem is proved and its Green function is constructed.

Geometry & Graphics

It is known that squaring the circle (the problem consisting in construction of a square with the... more It is known that squaring the circle (the problem consisting in construction of a square with the same area as a given circle), together with duplication of cube and angle trisection, is one of the most famous unsolv able problems of constructive geometry for construction with compass and straightedge. The solution of squaring the circle problem is reduced to the straightening of the circle, that is, to the construction of a segment equal in length to the circle, and its insolvability is connected with the pi character transcendence. In this paper, the limiting case of one of Christian Huygens theorems, which establishes an estimate for length of circumference of a circle through perimeters of regular polygons inscribed in circle and circumscribed about it, is proved. On this basis has been proposed and justified an approximate method for squaring the circle problem solving, which allows consistently construct arbitrarily exact solutions of the problem. We will approximate an arc of...

Математические заметки, 2015

Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с произво... more Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с производными Римана-Лиувилля

Математические заметки, 2015

Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с произво... more Том 97 выпуск 3 март 2015 УДК 517.95 Смешанная задача для нагруженной системы уравнений с производными Римана-Лиувилля

— We give well-posed statements of the main initial–boundary value problems in a rectangular doma... more — We give well-posed statements of the main initial–boundary value problems in a rectangular domain and in a half-strip for a second-order parabolic equation that contains partial Riemann–Liouville fractional derivatives with respect to one of the two independent variables. We construct Green functions and representations of solutions of these problems. We prove existence and uniqueness theorems for the first boundary value problem and the problem in the half-strip with the boundary condition of the first kind.

— We study a mixed boundary value problem in the general setting for a system of Riemann–Liouvill... more — We study a mixed boundary value problem in the general setting for a system of Riemann–Liouville fractional partial differential equations with constant matrix coefficients. By using a system of Volterra integral equations of the second kind, we reduce the problem to a special case for which the solution was earlier constructed in terms of the Green matrix. Existence and uniqueness theorems are proved for the problem in question.

—We consider a system of Riemann–Liouville fractional partial differential equations with constan... more —We consider a system of Riemann–Liouville fractional partial differential equations with constant coefficients and obtain a general representation of solutions in a rectangular domain. The asymptotic behavior and other properties of the fundamental solution are studied.