39 research outputs found
Note on K0-group and C*p-algebras
No full textDepartment of Mathematics
College of Science and Medical Studies
King Saud University
P. O. Box 22452
Riyadh 11495, Saudi ArabiaThe K0-group for unital C*p –algebra is defined. Then it is proven that the K0 -group of unital commutative C∗p-algebra (A, ||.|| p ) is
isomorphic to the K0-group of the commutative unital C*p –algebra ( (A, ||.|| p)1 p ). The concept of n-special C*p –algebra was introduced by Azmi in [2]. Let A be an n-special C*p –algebra then the characterization of these algebras as in [2] leads to a surjective group homomorphism from K0(A) to Z, which turns into isomorphism when A is a special C*p –algebr
Blow-up of solutions to parabolic inequalities in the Heisenberg group
No full textWe establish a Fujita-type theorem for the blow-up of nonnegative solutions to
a certain class of parabolic inequalities in the Heisenberg group.
Our proof is based on a duality argument
Nonexistence of global solutions for fractional temporal Schrödinger equations and systems
No full textWe, first, consider the nonlinear Schrödinger equation
iαC0 Dαtu + ∆u = λ|u|p + μα(x) ‧ ∇|u|q, t > 0, x ∈ ℝN,
where 0 < α < 1, iα is the principal value of iα, C0 Dαt is the Caputo fractional derivative of order α, λ ∈ ℂ\ {0}, μ ∈ ℂ, p > q > 1, u(t, x) is a complex-valued function, and α : ℝN → ℝN is a given vector function. We provide sufficient conditions for the nonexistence of global weak solution under suitable initial data. Next, we extend our study to the system of nonlinear coupled equations
iαC0 Dαtu + ∆u = λ|v|p> + μα(x) ‧ ∇|v|q, t > 0, x ∈ ℝN,
iβC0 Dβtv + ∆v = λ|u|k + μb(x) ‧ ∇|u|σ, t > 0, x ∈ ℝN,
where 0 < β ≤ α < 1, λ ∈ ℂ\{0}, μ ∈ ℂ, p > q > 1, k > σ > 1, and α, b : ℝN → ℝN are two given vector functions. Our approach is based on the test function method.Mathematic
Geospatial Analysis for the Determination of Hydro-Morphological Characteristics and Assessment of Flash Flood Potentiality in Arid Coastal Plains: A Case in Southwestern Sinai, Egypt
No full textCoastal plains with a unique geographic setting and renewable natural resources are promising for sustainable development; however, these areas may be subjected to some environmental hazards due to their geological setting. One of those hazards is the seasonal flash flood that can threaten existing and future development projects in such critical areas. Southwestern Sinai, Egypt, is a coastal plain that is characterized by complex geological setting an arid climate with seasonal rainfall which can result in a high runoff. The aim of this work is to model spatially the runoff amount and density related to flash flood development and to create a flash flood hazard map of the plain as an example of coastal plain in a desert environment with large and complex hydrologic setting. In this research, ASTER images are used to develop a digital elevation model (DEM) and land use/land cover (LULC) data sets of the study area. Geographic information system (GIS) was used to perform runoff and ash potential flood analyses of the created databases and to show distributed runoff and flooding potential in spatial maps. A module was created in a GIS environment to develop a flash flood potential index map. It was clear that the main two factors controlling runoff amounts and flash flood potential in such kinds of areas are the slope and soil types. The final dataset map procedure by this work can be very helpful in land use planning by highlighting the areas subjected to flash floods.
Análisis Geoespacial para Determinar las Características Hidromorfológicas y Evaluar las Inundaciones Potenciales en Llanuras Costeras Áridas: Caso de Estudio en el Suroccidente de Sinaí, Egipto
Resumen
Las llanuras costeras que poseen recursos naturales renovables y una configuración geográfíca única son promisorias para el desarrollo sostenible. Estas áreas, sin embargo, son objeto de algunas amenazas ambientales debido a su escenario geológico. Una de estas amenazas es la temporada de inundaciones rápidas que pueden poner en riesgo los proyectos de desarrollo existentes y los futuros en estas zonas críticas. El suroccidente de Sinaí, Egipto, es una llanura costera que se caracteriza por su compleja configuración geológica de clima árido, con temporadas de lluvia que pueden resultar en una gran escorrentía. El objetivo de este trabajo fue modelar espacialmente la cantidad y densidad de escorrentía relacionada al desarrollo de inundaciones rápidas y elaborar un mapa de amenazas de inundación rápida en este valle, como un ejemplo de llanura costera en un ambiente desértico con un escenario hidrológico grande y complejo. En este trabajo se utilizaron imágenes ASTER para desarrollar un Modelo de Elevación Digital (DEM, en inglés) y establecer la información de uso del suelo/cobertura del suelo (LULC, en inglés) en el área de estudio. A partir del Sistema de Información Geográfica (GIS) se analizaron la escorrentía y el potencial de inundación de las bases de datos creadas, y se mostró la escorrentía y el potencial de inundación en mapas espaciales. Se creó un módulo en un ambiente del GIS para desarrollar un mapa del índice inundación rápida potencial. Se estableció que los dos factores que controlan la cantidad de escorrentía y el potencial de inundaciones rápidas en estas áreas son la inclinación y los tipos de suelo. El mapa final de procemiento con el conjunto de datos de este trabajo es de gran ayuda en la planeación del uso de suelos, ya que evidencia las áreas con posibilidad de inundaciones rápidas
Nonexistence of global solutions for fractional temporal Schrodinger equations and systems
No full textWe, first, consider the nonlinear Schrodinger equation
where 0<\alpha lt;1, is the principal value of
, is the Caputo fractional derivative of
order , , ,
, is a complex-valued function, and
is a given vector function.
We provide sufficient conditions for the nonexistence of global weak solution
under suitable initial data. Next, we extend our study to the system of nonlinear
coupled equations
\displaylines{
i^\alpha {}_0^C D_t^\alpha u+\Delta u
= \lambda |v|^p+\mu a(x)\cdot\nabla |v|^q,
\quad t>0,\;x\in \mathbb{R}^N,\cr
i^\beta {}_0^C D_t^\beta v+\Delta v
= \lambda |u|^\kappa+\mu b(x)\cdot\nabla |u|^\sigma,
\quad t>0,\; x\in \mathbb{R}^N,
}
where , ,
, , , and
are two given vector functions.
Our approach is based on the test function method
REDUCTTON OF SO4-AND Cl-IONS FROM INDUSTRIAL WASTE WATER BY ION EXCHANGE
No full text This rvork was conduuted to study the removal of ionic irnpurities from industrial wastewater, and more particularly those in the cotton textile industry. The wastewater considered here, contains both cation and anion impurities. The method used is ion exchange. The results showed that the equilibrium isotherm is strongly favorable type, and it fitted well with Langrnuir equation. Chlorine and Sulphate ions were reduced greatly but not with the same degree ( SOa- > Cl - ).
