Existence of a solid solution from brucite to {beta}-Co(OH){sub 2}
Giovannelli, F., E-mail: fabien.giovannelli@univ-tours.fr [LEMA, UMR 6157 CNRS - CEA, Universite Francois Rabelais, 15 rue de la chocolaterie, 41000 Blois (France); Delorme, F.; Autret-Lambert, C. [LEMA, UMR 6157 CNRS - CEA, Universite Francois Rabelais, 15 rue de la chocolaterie, 41000 Blois (France); Seron, A.; Jean-Prost, V. [BRGM, 3 Avenue Claude Guillemin, BP 36009, 45060 Orleans Cedex 2 (France)
2012-05-15
Highlights: Black-Right-Pointing-Pointer A solid solution exist between Mg(OH){sub 2} and {beta}-Co(OH){sub 2}. Black-Right-Pointing-Pointer Synthesis has been performed through an easy and fast coprecipitation route. Black-Right-Pointing-Pointer No long range-ordering of the cations occurs. -- Abstract: This study shows that between brucite (Mg(OH){sub 2}) and {beta}-Co(OH){sub 2}, all the compositions are possible. The solid solution Mg{sub 1-x}Co{sub x}(OH){sub 2} has been synthesized by an easy and fast coprecipitation route and characterized by XRD and TEM. Single phase powders have been obtained. The particles exhibit platelets morphology with a size close to one hundred nanometers. XRD analysis shows an evolution of the cell parameters when x increases and demonstrates that no ordering of the cations occurs. However, extra reflections on TEM electron diffraction patterns seem to indicate that local ordering can exist. The compounds issued from this solid solution could be good candidates as precursors in order to obtain Mg-Co mixed oxide with all possible cationic ratios.
Co-existence of Distinct Supramolecular Assemblies in Solution and in the Solid State.
Reddy, G N Manjunatha; Huqi, Aida; Iuga, Dinu; Sakurai, Satoshi; Marsh, Andrew; Davis, Jeffery T; Masiero, Stefano; Brown, Steven P
2017-02-16
The formation of distinct supramolecular assemblies, including a metastable species, is revealed for a lipophilic guanosine (G) derivative in solution and in the solid state. Structurally different G-quartet-based assemblies are formed in chloroform depending on the nature of the cation, anion and the salt concentration, as characterized by circular dichroism and time course diffusion-ordered NMR spectroscopy data. Intriguingly, even the presence of potassium ions that stabilize G-quartets in chloroform was insufficient to exclusively retain such assemblies in the solid state, leading to the formation of mixed quartet and ribbon-like assemblies as revealed by fast magic-angle spinning (MAS) NMR spectroscopy. Distinct N-H⋅⋅⋅N and N-H⋅⋅⋅O intermolecular hydrogen bonding interactions drive quartet and ribbon-like self-assembly resulting in markedly different 2D (1) H solid-state NMR spectra, thus facilitating a direct identification of mixed assemblies. A dissolution NMR experiment confirmed that the quartet and ribbon interconversion is reversible-further demonstrating the changes that occur in the self-assembly process of a lipophilic nucleoside upon a solid-state to solution-state transition and vice versa. A systematic study for complexation with different cations (K(+) , Sr(2+) ) and anions (picrate, ethanoate and iodide) emphasizes that the existence of a stable solution or solid-state structure may not reflect the stability of the same supramolecular entity in another phase. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Existence of noncontinuable solutions
Miroslav Bartusek
2007-02-01
Full Text Available This paper presents necessary and sufficient conditions for an n-th order differential equation to have a non-continuable solution with finite limits of its derivatives up to the orders n-2 at the right-hand end point of the definition interval.
Growth of Solid Solution Crystals
Lehoczky, S. L.; Szofran, F. R.; Holland, L. R.
1985-01-01
The major objective of this program is to determine the conditions under which single crystals of solid solutions can be grown from the melt in a Bridgman configuration with a high degree of chemical homogeneity. The central aim is to assess the role of gravity in the growth process and to explore the possible advantages for growth in the absence of gravity. The alloy system being investigated is the solid solution semiconductor with x-values appropriate for infrared detector applications in Hg sub (1-x) Cd sub x Te the 8 to 14 micro m wavelength region. Both melt and Te-solvent growth are being considered. The study consists of an extensive ground-based experimental and theoretical research effort followed by flight experimentation where appropriate. Experimental facilities have been established for the purification, casting, and crystal growth of the alloy system. Facilities have been also established for the metallurgical, compositional, electric and optical characterization of the alloys. Crystals are being grown by the Bridgman-Stockbarger method and are analyzed by various experimental techniques to evaluate the effects of growth conditions on the longitudinal and radial compositional variations and defect densities in the crystals.
Existence of solutions for a nonlinear degenerate elliptic system
Nguyen Minh
2004-07-01
Full Text Available In this paper, we study the existence of solutions for degenerate elliptic systems. We use the sub-super solution method, and the existence of classical and weak solutions. Some sub-supersolutions are constructed explicitly, when the nonlinearities have critical or supercritical growth.
Existence of Solution for Fractional Differential Problem with a Parameter
Shi Ai-ling; Zhang Shu-qin
2014-01-01
We apply the method of lower and upper solutions combined with mono-tone iterations to fractional differential problem with a parameter. The existence of minimal and maximal solutions is proved for the fractional differential problem with a parameter.
Existence of extremal periodic solutions for quasilinear parabolic equations
Siegfried Carl
1997-01-01
bounded domain under periodic Dirichlet boundary conditions. Our main goal is to prove the existence of extremal solutions among all solutions lying in a sector formed by appropriately defined upper and lower solutions. The main tools used in the proof of our result are recently obtained abstract results on nonlinear evolution equations, comparison and truncation techniques and suitably constructed special testfunction.
Existence of solutions to nonlinear Hammerstein integral equations and applications
Li, Fuyi; Li, Yuhua; Liang, Zhanping
2006-11-01
In this paper, we study the existence and multiplicity of solutions of the operator equation Kfu=u in the real Hilbert space L2(G). Under certain conditions on the linear operator K, we establish the conditions on f which are able to guarantee that the operator equation has at least one solution, a unique solution, and infinitely many solutions, respectively. The monotone operator principle and the critical point theory are employed to discuss this problem, respectively. In argument, quadratic root operator K1/2 and its properties play an important role. As an application, we investigate the existence and multiplicity of solutions to fourth-order boundary value problems for ordinary differential equations with two parameters, and give some new existence results of solutions.
Solution-solid-solid mechanism: superionic conductors catalyze nanowire growth.
Wang, Junli; Chen, Kangmin; Gong, Ming; Xu, Bin; Yang, Qing
2013-09-11
The catalytic mechanism offers an efficient tool to produce crystalline semiconductor nanowires, in which the choice, state, and structure of catalysts are active research issues of much interest. Here we report a novel solution-solid-solid (SSS) mechanism for nanowire growth catalyzed by solid-phase superionic conductor nanocrystals in low-temperature solution. The preparation of Ag2Se-catalyzed ZnSe nanowires at 100-210 °C is exampled to elucidate the SSS model, which can be extendable to grow other II-VI semiconductor (e.g., CdSe, ZnS, and CdS) nanowires by the catalysis of nanoscale superionic-phase silver or copper(I) chalcogenides (Ag2Se, Ag2S, and Cu2S). The exceptional catalytic ability of these superionic conductors originates from their structure characteristics, known for high-density vacancies and fast mobility of silver or copper(I) cations in the rigid sublattice of Se(2-) or S(2-) ions. Insights into the SSS mechanism are provided based on the formation of solid solution and the solid-state ion diffusion/transport at solid-solid interface between catalyst and nanowire.
Existence and uniqueness of positive solutions of semilinear elliptic equations
2007-01-01
This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.
Existence and uniqueness of positive solutions of semilinear elliptic equations
Qiu-yi DAI; Yu-xia FU; Yong-geng GU
2007-01-01
This paper is devoted to the study of existence, uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations. A necessary and sufficient condition for the existence of positive solutions to problems is given. We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations, then they are still valid when one perturbs the differential operator a little bit. As consequences, some uniqueness results of positive solutions under the domain perturbation are also obtained.
Local Existence of Smooth Solutions to the FENE Dumbbell Model
Ge YANG
2012-01-01
The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b ＞ 2.
EXISTENCE OF POSITIVE SOLUTION TO A p-LAPLACIAN SYSTEM
无
2009-01-01
A p-Laplacian system with Dirichlet boundary conditions is investigated. By the fibering method introduced by Pohozaev,we discuss the existence of positive weak solutions to the system under some proper conditions.
Existence and Uniqueness of Solutions to Random Impulsive Differential Systems
Shu-jin Wu; Xiao-lin Guo; Song-qing Lin
2006-01-01
The existence and uniqueness in mean square of solutions to certain random impulsive differential systems is discussed in this paper. Cauchy-Schwarz inequality, Lipschtiz condition and techniques in stochastic analysis are employed in achieve the desired results.
Existence of solutions to fractional Hamiltonian systems with combined nonlinearities
Ziheng Zhang
2016-01-01
Full Text Available This article concerns the existence of solutions for the fractional Hamiltonian system $$\\displaylines{ - _tD^{\\alpha}_{\\infty}\\big(_{-\\infty}D^{\\alpha}_{t}u(t\\big -L(tu(t+\
Existence of solutions for elliptic systems with critical Sobolev exponent
Pablo Amster
2002-06-01
Full Text Available We establish conditions for existence and for nonexistence of nontrivial solutions to an elliptic system of partial differential equations. This system is of gradient type and has a nonlinearity with critical growth.
Existence of Weak Solutions for a Nonlinear Elliptic System
Gilbert RobertP
2009-01-01
Full Text Available We investigate the existence of weak solutions to the following Dirichlet boundary value problem, which occurs when modeling an injection molding process with a partial slip condition on the boundary. We have in ; in ; , and on .
Radionuclide solubility control by solid solutions
Brandt, F.; Klinkenberg, M.; Rozov, K.; Bosbach, D. [Forschungszentrum Juelich GmbH (Germany). Inst. of Energy and Climate Research - Nuclear Waste Management and Reactor Safety (IEK-6); Vinograd, V. [Frankfurt Univ. (Germany). Inst. of Geosciences
2015-07-01
The migration of radionuclides in the geosphere is to a large extend controlled by sorption processes onto minerals and colloids. On a molecular level, sorption phenomena involve surface complexation, ion exchange as well as solid solution formation. The formation of solid solutions leads to the structural incorporation of radionuclides in a host structure. Such solid solutions are ubiquitous in natural systems - most minerals in nature are atomistic mixtures of elements rather than pure compounds because their formation leads to a thermodynamically more stable situation compared to the formation of pure compounds. However, due to a lack of reliable data for the expected scenario at close-to equilibrium conditions, solid solution systems have so far not been considered in long-term safety assessments for nuclear waste repositories. In recent years, various solid-solution aqueous solution systems have been studied. Here we present state-of-the art results regarding the formation of (Ra,Ba)SO{sub 4} solid solutions. In some scenarios describing a waste repository system for spent nuclear fuel in crystalline rocks {sup 226}Ra dominates the radiological impact to the environment associated with the potential release of radionuclides from the repository in the future. The solubility of Ra in equilibrium with (Ra,Ba)SO{sub 4} is much lower than the one calculated with RaSO{sub 4} as solubility limiting phase. Especially, the available literature data for the interaction parameter W{sub BaRa}, which describes the non-ideality of the solid solution, vary by about one order of magnitude (Zhu, 2004; Curti et al., 2010). The final {sup 226}Ra concentration in this system is extremely sensitive to the amount of barite, the difference in the solubility products of the end-member phases, and the degree of non-ideality of the solid solution phase. Here, we have enhanced the fundamental understanding regarding (1) the thermodynamics of (Ra,Ba)SO{sub 4} solid solutions and (2) the
The theorem on existence of singular solutions to nonlinear equations
Prusinska А.
2005-01-01
Full Text Available The aim of this paper is to present some applications of pregularity theory to investigations of nonlinear multivalued mappings. The main result addresses to the problem of existence of solutions to nonlinear equations in the degenerate case when the linear part is singular at the considered initial point. We formulate conditions for existence of solutions of equation F(x = 0 when first p - 1 derivatives of F are singular.
Existence of solutions to quasilinear Schrodinger equations with indefinite potential
Zupei Shen
2015-04-01
Full Text Available In this article, we study the existence and multiplicity of solutions of the quasilinear Schrodinger equation $$ -u''+V(xu-(|u| ^2''u=f(u $$ on $\\mathbb{R}$, where the potential $V$ allows sign changing and the nonlinearity satisfies conditions weaker than the classical Ambrosetti-Rabinowitz condition. By a local linking theorem and the fountain theorem, we obtain the existence and multiplicity of solutions for the equation.
The Existence of Homoclinic Solutions for Second Order Hamiltonian System
Jie Gao
2011-10-01
Full Text Available The research of homoclinic orbits for Hamiltonian system is a classical problem, it has valuable applications in celestial mechanics, plasma physis, and biological engineering. For example, homoclinic orbits rupture can yield chaos lead to more complex dynamics behaviour. This paper studies the existence of homoclinic solutions for a class of second order Hamiltonian system, we will prove this system exists at least one nontrivial homoclinic solution.
Computer simulation of concentrated solid solution strengthening
Kuo, C. T. K.; Arsenault, R. J.
1976-01-01
The interaction forces between a straight edge dislocation moving through a three-dimensional block containing a random array of solute atoms were determined. The yield stress at 0 K was obtained by determining the average maximum solute-dislocation interaction force that is encountered by edge dislocation, and an expression relating the yield stress to the length of the dislocation and the solute concentration is provided. The magnitude of the solid solution strengthening due to solute atoms can be determined directly from the numerical results, provided the dislocation line length that moves as a unit is specified.
Existence of two nontrivial solutions for semilinear elliptic problems
Abdel R. El Amrouss
2006-09-01
Full Text Available This paper concerns the existence of multiple nontrivial solutions for some nonlinear problems. The first nontrivial solution is found using a minimax method, and the second by computing the Leray-Schauder index and the critical group near 0.
Existence theorems of solution to variational inequality problems
无
2001-01-01
This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for the existence of a solution to the problem. This condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. Sufficient solution conditions for a class of nonlinear complementarity problems with P0 mappings are also obtained.
Existence and Uniqueness of Solution to ODEs: Lipschitz Continuity
Swarup Poria; Aman Dhiman
2017-05-01
The study of existence and uniqueness of solution of ordinarydifferential equation (ODE) became important due to the lack ofgeneral formula for solving nonlinear ODEs. In this article, weshall discuss briefly about the existence and uniqueness of solutionof a first order ODE. A special emphasis is given on theLipschitz continuous functions in the discussion.
Synthesis of solid solutions of perovskites
Dambekalne, M.Y.; Antonova, M.K.; Perro, I.T.; Plaude, A.V.
1986-03-01
The authors carry out thermographic studies, using a derivatograph, in order to understand the nature of the processes taking place during the synthesis of solid solutions of perovskites. Based on the detailed studies on the phase transformations occurring in the charges of the PSN-PMN solid solutions and on the selection of the optimum conditions for carrying out their synthesis, the authors obtained a powder containing a minimum quantity of the undesirable pyrochlore phase and by sintering it using the hot pressing method, they produced single phase ceramic specimens containing the perovskite phase alone with a density close to the theoretical value and showing zero apparent porosity and water absorption.
Solid-solution thermodynamics in Al-Li alloys
Alekseev, A. A.; Lukina, E. A.
2016-05-01
The relative equilibrium concentrations of lithium atoms distributed over different electron-structural states has been estimated. The possibility of the existence of various nonequilibrium electron-structural states of Li atoms in the solid solution in Al has been substantiated thermodynamically. Upon the decomposition of the supersaturated solid solution, the supersaturation on three electron-structural states of Li atoms that arises upon the quenching of the alloy can lead to the formation of lithium-containing phases in which the lithium atoms enter in one electron-structural state.
Existence of bounded positive solutions of a nonlinear differential system
Sabrine Gontara
2012-04-01
Full Text Available In this article, we study the existence and nonexistence of solutions for the system $$displaylines{ frac{1}{A}(Au''=pu^{alpha }v^{s}quad hbox{on }(0,infty , cr frac{1}{B}(Bu''=qu^{r}v^{eta }quad hbox{on }(0,infty , cr Au'(0=0,quad u(infty =a>0, cr Bv'(0=0,quad v(infty =b>0, }$$ where $alpha ,eta geq 1$, $s,rgeq 0$, p,q are two nonnegative functions on $(0,infty $ and A, B satisfy appropriate conditions. Using potential theory tools, we show the existence of a positive continuous solution. This allows us to prove the existence of entire positive radial solutions for some elliptic systems.
Existence of Weak Solutions for the Incompressible Euler Equations
Wiedemann, Emil
2011-01-01
Using a recent result of C. De Lellis and L. Sz\\'{e}kelyhidi Jr. we show that, in the case of periodic boundary conditions and for dimension greater or equal 2, there exist infinitely many global weak solutions to the incompressible Euler equations with initial data $v_0$, where $v_0$ may be any solenoidal $L^2$-vectorfield. In addition, the energy of these solutions is bounded in time.
THE EXISTENCE AND THE NON-EXISTENCE OF GLOBAL SOLUTIONS OF A FREE BOUNDARY PROBLEM
Yin Rong; Yu Wanghui
2004-01-01
We study a free boundary problem of parabolic equations with a pos-itive parameter τ included in the coefficient of the derivative with respect to the timevariable t. This problem arises from some reaction-diffusion system. We prove that, ifτ is large enough, the solution exists for 0 ＜ t ＜ +∞; while, if τ is small enough, thesolution exists only in finite time.
Existence of solutions of abstract fractional impulsive semilinear evolution equations
K. Balachandran
2010-01-01
Full Text Available In this paper we prove the existence of solutions of fractional impulsive semilinear evolution equations in Banach spaces. A nonlocal Cauchy problem is discussed for the evolution equations. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the theory.
Solutions of fractional nabla difference equations - existence and uniqueness
Jagan Mohan Jonnalagadda
2016-01-01
Full Text Available In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.
Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations
N'Guérékata GastonM
2010-01-01
Full Text Available We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations , , , in a Banach space , where . New results are obtained by fixed point theorem. An application of the abstract results is also given.
Existence of solutions for neutral functional integrodifferential equations
R. Murugesu
2010-06-01
Full Text Available In this paper, by using fractional power of operators and Sadovskii's fixed point theorem, we study the existence of mild and strong solutions of nonlinear neutral functional integrodifferential equations. The results we obtained are a generalization and continuation of the recent results on this issue.
Existence of Three Solutions for $p$-biharmonic Equation
Lin Li
2011-10-01
Full Text Available In this paper, the existence of at least three solutions to a Navier boundary problem involving the $p$-biharmonic equation, will be established. The technical approach is mainly based on the three critical points theorem of B. Ricceri.
EXISTENCE OF SOLUTIONS OF NONLINEAR FRACTIONAL PANTOGRAPH EQUATIONS
K. BALACHANDRAN; S. KIRUTHIKA; J.J. TRUJILLO
2013-01-01
This article deals with the existence of solutions of nonlinear fractional pantograph equations.Such model can be considered suitable to be applied when the corresponding process occurs through strongly anomalous media.The results are obtained using fractional calculus and fixed point theorems.An example is provided to illustrate the main result obtained in this article.
Existence and regularity of positive solutions for an elliptic system
Abdelouahed El Khalil
2002-12-01
Full Text Available In this paper, we study the existence and regularity of positive solution for an elliptic system on a bounded and regular domain. The non linearities in this equation are functions of Caratheodory type satisfying some exponential growth conditions.
On existence and uniqueness of solutions for variational data assimilation
Bröcker, Jochen
2017-04-01
Data assimilation is a term from the geosciences and refers to methods for estimating orbits of dynamical models from observations. Variational techniques for data assimilation estimate these orbits by minimising an appropriate cost functional which takes the error with respect to the observations but also deviations of the orbits from the model equations into account. Such techniques are very important in practice. In this contribution, the problem of existence and uniqueness of solutions to variational data assimilation is investigated. Under mild hypotheses a solution to this problem exists. The problem of uniqueness is investigated as well, and several results (which all have analogues in optimal control) are established in the present context. The value function is introduced as the cost of an optimal trajectory starting from a given initial condition. The necessary conditions in combination with an envelope theorem can be used to demonstrate that the solution is unique if and only if the value function is differentiable at the given initial condition. This occurs for all initial conditions except maybe on a set of Lebesgue measure zero. Several examples are studied which demonstrate that non-uniqueness of solutions cannot be ruled out altogether though, which has important consequences in practice. References: J. Bröcker, "Existence and Uniqueness For Four Dimensional Variational Data Assimilation in Discrete Time.", SIAM Journal of Applied Dynamical Systems (accepted).
Existence of solutions for the dynamic equation of ferrimagnets
无
2007-01-01
Ferrimagnet is a kind of basic and important multi-sublattice magnet material. It has attracted more and more attention of physicists and mathematicians. Many results of solitons and numerical computations on this topic have appeared. In this article, the dynamic equation for an isotropic ferrimagnet with two non-equivalent sublattices is studied, existence of weak solutions in multi dimension case is proved through the penalized method, the uniqueness and smoothness of the solution in one dimension case are also obtained by the relation between this equation and hyperbolic equation.
Existence and multiplicity of solutions for nonlinear discrete inclusions
Nicu Marcu
2012-11-01
Full Text Available A non-smooth abstract result is used for proving the existence of at least one nontrivial solution of an algebraic discrete inclusion. Successively, a multiplicity theorem for the same class of discrete problems is also established by using a locally Lipschitz continuous version of the famous Brezis-Nirenberg theoretical result in presence of splitting. Some applications to tridiagonal, fourth-order and partial difference inclusions are pointed out.
Global Existence of Solutions for Stochastic Impulsive Differential Equations
Li Juan SHEN; Ji Tao SUN
2011-01-01
In this paper we obtain some results on the global existence of solution to It(o) stochastic impulsive differential equations in M([0, ∞),Rn) which denotes the family of Rn-valued stochastic processes x satisfying supt∈[0,∞) E|x(t)|2 ＜∞ under non-Lipschitz coefficients. The Schaefer fixed point theorem is employed to achieve the desired result. An example is provided to illustrate the obtained results.
Existence and Uniqueness of Mild Solution for Fractional Integrodifferential Equations
Fang Li
2010-01-01
Full Text Available We study the existence and uniqueness of mild solution of a class of nonlinear fractional integrodifferential equations dqu(t/dtq+Au(t=f(t,u(t+∫0ta(t−sg(s,u(sds, t∈[0,T], u(0=u0, in a Banach space X, where 0
Existence of positive solutions for a nonlinear fractional differential equation
Habib Maagli
2013-01-01
Full Text Available Using the Schauder fixed point theorem, we prove an existence of positive solutions for the fractional differential problem in the half line $mathbb{R}^+=(0,infty$: $$ D^{alpha}u=f(x,u,quad lim_{x o 0^+}u(x=0, $$ where $alpha in (1,2]$ and $f$ is a Borel measurable function in $mathbb{R}^+imes mathbb{R}^+$ satisfying some appropriate conditions.
Magnetic clusters in ilmenite-hematite solid solutions
Frandsen, Cathrine; Burton, B. P.; Rasmussen, Helge Kildahl;
2010-01-01
We report the use of high-field 57Fe Mössbauer spectroscopy to resolve the magnetic ordering of ilmenite-hematite [xFeTiO3−(1−x)Fe2O3] solid solutions with x>0.5. We find that nanometer-sized hematite clusters exist within an ilmenite-like matrix. Although both phases are antiferromagnetically or...
Existence and non-existence of solutions for a p(x-biharmonic problem
Ghasem A. Afrouzi
2015-06-01
Full Text Available In this article, we study the following problem with Navier boundary conditions $$\\displaylines{ \\Delta (|\\Delta u|^{p(x-2}\\Delta u+|u|^{p(x-2}u =\\lambda |u|^{q(x-2}u +\\mu|u|^{\\gamma(x-2}u\\quad \\text{in } \\Omega,\\cr u=\\Delta u=0 \\quad \\text{on } \\partial\\Omega. }$$ where $\\Omega$ is a bounded domain in $\\mathbb{R}^{N}$ with smooth boundary $\\partial \\Omega$, $N\\geq1$. $p(x,q(x$ and $\\gamma(x$ are continuous functions on $\\overline{\\Omega}$, $\\lambda$ and $\\mu$ are parameters. Using variational methods, we establish some existence and non-existence results of solutions for this problem.
Magnetic Damping of Solid Solution Semiconductor Alloys
Szofran, Frank R.; Benz, K. W.; Croell, Arne; Dold, Peter; Cobb, Sharon D.; Volz, Martin P.; Motakef, Shariar
1999-01-01
The objective of this study is to: (1) experimentally test the validity of the modeling predictions applicable to the magnetic damping of convective flows in electrically conductive melts as this applies to the bulk growth of solid solution semiconducting materials; and (2) assess the effectiveness of steady magnetic fields in reducing the fluid flows occurring in these materials during processing. To achieve the objectives of this investigation, we are carrying out a comprehensive program in the Bridgman and floating-zone configurations using the solid solution alloy system Ge-Si. This alloy system has been studied extensively in environments that have not simultaneously included both low gravity and an applied magnetic field. Also, all compositions have a high electrical conductivity, and the materials parameters permit reasonable growth rates. An important supporting investigation is determining the role, if any, that thermoelectromagnetic convection (TEMC) plays during growth of these materials in a magnetic field. TEMC has significant implications for the deployment of a Magnetic Damping Furnace in space. This effect will be especially important in solid solutions where the growth interface is, in general, neither isothermal nor isoconcentrational. It could be important in single melting point materials, also, if faceting takes place producing a non-isothermal interface. In conclusion, magnetic fields up to 5 Tesla are sufficient to eliminate time-dependent convection in silicon floating zones and possibly Bridgman growth of Ge-Si alloys. In both cases, steady convection appears to be more significant for mass transport than diffusion, even at 5 Tesla in the geometries used here. These results are corroborated in both growth configurations by calculations.
Existence of infinitely many radial solutions for quasilinear Schrodinger equations
Gui Bao
2014-10-01
Full Text Available In this article we prove the existence of radial solutions with arbitrarily many sign changes for quasilinear Schrodinger equation $$ -\\sum_{i,j=1}^{N}\\partial_j(a_{ij}(u\\partial_iu +\\frac{1}{2}\\sum_{i,j=1}^{N}a'_{ij}(u\\partial_iu\\partial_ju+V(xu =|u|^{p-1}u,~x\\in\\mathbb{R}^N, $$ where $N\\geq3$, $p\\in(1,\\frac{3N+2}{N-2}$. The proof is accomplished by using minimization under a constraint.
Existence of positive weak solutions for (, )-Laplacian nonlinear systems
Samira Ala; G A Afrouzi; A Niknam
2015-11-01
We mainly consider the existence of a positive weak solution of the following system \\begin{equation*} \\left\\{ \\begin{matrix} -_p u + |u|^{p-2} u = [g (x) a(u)+ c(x) f (v)], \\quad \\text{ in } ,\\\\ -_q v + |v|^{q-2} v = [g (x) b(v)+ c(x) h (u)], \\quad \\text{ in } ,\\\\ \\hspace{3cm} u = v = 0, \\hspace{3.8cm} \\text{ on } \\, , \\end{matrix} \\right. \\end{equation*} where $_p u = \\text{ div}(|\
Global Existence of Solutions for a Nonstrictly Hyperbolic System
De-yin Zheng
2014-01-01
Full Text Available We obtain the global existence of weak solutions for the Cauchy problem of the nonhomogeneous, resonant system. First, by using the technique given in Tsuge (2006, we obtain the uniformly bounded L∞ estimates z(ρδ,ε,uδ,ε≤B(x and w(ρδ,ε,uδ,ε≤β when a(x is increasing (similarly, w(ρδ,ε, uδ,ε≤B(x and z(ρδ,ε,uδ,ε≤β when a(x is decreasing for the ε-viscosity and δ-flux approximation solutions of nonhomogeneous, resonant system without the restriction z0(x≤0 or w0(x≤0 as given in Klingenberg and Lu (1997, where z and w are Riemann invariants of nonhomogeneous, resonant system; B(x>0 is a uniformly bounded function of x depending only on the function a(x given in nonhomogeneous, resonant system, and β is the bound of B(x. Second, we use the compensated compactness theory, Murat (1978 and Tartar (1979, to prove the convergence of the approximation solutions.
Sun Fuqin; Wang Mingxin
2004-01-01
In this paper, we study the non-negative solutions to a degenerate parabolic system with nonlinear boundary conditions in the multi-dimensional case.By the upper and lower solutions method, we give the conditions on the existence and non-existence of global solutions.
Existence of solutions for critical elliptic systems with boundary singularities
Jianfu Yang
2013-04-01
Full Text Available This article concerns the existence of positive solutions to the nonlinear elliptic system involving critical Hardy-Sobolev exponent $$displaylines{ -Delta u= frac{2lambdaalpha}{alpha+eta} frac{u^{alpha-1} v^eta}{|pi(x|^s}- u^p, quad hbox{in } Omega,cr -Delta v= frac{2lambdaeta}{alpha+eta} frac{u^alpha v^{eta-1}}{|pi(x|^s}- v^p, quad hbox{in } Omega,cr u>0,quad v>0, quad hbox{in } Omega,cr u=v=0, quad hbox{on } partialOmega, }$$ where $Ngeq 4$ and $Omega$ is a $C^1$ bounded domain in $mathbb{R}^N$, $01$, $lambda>0$ and $1leq p
无
2010-01-01
By different fixed point theorems in cones, sufficient conditions for the existence and multiple existence of positive solutions to a class of second-order multi-point boundary value problem for dynamic equation on time scales are obtained.
Existence theorems of solution to variational inequality problems
ZHANG; Liping
2001-01-01
［1］Harker, P. T., Pang, J. S., Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithm, and applications, Mathematical Programming, 1990, 48(2): 161.［2］Eaves, B. C., The linear complementarity problem, Management Science, 1971, 17(3): 612.［3］Eaves, B. C., On the basic theorem of complementarity problem, Math. Programming, 1971, 1(1): 68.［4］Karamardian, S., Generalized complementarity problem, J. Optim. Theory Appl., 1971, 8(1): 161.［5］Kojima, M., A unification of the existence theorems of the nonlinear complementarity problem, Math. Programming, 1975, 9(2): 257.［6］Moré, J. J., Classes of functions and feasibility conditions in nonlinear complementarity problems, Math. Programming, 1974, 6(2): 327.［7］Moré, J. J., Coercivity conditions in nonlinear complementarity problems, SIAM Rev., 1974, 16(1): 1.［8］Smith, T. E., A solution condition for complementarity problems, with an application to spatial price equilibrium, Appl. Math. Computation, 1984, 15(1): 61.［9］Isac, G., Bulavaski, V., Kalashnikov, V., Exceptional families, topological degree and complementarity problems, J. Global Optim., 1997, 10(2): 207.［10］Zhao, Y. B., Han, J. Y., Qi, H. D., Exceptional families and existence theorems for variational inequality problems, J. Optim. Theory Appl., 1999, 101(2): 475.［11］Zhao, Y. B., Han, J. Y., Exceptional family of elements for a variational inequality problem and its applications, Journal of Global Optimization, 1999, 14(2): 313.［12］Zhao, Y. B., Exceptional families and finite dimensional variational inequalities over polyhedral convex sets, Appl. Math. Computation, 1997, 87(1): 111.［13］Lloyd, N. Q., Degree Theory, Cambridge: Cambridge University Press, 1978, 6—54.［14］Ortega, J. M., Rheinholdt, W. C., Iterative Solution of Nonlinear Equations in Several Variables, New York: Academic Press, 1970, 30—45.［15］Isac, G., Obuchowska, W. T., Functions
Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids
Brauer, Uwe; Karp, Lavi
2014-01-01
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein-Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a C ∞ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. In Brauer and Karp (J Diff Eqs 251:1428-1446, 2011) we constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as Hughes et al. (Arch Ratl Mech Anal 63(3):273-294, 1977) got for the vacuum Einstein equations. However, due to the presence of an equation of state with fractional power, the regularity is bounded from above.
Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids
Brauer, Uwe
2011-01-01
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove a local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a $C^\\infty$ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. Previously the authors constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as the one of the classical result of Hughes, Kato and Marsden for the vacuum Einstein equations. However, due to the presence of an equation o...
EXISTENCE OF TRIPLE POSITIVE SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM
无
2011-01-01
We apply a fixed point theorem to verify the existence of at least three positive solutions to a multi-point boundary value problem with p-Laplacian. Existence criteria which ensure the existence of triple positive solutions are established.
End-Member Formulation of Solid Solutions and Reactive Transport
Lichtner, Peter C. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-09-01
A model for incorporating solid solutions into reactive transport equations is presented based on an end-member representation. Reactive transport equations are solved directly for the composition and bulk concentration of the solid solution. Reactions of a solid solution with an aqueous solution are formulated in terms of an overall stoichiometric reaction corresponding to a time-varying composition and exchange reactions, equivalent to reaction end-members. Reaction rates are treated kinetically using a transition state rate law for the overall reaction and a pseudo-kinetic rate law for exchange reactions. The composition of the solid solution at the onset of precipitation is assumed to correspond to the least soluble composition, equivalent to the composition at equilibrium. The stoichiometric saturation determines if the solid solution is super-saturated with respect to the aqueous solution. The method is implemented for a simple prototype batch reactor using Mathematica for a binary solid solution. Finally, the sensitivity of the results on the kinetic rate constant for a binary solid solution is investigated for reaction of an initially stoichiometric solid phase with an undersaturated aqueous solution.
Growth of Solid Solution Single Crystals
Lehoczky, Sandor L.; Szofran, F. R.; Gillies, Donald C.
2001-01-01
The solidification of a solid solution semiconductor, having a wide separation between liquidus and solidus has been extensively studied in ground based, high magnetic field and Spacelab experiments. Two alloys of mercury cadmium telluride have been studied; with 80.0 mole percent of HgTe and 84.8 mole percent of HgTe respectively, the remainder being cadmium telluride. Such alloys are extremely difficult to grow by directional solidification on earth due to high solutal and thermal density differences that give rise to fluid flow and consequent loss of interface shape and composition. Diffusion controlled growth is therefore impossible to achieve in conventional directional solidification. The ground based experiments consisted of growing crystals in several different configurations of heat pipe furnaces, NASA's Advanced Automated Directional Solidification Furnace (AADSF), and a similar furnace incorporated in a superconducting magnet capable of operating at up to 5T. The first microgravity experiment took place during the flight of STS-62 in March 1994, with the AADSF installed on the second United States Microgravity Payload (USMP-2). The alloy was solidified at 3/4 inch per day over a 9 day period, and for the first time a detailed evaluation was performed correlating composition variations to measured residual acceleration. The second flight experiment took place in the fourth United States Microgravity Payload Mission (USMP-4) in November 1997. Due to contamination of the furnace system, analysis shows that the conditions prevailing during the experiment were quite different from the requirements requested prior to the mission. The results indicate that the sample did accomplish the desired objectives.
40 CFR 258.16 - Closure of existing municipal solid waste landfill units.
2010-07-01
... 40 Protection of Environment 24 2010-07-01 2010-07-01 false Closure of existing municipal solid waste landfill units. 258.16 Section 258.16 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) SOLID WASTES CRITERIA FOR MUNICIPAL SOLID WASTE LANDFILLS Location Restrictions § 258.16...
Compositional Segregation in Unidirectionally Solidified Solid Solution Crystals
Wang, J. C.
1983-01-01
A computer program was developed to model compositional segregation in unidrectionally solidified solid-solution-semiconducting crystals. The program takes into account the variations of the interface segregation constant and solidification rate with composition. Calculations are performed for the HgCdTe solid solution system that is compared with experimental data.
Forces between Hydrophobic Solids in Concentrated Aqueous Salt Solution
Mastropietro, Dean J; Ducker, William A.
2012-01-01
Much research has focused on the discovery and description of long-ranged forces between hydrophobic solids immersed in water. Here we show that the force between high contact-angle solids in concentrated salt solution (1 M KCl) agrees very well with van der Waals forces calculated from Lifshitz theory for separations greater than 5 nm. The hydrophobic solids are octadecyltrichlorosilane-coated glass, with an advancing contact angle of 108 degrees. Thus, in 1 M salt solution, it is unnecessar...
The solution of location problems with certain existing facility structures
Juel, Henrik; Love, Robert F.
1983-01-01
It is known that in the Euclidean distance case, the optimal minisum location of a new facility in relation to four existing facilities is at the intersection of the two lines joining two pairs of the facilities. The authors extend this concept to minisum problems having any even number of existing...... facilities and characterized by generalized distance norms...
Radiation processes in crystal solid solutions
Gladyshev, Gennadi
2012-01-01
This is a monograph explaining processes occurring in two classes of crystal solids (metal alloys and doped alkali halide) under irradiation by various types of radiation (alpha, beta, gamma, X-radiations, ions). This e-book is a useful reference for advanced readers interested in the physics of radiation and solid state physics.
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL DIFFERENTIAL SYSTEM WITH DELAY
无
2010-01-01
This paper is concerned with the existence of solution to nonlinear second order neutral differential equations with infinite delay in a Banach space. Sufficient conditions for the existence of solution are obtained by a Schaefer fixed point theorem.
无
2008-01-01
The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.
Isomorphism and solid solutions among Ag- and Au-selenides
Palyanova, Galina A.; Seryotkin, Yurii V. [Sobolev Institute of Geology and Mineralogy, Novosibirsk (Russian Federation); Novosibirsk State University (Russian Federation); Kokh, Konstantin A., E-mail: k.a.kokh@gmail.com [Sobolev Institute of Geology and Mineralogy, Novosibirsk (Russian Federation); Novosibirsk State University (Russian Federation); Tomsk State University (Russian Federation); Bakakin, Vladimir V. [Nikolaev Institute of Inorganic Chemistry, Novosibirsk (Russian Federation)
2016-09-15
Au-Ag selenides were synthesized by heating stoichiometric mixtures of elementary substances of initial compositions Ag{sub 2−x}Au{sub x}Se with a step of x=0.25 (0≤x≤2) to 1050 °C and annealing at 500 °C. Scanning electron microscopy, optical microscopy, electron microprobe analysis and X-ray powder diffraction methods have been applied to study synthesized samples. Results of studies of synthesized products revealed the existence of three solid solutions with limited isomorphism Ag↔Au: naumannite Ag{sub 2}Se – Ag{sub 1.94}Au{sub 0.06}Se, fischesserite Ag{sub 3}AuSe{sub 2} - Ag{sub 3.2}Au{sub 0.8}Se{sub 2} and gold selenide AuSe - Au{sub 0.94}Ag{sub 0.06}Se. Solid solutions and AgAuSe phases were added to the phase diagram of Ag-Au-Se system. Crystal-chemical interpretation of Ag-Au isomorphism in selenides was made on the basis of structural features of fischesserite, naumannite, and AuSe. - Highlights: • Au-Ag selenides were synthesized. • Limited Ag-Au isomorphism in the selenides is affected by structural features. • Some new phases were introduced to the phase diagram Ag-Au-Se.
QUASI-CONVEX MULTIOBJECTIVE GAME-SOLUTION CONCEPTS, EXISTENCE AND SCALARIZATION
LIYUANXI
1995-01-01
This paper deals with the solution concepts,scalarization and existence of solutions for multiobjective generalized game,The scalarization method used in this paper can characterize completely the solutions and be applied to prove the existence of solutions for quasi-convex multiobjective generalized game,On the other hand,a new concept of security strategy is introduced and its existence is proved,At iast,some relations between these solutions are established.
Existence and Uniqueness of Stationary Solutions of Non—Newtonian Viscous Incompressible Fluids
BolingGUO; GuoguangLIN; 等
1999-01-01
The existence and uniqueness of stationary solution a bipolar incompressible viscous fluids is established .It is also obtained that the every solution of the system converges to the statonary solution as time t→∞
Modeling supercritical fluid extraction process involving solute-solid interaction
Goto, M.; Roy, B. Kodama, A.; Hirose, T. [Kumamoto Univ., Kumamoto (Japan)
1998-04-01
Extraction or leaching of solute from natural solid material is a mass transfer process involving dissolution or release of solutes from a solid matrix. Interaction between the solute and solid matrix often influences the supercritical fluid extraction process. A model accounting for the solute-solid interaction as well as mass transfer is developed. The BET equation is used to incorporate the interaction and the solubility of solutes into the local equilibrium in the model. Experimental data for the supercritical extraction of essential oil and cuticular wax from peppermint leaves are successfully analyzed by the model. The effects of parameters on the extraction behavior are demonstrated to illustrate the concept of the model. 18 refs., 5 figs., 1 tab.
Existence of Solution of the Pullback Equation Involving Volume Forms
Saugata Bandyopadhyay
2011-08-01
Let $\\subset\\mathbb{R}^n$ be a smooth, bounded domain. We study the existence and regularity of diffeomorphisms of satisfying the volume form equation $$^*(g)=f,\\quad\\text{in}\\, $$ where $f,g\\in C^{m,}(\\overline{};^n)$ are given positive volume forms.
The solution of location problems with certain existing facility structures
Juel, Henrik; Love, Robert F.
1983-01-01
It is known that in the Euclidean distance case, the optimal minisum location of a new facility in relation to four existing facilities is at the intersection of the two lines joining two pairs of the facilities. The authors extend this concept to minisum problems having any even number of existi...
Existence and breaking property of real loop-solutions of two nonlinear wave equations
Ji-bin LI
2009-01-01
Dynamical analysis has revealed that,for some nonlinear wave equations,loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loop-soliton solution consists of three solutions,and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a "real" loop-solution exists,and if so,what are the precise parametric representations of these loop traveling wave solutions.
Logit dynamic for continuous strategy games: existence of solutions
Lahkar, R.
2007-01-01
We define the logit dynamic in the space of probability measures for a game with a compact and continuous strategy set. The original Burdett and Judd (1983) model of price dispersion comes under this framework. We then show that if the payoff functions of the game satisfy Lipschitz continuity under the strong topology in the space of signed measures, the logit dynamic admits a unique solution in the space of probability measures. As a corollary, we obtain that logit dynamic gen...
Elliptic partial differential equations existence and regularity of distributional solutions
Boccardo, Lucio
2013-01-01
Elliptic partial differential equations is one of the main and most active areas in mathematics. In our book we study linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason the book is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Several Existence Theorems for Positive Radial Solutions to a Semilinear Elliptic BVP
Yao Qing-Liu
2001-01-01
The existence of positive radial solutions to the second order semilinear elliptic BVP is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that liml→0f(l)/l and liml→∞f(l)/l exist.
Shi Ping LU; Wei Gao GE
2005-01-01
By means of the continuation theorem of coincidence degree theory, some new results on the non-existence, existence and unique existence of periodic solutions for a kind of second order neutral functional differential equation are obtained.
Bioclimatic solutions existing in vernacular architecture - geothermal climatization
Ferreira, Débora; Luso, Eduarda; Vaz, António Jorge Ferreira; Fernandes, Sílvia
2014-01-01
The traditional architecture is founded as a defining element of the identity of a region, and its essence should be preserved and conserved by means of maintenance and recovery actions. Thus, the best solutions and proposals for intervention should be looked for but this doesn’t imply a back to back on both innovation and construction progress. This work is part of the BIOURB project, a cross-border project between Portugal and Spain, which intended to contribute to the change of the curr...
Fluoride-conversion synthesis of homogeneous actinide oxide solid solutions
Silva, G W Chinthaka M [ORNL; Hunn, John D [ORNL; Yeamans, Charles B. [University of California, Berkeley; Cerefice, Gary S. [University of Nevada, Las Vegas; Czerwinski, Ken R. [University of Nevada, Las Vegas
2011-01-01
Here, a novel route to synthesize (U, Th)O2 solid solutions at a relatively low temperature of 1100 C is demonstrated. First, the separate actinide oxides reacted with ammonium bifluoride to form ammonium actinide fluorides at room temperature. Subsequently, this mixture was converted to the actinide oxide solid solution using a two-phased heat treatment, first at 610 C in static air, then at 1100 C in flowing argon. Solid solutions obeying Vegard s Law were synthesized for ThO2 content from 10 to 90 wt%. Microscopy showed that the (U, Th)O2 solid solutions synthesized with this method to have considerably high crystallinity and homogeneity, suggesting the suitability of material thus synthesized for sintering into nuclear fuel pellets at low temperatures.
Solid solution hardening of molecular crystals: tautomeric polymorphs of omeprazole.
Mishra, Manish Kumar; Ramamurty, Upadrasta; Desiraju, Gautam R
2015-02-11
In the context of processing of molecular solids, especially pharmaceuticals, hardness is an important property that often determines the manufacturing steps employed. Through nanoindentation studies on a series of omeprazole polymorphs, in which the proportions of the 5- and 6-methoxy tautomers vary systematically, we demonstrate that solid-solution strengthening can be effectively employed to engineer the hardness of organic solids. High hardness can be attained by increasing lattice resistance to shear sliding of molecular layers during plastic deformation.
Thermal vacancy formation energies of random solid solutions
Luo, H. B.; Hu, Q. M.; Du, J.; Yan, A. R.; Liu, J. P.
2017-01-01
Vacancy mechanism plays a dominant role in the atomic migration when a close-packed disordered alloy undergoes ordering transition. However, the calculation of thermal vacancy formation energies (VFEs) of random solid solutions is usually cumbersome due to the difficulty in considering various local atomic environments. Here, we propose a transparent way that combines coherent potential approximation and supercell-local cluster expansion to investigate VFEs of random solid solutions. This met...
A New Approach for Solid Waste Handling in Mosul City, Comparison Study with the Existing System
Amar T. Hamad
2013-05-01
Full Text Available Municipal Solid waste management constitutes a serious problem in many developing countries. Cities spend increasing resources to improve their Municipal solid waste management. Based on the concept that solid waste is a resource containing significant amounts of valuable materials, new approaches of solid waste management are adopted. The present work proposes a policy framework for improving a low-cost waste management system in Mosul city. The new approach induces additional services to the existing solid waste system to reduce the unit cost per ton of solid waste generated. The proposed system includes sorting, recycling and composting units. This paper presents an application of a new computerized decision package for an integrated solid waste management within Mosul city. New software called "COSEPRE" is used to analyze the service cost for both existing and proposed solid waste management system. The input data is collected from different related directorates in Mosul city. Data that are difficult to be obtained are prepared by laboratory analysis or field investigations. The results revealed a 58% reduction in unit cost by employing the new system of solid waste management.
Intelligent packaging in meat industry: An overview of existing solutions.
Mohebi, Ehsan; Marquez, Leorey
2015-07-01
Traditional packaging systems are refused since these systems do not provide any information about the quality of food products to the consumers and manufacturers at any stage of supply chain. The essence of a new technology to monitor the food spoilage from farm to fork is emerged to reduce hazards such as food borne diseases. Moreover, the food quality monitoring systems clarify the main factors in food wastage during supply chain. Intelligent packaging is employed to provide information about the history of food handling and storage to enhance food products quality and meet consumer satisfactions. Meat is one of the most perishable foods which causes sever illnesses in the case of spoilage. Variety of indicators and sensors have been proposed to warn about meat spoilage in meat industry. In this paper an overview of proposed approaches as well as commercial technologies to monitor the quality of meat during storage and transportation is presented. Furthermore, the existing technologies are compared in the sense of advantages and disadvantages in meat packaging applications.
EXISTENCE OF SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS WITH UNBOUNDED COEFFICIENTS ON RN
Wei Gongming
2008-01-01
In this paper a class of p-Laplace type elliptic equations with unbounded coefficients on RN is considered.It is proved that there exist radial solutions on RN.On sufiiciently large ball,radial and nonradial solutions axe obtained.Finally,some necessary conditions for the existence of solutions axe given.
无
2011-01-01
This paper is concerned with the existence of extreme solutions to three-point boundary value problems with nonlinear boundary conditions for a class of first order impulsive differential equations. We obtain suficient conditions for the existence of extreme solutions by the upper and lower solutions method coupled with a monotone iterative technique.
王金良; 周笠
2003-01-01
In this paper,our main aim is to study the existence and uniqueness of the periodic solution of delayed Logistic equation and its asymptotic behavior.In case the coefficients are periodic,we give some sufficient conditions for the existence and uniqueness of periodic solution.Furthermore,we also study the effect of time-delay on the solution.
Analytical Solution for Isentropic Flows in Solids
Heuzé, Olivier
2009-12-01
In the XIXth century, Riemann gave the equations system and the exact solution for the isentropic flows in the case of the ideal gas. But to our knowledge, nothing has been done to apply it to condensed media. Many materials of practical interest, for instance metals, obey to the linear law D = c+s u, where D is the shock velocity, u the particle velocity, and c and s properties of the material. We notice that s is strongly linked to the fundamental derivative. This means that the assumption of constant fundamental derivative is useful in this case, as it was with the isentropic gamma in the Riemann solution. Then we can apply the exact Riemann solution for these materials. Although the use of the hypergeometric function is complicated in this case, we obtain a very good approximation with the development in power series.
ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR NONLINEAR SYSTEM WITH MULTIPLE DELAYS
曹显兵
2003-01-01
The existence of T-periodic solutions of the nonlinear system with multiple delaysis studied. By using the topological degree method, sufficient conditions are obtained forthe existence of T-periodic solutions. As an application, the existence of positive periodicsolution for a logarithmic population model is established under some conditions.
EXISTENCE AND NONEXISTENCE OF POSITIVE SOLUTIONS TO A THREE-POINT BOUNDARY VALUE PROBLEM
无
2012-01-01
In this paper, we are concerned with the existence and nonexistence of positive solutions to a three-point boundary value problems. By Krasnoselskii's fixed point theorem in Banach space, we obtain sufficient conditions for the existence and non-existence of positive solutions to the above three-point boundary value problems.
Rai, R.N., E-mail: rn_rai@yahoo.co.in [Department of Chemistry, Centre of Advanced Study, Banaras Hindu University, Varanasi 221005 (India); Kant, Shiva; Reddi, R.S.B. [Department of Chemistry, Centre of Advanced Study, Banaras Hindu University, Varanasi 221005 (India); Ganesamoorthy, S. [Materials Science Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu (India); Gupta, P.K. [Laser Materials Development & Devices Division, Raja Ramanna Centre for Advanced Technology, Indore 452013 (India)
2016-01-15
Urea is an attractive material for frequency conversion of high power lasers to UV (for wavelength down to 190 nm), but its usage is hindered due to its hygroscopic nature, though there is no alternative organic NLO crystal which could be transparent up to 190 nm. The hygroscopic character of urea has been modified by making the solid solution (UCNB) of urea (U) and p-chloronitrobenzene (CNB). The formation of the solid solution of CNB in U is explained on the basis of phase diagram, powder XRD, FTIR, elemental analysis and single crystal XRD studies. The solubility of U, CNB and UCNB in ethanol solution is evaluated at different temperatures. Transparent single crystals of UCNB are grown from its saturated solution in ethanol. Optical properties e.g., second harmonic generation (SHG), refractive index and the band gap for UCNB crystal were measured and their values were compared with the parent compounds. Besides modification in hygroscopic nature, UCNB has also shown the higher SHG signal and mechanical hardness in comparison to urea crystal. - Highlights: • The hygroscopic character of urea was modified by making the solid solution • Solid solution formation is support by elemental, powder- and single crystal XRD • Crystal of solid solution has higher SHG signal and mechanical stability. • Refractive index and band gap of solid solution crystal have determined.
Uniformly Asymptotic Stability and Existence of Periodic Solutions and Almost Periodic Solutions
林发兴
1994-01-01
We introduce the concepts of uniformly stable solutions and uniformly-asymptotically stable solutions, and then give the relation between Lyapunov function and those concepts. Furthermore, we establish the theorem that an almost periodic system or periodic system has uniformly-asymptotically stable solutions and Lipschitz’ condition has an almost periodic solution or periodic solution.
Noundjeu, P
2003-01-01
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
Park Jong Yeoul
2007-01-01
Full Text Available We study the existence of global weak solutions for a hyperbolic differential inclusion with a source term, and then investigate the asymptotic stability of the solutions by using Nakao lemma.
Existence of positive radial solutions for a weakly coupled system via blow up
Marta García-Huidobro
1998-01-01
Full Text Available The existence of positive solutions to certain systems of ordinary differential equations is studied. Particular forms of these systems are satisfied by radial solutions of associated partial differential equations.
Solid Tumors: Facts, Challenges and Solutions
Gavhane Y. N.
2011-01-01
Full Text Available In 2005, 7.6 million people died of cancer out of 58 million deaths worldwide. Based on projections, cancer deaths will continue to rise with an estimated 9 million people dying from cancer in 2015, and 11.4 million dying in 2030. The increasing trend of cancer incidence has forced the humanity to work more on the cancer prevention and treatments. It is important for the public health professionals to understand the dynamics and kinetics of tumor incidence for future strategies. Over here we have reviewed solid tumor modeling, their detail classification, treatment strategies available along with their merits and demerits. To overcome these limitations, design focus for future studies is suggested.
EXISTENCE OF SOLUTIONS TO A THIRD-ORDER THREE-POINT BOUNDARY VALUE PROBLEM
无
2012-01-01
In this paper,we study the existence of solutions to a third-order three-point boundary value problem.By imposing certain restrictions on the nonlinear term,we prove the existence of at least one solution to the boundary value problem by the method of lower and upper solutions.We are interested in the construction of lower and upper solutions.
EXISTENCE AND UNIQUENESS OF SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATION WITH RANDOM COEFFICIENTS
无
2010-01-01
This paper mainly deals with a stochastic differential equation (SDE) with random coefficients. Sufficient conditions which guarantee the existence and uniqueness of solutions to the equation are given.
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations
Yuanhong Wei
2014-01-01
We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.
Existence of solutions of a nonlinear system modelling fluid flow in porous media
dam Besenyei
2006-12-01
Full Text Available We investigate the existence of weak solutions for nonlinear differential equations that describe fluid flow through a porous medium. Existence is proved using the theory of monotone operators, and some examples are given.
EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO A SECOND-ORDER DIFFERENTIAL INCLUSION
无
2012-01-01
In this paper,the existence of positive periodic solutions to a second-order differential inclusion is considered.Some existence results are established by the fixed-point theorem for multivalued operators and Sobolev constant.
Bapurao C. Dhage
2006-03-01
Full Text Available In this paper, we prove an existence theorem for hyperbolic differential equations in Banach algebras under Lipschitz and Caratheodory conditions. The existence of extremal solutions is also proved under certain monotonicity conditions.
Study on solid solution and aging process of AZ91D magnesium alloy with cerium
GUO
2010-01-01
The influence of Ce on solid solution and aging process of AZ91D magnesium alloy was analyzed.The results showed that the decomposition of β-Mg17Al12 phase in AZ91D magnesium alloy at 420 ℃ could be completed within 12 h,while this process in the Ce-containing alloy required more time.In subsequent aging process at 175 ℃,Ce obviously delayed the aging process of AZglD.It was inferred that the influence of Ce on process of solid solution and aging was relative to the Ce that existed in β-Mg17Al12 phase of original structure in the form of solid solution,and the interaction of the Ce and Al was an important factor to get process of solution and aging slowly.
Alloy softening in binary iron solid solutions
Stephens, J. R.; Witzke, W. R.
1976-01-01
An investigation was conducted to determine softening and hardening behavior in 19 binary iron-alloy systems. Microhardness tests were conducted at four temperatures in the range 77 to 411 K. Alloy softening was exhibited by 17 of the 19 alloy systems. Alloy softening observed in 15 of the alloy systems was attributed to an intrinsic mechanism, believed to be lowering of the Peierls (lattice friction) stress. Softening and hardening rates could be correlated with the atomic radius ratio of solute to iron. Softening observed in two other systems was attributed to an extrinsic mechanism, believed to be associated with scavenging of interstitial impurities.
Wu, Fuke; Yin, George; Mei, Hongwei
2017-02-01
This work is devoted to stochastic functional differential equations (SFDEs) with infinite delay. First, existence and uniqueness of the solutions of such equations are examined. Because the solutions of the delay equations are not Markov, a viable alternative for studying further asymptotic properties is to use solution maps or segment processes. By examining solution maps, this work investigates the Markov properties as well as the strong Markov properties. Also obtained are adaptivity and continuity, mean-square boundedness, and convergence of solution maps from different initial data. This paper then examines the ergodicity of underlying processes and establishes existence of the invariant measure for SFDEs with infinite delay under suitable conditions.
Efficient and Color-Tunable Oxyfluoride Solid Solution Phosphors for Solid-State White Lighting
Im, Won Bin; George, Nathan; Kurzman, Joshua; Brinkley, Stuart; Mikhailovsky, Alexander; Hu, Jerry; Chmelka, Bradley F.; DenBaars, Steven P.; Seshadri, Ram (UCSB)
2012-09-06
A solid solution strategy helps increase the efficiency of Ce{sup 3+} oxyfluoride phosphors for solid-state white lighting. The use of a phosphor-capping architecture provides additional light extraction. The accompanying image displays electroluminescence spectra from a 434-nm InGaN LED phosphor that has been capped with the oxyfluoride phosphor.
Heterogeneous Ferroelectric Solid Solutions Phases and Domain States
Topolov, Vitaly
2012-01-01
The book deals with perovskite-type ferroelectric solid solutions for modern materials science and applications, solving problems of complicated heterophase/domain structures near the morphotropic phase boundary and applications to various systems with morphotropic phases. In this book domain state–interface diagrams are presented for the interpretation of heterophase states in perovskite-type ferroelectric solid solutions. It allows to describe the stress relief in the presence of polydomain phases, the behavior of unit-cell parameters of coexisting phases and the effect of external electric fields. The novelty of the book consists in (i) the first systematization of data about heterophase states and their evolution in ferroelectric solid solutions (ii) the general interpretation of heterophase and domain structures at changing temperature, composition or electric field (iii) the complete analysis of interconnection domain structures, unit-cell parameters changes, heterophase structures and stress relief.
Forces between hydrophobic solids in concentrated aqueous salt solution.
Mastropietro, Dean J; Ducker, William A
2012-03-09
Much research has focused on the discovery and description of long-ranged forces between hydrophobic solids immersed in water. Here we show that the force between high contact-angle solids in concentrated salt solution (1 M KCl) agrees very well with van der Waals forces calculated from Lifshitz theory for separations greater than 5 nm. The hydrophobic solids are octadecyltrichlorosilane-coated glass, with an advancing contact angle of 108°. Thus, in 1 M salt solution, it is unnecessary to invoke the presence of a hydrophobic force at separations greater than 5 nm. Through measurement in salt solution, we avoid the necessity of accounting for large electrostatic forces that frequently occur in pure water and may obscure resolution of other forces.
无
2008-01-01
In this paper,we study the existence and approximation of solution to boundary value problems for impulsive differential equations with delayed arguments.Sufficient conditions are established for the existence of a unique solution or extremal ones to the given problem.A monotone iterative technique is applied.
徐西安
2004-01-01
In this paper, we first obtain some New results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.
EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS
钟金标; 陈祖墀
2002-01-01
In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given.
Qing Liu YAO
2005-01-01
The existence, multiplicity and infinite solvability of positive solutions are established for some two-point boundary value problems of one-dimensional p-Laplacian. In this paper, by multiplicity we mean the existence of m solutions, where m is an arbitrary natural number.
EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS TO THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM
无
2011-01-01
The existence and multiplicity of positive solutions to a periodic boundary value problem for nonlinear third-order ordinary differential equation are established, based on the zero point theorem concerning cone expansion and compression of order type. Our main approach is different from the previous papers on the existence of multiple positive solutions to the similar problem.
EXISTENCE THEOREM ABOUT MULTIPLE POSITIVE SOLUTIONS TO p-LAPLACIAN BOUNDARY VALUE PROBLEM
无
2012-01-01
In this paper,we apply a fixed point theorem to verify the existence of multiple positive solutions to a p-Laplacian boundary value problem.Sufficient conditions are established which guarantee the existence of multiple positive solutions to the problem.
EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS
无
2006-01-01
In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.
EXISTENCE OF SOLUTIONS TO 2m-ORDER PERIODIC BOUNDARY VALUE PROBLEM
无
2012-01-01
In this paper, we are concerned with the existence of nontrivial solutions to a 2m-order nonlinear periodic boundary value problem. By the infinite dimensional Morse theory, under some conditions on nonlinear term, we obtain that there exist at least two nontrivial solutions.
On the Existence of Positive Solutions ofSingular Second Order BoundaryValue Problems
LIHe-cheng
2004-01-01
This paper deals with the existence of positive solutions of the equation u"+f(t,u)=0 with linear boundary conditions. We show the existence of at least onepositive solution if f is neither superlinear nor sublinear on u by a simple application of afixed point Theorem in cones.
EXISTENCE OF MULTIPLE POSITIVE PERIODIC SOLUTIONS TO A CLASS OF INTEGRO-DIFFERENTIAL EQUATION
无
2011-01-01
In this paper,by the Avery-Henderson fixed point theorem,we investigate the existence of multiple positive periodic solutions to a class of integro-differential equation. Some suficient conditions are obtained for the existence of multiple positive periodic solutions.
EXISTENCE OF PERIODIC SOLUTION TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT
无
2009-01-01
In this paper,using the coincidence degree theory of Mawhin,we investigate the existence of periodic solutions to higher order differential equations with deviating argument. Some new results on the existence of periodic solutions to the equations are obtained. In addition,we give an example to illustrate the main results.
EXISTENCE OF MILD SOLUTIONS TO NEUTRAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY
无
2012-01-01
In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.
THE EXISTENCE, UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTION FOR A CLASS OF NONLINEAR SYSTEM
方聪娜; 王全义
2004-01-01
In this paper, we study the problems on the existence, uniqueness and stability of almost periodic solution for a class of nonlinear system. Using fixed point theorem and Lyapunov functional, the sufficient conditions are given which guarantee the existence, uniqueness and stability of almost periodic solution for the system.
Existence of almost periodic solution of a model of phytoplankton allelopathy with delay
Abbas, Syed; Mahto, Lakshman
2012-09-01
In this paper we discuss a non-autonomous two species competitive allelopathic phytoplankton model in which both species are producing chemical which stimulate the growth of each other. We have studied the existence and uniqueness of an almost periodic solution for the concerned model system. Sufficient conditions are derived for the existence of a unique almost periodic solution.
Synthesis and characterization of mesostructured ceria-zirconia solid solution
LI Changlin; GU Xin; WANG Yanqin; WANG Yaojun; WANG Yangang; LIU Xiaohui; LU Guanzhong
2009-01-01
Mesostructured Ce0.6Zr0.4O2 solid solutions were synthesized by coprecipitation combined with evaporation-induced self-assembly process. The obtained materials were characterized by X-ray diffractometer (XRD), Raman, transmission electron microscopy (TEM), N2 sorption, and hydrogen temperature programmed reduction (H2-TPR). The results showed that the solid solutions consisted of uniform nanocrystals, which piled homogeneous mesopores of about 4 nm. Furthermore, different surfactants had little influence on the mesoporous structures. All these samples exhibited high thermal stability.
Global Existence and Uniqueness of Solutions to Evolution p-Laplacian Systems with Nonlinear Sources
WEI Yingjie; GAO Wenjie
2013-01-01
This paper presents the global existence and uniqueness of the initial and boundary value problem to a system of evolution p-Laplacian equations coupled with general nonlinear terms.The authors use skills of inequality estimation and the method of regularization to construct a sequence of approximation solutions,hence obtain the global existence of solutions to a regularized system.Then the global existence of solutions to the system of evolution p-Laplacian equations is obtained with the application of a standard limiting process.The uniqueness of the solution is proven when the nonlinear terms are local Lipschitz continuous.
Syed Abbas
2011-01-01
Full Text Available In this article, we discuss the existence and uniqueness of solution to fractional order ordinary and delay differential equations. We apply our results on the single species model of Lotka Volterra type. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First we use Banach contraction principle and then Krasnoselskii's fixed point theorem to show the existence and uniqueness of the solution under certain conditions. Moreover, we prove that the solution can be extended to maximal interval of existence.
Ab initio identified design principles of solid-solution strengthening in Al
Duancheng Ma, Martin Friák, Johann von Pezold, Dierk Raabe and Jörg Neugebauer
2013-01-01
Full Text Available Solid-solution strengthening in six Al–X binary systems is investigated using first-principle methods. The volumetric mismatch parameter and the solubility enthalpy per solute were calculated. We derive three rules for designing solid-solution strengthened alloys: (i the solubility enthalpy per solute is related to the volumetric mismatch by a power law; (ii for each annealing temperature, there exists an optimal solute–volume mismatch to achieve maximum strength; and (iii the strengthening potential of high volumetric mismatch solutes is severely limited by their low solubility. Our results thus show that the thermodynamic properties of the system (here Al–X alloys set clear upper bounds to the achievable strengthening effects owing to the reduced solubility with increasing volume mismatch.
Existence and stability of traveling wave solutions for multilayer cellular neural networks
Hsu, Cheng-Hsiung; Lin, Jian-Jhong; Yang, Tzi-Sheng
2015-08-01
The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.
Alain Mignot
2005-09-01
Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.
Existence of axially symmetric solutions in SU(2)-Yang-Mills and related theories
Hannibal, L; Hannibal, Ludger; Ossietzky, Carl von
1999-01-01
It is shown that the static axially symmetric solutions of SU(2) Einstein-Yang-Mills-Dilaton theory constructed by Kleihaus and Kunz are gauge-equivalent to two-parameter families of embedded abelian solutions, characterized by mass and magnetic dipole moment. The existence of other particle-like solutions is excluded.
Existence and Uniqueness of Weak Solutions to the p-biharmonic Parabolic Equation
Guo Jin-yong
2013-01-01
We consider an initial-boundary value problem for a p-biharmonic parabo-lic equation. Under some assumptions on the initial value, we construct approximate solutions by the discrete-time method. By means of uniform estimates on solutions of the time-difference equations, we establish the existence of weak solutions, and also discuss the uniqueness.
Existence and uniqueness of positive solutions for a nonlocal dispersal population model
Jian-Wen Sun
2014-06-01
Full Text Available In this article, we study the solutions of a nonlocal dispersal equation with a spatial weight representing competitions and aggregation. To overcome the limitations of comparison principles, we introduce new definitions of upper-lower solutions. The proof of existence and uniqueness of positive solutions is based on the method of monotone iteration sequences.
无
2009-01-01
In this paper, by fixed point theorem of Krasnoselskii, we study the positive pe- riodic solution to a class of nonautonomous differential equation with impulses and delay. Firstly, definition of periodic solution and some lemmas are stated. Then some results on the existence of positive periodic solution to the equation are obtained.
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
Said Kouachi
2001-10-01
Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].
Existence of solutions for a Schrödinger system with linear and nonlinear couplings
Li, Kui; Zhang, Zhitao
2016-08-01
We study an important system of Schrödinger equations with linear and nonlinear couplings arising from Bose-Einstein condensates. We use the Nehari manifold to prove the existence of a ground state solution; moreover, we give the sign of the solutions depending on linear coupling; by using index theory and Nehari manifold, we prove that there exist infinitely many positive bound state solutions.
Runzhang, Xu; Yanbing, Yang; Bowei, Liu; Jihong, Shen; Shaobin, Huang
2015-06-01
This paper is concerned with the Cauchy problem of solutions for some nonlinear multidimensional "good" Boussinesq equation of sixth order at three different initial energy levels. In the framework of potential well, the global existence and blowup of solutions are obtained together with the concavity method at both low and critical initial energy level. Moreover by introducing a new stable set, we present some sufficient conditions on initial data such that the weak solution exists globally at supercritical initial energy level.
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities
Gong-Ming Wei
2008-04-01
Full Text Available In this paper we study the existence of nontrivial solutions of elliptic systems with critical nonlinearities and subcritical nonlinear coupling interactions, under Dirichlet or Neumann boundary conditions. These equations are motivated from solitary waves of nonlinear Schrodinger systems in physics. Using minimax theorem and by estimates on the least energy, we prove the existence of nonstandard least energy solutions, i.e. solutions with least energy and each component is nontrivial.
Extended solid solutions and coherent transformations in nanoscale olivine cathodes.
Ravnsbæk, D B; Xiang, K; Xing, W; Borkiewicz, O J; Wiaderek, K M; Gionet, P; Chapman, K W; Chupas, P J; Chiang, Y-M
2014-03-12
Nanoparticle LiFePO4, the basis for an entire class of high power Li-ion batteries, has recently been shown to exist in binary lithiated/delithiated states at intermediate states of charge. The Mn-bearing version, LiMn(y)Fe(1-y)PO4, exhibits even higher rate capability as a lithium battery cathode than LiFePO4 of comparable particle size. To gain insight into the cause(s) of this desirable performance, the electrochemically driven phase transformation during battery charge and discharge of nanoscale LiMn0.4Fe0.6PO4 of three different average particle sizes, 52, 106, and 152 nm, is investigated by operando synchrotron radiation powder X-ray diffraction. In stark contrast to the binary lithiation states of pure LiFePO4 revealed in recent investigations, the formations of metastable solid solutions covering a remarkable wide compositional range, including while in two-phase coexistence, are observed. Detailed analysis correlates this behavior with small elastic misfits between phases compared to either pure LiFePO4 or LiMnPO4. On the basis of time- and state-of-charge dependence of the olivine structure parameters, we propose a coherent transformation mechanism. These findings illustrate a second, completely different phase transformation mode for pure well-ordered nanoscale olivines compared to the well-studied case of LiFePO4.
Existence of Weak Solutions for Nonlinear Time-Fractional p-Laplace Problems
Meilan Qiu
2014-01-01
Full Text Available The existence of weak solution for p-Laplace problem is studied in the paper. By exploiting the relationship between the Nehari manifold and fibering maps and combining the compact imbedding theorem and the behavior of Palais-Smale sequences in the Nehari manifold, the existence of weak solutions is established. By means of the Arzela-Ascoli fixed point theorem, some existence results of the corresponding time-fractional equations of the p-Laplace problem are obtained.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Surface Defects Enhanced Visible Light Photocatalytic H2 Production for Zn-Cd-S Solid Solution.
Zhang, Xiaoyan; Zhao, Zhao; Zhang, Wanwan; Zhang, Guoqiang; Qu, Dan; Miao, Xiang; Sun, Shaorui; Sun, Zaicheng
2016-02-10
In order to investigate the defect effect on photocatalytic performance of the visible light photocatalyst, Zn-Cd-S solid solution with surface defects is prepared in the hydrazine hydrate. X-ray photoelectron spectra and photoluminescence results confirm the existence of defects, such as sulfur vacancies, interstitial metal, and Zn and Cd in the low valence state on the top surface of solid solutions. The surface defects can be effectively removed by treating with sulfur vapor. The solid solution with surface defect exhibits a narrower band gap, wider light absorption range, and better photocatalytic perfomance. The optimized solid solution with defects exhibits 571 μmol h(-1) for 50 mg photocatalyst without loading Pt as cocatalyst under visible light irradiation, which is fourfold better than that of sulfur vapor treated samples. The wavelength dependence of photocatalytic activity discloses that the enhancement happens at each wavelength within the whole absorption range. The theoretical calculation shows that the surface defects induce the conduction band minimum and valence band maximum shift downward and upward, respectively. This constructs a type I junction between bulk and surface of solid solution, which promotes the migration of photogenerated charges toward the surface of nanostructure and leads to enhanced photocatalytic activity. Thus a new method to construct highly efficient visible light photocatalysts is opened.
Solid and solution phase combinatorial synthesis of ureas
Nieuwenhuijzen, JW; Conti, PGM; Ottenheijm, HCJ; Linders, JTM
1998-01-01
An efficient parallel synthesis of ureas based on amino acids is described, both in solution and on solid phase. 1,1'-Carbonylbisbenzotriazole 2 is used as the coupling reagent. The ureas 5 and 10 were obtained in high yield (80-100%) and purity (71-97%). (C) 1998 Elsevier Science Ltd. All rights re
KNH2-KH: a metal amide-hydride solid solution.
Santoru, Antonio; Pistidda, Claudio; Sørby, Magnus H; Chierotti, Michele R; Garroni, Sebastiano; Pinatel, Eugenio; Karimi, Fahim; Cao, Hujun; Bergemann, Nils; Le, Thi T; Puszkiel, Julián; Gobetto, Roberto; Baricco, Marcello; Hauback, Bjørn C; Klassen, Thomas; Dornheim, Martin
2016-09-27
We report for the first time the formation of a metal amide-hydride solid solution. The dissolution of KH into KNH2 leads to an anionic substitution, which decreases the interaction among NH2(-) ions. The rotational properties of the high temperature polymorphs of KNH2 are thereby retained down to room temperature.
Cordier, S.
1995-05-01
In this work a 1-D model of electrons and ions plasma is considered. Electrons are supposed to be in Maxwell-Boltzmann thermodynamic equilibrium while ions are described with an isothermal flow model of charged particles submitted to a self-consistent electric field. A collision term between neutral particles and ions simulates the presence of neutral particles. This work demonstrates the existence of low entropy solutions for this simple model with arbitrary initial conditions. Most of the paper is devoted to the demonstration of this theorem and follows the successive steps: construction of a numerical scheme, recall of the classical properties of Riemann problem solutions using Glimm method, uniform estimations for the whole variation norm, and finally, convergence of the constructed solutions towards a low entropy solution for the non-linear Euler/Poisson system. Domains of application for this type of model are listed in the conclusion. (J.S.). 18 refs.
Existence of solutions to boundary value problem of fractional differential equations with impulsive
Weihua JIANG
2016-12-01
Full Text Available In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.
On the Existence of Solutions for Stationary Mean-Field Games with Congestion
Evangelista, David
2017-09-11
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFGs with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians.
Existence and Attractiveness of Order One Periodic Solution of a Holling I Predator-Prey Model
Huidong Cheng
2012-01-01
Full Text Available According to the integrated pest management strategies, a Holling type I functional response predator-prey system concerning state-dependent impulsive control is investigated. By using differential equation geometry theory and the method of successor functions, we prove the existence of order one periodic solution, and the attractivity of the order one periodic solution by sequence convergence rules and qualitative analysis. Numerical simulations are carried out to illustrate the feasibility of our main results which show that our method used in this paper is more efficient than the existing ones for proving the existence and attractiveness of order one periodic solution.
Global existence and blowup of solutions to a free boundary problem for mutualistic model
KIM; KwangIk
2010-01-01
This article is concerned with a system of semilinear parabolic equations with a free boundary,which arises in a mutualistic ecological model.The local existence and uniqueness of a classical solution are obtained.The asymptotic behavior of the free boundary problem is studied.Our results show that the free problem admits a global slow solution if the inter-specific competitions are strong,while if the inter-specific competitions are weak there exist the blowup solution and global fast solution.
Solid-like mechanical behaviors of ovalbumin aqueous solutions.
Ikeda, S; Nishinari, K
2001-04-12
Flow and dynamic mechanical properties of ovalbumin (OVA) aqueous solutions were investigated. OVA solutions exhibited relatively large zero-shear viscosity values under steady shear flow and solid-like mechanical responses against oscillating small shear strains, that is, the storage modulus was always larger than the loss modulus in the examined frequency range (0.1--100 rad s(-1)). These results suggest that dispersed OVA molecules arranged into a colloidal crystal like array stabilized by large interparticle repulsive forces. However, marked solid-like mechanical behaviors were detected even when electrostatic repulsive forces among protein molecules were virtually absent, which could not be explained solely on the basis of conventional Derjaguin--Landau--Verwey--Overbeek (DLVO) theory. Large non-DLVO repulsive forces seem to stabilize native OVA aqueous solutions.
Existence of positive solutions to a Laplace equation with nonlinear boundary condition
Kim, C.-G.; Liang, Z.-P.; Shi, J.-P.
2015-12-01
The positive solutions of a Laplace equation with a superlinear nonlinear boundary condition on a bounded domain are studied. For higher-dimensional domains, it is shown that non-constant positive solutions bifurcate from a branch of trivial solutions at a sequence of bifurcation points, and under additional conditions on nonlinearity, the existence of a non-constant positive solution for any sufficiently large parameter value is proved by using variational approach. It is also proved that for one-dimensional domain, there is only one bifurcation point, all non-constant positive solutions lie on the bifurcating curve, and for large parameter values, there exist at least two non-constant positive solutions. For a special case, there are exactly two non-constant positive solutions.
Existence and Uniqueness of Solutions to the Einstein Field Equations in Eternal Inflation
Kohli, Ikjyot Singh
2014-01-01
In this paper, we consider the problem of existence and uniqueness of solutions to the Einstein field equations for an arbitrary FLRW universe in the context of stochastic eternal inflation where the stochastic mechanism is modeled by adding a stochastic forcing term representing Gaussian white noise to the Klein-Gordon equation. We show that under these considerations, the Klein-Gordon equation actually becomes a stochastic differential equation. Therefore, the existence and uniqueness of solutions to Einsteins equations depend on whether the drift coefficient of this stochastic differential equation obeys global Lipschitz continuity and growth conditions. We then show that only three unique solutions are possible in the context of this model. The first unique solution we obtain is a de Sitter space solution with a linear inflation potential. The other two solutions that we obtain are both Einstein static universe solutions with linear and quadratic potentials. An important implication of this work is that o...
EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIENARD SYSTEM
肖海滨
2003-01-01
The existence of monotone and non-monotone solutions of boundary value problem on the real line for Lienard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Lienard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.
EXISTENCE AND ITERATION OF POSITIVE SYMMETRIC SOLUTIONS TO A MULTI-POINT BOUNDARY VALUE PROBLEM
无
2011-01-01
In this paper,we consider the existence of symmetric solutions to a nonlinear second order multi-point boundary value problem,and establish corresponding iterative schemes based on the monotone iterative method.
Existence of the time periodic solution for damped Schroedinger-Boussinesq equation
BolingGUO; XianyunDU
2000-01-01
In this paper, we study the time priodic solution for the weakly damped Schroedinger-Boussinesq equation, by Galerkin method, and prove the existence and uniqueness of the equations under some appropriate conditions.
EXISTENCE OF PERIODIC SOLUTIONS TO THIRD-ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION
A.M.A.Abou-El-Ela; A.I.Sadek; R.O.A.Taie
2011-01-01
By means of the continuation theorem of the coincidence degree theory and analysis techniques,sufficient conditions for the existence of periodic solutions to a kind of third-order neutral delay functional differential equation with deviating arguments are obtained.
Existence and uniqueness of solutions for a Neumann boundary-value problem
Safia Benmansour
2011-09-01
Full Text Available In this article, we show the existence and uniqueness of positive solutions for perturbed Neumann boundary-value problems of second-order differential equations. We use a fixed point theorem for general $alpha$-concave operators.
Brahim Tellab; Kamel Haouam
2016-01-01
In this paper, we investigate the existence and uniqueness of solutions for second order nonlinear fractional differential equation with integral boundary conditions. Our result is an application of the Banach contraction principle and the Krasnoselskii fixed point theorem.
Wang Lihe; Zhou Shulin
2006-01-01
In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a nonlinear parabolic partial differential equation, which is related to the Malik-Perona model in image analysis.
Existence and uniqueness of periodic solutions for forced Liénard-type equations
LIU Bing-wen
2008-01-01
By using topological degree theory and some analysis skill, some sufficient conditions for the existence and uniqueness of periodic solutions for a class of forced Liénard-type equations are obtained.
ON THE EXISTENCE OF POSITIVE ALMOST PERIODIC SOLUTIONS TO AN IMPULSIVE NEURAL NETWORKS WITH DELAY
无
2012-01-01
In this paper,Hopfield neural networks with delays and impulses are considered.By means of mathematical analysis techniques,some sufficient conditions for the existence of positive almost periodic solutions are obtained.
Yongkun Li
2005-01-01
Full Text Available We study the existence and exponential attractivity of periodic solutions to Cohen-Grossberg neural network with distributed delays. Our results are obtained by applying the continuation theorem of coincidence degree theory and a general Halanay inequality.
EXISTENCE OF PERIODIC SOLUTIONS TO A LINARD EQUATION WITH MULTIPLE DELAYS
无
2011-01-01
In this paper,by a coincidence degree theory,the existence of periodic solutions to a Linard equation with multiple delays is established,which substantially extends some results in the previous literatures.
EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY
无
2010-01-01
This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.
EXISTENCE OF PERIODIC SOLUTIONS TO A KIND OF n-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION
无
2009-01-01
By means of the continuation theorem of coincidence degree theory, we study a kind of n-order neutral functional differential equation. Some new results on the existence of periodic solutions are obtained.
EXISTENCE AND GLOBAL ATTRACTIVITY OF ALMOST PERIODIC SOLUTION TO A DELAYED DIFFERENTIAL EQUATION
无
2011-01-01
A new fixed point theorem is presented and sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive almost periodic solution to a delayed differential equation with almost periodic factors.
Existence of solutions for a system of elliptic partial differential equations
Robert Dalmasso
2011-05-01
Full Text Available In this article, we establish the existence of radial solutions for a system of nonlinear elliptic partial differential equations with Dirichlet boundary conditions. Also we discuss the question of uniqueness, and illustrate our results with examples.
Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit
Zhen LEI
2006-01-01
In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data are sufficiently small.
EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS TO A HIGHER DIMENSIONAL PERIODIC SYSTEM WITH DELAY
无
2008-01-01
In this paper, using fixed point theorem, we discuss a higher dimensional nonautonomous periodic system with delay and give some suffcient criteria for the existence and uniqueness of periodic solution. Our results extend and improve some results in previous researches.
无
2011-01-01
In this paper, we consider a semilinear difference equation in a Banach space. Under some suitable conditions on f, we prove the existence and uniqueness of a weighted pseudo almost automorphic sequence solution to the equation.
无
2008-01-01
In this paper, we consider almost periodic discrete two-species competitive sys-tems. By using Lyapunov functional, the existence conditions and uniqueness of almost periodic solutions for the this type of systems are obtained.
Dhakne Machindra B.
2017-04-01
Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.
ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS
SunYan; XuBenlong; SunYongping
2005-01-01
By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.
EXISTENCE OF PERIODIC SOLUTIONS OF THE BURGERS-GINZBURG-LANDAU EQUATIONS
黄海洋
2004-01-01
In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by LeraySchauder fixed point theorem and Galerkin method under appropriate conditions.
Existence of Solutions to Elliptic Equations with Variable Exp onents and a Singular Term
Chen Xu-sheng
2016-01-01
The purpose of this paper is to study a class of elliptic equations with variable exponents. By using the method of regularization and a priori estimates, we obtain the existence of weak solutions to these problems.
Existence of solutions to the Guderley implosion problem in arbitrary media
Boyd, Zachary; Ramsey, Scott; Baty, Roy
2016-11-01
It is known classically that in an ideal gas, there exist self-similar, spherical, converging shock solutions, but much less is understood about the existence of such solutions in compressible flow of real materials. On the other hand, it has recently been pointed out that there exist self-similar solutions for the Euler equations regardless of the equation of state closure model, which suggests the possibility that the Guderley problem might be solvable in general. In this work, we rigorously determine what properties are required of an equation of state in order for an exact, self-similar Guderley flow to be realized, including a generic solution procedure in the cases where existence holds. Among other contexts, this result is of great practical interest for the verification of codes intended to treat shock propagation in a wide variety of real materials.
Existence of Three Positive Solutions to Some p-Laplacian Boundary Value Problems
Moulay Rchid Sidi Ammi
2013-01-01
Full Text Available We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some p-Laplacian boundary value problems on time scales.
Johnny Henderson
2016-01-01
Full Text Available We investigate the existence and nonexistence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations with two parameters, subject to coupled integral boundary conditions.
EXISTENCE OF MILD SOLUTIONS TO SEMILINEAR FRACTIONAL ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS
无
2011-01-01
In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.
K Balachandran; K Uchiyama
2000-05-01
In this paper we prove the existence of mild and strong solutions of a nonlinear integrodifferential equation of Sobolev type with nonlocal condition. The results are obtained by using semigroup theory and the Schauder fixed point theorem.
Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model
Zhijian Wei
2015-01-01
Full Text Available We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known results.
Existence and uniqueness of solution for a class of stochastic differential equations.
Cao, Junfei; Huang, Zaitang; Zeng, Caibin
2013-01-01
A class of stochastic differential equations given by dx(t) = f(x(t))dt + g(x(t))dW(t), x(t 0) = x 0, t 0 ≤ t ≤ T existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution for stochastic Lorenz system, which is illustrated by example, are in good agreement with the theoretical analysis.
EXISTENCE AND UNIQUENESS AND STABILITY OF SOLUTIONS FOR STOCHASTIC IMPULSIVE SYSTEMS
Bin LIU; Xinzhi LIU; Xiaoxin LIAO
2007-01-01
This paper studies the existence,uniqueness,and stability of solutions for stochastic impul sive systems.By employing Lyapunov-like functions,some sufficient conditions of the global existence,uniqueness,and stability of solutions for stochastic impulsive systems are established.Furthermore,the results are specialized to the case of linear stochastic impulsive systems.Finally,some examples are given to illustrate the applications of our theory.
Existence of Almost-Periodic Solutions for Lotka-Volterra Cooperative Systems with Time Delay
Kaihong Zhao
2012-01-01
Full Text Available This paper considers the existence of positive almost-periodic solutions for almost-periodic Lotka-Volterra cooperative system with time delay. By using Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost-periodic solutions are obtained. An example and its simulation figure are given to illustrate the effectiveness of our results.
Existence of Solutions of a Riccati Differential System from a General Cumulant Control Problem
Stanley R. Liberty
2011-01-01
Full Text Available We study a system of infinitely many Riccati equations that arise from a cumulant control problem, which is a generalization of regulator problems, risk-sensitive controls, minimal cost variance controls, and k-cumulant controls. We obtain estimates for the existence intervals of solutions of the system. In particular, new existence conditions are derived for solutions on the horizon of the cumulant control problem.
Existence Analysis of Traveling Wave Solutions for a Generalization of KdV Equation
Yao Long
2013-01-01
Full Text Available By using the bifurcation theory of dynamic system, a generalization of KdV equation was studied. According to the analysis of the phase portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave, and compactons were discussed. In some parametric conditions, exact traveling wave solutions of this generalization of the KdV equation, which are different from those exact solutions in existing references, were given.
On the existence of positive solutions for fractional differential inclusions at resonance.
Hu, Lei
2016-01-01
In this paper, we discuss the existence of positive solutions for a boundary value problem of fractional differential inclusions with resonant boundary conditions. By using the Leggett-Williams theorem for coincidences of multi-valued operators due to O'Regan and Zima, results on the existence of positive solutions are established. An example is given to illustrate the efficiency of the main theorems.
VANGQUANYI
1997-01-01
This paper deals with the problems on the existence and uniqueness and stability of almostperiodic solutions for functional differential equations with infinite delays. The author obtainssome sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment. The results extend all the results of the paper[1] and solve the two open problems proposed in [1] under much weaker conditions than that proposed in [1].
EXISTENCE OF PERIODIC SOLUTIONS FOR A DISCRETE-TIME MODEL OF TWO-CELL CNNS
无
2006-01-01
We investigate a class of discrete-time model of two-cell cellular neural networks with symmetric template. By using the Lyapunov direct method, La-Salle's invariance principle, we discuss the existence and the stability of periodic solutions. The model considered has attractive 2-periodic and unstable 2-periodic solutions.
Archana Chauhan
2011-08-01
Full Text Available In this work we consider a class of impulsive fractional-order semilinear evolution equations with a nonlocal initial condition. By means of solution operator and application of fixed point theorems we established the existence and uniqueness of a mild solution.
EXISTENCE OF WEAK SOLUTIONS FOR A DEGENERATE GENERALIZED BURGERS EQUATION WITH LARGE INITIAL DATA
张辉
2002-01-01
It is obtained the existence of the weak solution for a degenerate generalized Burgers equation under the restriction u0 ∈ L∞. The main method is to add viscosity perturbation and obtain some estimates in L1 norm. Meanwhile it is obtained the solution is exponential decay when the initial data has compact support.
Existence of global weak solution for a reduced gravity two and a half layer model
Guo, Zhenhua, E-mail: zhenhua.guo.math@gmail.com; Li, Zilai, E-mail: lizilai0917@163.com; Yao, Lei, E-mail: yaolei1056@hotmail.com [Department of Mathematics and CNS, Northwest University, Xi' an 710127 (China)
2013-12-15
We investigate the existence of global weak solution to a reduced gravity two and a half layer model in one-dimensional bounded spatial domain or periodic domain. Also, we show that any possible vacuum state has to vanish within finite time, then the weak solution becomes a unique strong one.
Direct evidence on the existence of [Mo132]Keplerate-type species in aqueous solution.
Roy, Soumyajit; Planken, Karel L; Kim, Robbert; Mandele, Dexx v d; Kegel, Willem K
2007-10-15
We demonstrate the existence of discrete single molecular [Mo(132)] Keplerate-type clusters in aqueous solution. Starting from a discrete spherical [Mo(132)] cluster, the formation of an open-basket-type [Mo(116)] defect structure is shown for the first time in solution using analytical ultracentrifugation sedimentation velocity experiments.
Existence of solutions for nonlinear mixed type integrodifferential equation of second order
Haribhau Laxman Tidke
2010-04-01
Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.
Existence of solutions to fractional differential inclusions with p-Laplacian operator
Ahmet Yantir
2014-12-01
Full Text Available In this article, we prove the existence of solutions for three-point fractional differential inclusions with p-Laplacian operator. We use fixed point theory for set valued upper semi-continuous maps for obtaining the solutions.
THE EXISTENCE AND UNIQUENESS OF A POSITIVE SOLUTION OF AN ELLIPTIC SYSTEM
Joon Hyuk Kang; Yun Myung Oh
2004-01-01
The existence and uniqueness of the positive solution for the generalized Lotka-Volterra competition model for several competing species Δui+ui(a-g(u1,…,un))=0 in Ω,ui=0 on бΩ for I = 1, ..., N were investigated. The techniques used in this paper are elliptic theory,upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.
Can there be a general nonlinear PDE theory for the existence of solutions ?
2004-01-01
Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with associated initial and/or boundary value problems. The solutions obtained can be assimilated with usual ...
Existence and Uniqueness of Periodic Solutions for Second Order Differential Equations
Yuanhong Wei
2014-01-01
Full Text Available We study some second order ordinary differential equations. We establish the existence and uniqueness in some appropriate function space. By using Schauder’s fixed-point theorem, new results on the existence and uniqueness of periodic solutions are obtained.
Toka Diagana
2011-02-01
Full Text Available First we show that if the doubly-weighted Bohr spectrum of an almost periodic function exists, then it is either empty or coincides with the Bohr spectrum of that function. Next, we investigate the existence of doubly-weighted pseudo-almost periodic solutions to some non-autonomous abstract differential equations.
Existence of local and global solutions to some impulsive fractional differential equation
Said Mazouzi
2009-10-01
Full Text Available First, by using Schauder's fixed-point theorem we establish the existence uniqueness of locals for some fractional differential equation with a finite number of impulses. On the other hand, by using Brouwer's fixed-point theorem, we establish existence of the global solutions under suitable assumptions.
EXISTENCE OF SOLUTIONS TO A CLASS OF NONLINEAR n-DIMENSIONAL DISCRETE BOUNDARY VALUE PROBLEMS
无
2012-01-01
In this paper,using the critical point theory,we obtain a new result on the existence of the solutions to a class of n-dimensional discrete boundary value problems.Results obtained extend or improve the existing ones.
Existence of Solutions for Nonlinear Four-Point -Laplacian Boundary Value Problems on Time Scales
Topal SGulsan
2009-01-01
Full Text Available We are concerned with proving the existence of positive solutions of a nonlinear second-order four-point boundary value problem with a -Laplacian operator on time scales. The proofs are based on the fixed point theorems concerning cones in a Banach space. Existence result for -Laplacian boundary value problem is also given by the monotone method.
Existence and non-uniqueness of similarity solutions of a boundary-layer problem
Hussaini, M. Y.; Lakin, W. D.
1986-01-01
A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.
Existence and non-uniqueness of similarity solutions of a boundary layer problem
Hussaini, M. Y.; Lakin, W. D.
1984-01-01
A Blasius boundary value problem with inhomogeneous lower boundary conditions f(0) = 0 and f'(0) = - lambda with lambda strictly positive was considered. The Crocco variable formulation of this problem has a key term which changes sign in the interval of interest. It is shown that solutions of the boundary value problem do not exist for values of lambda larger than a positive critical value lambda. The existence of solutions is proven for 0 lambda lambda by considering an equivalent initial value problem. It is found however that for 0 lambda lambda, solutions of the boundary value problem are nonunique. Physically, this nonuniqueness is related to multiple values of the skin friction.
Theorems about the Existence of Solutions to Problems with Nonlocal Initial Value
Yuan Di WANG
2001-01-01
Recently much work has been devoted to nonlocal problems. However, very little has beenaccomplishe d in the literature for nonlocal initial problems with nonlinear boundary conditions. It isthe purpose of this paper to prove the existence results for solutions to a semilinear parabolic PDEwith linear homogeneous boundary conditions, and to other ones with nonlinear boundary conditions,provided the ordered upper and lower solutions are given. Semigroup, fractional order function spacesand generalized Poincaré operators play an important role in proving the existence of solutions.
Existence of Young measure solutions of a class of singular diffusion equations
无
2002-01-01
The first initial-boundary value problem of a class of singular diffusion equations with the flux sublinear growth and the potential without convexity is investigated. Such equations may be strongly degenerate, singular and forward-backward. Inspired by the idea in a recent work of Demoulini, we first discuss the regular case by introducing the Young measure solutions and prove the existence of such solutions. Consequently, we approximate the extreme case by the method of regularization. By means of some uniform estimates and some techniques, the existence of Young measure solutions with bounded variation is established.
Short-time existence of solutions for mean-field games with congestion
Gomes, Diogo A.
2015-11-20
We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.
Luminescence spectra and kinetics of disordered solid solutions
Klochikhin, A.; Reznitsky, A.; Permogorov, S.;
1999-01-01
We have studied both theoretically and experimentally the luminescence spectra and kinetics of crystalline, disordered solid solutions after pulsed excitation. First, we present the model calculations of the steady-state luminescence band shape caused by recombination of excitons localized in the......-time limit at excitation below the exciton mobility edge. At excitation by photons with higher energies the diffusion of electrons can account for the observed behavior of the luminescence. [S0163-1829(99)11419-X]....
Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation
M. B. A. Mansour
2009-01-01
In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations (ODEs). Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits.
Existence of solutions for differential equations systems with p-Laplacian at resonance
Weihua JIANG
2017-08-01
Full Text Available In order to study the existence of solutions for boundary value problems at resonance with nonlinear fractional differential operator, a generalization of Mawhin's continuous theorem is introduced. By defining suitable Banach space and norm, constructing the proper operators and using the extension of Mawhin continuation theorem, the existence of solutions for fractional differential equations systems boundary value problem with p-Laplacian at resonance is studied. An example is given to illustrate the main results. The results are the improvement and generalization of some existing results of boundary value problems at resonance.
Evaluation of existing Hanford buildings for the storage of solid wastes
Carlson, M.C.; Hodgson, R.D.; Sabin, J.C.
1993-05-01
Existing storage space at the Hanford Site for solid low-level mixed waste (LLMW) will be filled up by 1997. Westinghouse Hanford Company (WHC) has initiated the project funding cycle for additional storage space to assure that new facilities are available when needed. In the course of considering the funding request, the US Department of Energy (DOE) has asked WHC to identify and review any existing Hanford Site facilities that could be modified and used as an alternative to constructing the proposed W-112 Project. This report documents the results of that review. In summary, no buildings exist at the Hanford Site that can be utilized for storage of solid LLMW on a cost-effective basis when compared to new construction. The nearest approach to an economically sensible conversion would involve upgrade of 100,000 ft{sup 2} of space in the 2101-M Building in the 200 East Area. Here, modified storage space is estimated to cost about $106 per ft{sup 2} while new construction will cost about $50 per ft{sup 2}. Construction costs for the waste storage portion of the W-112 Project are comparable with W-016 Project actual costs, with escalation considered. Details of the cost evaluation for this building and for other selected candidate facilities are presented in this report. All comparisons presented address the potential decontamination and decommissioning (D&D) cost avoidances realized by using existing facilities.
Shuang Ping TAO; Shang Bin CUI
2005-01-01
This paper is devoted to studying the initial value problem of the modified nonlinear Kawahara equation ()u/()t+ a u2()u/()m + β()3u/()x3 + γ()5u-()x5 = 0, (x, t) ∈ We first establish several Strichartz type estimates for the fundamental solution of the corresponding linear problem. Then we apply such estimates to prove local and global existence of solutions for the initial value problem of the modified nonlinear Karahara equation. The results show that a local solution exists if the initial function u0(x) ∈ Hs(R) with s ≥ 1/4, and a global solution exists if s ≥ 2.
Development and characterization of solid solution tri-carbides
Knight, Travis; Anghaie, Samim
2001-02-01
Solid-solution, binary uranium/refractory metal carbide fuels have been shown to be capable of performing at high temperatures for nuclear thermal propulsion applications. More recently, tri-carbide fuels such as (U, Zr, Nb)C1+x with less than 10% metal mole fraction uranium have been studied for their application in ultra-high temperature, high performance space nuclear power systems. These tri-carbide fuels require high processing temperatures greater than 2600 K owing to their high melting points in excess of 3600 K. This paper presents the results of recent studies involving hypostoichiometric, single-phase tri-carbide fuels. Processing techniques of cold uniaxial pressing and sintering were investigated to optimize the processing parameters necessary to produce high density (low porosity), single phase, solid solution mixed carbide nuclear fuels for testing. Scanning electron microscopy and xray diffraction were used to analyze samples. Liquid phase sintering with UC1+x at temperatures near 2700 K was shown to be instrumental in achieving good densification in hyper- and near-stoichiometric mixed carbides. Hypostoichiometric carbides require even higher processing temperatures greater than 2800 K in order to achieve liquid phase sintering with a UC liquid phase and good densification of the final solid solution, tri-carbide fuel. .
EXISTENCE AND UNIQUENESS OF THE ENTROPY SOLUTION TO A NONLINEAR HYPERBOLIC EQUATION
R.EYMARD; T.Gallouёt; R.Herbin
1995-01-01
This work is concerned with the proof of the existence and uniqueness of the entropy weak solution to the following nonlinear hyperbolic equation: ut+div(vf(u)） = 0 in IRN×（0, T）, with initial data u(-, 0) = u0(-) in IRN, where u0 ∈ L∞（IRN) is a given function, v is a divergence-free bounded fnnction of class C1 from IRN × [0, T] to IRN, and f is a 5motion of class C1 from IR to IR. It also gives a result of convergence of a numerical scheme for the discretization of this equation. The authors first show the existence of a “process” solution (which generalizes the concept of entropy weak solutions, and can be obtained by passing to the limit of solutions ofthe numerical scheme). The uniqueness of this entropy process solution is then proven; it isalso proven that the entropy process solution is in fact an entropy weak solution. Hence the existence and uniqueness of the entropy weak solution are proven.
Zhu, C
2003-01-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
Zhu, Changjiang; Duan, Renjun [Laboratory of Nonlinear Analysis, Department of Mathematics, Central China Normal University, Wuhan 430079, People' s Republic of China (China)
2003-02-28
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
Benson, Steven; Palo, Daniel; Srinivasachar, Srivats; Laudal, Daniel
2014-12-01
Under contract DE-FE0007603, the University of North Dakota conducted the project Evaluation of Carbon Dioxide Capture from Existing Coal Fired Plants by Hybrid Sorption Using Solid Sorbents. As an important element of this effort, an Environmental Health and Safety (EH&S) Assessment was conducted by Barr Engineering Co. (Barr) in association with the University of North Dakota. The assessment addressed air and particulate emissions as well as solid and liquid waste streams. The magnitude of the emissions and waste streams was estimated for evaluation purposes. EH&S characteristics of materials used in the system are also described. This document contains data based on the mass balances from both the 40 kJ/mol CO2 and 80 kJ/mol CO2 desorption energy cases evaluated in the Final Technical and Economic Feasibility study also conducted by Barr Engineering.
Moses, Julianne I.; Nash, Douglas B.
1991-01-01
Laboratory investigations have been conducted on the effects of variations in sulfur sample histories on their solid-state transformation rate and the corresponding spectral variation of freshly frozen sulfur. The temporal variations in question may be due to differences in the amount and type of metastable allotropes present in the sulfur after solidification, as well as to the physics of the phase-transformation process itself. The results obtained are pertinent to the physical behavior and spectral variation of such freshly solidified sulfur as may exist on the Jupiter moon Io; this would initially solidify into a glassy solid or monoclinic crystalline lattice, then approach ambient dayside temperatures. Laboratory results imply that the monoclinic or polymeric allotropes can in these circumstances be maintained, and will take years to convert to the stable orthorhombic crystalline form.
Extended Hansen approach: calculating partial solubility parameters of solid solutes.
Wu, P L; Beerbower, A; Martin, A
1982-11-01
A multiple linear regression method, known as the extended Hansen solubility approach, was used to estimate the partial solubility parameters, delta d, delta p, and delta h for crystalline solutes. The method is useful, since organic compounds may decompose near their melting points, and it is not possible, to determine solubility parameters for these solid compounds by the methods used for liquid solvents. The method gives good partial and total solubility parameters for naphthalene; with related compounds, less satisfactory results were obtained. At least three conditions, pertaining to the regression equation and the solvent systems, must be met in order to obtain reasonable solute solubility parameters. In addition to providing partial solubility parameters, the regression equations afford a calculation of solute solubility in both polar and nonpolar solvents.
B Nageswara Sarma; S Srinivas Prasad; S Vijayvergiya; V Bharath Kumar; S Lele
2003-06-01
The thermodynamic origin of various types of phase diagrams in simple binary systems exhibiting two phases (e.g. a liquid and a solid phase) has been examined using the regular solution model. The necessary conditions for the occurrence of each of these types are identified in terms of the appropriate intersections of the miscibility gap boundaries (in solid/liquid phases) and the liquidus/solidus/iso- curves. Thus, the regions of occurrence of the different types of possible phase diagrams in the space of the regular solution interchange energy parameters (, ) are clearly delineated. This analysis makes it easier to make intelligent initial selections of model (energy) parameters for their optimization in the calculation of phase diagrams using thermodynamic models such as CALPHAD/CVM.
Summary of existing information on gamma-ray and X-ray attenuation coefficients of solutions
Singh, K.; Gerward, Leif
2002-01-01
Accurate values of X-ray and gamma-ray attenuation coefficients of different chemicals are required in spectrometry as well as in many other scientific, engineering and medical disciplines involving photon radiation. The current state of knowledge of experimental and theoretical gamma-ray and X......-ray attenuation coefficients in aqueous solutions of salts is presented and exemplified by recent work. The results presented provide a basis for studying X-ray and gamma-ray photon interactions with ions in solution (hydrated ions) rather than ion compounds in solid form....
Theromdynamics of carbon in nickel-based multicomponent solid solutions
Bradley, D. J.
1978-04-01
The activity coefficient of carbon in nickel, nickel-titanium, nickel-titanium-chromium, nickel-titanium-molybdenum and nickel-titanium-molybdenum-chromium alloys has been measured at 900, 1100 and 1215/sup 0/C. The results indicate that carbon obeys Henry's Law over the range studied (0 to 2 at. percent). The literature for the nickel-carbon and iron-carbon systems are reviewed and corrected. For the activity of carbon in iron as a function of composition, a new relationship based on re-evaluation of the thermodynamics of the CO/CO/sub 2/ equilibrium is proposed. Calculations using this relationship reproduce the data to within 2.5 percent, but the accuracy of the calibrating standards used by many investigators to analyze for carbon is at best 5 percent. This explains the lack of agreement between the many precise sets of data. The values of the activity coefficient of carbon in the various solid solutions are used to calculate a set of parameters for the Kohler-Kaufman equation. The calculations indicate that binary interaction energies are not sufficient to describe the thermodynamics of carbon in some of the nickel-based solid solutions. The results of previous workers for carbon in nickel-iron alloys are completely described by inclusion of ternary terms in the Kohler-Kaufman equation. Most of the carbon solid solution at high temperatures in nickel and nickel-titantium alloys precipitates from solution on quenching in water. The precipitate is composed of very small particles (greater than 2.5 nm) of elemental carbon. The results of some preliminary thermomigration experiments are discussed and recommendations for further work are presented.
Benson, Steven; Browers, Bruce; Srinivasachar, Srivats; Laudal, Daniel
2014-12-31
Under contract DE-FE0007603, the University of North Dakota conducted the project Evaluation of Carbon Dioxide Capture from Existing Coal Fired Plants by Hybrid Sorption Using Solid Sorbents. As an important element of this effort, a Technical and Economic Feasibility Study was conducted by Barr Engineering Co. (Barr) in association with the University of North Dakota. The assessment developed a process flow diagram, major equipment list, heat balances for the SCPC power plant, capital cost estimate, operating cost estimate, levelized cost of electricity, cost of CO2 capture ($/ton) and three sensitivity cases for the CACHYS™ process.
Existence of positive periodic solution of mutualism system with several delays
Wu Haihui [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China); Department of Computer Science and Technology, Sunshine College, Fuzhou University, Fuzhou 350002 (China); Xia Yonghui [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China)], E-mail: yhxia@fzu.edu.cn; Lin Muren [College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002 (China)
2008-04-15
In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solutions of a mutualism systems with bounded and unbounded delays. Our results generalize significantly improve those of Gopalsamy and He [Gopalsamy K, He XZ. Persistence, attractivity, and delay in facultative mutualism. J Math Anal Appl 1997;215:154-73], Yang et al. [Yang F, Jiang D, Ying A. Existence of positive solution of multidelays facultative mutualism system. J Eng Math 2002;3:64-8], Chen et al. [Chen FD, Shi JL, Chen XX. Periodicity in Lotka-Volterra facultative mutualism system with several delays. J Eng Math 2004;21(3)] and Xia and Lin [Xia YH, Lin M, Existence of positive periodic solution of mutualism system with infinite delays. Ann Diff Eqs 2005;21(3):448-53].
Existence and Stability of Solutions for Steady Flows of Fibre Suspension Flows
Munganga, J. M. W.
2013-03-01
We establish existence, uniqueness, convergence and stability of solutions to the equations of steady flows of fibre suspension flows. The existence of a unique steady solution is proven by using an iterative scheme. One of the restrictions imposed on the data confirms a well known fact proven in Galdi and Reddy (J Non-Newtonian Fluid Mech 83:205-230, 1999), Munganga and Reddy (Math Models Methods Appl Sci 12:1177-1203, 2002) and Munganga et al. (J Non-Newtonian fluid Mech 92:135-150, 2000) that the particle number N p must be less than 35/2. Exact solutions are calculated for Couette and Poiseuille flows. Solutions of Poiseuille flows are shown to be more accurate than those of Couette flow when a time perturbation is considered.
Existence of traveling wave solutions for diffusive predator-prey type systems
Hsu, Cheng-Hsiung; Yang, Chi-Ru; Yang, Ting-Hui; Yang, Tzi-Sheng
In this work we investigate the existence of traveling wave solutions for a class of diffusive predator-prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalle's Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.
Tang Zhongwei
2006-01-01
The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -Au = φ(r)up-1, u ＞ 0 in RN, u ∈ D1,2(RN), where N ≥ 3, x =(x',z) ∈ RK × RN-K,2 ≤ K ≤ N,r = |x'|. It is proved that for 2(N-s)/(N-2) ＜p ＜ 2* = 2N/(N - 2), 0 ＜ s ＜ 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2*, the above equation does not have a ground state solution but a cylindrically symmetric.solution, and when p close to 2*, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2*, the ground state solution up has a unique maximum point xp = (x'p, zp) and as p → 2*, |x'p| → r0 which attains the maximum of φ on RN. The asymptotic behavior ofground state solution up is also given, which also deduces that the ground state solutionis not cylindrically symmetric as p goes to 2*.
On the Global Existence and Uniqueness of Solutions to Prandtl's System
Xin Ying XU; Jun Ning ZHAO
2009-01-01
In this paper, we consider the Prandtl system for the non-stationary boundary layer in the vicinity of a point where the outer flow has zero velocity. It is assumed that U(t, x, y) = xmU1(t, x), where 0≤x≤L and m≥1. We establish the global existence of the weak solution to this problem. Moreover the uniqueness of the weak solution is proved.
Existence and uniqueness of solutions in general multisolute renal flow problems.
Garner, J B; Kellogg, R B
1988-01-01
This paper considers systems of differential equations that describe flows in renal networks. The flow geometry is of the type that occurs in modelling the renal medulla. The unknowns in the system include the flow rate, the hydrostatic pressure, and the concentrations of the various solutes. Existence and uniqueness of solutions of the appropriate boundary value problems are established, in the case of small permeability coefficients and transport rates, or large diffusion coefficients and small resistance to flow constants.
On the global existence and uniqueness of solutions to the nonstationary boundary layer system
ZHANG; Jianwen; ZHAO; Junning
2006-01-01
In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.
Global existence and decay of solutions of the Cauchy problem in thermoelasticity with second sound
Kasimov, Aslan R.
2013-06-04
We consider the one-dimensional Cauchy problem in non-linear thermoelasticity with second sound, where the heat conduction is modelled by Cattaneo\\'s law. After presenting decay estimates for solutions to the linearized problem, including refined estimates for data in weighted Lebesgue-spaces, we prove a global existence theorem for small data together with improved decay estimates, in particular for derivatives of the solutions. © 2013 Taylor & Francis.
Reem A. Al-Omair
2009-03-01
Full Text Available In this paper we prove the existence of a mild solution for a semilinear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator generated by the family operators. Also, we prove that the set of mild solutions is compact.
Existence and Stability of Solutions for Implicit Multivalued Vector Equilibrium Problems
Li Qiuying
2011-01-01
Full Text Available A class of implicit multivalued vector equilibrium problems is studied. By using the generalized Fan-Browder fixed point theorem, some existence results of solutions for the implicit multivalued vector equilibrium problems are obtained under some suitable assumptions. Moreover, a stability result of solutions for the implicit multivalued vector equilibrium problems is derived. These results extend and unify some recent results for implicit vector equilibrium problems, multivalued vector variational inequality problems, and vector variational inequality problems.
Existence of mild solutions to partial differential equations with non-instantaneous impulses
Pengyu Chen
2016-09-01
Full Text Available In this article, we study the existence of piecewise-continuous mild solutions for the initial value problems for a class of semilinear evolution equations. These equations have non-instantaneous impulses in Banach spaces and the corresponding solution semigroup is noncompact. We assume that the nonlinear term satisfies certain local growth condition and a noncompactness measure condition. Also we assume the non-instantaneous impulsive functions satisfy some Lipschitz conditions. An example is given to illustrate our results.
Xiao-Bao Shu
2013-06-01
Full Text Available In this article, we study the existence of an infinite number of subharmonic periodic solutions to a class of second-order neutral nonlinear functional differential equations. Subdifferentiability of lower semicontinuous convex functions $varphi(x(t,x(t-au$ and the corresponding conjugate functions are constructed. By combining the critical point theory, Z2-group index theory and operator equation theory, we obtain the infinite number of subharmonic periodic solutions to such system.
Existence and Numerical Solution of the Volterra Fractional Integral Equations of the Second Kind
Abdon Atangana
2013-01-01
Full Text Available This work presents the possible generalization of the Volterra integral equation second kind to the concept of fractional integral. Using the Picard method, we present the existence and the uniqueness of the solution of the generalized integral equation. The numerical solution is obtained via the Simpson 3/8 rule method. The convergence of this scheme is presented together with numerical results.
Global existence of weak solution to the heat and moisture transport system in fibrous porous media
Li, Buyang; Wang, Yi
2009-01-01
This paper is concerned with theoretical analysis of a heat and moisture transfer model arising from textile industries, which is described by a degenerate and strongly coupled parabolic system. We prove the global (in time) existence of weak solution by constructing an approximate solution with some standard smoothing. The proof is based on the physcial nature of gas convection, in which the heat (energy) flux in convection is determined by the mass (vapor) flux in convection.
Existence and uniqueness of solutions to the multispecies virtual population analysis equations.
Magnus, R J; Magnusson, K G
1987-01-01
This paper deals with the question of existence and uniqueness of solutions to multispecies virtual population analysis equations for predator-prey systems. By formulating the question as a fixed-point problem for a certain function F, it is shown that at least one solution always exists. By using Brouwer degree, sufficient conditions for uniqueness are derived which are more likely to be satisfied than those based on the requirement that F be a contraction. Some of these are formulated as inequalities which could be verified in the course of solving the equations numerically.
Chun Hui ZHOU
2012-01-01
The purpose of this paper is to prove the existence of a spatially periodic weak solution to the steady compressible isentropic MHD equations in R3 for any specific heat ratio γ＞ 1.The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density,and the method of weak convergence.According to the author's knowledge,it is the first result that treats in three dimensions the existence of weak solutions to the steady compressible MHD equations with γ ＞ 1.
Helge Holden
2003-04-01
Full Text Available We prove existence and uniqueness of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general $L^p$ compactness criterion. The uniqueness proof is an adaption of Kruzkov's ``doubling of variables'' proof. We also present a numerical example motivated by biodegradation in porous media.
Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions
Idriss Ellahiani
2016-01-01
Full Text Available The paper deals with global existence of weak solutions to a one-dimensional mathematical model describing magnetoelastic interactions. The model is described by a fractional Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We prove global existence by using Faedo-Galerkin/penalty method. Some commutator estimates are used to prove the convergence of nonlinear terms.
1985-10-01
many more resu -s of this kind, including existence results in cases where nonuniqueness is possible and the existence of minimal solutions. We also...in these works. -4- . .. . . . . . . . . * .. ..-.. .. ... . .. . .. . .. . .. . .. . .. . . H CONTENTS I. Lipschitz Hamiltonians and the stationary...condition~s at infinity VII. Further remarks on the Cauchy problem V -5-r 1. LIPSCHITZ HAMILTONIANS AN-D THE STATIONARY PROBLEM. wilIn this section we
1966-01-01
SINGLE CRYSTALS WITH RHENIUM IN DILUTE SOLID SOLUTION Sby M. Garfinkle Lewis Research Center Cleveland, Ohio 20060516196 NATIONAL AERONAUTICS AND...WITH RHENIUM IN DILUTE SOLID SOLUTION By M. Garfinkle Lewis Research Center Cleveland, Ohio NATIONAL AERONAUTICS AND SPACE ADMINISTRATION For sale by...ORIENTED TUNGSTEN SINGLE CRYSTALS WITH RHENIUM IN DILUTE SOLID SOLUTION * by M. Garfinkle Lewis Research Center SUMMARY Tungsten single crystals
The existence and the stability of solutions for equilibrium problems with lower and upper bounds
Congjun Zhang
2012-12-01
Full Text Available In this paper, we study a class of equilibrium problems with lower and upper bounds. We obtain some existence results of solutions for equilibrium problems with lower and upper bounds by employing some classical fixed-point theorems. We investigate the stability of the solution sets for the problems, and establish sufficient conditions for the upper semicontinuity, lower semicontinuity and continuity of the solution set mapping $S:Lambda_1imesLambda_2o2^{X}$ in a Hausdorff topological vector space, in the case where a set $K$ and a mapping $f$ are perturbed respectively by parameters $lambda$ and $mu.$
Harrabi, Abdellaziz; Rebhi, Salem; Selmi, Abdelbaki
In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in R, N⩾3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u, using the uniqueness result due to Tanaka (2008) [21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k.
Lijun Zhang
2014-01-01
Full Text Available An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions. The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.
EXISTENCE AND REGULARITY OF SOLUTIONS TO MODEL FOR LIQUID MIXTURE OF 3HE-4HE
Luo Hong; Pu Zhilin
2012-01-01
Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper.First,it is proved that this system possesses a unique global weak solution in H1(Ω,C × R) by using Galerkin method.Secondly,by using an iteration procedure,regularity estimates for the linear semigroups,it is proved that the model for liquid mixture of 3He-4He has a unique solution in Hk(Ω,C × R) for all k ≥ 1.
Jian Liu
2013-09-01
Full Text Available In this article, we consider the free boundary value problem for one-dimensional compressible bipolar Navier-Stokes-Possion (BNSP equations with density-dependent viscosities. For general initial data with finite energy and the density connecting with vacuum continuously, we prove the global existence of the weak solution. This extends the previous results for compressible NS [27] to NSP.
无
2010-01-01
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.
Ze-qing Liu; Shin Min Kang
2007-01-01
In this paper we establish the existence,uniqueness and iterative approxinlation of solutions for two classes of functional equations arising in dynamic programming of multistage decision Processes.The resultspresented here extend,and unify the corresponding results due to Bellman,Bhakta and Choudhury,Bhakta and Mitra,Liu and others.
Existence and uniqueness of positive solutions to a quasilinear elliptic problem in $R^N$
Dragos-Patru Covei
2005-12-01
Full Text Available We prove the existence of a unique positive solution to the problem $$ -Delta _{p}u=a(xf(u $$ in $mathbb{R}^{N}$, $N>2$. Our result extended previous works by Cirstea-Radulescu and Dinu, while the proofs are based on two theorems on bounded domains, due to Diaz-Saa and Goncalves-Santos.
Bishop, S. A.; Ayoola, E. O.; Oghonyon, G. J.
2016-08-01
New results on existence and uniqueness of solution of impulsive quantum stochastic differential equation with nonlocal conditions are established. The nonlocal conditions are completely continuous. The methods applied here are simple extension of the methods applied in the classical case to this noncummutative quantum setting.
V. Vijayakumar
2014-09-01
Full Text Available In this article, we study the existence of mild solutions for nonlocal Cauchy problem for fractional neutral evolution equations with infinite delay. The results are obtained by using the Banach contraction principle. Finally, an application is given to illustrate the theory.
Existence of Renormalized Solutions for p(x-Parabolic Equation with three unbounded nonlinearities
Youssef Akdim
2016-04-01
Full Text Available In this article, we study the existence of renormalized solution for the nonlinear $p(x$-parabolic problem of the form:\\\\ $\\begin{cases} \\frac{\\partial b(x,u}{\\partial t} - div (a(x,t,u,\
无
2010-01-01
By the generalized Borsuk theorem in coincidence degree theory, a p-Laplacian neutral functional differential equation is studied. A new result on the existence of periodic solution is obtained. The interest is that some coeffcient in it is not a constant function and its sign can be changeable, which is different from that in the known literatures.
Existence of positive almost periodic solutions for delay Lotka-Volterra cooperative systems
Kaihong Zhao
2013-07-01
Full Text Available In this article, we study a Lotka-Volterra cooperative system of equations with time-varying delays and distributed delays. By using Mawhin's continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive almost periodic solutions. Also we present an example to illustrate our results.
Zhao Hongyong [Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 (China)]. E-mail: hongyongz@126.com; Ding Nan [Department of Mathematics, Xinjiang Normal University, Urumqi 830054 (China)
2006-07-15
In this paper, Lotka-Volterra competition-predator system with variable delays is considered. Some sufficient conditions ensuring the existence and global attractivity of periodic solution for this system are obtained by using coincidence degree theory and Lyapunov functional method. An example is also worked out to demonstrate the advantages of our results.
Existence of global solution for a differential system with initial data in Lp
Peter Bates
1999-01-01
field within the earth. The system is similar to the magnetohydrodynamic (MHD equations. By establishing a new priori estimates and following Calderón's procedure for the Navier Stokes equations [1], we obtained, for initial data in space Lp, the global in time existence and uniqueness of weak solution of the system subject to appropriate conditions.
Existence of Positive Periodic Solutions to -Species Nonautonomous Food Chains with Harvesting Terms
Li Yongkun
2010-01-01
Full Text Available By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least positive periodic solutions for -species nonautonomous Lotka-Volterra type food chains with harvesting terms. An example is given to illustrate the effectiveness of our results.
Pradeep Kumar
2013-10-01
Full Text Available The objective of this article is to prove the existence of piecewise continuous mild solutions to impulsive functional differential equation with iterated deviating arguments in a Banach space. The results are obtained by using the theory of analytic semigroups and fixed point theorems.
Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales
Meng Hu
2012-01-01
Full Text Available By using the theory of calculus on time scales and M-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.
Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales
Meng Hu; Lili Wang
2012-01-01
By using the theory of calculus on time scales and M-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.
Existence of non-negative solutions for nonlinear equations in the semi-positone case
Naji Yebari
2006-09-01
Full Text Available Using the fibring method we prove the existence of non-negative solution of the p-Laplacian boundary value problem $-Delta_pu=lambda f(u$, for any $lambda >0$ on any regular bounded domain of $mathbb{R}^N$, in the special case $f(t=t^q-1$.
Hassane Bouzahir
2006-08-01
Full Text Available In this paper, we establish results concerning, existence, uniqueness, global continuation, and regularity of integral solutions to some partial neutral functional differential equations with infinite delay. These equations find their origin in the description of heat flow models, viscoelastic and thermoviscoelastic materials, and lossless transmission lines models; see for example [15] and [38].
EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS
赵才地
2004-01-01
This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.
A STUDY ON SOME PROBLEMS ON EXISTENCE OF SOLUTIONS FOR NONLINEAR FUNCTIONAL-INTEGRAL EQUATIONS
DEEPMALA; H.K. PATHAK
2013-01-01
In this paper, we prove the existence of solutions of some nonlinear functional-integral equation by using a fixed point theorem which satisfy the Darbo condition. The results extend the corresponding results of many authors. In the sequel, we give an example of our main result to highlight the realized improvements.
THE EXISTENCE OF PERIODIC SOLUTIONS TO SECOND ORDER SELF-ADJOINT DIFFERENCE EQUATIONS
无
2010-01-01
In this paper, we consider the existence of periodic solutions to a class of second order self-adjoint difference equations. By the least action principle and saddle point theorem in the critical point theory, some new results are obtained. As an application, we also give two examples to demonstrate our main results.
Existence of periodic and subharmonic solutions for second-order superlinear difference equations
郭志明; 庾建设
2003-01-01
By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations △2xn-1 + f(n,xn) = 0,some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.
EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM
无
2011-01-01
The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.
Chunyan Ji
2010-01-01
Full Text Available We discuss a two-species Lotka-Volterra mutualism system with stochastic perturbation. We show that there is a unique nonnegative solution of this system. Furthermore, we investigate that there exists a stationary distribution for this system, and it has ergodic property.
ON THE EXISTENCE OF POSITIVE RADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS
杨作东; 陆启韶
2001-01-01
We study the existence of positive radial solutions for a class of quasilinear elliptic systems in a ball domains via the blowing up argument and degree theory.The main results of the present paper are new and extend the previously known results.
EXISTENCE OF PERIODIC SOLUTIONS TO A PERTURBED FOUR-DIMENSIONAL SYSTEM
无
2009-01-01
Consider a k multiple closed orbit on an invariant surface of a four dimensional system, after a suitable perturbation, the closed orbit can generate periodic orbits and double-period orbits. Using bifurcation methods and techniques, sufficient conditions for the existence of periodic solutions to the perturbed four dimensional system are obtained, and the period-doubling bifurcations is discussed.
Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations
Jianwen Zhang
2008-02-01
Full Text Available This paper is concerned with an initial boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.
Global Existence and Uniqueness of Strong Solutions for the Magnetohydrodynamic Equations
Zhang Jianwen
2008-01-01
Full Text Available This paper is concerned with an initial boundary value problem in one-dimensional magnetohydrodynamics. We prove the global existence, uniqueness, and stability of strong solutions for the planar magnetohydrodynamic equations for isentropic compressible fluids in the case that vacuum can be allowed initially.
EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
无
2011-01-01
The initial value problem of a nonlinear fractional differential equation is discussed in this paper. Using the nonlinear alternative of Leray-Schauder type and the contraction mapping principle,we obtain the existence and uniqueness of solutions to the fractional differential equation,which extend some results of the previous papers.
Existence of three solutions for impulsive nonlinear fractional boundary value problems
Shapour Heidarkhani
2017-01-01
Full Text Available In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.
Massimiliano Ferrara
2016-01-01
Full Text Available This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals.
Existence of Two Solutions of Nonlinear m-Point Boundary Value Problems
任景莉; 葛渭高
2003-01-01
Sufficient conditions for the existence of at least two positive solutions of a nonlinear m-points boundary value problems are established. The results are obtained by using a new fixed point theorem in cones. An example is provided to illustrate the theory.
AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS
无
2001-01-01
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.
Carlos von Plessing Rossel
2000-12-01
Full Text Available Complexation between acyclovir (ACV, an antiviral drug used for the treatment of herpes simplex virus infection, and beta-cyclodextrin (beta-CD was studied in solution and in solid states. Complexation in solution was evaluated using solubility studies and nuclear magnetic resonance spectroscopy (¹H-NMR. In the solid state, X-ray diffraction, differential scanning calorimetry (DSC, thermal gravimetric analysis (TGA and dissolution studies were used. Solubility studies suggested the existence of a 1:1 complex between ACV and beta-CD. ¹H-NMR spectroscopy studies showed that the complex formed occurs with a stoichiometry ratio of 1:1. Powder X-ray diffraction indicated that ACV exists in a semicrystalline state in the complexed form with beta-CD. DSC studies showed the existence of a complex of ACV with beta-CD. The TGA studies confirmed the DSC results of the complex. Solubility of ACV in solid complexes was studied by the dissolution method and it was found to be much more soluble than the uncomplexed drug.
Wu Xuesong; Gao Wenjie; Cao Jianwen
2011-01-01
In this paper, the authors discuss the global existence and blow-up of the solution to an evolution ρ-Laplace system with nonlinear sources and nonlinear boundary condition. The authors first establish the local existence of solutions, then give a necessary and sufficient condition on the global existence of the positive solution.
Effect of shear stress in ferroelectric solid solutions with coexisting phases
Lu, Xiaoyan; Zhang, Hangbo; Zheng, Limei; Cao, Wenwu
2017-08-01
One common feature of ferroelectric solid solutions with large piezoelectricity is the coexistence of two or more phases. Due to the strain mismatch among coexisting phases, adaptive structures near the interfaces or domain walls develop to maintain the atomic coherency. Shear stresses commonly exist, especially when the domain size is small. The effect of shear stresses on phase morphology in Pb(Zr1-xTix)O3 solid solutions with compositions within the morphotropic phase boundary region was studied within the framework of Landau phenomenological theory. Our results show that the coexisting rhombohedral (R) and tetragonal (T) phases can be modified to form stable or metastable R-like and/or T-like monoclinic phases under shear stresses. Large stresses may also induce first order or second order phase transitions.
The Existence of Positive Bounded Entire Solutions of Second Order Quasilinear Elliptic Equations
无
2002-01-01
In this paper we are concerned with the existence of positive entire solutions of second order quasilinear elliptic equations of the type div(|Du|p-2Du)+f(x,u)=0, x∈RN, (1) where f(x, u) is a continuous function on RN×(0,∞). This problem appears in the study of non-Newtonian fluids and non-Newtonian filtration. The quantity p is a characteristic of the madium. Media with p>2 are called dilatant fluids and those with p<2 are called pseudoplastics. If p=2, they are Newtonian fluid. In the present paper we give new sufficient conditions which ensure the existence of positive entire solutions of (1).When p=2, the related results have been obtained by [1,2]. Our theorem for existence complement and extent to the results by [1,2].
Atomistic interpretation of solid solution hardening from spectral analysis.
Plendl, J N
1971-05-01
From analysis of a series of vibrational spectra of ir energy absorption and laser Raman, an attempt is made to interpret solid solution hardening from an atomistic point of view for the system CaF(2)/SrF(2). It is shown to be caused by the combined action of three atomic characteristics, i.e., their changes as a function of composition. They are deformation of the atomic coordination polyhedrons, overlap of the outer electron shells of the atom pairs, and the ratio of the ionic to covalent share of binding. A striking nonlinear behavior of the three characteristics, as a function of composition, gives maximum atomic bond strength to the 55/45 position of the system CaF(2)/SrF(2), in agreement with the measured data of the solid solution hardening. The curve for atomic bond strength, derived from the three characteristics, is almost identical to the curve for measured microhardness data. This result suggests that the atomistic interpretation, put forward in this paper, is correct.
Zn₃P₂-Zn₃As₂ solid solution nanowires.
Im, Hyung Soon; Park, Kidong; Jang, Dong Myung; Jung, Chan Su; Park, Jeunghee; Yoo, Seung Jo; Kim, Jin-Gyu
2015-02-11
Semiconductor alloy nanowires (NWs) have recently attracted considerable attention for applications in optoelectronic nanodevices because of many notable properties, including band gap tunability. Zinc phosphide (Zn3P2) and zinc arsenide (Zn3As2) belong to a unique pseudocubic tetragonal system, but their solid solution has rarely been studied. Here In this study, we synthesized composition-tuned Zn3(P1-xAsx)2 NWs with different crystal structures by controlling the growth conditions during chemical vapor deposition. A first type of synthesized NWs were single-crystalline and grew uniformly along the [110] direction (in a cubic unit cell) over the entire compositional range (0 ≤ x ≤ 1) explored. The use of an indium source enabled the growth of a second type of NWs, with remarkable cubic-hexagonal polytypic twinned superlattice and bicrystalline structures. The growth direction of the Zn3P2 and Zn3As2 NWs was also switched to [111] and [112], respectively. These structural changes are attributable to the Zn-depleted indium catalytic nanoparticles which favor the growth of hexagonal phases. The formation of a solid solution at all compositions allowed the continuous tuning of the band gap (1.0-1.5 eV). Photocurrent measurements were performed on individual NWs by fabricating photodetector devices; the single-crystalline NWs with [110] growth direction exhibit a higher photoconversion efficiency compared to the twinned crystalline NWs with [111] or [112] growth direction.
Rai, R. N.; Kant, Shiva; Reddi, R. S. B.; Ganesamoorthy, S.; Gupta, P. K.
2016-01-01
Urea is an attractive material for frequency conversion of high power lasers to UV (for wavelength down to 190 nm), but its usage is hindered due to its hygroscopic nature, though there is no alternative organic NLO crystal which could be transparent up to 190 nm. The hygroscopic character of urea has been modified by making the solid solution (UCNB) of urea (U) and p-chloronitrobenzene (CNB). The formation of the solid solution of CNB in U is explained on the basis of phase diagram, powder XRD, FTIR, elemental analysis and single crystal XRD studies. The solubility of U, CNB and UCNB in ethanol solution is evaluated at different temperatures. Transparent single crystals of UCNB are grown from its saturated solution in ethanol. Optical properties e.g., second harmonic generation (SHG), refractive index and the band gap for UCNB crystal were measured and their values were compared with the parent compounds. Besides modification in hygroscopic nature, UCNB has also shown the higher SHG signal and mechanical hardness in comparison to urea crystal.
Creep Behavior of Solid Solution Strengthened Y3Al5O12
2007-11-02
DATES COVERED Final Technical Report 15 Feb 97 to 29 Aug 97 4. TITLE AND SUBTITLE Creep Behavior of Solid Solution Strengthened Y3A15012 6...Final Report Title: Creep Behavior of Solid Solution Strengthened Y3AI5012 Award Number: F49620-97-1-0097 For the period of: 2/14/97-8/31/97...been investigated at present in these oxides is through the formation of solid solution alloys. For the case of oxides two different possible solid
Reaction paths and equilibrium end-points in solid-solution aqueous-solution systems
Glynn, P.D.; Reardon, E.J.; Plummer, L.N.; Busenberg, E.
1990-01-01
Equations are presented describing equilibrium in binary solid-solution aqueous-solution (SSAS) systems after a dissolution, precipitation, or recrystallization process, as a function of the composition and relative proportion of the initial phases. Equilibrium phase diagrams incorporating the concept of stoichiometric saturation are used to interpret possible reaction paths and to demonstrate relations between stoichiometric saturation, primary saturation, and thermodynamic equilibrium states. The concept of stoichiometric saturation is found useful in interpreting and putting limits on dissolution pathways, but there currently is no basis for possible application of this concept to the prediction and/ or understanding of precipitation processes. Previously published dissolution experiments for (Ba, Sr)SO4 and (Sr, Ca)C??O3orth. solids are interpreted using equilibrium phase diagrams. These studies show that stoichiometric saturation can control, or at least influence, initial congruent dissolution pathways. The results for (Sr, Ca)CO3orth. solids reveal that stoichiometric saturation can also control the initial stages of incongruent dissolution, despite the intrinsic instability of some of the initial solids. In contrast, recrystallisation experiments in the highly soluble KCl-KBr-H2O system demonstrate equilibrium. The excess free energy of mixing calculated for K(Cl, Br) solids is closely modeled by the relation GE = ??KBr??KClRT[a0 + a1(2??KBr-1)], where a0 is 1.40 ?? 0.02, a1, is -0.08 ?? 0.03 at 25??C, and ??KBr and ??KCl are the mole fractions of KBr and KCl in the solids. The phase diagram constructed using this fit reveals an alyotropic maximum located at ??KBr = 0.676 and at a total solubility product, ???? = [K+]([Cl-] + [Br-]) = 15.35. ?? 1990.
Stability of phases in (Ba, Gd)MnO3 solid solution system
Migaku Kobayashi; Hidenori Tamura; Hiromi Nakano; Hirohisa Satoh; Naoki Kamegashira
2008-01-01
The existing phases in BaxGd1-xMnO3 solid solution system (0≦x≦1) were studied by analyzing the detailed crystal structure of each composition from the results of the Rietveld method using powder X-ray diffraction data. For a small substitution of Ba for Gd (0≦x<0.1), the orthorhombic phase with a perovskite type structure (Pnma space group) was stably formed and this fact was supported by the electron diffraction data. There existed an intermediate phase of Ba0.33Gd0.67MnO3, which was characterized as the tetragonal phase with perovskite structure. The composition range of this phase was narrow and almost line compound. Between the regions of these phases, there existed two-phase region. There was also a two-phase region between the intermediate tetragonal phase and BaMnO3. Measurement of electrical conductivities of these orthorhombic solid solutions and tetragonal phases showed semiconducting behaviors for both phases and the existence of the phase transition at high temperature for the orthorhombic phase. The transition temperature decreased as the Ba content increased.
Existence and multiplicity of solutions to 2mth-order ordinary differential equations
Li, Fuyi; Li, Yuhua; Liang, Zhanping
2007-07-01
In this paper, the existence and multiplicity of solutions are obtained for the 2mth-order ordinary differential equation two-point boundary value problems u(2(m-i))(t)=f(t,u(t)) for all t[set membership, variant][0,1] subject to Dirichlet, Neumann, mixed and periodic boundary value conditions, respectively, where f is continuous, for all i=1,2,...,m. Since these four boundary value problems have some common properties and they can be transformed into the integral equation of form , we firstly deal with this nonlinear integral equation. By using the strongly monotone operator principle and the critical point theory, we establish some conditions on f which are able to guarantee that the integral equation has a unique solution, at least one nonzero solution, and infinitely many solutions. Furthermore, we apply the abstract results on the integral equation to the above four 2mth-order two-point boundary problems and successfully resolve the existence and multiplicity of their solutions.
Zhu, Changjiang; Duan, Renjun
2003-02-01
This paper is concerned with the existence and uniqueness of the entropy solution to the initial boundary value problem for the inviscid Burgers equation \\left\\{\\begin{array}{@{}l@{\\qquad}l@{}} u_t+\\big(\\frac{u^2}{2}\\big)_x=0 x\\gt0\\quad t\\gt0\\\\ u(x,0)=u_0(x) x\\geq0\\\\ u(0,t)=0 t\\geq0. \\end{array}\\right. To apply the method of vanishing viscosity to study the existence of the entropy solution, we first introduce the initial boundary value problem for the viscous Burgers equation, and as in Evans (1998 Partial Differential Equations (Providence, RI: American Mathematical Society) and Hopf (1950 Commun. Pure Appl. Math. 3 201-30), give the formula of the corresponding viscosity solutions by Hopf-Cole transformation. Secondly, we prove the convergence of the viscosity solution sequences and verify that the limiting function is an entropy solution. Finally, we give an example to show how our main result can be applied to solve the initial boundary value problem for the Burgers equation.
Existence and regularity of weak solutions to a model for coarsening in molecular beam epitaxy
Zhang, Jun
2011-01-01
Taking into account the occurrence of a zero of the surface diffusion current and the requirement of the Ehrlich-Schwoebel effect, Siegert et al \\cite{Siegert94} formulate a model of Langevin type that describes the growth of pyramidlike structures on a surface under conditions of molecular beam epitaxy, and that the slope of these pyramids is selected by the crystalline symmetries of the growing film. In this article, the existence and uniqueness of weak solution to an initial boundary value problem for this model is proved, in the case that the noise is neglected. The regularity of the weak solution to models, with/without slope selection, is also investigated.
无
2006-01-01
Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.
Existence of solutions for second-order differential inclusions involving proximal normal cones
Bernicot, Frederic
2010-01-01
In this work, we prove global existence of solutions for second order differential problems in a general framework. More precisely, we consider second order differential inclusions involving proximal normal cone to a set-valued map. This set-valued map is supposed to take admissible values (so in particular uniformly prox-regular values, which may be non-smooth and non-convex). Moreover we require the solution to satisfy an impact law, appearing in the description of mechanical systems with inelastic shocks.
Existence and uniqueness of mild solutions for fractional semilinear differential equations
Bambang Hendriya Guswanto
2015-06-01
Full Text Available In this article, we study the existence and uniqueness of a local mild solution for a class of semilinear differential equations involving the Caputo fractional time derivative of order $\\alpha$ $(0<\\alpha<1$ and, in the linear part, a sectorial linear operator A. We put some conditions on a nonlinear term f and an initial data $u_0$ in terms of the fractional power of A. By applying Banach's Fixed Point Theorem, we obtain a unique local mild solution with smoothing effects, estimates, and a behavior at t close to 0. An example as an application of our results is also given.
Existence of solutions for non-autonomous functional evolution equations with nonlocal conditions
Xianlong Fu
2012-07-01
Full Text Available In this work, we study the existence of mild solutions and strict solutions of semilinear functional evolution equations with nonlocal conditions, where the linear part is non-autonomous and generates a linear evolution system. The fraction power theory and alpha-norm are used to discuss the problems so that the obtained results can be applied to the equations in which the nonlinear terms involve spatial derivatives. In particular, the compactness condition or Lipschitz condition for the function g in the nonlocal conditions appearing in various literatures is not required here. An example is presented to show the applications of the obtained results
ZENG Luchuan
2004-01-01
The purpose of this paper is to introduce and study a new class of generalized strongly mixed implicit quasi-variational inequalities in Hilbert spaces, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case.By applying the auxiliary variational principle technique, the existence of solutions for this class of quasi-variational inequalities is proved. Moreover, a new iterative algorithm for computing approximate solutions is constructed and the convergence criteria for this iterative algorithm are also established.
SONG Li-mei; WENG Pei-xuan
2012-01-01
In this paper,we study a Dirichlet-type boundary value problem(BVP) of nonlinear fractional differential equation with an order α ∈ (3,4],where the fractional derivative D0α+ is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel'skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.
Existence of Solutions to Nonlinear Impulsive Volterra Integral Equations in Banach Spaces
CHEN Fangqi; TIAN Ruilan
2005-01-01
In this paper, the existence of solutions is studied for nonlinear impulsive Volterra integral equations with infinite moments of impulse effect on the half line R+ in Banach spaces.By the use of a new comparison result and recurrence method, the new existence theorems are achieved under a weaker compactness-type condition, which generalize and improve the related results for this class of equations with finite moments of impulse effect on finite interval and infinite moments of impulse effect on infinite interval.
Existence of T-solution for Degenerated Problem via Minty's Lemma
Y. AKDIME; E. AZROUL; M. RHOUDAF
2008-01-01
We study the existence result of solutions for the nonlinear degenerated elliptic problem of the form, -div(a(x,u,▽u))=F in Ω,where Ω is a bounded of RN,N≥2 ,a Ω×R×R N→R N is a Caratheodory function satisfying the natural growth condition and the coercivity condition,but they verify only the large monotonicity.The second term F belongs to W-1p'(Ω,w*). The existence result is proved by using the L1-version of Minty 's lemma.
Existence Solutions of Vector Equilibrium Problems and Fixed Point of Multivalued Mappings
Kanokwan Sitthithakerngkiet
2013-01-01
Full Text Available Let K be a nonempty compact convex subset of a topological vector space. In this paper-sufficient conditions are given for the existence of x∈K such that F(T∩VEP(F≠∅, where F(T is the set of all fixed points of the multivalued mapping T and VEP(F is the set of all solutions for vector equilibrium problem of the vector-valued mapping F. This leads us to generalize and improve some existence results in the recent references.
Zhang Zhijiun
2008-01-01
By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem △u = k(x)g(u),u>0, x∈Ω, u|(e)Ω = +∞, where Ω is a bounded domain with smooth boundary in RN; g ∈ C1[0,∞), g(0) = g'(0) = 0, and there exists p > 1, such that lims→∞ g(sξ)/g(s)=ξp, (A)ξ > 0, and k∈Cαloc(Ω) is non-negative non-trivial in Ω which may be singular on the boundary.
Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas
Cheng, Bin; Tronci, Cesare
2016-01-01
We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible Navier--Stokes system for the bulk fluid; and a parabolic evolution equation, involving magnetic diffusivity, for the magnetic field. The physical derivation of our model is given. It is also shown that the weak solution, whose existence is established, has nonincreasing total energy, and that it satisfies a number of physically relevant properties, including conservation of the total momentum, conservation of the total mass, and nonnegativity of the probability density function for the energetic particles. The proof is based on a one-level approximation scheme, which is carefully devised to avoid increase of the total energy for the sequence...
Existence and Uniqueness of Positive Solution for Discrete Multipoint Boundary Value Problems.
Ma, Huili; Ma, Huifang
2014-01-01
It is expected in this paper to investigate the existence and uniqueness of positive solution for the following difference equation: -Δ(2) u(t - 1) = f(t, u(t)) + g(t, u(t)), t ∈ ℤ 1, T , subject to boundary conditions either u(0) - βΔu(0) = 0, u(T + 1) = αu(η) or Δu(0) = 0, u(T + 1) = αu(η), where 0 0, and η ∈ ℤ 2,T-1. The proof of the main result is based upon a fixed point theorem of a sum operator. It is expected in this paper not only to establish existence and uniqueness of positive solution, but also to show a way to construct a series to approximate it by iteration.
Existence of solutions for fourth-order PDEs with variable exponents
Mimoun Moussaoui
2009-11-01
Full Text Available In this article, we study the following problem with Navier boundary conditions $$displaylines{ Delta _{p(x}^2u=lambda | u| ^{p(x-2}u+f(x,uquad hbox{in }Omega , cr u=Delta u=0quad hbox{on }partial Omega . }$$ Where $Omega $ is a bounded domain in $mathbb{R}^{N}$ with smooth boundary $partial Omega $, $Ngeq 1$, $Delta _{p(x}^2u:=Delta (|Delta u| ^{p(x-2}Delta u $, is the $p(x$-biharmonic operator, $lambda leq 0$, $p$ is a continuous function on $overline{Omega } $ with $inf_{xin overline{Omega }} p(x>1$ and $f:Omega imes mathbb{R}o mathbb{R}$ is a Caratheodory function. Using the Mountain Pass Theorem, we establish the existence of at least one solution of this problem. Especially, the existence of infinite many solutions is obtained.
Existence and decay estimates of solutions to complex Ginzburg-Landau type equations
Shimotsuma, Daisuke; Yokota, Tomomi; Yoshii, Kentarou
2016-02-01
This paper deals with the initial-boundary value problem (denoted by (CGL)) for the complex Ginzburg-Landau type equation ∂u/∂t - (λ + iα) Δu + (κ + iβ)| u | q - 1 u - γu = 0 with initial data u0 ∈Lp (Ω) in the case 1 0, α , β , γ , κ ∈ R. There are a lot of studies on local and global existence of solutions to (CGL) including the physically relevant case q = 3 and κ > 0. This paper gives existence results with precise properties of solutions and rigorous proof from a mathematical point of view. The physically relevant case can be considered as a special case of the results. Moreover, in the case κ inequality with Re .
On the existence of classical solutions for stationary extended mean field games
Gomes, Diogo A.
2014-04-01
In this paper we consider extended stationary mean-field games, that is mean-field games which depend on the velocity field of the players. We prove various a-priori estimates which generalize the results for quasi-variational mean-field games in Gomes et al. (2012). In addition we use adjoint method techniques to obtain higher regularity bounds. Then we establish the existence of smooth solutions under fairly general conditions by applying the continuity method. When applied to standard stationary mean-field games as in Lasry and Lions (2006), Gomes and Sanchez-Morgado (2011) or Gomes et al. (2012) this paper yields various new estimates and regularity properties not available previously. We discuss additionally several examples where the existence of classical solutions can be proved. © 2013 Elsevier Ltd. All rights reserved.
Existence of solutions to fractional boundary-value problems with a parameter
Ya-Ning Li
2013-06-01
Full Text Available This article concerns the existence of solutions to the fractional boundary-value problem $$displaylines{ -frac{d}{dt} ig(frac{1}{2} {}_0D_t^{-eta}+ frac{1}{2}{}_tD_{T}^{-eta}igu'(t=lambda u(t+abla F(t,u(t,quad hbox{a.e. } tin[0,T], cr u(0=0,quad u(T=0. }$$ First for the eigenvalue problem associated with it, we prove that there is a sequence of positive and increasing real eigenvalues; a characterization of the first eigenvalue is also given. Then under different assumptions on the nonlinearity F(t,u, we show the existence of weak solutions of the problem when $lambda$ lies in various intervals. Our main tools are variational methods and critical point theorems.
Jingfu Jin
2012-04-01
Full Text Available This article shows the existence of a positive solution for the singular fractional differential equation with integral boundary condition $$displaylines{ {}^C!D^p u(t=lambda h(tf(t, u(t, quad tin(0, 1, cr u(0-au(1=int^1_0g_0(su(s,ds, cr u'(0-b,{}^C!D^qu(1=int^1_0g_1(su(s,ds, cr u''(0=u'''(0=dots =u^{(n-1}(0=0, }$$ where $lambda $ is a parameter and the nonlinear term is allowed to be singular at $t=0, 1$ and $u=0$. We obtain an explicit interval for $lambda$ such that for any $lambda$ in this interval, existence of at least one positive solution is guaranteed. Our approach is by a fixed point theory in cones combined with linear operator theory.
Existence of the solutions and the attractors for the large-scale atmospheric equations
HUANG; Haiyang; GUO; Boling
2006-01-01
In this paper, firstly, the proper function space is chosen, and the proper expression of the operators is introduced such that the complex large-scale atmospheric motion equations can be described by a simple and abstract equation, by which the definition of the weak solution of the atmospheric equations is made. Secondly, the existence of the weak solution for the atmospheric equations and the steady state equations is proved by using the Galerkin method. The existence of the non-empty global attractors for the atmospheric equations in the sense of the Chepyzhov-Vishik's definition is obtained by constructing a trajectory attractor set of the atmospheric motion equations.The result obtained here is the foundation for studying the topological structure and the dynamical behavior of the atmosphere attractors. Moreover, the methods used here are also valid for studying the other atmospheric motion models.
Existence of lattice solutions to semilinear elliptic systems with periodic potential
Nicholas D. Alikakos
2012-01-01
Full Text Available Under the assumption that the potential W is invariant under a general discrete reflection group $G'=TG$ acting on $mathbb{R}^n$, we establish existence of G'-equivariant solutions to $Delta u - W_u(u = 0$, and find an estimate. By taking the size of the cell of the lattice in space domain to infinity, we obtain that these solutions converge to G-equivariant solutions connecting the minima of the potential W along certain directions at infinity. When particularized to the nonlinear harmonic oscillator $u''+alpha sin u=0$, $alpha>0$, the solutions correspond to those in the phase plane above and below the heteroclinic connections, while the G-equivariant solutions captured in the limit correspond to the heteroclinic connections themselves. Our main tool is the G'-positivity of the parabolic semigroup associated with the elliptic system which requires only the hypothesis of symmetry for W. The constructed solutions are positive in the sense that as maps from $mathbb{R}^n$ into itself leave the closure of the fundamental alcove (region invariant.
Jose Luiz Boldrini
2003-11-01
Full Text Available We study the existence and regularity of weak solutions of a phase field type model for pure material solidification in presence of natural convection. We assume that the non-stationary solidification process occurs in a two dimensional bounded domain. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and a modified Navier-Stokes equation. These equations include buoyancy forces modelled by Boussinesq approximation and a Carman-Koseny term to model the flow in mushy regions. Since these modified Navier-Stokes equations only hold in the non-solid regions, which are not known a priori, we have a free boundary-value problem.
EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L2-SPACES
WeiLi; ZhouHaiyun
2005-01-01
By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers. Especially,some new techniques are used in this paper.
Cuong LE VAN; Morhaim, Lisa; Vailakis, Yiannis
2008-01-01
We propose a new approach to the issue of existence and uniqueness of solutions to the Bellman equation, exploiting an emerging class of methods, called monotone map methods, pioneered in the work of Krasnosel’skii (1964) and Krasnosel’skii-Zabreiko (1984). The approach is technically simple and intuitive. It is derived from geometric ideas related to the study of fixed points for monotone concave operators defined on partially order spaces.
EXISTENCE OF GLOBAL SMOOTH SOLUTION TO JIN-XIN MODEL WITH LARGE INITIAL DATA
Ruan Lizhi; Zhang Zhiyong
2004-01-01
In this paper, Under the assumption that the relaxation time e is suf-ficiently small, we prove the existence of the global smooth solution to the Cauchyproblem for the Jin-Xin model without any smallness assumption for the initial data.The analysis is based on some a priori estimates which are obtained by the method ofcharacteristic and the maximum principle of first-order quasilinear hyperbolic system.
EXISTENCE OF INFINITE ENERGY SOLUTION TO THE INELASTIC BOLTZMANN EQUATION WITH EXTERNAL FORCE
Wei Jinbo; Zhang Xianwen
2012-01-01
In this paper,the Cauchy problem for the inelastic Boltzmann equation with external force is considered in the case of initial data with infinite energy.More precisely,under the assumptions on the bicharacteristic generated by external force,we prove the global existence of solution for small initial data compared to the local Maxwellian exp{-p|x-v|2},which has infinite mass and energy.
郭柏灵; 苗长兴
1995-01-01
The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
Yuan Hongjun; Jin Yang
2005-01-01
The aim of this paper is to discuss the existence and uniqueness of solutions for the porous medium equation ut - (um)xx = μ(x) in (x,t) ∈ R × (0, +∞) with initial condition u(x, 0) = uo(x) x ∈ (-∞, +∞),whereμ(x) is a nonnegative finite Radon measure, u0 ∈ L1 (R)∩L∞ (R) is a nonnegative function, and m ＞ 1, and R ≡ (-∞, +∞).
Hui-Sheng Ding
2013-04-01
Full Text Available In this paper, we first introduce a new class of pseudo almost periodic type functions and investigate some properties of pseudo almost periodic type functions; and then we discuss the existence of pseudo almost periodic solutions to the class of abstract partial functional differential equations $x'(t=Ax(t+f(t,x_t$ with finite delay in a Banach space X.
Existence of Positive Solutions for Higher Order Boundary Value Problem on Time Scales
XIE DA-PENG; LIU YANG; SUN MING-ZHE; Li Yong
2013-01-01
In this paper,we investigate the existence of positive solutions of a class higher order boundary value problems on time scales.The class of boundary value problems educes a four-point (or three-point or two-point) boundary value problems,for which some similar results are established.Our approach relies on the Krasnosel'skii fixed point theorem.The result of this paper is new and extends previously known results.
LINEAR STIELTJES EQUATION WITH GENERALIZED RIEMANN INTEGRAL AND EXISTENCE OF REGULATED SOLUTIONS
L. BARBANTI
2001-01-01
In this work we establish an existence theorem of regulated solutions for a class of Stieltjes equations which involve generalized Riemann kind of integrals. The general method applied consists in considering the continuous-time Stieltjes equation as limit of discrete processes. This approach will prove fruitful in the study of the controllability of Stieltjes systems, because it will be possible to get properties on the continuous time equation by transferring properties of the discrete ones.
Existence of global strong solutions for the shallow-water equations with large initial data
Haspot, Boris
2011-01-01
This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\\geq 2$ in critical spaces for the scaling of the equations. More precisely, we introduce as in \\cite{Hprepa} a new unknown,\\textit{a effective velocity} $v=u+\\mu\
Existence of Sign-changing Solution for Three-point Boundary Value Problems
LI Chun-yan; SU Ya-juan
2012-01-01
In this paper,by using the fixed-point index theory,we study the existence of sign-changing solution of some three-point boundary value problems {y″(t) + f(y) =0, t ∈ [0,1],y′(0) =0, y( 1 ) =αy(η),where 0 ＜ a ＜ 1,0 ＜ η ＜ 1,f:R → R is continuous,strictly increasing and f(0) =0.
Acker, A.
Under reasonably general assumptions, we prove the existence of convex classical solutions for the Prandtl-Batchelor free boundary problem in fluid dynamics, in which a flow of constant vorticity density is embedded in a potential flow, with a vortex sheet of constant vorticity density as the flow interface. These results apply to Batchelor flows which are confined to a bounded, convex vessel, and for which the limiting interior flow-speed exceeds the limiting exterior flow-speed along the interface.
Solid state and solution nitrate photochemistry: photochemical evolution of the solid state lattice.
Asher, Sanford A; Tuschel, David D; Vargson, Todd A; Wang, Luling; Geib, Steven J
2011-05-01
We examined the deep UV 229 nm photochemistry of NaNO(3) in solution and in the solid state. In aqueous solution excitation within the deep UV NO(3)¯ strong π → π* transition causes the photochemical reaction NO(3)¯ → NO(2)¯ + O·. We used UV resonance Raman spectroscopy to examine the photon dose dependence of the NO(2)¯ band intensities and measure a photochemical quantum yield of 0.04 at pH 6.5. We also examined the response of solid NaNO(3) samples to 229 nm excitation and also observe formation of NO(2)¯. The quantum yield is much smaller at ∼10(-8). The solid state NaNO(3) photochemistry phenomena appear complex by showing a significant dependence on the UV excitation flux and dose. At low flux/dose conditions NO(2)¯ resonance Raman bands appear, accompanied by perturbed NO(3)¯ bands, indicating stress in the NaNO(3) lattice. Higher flux/dose conditions show less lattice perturbation but SEM shows surface eruptions that alleviate the stress induced by the photochemistry. Higher flux/dose measurements cause cratering and destruction of the NaNO(3) surface as the surface layers are converted to NO(2)¯. Modest laser excitation UV beams excavate surface layers in the solid NaNO(3) samples. At the lowest incident fluxes a pressure buildup competes with effusion to reach a steady state giving rise to perturbed NO(3)¯ bands. Increased fluxes result in pressures that cause the sample to erupt, relieving the pressure.
Jian Wang
2009-01-01
Full Text Available We here investigate the existence and uniqueness of the nontrivial, nonnegative solutions of a nonlinear ordinary differential equation: (|f′|p−2f′′+βrf′+αf+(fq′=0 satisfying a specific decay rate: limr→∞rα/βf(r=0 with α:=(p−1/(pq−2p+2 and β:=(q−p+1/(pq−2p+2. Here p>2 and q>p−1. Such a solution arises naturally when we study a very singular self-similar solution for a degenerate parabolic equation with nonlinear convection term ut=(|ux|p−2uxx+(uqx defined on the half line [0,+∞.
Caciotta, G
2016-01-01
The main goal of this work consists in showing that the analytic solutions for a class of characteristic problems for the Einstein vacuum equations have an existence region larger than the one provided by the Cauchy-Kowalevski theorem, due to the intrinsic hyperbolicity of the Einstein equations. The magnitude of this region depends only on suitable $H_s$ Sobolev norms of the initial data for a fixed $s\\leq 7$ and if the initial data are sufficiently small the analytic solution is global. In a previous paper, hereafter "I", we have described a geometric way of writing the vacuum Einstein equations for the characteristic problems we are considering and a local solution in a suitable "double null cone gauge" characterized by the use of a double null cone foliation of the spacetime.
Decay of oxygen solid solution in plastically deformed silicon
Yarykin, N. [Institute of Microelectronics Technology RAS, Chernogolovka (Russian Federation); Vdovin, V.I. [Institute for Chemical Problems of Microelectronics, Moscow (Russian Federation)
2005-04-01
Decay of the oxygen solid solution in silicon during annealing at 550-700 C is studied by the IR absorption technique in the single crystalline samples subjected to the plastic deformation to a high dislocation density at 680 C. The deformation is shown to significantly enhance the rate of the decay in the whole temperature range studied. Based on the simple model, which assumes the heterogeneous oxygen aggregation at dislocations, the effective oxygen diffusivity is calculated from the experimental data. The activation energy of oxygen diffusion in this temperature range is found to be about 1.6 eV, which is essentially lower than that for the isolated interstitial oxygen atom. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Nucleation of the diamond phase in aluminium-solid solutions
Hornbogen, E.; Mukhopadhyay, A. K.; Starke, E. A., Jr.
1993-01-01
Precipitation was studied from fcc solid solutions with silicon, germanium, copper and magnesium. Of all these elements only silicon and germanium form diamond cubic (DC) precipitates in fcc Al. Nucleation of the DC structure is enhanced if both types of atom are dissolved in the fcc lattice. This is interpreted as due to atomic size effects in the prenucleation stage. There are two modes of interference of fourth elements with nucleation of the DC phase in Al + Si, Ge. The formation of the DC phase is hardly affected if the atoms (for example, copper) are rejected from the (Si, Ge)-rich clusters. If additional types of atom are attracted by silicon and/or germanium, DC nuclei are replaced by intermetallic compounds (for example Mg2Si).
Magneto-volume effects in Fe-Cu solid solutions
Gorria, P. [Departamento de Fisica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo (Spain)]. E-mail: pgorria@uniovi.es; Martinez-Blanco, D. [Departamento de Fisica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo (Spain); Iglesias, R. [Departamento de Fisica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo (Spain); Palacios, S.L. [Departamento de Fisica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo (Spain); Perez, M.J. [Departamento de Fisica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo (Spain); Blanco, J.A. [Departamento de Fisica, Universidad de Oviedo, Calvo Sotelo, s/n, 33007 Oviedo (Spain); Fernandez Barquin, L. [Departamento CITIMAC, F. Ciencias, Universidad de Cantabria, 39005 Santander (Spain); Hernando, A. [Instituto de Magnetismo Aplicado, UCM-RENFE, 28230 Las Rozas, Madrid (Spain); Gonzalez, M.A. [Instituto de Ciencia de Materiales de Aragon, CSIC, 50009 Zaragoza (Spain); Institut Laue-Langevin, BP 156, F-38042 Grenoble Cedex 9 (France)
2006-05-15
The magnetic properties of Fe-Cu metastable solid solutions have been investigated by means of neutron diffraction and magnetisation measurements. These compounds exhibit ferromagnetic order with Curie temperatures above room temperature for concentrations beyond 40 at% in Fe. The magnetic moment at 5 K can reach values over 2 {mu} {sub B}, while the high field susceptibility is similar to that found in FCC-FeNi Invar alloys. These features together with the low values for the linear coefficient for thermal expansion in the ferromagnetic region suggest that magneto-volume anomalies, including Invar behaviour, play a major role in the magnetic properties of this system when the crystal structure is face centred cubic. Such behaviour could be explained using theoretical total-band energy calculations.
Preparation and characterization of barium titanate stannate solid solutions
Horchidan, Nadejda, E-mail: NHorchidan@stoner.phys.uaic.ro [Department of Physics, ' Al. I. Cuza' University, Bv. Carol 11, Iasi 700506 (Romania); Ianculescu, Adelina C. [Department of Oxide Materials Science and Engineering, Polytechnics University, 1-7 Gh. Polizu, P.O. Box 12-134, 011061 Bucharest (Romania); Curecheriu, Lavinia P.; Tudorache, Florin [Department of Physics, ' Al. I. Cuza' University, Bv. Carol 11, Iasi 700506 (Romania); Musteata, Valentina [Institute of Macromolecular Chemistry ' Petru Poni' , Aleea Grigore Ghica Voda 41A, 700487 Iasi (Romania); Stoleriu, Stefania [Department of Oxide Materials Science and Engineering, Polytechnics University, 1-7 Gh. Polizu, P.O. Box 12-134, 011061 Bucharest (Romania); Dragan, Nicolae; Crisan, Dorel [Institute of Physical Chemistry ' Ilie Murgulescu' , Lab. of Oxide Materials Science, 202 Splaiul Independentei, 060021 Bucharest (Romania); Tascu, Sorin; Mitoseriu, Liliana [Department of Physics, ' Al. I. Cuza' University, Bv. Carol 11, Iasi 700506 (Romania)
2011-04-07
Research highlights: > BaSnxTi1-xO3 (x = 0; 0.05; 0.1; 0.15; 0.2) ceramics were prepared by solid state reaction and sintered at 13000C for 4h. > The phase purity, structural parameters and microstructural characteristics were investigated. > The dielectric properties were studied as function of temperature and frequency and empirical parameters {eta} and {delta} were calcutate. > The non-linear dielectric properties (tunability) of the samples were studied at room temperature. > By increasing the Sn addition, the {epsilon}(E) dependence tends to reduce its hysteresis behaviour. - Abstract: BaSn{sub x}Ti{sub 1-x}O{sub 3} (x = 0; 0.05; 0.1; 0.15; 0.2) solid solutions were prepared via conventional solid state reaction and sintered at 1300 {sup o}C for 4 h, resulting in dense single phase ceramics with homogeneous microstructures. Tetragonal symmetry for x {<=} 0.1, cubic for x = 0.2 and a superposition of tetragonal and cubic for x = 0.15 compositions were found by X-ray diffraction analysis. The temperature and frequency dependence of the complex dielectric constant and dc tunability were determined. A transformation from normal ferroelectric to relaxor with diffuse phase transition was observed with increasing the Sn concentration. All the investigated compositions show a relative tunability between 0.55 (for x = 0.2) and 0.74 (for x = 0.1), at a field amplitude of E = 20 kV/cm.
Abdel-Shakoor M Sarhan
2016-05-01
Full Text Available Abstract We consider two nonlinear matrix equations X r ± ∑ i = 1 m A i ∗ X δ i A i = I $X^{r} \\pm \\sum_{i = 1}^{m} A_{i}^{*}X^{\\delta_{i}}A_{i} = I$ , where − 1 < δ i < 0 $- 1 < \\delta_{i} < 0$ , and r, m are positive integers. For the first equation (plus case, we prove the existence of positive definite solutions and extremal solutions. Two algorithms and proofs of their convergence to the extremal positive definite solutions are constructed. For the second equation (negative case, we prove the existence and the uniqueness of a positive definite solution. Moreover, the algorithm given in (Duan et al. in Linear Algebra Appl. 429:110-121, 2008 (actually, in (Shi et al. in Linear Multilinear Algebra 52:1-15, 2004 for r = 1 $r = 1$ is proved to be valid for any r. Numerical examples are given to illustrate the performance and effectiveness of all the constructed algorithms. In Appendix, we analyze the ordering on the positive cone P ( n ‾ $\\overline{P(n}$ .
Babanov, Yu.A., E-mail: babanov@imp.uran.ru [M.N. Miheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Ekaterinburg 620990 (Russian Federation); Ponomarev, D.A.; Ustinov, V.V. [M.N. Miheev Institute of Metal Physics, Ural Branch, Russian Academy of Sciences, Ekaterinburg 620990 (Russian Federation); Baranov, A.N. [M.V. Lomonosov Moscow State University, Moscow 119991 (Russian Federation); Zubavichus, Ya.V. [Russian Research Centre “Kurchatov Institute”, 123182 Moscow (Russian Federation)
2016-08-15
Highlights: • A method for determining bond lengths from combined EXAFS spectra for solid oxide solutions is proposed. • We have demonstrated a high resolution in r-space of close spacing atoms in the Periodical Table. • These results were obtained without any assumptions concerning interatomic distances for multi-component systems. • Coordinates ions for the solid solution with rock salt structure are determined. - Abstract: The regularization method of solving ill-posed problem is used to determine five partial interatomic distances on the basis of combined two EXAFS spectra. Mathematical algorithm and experimental results of the EXAFS analysis for Ni{sub c}Zn{sub 1−c}O (c = 0.0, 0.3, 0.5, 0.7, 1.0) solid solutions with the rock salt (rs) crystal structure are discussed. Samples were synthesized from the binary oxide powders at pressure of 7.7 GPa and temperatures 1450–1650 K. The measurements were performed using synchrotron facilities (Russian Research Centre “Kurchatov Institute”, Moscow). The Ni and Zn K absorption spectra were recorded in transmission mode under room temperature. It is shown, the ideal rock salt lattice is distorted and long-range order exists only in the average (Vegard law). In order to determine coordinates ions for the solid solution with rock salt structure, we used the Pauling model. The simulation is performed for 343,000 cluster of oxide ions. The distribution functions for ions (Ni−O, Ni−Ni, Ni−Zn, Zn−Zn, Zn−O, O−O) depending on the distance are obtained. The width of the Gaussian distribution function is determined by the difference of the radii of the metal ions. The results are consistent with the data both X-ray diffraction and the EXAFS spectroscopy.
曾六川
2003-01-01
A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case, introduced and studied by Ding Xieping. The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex, lower semicontinuous, binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality. Secondly, this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities. Here, the equivalence guarantees that the algorithm can generate a sequence of approximate solutions.Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative anwer to the open question raised by M . A. Noor , and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set-valued mappings in the recent literature.
Shuang Ping TAO; Shang Bin CUI
2005-01-01
This paper is devoted to studying the initial value problems of the nonlinear KaupKupershmidt equations (e)u/(e)t + α1u(e)2u/(e)x2+β(e)3u/(e)x3+γ(e)5u/( )x5= 0, (x, t) ∈ R2, and (e)u/(e)t+α2 (e)u/(e)x (e)2u/(e)x2+β(e)3u/(e)x3+γ(e)5u/(e)x5 = 0, (x, t) ∈R2. Several important Strichartz type estimates for the fundamental solution of the corresponding linear problem are established. Then we apply such estimates to prove the local and global existence of solutions for the initial value problems of the nonlinear Kaup-Kupershmidt equations. The results show that a local solution exists if the initial function u0(x) ∈ Hs(R), and s ≥ 5/4 for the first equation and s ≥ 301/108 for the second equation.
YANG Ling'e; GUO Boling
2006-01-01
By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid limit to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the solution to the Ginzburg-Landau equations converges to the weak solution to the derivative nonlinear Schrodinger equations.
Bo Ling GUO; Gan Shan YANG
2004-01-01
We prove the existence of solutions of the static Landau-Lifshitz equation with multidirect effective field and with Dirichlet boundary condition, and establish the stability of the solution of Landau-Lifshitz equation with respect to time.
Ahmad Bashir
2010-01-01
Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.
Existence of global strong solutions to a beam-fluid interaction system
Grandmont, C
2015-01-01
We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure.
On existence and uniqueness of positive solutions to a class of fractional boundary value problems
Caballero J
2011-01-01
Full Text Available Abstract The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fractional boundary value problem D 0 + α u ( t + f ( t , u ( t = 0 , 0 < t < 1 , u ( 0 = u ( 1 = u ′ ( 0 = 0 , where 2 < α ≤ 3 and D 0 + α is the Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem in partially ordered metric spaces. The autonomous case of this problem was studied in the paper [Zhao et al., Abs. Appl. Anal., to appear], but in Zhao et al. (to appear, the question of uniqueness of the solution is not treated. We also present some examples where we compare our results with the ones obtained in Zhao et al. (to appear. 2010 Mathematics Subject Classification: 34B15
Imran Talib
2015-12-01
Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.
On the existence of Lipschitz solutions to some forward-backward parabolic equations
Kim, Seonghak
In this dissertation we discuss a new approach for studying forward-backward quasilinear diffusion equations. Our main idea is motivated by a reformulation of such equations as non-homogeneous partial differential inclusions and relies on a Baire's category method. In this way the existence of Lipschitz solutions to the initial-boundary value problem of those equations is guaranteed under a certain density condition. Finally we study two important cases of anisotropic diffusion in which such density condition can be realized. The first case is on the Perona-Malik type equations. In 1990, P. Perona and J. Malik [35] proposed an anisotropic diffusion model, called the Perona-Malik model, in image processing ut = div (| Du|/ 1 + Du 2) for denoising and edge enhancement of a computer vision. Since then the dichotomy of numerical stability and theoretical ill-posedness of the model has attracted many interests in the name of the Perona-Malik paradox [28]. Our result in this case provides the model with mathematically rigorous solutions in any dimension that are even reflecting some phenomena observed in numerical simulations. The other case deals with the existence result on the Hollig type equations. In 1983, K. Hollig [20] proved, in dimension n = 1, the existence of infinitely many L2-weak solutions to the initial-boundary value problem of a forward-backward diffusion equation with non-monotone piecewise linear heat flux, and this piecewise linearity was much relaxed later by K. Zhang [45]. The work [20] was initially motivated by the Clausius-Duhem inequality in the second law of thermodynamics, where the negative of the heat flux may violate the monotonicity but should obey the Fourier inequality at least. Our result in this case generalizes [20, 45] to all dimensions.
Investigation of Propellant and Explosive Solid Solution Systems II X-Ray Studies
1978-03-01
A\\Yj* ^\\C/*^ ^ 1 tatf AD 7t ott w AD-E400 125 TECHNICAL REPORT ARLCD-TR-77066 INVESTIGATION OF PROPELLANT AND EXPLOSIVE SOLID SOLUTION SYSTEMS...Report ARLCD-TR-77066 2. GOVT ACCESSION NO. *. TITLE (and Subtitle) INVESTIGATION OF PROPELLANT AND EXPLOSIVE SOLID SOLUTION SYSTEMS II X-RAY...Interplanar spacings and x-ray diffraction 9 intensities of AP, KP and their physical mixtures and solid solutions 4 X-ray data of 3 AN: KP solid solution and
THE EXISTENCE OF POSITIVE PERIODIC SOLUTIONS IN A LOGISTIC DIFFERENCE MODEL WITH A FEEDBACK CONTROL
刘智钢; 陈安平
2004-01-01
Consider the following nonautonomous delayed periodic logistic difference model with feedback control term N(k+1)=N(k)exp[r(k)-a1(k)N(k)-a2(k)N(k-τ(k))-c(k)u(k)],Δu(k)=-a(k)u(k)+b(k)N(k-τ(k)), which describes the evolution of a single species. The existence of a positive periodic solution is established by using the method of Mawhin's coincidence degree. This work has important significance in both theory and applications.
Study on the Existence and Uniqueness of Solution of Generalized Capillarity Problem
Li Wei
2012-01-01
Full Text Available By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta (1978, the abstract result on the existence and uniqueness of the solution in Lp(Ω of the generalized Capillarity equation with nonlinear Neumann boundary value conditions, where 2N/(N+1
On existence of weak solutions to a Cauchy problem for one class of conservation laws
P. I. Kogut
2015-02-01
Full Text Available We discuss the existence of weak solutions to the Cauchy problem for one classof hyperbolic conservation laws that models a highly re-entrant production system.The output of the factory is described as a function of the work in progress and theposition of the so-called push-pull point (PPP where we separate the beginning ofthe factory employing a push policy from the end of the factory, which uses a pullpolicy. The main question we discuss in this paper is about the optimal choice ofthe input in-ux, push and pull constituents, and the position of PPP.
Gao Da-peng; Feng Shi-qiang
2014-01-01
In this paper, we introduce and study a class of generalized vector quasi-variational-like inequality problems, which includes generalized nonlinear vector vari-ational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any mono-tonicity conditions in the setting of locally convex topological vector space.
Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems
Yanping Guo
2007-01-01
Full Text Available By using a new fixed-point theorem introduced by Avery and Peterson (2001, we obtain sufficient conditions for the existence of at least three positive solutions for the equation Δ2x(k−1+q(kf(k,x(k,Δx(k=0, for k∈{1,2,…,n−1}, subject to the following two boundary conditions: x(0=x(n=0 or x(0=Δx(n−1=0, where n≥3.
Existence of solutions for a third order non-local equation appearing in crack dynamics
Imbert, Cyril
2010-01-01
In this paper, we prove the existence of non-negative solutions for a non-local third order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann type operator (which can be defined using the periodic Hilbert transform). The main difficulties are due to the fact that this equation is non-local, and that the natural energy estimates are not as good as in the case of the thin film equation.
Existence and decay of solutions of some nonlinear parabolic variational inequalities
Mitsuhiro Nakao
1980-01-01
Full Text Available This paper discusses the existence and decay of solutions u(t of the variational inequality of parabolic type: ≧0for ∀v∈Lp([0,∞;V(p≧2 with v(t∈K a.e. in [0,∞, where K is a closed convex set of a separable uniformly convex Banach space V, A is a nonlinear monotone operator from V to V* and B is a nonlinear operator from Banach space W to W*. V and W are related as V⊂W⊂H for a Hilbert space H. No monotonicity assumption is made on B.
Huang Zhenkun [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China) and School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)]. E-mail: huangdoc@tom.com; Wang Xinghua [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China); Gao Feng [School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)
2006-02-06
In this Letter, we discuss discrete-time analogue of a continuous-time cellular neural network. Sufficient conditions are obtained for the existence of a unique almost periodic sequence solution which is globally attractive. Our results demonstrate dynamics of the formulated discrete-time analogue as mathematical models for the continuous-time cellular neural network in almost periodic case. Finally, a computer simulation illustrates the suitability of our discrete-time analogue as numerical algorithms in simulating the continuous-time cellular neural network conveniently.
Existence and concentration of positive solutions for a quasilinear elliptic equation in R
Elisandra Gloss
2010-05-01
Full Text Available We study the existence and concentration of positive solutions for the quasilinear elliptic equation $$ -varepsilon^2u'' -varepsilon^2(u^2''u+V(x u = h(u $$ in $mathbb{R}$ as $varepsilono 0$, where the potential $V:mathbb{R}o mathbb{R}$ has a positive infimum and $inf_{partial Omega}V>inf_{ Omega}V$ for some bounded domain $Omega$ in $mathbb{R}$, and $h$ is a nonlinearity without having growth conditions such as Ambrosetti-Rabinowitz.
Existence of positive solutions for nonlinear dynamic systems with a parameter on a measure chain
Shuang-Hong Ma
2007-05-01
Full Text Available In this paper, we consider the following dynamic system with parameter on a measure chain $mathbb{T}$, $$displaylines{ u^{DeltaDelta}_{i}(t+lambda h_{i}(tf_{i}(u_{1}(sigma(t, u_{2}(sigma(t,dots ,u_{n}(sigma(t=0,quad tin[a,b], cr alpha u_{i}(a-eta u^{Delta}_{i}(a=0,quad gamma u_{i}(sigma(b+delta u^{Delta}_{i}(sigma(b=0, }$$ where $i=1,2,dots ,n$. Using fixed-point index theory, we find sufficient conditions the existence of positive solutions.
Sabri Bensid
2010-04-01
Full Text Available We study the nonlinear elliptic problem with discontinuous nonlinearity $$displaylines{ -Delta u = f(uH(u-mu quadhbox{in } Omega, cr u =h quad hbox{on }partial Omega, }$$ where $H$ is the Heaviside unit function, $f,h$ are given functions and $mu$ is a positive real parameter. The domain $Omega$ is the unit ball in $mathbb{R}^n$ with $ngeq 3$. We show the existence of a positive solution $u$ and a hypersurface separating the region where $-Delta u=0$ from the region where $-Delta u=f(u$. Our method relies on the implicit function theorem and bifurcation analysis.
Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations
Bessaih, Hakima
2016-01-27
We study a modified three-dimensional incompressible anisotropic Navier−Stokes equations. The modification consists in the addition of a power term to the nonlinear convective one. This modification appears naturally in porous media when a fluid obeys the Darcy−Forchheimer law instead of the classical Darcy law. We prove global in time existence and uniqueness of solutions without assuming the smallness condition on the initial data. This improves the result obtained for the classical 3D incompressible anisotropic Navier−Stokes equations.
EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR A FOURTH-ORDER P-LAPLACE EQUATIONS
白占兵
2001-01-01
The solvability of one dimensional fourth-order p-Laplace equations of the type(g(u″))″+λa(t)f(u)=0, 0＜t＜1,u(0)=u(1)=u″(0)=u″(1)=0,where, g(v):= |v|p-2 v, p ＞ 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form fat zero and at infinity.
Existence of Nontrivial Weak Solutions to Quasi-Linear Elliptic Equations with Exponential Growth
WANG Chong
2013-01-01
In this paper,we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations -△nu+V(x)｜u｜n-2u-f(x,u)/｜x｜β,x∈Rn (n≥2),where-△nu=-div(｜▽u｜n-2▽7u),0≤β ＜ n,V∶ Rn → R is a continuous function,f (x,u)is continuous in Rn × R and behaves like eαun/n-1 as u → +∞.
Purification of uranothorite solid solutions from polyphase systems
Clavier, Nicolas, E-mail: nicolas.clavier@icsm.fr [ICSM, UMR 5257 CEA/CNRS/UM2/ENSCM, Site de Marcoule – Bât. 426, BP 17171, 30207 Bagnols/Cèze cedex (France); Szenknect, Stéphanie; Costin, Dan Tiberiu; Mesbah, Adel; Ravaux, Johann [ICSM, UMR 5257 CEA/CNRS/UM2/ENSCM, Site de Marcoule – Bât. 426, BP 17171, 30207 Bagnols/Cèze cedex (France); Poinssot, Christophe [CEA/DEN/DRCP/DIR, Site de Marcoule – Bât. 400, BP 17171, 30207 Bagnols/Cèze cedex (France); Dacheux, Nicolas [ICSM, UMR 5257 CEA/CNRS/UM2/ENSCM, Site de Marcoule – Bât. 426, BP 17171, 30207 Bagnols/Cèze cedex (France)
2013-10-15
Graphical abstract: Display Omitted -- Highlights: •Purification of Th{sub 1−x}U{sub x}SiO{sub 4} uranothorites from oxide mixture was investigated. •Repetition of centrifugation steps was discarded due to poor recovery yields. •Successive washings in acid and basic media allowed the elimination of oxide secondary phases. •Structural and microstructural characterization of the purified samples was provided. -- Abstract: The mineral coffinite, nominally USiO{sub 4}, and associated Th{sub 1−x}U{sub x}SiO{sub 4} uranothorite solid solutions are of great interest from a geochemical point of view and in the case of the direct storage of spent nuclear fuels. Nevertheless, they clearly exhibit a lack in the evaluation of their thermodynamic data, mainly because of the difficulties linked with their preparation as pure phases. This paper thus presents physical and chemical methods aiming to separate uranothorite solid solutions from oxide additional phases such as amorphous SiO{sub 2} and nanometric crystallized Th{sub 1−y}U{sub y}O{sub 2}. The repetition of centrifugation steps envisaged in first place was rapidly dropped due to poor recovery yields, to the benefit of successive washings in acid then basic media. Under both static and dynamic flow rates (i.e. low or high rate of leachate renewal), ICP-AES (Inductively Coupled Plasma – Atomic Emission Spectroscopy) analyses revealed the systematic elimination of Th{sub 1−y}U{sub y}O{sub 2} in acid media and of SiO{sub 2} in basic media. Nevertheless, two successive steps were always needed to reach pure samples. On this basis, a first cycle performed in static conditions was chosen to eliminate the major part of the accessory phases while a second one, in dynamic conditions, allowed the elimination of the residual impurities. The complete purification of the samples was finally evidenced through the characterization of the samples by the means of PXRD (Powder X-Ray Diffraction), SEM (Scanning Electron
Temperature evolution of the crystal structure of Bi1 - xPrxFeO3 solid solutions
Karpinsky, D. V.; Troyanchuk, I. O.; Sikolenko, V. V.; Efimov, V.; Efimova, E.; Silibin, M. V.; Chobot, G. M.; Willinger, E.
2014-11-01
The crystal structure of solid solutions in the Bi1 - xPrxFeO3 system near the structural transition between the rhombohedral and orthorhombic phases (0.125 ≤ x ≤ 0.15) has been studied. The structural phase transitions induced by changes in the concentration of praseodymium ions and in the temperature have been investigated using X-ray diffraction, transmission electron microscopy, and differential scanning calorimetry. It has been established that the sequence of phase transformations in the crystal structure of Bi1 - xPrxFeO3 solid solutions with variations in the temperature differs significantly from the evolution of the crystal structure of the BiFeO3 compounds with the substitution of other rare-earth elements for bismuth ions. The regions of the existence of the single-phase structural state and regions of the coexistence of the structural phases have been determined in the investigation of the crystal structure of the Bi1 - xPrxFeO3 solid solutions. A three-phase structural state has been revealed for the solid solution with x = 0.125 at temperatures near 400°C. The specific features of the structural phase transitions of the compounds in the vicinity of the morphotropic phase boundary have been determined by analyzing the obtained results. It has been found that the solid solutions based on bismuth ferrite demonstrate a significant improvement in their physical properties.
Sustainable solutions for solid waste management in Southeast Asian countries.
Ngoc, Uyen Nguyen; Schnitzer, Hans
2009-06-01
Human activities generate waste and the amounts tend to increase as the demand for quality of life increases. Today's rate in the Southeast Asian Nations (ASEANs) is alarming, posing a challenge to governments regarding environmental pollution in the recent years. The expectation is that eventually waste treatment and waste prevention approaches will develop towards sustainable waste management solutions. This expectation is for instance reflected in the term 'zero emission systems'. The concept of zero emissions can be applied successfully with today's technical possibilities in the agro-based processing industry. First, the state-of-the-art of waste management in Southeast Asian countries will be outlined in this paper, followed by waste generation rates, sources, and composition, as well as future trends of waste. Further on, solutions for solid waste management will be reviewed in the discussions of sustainable waste management. The paper emphasizes the concept of waste prevention through utilization of all wastes as process inputs, leading to the possibility of creating an ecosystem in a loop of materials. Also, a case study, focusing on the citrus processing industry, is displayed to illustrate the application of the aggregated material input-output model in a widespread processing industry in ASEAN. The model can be shown as a closed cluster, which permits an identification of opportunities for reducing environmental impacts at the process level in the food processing industry. Throughout the discussion in this paper, the utilization of renewable energy and economic aspects are considered to adapt to environmental and economic issues and the aim of eco-efficiency. Additionally, the opportunities and constraints of waste management will be discussed.
Study of solid solution strengthening of alloying element with phase structure factors
无
2003-01-01
Using the empirical electron theory of solids and molecules (EET), the phase structure factors, nA and nB, of the carbon-containing structural units with mass fraction of carbon (wC) below 0.8% and the mono-alloy structural units with wC at 0.2% in austenite and martensite are calculated. The solid solution strengthening brought by C-containing interstitial solid solution and alloy-substitutional solid solution in γ-Fe and α-Fe is discussed at electron structural level. The coefficient (s) of solid solution strengthening is advanced according to the bonding force between atoms. The study shows that when the criterion is applied to the carbonaceous or alloying element-containing solid solution the results of calculation will coincide with the experimental result very well.
Supramolecular stabilization of metastable tautomers in solution and the solid state.
Juribašić, Marina; Bregović, Nikola; Stilinović, Vladimir; Tomišić, Vladislav; Cindrić, Marina; Sket, Primož; Plavec, Janez; Rubčić, Mirta; Užarević, Krunoslav
2014-12-22
This work presents a successful application of a recently reported supramolecular strategy for stabilization of metastable tautomers in cocrystals to monocomponent, non-heterocyclic, tautomeric solids. Quantum-chemical computations and solution studies show that the investigated Schiff base molecule, derived from 3-methoxysalicylaldehyde and 2-amino-3-hydroxypyridine (ap), is far more stable as the enol tautomer. In the solid state, however, in all three obtained polymorphic forms it exists solely as the keto tautomer, in each case stabilized by an unexpected hydrogen-bonding pattern. Computations have shown that hydrogen bonding of the investigated Schiff base with suitable molecules shifts the tautomeric equilibrium to the less stable keto form. The extremes to which supramolecular stabilization can lead are demonstrated by the two polymorphs of molecular complexes of the Schiff base with ap. The molecules of both constituents of molecular complexes are present as metastable tautomers (keto anion and protonated pyridine, respectively), which stabilize each other through a very strong hydrogen bond. All the obtained solid forms proved stable in various solid-state and solvent-mediated methods used to establish their relative thermodynamic stabilities and possible interconversion conditions.
Thermodynamic properties of the cubic plutonium hydride solid solution
Haschke, J M
1981-12-01
Pressure, temperature, and composition data for the cubic solid solution plutonium hydride phase, PuH/sub x/, have been measured by microbalance methods. Integral enthalpies and entropies of formation have been evaluated for the composition range 1.90 less than or equal to X less than or equal to 3.00. At 550/sup 0/K, ..delta..H/sup 0/ /sub f/(PuH/sub x/(s)) varies linearly from approximately (-38 +- 1) kcal mol/sup -1/ at PuH/sub 190/ to (-50 +- 1 kcal mol/sup -1/) at PuH/sub 3/ /sub 00/. Thermochemical values obtained by reevaluating tensimetric data from the literature are in excellent agreement with these results. Isotopic effects have been quantified by comparing the results for hydride and deuteride, and equations are presented for predicting ..delta..H/sup 0/ /sub f/ and ..delta..S/sup 0/ /sub f/ values for PuH/sub x/(s) and PuD/sub x/(s).
Solidification and crystal growth of solid solution semiconducting alloys
Lehoczky, S.L.; Szofran, F.R.
1984-10-01
Problems associated with the solidification and crytal growth of solid-solution semiconducting alloy crystals in a terrestrial environment are described. A detailed description is given of the results for the growth of mercury cadmium telluride (HgCdTe) alloy crystals by directional solidification, because of their considerable technological importance. A series of HgCdTe alloy crystals are grown from pseudobinary melts by a vertical Bridgman method using a wide range of growth rates and thermal conditions. Precision measurements are performed to establish compositional profiles for the crystals. The compositional variations are related to compositional variations in the melts that can result from two-dimensional diffusion or density gradient driven flow effects ahead of the growth interface. These effects are discussed in terms of the alloy phase equilibrium properties, the recent high temperature thermophysical data for the alloys and the highly unusual heat transfer characteristics of the alloy/ampule/furnace system that may readily lead to double diffusive convective flows in a gravitational environment.
Solidification and crystal growth of solid solution semiconducting alloys
Lehoczky, S. L.; Szofran, F. R.
1984-01-01
Problems associated with the solidification and crytal growth of solid-solution semiconducting alloy crystals in a terrestrial environment are described. A detailed description is given of the results for the growth of mercury cadmium telluride (HgCdTe) alloy crystals by directional solidification, because of their considerable technological importance. A series of HgCdTe alloy crystals are grown from pseudobinary melts by a vertical Bridgman method using a wide range of growth rates and thermal conditions. Precision measurements are performed to establish compositional profiles for the crystals. The compositional variations are related to compositional variations in the melts that can result from two-dimensional diffusion or density gradient driven flow effects ahead of the growth interface. These effects are discussed in terms of the alloy phase equilibrium properties, the recent high temperature thermophysical data for the alloys and the highly unusual heat transfer characteristics of the alloy/ampule/furnace system that may readily lead to double diffusive convective flows in a gravitational environment.
Efficient Solutions and Cost-Optimal Analysis for Existing School Buildings
Paolo Maria Congedo
2016-10-01
Full Text Available The recast of the energy performance of buildings directive (EPBD describes a comparative methodological framework to promote energy efficiency and establish minimum energy performance requirements in buildings at the lowest costs. The aim of the cost-optimal methodology is to foster the achievement of nearly zero energy buildings (nZEBs, the new target for all new buildings by 2020, characterized by a high performance with a low energy requirement almost covered by renewable sources. The paper presents the results of the application of the cost-optimal methodology in two existing buildings located in the Mediterranean area. These buildings are a kindergarten and a nursery school that differ in construction period, materials and systems. Several combinations of measures have been applied to derive cost-effective efficient solutions for retrofitting. The cost-optimal level has been identified for each building and the best performing solutions have been selected considering both a financial and a macroeconomic analysis. The results illustrate the suitability of the methodology to assess cost-optimality and energy efficiency in school building refurbishment. The research shows the variants providing the most cost-effective balance between costs and energy saving. The cost-optimal solution reduces primary energy consumption by 85% and gas emissions by 82%–83% in each reference building.
A Proof Of Existence Of Particle-like Solutions Of Einstein Dirac Equations
Bird, E J
2005-01-01
We prove existence of a ground state particle-like solution to the Einstein-Dirac equations: a b ′= 1&parl0;r Ar&parr0; -wTr +m&parl0;A r&parr0; wT r- m&parl0; Ar&parr0; -1&parl0;rA r&parr0; ˙a b A′r= 1- Ar r- 16pwr T2r a2r+b 2r T′r=T rA r-1 2rAr -16pwT3r &parl0;a2r +b2r&parr0; 2rAr +32pT2r ab2r2 Ar +16pmT2r a2r -b2r 2rAr By a ground state particle-like solution we mean a solution of the above equations that satisfies the constraints: limr→∞ r1-Ar <∞lim r- ∞Tr <∞0∞ &parl0;a2r +b2r&parr0; TAdr<∞ .
The effect of co-existing solutes on arsenate removal with hydrotalcite compound.
Kiso, Y; Jung, Y J; Yamamoto, H; Oguchi, T; Kuzawa, K; Yamada, T; Kim, S S; Ahn, K H
2010-01-01
Hydrotalcite (HTAL-Cl), an inorganic anion exchanger, is of use as an adsorbent for the removal of arsenate (As(V)) in water systems. The adsorption properties of HTAL-Cl for As(V) and the effects of co-existing anions on the As(V) removal performance were investigated in this work. Under the conditions of pH>or=4, the adsorption capacity for As(V) gradually decreased with an increase of pH, but As(V) was removed effectively within the range of pH = 5-8. Co-existing anions interfered As(V) removal, and the effect decreased in the order of HPO(4)(2-) > HCO(3)(-) > SO(4)(2-) > Cl(-). In binary solute systems containing phosphate and As(V), the maximum adsorption capacity of HTAL-Cl was 0.95 mmol g(-1) for phosphate and 0.65 mmol g(-1) for As(V): the total of these values corresponded to the maximum adsorption capacity for As(V) in single solute systems. The adsorption isotherms in these binary solute systems were approximated by the following modified Langmuir equations:As(V): q(As) = 18.7 radicalC(As)/(1 + 21.5 radicalC(P) + 12.8 radicalC(As)), phosphate : q(P) = 33.1 radicalC(P)/(1 + 21.5 radicalC(P) + 12.8 radicalC(As)). The column adsorption experiments showed that the adsorbed As(V) was released by the phosphate adsorption, because phosphate was adsorbed more strongly on HTAL-CL than As(V).
WU YUE-XIANG; HUO YAN-MEI; WU YA-KUN
2012-01-01
The main purpose of this paper is to examine the existence of coupled solutions and coupled minimal-maximal solutions for a kind of nonlinear operator equations in partial ordered linear topology spaces by employing the semi-order method.Some new existence results are obtained.
Jin Zhen E-mail: jinzhn@263.net; Ma Zhien; Maoan Han
2004-10-01
In this paper, we study the existence of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with impulses. By using the method coincidence degree theorem, a set of easily verifiable sufficient conditions are obtained for the existence of at least one strictly positive periodic solutions. Some known results are improved and generalized.
Zhiyong Wang
2008-09-01
Full Text Available In this paper, we study the existence of positive solutions for the nonlinear nth-order with m-point singular boundary-value problem. By using the fixed point index theory and a new fixed point theorem in cones, the existence of countably many positive solutions for a nonlinear singular boundary value problem are obtained.
Wen, Zijuan; Fan, Meng; Asiri, Asim M; Alzahrani, Ebraheem O; El-Dessoky, Mohamed M; Kuang, Yang
2017-04-01
This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.
薛强; 梁冰; 刘晓丽; 李宏艳
2003-01-01
The process of contaminant transport is a problem of multicomponent and multiphase flow in unsaturated zone. Under the presupposition that gas existence affects water transport , a coupled mathematical model of contaminant transport in unsaturated zone has been established based on fluid-solid interaction mechanics theory. The asymptotical solutions to the nonlinear coupling mathematical model were accomplished by the perturbation and integral transformation method. The distribution law of pore pressure,pore water velocity and contaminant concentration in unsaturated zone has been presented under the conditions of with coupling and without coupling gas phase. An example problem was used to provide a quantitative verification and validation of the model. The asymptotical solution was compared with Faust model solution. The comparison results show reasonable agreement between asymptotical solution and Faust solution, and the gas effect and media deformation has a large impact on the contaminant transport. The theoretical basis is provided for forecasting contaminant transport and the determination of the relationship among pressure-saturation-permeability in laboratory.
Comparative solution and solid-phase glycosylations toward a disaccharide library
Agoston, K.; Kröger, Lars; Agoston, Agnes
2009-01-01
A comparative study on solution-phase and solid-phase oligosaccharide synthesis was performed. A 16-member library containing all regioisomers of Glc-Glc, Glc-Gal, Gal-Glc, and Gal-Gal disaccharides was synthesized both in solution and on solid phase. The various reaction conditions for different...
Alloying Solid Solution Strengthening of Fe-Ga Alloys: A First-Principle Study
2006-01-01
effect from alloying additions of Nb, Mo, V, Cr and Co in cubic solid solution of Fe-Ga alloys. Mayer bond order "BO" values were used to evaluate the...that transition metal Nb achieves the best strengthening effect in Fe-Ga alloys. The solid solution strengthening follows a trend from larger to
Kleihaus, B; Kunz, Jutta
1999-01-01
In [hep-th/9907222] Hannibal claims to exclude the existence of particle-like static axially symmetric non-abelian solutions in SU(2) Einstein-Yang-Mills-dilaton theory. His argument is based on the asymptotic behaviour of such solutions. Here we disprove his claim by giving explicitly the asymptotic form of non-abelian solutions with winding number n=2.
Le Quang, Thuan; Camlibel, M. K.
2014-01-01
In this paper, we deal with the well-posedness (in the sense of existence and uniqueness of solutions) and nature of solutions for discontinuous bimodal piecewise affine systems in a differential inclusion setting. First, we show that the conditions guaranteeing uniqueness of Filippov solutions in t
Syed ABBAS; Yonghui XIA
2013-01-01
In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks.We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution.Almost automorphic function is a good generalization of almost periodic function.This is the first paper considering such solutions of the neural networks.
Solid solution, phase separation, and cathodoluminescence of GaP-ZnS nanostructures.
Liu, Baodan; Bando, Yoshio; Dierre, Benjamin; Sekiguchi, Takashi; Golberg, Dmitri; Jiang, Xin
2013-09-25
Quaternary solid-solution nanowires made of GaP and ZnS have been synthesized through well-designed synthetic routines. The as-synthesized GaP-ZnS solid-solution nanowires exhibit decent crystallinity with the GaP phase as the host, while a large amount of twin structural defects are observed in ZnS-rich nanowires. Cathodoluminescence studies showed that GaP-rich solid-solution nanowires have a strong visible emission centered at 600 nm and the ZnS-rich solid-solution nanowires exhibited a weak emission peak in the UV range and a broad band in the range 400-600 nm. The formation mechanism, processes, and optical emissions of GaP-ZnS solid-solution nanowires were discussed in detail.
Existence of solutions to Burgers equations in domains that can be transformed into rectangles
Yassine Benia
2016-06-01
Full Text Available This work is concerned with Burgers equation $\\partial _{t}u+u\\partial_x u-\\partial _x^2u=f$ (with Dirichlet boundary conditions in the non rectangular domain $\\Omega =\\{(t,x\\in R^2;\\ 0
EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT
康东升
2004-01-01
This paper is concerned with the quasi-linear equation with critical SobolevHardy exponent where Ω RN(N ≥ 3) is a smooth bounded domain, 0 ∈Ω, 0 ≤ s ＜ p, 1 ＜ p ＜ N,p* (s) :=p(N- s)/N-p is the critical Sobolev-Hardy exponent, λ＞ 0,p ≤ r ＜ p* ,p* := Np/N-p is the critical Sobolev exponent, μ＞ 0, 0 ≤ t ＜ p, p ≤ q ＜ p* (t) = P(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.
Tervo, J; Frank, M; Herty, M
2016-01-01
The paper considers a coupled system of linear Boltzmann transport equation (BTE), and its Continuous Slowing Down Approximation (CSDA). This system can be used to model the relevant transport of particles used e.g. in dose calculation in radiation therapy. The evolution of charged particles (e.g. electrons and positrons) are in practice often modelled using the CSDA version of BTE because of the so-called forward peakedness of scattering events contributing to the particle fluencies (or particle densities), which causes severe problems for numerical methods. First, we prove the existence and uniqueness of solutions, under sufficient criteria and in appropriate $L^2$-based spaces, of a single (particle) CSDA-equation by using two complementary techniques, the Lions-Lax-Milgram Theorem (variational approach), and the theory evolution operators (semigroup approach). The necessary a priori estimates are shown. In addition, we prove the corresponding results and estimates for the system of coupled transport equat...
Carlos Lizama
2012-01-01
Full Text Available Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t=Au(t+∫0tB(t-su(sds+f(t,u(t, t∈[0,1], u(0=g(u, where A:D(A⊆X→X, and for every t∈[0,1] the maps B(t:D(B(t⊆X→X are linear closed operators defined in a Banach space X. We assume further that D(A⊆D(B(t for every t∈[0,1], and the functions f:[0,1]×X→X and g:C([0,1];X→X are X-valued functions which satisfy appropriate conditions.
Majda Chaieb
2016-01-01
Full Text Available Let \\(\\Omega\\ be a bounded domain in \\(\\mathbb{R}^{n}\\ (\\(n\\geq 2\\ with a smooth boundary \\(\\partial \\Omega\\. We discuss in this paper the existence and the asymptotic behavior of positive solutions of the following semilinear elliptic system \\[\\begin{aligned} -\\Delta u&=a_{1}(xu^{\\alpha}v^{r}\\quad\\text{in}\\;\\Omega ,\\;\\;\\,u|_{\\partial\\Omega}=0,\\\\ -\\Delta v&=a_{2}(xv^{\\beta}u^{s}\\quad\\text{in}\\;\\Omega ,\\;\\;\\,v|_{\\partial\\Omega }=0.\\end{aligned}\\] Here \\(r,s\\in \\mathbb{R}\\, \\(\\alpha,\\beta \\lt 1\\ such that \\(\\gamma :=(1-\\alpha(1-\\beta-rs\\gt 0\\ and the functions \\(a_{i}\\ (\\(i=1,2\\ are nonnegative and satisfy some appropriate conditions with reference to Karamata regular variation theory.
J. CABALLERO; B. L(ó)PEZ; K. SADARANGANI
2007-01-01
We use a technique associated with measures of noncompactness to prove the existence of nondecreasing solutions to an integral equation with linear modification of the argument in the space C[0,1]. In the last thirty years there has been a great deal of work in the field of differential equations with a modified argument. A special class is represented by the differential equation with affine modification of the argument which can be delay differential equations or differential equations with linear modifications of the argument. In this case we study the following integral equation x(t) = a(t) + (Tx)(t)∫σ(t)o u(t,s,x(s),x(λs))ds 0λ1 which can be considered in connection with the following Cauchy problem x'(t) = u(t,s,x(t),x(λt)), t∈[0,1], 0 λ 1 x(0) = uo.
Existence of solutions for second-order differential equations and systems on infinite intervals
Toufik Moussaoui
2009-08-01
Full Text Available We study the existence of nontrivial solutions to the boundary-value problem $$displaylines{ -u''+cu'+lambda u = f(x,u,quad -infty
Global existence of solutions to a tear film model with locally elevated evaporation rates
Gao, Yuan; Ji, Hangjie; Liu, Jian-Guo; Witelski, Thomas P.
2017-07-01
Motivated by a model proposed by Peng et al. (2014) for break-up of tear films on human eyes, we study the dynamics of a generalized thin film model. The governing equations form a fourth-order coupled system of nonlinear parabolic PDEs for the film thickness and salt concentration subject to non-conservative effects representing evaporation. We analytically prove the global existence of solutions to this model with mobility exponents in several different ranges and present numerical simulations that are in agreement with the analytic results. We also numerically capture other interesting dynamics of the model, including finite-time rupture-shock phenomenon due to the instabilities caused by locally elevated evaporation rates, convergence to equilibrium and infinite-time thinning.
Existence of positive solutions for semipositone dynamic system on time scales
You-Wei Zhang
2008-08-01
Full Text Available In this paper, we study the following semipositone dynamic system on time scales $$displaylines{ -x^{DeltaDelta}(t=f(t,y+p(t, quad tin(0,T_{mathbb{T}},cr -y^{DeltaDelta}(t=g(t,x, quad tin(0,T_{mathbb{T}},cr x(0=x(sigma^{2}(T=0, cr alpha{y(0}-eta{y^{Delta}{(0}}= gamma{y(sigma(T}+delta{y^{Delta}(sigma(T}=0. }$$ Using fixed point index theory, we show the existence of at least one positive solution. The interesting point is the that nonlinear term is allowed to change sign and may tend to negative infinity.
Existence of Solutions for a Modified Nonlinear Schrödinger System
Yujuan Jiao
2013-01-01
Full Text Available We are concerned with the following modified nonlinear Schrödinger system: -Δu+u-(1/2uΔ(u2=(2α/(α+β|u|α-2|v|βu, x∈Ω, -Δv+v-(1/2vΔ(v2=(2β/(α+β|u|α|v|β-2v, x∈Ω, u=0, v=0, x∈∂Ω, where α>2, β>2, α+β<2·2*, 2*=2N/(N-2 is the critical Sobolev exponent, and Ω⊂ℝN (N≥3 is a bounded smooth domain. By using the perturbation method, we establish the existence of both positive and negative solutions for this system.
Lingju Kong
2013-04-01
Full Text Available We study the existence of multiple solutions to the boundary value problem $$displaylines{ frac{d}{dt}Big(frac12{}_0D_t^{-eta}(u'(t+frac12{}_tD_T^{-eta}(u'(t Big+lambda abla F(t,u(t=0,quad tin [0,T],cr u(0=u(T=0, }$$ where $T>0$, $lambda>0$ is a parameter, $0leqeta<1$, ${}_0D_t^{-eta}$ and ${}_tD_T^{-eta}$ are, respectively, the left and right Riemann-Liouville fractional integrals of order $eta$, $F: [0,T]imesmathbb{R}^Nomathbb{R}$ is a given function. Our interest in the above system arises from studying the steady fractional advection dispersion equation. By applying variational methods, we obtain sufficient conditions under which the above equation has at least three solutions. Our results are new even for the special case when $eta=0$. Examples are provided to illustrate the applicability of our results.
Sun, Juntao; Wu, Tsung-Fang; Wu, Yuanze
2017-06-01
In this paper, we study a class of nonlinear Schrödinger-Poisson systems with indefinite steep potential well: -Δ u+V_{λ }(x)u+K(x)φ u=|u|^{p-2}u in R3, -Δ φ =K( x) u2 in R3, where 30 and K(x)≥ 0 for all x\\in R3. We require that a\\in C( R3) is nonnegative and has a potential well Ω a, namely a(x)≡ 0 for x\\in Ω a and a(x)>0 for x\\in R3\\setminus \\overline{Ω a}. Unlike most other papers on this problem, we allow that b\\in C(R3) is unbounded below and sign-changing. By introducing some new hypotheses on the potentials and applying the method of penalized functions, we obtain the existence of nontrivial solutions for λ sufficiently large. Furthermore, the concentration behavior of the nontrivial solution is also described as λ → ∞.
Thermoelectric properties of the Ca(5)Al(2-x)In(x)Sb(6) solid solution.
Zevalkink, Alex; Swallow, Jessica; Ohno, Saneyuki; Aydemir, Umut; Bux, Sabah; Snyder, G Jeffrey
2014-11-14
Zintl phases are attractive for thermoelectric applications due to their complex structures and bonding environments. The Zintl compounds Ca(5)Al(2)In(x)Sb(6)and Ca(5)Al(2)In(x)Sb(6) have both been shown to have promising thermoelectric properties, with zT values of 0.6 and 0.7, respectively, when doped to control the carrier concentration. Alloying can often be used to further improve thermoelectric materials in cases when the decrease in lattice thermal conductivity outweighs reductions to the electronic mobility. Here we present the high temperature thermoelectric properties of the Ca(5)Al(2-x)In(x)Sb(6)solid solution. Undoped and optimally Zn-doped samples were investigated. X-ray diffraction confirms that a full solid solution exists between the Al and In end-members. We find that the Al : In ratio does not greatly influence the carrier concentration or Seebeck effect. The primary effect of alloying is thus increased scattering of both charge carriers and phonons, leading to significantly reduced electronic mobility and lattice thermal conductivity at room temperature. Ultimately, the figure of merit is unaffected by alloying in this system, due to the competing effects of reduced mobility and lattice thermal conductivity.
The origin of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution crystals
Li, Fei; Zhang, Shujun; Yang, Tiannan; Xu, Zhuo; Zhang, Nan; Liu, Gang; Wang, Jianjun; Wang, Jianli; Cheng, Zhenxiang; Ye, Zuo-Guang; Luo, Jun; Shrout, Thomas R.; Chen, Long-Qing
2016-01-01
The discovery of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution single crystals is a breakthrough in ferroelectric materials. A key signature of relaxor-ferroelectric solid solutions is the existence of polar nanoregions, a nanoscale inhomogeneity, that coexist with normal ferroelectric domains. Despite two decades of extensive studies, the contribution of polar nanoregions to the underlying piezoelectric properties of relaxor ferroelectrics has yet to be established. Here we quantitatively characterize the contribution of polar nanoregions to the dielectric/piezoelectric responses of relaxor-ferroelectric crystals using a combination of cryogenic experiments and phase-field simulations. The contribution of polar nanoregions to the room-temperature dielectric and piezoelectric properties is in the range of 50–80%. A mesoscale mechanism is proposed to reveal the origin of the high piezoelectricity in relaxor ferroelectrics, where the polar nanoregions aligned in a ferroelectric matrix can facilitate polarization rotation. This mechanism emphasizes the critical role of local structure on the macroscopic properties of ferroelectric materials. PMID:27991504
The origin of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution crystals
Li, Fei; Zhang, Shujun; Yang, Tiannan; Xu, Zhuo; Zhang, Nan; Liu, Gang; Wang, Jianjun; Wang, Jianli; Cheng, Zhenxiang; Ye, Zuo-Guang; Luo, Jun; Shrout, Thomas R.; Chen, Long-Qing (Penn); (Xian Jiaotong); (CIW); (Simon); (TRS Techn); (Wollongong)
2016-12-19
The discovery of ultrahigh piezoelectricity in relaxor-ferroelectric solid solution single crystals is a breakthrough in ferroelectric materials. A key signature of relaxor-ferroelectric solid solutions is the existence of polar nanoregions, a nanoscale inhomogeneity, that coexist with normal ferroelectric domains. Despite two decades of extensive studies, the contribution of polar nanoregions to the underlying piezoelectric properties of relaxor ferroelectrics has yet to be established. Here we quantitatively characterize the contribution of polar nanoregions to the dielectric/piezoelectric responses of relaxor-ferroelectric crystals using a combination of cryogenic experiments and phase-field simulations. The contribution of polar nanoregions to the room-temperature dielectric and piezoelectric properties is in the range of 50–80%. A mesoscale mechanism is proposed to reveal the origin of the high piezoelectricity in relaxor ferroelectrics, where the polar nanoregions aligned in a ferroelectric matrix can facilitate polarization rotation. This mechanism emphasizes the critical role of local structure on the macroscopic properties of ferroelectric materials.
Solid lipid nanoparticles suspension versus commercial solutions for dermal delivery of minoxidil.
Padois, Karine; Cantiéni, Céline; Bertholle, Valérie; Bardel, Claire; Pirot, Fabrice; Falson, Françoise
2011-09-15
Solid lipid nanoparticles have been reported as possible carrier for skin drug delivery. Solid lipid nanoparticles are produced from biocompatible and biodegradable lipids. Solid lipid nanoparticles made of semi-synthetic triglycerides stabilized with a mixture of polysorbate and sorbitan oleate were loaded with 5% of minoxidil. The prepared systems were characterized for particle size, pH and drug content. Ex vivo skin penetration studies were performed using Franz-type glass diffusion cells and pig ear skin. Ex vivo skin corrosion studies were realized with a method derived from the Corrositex(®) test. Solid lipid nanoparticles suspensions were compared to commercial solutions in terms of skin penetration and skin corrosion. Solid lipid nanoparticles suspensions have been shown as efficient as commercial solutions for skin penetration; and were non-corrosive while commercial solutions presented a corrosive potential. Solid lipid nanoparticles suspensions would constitute a promising formulation for hair loss treatment. Copyright © 2011 Elsevier B.V. All rights reserved.
A Local Composition Model for Paraffinic Solid Solutions
Coutinho, A.P. João; Knudsen, Kim; Andersen, Simon Ivar
1996-01-01
The description of the solid-phase non-ideality remains the main obstacle in modelling the solid-liquid equilibrium of hydrocarbons. A theoretical model, based on the local composition concept, is developed for the orthorhombic phase of n-alkanes and tested against experimental data for binary sy...... systems. It is shown that it can adequately predict the experimental phase behaviour of paraffinic mixtures. This work extends the applicability of local composition models to the solid phase. Copyright (C) 1996 Elsevier Science Ltd....
Evolution of mixed surfactant aggregates in solutions and at solid/solution interfaces
Zhang, Rui
Surfactant systems have been widely used in such as enhanced oil recovery, waste treatment and metallurgy, etc., in order to solve the problem of global energy crisis, to remove the pollutants and to generate novel energy resources. Almost all surfactant systems are invariably mixtures due to beneficial and economic considerations. The sizes and shapes of aggregates in solutions and at solid/solution interfaces become important, since the nanostructures of mixed aggregates determine solution and adsorption properties. A major hurdle in science is the lack of information on the type of complexes and aggregates formed by mixtures and the lack of techniques for deriving such information. Using techniques such as analytical ultracentrifuge, small angle neutron scattering, surface tension, fluorescence, cryo-TEM, light scattering and ultrafiltration, the nanostructures of aggregates of sugar based n-dodecyl-beta-D-maltoside (DM) and nonionic pentaethyleneglycol monododecyl ether or nonyl phenol ethoxylated decyl ether (NP-10) and their mixtures have been investigated to prove the hypothesis that the aggregation behavior is linked to packing of the surfactant governed by the molecular interactions as well as the molecular structures. The results from both sedimentation velocity and sedimentation equilibrium experiments suggest coexistence of two types of micelles in nonyl phenol ethoxylated decyl ether solutions and its mixtures with n-dodecyl-beta-D-maltoside while only one micellar species is present in n-dodecyl-beta-D-maltoside solutions, in good agreement with those from small angle neutron scattering, cryo-TEM, light scattering and ultrafiltration. Type I micelles were primary micelles at cmc while type II micelles were elongated micelles. On the other hand, the nanostructures of mixed surface aggregates have been quantitatively predicted for the first time using a modified packing index. As a continuation of the Somasundaran-Fuersteneau adsorption model, a
Zhijian, Yang
The paper studies the global existence, asymptotic behavior and blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with dissipative term. It proves that under rather mild conditions on nonlinear terms and initial data the above-mentioned problem admits a global weak solution and the solution decays exponentially to zero as t→+∞, respectively, in the states of large initial data and small initial energy. In particular, in the case of space dimension N=1, the weak solution is regularized to be a unique generalized solution. And if the conditions guaranteeing the global existence of weak solutions are not valid, then under the opposite conditions, the solutions of above-mentioned problem blow up in finite time. And an example is given.
Facão, M; Carvalho, M I
2015-08-01
We found two stationary solutions of the cubic complex Ginzburg-Landau equation (CGLE) with an additional term modeling the delayed Raman scattering. Both solutions propagate with nonzero velocity. The solution that has lower peak amplitude is the continuation of the chirped soliton of the cubic CGLE and is unstable in all the parameter space of existence. The other solution is stable for values of nonlinear gain below a certain threshold. The solutions were found using a shooting method to integrate the ordinary differential equation that results from the evolution equation through a change of variables, and their stability was studied using the Evans function method. Additional integration of the evolution equation revealed the basis of attraction of the stable solutions. Furthermore, we have investigated the existence and stability of the high amplitude branch of solutions in the presence of other higher order terms originating from complex Raman, self-steepening, and imaginary group velocity.
Growth and structural investigations of La1-xPrxCaO3 solid solution single crystals
Berkowski, M; Fink-Finowicki, J; Byszewski, P; Diduszko, R; Kowalska, E; Aleksiyko, R; Piekarczyk, W; Vasylechko, LO; Savytskij, DI; Perchuc, L
Growth of single crystals in the pseudobinary LaGaO3-PrGaO3 system by the Czochralski and floating-zone methods was investigated. It has been found that solid solution crystals La1-xPrxGaO3 exist in the whole concentration range x, The segregation coefficients of Pr in LaGaO3 and La in PrGaO3 have
Growth and structural investigations of La1-xPrxCaO3 solid solution single crystals
Berkowski, M; Fink-Finowicki, J; Byszewski, P; Diduszko, R; Kowalska, E; Aleksiyko, R; Piekarczyk, W; Vasylechko, LO; Savytskij, DI; Perchuc, L
2001-01-01
Growth of single crystals in the pseudobinary LaGaO3-PrGaO3 system by the Czochralski and floating-zone methods was investigated. It has been found that solid solution crystals La1-xPrxGaO3 exist in the whole concentration range x, The segregation coefficients of Pr in LaGaO3 and La in PrGaO3 have b
Abbasbandy, S.; Van Gorder, R. A.; Hajiketabi, M.; Mesrizadeh, M.
2015-10-01
We consider traveling wave solutions to the Casimir equation for the Ito system (a two-field extension of the KdV equation). These traveling waves are governed by a nonlinear initial value problem with an interesting nonlinearity (which actually amplifies in magnitude as the size of the solution becomes small). The nonlinear problem is parameterized by two initial constant values, and we demonstrate that the existence of solutions is strongly tied to these parameter values. For our interests, we are concerned with positive, bounded, periodic wave solutions. We are able to classify parameter regimes which admit such solutions in full generality, thereby obtaining a nice existence result. Using the existence result, we are then able to numerically simulate the positive, bounded, periodic solutions. We elect to employ a group preserving scheme in order to numerically study these solutions, and an outline of this approach is provided. The numerical simulations serve to illustrate the properties of these solutions predicted analytically through the existence result. Physically, these results demonstrate the existence of a type of space-periodic structure in the Casimir equation for the Ito model, which propagates as a traveling wave.
黎勇; 陈丽
2002-01-01
In this paper, we study the asymptotic behavior of global smooth solution to the initial boundary problem for the 1-D energy transport model in semiconductor science. We prove that the smooth solution of the problem converges to a stationary solution exponentially fast as t - ∞ when the initial data is a small perturbation of the stationary solution.
Preparation and Photocatalytic Properties of Ti1-xZrxO2 Solid Solution
GAO,Bi-Fen; MA,Ying; CAO,Ya-An; GU,Zhan-Jun; ZHANG,Guang-Jin; YAO,Jian-Nian
2007-01-01
A series of Ti1-xZrxO2 materials were synthesized through a multistep sol-gel process.The structural characteristics were investigated using X-ray diffraction(XRD),X-ray photoelectron spectroscopy(XPS)and Raman measurements.The experimental results showed that a solid solution could be obtained at low Zr/(Ti+Zr)molar ratios(x≤0.319).Raman measurements exhibited that the presence of zirconium in the solid solutions greatly retarded the amoorphous-anatase and anatase-rutile transitions.The diffuse reflectance UV-Vis spectra revealed that the bandgap of the solid solution was enlarged gradually with the increment of incorporated zirconium content.The Til-xZrxO2solid solutions exhibited higher photocatalytic activity than pure TiO2 for the degradation of 4-chlorophenol aqueous solution.
Comparisons of species and coagulation effects of PFS solution and solid PFS from pyrite cinders
郑雅杰; 龚竹青; 刘立华; 陈白珍
2002-01-01
Pyrite cinder is a kind of solid waste of sulfuric acid industry. After mixing pyrite cinders with sulfuric acid, ferric sulfate was obtained by heating, maturing, dissolving and filtrating. Suitable amounts of FeSO4 * 7H2O and NaClO3 were added into ferric sulfate solution and polyferric sulfate(PFS) solution was produced. Solid PFS was made by concentrating and drying PFS solution. Time-dependent complex colorimetric tests were done while ferron agent reacted with Fe3+ in the solution. The results show that the proportion of transitional low polymeric species and high polymeric species are increased after PFS solution is transferred into solid PFS. It was discovered by jar tests that solid PFS has very good coagulation effects relevant to the increase of transitional lower polymeric species.
Wang, J. C.
1982-01-01
Compositional segregation of solid solution semiconducting alloys in the radial direction during unidirectional solidification was investigated by calculating the effect of a curved solid liquid interface on solute concentration at the interface on the solid. The formulation is similar to that given by Coriell, Boisvert, Rehm, and Sekerka except that a more realistic cylindrical coordinate system which is moving with the interface is used. Analytical results were obtained for very small and very large values of beta with beta = VR/D, where V is the velocity of solidification, R the radius of the specimen, and D the diffusivity of solute in the liquid. For both very small and very large beta, the solute concentration at the interface in the solid C(si) approaches C(o) (original solute concentration) i.e., the deviation is minimal. The maximum deviation of C(si) from C(o) occurs for some intermediate value of beta.
Chengyuan Qu; Yang Cao
2013-11-01
We consider a class of nonlinear viscous Cahn–Hilliard equations with gradient dependent potentials and sources. By a Galerkin approximation scheme combined with the potential well method, we prove the global existence of weak solutions.
A note on the global existence of small amplitude solutions to a generalized Davey-Stewartson system
Eden, Alp [Department of Mathematics, Bogazici University, 34342 Bebek-Istanbul (Turkey); Hacinliyan, Irma [Department of Mathematics, Istanbul Technical University, 34469 Maslak-Istanbul (Turkey)], E-mail: hacinliy@itu.edu.tr
2009-06-19
In this paper, we are interested in the Cauchy problem for a generalized Davey-Stewartson (GDS) system. We establish the global time existence of small mass solutions for the GDS system in the elliptic-hyperbolic-hyperbolic case.
Assia Guezane-Lakoud
2011-01-01
Full Text Available We consider a telegraph equation with nonlocal boundary conditions, and using the application of Galerkin's method we established the existence and uniqueness of a generalized solution.
Mabrouk Briki
2016-05-01
Full Text Available In this paper, a fourth-order boundary value problem on the half-line is considered and existence of solutions is proved using a minimization principle and the mountain pass theorem.
无
2001-01-01
The existence of positive solutions and the global attractivity of the difference equation △yn=rnyn are investigated. And some sufficient conditions are obtained,which greatly improve and extend the known results.
Yan Lv; Wei Lv; Jian-hua Sun
2007-01-01
By using the continuation theorem of coincidence degree theory, the sufficient conditions to guarantee the existence of positive periodic solutions are established for nonautonomous predator-prey systems with discrete and continuously distributed delays.
无
2001-01-01
The existence and uniqueness of a strong periodic solution of the evolution system describing geophysical flow in bounded domains of RN(N = 3, 4) are proven if external forces are periodic in time and sufficiently small.
无
2006-01-01
Using a fixed point theorem in a cone, we obtain some optimal existence results for single and multiple positive periodic solutions to a functional difference system with feedback control. Moreover, we apply our results to a population model.
Alfonso Castro
1998-01-01
Full Text Available In this article we apply the minmax principle we developed in [6] to obtain sign-changing solutions for superlinear and asymptotically linear Dirichlet problems. We prove that, when isolated, the local degree of any solution given by this minmax principle is $+1$. By combining the results of [6] with the degree-theoretic results of Castro and Cossio in [5], in the case where the nonlinearity is asymptotically linear, we provide sufficient conditions for: i the existence of at least four solutions (one of which changes sign exactly once, ii the existence of at least five solutions (two of which change sign, and iii the existence of precisely two sign-changing solutions.
Schmidt, Moritz; Heck, Stephanie; Bosbach, Dirk; Ganschow, Steffen; Walther, Clemens; Stumpf, Thorsten
2013-01-01
We present a comprehensive study of the solid solution system Ca-2(MoO4)(2)-NaGd(MoO4)(2) on the molecular scale, by means of site-selective time resolved laser fluorescence spectroscopy (TRLFS). Eu3+ is used as a trace fluorescent probe, homogeneously substituting for Gd3+ in the solid solution crystal structure. Site-selective TRLFS of a series of polycrystalline samples covering the whole composition range of the solid solution series from 10% substitution of Ca2+ to the NaGd end-member re...
Iron salts in solid state and in frozen solutions as dosimeters for low irradiation temperatures
Martinez, T. [Facultad de Quimica UNAM, Ciudad Universitaria, D.F. Mexico (Mexico); Lartigue, J. [Facultad de Quimica UNAM, Ciudad Universitaria, D.F. Mexico (Mexico); Ramos-Bernal, S. [Instituto de Ciencias Nucleares, UNAM, A.P. 70-543 C.P.4510, Ciudad Universitaria, D.F. Mexico (Mexico); Ramos, A. [Instituto de Ciencias Nucleares, UNAM, A.P. 70-543 C.P.4510, Ciudad Universitaria, D.F. Mexico (Mexico); Mosqueira, G.F. [Direccion General de Divulgacion de la Ciencia de la UNAM, A.P. 70-487, C:P, D.F. Mexico 04510 (Mexico); Negron-Mendoza, A. [Instituto de Ciencias Nucleares, UNAM, A.P. 70-543 C.P.4510, Ciudad Universitaria, D.F. Mexico (Mexico)]. E-mail: negron@nuclecu.unam.mx
2005-12-01
The aim of this work is to study the irradiation of iron salts in solid state (heptahydrated ferrous sulfate) and in frozen acid solutions. The study is focused on finding their possible use as dosimeters for low temperature irradiations and high doses. The analysis of the samples was made by UV-visible and Moessbauer spectroscopies. The output signal was linear from 0 to 10 MGy for the solid samples, and 0-600 Gy for the frozen solutions. The obtained data is reproducible and easy to handle. For these reasons, heptahydrate iron sulfate is a suitable dosimeter for low temperature and high irradiation doses, in solid state, and in frozen solution.
Local structure in the disordered solid solution of cis- and trans-perinones
Teteruk, Jaroslav L.; Glinnemann, Juergen; Heyse, Winfried;
2016-01-01
The cis- and trans-isomers of the polycyclic aromatic compound perinone, C26H12N4O2, form a solid solution (Vat Red 14). This solid solution is isotypic to the crystal structures of cis-perinone (Pigment Red 194) and trans-perinone (Pigment Orange 34) and exhibits a combined positional....... The crystal structure of the solid solution was determined by single-crystal X-ray analysis. Extensive lattice-energy minimizations with force-field and DFT-D methods were carried out on combinatorially complete sets of ordered models. For the disordered systems, local structures were calculated, including...
Snežana Bošković
2012-09-01
Full Text Available In this paper a short review of our results on the synthesis of nanosized CeO2, CaMnO3 and BaCeO3 solid solutions are presented. The nanopowders were prepared by two innovative methods: self propagating room temperature synthesis (SPRT and modified glycine/nitrate procedure (MGNP. Different types of solid solutions with rare earth dopants in concentrations ranging from 0–0.25 mol% were synthesized. The reactions forming solid solutions were studied. In addition, the characteristics of prepared nanopowders, phenomena during sintering and the properties of sintered samples are discussed.
The Effect of Hydrogen on the Solid Solution Strengthening and Softening of Nickel.
1981-11-01
Afl-A108 654e ILLINOIS UNIV AT URBANA DEPT OF METALLURGY AND MININS--ETC F/6 11/6 THE EFFECT OF HYDROGEN ON THE SOLID SOLUTION STRFNSTNFNING ANfl...RESOLUTION TEST CHART NATIONAL HUR[AU OF STANDARDS 1963 A, " , ..... . .... .. i ....... .. .. . t , LEVEL THE EFFECT OF HYDROGEN ON THE SOLID SOLUTION STRENGTHENING...Availability Codes IIAvail and/or Dist Special THE EFFECT OF HYDROGEN ON THE SOLID SOLUTION STRENGTHENING AND SOFTENING OF NICKEL J. Eastman, F. Heuhaum, T
Magnetic properties of Ho1- x Lu x B12 solid solutions
Gabáni, S.; Gaz̆o, E.; Pristás̆, G.; Takác̆ová, I.; Flachbart, K.; Shitsevalova, N.; Siemensmeyer, K.; Sluchanko, N.
2013-05-01
Magnetic properties of the geometrically frustrated antiferromagnet HoB12 (with T N = 7.4 K) modified by substitution of magnetic Ho atoms through non-magnetic Lu ones are presented and discussed. In this case, in Ho1- x Lu x B12 solid solutions, both chemical pressure resulting from different Lu3+ and Ho3+ radii and magnetic dilution take place with increasing Lu content ( x) that change properties of the system. The received results show strong indication for the existence of a quantum critical point near x = 0.9, which separates the region of magnetic order (starting with HoB12 for x = 0) and the nonmagnetic region (ending with superconducting LuB12 for x = 1).
Ruihui Huang
2013-01-01
Full Text Available We study the existence and uniqueness of solutions for a class of antiperiodic boundary value problems of the fractional differential equation with a p-Laplacian operator. Based on the Leray-Schauder nonlinear alternative, several sufficient conditions of the existence and uniqueness of solution of the above problem are established. Our results improve and complement the recent work of Chen and Liu, 2012.
Jing Bao YANG; Zhong Li WEI
2011-01-01
By employing the fixed point theorem of cone expansion and compression of norm type,we investigate the existence of positive solutions of generalized Sturm-Liouville boundary value problems for a nonlinear singular differential equation with a parameter.Some sufficient conditions for the existence of positive solutions are established.In the last section,an example is presented to illustrate the applications of our main results.
Giai Giang Vo
2015-01-01
Full Text Available This paper is devoted to the study of a wave equation with a boundary condition of many-point type. The existence of weak solutions is proved by using the Galerkin method. Also, the uniqueness and the stability of solutions are established.
V. Rukavishnikov
2014-01-01
Full Text Available The existence and uniqueness of the Rv-generalized solution for the first boundary value problem and a second order elliptic equation with coordinated and uncoordinated degeneracy of input data and with strong singularity solution on all boundary of a two-dimensional domain are established.
无
2012-01-01
In this paper,we aim to study the existence and uniqueness of square-mean almost automorphic mild solution to a stochastic delay equation under some suitable assumptions imposed on its coefficients.As an application,almost automorphic mild solutions to a class of stochastic partial functional differential equations are analyzed,which shows the feasibility of our results.
Escher, Joachim; Matioc, Bogdan-Vasile
2011-01-01
We prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate towards flat equilibria.
无
2012-01-01
The positive periodic solutions to a three-species delayed Lotka-Volterra model with dispersion and harvesting terms are studied in this paper. By the coincidence degree theory, the sufficient conditions for existence of eight positive periodic solutions to the model are obtained.
Yimin Zhang
2009-01-01
Full Text Available By the continuation theorem of coincidence degree and M-matrix theory, we obtain some sufficient conditions for the existence and exponential stability of periodic solutions for a class of generalized neural networks with arbitrary delays, which are milder and less restrictive than those of previous known criteria. Moreover our results generalize and improve many existing ones.
Naji Qatanani
2007-11-01
Full Text Available This article gives very significant and up-to-date analytical results on the conductive-radiative heat transfer model containing two conducting and opaque materials which are in contact by radiation through a transparent medium bounded by diffuse-gray surfaces. Some properties of the radiative integral operator will be presented. The main emphasis of this work deals also with the question of existence and uniqueness of weak solution for this problem. The existence of weak solution will be proved by showing that our problem is pseudomonotone and coercive. The uniqueness of the solution will be proved using an idea from the analysis of nonlinear heat conduction.
The Existence and Long-Time Behavior of Weak Solution to Bipolar Quantum Drift-Diffusion Model
Xiuqing CHEN; Li CHEN; Huaiyu JIAN
2007-01-01
The authors study the existence and long-time behavior of weak solutions to the bipolar transient quantum drift-diffusion model, a fourth order parabolic system. Using semi-discretization in time and entropy estimate, the authors get the global existence of nonnegative weak solutions to the one-dimensional model with nonnegative initial and homogenous Neumann (or periodic) boundary conditions. Furthermore, by a logarithmic Sobolev inequality, it is proved that the periodic weak solution exponentially approaches its mean value as time increases to infinity.
The growth and tensile deformation behavior of the silver solid solution phase with zinc
Wu, Jiaqi, E-mail: jiaqw10@uci.edu [Department of Electrical Engineering and Computer Science, University of California, Irvine, CA 92697-2660 (United States); Materials and Manufacturing Technology, University of California, Irvine, CA 92697-2660 (United States); Lee, Chin C. [Department of Electrical Engineering and Computer Science, University of California, Irvine, CA 92697-2660 (United States); Materials and Manufacturing Technology, University of California, Irvine, CA 92697-2660 (United States)
2016-06-21
The growth of homogeneous silver solid solution phase with zinc are conducted at two different compositions. X-ray diffraction (XRD) and Scanning electron microscope/Energy dispersive X-ray spectroscopy (SEM/EDX) are carried out for phase identification and chemical composition verification. The mechanical properties of silver solid solution phase with zinc are evaluated by tensile test. The engineering and true stress vs. strain curves are presented and analyzed, with those of pure silver in comparison. According to the experimental results, silver solid solution phase with zinc at both compositions show tempered yield strength, high tensile strength and large uniform strain compared to those of pure silver. Fractography further confirmed the superior ductility of silver solid solution phase with zinc at both compositions. Our preliminary but encouraging results may pave the way for the silver based alloys to be applied in industries such as electronic packaging and structure engineering.
Local Structure and Short-Range Order in a NiCoCr Solid Solution Alloy
Zhang, F. X.; Zhao, Shijun; Jin, Ke; Xue, H.; Velisa, G.; Bei, H.; Huang, R.; Ko, J. Y. P.; Pagan, D. C.; Neuefeind, J. C.; Weber, W. J.; Zhang, Yanwen
2017-05-01
Multielement solid solution alloys are intrinsically disordered on the atomic scale, and many of their advanced properties originate from the local structural characteristics. The local structure of a NiCoCr solid solution alloy is measured with x-ray or neutron total scattering and extended x-ray absorption fine structure (EXAFS) techniques. The atomic pair distribution function analysis does not exhibit an observable structural distortion. However, an EXAFS analysis suggests that the Cr atoms are favorably bonded with Ni and Co in the solid solution alloys. This short-range order (SRO) may make an important contribution to the low values of the electrical and thermal conductivities of the Cr-alloyed solid solutions. In addition, an EXAFS analysis of Ni ion irradiated samples reveals that the degree of SRO in NiCoCr alloys is enhanced after irradiation.
THE ROLE OF ELECTRON CONFIGURATION ON PROPERTIES IN DILUTE SOLID SOLUTION ALLOYS
THE ROLE OF ELECTRON CONFIGURATION ON THE PROPERTIES OF DILUTE SOLID SOLUTION ALLOYS IS DISCUSSED IN TERMS OF THE EFFECT OF DILUTE IMPURITIES ON THE RECRYSTALLIZATION CHARACTERISTICS OF PURE METALLIC ELEMENTS.
Miller, Philip J.; Tong, William G.
1980-01-01
Presents a physical inorganic experiment in which large single crystals of the alkali halides doped with divalent ion impurities are prepared easily. Demonstrates the ion pairing of inorganic ions in solid solution. (CS)
Junping YIN; Zhong TAN
2008-01-01
The authors prove two global existence results of strong solutions of the isen- tropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.
Luminescence properties of solid solutions of borates doped with rare-earth ions
Levushkina, V. S.; Mikhailin, V. V.; Spassky, D. A.; Zadneprovski, B. I.; Tret'yakova, M. S.
2014-11-01
The structural and luminescence properties of LuxY1 - xBO3 solid solutions doped with Ce3+ or Eu+3 have been investigated. It has been found that the solid solutions crystallize in the vaterite phase with a lutetium concentration x spectra are characterized by intensive impurity emission under excitation with the synchrotron radiation in the X-ray and ultraviolet spectral ranges. It has been shown that, as the lutetium concentration x in the LuxY1 - xBO3: Ce3+ solid solutions increases, the emission intensity smoothly decreases, which is associated with a gradual shift of the Ce3+ 5 d(1) level toward the bottom of the conduction band, as well as with a decrease in the band gap. It has been established that, in the LuxY1 - xBO3: Eu3+ solid solutions with intermediate concentrations x, the efficiency of energy transfer to luminescence centers increases. This effect is explained by the limited spatial separation of electrons and holes in the solid solutions. It has been demonstrated that the calcite phase adversely affects the luminescence properties of the solid solutions.
Haspot, Boris
2016-06-01
We consider the compressible Navier-Stokes equations for viscous and barotropic fluids with density dependent viscosity. The aim is to investigate mathematical properties of solutions of the Navier-Stokes equations using solutions of the pressureless Navier-Stokes equations, that we call quasi solutions. This regime corresponds to the limit of highly compressible flows. In this paper we are interested in proving the announced result in Haspot (Proceedings of the 14th international conference on hyperbolic problems held in Padova, pp 667-674, 2014) concerning the existence of global weak solution for the quasi-solutions, we also observe that for some choice of initial data (irrotationnal) the quasi solutions verify the porous media, the heat equation or the fast diffusion equations in function of the structure of the viscosity coefficients. In particular it implies that it exists classical quasi-solutions in the sense that they are {C^{∞}} on {(0,T)× {R}N} for any {T > 0}. Finally we show the convergence of the global weak solution of compressible Navier-Stokes equations to the quasi solutions in the case of a vanishing pressure limit process. In particular for highly compressible equations the speed of propagation of the density is quasi finite when the viscosity corresponds to {μ(ρ)=ρ^{α}} with {α > 1}. Furthermore the density is not far from converging asymptotically in time to the Barrenblatt solution of mass the initial density {ρ0}.
Analysis of Valence Electron Structure of RE in Solid Solution in Medium and Low Carbon Steel
朱莹光; 刘艳; 刘志林; 刘伟东
2004-01-01
According to EET theory,the valence electron structures of RE in the solid solution of austenite,pearlite and martensite were calculated.The influence of RE in solid solution on phase transformation of pearlite and recrystallization of martensite was explained by the valence electron structure data of phases.Calculating results indicate that C element is favorite to enhance the number of RE in the solid solution.RE in the solute solution shortens the incubation period of proeutectoid ferrite,increases its quantity and carbon content,decreases the quantity of pearlite and thickness of its lamellas and lamellar spacing,then the strength and hardness of pearlite are improved and granular pearlite can be obtained.RE dissolved in martensite intensifies martensite,enhances tempering stability of martensite,increases its recrystallization temperature and prolongs the holding time needed during tempering.
Repowering of an Existing Power Plant by Means of Gas Turbine and Solid Oxide Fuel Cell
Rokni, Masoud
2014-01-01
Repowering is a process consisting in a transformation of an old power plant in order to have a greater nameplate capacity or more efficiency, which result in a net increase of power generated. As a consequence of the higher efficiency, the repow ered plant is characterized by higher power output...... for topping an existing steam cycle, instead of gas turbine on the top. This is also the target of this study, r epowering of an existing power plant with SOFC as well as gas turbines. The plant used here for repowering is the Kyndby power station is an emergency and peak load facility for Zealand in Denmark....... This means the facilities at the station can be started up within minutes if operational irregularities occur in the high voltage electricity grid or problems arise at other power stations. Nowadays this station is repowered with two gas turbines but the current study is about the original steam plant before...
Global Existence of Smooth Solutions of Compressible Bipolar Euler-Maxwell Equations
XU Qian-jin; LI Xin; FENG Yue-hong
2013-01-01
The bipolar compressible Euler-Maxwell equations as a fluid dynamic model arising from plasma physics to describe the dynamics of the compressible electrons and ions is investigated.This work is concerned with three-dimensional Euler-Maxwell equations with smooth periodic solutions.With the help of the symmetry operator techniques and energy method,the global smooth solution with small amplitude is constructed around a constant equilibrium solution with asymptotic stability property.
Repowering of an Existing Power Plant by Means of Gas Turbine and Solid Oxide Fuel Cell
Rokni, Masoud
2014-01-01
Repowering is a process consisting in a transformation of an old power plant in order to have a greater nameplate capacity or more efficiency, which result in a net increase of power generated. As a consequence of the higher efficiency, the repow ered plant is characterized by higher power output and less specific CO2 emissions. Usually, a repowering is performed adding one or more gas turbines to an existing steam cycle which was built decades ago. Thus, traditional repowering results in com...
Rolland, A.; Aufray, B.
1985-10-01
This paper deals with a comparative study of surface segragation of Pb and Ni respectively from Ag(Pb)(111) and Ag(Ni)(111) solid solutions. A high level of segregation of the solute is observed for both systems characterized by very low solute solubility. However, the superficial composition strongly depends on the relative surface tensions of the pure elements: the solute atoms are strictly on superficial sites when γ solute is smaller than γ solvent; in contrast uppermost layer consists purely of solvent when γ solute is greater than γ solvent. Two schematic distributions in close proximity to the surface are proposed in the last case.
High-temperature thermoelectric properties of the β-As2-xBixTe3 solid solution
Vaney, J.-B.; Delaizir, G.; Piarristeguy, A.; Monnier, J.; Alleno, E.; Lopes, E. B.; Gonçalves, A. P.; Pradel, A.; Dauscher, A.; Candolfi, C.; Lenoir, B.
2016-10-01
Bi2Te3-based compounds are a well-known class of outstanding thermoelectric materials. β-As2Te3, another member of this family, exhibits promising thermoelectric properties around 400 K when appropriately doped. Herein, we investigate the high-temperature thermoelectric properties of the β-As2-xBixTe3 solid solution. Powder X-ray diffraction and scanning electron microscopy experiments showed that a solid solution only exists up to x = 0.035. We found that substituting Bi for As has a beneficial influence on the thermopower, which, combined with extremely low thermal conductivity values, results in a maximum ZT value of 0.7 at 423 K for x = 0.017 perpendicular to the pressing direction.
Effect of current density on distribution coefficient of solute at solid-liquid interface
常国威; 王自东; 吴春京; 胡汉起
2003-01-01
When current passes through the solid-liquid interface, the growth rate of crystal, solid-liquid interfaceenergy and radius of curvature at dendritic tip will change. Based on this fact, the theoretical relation between thedistribution of solute at solid-liquid interface and current density was established, and the effect of current on thedistribution coefficient of solute through effecting the rate of crystal growth, the solid-liquid interface energy and theradius of curvature at the dendritic tip was discussed. The results show that as the current density increases, thedistribution coefficient of solute tends to rise in a whole, and when the former is larger than about 400 A/cm2 , thelatter varies significantly.
Theoretical and Experimental Study of LiBH4-LiCl Solid Solution
Torben R. Jensen
2012-03-01
Full Text Available Anion substitution is at present one of the pathways to destabilize metal borohydrides for solid state hydrogen storage. In this work, a solid solution of LiBH4 and LiCl is studied by density functional theory (DFT calculations, thermodynamic modeling, X-ray diffraction, and infrared spectroscopy. It is shown that Cl substitution has minor effects on thermodynamic stability of either the orthorhombic or the hexagonal phase of LiBH4. The transformation into the orthorhombic phase in LiBH4 shortly after annealing with LiCl is for the first time followed by infrared measurements. Our findings are in a good agreement with an experimental study of the LiBH4-LiCl solid solution structure and dynamics. This demonstrates the validity of the adopted combined theoretical (DFT calculations and experimental (vibrational spectroscopy approach, to investigate the solid solution formation of complex hydrides.
Froggett, Stephan J; Clancy, Shaun F; Boverhof, Darrell R; Canady, Richard A
2014-04-07
Advances in adding nanomaterials to various matrices have occurred in tandem with the identification of potential hazards associated with exposure to pure forms of nanomaterials. We searched multiple research publication databases and found that, relative to data generated on potential nanomaterial hazards or exposures, very little attention has focused on understanding the potential and conditions for release of nanomaterials from nanocomposites. However, as a prerequisite to exposure studying release is necessary to inform risk assessments. We identified fifty-four studies that specifically investigated the release of nanomaterials, and review them in the following release scenario groupings: machining, weathering, washing, contact and incineration. While all of the identified studies provided useful information, only half were controlled experiments. Based on these data, the debris released from solid, non-food nanocomposites contains in varying frequencies, a mixture of four types of debris. Most frequently identified are (1) particles of matrix alone, and slightly less often, the (2) matrix particles exhibit the nanomaterial partially or fully embedded; far less frequently is (3) the added nanomaterial entirely dissociated from the matrix identified: and most rare are (4) dissolved ionic forms of the added nanomaterial. The occurrence of specific debris types appeared to be dependent on the specific release scenario and environment. These data highlight that release from nanocomposites can take multiple forms and that additional research and guidance would be beneficial, allowing for more consistent characterization of the release potential of nanomaterials. In addition, these data support calls for method validation and standardization, as well as understanding how laboratory release scenarios relate to real-world conditions. Importantly, as risk is considered to be a function of the inherent hazards of a substance and the actual potential for exposure, data
Haspot, Boris
2012-01-01
We show existence of global strong solutions with large initial data on the irrotational part for the shallow-water system in dimension $N\\geq 2$. We introduce a new notion of \\textit{quasi-solutions} when the initial velocity is assumed to be irrotational, these last one exhibit regularizing effects both on the velocity and in a very surprising way also on the density (indeed the density is a priori governed by an hyperbolic equation). We would like to point out that this smoothing effect is purely non linear and is absolutely crucial in order to deal with the pressure term as it provides new damping effects in high frequencies. In particular our result gives a first kind of answer to the problem of the existence of global weak solution for the shallow-water system. We conclude by giving new point wise decay estimates on the solution which improves the previous works \\cite{HZ1,HZ2}.
Existence of high-energy solutions for supercritical fractional Schrodinger equations in R^N
Lu Gan
2016-12-01
Full Text Available In this article, we study supercritical fractional Schr\\"odinger equations. Applying the finite-dimensional reduction method and the penalization method, we obtain the high-energy solutions for this equation.
Existence of infinitely many periodic solutions for second-order nonautonomous Hamiltonian systems
Wen Guan
2015-04-01
Full Text Available By using minimax methods and critical point theory, we obtain infinitely many periodic solutions for a second-order nonautonomous Hamiltonian systems, when the gradient of potential energy does not exceed linear growth.
Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries
2007-01-01
This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented.
Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries
Ling-hua KONG; Ming-xin WANG
2007-01-01
This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super- and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and v blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.
刘法贵; 孔德兴
2004-01-01
By means of maximum principle for nonlinear hyperbolic systems,the results given by HSIAO Ling and D.Serre was improved for Cauchy problem of compressible adiabatic flow through porous media,and a complete result on the global existence and the blow-up phenomena of classical solutions of these systems.These results show that the dissipation is strong enough to preserve the smoothness of 'small ' solution.
Bao-qiang Yan; Donal O'Regan; Ravi P.Agarwal
2008-01-01
This paper discusses both the nonexistence of positive solutions for second-order three-point bound ary value problems when the nonlinear term f(t,x,y) is superlinear in y at y=0 and the existence of multiple positive solutions for second-order three-point boundary value problems when the nonlinear term f(t,x,y) is superlinear in x at +∞.
Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces
Rigoberto Medina
2016-01-01
Full Text Available We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.
Existence of Generalized Homoclinic Solutions of Lotka-Volterra System under a Small Perturbation
Yuzhen Mi
2016-01-01
Full Text Available This paper investigates Lotka-Volterra system under a small perturbation vxx=-μ(1-a2u-vv+ϵf(ϵ,v,vx,u,ux, uxx=-(1-u-a1vu+ϵg(ϵ,v,vx,u,ux. By the Fourier series expansion technique method, the fixed point theorem, the perturbation theorem, and the reversibility, we prove that near μ=0 the system has a generalized homoclinic solution exponentially approaching a periodic solution.
Zhiren Jin
2008-02-01
Full Text Available We prove growth rate estimates and existence of solutions to Dirichlet problems for prescribed mean curvature equation on unbounded domains inside the complement of a cone or a parabola like region in $mathbb{R}^n$ ($ngeq 2$. The existence results are proved using a modified Perron's method by which a subsolution is a solution to the minimal surface equation, while the role played by a supersolution is replaced by estimates on the uniform $C^{0}$ bounds on the liftings of subfunctions on compact sets.
Holden, Helge; Karlsen, Kenneth H.; Risebro, Nils H.
2002-04-01
We prove uniqueness and existence of entropy solutions for the Cauchy problem of weakly coupled systems of nonlinear degenerate parabolic equations. The uniqueness proof is an adaption of Kruzkov's ''doubling of variables'' proof. We prove existence of an entropy solution by demonstrating that the Engquist-Osher finite difference scheme is convergent and that any limit function satisfies the entropy condition. The convergence proof is based on deriving a series of a priori estimates and using a general L{sup p} compactness criterion. We also present a numerical example motivated by biodegradation in porous media.
Marwan Amin Kutbi
2013-01-01
Full Text Available We introduce two new concepts of weakly relaxed η-α monotone mappings and weakly relaxed η-α semimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxed η-α monotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxed η-α semimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.
YUAN Hongjun; YAN Han
2009-01-01
The existence and uniqueness of the solutions for the Boltzmann equations with measures as initial value are still an open problem which is posed by P. L. Lions (2000). The aim of this paper is to discuss the Cauchy problem of the system of discrete Boltzmann equations of the form etf∫i+(∫mii)x=Qi(∫1,∫2,…,∫n), (mi1, i=1,…,n) with non-negative finite Radon measures as initial conditions. In particular, the existence and uniqueness of BV solutions for the above problem are obtained.
无
2001-01-01
This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =～φ (X), where ～φ: B → B and B is a Banach space consisted of all left-continuous. (Ft)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the existence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.
Zhensheng GAO; Zhong TAN; Guochun WU
2014-01-01
In this paper, we are concerned with the global existence and convergence rates of the smooth solutions for the compressible magnetohydrodynamic equations without heat conductivity, which is a hyperbolic-parabolic system. The global solutions are obtained by combining the local existence and a priori estimates if H3-norm of the initial perturbation around a constant states is small enough and its L1-norm is bounded. A priori decay-in-time estimates on the pressure, velocity and magnetic field are used to get the uniform bound of entropy. Moreover, the optimal convergence rates are also obtained.
Colloidal quantum dot solids for solution-processed solar cells
Yuan, Mingjian
2016-02-29
Solution-processed photovoltaic technologies represent a promising way to reduce the cost and increase the efficiency of solar energy harvesting. Among these, colloidal semiconductor quantum dot photovoltaics have the advantage of a spectrally tuneable infrared bandgap, which enables use in multi-junction cells, as well as the benefit of generating and harvesting multiple charge carrier pairs per absorbed photon. Here we review recent progress in colloidal quantum dot photovoltaics, focusing on three fronts. First, we examine strategies to manage the abundant surfaces of quantum dots, strategies that have led to progress in the removal of electronic trap states. Second, we consider new device architectures that have improved device performance to certified efficiencies of 10.6%. Third, we focus on progress in solution-phase chemical processing, such as spray-coating and centrifugal casting, which has led to the demonstration of manufacturing-ready process technologies.
Colloidal quantum dot solids for solution-processed solar cells
Yuan, Mingjian; Liu, Mengxia; Sargent, Edward H.
2016-03-01
Solution-processed photovoltaic technologies represent a promising way to reduce the cost and increase the efficiency of solar energy harvesting. Among these, colloidal semiconductor quantum dot photovoltaics have the advantage of a spectrally tuneable infrared bandgap, which enables use in multi-junction cells, as well as the benefit of generating and harvesting multiple charge carrier pairs per absorbed photon. Here we review recent progress in colloidal quantum dot photovoltaics, focusing on three fronts. First, we examine strategies to manage the abundant surfaces of quantum dots, strategies that have led to progress in the removal of electronic trap states. Second, we consider new device architectures that have improved device performance to certified efficiencies of 10.6%. Third, we focus on progress in solution-phase chemical processing, such as spray-coating and centrifugal casting, which has led to the demonstration of manufacturing-ready process technologies.
Benson, Steven [Univ. of North Dakota, Grand Forks, ND (United States); Srinivasachar, Srivats [Envergex LLC, Sturbridge, MA (United States); Laudal, Daniel [Univ. of North Dakota, Grand Forks, ND (United States); Browers, Bruce [Barr Engineering, Minneapolis, MN (United States)
2014-12-31
A novel hybrid solid sorbent technology for CO₂ capture and separation from coal combustion-derived flue gas was evaluated. The technology – Capture of CO₂ by Hybrid Sorption (CACHYS™) – is a solid sorbent technology based on the following ideas: 1) reduction of energy for sorbent regeneration, 2) utilization of novel process chemistry, 3) contactor conditions that minimize sorbent-CO₂ heat of reaction and promote fast CO₂ capture, and 4) low-cost method of heat management. This report provides key information developed during the course of the project that includes sorbent performance, energy for sorbent regeneration, physical properties of the sorbent, the integration of process components, sizing of equipment, and overall capital and operational cost of the integrated CACHYS™ system. Seven sorbent formulations were prepared and evaluated at the lab-scale for energy requirements and CO₂ capture performance. Sorbent heat of regeneration ranged from 30-80 kJ/mol CO₂ and was found to be dependent on process conditions. Two sorbent formulations (designated HCK-4 & HCK-7) were down-selected for additional fixed-bed testing. Additional testing involved subjecting the sorbents to 100 continuous cycles in the fixed-bed reactor to determine performance as a function of time. The working capacity achieved for HCK-4 sorbent ranged from 5.5-8.0 g CO₂/100 g sorbent, while the HCK-7 typically ranged from 8.0-10.0 g CO₂/100 g sorbent. Overall, there was no deterioration in capacity with continuous cycling for either sorbent. The CACHYS™ bench-scale testing system designed and fabricated under this award consists of a dual circulating fluidized-bed adsorber and a moving-bed regenerator. The system takes a flue gas slipstream from the University of North Dakota’s coal-fired steam plant. Prior to being sent to the adsorber, the flue gas is scrubbed to remove SO₂ and particulate. During parametric testing of the adsorber, CO₂ capture achieved using
Benson, Steven [Univ. of North Dakota, Grand Forks, ND (United States); Srinivasachar, Srivats [Envergex LLC, Sturbridge, MA (United States); Laudal, Daniel [Univ. of North Dakota, Grand Forks, ND (United States); Browers, Bruce [Barr Engineering, Minneapolis, MN (United States)
2014-12-31
A novel hybrid solid sorbent technology for CO₂ capture and separation from coal combustion-derived flue gas was evaluated. The technology – Capture of CO₂ by Hybrid Sorption (CACHYS™) – is a solid sorbent technology based on the following ideas: 1) reduction of energy for sorbent regeneration, 2) utilization of novel process chemistry, 3) contactor conditions that minimize sorbent-CO₂ heat of reaction and promote fast CO₂ capture, and 4) low-cost method of heat management. This report provides key information developed during the course of the project that includes sorbent performance, energy for sorbent regeneration, physical properties of the sorbent, the integration of process components, sizing of equipment, and overall capital and operational cost of the integrated CACHYS™ system. Seven sorbent formulations were prepared and evaluated at the lab-scale for energy requirements and CO₂ capture performance. Sorbent heat of regeneration ranged from 30-80 kJ/mol CO₂ and was found to be dependent on process conditions. Two sorbent formulations (designated HCK-4 & HCK-7) were down-selected for additional fixed-bed testing. Additional testing involved subjecting the sorbents to 100 continuous cycles in the fixed-bed reactor to determine performance as a function of time. The working capacity achieved for HCK-4 sorbent ranged from 5.5-8.0 g CO₂/100 g sorbent, while the HCK-7 typically ranged from 8.0-10.0 g CO₂/100 g sorbent. Overall, there was no deterioration in capacity with continuous cycling for either sorbent. The CACHYS™ bench-scale testing system designed and fabricated under this award consists of a dual circulating fluidized-bed adsorber and a moving-bed regenerator. The system takes a flue gas slipstream from the University of North Dakota’s coal-fired steam plant. Prior to being sent to the adsorber, the flue gas is scrubbed to remove SO₂ and particulate. During parametric testing of the adsorber, CO₂ capture achieved using
Wu, Sainan; Shi, Junping; Wu, Boying
2016-04-01
This paper proves the global existence and boundedness of solutions to a general reaction-diffusion predator-prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence of the system under some additional conditions. Applications to models from ecology and chemotaxis are discussed.
Liu, Jianzhou; Zhang, Juan
2011-08-01
In this article, applying the properties of M-matrix and non-negative matrix, utilising eigenvalue inequalities of matrix's sum and product, we firstly develop new upper and lower matrix bounds of the solution for discrete coupled algebraic Riccati equation (DCARE). Secondly, we discuss the solution existence uniqueness condition of the DCARE using the developed upper and lower matrix bounds and a fixed point theorem. Thirdly, a new fixed iterative algorithm of the solution for the DCARE is shown. Finally, the corresponding numerical examples are given to illustrate the effectiveness of the developed results.
Xiu Hui YANG; Fu Cai LI; Chun Hong XIE
2005-01-01
In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions:({ut-α(u,v)△u=g(u,v),vt-b(u,v)△v=h(u,v),(e)u/(e)(g)=d(u,v),(e)u/(e)(g)=f(u,v),)Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques.
Existence and Uniqueness of Solution of Schrodinger equation in extended Colombeau algebra
Fariba Fattahi
2014-09-01
Full Text Available In this paper, we establish the existence and uniquenessresult of the linear Schr¨odinger equation with Marchaudfractional derivative in Colombeau generalized algebra.The purpose of introducing Marchaud fractional derivativeis regularizing it in Colombeau sense.
Chen Yi
2011-01-01
Full Text Available We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.
EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR GRADIENT SYSTEMS IN FINITE DIMENSIONAL SPACES
Sahbi BOUSSANDEL
2016-01-01
This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
A Note on Existence and Stability of Solutions for Semilinear Dirichlet Problems
Marek Galewski
2011-05-01
We provide existence and stability results for a fourth-order semilinear Dirichlet problem in the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. We use a dual variational method.
Charve, Frédéric
2011-01-01
In the first part of this paper, we prove the existence of global strong solution for Korteweg system in one dimension. In the second part, motivated by the processes of vanishing capillarity-viscosity limit in order to select the physically relevant solutions for a hyperbolic system, we show that the global strong solution of the Korteweg system converges in the case of a $\\gamma$ law for the pressure ($P(\\rho)=a\\rho^{\\gamma}$, $\\gamma>1$) to entropic solution of the compressible Euler equations. In particular it justifies that the Korteweg system is suitable for selecting the physical solutions in the case where the Euler system is strictly hyperbolic. The problem remains open for a Van der Waals pressure because in this case the system is not strictly hyperbolic and in particular the classical theory of Lax and Glimm (see \\cite{Lax,G}) can not be used.
Chen, Huyuan
2017-02-06
The purpose of this paper is to study the weak solutions of the fractional elliptic problem(Formula presented.) where (Formula presented.), (Formula presented.) or (Formula presented.), (Formula presented.) with (Formula presented.) is the fractional Laplacian defined in the principle value sense, (Formula presented.) is a bounded (Formula presented.) open set in (Formula presented.) with (Formula presented.), (Formula presented.) is a bounded Radon measure supported in (Formula presented.) and (Formula presented.) is defined in the distribution sense, i.e.(Formula presented.) here (Formula presented.) denotes the unit inward normal vector at (Formula presented.). In this paper, we prove that (0.1) with (Formula presented.) admits a unique weak solution when g is a continuous nondecreasing function satisfying(Formula presented.) Our interest then is to analyse the properties of weak solution when (Formula presented.) with (Formula presented.), including the asymptotic behaviour near (Formula presented.) and the limit of weak solutions as (Formula presented.). Furthermore, we show the optimality of the critical value (Formula presented.) in a certain sense, by proving the non-existence of weak solutions when (Formula presented.). The final part of this article is devoted to the study of existence for positive weak solutions to (0.1) when (Formula presented.) and (Formula presented.) is a bounded nonnegative Radon measure supported in (Formula presented.). We employ the Schauder’s fixed point theorem to obtain positive solution under the hypothesis that g is a continuous function satisfying(Formula presented.)-pagination
Xia, Chuan
2017-01-06
An effective multifaceted strategy is demonstrated to increase active edge site concentration in NiCoSe solid solutions prepared by in situ selenization process of nickel cobalt precursor. The simultaneous control of surface, phase, and morphology result in as-prepared ternary solid solution with extremely high electrochemically active surface area (C = 197 mF cm), suggesting significant exposure of active sites in this ternary compound. Coupled with metallic-like electrical conductivity and lower free energy for atomic hydrogen adsorption in NiCoSe, identified by temperature-dependent conductivities and density functional theory calculations, the authors have achieved unprecedented fast hydrogen evolution kinetics, approaching that of Pt. Specifically, the NiCoSe solid solutions show a low overpotential of 65 mV at -10 mV cm, with onset potential of mere 18 mV, an impressive small Tafel slope of 35 mV dec, and a large exchange current density of 184 μA cm in acidic electrolyte. Further, it is shown that the as-prepared NiCoSe solid solution not only works very well in acidic electrolyte but also delivers exceptional hydrogen evolution reaction (HER) performance in alkaline media. The outstanding HER performance makes this solid solution a promising candidate for mass hydrogen production.
Organic solid solution composed of two structurally similar porphyrins for organic solar cells.
Zhen, Yonggang; Tanaka, Hideyuki; Harano, Koji; Okada, Satoshi; Matsuo, Yutaka; Nakamura, Eiichi
2015-02-18
A solid solution of a 75:25 mixture of tetrabenzoporphyrin (BP) and dichloroacenaphtho[q]tribenzo[b,g,l]porphyrin (CABP) forms when they are generated in a matrix of (dimethyl(o-anisyl)silylmethyl)(dimethylphenylsilylmethyl)[60]fullerene. This solid solution provides structural and optoelectronic properties entirely different from those of either pristine compounds or a mixture at other blending ratios. The use of this BP:CABP solid solution for organic solar cell (OSC) devices resulted in a power conversion efficiency (PCE) value higher by 16 and 300% than the PCE values obtained for the devices using the single donor BP and CABP, respectively, in a planar heterojunction architecture. This increase originates largely from the increase in short circuit current density, and hence by enhanced charge carrier separation at the donor/acceptor interface, which was probably caused by suitable energy level for the solid solution state, where electronic coupling between the two porphyrins occurred. The results suggest that physical and chemical modulation in solid solution is beneficial as an operationally simple method to enhance OSC performance.
Corridor of existence of thermodynamically consistent solution of the Ornstein-Zernike equation.
Vorob'ev, V S; Martynov, G A
2007-07-14
We obtain the exact equation for a correction to the Ornstein-Zernike (OZ) equation based on the assumption of the uniqueness of thermodynamical functions. We show that this equation is reduced to a differential equation with one arbitrary parameter for the hard sphere model. The compressibility factor within narrow limits of this parameter variation can either coincide with one of the formulas obtained on the basis of analytical solutions of the OZ equation or assume all intermediate values lying in a corridor between these solutions. In particular, we find the value of this parameter when the thermodynamically consistent compressibility factor corresponds to the Carnahan-Stirling formula.
Z. Denton
2017-01-01
Full Text Available In this work we investigate integro-differential initial value problems with Riemann Liouville fractional derivatives where the forcing function is a sum of an increasing function and a decreasing function. We will apply the method of lower and upper solutions and develop two monotone iterative techniques by constructing two sequences that converge uniformly and monotonically to minimal and maximal solutions. In the first theorem we will construct two natural sequences and in the second theorem we will construct two intertwined sequences. Finally, we illustrate our results with an example.
EXISTENCE AND UNIQUENESS OF RADIAL SOLUTIONS OF QUASILINEAR EQU ATIONS IN A BALL
WeiGongming; ChenZuchi
2002-01-01
We consider the boundary value problem for the quasilinear equation div(A(|Du|)Du)+f(u)=0,u>0,x∈BR(0),u|δBR(0)=0,where A and f are continuous functions in (0,∞) and f is positive in (0,1),f(1)=0. We prove that (1) if f is strictly decreasing,the problem has a unique classical radial solution for any real number R>0;(2)if f is not monotonous,the problem has at least one classical solution for some R>0 large enough.
Janvier, C.
1998-04-02
The oxides-gaseous dioxygen equilibria and the textural thermal stability of six zirconium-cerin solutions Ce{sub 1-x}Zr{sub x}O{sub 2} (0
无
2008-01-01
In this paper, by the theory of Fourier series, Bernoulli number theory and continu-ation theorem of coincidence degree theory, we study a kind of higher order functional differential equation with two deviating arguments. Some new results on the existence of periodic solutions are obtained.
Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt=F(x,t,u,ux
L. Byszewski
1990-01-01
Full Text Available The aim of the paper is to give two theorems about existence and uniqueness of continuous solutions for hyperbolic nonlinear differential problems with nonlocal conditions in bounded and unbounded domains. The results obtained in this paper can be applied in the theory of elasticity with better effect than analogous known results with classical initial conditions.
秦玉明; 李海燕
2014-01-01
This article is devoted to the study of global existence and exponential stability of solutions to an initial-boundary value problem of the quasilinear thermo-diffusion equations with second sound by means of multiplicative techniques and energy method provided that the initial data are close to the equilibrium and the relaxation kernel is strongly positive definite and decays exponentially.
Bogdan, V. M.
1981-01-01
A proof is given of the existence and uniqueness of the solution to the automatic control problem with a nonlinear state equation of the form y' = f(t,y,u) and nonlinear operator controls u = U(y) acting onto the state function y which satisfies the initial condition y(t) = x(t) for t or = 0.
Reza Saadati
2016-08-01
Full Text Available Abstract In this paper, our aim is to address the existence and uniqueness of solutions for a class of integral equations in IFMT-space. Therefore, we introduce the concept of IFMT-spaces and prove a common fixed point theorem in a complete IFMT-space; next we study an application.
Allaberen Ashyralyev
2012-01-01
Full Text Available In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.
Qing-liu Yao
2003-01-01
The existence of n positive solutions for a class of third-order three-point boundary value problems is investigated, where n is an arbitrary natural number. The main tool is Krasnosel'skii fixed point theorem on the cone.
Lv Xuezhe
2010-01-01
Full Text Available Abstract The existence and uniqueness of positive solution is obtained for the singular second-order -point boundary value problem for , , , where , , are constants, and can have singularities for and/or and for . The main tool is the perturbation technique and Schauder fixed point theorem.
LiBiwen; ZengXianwu
2003-01-01
By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two-patches competition system with diffusion and time delay and functional response ｛x′(t)=x1(t)[a1(t)-b1(t)x1(t)-c1(t)y(t)/[1+m(t)x1(t)
Yongkun Li
2010-01-01
Full Text Available By using Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, we establish the existence of at least 2n positive periodic solutions for n-species nonautonomous Lotka-Volterra type food chains with harvesting terms. An example is given to illustrate the effectiveness of our results.
无
2008-01-01
By using Gaines and Mawhin's continuation theorem of coincidence degree theory and constructing Lyapunov functionals,a set of easily verifiable sufficient conditions are derived for the existence and global attractivity of a positive periodic solution to a predator-prey system with delays and impulses.
Global Existence of Classical Solutions to a Three-Species Predator-Prey Model with Two Prey-Taxes
Chenglin Li
2012-01-01
Full Text Available We are concerned with three-species predator-prey model including two prey-taxes and Holling type II functional response under no flux boundary condition. By applying the contraction mapping principle, the parabolic Schauder estimates, and parabolic Lp estimates, we prove that there exists a unique global classical solution of this system.
Li, Meili; Han, Maoan; Kou, Chunhai
2008-10-01
In this paper, the existence of positive periodic solutions of a class of periodic -species Gilpin-Ayala impulsive competition systems is studied. By using the continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions is obtained. Our results are general enough to include some known results in this area.
Jing Zhao
2013-01-01
Full Text Available We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using the G2 algorithm.
Qin, Yuming; Zhang, Jianlin
2016-12-01
In this paper, we establish the global existence, uniqueness and asymptotic behavior of cylindrically symmetric solutions for the 3D infrarelativistic model with radiation in H^i× (H^i)^3× H^i× H^{i+1}(i=1,2,4) . The key point is that the smallness of initial data is not needed.
Wen-Zhen Gong
2012-01-01
Full Text Available By using minimax methods in critical point theory, a new existence theorem of infinitely many periodic solutions is obtained for a class of second-order p-Laplacian systems with impulsive effects. Our result generalizes many known works in the literature.
Che, Jiahang; Chen, Li; Duan, Ben; Luo, Zhen
2016-12-01
In this paper, motivated by the chemotaxis-Navier-Stokes system arising from mathematical biology [43], a modified shallow water type chemotactic model is derived. For large initial data allowing vacuum, the local existence of strong solutions together with the blow-up criterion is established.
Tomasz S. Zabawa
2005-01-01
Full Text Available The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem. The result is based on Chaplygin's method of lower and upper functions.
无
2009-01-01
In this paper, we consider a two-point boundary value problem for a system of second order ordinary differential equations. Under some conditions, we show the existence of positive solution to the system of second order ordinary differential equa-tions.
Xing-qiu Zhang; Jing-xian Sun
2009-01-01
By constructing a special cone and using cone compression and expansion fixed point theorem,this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation.As applications of the main results,two examples are given at the end of this paper.
S. Marshal Anthoni
2004-01-01
Full Text Available We study the existence of mild solutions of the nonlinear second-order neutral functional differential and integrodifferential inclusions with nonlocal conditions in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of bounded linear operators and a fixed point theorem for condensing maps due to Martelli.
AKDIM Y; BENNOUNA J; MEKKOUR M; REDWANE H
2013-01-01
We study the existence of renormalized solutions for a class of nonlinear degenerated parabolic problem.The Carathéodory function satisfying the coercivity condition,the growth condition and only the large monotonicity.The data belongs to L1(Q).
ANALYSIS AND PERFORMANCE MEASUREMENT OF EXISTING SOLUTION METHODS OF QUADRATIC ASSIGNMENT PROBLEM
Morteza KARAMI
2014-01-01
Full Text Available Quadratic Assignment Problem (QAP is known as one of the most difficult combinatorial optimization problems that is classified in the category of NP-hard problems. Quadratic Assignment Problem Library (QAPLIB is a full database of QAPs which contains several problems from different authors and different sizes. Many exact and meta-heuristic solution methods have been introduced to solve QAP. In this study we focus on previously introduced solution methods of QAP e.g. Branch and Bound (B&B, Simulated Annealing (SA Algorithm, Greedy Randomized Adaptive Search Procedure (GRASP for dense and sparse QAPs. The codes of FORTRAN for these methods were downloaded from QAPLIB. All problems of QAPLIB were solved by the abovementioned methods. Several results were obtained from the computational experiments part. The Results show that the Branch and Bound method is able to introduce a feasible solution for all problems while Simulated Annealing Algorithm and GRASP methods are not able to find any solution for some problems. On the other hand, Simulated Annealing and GRASP methods have shorter run time comparing to the Branch and Bound method. In addition, the performance of the methods on the objective function value is discussed.