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Full-Text Articles in Mathematics
[See Pdf For Notation]-Reularity For The Solution Of Strongly Nonlinear Eigenvalue Problems On Orlicz-Sobolev Spaces, Pierre A. Vuillermot
[See Pdf For Notation]-Reularity For The Solution Of Strongly Nonlinear Eigenvalue Problems On Orlicz-Sobolev Spaces, Pierre A. Vuillermot
Mathematics Technical Papers - Archive
We present a new method to prove the [see pdf for notation]-regularity of the eigenfunctions for Dirichlet problems with strictly convex Young functionnonlinearities in their principal part. The basic idea is threefold: we first invoke the topological methods of [12] to infer the existence of a countable infinity of [see pdf for notation]-eigensolutions; we then use Schauder's inversion technique to associate with each one of these eigensolutions a unique [see pdf for notation]-solution of an auxiliary Dirichlet problem; we finally prove the [see pdf for notation]-regularity of the original elgensolutions from the [see pdf for notation]-regularity of the auxiliary solutions, …
Particle Simulation Of Compression Waves, Donald Greenspan
Particle Simulation Of Compression Waves, Donald Greenspan
Mathematics Technical Papers - Archive
Compression waves are studied using a quasi-molecular, particle approach. Explosive type disturbances are simulated to generate such waves, which propagate by the interaction of each particle with its immediate neighbors. Obstacles to wave motions are studied by the introduction of variable densities. Computer examples are described and discussed.
Computer Studies In Particle Modeling Of Fluid Phenomena, Donald Greenspan
Computer Studies In Particle Modeling Of Fluid Phenomena, Donald Greenspan
Mathematics Technical Papers - Archive
A new, numerical approach is developed for modeling fluid phenomena. Unlike the continuum and statistical mechanics approaches, it uses relatively small sets of quasi-molecular particles which interact in accordance with classical, molecular-type formulas. Computer examples are described and discussed, as is the potential for modeling turbulent behavior.
On A Class Of Strongly Nonlinear Dirichlet Boundary-Value Problems: Beyond Pohozaev's Results, Pierre A. Vuillermot
On A Class Of Strongly Nonlinear Dirichlet Boundary-Value Problems: Beyond Pohozaev's Results, Pierre A. Vuillermot
Mathematics Technical Papers - Archive
Let [see pdf for notation] be an open bounded domain with closure [see pdf for notation] and smooth boundary [see pdf for notation]. Consider the class of nonlinear boundary-value problems defined by [see pdf for notation] with [see pdf for notation] regular enough,[see pdf for notation] and where [see pdf for notation] denotes Laplacian. If n = 2, it is known that the boundary-value problem (1.1) possesses nontrivial, classical eigensolutions (with appropriate eigenvalues ^) even if ø grows exponentially fasts if n ≥ 3, it is also known that problem (1.1) has, with ^ starshaped, no nontrivial, classical solutions as …
A Class Of Elliptic Partial Differential Equations With Exponential Nonlineraities, Pierre A. Vuillermot
A Class Of Elliptic Partial Differential Equations With Exponential Nonlineraities, Pierre A. Vuillermot
Mathematics Technical Papers - Archive
This is the second of a series of papers devoted to systems of ordinary and partial differential equations with exponential nonlinearities [20], in which we prove the existence of at least a countable infinity of one- parameter families of nontrivial, Hölder continuous solutions for a class of second-order, strongly nonlinear Dirichlet boundary-value problems in two and more dimensions. Let Y be a C(2)-Young function, namely a twice continuously differentiable, even convex lR—valued function on IR such that[see pdf for notation] and[see pdf for notation]. By C(2)-function, we shall mean a function which is twice continuously differentiable everywhere except possibly at …
Particle Modeling Of Unstable Mode Configurations And Elastic Bending Of Deformable Shells, Vincenzo Casulli, Donald Greenspan
Particle Modeling Of Unstable Mode Configurations And Elastic Bending Of Deformable Shells, Vincenzo Casulli, Donald Greenspan
Mathematics Technical Papers - Archive
A new particle-type of modeling is developed for the simulation of phenomena related to the bending of elastic shells. Application is made to the determination of unstable equilibrium modes and to the simulation of snap-through inversion. Computer examples are described and discussed.
A Mathematical Curiosity In Estimating The Radius Of The First Ring Electrons Of An Arbitary Atom, Donald Greenspan
A Mathematical Curiosity In Estimating The Radius Of The First Ring Electrons Of An Arbitary Atom, Donald Greenspan
Mathematics Technical Papers - Archive
In this note, we explore an elementary method for approximating the radii and speeds of first ring electrons in atoms. The approach uses only a single algebraic equation with parameters. Any particular atom under study defines all the parameters. A simple hand calculator technique always applies for solving any resulting equation. Results are given through calcium and, to three decimal places, are shown, unexpectedly, to be essentially identical to available quantum mechanics calculations.
The Role Of Nonreal Eigenvalues In The Identification Of Cycles In A Compartmental System, Jerome Eisenfeld, S. M. Grundy, W. F. Beltz
The Role Of Nonreal Eigenvalues In The Identification Of Cycles In A Compartmental System, Jerome Eisenfeld, S. M. Grundy, W. F. Beltz
Mathematics Technical Papers - Archive
The paper concerns the relationship between the cycles in the graph of a compartmental system and the modes of the impulse response function associated with an input-output experiment. Suppose that there is at least one oscillatory mode, [see pdf for notation]. Let [see pdf for notation] be the slowest mode. The main result is that the system contains a cycle of length three or longer and that the length of the longest cycle is at least [see pdf for notation]. The paper also deals with the problem of estimating cycle length from discrete data.
Volterra Integral Equations In Abstract Cones And Monotone Iterative Technique, G. R. Shendge
Volterra Integral Equations In Abstract Cones And Monotone Iterative Technique, G. R. Shendge
Mathematics Technical Papers - Archive
The objective of this paper is to develop monotone technique for obtaining extremal solutions of Volterra integral equations in abstract Banach spaces via coupled lower and upper quasi-solutions. To generate the iterates, different schemes are given which would be of special interest from computational point of view.
Monotone Method For Boundary Value Problems Describing Periodic Transport Processes, G. R. Shendge
Monotone Method For Boundary Value Problems Describing Periodic Transport Processes, G. R. Shendge
Mathematics Technical Papers - Archive
One of the powerful methods of proving the existence of extremal solutions of initial and boundary value problems is the monotone iterative technique [1-4,6,7]. This has recently been applied [5] to a rather special type of boundary value problem [see pdf for notation] because, particular cases of (*) represent equations arising in the transport process of different types of particles moving in opposite directions, which are subjected to certain fluxes [8]. However (*) does not include situations in which the initial and final fluxes in a certain direction coincide. To cover this situation one needs to study a typical periodic …
Conserving Numerical Methods For X = F(X), Donald Greenspan
Conserving Numerical Methods For X = F(X), Donald Greenspan
Mathematics Technical Papers - Archive
Physics is characterized by conservation laws and by symmetry [1]. Unfortunately, the application of numerical methodology in approximating solutions of initial value problems usually does not preserve either of these invariants. In this sense, the use of a computer destroys the physics of a dynamical model. We will show here how to conserve total energy when solving the nonlinear initial value problem [see pdf for notation] on a computer. Moreover, the energy conserved will be exactly that of (1.1), not a new "energy" which is defined by the numerical method (see, e.g., Langdon [5]). Two distinctly different methods will be …
Extension Of Compartmental Parameters To Blocks Of Compartments With Application To Lipoprotein Kinetics, S. M. Grundy, Jerome Eisenfeld
Extension Of Compartmental Parameters To Blocks Of Compartments With Application To Lipoprotein Kinetics, S. M. Grundy, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Suppose that the compartments of a compartmental model are separated into blocks (sets of compartments). In general, the blocks can not be regarded as compartments but it may be possible to construct a "condensation model," the compartments of which correspond to the blocks, in such a fashion so as to retain certain salient properties of the blocks. Condensation is a way of formally summarizing a large model by presenting a smaller one in order to emphasize certain characteristics.of the larger model. Suppose that the parameters to be retained are the mean residence times through the blocks. The paper deals with …
Quasi-Molecular, Particle Modeling Of Crack Generation And Fracture, Donald Greenspan
Quasi-Molecular, Particle Modeling Of Crack Generation And Fracture, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper a new, particle-type approach is developed for the simulation of crack generation and fracture. Rectangular plates are modeled as particle aggregates and then stressed by using molecular type force formulas. Computer examples which include wedges and holes are described and discussed.
Computer-Oriented, N-Body Modelling Of Minimal Surfaces, Donald Greenspan
Computer-Oriented, N-Body Modelling Of Minimal Surfaces, Donald Greenspan
Mathematics Technical Papers - Archive
In this paper a new approach to the modeling of minimal surfaces is described and applied. Rather than use a continuous model, we develop a discrete n-body model with basic tensile interactions derived from classical molecular force formulas. Computer results area described and discussed.
Comparison Results For Parabolic Differential Equations At Resonance, A. S. Vatsala, G. R. Shendge
Comparison Results For Parabolic Differential Equations At Resonance, A. S. Vatsala, G. R. Shendge
Mathematics Technical Papers - Archive
It is very well known that comparison principles for initial and boundary value problems for nonresonance cases have been very much used in the existence of solutions and the development of the monotone method [1,2,3,4,5,9]. These comparison techniques do not cover the resonance cases. Hence it is of practical interest to look at such results for resonance cases. With this view, different comparison results were recently developed for first and second order periodic boundary value problems [10]. Some special cases of these have been used in [6,7] and in developing the monotone method for first order periodic systems in [11]. …
Computer Simulation Of A Dynamical Model Of The Water Molecule, Donald Greenspan
Computer Simulation Of A Dynamical Model Of The Water Molecule, Donald Greenspan
Mathematics Technical Papers - Archive
A new computer-orlented theory for molecular dynamics is applied to modeling the water molecule. The dynamical equations are derived from molecular stability properties and from aspects of modern particle theory, especially as it relates to the structure of the electron. Computer studies are described and discussed.
Monotone Method For Second Order Periodic Boundary Value Problems, S. Leela
Monotone Method For Second Order Periodic Boundary Value Problems, S. Leela
Mathematics Technical Papers - Archive
In recent years, there has been an extensive study of the existence of periodic solutions [1,8-11,14,15]. In, [8,11], the existence of solutions of first and second order PBVP (periodic boundary value problems) has been obtained by a novel approach of combining the classical method of lower and upper solutions and the method of alternative problems (Lyapunov-Schmidt method), which provide conditions that are easily verifiable and which covers previous known results of other authors. As a constructive method for obtaining extremal solutions of initial and boundary value problems, the monotone iterative procedure has been employed by several researchers [5-7,11-13,15]. The objective …
Discrete Modeling Of Minimal Surfaces, C. Coppin, Donald Greenspan
Discrete Modeling Of Minimal Surfaces, C. Coppin, Donald Greenspan
Mathematics Technical Papers - Archive
A new computer approach to the modeling of minimal surfaces is described and implemented. Quasi-molecular particles and forces are used to simulate actual molecular structure and forces. Detailed formulas and computer techniques are given. As an example, the approximation of the unique minimal surface through a skew quadrilateral is constructed and displayed.
Remarks On First And Second Order Periodic Boundary Value Problems, V. Lakshmikantham
Remarks On First And Second Order Periodic Boundary Value Problems, V. Lakshmikantham
Mathematics Technical Papers - Archive
We consider the first and second order periodic boundary value problems (PBVP for brevity)[see pdf for notation] and [see pdf for notation]and obtain the existence of extremal solutions as limits of monotone iterates. In [2] and [3], the monotone method was employed for the problems (1.1) and (1.2) when the corresponding lower and upper solutions a(t),B(t) satisfy [see pdf for notation] in addition to other conditions. Furthermore, when f is increasing, it is shown [2,3] that the conditions (1.3) and (1.4) are tantamount to assuming the existence of a periodic solution. Accordingly, the problem of proving the existence of periodic …
Structural Identification Of Large Systems By Reduction To Subsystems: Vldl Triglycerides, S. M. Grundy, Jerome Eisenfeld
Structural Identification Of Large Systems By Reduction To Subsystems: Vldl Triglycerides, S. M. Grundy, Jerome Eisenfeld
Mathematics Technical Papers - Archive
Experiments are performed for identification purposes, i.e. to identify the values of unknown paprameters from data. In the event that one or more parameters can not be identified, the cause could be the result of a variety of problems: insuffcient or infrequent sampling, random or nonrandom disturbances, numerical ill-conditioning and etc. The input-output configuration may also be the cause of non-identifiability. In other words, evenif the sampling and numerical procedure could be carried out under the most ideal conditions, certain parameters may not be identifiable because these parameters are not uniquely contained in the transfer function, in which case these …
Existence Of Periodic Solutions Of Semilinear Parabolic Equations And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Existence Of Periodic Solutions Of Semilinear Parabolic Equations And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Mathematics Technical Papers - Archive
The existence of periodic solutions of semilinear parabolic equations has been investigated by several authors [1-10,15-18] by different methods such as the method of Poincare operator and the theory of monotone operators. In a recent paper [1] Amann also obtains multiplicity results. Recently, an attempt was made successfully in [11,12,16] to combine the two basic techniques, namely the method of upper and lower solutions and the method of Lyapunov-Schmidt to investigate existence of periodic solutions of first and second order equations. In this paper we continue this fruitful approach to study existence of periodic solutions of semilinear parabolic equations with …
Problems At Resonance For First And Second Order Differential Equations Via Lyapunov-Like Functions, J. J. Nieto
Problems At Resonance For First And Second Order Differential Equations Via Lyapunov-Like Functions, J. J. Nieto
Mathematics Technical Papers - Archive
Recently [7,8,10] an attempt is made successfully to combine the two basic techniques namely, Lyapunov-Schmidt method and the method of upper and lower solutions, to investigate the existence of periodic solutions of differential equations. When we wish to extend such results for systems of differential equations there are two possibilities to follow. One is to generalize the method of upper and lower solutions using a suitable cone, and the other is to utilize the concept of tyapunov-like functions and the theory of differential inequalities. In the paper, we shall discuss the existence of problems at resonance for first and second …
Monotone Iterative Technique For Delay Differantial Equations In Abstract Cones, Sen-Wo Du
Monotone Iterative Technique For Delay Differantial Equations In Abstract Cones, Sen-Wo Du
Mathematics Technical Papers - Archive
Monotone iterative technique is developed for delay differential equations in a Banach space by utilizing the method of upper and lower solutions.
An Algorithm For Finding The Generalized Nucleolus Of A Finite Set And The Multiobjective Discrete Programming Problems, Irinel C. Dragan
An Algorithm For Finding The Generalized Nucleolus Of A Finite Set And The Multiobjective Discrete Programming Problems, Irinel C. Dragan
Mathematics Technical Papers - Archive
No abstract provided.
General Uniqueness Criteria For Ordinary Differential Equations, V. Lakshmikantham, Mansour Samimi
General Uniqueness Criteria For Ordinary Differential Equations, V. Lakshmikantham, Mansour Samimi
Mathematics Technical Papers - Archive
This paper generalizes various uniqueness results and offers very general uniqueness criteria which include different types of results considered so far.
A New Approach To The Stability Theory Of Functional Differential Systems, G. R. Shendge
A New Approach To The Stability Theory Of Functional Differential Systems, G. R. Shendge
Mathematics Technical Papers - Archive
In the study of stability theory for delay differential equations using Lyapunov functions and the theory of differential inequalities, it becomes necessary to choose an appropriate minimal class of functions relative to which [see pdf for notation] is estimated [3]. This approach has recently been recognized [3] as a very natural method in the study of the qualitative behavior of delay differential equations.
Bifurcation And Total Stability, V. Moauro, M. L. Bertotti
Bifurcation And Total Stability, V. Moauro, M. L. Bertotti
Mathematics Technical Papers - Archive
In this paper we are concerned with the problem of bifurcation of invariant sets from an invariant set with respect to a family of flows. In particular, we will suppose that such flows are defined by a one-parameter family of ordinary differential equations: [see pdf for notation] where [see pdf for notation], f is locally Lipschitzian with respect to x, f(µ,0) = 0. As is well known, bifurcation phenomenon is often associated with a drastic change of suitable stability properties. For example, let suppose that the origin 0 of Rn be, with respect to (1), asymptotically stable for µ = …
Existence Of Periodic Solutions Of Nonlinear Boundary Value Problems And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Existence Of Periodic Solutions Of Nonlinear Boundary Value Problems And The Method Of Upper And Lower Solutions, V. Lakshmikantham, R. Kannan
Mathematics Technical Papers - Archive
We study the existence of periodic solutions of second order nonlinear differential equations by combining the method of upper and lower solutions and the method of Alternative problems. Besides including previous results of other authors, we obtain criteria which are easily verifiable. These criteria are in a form that they can be adapted for partial differential equations of parabolic and elliptic type.
Nonuniqueness Criteria For Ordinary Differential Equations, Mansour Samimi
Nonuniqueness Criteria For Ordinary Differential Equations, Mansour Samimi
Mathematics Technical Papers - Archive
We consider an initial value problem (1.1) [see pdf for notation] where [see pdf for notation]. Several uniqueness results weaker than a Lipschitz condition are known, see [1,4]. However, results concerning with nonuniqueness criteria are rare. For the case n = 1, a nonuniqueness result was given in [5,6], see also [4]. Very recently the general case was also investigated in [3]. In this paper, we consider nonuniqueness problem from a very general point of view. Our first nonuniqueness result deals with the scalar case which extends the results of [5,6]. It also shows that when the conditions of general …
Existence And Monotone Method For Periodic Solutions Of First Order Differential Equations, S. Leela, V. Lakshmikantham
Existence And Monotone Method For Periodic Solutions Of First Order Differential Equations, S. Leela, V. Lakshmikantham
Mathematics Technical Papers - Archive
An attempt was made recently in [3] to combine fruitfully the two basic techniques, namely the method of upper and lower solutions and the Lyapunov-Schmitt method to investigate the existence of periodic solutions of second order nonlinear boundary value problems. in this paper, we utilize this fruitful approach to study existence of periodic solutions of first order nonlinear differential equations. We also develope monotone iterative technique for obtaining multiple periodic solutions which are obtained as limits of monotone sequences. Since each member of these sequences is a periodic solution of a linear differential equation of first order which can explicitly …