Search results for "integral"
showing 10 items of 902 documents
Fuzzy Stochastic Integral Equations Driven by Martingales
2011
Exploiting the properties of set-valued stochastic trajectory integrals we consider a notion of fuzzy stochastic Lebesgue–Stieltjes trajectory integral and a notion of fuzzy stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of fuzzy stochastic integral equations. We investigate the existence and uniqueness of solution to such the equations.
Boundary Integral Formulation for Composite Laminates in Torsion
1997
The three-dimensional elastic stress state in a general composite laminate under twisting load is given. The analysis is carried out through an integral equation formulation that is numerically solved by the boundary element method. The integral representation of the elastic behavior is deduced by means of the reciprocity theorem applied to the actual response of each ply and the problem's analytical singular fundamental solutions. The interface continuity conditions due to perfect bonding are considered to complete the laminate mathematical model. The method permits the analysis for generally stacked laminates having general shape of the cross section. By virtue of the formulation characte…
Stress fields in general composite laminates
1996
A direct approach is employed to obtain a general boundary integral formulation for the analysis of composite laminates subjected to uniform axial strain. The integral equations governing the problem are directly deduced from the reciprocity theorem, employing the generalized orthotropic elasticity fundamental solutions expressly inferred. The solution is achieved by the boundary element method, which gives, once the traction-free boundary conditions and the interfacial continuity conditions are enforced, a linear system of algebraic equations. The formulation does not present restrictions with regard to the laminate stacking sequence and it does not require any aprioristic assumption. The …
Integration of Pedagogical Knowledge in the Light of Questions about the Empirical Foundations of General Pedagogy and Understanding of the Concept o…
2018
The main purpose of the article is to show that the studies undertaken by pedagogues, regarding both the experimental foundations of pedagogy and generality, have some common points and that an in-depth reflection on those issues highlights the postulate to treat pedagogical knowledge in an integral manner. The first part presents the relationship between the issue of the empirical foundations of pedagogy and the problems of integrity of pedagogical knowledge; the second part – the relationship between the concept of generality and the problems of integrity, and the concluding part presents a proposed understanding of general pedagogy as integral pedagogy in which the approach towards both …
Subdifferential and conjugate calculus of integral functions with and without qualification conditions
2023
We characterize the subdifferential and the Fenchel conjugate of convex integral functions by means of respectively the approximate subdifferential and the conjugate of the associated convex normal integrands. The results are stated in Suslin locally convex spaces, and do not require continuity-type qualification conditions on the functions, nor special topological or algebraic structures on the index set. Consequently, when confined to separable Banach spaces, the characterizations of such a subdifferential are obtained using only the exact subdifferential of the given integrand but at nearby points. We also provide some simplifications of our formulas when additional continuity conditions…
Efficient Analysis of Arbitrarily Shaped Inductive Obstacles in Rectangular Waveguides Using a Surface Integral Equation Formulation
2007
In this paper we propose to use the Surface Integral Equation technique for the analysis of arbitrarily shaped Hplane obstacles in rectangular waveguides, which can contain both metallic and/or dielectric objects. The Green functions are formulated using both spectral and spatial images series, whose convergence behavior has been improved through several acceleration techniques. Proceeding in this way, the convergence of the series is not attached to the employment of any particular basis or test function, thus consequently increasing the flexibility of the implemented technique. In order to test the accuracy and numerical efficiency of the proposed method, results for practical microwave c…
Structure and Dynamics of the Instantaneous Water/Vapor Interface Revisited by Path-Integral and Ab Initio Molecular Dynamics Simulations
2015
The structure and dynamics of the water/vapor interface is revisited by means of path-integral and second-generation Car-Parrinello ab-initio molecular dynamics simulations in conjunction with an instantaneous surface definition [A. P. Willard and D. Chandler, J. Phys. Chem. B 114, 1954 (2010)]. In agreement with previous studies, we find that one of the OH bonds of the water molecules in the topmost layer is pointing out of the water into the vapor phase, while the orientation of the underlying layer is reversed. Therebetween, an additional water layer is detected, where the molecules are aligned parallel to the instantaneous water surface.
Wavelet-like efficient analysis of two-dimensional arbitrarily shaped radomes using a surface formulation
2007
[1] Radomes are usually made of lossy dielectric materials, and their accurate analysis is often cumbersome because of their typical large electrical size and geometrical complexity. In real reflector antenna structures, there are always complex interactions between the radome, the reflector surfaces and the directional feeds, which are typically neglected for the sake of simplicity. In this paper we will consider all such interactions in a very accurate way, thus requiring a high number of unknowns for the numerical solution of the problem. To overcome such drawback, an integral equation formulation based on the Equivalence Principle in combination with the wavelet transform has been emplo…
Stefan-Boltzmann Radiation on Non-convex Surfaces
1997
We consider the stationary heat equation for a non-convex body with Stefan–Boltzmann radiation condition on the surface. The main virtue of the resulting problem is non-locality of the boundary condition. Moreover, the problem is non-linear and in the general case also non-coercive and non-monotone. We show that the boundary value problem has a maximum principle. Hence, we can prove the existence of a weak solution assuming the existence of upper and lower solutions. In the two dimensional case or when a part of the radiation can escape the system we obtain coercivity and stronger existence result. © 1997 by B.G. Teubner Stuttgart-John Wiley & Sons, Ltd.
Bridging scales with thermodynamics: from nano to macro
2014
We have recently developed a method to calculate thermodynamic properties of macroscopic systems by extrapolating properties of systems of molecular dimensions. Appropriate scaling laws for small systems were derived using the method for small systems thermodynamics of Hill, considering surface and nook energies in small systems of varying sizes. Given certain conditions, Hill's method provides the same systematic basis for small systems as conventional thermodynamics does for large systems. We show how the method can be used to compute thermodynamic data for the macroscopic limit from knowledge of fluctuations in the small system. The rapid and precise method offers an alternative to curre…