Search results for "integral"
showing 10 items of 902 documents
Long-range cohesive interactions of non-local continuum faced by fractional calculus
2008
Abstract A non-local continuum model including long-range forces between non-adjacent volume elements has been studied in this paper. The proposed continuum model has been obtained as limit case of two fully equivalent mechanical models: (i) A volume element model including contact forces between adjacent volumes as well as long-range interactions, distance decaying, between non-adjacent elements. (ii) A discrete point-spring model with local springs between adjacent points and non-local springs with distance-decaying stiffness connecting non-adjacent points. Under the assumption of fractional distance-decaying interactions between non-adjacent elements a fractional differential equation in…
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
2012
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
Convergence for varying measures
2023
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.
Non absolutely convergent integrals of functions taking values in a locally convex space
2006
Properties of McShane and Kurzweil-Henstock integrable functions taking values in a locally convex space are considered and the relations with other integrals are studied. A convergence theorem for the Kurzweil-Henstock integral is given
Riemann type integrals for functions taking values in a locally convex space
2006
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Three viewpoints on the integral geometry of foliations
1999
We deal with three different problems of the multidimensional integral geometry of foliations. First, we establish asymptotic formulas for integrals of powers of curvature of foliations obtained by intersecting a foliation by affine planes. Then we prove an integral formula for surfaces of contact of an affine hyperplane with a foliation. Finally, we obtain a conformally invariant integral-geometric formula for a foliation in three-dimensional space.
A parametric analysis of the transient behavior of lightning protection systems
2005
The paper have the purpose of investigate the influence of different parameters to enable better understanding of the transient performance of complex lightning protection systems (LPS). Lightning discharges constitute the major source of atmospheric or natural noise that can interfere with electric and electronic installations. The electromagnetic characterisation of the LPS environment plays a fundamental role in order to prevent unwanted coupling phenomena that may generate abnormal signals, electric stresses dangerous for the insulation of electric components, disruptive discharges and danger to persons. The model, developed by the authors, is based on a field-approach: the numerical so…
A wideband car-to-car channel model based on a geometrical semicircular tunnel scattering model
2013
In this paper, we present a wideband single-input single-output (SISO) car-to-car (C2C) channel model based on a geometrical semicircular tunnel (SCT) scattering model. Starting from the geometrical scattering model, a reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS) and non-LOS (NLOS) propagation environments. In the proposed channel model, it is assumed that an infinite number of scatterers are uniformly distributed on the tunnel wall. Starting from the geometrical scattering model, the time-variant transfer function (TVTF) is derived and its correlation properties are studied. Expressions are presented for the two-dimensional (2D)…
Path integral quantization for massive vector bosons
2010
A parity-conserving and Lorentz-invariant effective field theory of self-interacting massive vector fields is considered. For the interaction terms with dimensionless coupling constants the canonical quantization is performed. It is shown that the self-consistency condition of this system with the second-class constraints in combination with the perturbative renormalizability leads to an SU(2) Yang-Mills theory with an additional mass term.
Modelling resonant coupling between microring resonators addressed by optical evanescent waves
2004
In this paper we study the properties of microring resonator structures fabricated with high-index-of-refraction dielectric material. These structures concentrate light and can produce very strong optical potential gradients. They are of great interest for the trapping, manipulation and transport of cold atoms near surfaces. The study consists of two parts: in the first part we investigate the symmetry properties of the resonator response for simple models of the microring structures. In the second part we present detailed numerical calculations of the actual spectra for realistic microfabricated structures. We employ the direct space integral equation method (DSIEM). This method, based on …