Search results for " function"
showing 10 items of 9395 documents
A remark on differentiable functions with partial derivatives in Lp
2004
AbstractWe consider a definition of p,δ-variation for real functions of several variables which gives information on the differentiability almost everywhere and the absolute integrability of its partial derivatives on a measurable set. This definition of p,δ-variation extends the definition of n-variation of Malý and the definition of p-variation of Bongiorno. We conclude with a result of change of variables based on coarea formula.
2019
Abstract Background In old age, decline in functioning may cause changes in walking ability. Our aim was to study whether older people who report adaptive, maladaptive, or no walking modifications differ in outdoor mobility. Methods Community-dwelling people aged 75–90 years (N = 848) were interviewed at baseline, of whom 761 participated in the 2-year follow-up. Walking modifications were assessed by asking the participants whether they had modified their way of walking 2 km due to their health. Based on the responses, three categories were formed: no walking modifications (reference), adaptive (eg, walking more slowly, using an aid), and maladaptive walking modifications (reduced frequenc…
On the statistical properties of the capacity of OSTBC Nakagami-lognormal MIMO channels
2010
This article presents a thorough statistical analysis of the capacity of orthogonal space-time block coded (OSTBC) Nakagami-lognormal (NLN) multiple-input multipleoutput (MIMO) channels. The NLN channel model allows to study the joint effects of fast fading and shadowing on the statistical properties of the channel capacity. We have derived exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the capacity of NLN MIMO channels. It is observed that an increase in the MIMO dimension1 or a decrease in the severity of fading results in an increase in the mean channel capa…
The Influence of the Severity of Fading and Shadowing on the Statistical Properties of the Capacity of Nakagami-Lognormal Channels
2008
This paper deals with the study of the statistical properties of the capacity of Nakagami-lognormal (NLN) channels for various fading environments. Specifically, the impact of shadowing and the severity of fading on the channel capacity is investigated. We have derived analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. These results are analyzed for different levels of shadowing and for various fading conditions, corresponding to different terrestrial environments. It is observed that the severity of fading and shadowing has a significant influence …
On the statistical properties of the capacity of double Hoyt fading channels
2010
The statistical properties of the capacity of narrowband double Hoyt fading channels are studied. Toward this end, analytical expressions for the probability density function (PDF) and cumulative distribution function (CDF) of the instantaneous channel capacity process are derived. Furthermore, for the characterization of the dynamical behavior of the time-varying channel capacity, expressions are provided for the level-crossing rate (LCR) and the average duration of fades (ADF). Since the double Rayleigh fading channel is a special case of the double Hoyt model, it is shown that the derived expressions can be reduced to the corresponding results already known for the capacity of the double…
Statistical properties of the capacity of multipath fading channels
2009
It is well known that a frequency-nonselective multipath fading channel can be modeled by a sum of complex sinusoids, also called sum-of-cisoids (SOC). By using the SOC, we can efficiently model the scattered component of the received signal in non-isotropic scattering environments. Such SOC-based multipath channel models provide the flexibility of having correlated in-phase and quadrature phase components of the received signal. This paper presents the derivation and analysis of the statistical properties of the capacity of multipath fading channels under LOS conditions. As an appropriate stochastic model for the multipath fading channel, we have adopted the SOC model. We have derived the …
An RF-Based Positioning Method for Tracing a Cluster of Moving Scatterers in Non-Stationary Indoor Environments
2021
Author's accepted manuscript © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This letter presents a novel iterative positioning method for tracing the body segments of a person moving indoors using radio-frequency (RF) signals. The indoor space is equipped with a multiple-input multiple-output (MIMO) communication system. The person is modelled by a cluster of …
A Trajectory-Driven 3D Channel Model for Human Activity Recognition
2021
This paper concerns the design, analysis, and simulation of a 3D non-stationary channel model fed with inertial measurement unit (IMU) data. The work in this paper provides a framework for simulating the micro-Doppler signatures of indoor channels for human activity recognition by using radiofrequency-based sensing technologies. The major human body segments, such as wrists, ankles, torso, and head, are modelled as a cluster of moving point scatterers. We provide expressions for the time variant (TV) speed and TV angles of motion based on 3D trajectories of the moving person. Moreover, we present mathematical expressions for the TV Doppler shifts and TV path gains associated with each movin…
Degrees of irreducible characters of the symmetric group and exponential growth
2015
We consider sequences of degrees of ordinary irreducible S n S_n - characters. We assume that the corresponding Young diagrams have rows and columns bounded by some linear function of n n with leading coefficient less than one. We show that any such sequence has at least exponential growth and we compute an explicit bound.