37,861 research outputs found
Integrable dispersionless KdV hierarchy with sources
An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived.
Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated.
Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is
obtained via hodograph transformation. Furthermore, the dispersionless
Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.Comment: 15 pages, to be published in J. Phys. A: Math. Ge
Deriving N-soliton solutions via constrained flows
The soliton equations can be factorized by two commuting x- and t-constrained
flows. We propose a method to derive N-soliton solutions of soliton equations
directly from the x- and t-constrained flows.Comment: 8 pages, AmsTex, no figures, to be published in Journal of Physics
Constructing N-soliton solution for the mKdV equation through constrained flows
Based on the factorization of soliton equations into two commuting integrable
x- and t-constrained flows, we derive N-soliton solutions for mKdV equation via
its x- and t-constrained flows. It shows that soliton solution for soliton
equations can be constructed directly from the constrained flows.Comment: 10 pages, Latex, to be published in "J. Phys. A: Math. Gen.
Joint Coding and Scheduling Optimization in Wireless Systems with Varying Delay Sensitivities
Throughput and per-packet delay can present strong trade-offs that are
important in the cases of delay sensitive applications.We investigate such
trade-offs using a random linear network coding scheme for one or more
receivers in single hop wireless packet erasure broadcast channels. We capture
the delay sensitivities across different types of network applications using a
class of delay metrics based on the norms of packet arrival times. With these
delay metrics, we establish a unified framework to characterize the rate and
delay requirements of applications and optimize system parameters. In the
single receiver case, we demonstrate the trade-off between average packet
delay, which we view as the inverse of throughput, and maximum ordered
inter-arrival delay for various system parameters. For a single broadcast
channel with multiple receivers having different delay constraints and feedback
delays, we jointly optimize the coding parameters and time-division scheduling
parameters at the transmitters. We formulate the optimization problem as a
Generalized Geometric Program (GGP). This approach allows the transmitters to
adjust adaptively the coding and scheduling parameters for efficient allocation
of network resources under varying delay constraints. In the case where the
receivers are served by multiple non-interfering wireless broadcast channels,
the same optimization problem is formulated as a Signomial Program, which is
NP-hard in general. We provide approximation methods using successive
formulation of geometric programs and show the convergence of approximations.Comment: 9 pages, 10 figure
Negaton and Positon solutions of the soliton equation with self-consistent sources
The KdV equation with self-consistent sources (KdVES) is used as a model to
illustrate the method. A generalized binary Darboux transformation (GBDT) with
an arbitrary time-dependent function for the KdVES as well as the formula for
-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund
transformation between two KdV equations with different degrees of sources and
enable us to construct more general solutions with arbitrary -dependent
functions. By taking the special -function, we obtain multisoliton,
multipositon, multinegaton, multisoliton-positon, multinegaton-positon and
multisoliton-negaton solutions of KdVES. Some properties of these solutions are
discussed.Comment: 13 pages, Latex, no figues, to be published in J. Phys. A: Math. Ge
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Effects of Surface Roughness on the Electrochemical Reduction of CO2 over Cu
We have investigated the role of surface roughening on the CO2 reduction reaction (CO2RR) over Cu. The activity and product selectivity of Cu surfaces roughened by plasma pretreatment in Ar, O2, or N2 were compared with that of electrochemically polished Cu samples. Differences in total and product current densities, the ratio of current densities for HER (the hydrogen evolution reaction) to CO2RR, and the ratio of current densities for C2+ to C1 products depend on the electrochemically active surface and are nearly independent of plasma composition. Theoretical analysis of an electropolished and roughened Cu surface reveals a higher fraction of undercoordinated Cu sites on the roughened surface, sites that bind CO preferentially. Roughened surfaces also contain square sites similar to those on a Cu(100) surface but with neighboring step sites, which adsorb OC-COH, a precursor to C2+ products. These findings explain the increases in the formation of oxygenates and hydrocarbons relative to CO and the ratio of oxygenates to hydrocarbons observed with increasing surface roughness
Wearable Sensor Data Based Human Activity Recognition using Machine Learning: A new approach
Recent years have witnessed the rapid development of human activity
recognition (HAR) based on wearable sensor data. One can find many practical
applications in this area, especially in the field of health care. Many machine
learning algorithms such as Decision Trees, Support Vector Machine, Naive
Bayes, K-Nearest Neighbor, and Multilayer Perceptron are successfully used in
HAR. Although these methods are fast and easy for implementation, they still
have some limitations due to poor performance in a number of situations. In
this paper, we propose a novel method based on the ensemble learning to boost
the performance of these machine learning methods for HAR
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