Particle physics is increasingly being linked to engineering applications via electron 
                  microscopy, nuclear instrumentation, and numerous other applications. It is well known that
                   relativistic particle equations notoriously fail over very short space-time intervals. This paper
                    introduces new versions of Dirac&#39;s equation and of the Klein-Gordon equation that are suitable for
short-range phenomena. Another objective of the paper is to demonstrate
that pulse measurement methods that are based on the wave nature of matter
do not necessarily correlate with physical definitions that are based on
the corpuscular nature of particles.

Ezzat G. Bakhoum

Cristian Toma

Relativistic Short Range Phenomena and Space-Time Aspects of Pulse 
                        Measurements

An important aspect in modeling dynamic phenomena consists in measuring
with higher accuracy some physical quantities corresponding to the
dynamic system. Yet for measurements performed on limited time interval 
at high working frequency, certain intelligent methods should be added. The
high working frequency requires that the measurement and data processing
time interval should be greater than the time interval when the step input is
received, so as to allow an accurate measurement. This paper will show that
an intelligent processing method based on oscillating second-order systems
working on limited time interval can differentiate between large step inputs
(which are active on the whole limited time interval) and short step inputs
(which are active on a time interval shorter than the limited working period).
Some resonance aspects (appearing when the input frequency is close 
to the working frequency of the oscillating second-order system) will be also
presented.

Alexandru Toma

Cristian Morarescu

Detection of Short-Step Pulses Using Practical Test-Functions and Resonance 
                        Aspects

This study presents mathematical aspects of wave equation 
considered on closed space intervals. It is shown that a solution of this
equation can be represented by a certain superposition of traveling waves
with null values for the amplitude and for the time derivatives of the resulting
wave in the endpoints of this interval. Supplementary aspects
connected with the possible existence of initial conditions for a secondorder
differential system describing the amplitude of these localized oscillations
are also studied, and requirements necessary for establishing
a certain propagation direction for the wave (rejecting the possibility of
reverse radiation) are also presented. Then it is shown that these aspects
can be extended to a set of adjacent closed space intervals, by considering
that a certain traveling wave propagating from an endpoint to the
other can be defined on each space interval and a specific mathematical
law (which can be approximated by a differential equation) describes the
amplitude of these localized traveling waves as related to the space coordinates
corresponding to the middle point of the interval. Using specific
differential equations, it is shown that the existence of such propagating
law for the amplitude of localized oscillations can generate periodical
patterns and can explain fracture phenomena inside materials as well.

Ghiocel Toma

Flavia Doboga

Vanishing Waves on Closed Intervals and Propagating Short-Range Phenomena

Due to wide range of interest in use of bioeconomic models to gain insight into the 
                  scientific management of renewable resources like fisheries and forestry, homotopy perturbation 
                  method is employed to approximate the solution of the ratio-dependent predator-prey system with
                   constant effort prey harvesting. The results are compared with the results obtained by Adomian 
                   decomposition method. The results show that, in new model, there are less computations needed
                    in comparison to Adomian decomposition method.

Abdoul R. Ghotbi

A. Barari

D. D. Ganji

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting 
                        Using Homotopy Perturbation Method

Nonnegative matrix factorization (NMF) is a promising approach for local feature extraction in face recognition tasks. However, there are two major drawbacks in almost all existing NMF-based methods. One shortcoming is that the computational cost is expensive for large matrix decomposition. The other is that it must conduct repetitive learning, when the training samples or classes are updated. To overcome these two limitations, this paper proposes a novel incremental nonnegative matrix factorization (INMF) for face representation and recognition. The proposed INMF approach is based on a novel constraint criterion and our previous block strategy. It thus has some good properties, such as low computational complexity, sparse coefficient matrix. Also, the coefficient column vectors between different classes are orthogonal. In particular, it can be applied to incremental learning. Two face databases, namely FERET and CMU PIE face databases, are selected for evaluation. Compared with PCA and some state-of-the-art NMF-based methods, our INMF approach gives the best performance.

Wen-Sheng Chen

Binbin Pan

Bin Fang

Ming Li

Jianliang Tang

Incremental Nonnegative Matrix Factorization for Face Recognition

The aim of distributed denial-of-service (DDOS) flood attacks is to overwhelm the attacked site or to make its service performance deterioration considerably by sending flood packets to the target from the machines distributed all over the world. This is a kind of local behavior of traffic at the protected site because the attacked site can be recovered to its normal service state sooner or later even though it is in reality overwhelmed during attack. From a view of mathematics, it can be taken as a kind of short-range phenomenon in computer networks. In this paper, we use the Hurst parameter (H) to measure the local irregularity or self-similarity of traffic under DDOS flood attack provided that fractional Gaussian noise (fGn) is used as the traffic model. As flood attack packets of DDOS make the H value of arrival traffic vary significantly away from that of traffic normally arriving at the protected site, we discuss a method to statistically detect signs of DDOS flood attacks with predetermined detection probability and false alarm probability.

Wei Zhao

Detection of Variations of Local Irregularity of Traffic under DDOS Flood Attack

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Mathematical Problems in Engineering is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.

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Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.

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Mathematical Problems in Engineering

This Issue is now open for submissions.
Papers are published upon acceptance, regardless of the Special Issue publication date.

Mathematical Problems in Engineering

Short Range Phenomena: Modeling, Computational Aspects, and Applications

Short Range Phenomena: Modeling, Computational Aspects, and Applications

Articles

Relativistic Short Range Phenomena and Space-Time Aspects of Pulse Measurements

Detection of Short-Step Pulses Using Practical Test-Functions and Resonance Aspects

Vanishing Waves on Closed Intervals and Propagating Short-Range Phenomena

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting Using Homotopy Perturbation Method

Incremental Nonnegative Matrix Factorization for Face Recognition

Detection of Variations of Local Irregularity of Traffic under DDOS Flood Attack