Nonexistence of eventually positive solutions of a difference inequality with multiple and variable delays and coefficients

AbstractIn this paper, we consider the nonexistence of eventually positive solutions of the difference inequality ϰn+1 − ϰn + ∑i=1mpi(n)ϰn−ki(n) ≤ 0.Let m be a positive integer. Then for each positive integer i: 1 ≤ i ≤ m, {ki(n)}∞n=0 and {pi(n)}∞n=0 are a sequence of positive integers and a sequence of nonnegative real numbers, respectively. A sufficient condition guaranteeing the nonexistence of eventually positive solutions is obtained with the help of a new method. As an application of the main result, a conjecture is proved

Periodic solutions of a single species discrete population model with periodic harvest/stock

AbstractWe discuss a discrete population model describing single species growth with periodic harvest/stock. The theory of coincidence degree is applied to show that the model equation admits two periodic solutions. Under minor technical assumptions, we show that one of these two periodic solutions is positive and attracts almost all positive solutions

Understanding of hydrogel network formation and its application in the architecture of significantly enhanced hydrogel

An understanding of the physical hydrogel network formation has been obtained by dynamic rheological experiments. The evidence shows that the network formation turns out to be a nucleation-controlled process. It was found that there exists a critical temperature Tc; fiber branching is greatly enhanced when the network formation is performed in the regime of T&lt;Tc (T, the final setting temperature). This finding enables the authors to build significantly enhanced gel networks. So far G&prime; (elastic modulus) of the hydrogel network has been enhanced by 187% while the formation period can be greatly shortened to only 1/20 of the previous process.<br /

A Stackelberg game theoretic model for optimizing product family architecting with supply chain consideration

Planning of an optimal product family architecture (PFA) plays a critical role in defining an organization's product platforms for product variant configuration while leveraging commonality and variety. The focus of PFA planning has been traditionally limited to the product design stage, yet with limited consideration of the downstream supply chain-related issues. Decisions of supply chain configuration have a profound impact on not only the end cost of product family fulfillment, but also how to design the architecture of module configuration within a product family. It is imperative for product family architecting to be optimized in conjunction with supply chain configuration decisions. This paper formulates joint optimization of PFA planning and supply chain configuration as a Stackelberg game. A nonlinear, mixed integer bilevel programming model is developed to deal with the leader–follower game decisions between product family architecting and supply chain configuration. The PFA decision making is represented as an upper-level optimization problem for optimal selection of the base modules and compound modules. A lower-level optimization problem copes with supply chain decisions in accordance with the upper-level decisions of product variant configuration. Consistent with the bilevel optimization model, a nested genetic algorithm is developed to derive near optimal solutions for PFA and the corresponding supply chain network. A case study of joint PFA and supply chain decisions for power transformers is reported to demonstrate the feasibility and potential of the proposed Stackelberg game theoretic joint optimization of PFA and supply chain decisions

Using dual neural network architecture to detect the risk of dementia with community health data: Algorithm development and validation study

Background: Recent studies have revealed lifestyle behavioral risk factors that can be modified to reduce the risk of dementia. As modification of lifestyle takes time, early identification of people with high dementia risk is important for timely intervention and support. As cognitive impairment is a diagnostic criterion of dementia, cognitive assessment tools are used in primary care to screen for clinically unevaluated cases. Among them, Mini-Mental State Examination (MMSE) is a very common instrument. However, MMSE is a questionnaire that is administered when symptoms of memory decline have occurred. Early administration at the asymptomatic stage and repeated measurements would lead to a practice effect that degrades the effectiveness of MMSE when it is used at later stages. Objective: The aim of this study was to exploit machine learning techniques to assist health care professionals in detecting high-risk individuals by predicting the results of MMSE using elderly health data collected from community-based primary care services. Methods: A health data set of 2299 samples was adopted in the study. The input data were divided into two groups of different characteristics (ie, client profile data and health assessment data). The predictive output was the result of two-class classification of the normal and high-risk cases that were defined based on MMSE. A dual neural network (DNN) model was proposed to obtain the latent representations of the two groups of input data separately, which were then concatenated for the two-class classification. Mean and k-nearest neighbor were used separately to tackle missing data, whereas a cost-sensitive learning (CSL) algorithm was proposed to deal with class imbalance. The performance of the DNN was evaluated by comparing it with that of conventional machine learning methods. Results: A total of 16 predictive models were built using the elderly health data set. Among them, the proposed DNN with CSL outperformed in the detection of high-risk cases. The area under the receiver operating characteristic curve, average precision, sensitivity, and specificity reached 0.84, 0.88, 0.73, and 0.80, respectively. Conclusions: The proposed method has the potential to serve as a tool to screen for elderly people with cognitive impairment and predict high-risk cases of dementia at the asymptomatic stage, providing health care professionals with early signals that can prompt suggestions for a follow-up or a detailed diagnosis

Poynting vector, energy density and energy velocity in anomalous dispersion medium

The Poynting vector, energy density and energy velocity of light pulses propagating in anomalous dispersion medium (used in WKD-like experiments) are calculated. Results show that a negative energy density in the medium propagates along opposite of incident direction with such a velocity similar to the negative group velocity while the direction of the Poynting vector is positive. In other words, one might say that a positive energy density in the medium would propagate along the positive direction with a speed having approximately the absolute valueof the group velocity. We further point out that neither energy velocity nor group velocity is a good concept to describe the propagation process of light pulse inside the medium in WKD experiment owing to the strong accumulation and dissipation effects.Comment: 6 page

Superoscillations and tunneling times

It is proposed that superoscillations play an important role in the interferences which give rise to superluminal effects. To exemplify that, we consider a toy model which allows for a wave packet to travel, in zero time and negligible distortion a distance arbitrarily larger than the width of the wave packet. The peak is shown to result from a superoscillatory superposition at the tail. Similar reasoning applies to the dwell time.Comment: 12 page

Superluminal optical pulse propagation in nonlinear coherent media

The propagation of light-pulse with negative group-velocity in a nonlinear medium is studied theoretically. We show that the necessary conditions for these effects to be observable are realized in a three-level $\Lambda$-system interacting with a linearly polarized laser beam in the presence of a static magnetic field. In low power regime, when all other nonlinear processes are negligible, the light-induced Zeeman coherence cancels the resonant absorption of the medium almost completely, but preserves the dispersion anomalous and very high. As a result, a superluminal light pulse propagation can be observed in the sense that the peak of the transmitted pulse exits the medium before the peak of the incident pulse enters. There is no violation of causality and energy conservation. Moreover, the superluminal effects are prominently manifested in the reshaping of pulse, which is caused by the intensity-dependent pulse velocity. Unlike the shock wave formation in a nonlinear medium with normal dispersion, here, the self-steepening of the pulse trailing edge takes place due to the fact that the more intense parts of the pulse travel slower. The predicted effect can be easily observed in the well known schemes employed for studying of nonlinear magneto-optical rotation. The upper bound of sample length is found from the criterion that the pulse self-steepening and group-advance time are observable without pulse distortion caused by the group-velocity dispersion.Comment: 16 pages, 7 figure

Adoption of the reference framework for diabetes care by primary care physicians

No abstract available