2019 No. 6
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2019, (6): 1-6.
doi: 10.3969/j.issn.1000-5641.2019.06.001
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Abstract:
In this paper, anti-periodic solutions for a class of nonlinear discrete perturbed systems with exponential dichotomy are studied. By means of the Banach fixed point theorem, new sufficient conditions for the existence and uniqueness of anti-periodic solutions for nonlinear discrete perturbed systems are established. An example is given to illustrate the results we obtained.
In this paper, anti-periodic solutions for a class of nonlinear discrete perturbed systems with exponential dichotomy are studied. By means of the Banach fixed point theorem, new sufficient conditions for the existence and uniqueness of anti-periodic solutions for nonlinear discrete perturbed systems are established. An example is given to illustrate the results we obtained.
2019, (6): 7-20.
doi: 10.3969/j.issn.1000-5641.2019.06.002
Abstract:
Applying the genus theory of Gauss on the real quadratic fields, we derive identities involving quadratic forms and genus characters.
Applying the genus theory of Gauss on the real quadratic fields, we derive identities involving quadratic forms and genus characters.
2019, (6): 21-28.
doi: 10.3969/j.issn.1000-5641.2019.06.003
Abstract:
In this paper, a class of nonlinear forced disturbed Klein-Gordon equations are considered using the method of generalized variational iteration. Firstly, the solitary waves of an undisturbed Klein-Gordon equation are solved using the method of undetermined coefficients for hyperbolic functions. Then, perturbed approximate solutions for a soliton of a nonlinear forced disturbed Klein-Gordon equation are obtained using the functional variational iterative principle. Finally, the uniform validity for the approximate solutions is proved. The obtained approximate solution is an analytic expression. So it can be used for carrying out analytic operations. However, these cannot be obtained via a simple simulation.
In this paper, a class of nonlinear forced disturbed Klein-Gordon equations are considered using the method of generalized variational iteration. Firstly, the solitary waves of an undisturbed Klein-Gordon equation are solved using the method of undetermined coefficients for hyperbolic functions. Then, perturbed approximate solutions for a soliton of a nonlinear forced disturbed Klein-Gordon equation are obtained using the functional variational iterative principle. Finally, the uniform validity for the approximate solutions is proved. The obtained approximate solution is an analytic expression. So it can be used for carrying out analytic operations. However, these cannot be obtained via a simple simulation.
2019, (6): 29-34.
doi: 10.3969/j.issn.1000-5641.2019.06.004
Abstract:
Combining the strategy of weighted and simpler GMRES methods, this paper presents a weighted simpler GMRES algorithm for solving shifted linear systems, and gives some properties of the proposed algorithm. Numerical results illustrate the performance and effectiveness of the algorithm.
Combining the strategy of weighted and simpler GMRES methods, this paper presents a weighted simpler GMRES algorithm for solving shifted linear systems, and gives some properties of the proposed algorithm. Numerical results illustrate the performance and effectiveness of the algorithm.
2019, (6): 35-41, 87.
doi: 10.3969/j.issn.1000-5641.2019.06.005
Abstract:
Using the monotone iterative method, we demonstrate the existence of nontrivial solutions for a nonlinear third-order two-point boundary value problem by constructing two monotone iterative sequences.
Using the monotone iterative method, we demonstrate the existence of nontrivial solutions for a nonlinear third-order two-point boundary value problem by constructing two monotone iterative sequences.
2019, (6): 42-60.
doi: 10.3969/j.issn.1000-5641.2019.06.006
Abstract:
Numerical approximations of Bessel functions are both of important theoretical significance and widely applied in mathematics, physics, engineering. In this work, we apply two variants of Prony's method on Bessel functions of the first kind of integer order. The Prony-like methods in cosine or sine version yield approximations as sums of sinusoidal functions of Bessel functions of the first kind of integer order. In the symbolic computation software Maple, we compute the approximations for different orders and over different intervals, and compare these approximations with those obtained through the Fourier method. Experiments show that Prony-like methods perform much better than the Fourier method.
Numerical approximations of Bessel functions are both of important theoretical significance and widely applied in mathematics, physics, engineering. In this work, we apply two variants of Prony's method on Bessel functions of the first kind of integer order. The Prony-like methods in cosine or sine version yield approximations as sums of sinusoidal functions of Bessel functions of the first kind of integer order. In the symbolic computation software Maple, we compute the approximations for different orders and over different intervals, and compare these approximations with those obtained through the Fourier method. Experiments show that Prony-like methods perform much better than the Fourier method.
2019, (6): 61-72.
doi: 10.3969/j.issn.1000-5641.2019.06.007
Abstract:
In light of the limitations and locality problems of the bit permutation process in existing bit-level encryption algorithms, a novel algorithm for self-adaptive diffusion and combined global scrambling was proposed. In the diffusion phase, the reorganization and subsequent scrambling process of bit planes is performed randomly, so that the scrambling process is not limited to just some bit planes, and we achieve the effect of global scrambling. The algorithm employed several chaotic mapping systems, allowing permutation and diffusion operations to be implemented simultaneously. To increase sensitivity to plain images and effectively resist attacks, the self-adaptive process of bit planes was added, thereby further modifying the original image data based on given rules. Simulation results demonstrate that the proposed scheme is sensitive to plain images and keys, and can resist Chosen-Plaintext Attack effectively. The cipher image has uniform pixel distribution and good image encryption.
In light of the limitations and locality problems of the bit permutation process in existing bit-level encryption algorithms, a novel algorithm for self-adaptive diffusion and combined global scrambling was proposed. In the diffusion phase, the reorganization and subsequent scrambling process of bit planes is performed randomly, so that the scrambling process is not limited to just some bit planes, and we achieve the effect of global scrambling. The algorithm employed several chaotic mapping systems, allowing permutation and diffusion operations to be implemented simultaneously. To increase sensitivity to plain images and effectively resist attacks, the self-adaptive process of bit planes was added, thereby further modifying the original image data based on given rules. Simulation results demonstrate that the proposed scheme is sensitive to plain images and keys, and can resist Chosen-Plaintext Attack effectively. The cipher image has uniform pixel distribution and good image encryption.
2019, (6): 73-87.
doi: 10.3969/j.issn.1000-5641.2019.06.008
Abstract:
Graph mining is an important part of data mining, and significant research has been dedicated to the field. Due to the inevitability of noise during data acquisition, it is crucial to address the issue of approximation in mining frequent subgraphs. Previous work has only considered the absolute value of the graph edit distance (GED); however, the relative value between the GED and the size of the subgraph should also be considered. Hence, in this paper, we propose a novel algorithm to mine approximate frequent subgraphs in a single graph; this algortihm takes into account the size of current subgraphs for the calculation of approximations. We increase the efficiency of this algorithm by estimating the upper bound of frequent subgraphs, and pruning according to local anti-monotonicity. Experimental results show that this algorithm can find subgraphs that are missed by traditional mining algorithms, and our proposed approach is relatively efficent compared to other algorithms.
Graph mining is an important part of data mining, and significant research has been dedicated to the field. Due to the inevitability of noise during data acquisition, it is crucial to address the issue of approximation in mining frequent subgraphs. Previous work has only considered the absolute value of the graph edit distance (GED); however, the relative value between the GED and the size of the subgraph should also be considered. Hence, in this paper, we propose a novel algorithm to mine approximate frequent subgraphs in a single graph; this algortihm takes into account the size of current subgraphs for the calculation of approximations. We increase the efficiency of this algorithm by estimating the upper bound of frequent subgraphs, and pruning according to local anti-monotonicity. Experimental results show that this algorithm can find subgraphs that are missed by traditional mining algorithms, and our proposed approach is relatively efficent compared to other algorithms.
2019, (6): 88-102.
doi: 10.3969/j.issn.1000-5641.2019.06.009
Abstract:
To meet the soaring demand of share bike using and improve the service efficiency of bicycle-sharing, this paper proposes a two-stage shared bicycle real-time delivery and scheduling framework based on road condition information. At the offline modeling phase, clustering is implemented on the historical short-distance taxi trajectory data using RET(Regional Extraction Technique) algorithm, to obtain the popular regions of pick-up (or drop-off), and the frequencies of the pick-up (or drop-off) at different time periods. At the online scheduling phase, a dynamic scheduling optimization model (called ROM (Real-time Optimization Model)) for bicycle-sharing is designed to obtain the popular pick-up regions in the next time period. Specifically, searching for the k-nearest neighbor bicycle drop-off regions within the current time period, and combining them with the real-time road conditions to recommend the top-k roads with convenient vehicular access for the bike dispatching car. Experiments on the taxi trajectory dataset show that the proposed method is more effective than the traditional bicycle scheduling strategies.
To meet the soaring demand of share bike using and improve the service efficiency of bicycle-sharing, this paper proposes a two-stage shared bicycle real-time delivery and scheduling framework based on road condition information. At the offline modeling phase, clustering is implemented on the historical short-distance taxi trajectory data using RET(Regional Extraction Technique) algorithm, to obtain the popular regions of pick-up (or drop-off), and the frequencies of the pick-up (or drop-off) at different time periods. At the online scheduling phase, a dynamic scheduling optimization model (called ROM (Real-time Optimization Model)) for bicycle-sharing is designed to obtain the popular pick-up regions in the next time period. Specifically, searching for the k-nearest neighbor bicycle drop-off regions within the current time period, and combining them with the real-time road conditions to recommend the top-k roads with convenient vehicular access for the bike dispatching car. Experiments on the taxi trajectory dataset show that the proposed method is more effective than the traditional bicycle scheduling strategies.
2019, (6): 103-114.
doi: 10.3969/j.issn.1000-5641.2019.06.010
Abstract:
Using the Manhattan World assumption with plane-based indoor localization, an indoor positioning scheme based on plane features in RGB-D vision is proposed, which can be used to extend SLAM (Simultaneous Localization and Mapping) systems. A matching process based on the main direction of the Manhattan Frame is designed to reduce the exponentially increasing time consumed. Simplified localization with 4 degrees of freedom is adopted after the initial pose determination for the problem of low efficiency during exploration. Small subgraphs in each frame are merged into one subgraph for matching to reduce the time consumed for repetitive subgraph matching. The proposed scheme not only effectively increases the success rate of scene matching, but also simplifies positioning in unknown scenes and improves positioning efficiency. Experimental results show that the method can achieve successful localization with shorter path lengths and reduce computational cost for real-time applications.
Using the Manhattan World assumption with plane-based indoor localization, an indoor positioning scheme based on plane features in RGB-D vision is proposed, which can be used to extend SLAM (Simultaneous Localization and Mapping) systems. A matching process based on the main direction of the Manhattan Frame is designed to reduce the exponentially increasing time consumed. Simplified localization with 4 degrees of freedom is adopted after the initial pose determination for the problem of low efficiency during exploration. Small subgraphs in each frame are merged into one subgraph for matching to reduce the time consumed for repetitive subgraph matching. The proposed scheme not only effectively increases the success rate of scene matching, but also simplifies positioning in unknown scenes and improves positioning efficiency. Experimental results show that the method can achieve successful localization with shorter path lengths and reduce computational cost for real-time applications.
2019, (6): 115-122.
doi: 10.3969/j.issn.1000-5641.2019.06.011
Abstract:
A new type of suspended filler containing zeolite powder and nitrifying bacteria was proposed in this study. The new filler was used in an enhanced nitrification model experiment of wastewater treatment plant (WWTP), in which three devices were designed with combinations of zeolite powder and nitrifying bacteria. The nitrification performance of the new suspended fillers were evaluated by monitoring changes in NH4+-N, NO2--N and NO3--N concentration in the three devices. The microbial community structure and diversity in the biofilm of the fillers, furthermore, were analyzed to reveal the nitrification mechanism. The results showed that compared with a single suspension filler containing only zeolite powder or nitrifying bacteria, the composite suspension filler containing zeolite powder and nitrifying bacteria had the highest average removal rate of NH4+-N (68.3%), the lowest average concentration of NO2--N (12.62 mg/L), and the highest average concentration of NO3--N (7.81 mg/L). Hence, the study demonstrated that the combination of zeolite powder and nitrifying bacteria can significantly improve the nitrification performance of the filler, and zeolite powder may promote the microbial nitrification process. The addition of zeolite powder in the new suspended filler was more conducive to the enrichment and growth of nitrifying bacteria, resulting in the decrease of microbial species diversity. The Nitrosomonas genus in the biofilm of the new suspension filler for enhanced nitrification has an advantage, which provides a strong guarantee for the conversion of NH4+-N in the system. The introduction of zeolite powder in the filler can further promote an increase in the proportion of the Nitrospira genus, thereby reducing the possibility of NO2--N accumulation in the system. The purpose of this study was to improve the basis and parameters for the engineering application of new types of suspended fillers.
A new type of suspended filler containing zeolite powder and nitrifying bacteria was proposed in this study. The new filler was used in an enhanced nitrification model experiment of wastewater treatment plant (WWTP), in which three devices were designed with combinations of zeolite powder and nitrifying bacteria. The nitrification performance of the new suspended fillers were evaluated by monitoring changes in NH4+-N, NO2--N and NO3--N concentration in the three devices. The microbial community structure and diversity in the biofilm of the fillers, furthermore, were analyzed to reveal the nitrification mechanism. The results showed that compared with a single suspension filler containing only zeolite powder or nitrifying bacteria, the composite suspension filler containing zeolite powder and nitrifying bacteria had the highest average removal rate of NH4+-N (68.3%), the lowest average concentration of NO2--N (12.62 mg/L), and the highest average concentration of NO3--N (7.81 mg/L). Hence, the study demonstrated that the combination of zeolite powder and nitrifying bacteria can significantly improve the nitrification performance of the filler, and zeolite powder may promote the microbial nitrification process. The addition of zeolite powder in the new suspended filler was more conducive to the enrichment and growth of nitrifying bacteria, resulting in the decrease of microbial species diversity. The Nitrosomonas genus in the biofilm of the new suspension filler for enhanced nitrification has an advantage, which provides a strong guarantee for the conversion of NH4+-N in the system. The introduction of zeolite powder in the filler can further promote an increase in the proportion of the Nitrospira genus, thereby reducing the possibility of NO2--N accumulation in the system. The purpose of this study was to improve the basis and parameters for the engineering application of new types of suspended fillers.
2019, (6): 123-131.
doi: 10.3969/j.issn.1000-5641.2019.06.012
Abstract:
Based on an investigation of Fengxian tidal flats, this study analyzed the feeding preference and influencing factors of two dominant crabs-Helice tientsinensis and Sesarma plicata-on typical salt marsh plants Spartina alterniflora and Phragmites australis via an indoor feeding experiment. The study provides a reference to further understanding of the control mechanisms for competition between Spartina and Phragmites. The results showed that the preference of the two crabs for different plant organs was:Leaves > Roots > Stalk. However, the preference varies across different plants; namely, Helice tientsinensis prefers Phragmites leaves, while Sesarma plicata prefers Spartina leaves. The consumption of stalk and roots of Spartina is higher than Phragmites. In addition to crab weight and species, the feeding preference is also positively correlated with the content of crude protein in plants.
Based on an investigation of Fengxian tidal flats, this study analyzed the feeding preference and influencing factors of two dominant crabs-Helice tientsinensis and Sesarma plicata-on typical salt marsh plants Spartina alterniflora and Phragmites australis via an indoor feeding experiment. The study provides a reference to further understanding of the control mechanisms for competition between Spartina and Phragmites. The results showed that the preference of the two crabs for different plant organs was:Leaves > Roots > Stalk. However, the preference varies across different plants; namely, Helice tientsinensis prefers Phragmites leaves, while Sesarma plicata prefers Spartina leaves. The consumption of stalk and roots of Spartina is higher than Phragmites. In addition to crab weight and species, the feeding preference is also positively correlated with the content of crude protein in plants.
2019, (6): 132-139, 152.
doi: 10.3969/j.issn.1000-5641.2019.06.013
Abstract:
This study tested the ovipositional response of Cx. pipiens pallens to five species of plants and their volatiles:Acorus tatarinowii, Hydrocotyle vulgaris, Houttuynia cordata Thunb, Myriophyllum aquaticum (Vell.) Verdc. and Mentha spicata. The results showed that the oviposition activity index (OAI) value of Acorus tatarinowii was +0.58 with an effective repellency (ER) of 0%; Hence, Acorus tatarinowii can be considered as an oviposition attractant/stimulant. The OAI of Hydrocotyle vulgaris, Houttuynia cordata Thunb, and Myriophyllum aquaticum (Vell.) Verdc were measured as -0.70, -0.64 and -0.16 with an ER of 82.46%, 78.36% and 27.05%, respectively. Among these, Hydrocotyle vulgaris and Houttuynia cordata Thunb can be considered as repellents/deterrents. Meanwhile, the OAI of Mentha spicata was -1.00 with an ER of 100%, i.e., the strongest inhibiting effect, and hence considered the most suitable plant for repelling mosquitos. According to correlation analyses, there were significantly negative correlations between benzenoids and OAI values (p < 0.05). Terpenes, especially monoterpenes, had a significant positive correlation with OAI values (p < 0.05). This study provides a basis for the synergetic development of river ecological restoration and mosquito control.
This study tested the ovipositional response of Cx. pipiens pallens to five species of plants and their volatiles:Acorus tatarinowii, Hydrocotyle vulgaris, Houttuynia cordata Thunb, Myriophyllum aquaticum (Vell.) Verdc. and Mentha spicata. The results showed that the oviposition activity index (OAI) value of Acorus tatarinowii was +0.58 with an effective repellency (ER) of 0%; Hence, Acorus tatarinowii can be considered as an oviposition attractant/stimulant. The OAI of Hydrocotyle vulgaris, Houttuynia cordata Thunb, and Myriophyllum aquaticum (Vell.) Verdc were measured as -0.70, -0.64 and -0.16 with an ER of 82.46%, 78.36% and 27.05%, respectively. Among these, Hydrocotyle vulgaris and Houttuynia cordata Thunb can be considered as repellents/deterrents. Meanwhile, the OAI of Mentha spicata was -1.00 with an ER of 100%, i.e., the strongest inhibiting effect, and hence considered the most suitable plant for repelling mosquitos. According to correlation analyses, there were significantly negative correlations between benzenoids and OAI values (p < 0.05). Terpenes, especially monoterpenes, had a significant positive correlation with OAI values (p < 0.05). This study provides a basis for the synergetic development of river ecological restoration and mosquito control.
2019, (6): 140-152.
doi: 10.3969/j.issn.1000-5641.2019.06.014
Abstract:
The invasion of the exotic plant Spartina alterniflora has caused a series of ecological risks to coastal wetland ecosystems. In order to study the influence of environmental factors on the invasion of S. alterniflora, S. alterniflora rhizomes were transplanted from land to sea on two types of tidal flats (sandy and silty)in Nanhui Dongtan, Shanghai. We monitored environmental factors such as elevation, hydrodynamic conditions, sediment characteristics, and survival rates of S. alterniflora simultaneously. Redundancy Analysis (RDA) was used to analyze the dominant factors on the settlement of S.alterniflora. The results showed that:(1) The critical shear stress, median diameter, elevation, and maximum flow velocity had dominant effects on the settlement of S.alterniflora rhizome (P < 0.05). (2) The dominant environmental factors that affected S.alterniflora settlement were different on each of the tidal flat types. On the sandy flat (northern), elevation and median diameter were the dominant factors affecting S.alterniflora settlement (P < 0.05). The survival rate of S.alterniflora increased with an increase in elevation and with a decrease in sediment median diameter. On the silty flat (southern), critical shear stress was the dominant factor for the settlement of S.alterniflora (P < 0.05), and there was a positive correlation between critical shear stress and the survival rate of S.alterniflora. The results of the study have theoretical value and significance in guiding mechanism research, prevention, and control of S.alterniflora invasion.
The invasion of the exotic plant Spartina alterniflora has caused a series of ecological risks to coastal wetland ecosystems. In order to study the influence of environmental factors on the invasion of S. alterniflora, S. alterniflora rhizomes were transplanted from land to sea on two types of tidal flats (sandy and silty)in Nanhui Dongtan, Shanghai. We monitored environmental factors such as elevation, hydrodynamic conditions, sediment characteristics, and survival rates of S. alterniflora simultaneously. Redundancy Analysis (RDA) was used to analyze the dominant factors on the settlement of S.alterniflora. The results showed that:(1) The critical shear stress, median diameter, elevation, and maximum flow velocity had dominant effects on the settlement of S.alterniflora rhizome (P < 0.05). (2) The dominant environmental factors that affected S.alterniflora settlement were different on each of the tidal flat types. On the sandy flat (northern), elevation and median diameter were the dominant factors affecting S.alterniflora settlement (P < 0.05). The survival rate of S.alterniflora increased with an increase in elevation and with a decrease in sediment median diameter. On the silty flat (southern), critical shear stress was the dominant factor for the settlement of S.alterniflora (P < 0.05), and there was a positive correlation between critical shear stress and the survival rate of S.alterniflora. The results of the study have theoretical value and significance in guiding mechanism research, prevention, and control of S.alterniflora invasion.
2019, (6): 153-168.
doi: 10.3969/j.issn.1000-5641.2019.06.015
Abstract:
The 1D physics-ecological system model GOTM-FABM-ERSEM is used to simulate the seasonal variation in pelagic ecosystem components in the central East China Sea. The interaction between physical and bio-chemical components is well characterized. The biophysical drivers of seasonality are light, temperature, vertical stratification, and nutrient concentrations as well as their respective rates of supply. There are two blooming periods for phytoplankton:these are April and October. In summer, the seawater temperature is the highest and stratification is the strongest, with high nutrient concentrations found below the thermocline; these concentrations reach a maximum in September with phytoplankton biomass reaching a maximum of 5.3 mg C·m-3 in the subsurface layer (about 20 m depth) and periodic growth promoted by tidal mixing. The temporal variability of zooplankton and bacteria is tightly coupled with that of phytoplankton, but with a 3 d lag in spring blooming; hence, the zooplankton and bacteria reach maximum concentrations after the spring phytoplankton bloom. Bacterial biomass in the upper layer is controlled by phytoplankton standing stock and temperatures during the summer.
The 1D physics-ecological system model GOTM-FABM-ERSEM is used to simulate the seasonal variation in pelagic ecosystem components in the central East China Sea. The interaction between physical and bio-chemical components is well characterized. The biophysical drivers of seasonality are light, temperature, vertical stratification, and nutrient concentrations as well as their respective rates of supply. There are two blooming periods for phytoplankton:these are April and October. In summer, the seawater temperature is the highest and stratification is the strongest, with high nutrient concentrations found below the thermocline; these concentrations reach a maximum in September with phytoplankton biomass reaching a maximum of 5.3 mg C·m-3 in the subsurface layer (about 20 m depth) and periodic growth promoted by tidal mixing. The temporal variability of zooplankton and bacteria is tightly coupled with that of phytoplankton, but with a 3 d lag in spring blooming; hence, the zooplankton and bacteria reach maximum concentrations after the spring phytoplankton bloom. Bacterial biomass in the upper layer is controlled by phytoplankton standing stock and temperatures during the summer.
2019, (6): 169-178.
doi: 10.3969/j.issn.1000-5641.2019.06.016
Abstract:
Due to differences in the distribution of urban service facilities, people need to pay higher prices for better services. We use the Geodetector model to explore the impact of city service facilities on house prices. The results show that:① House prices decline from the center of the city to the surrounding suburbs. ② The closer to the city center, the stronger the influence of city service facilities on house prices. ③ Traffic facilities have the greatest influence on the distribution pattern of Shanghai's housing prices. In different urban functional areas, urban service facilities have different influences on house prices. It is important to pay attention to the optimization of urban service facilities in the regulation of house prices.
Due to differences in the distribution of urban service facilities, people need to pay higher prices for better services. We use the Geodetector model to explore the impact of city service facilities on house prices. The results show that:① House prices decline from the center of the city to the surrounding suburbs. ② The closer to the city center, the stronger the influence of city service facilities on house prices. ③ Traffic facilities have the greatest influence on the distribution pattern of Shanghai's housing prices. In different urban functional areas, urban service facilities have different influences on house prices. It is important to pay attention to the optimization of urban service facilities in the regulation of house prices.
2019, (6): 179-185.
doi: 10.3969/j.issn.1000-5641.2019.06.017
Abstract:
Household environment adaptability reflects the quality of an elderly family's living conditions. The basic influencing factors of adaptive design include:social relationships, family relationships, living conditions, economic income, physical conditions, etc. Using questionnaires and subsequent data analysis, we summarize the quantitative or qualitative relationships between these respective factors. We also construct an influencing factor system that can be used as a reference for adaptive design of household environments for the elderly.
Household environment adaptability reflects the quality of an elderly family's living conditions. The basic influencing factors of adaptive design include:social relationships, family relationships, living conditions, economic income, physical conditions, etc. Using questionnaires and subsequent data analysis, we summarize the quantitative or qualitative relationships between these respective factors. We also construct an influencing factor system that can be used as a reference for adaptive design of household environments for the elderly.
