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Changes in motor function in the unaffected hand of stroke patients should not be ignored
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作者 Lingli Zhang Peihong Li +3 位作者 Zhibang Mao Xiang Qi Jun Zou Zhusheng Yu 《Neural Regeneration Research》 SCIE CAS CSCD 2014年第13期1323-1328,共6页
Motor function changes in the unaffected hand of stroke patients with hemiplegia. These changes are often ignored by clinicians owing to the extent of motor disability of the affected hand. Finger tapping frequency an... Motor function changes in the unaffected hand of stroke patients with hemiplegia. These changes are often ignored by clinicians owing to the extent of motor disability of the affected hand. Finger tapping frequency and Lind-mark hand function score showed that the motor function of unaffected hands in stroke patients was poorer than that of a healthy control hand. After 2 weeks of rehabilitation treatment, motor function of the unaffected hand of stroke patients was obviously improved. Therefore, attention should also be paid to motor function in the unaffected hand of stroke patients with hemiplegia during rehabilitation. 展开更多
关键词 nerve regeneration STROKE unaffected hand dominant hand right hand finger tapping Lind-mark hand function assessment rehabilitation training neural regeneration
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An Analysis of the Relationship between Output Corpus and Language Output Function
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作者 罗珂 《海外英语》 2019年第4期93-94,共2页
The study is to verify the relationship between the output corpus and language output function and to test the three func-tions of pushed output. It attempts to give some implications for non-English major and English... The study is to verify the relationship between the output corpus and language output function and to test the three func-tions of pushed output. It attempts to give some implications for non-English major and English-learning. The results show that theoutput corpus is related to language output function. 展开更多
关键词 OUTPUT CORPUS language OUTPUT function pushed OUTPUT teacher feedback students’discourse
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Lower Bounds on the Majority Domination Number of Graphs
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作者 刘海龙 孙良 田贺民 《Journal of Beijing Institute of Technology》 EI CAS 2002年第4期436-438,共3页
Let G=(V,E) be a simple graph. For any real valued function f∶V→R and SV, let f(S)=∑ u∈S?f(u). A majority dominating function is a function f∶V→{-1,1} such that f(N)≥1 for at least half the vertices v∈V. Th... Let G=(V,E) be a simple graph. For any real valued function f∶V→R and SV, let f(S)=∑ u∈S?f(u). A majority dominating function is a function f∶V→{-1,1} such that f(N)≥1 for at least half the vertices v∈V. Then majority domination number of a graph G is γ maj(G)=min{f(V)|f is a majority dominating function on G}. We obtain lower bounds on this parameter and generalize some results of Henning. 展开更多
关键词 dominating function signed domination number majority domination number
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The Signed Domination Number of Cartesian Product of Two Paths 被引量:1
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作者 Mohammad Hassan Muhsin Al Hassan Mazen Mostafa 《Open Journal of Discrete Mathematics》 2020年第2期45-55,共11页
Let G be a finite connected simple graph with vertex set V(G) and edge set E(G). A function f:V(G) → {1,1} is a signed dominating function if for every vertex v∈V(G), the closed neighborhood of v contains more verti... Let G be a finite connected simple graph with vertex set V(G) and edge set E(G). A function f:V(G) → {1,1} is a signed dominating function if for every vertex v∈V(G), the closed neighborhood of v contains more vertices with function values 1 than with &#8722;1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. In this paper, we calculate The signed domination numbers of the Cartesian product of two paths Pm and Pn for m = 3, 4, 5 and arbitrary n. 展开更多
关键词 PATH CARTESIAN Product SIGNED dominating function SIGNED DOMINATION NUMBER
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On the Signed Domination Number of the Cartesian Product of Two Directed Cycles
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作者 Ramy Shaheen 《Open Journal of Discrete Mathematics》 2015年第3期54-64,共11页
Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ?is called a signed dominating function (SDF) if ?for each vertex . The weight ?of f is defined by . The signed domination numb... Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ?is called a signed dominating function (SDF) if ?for each vertex . The weight ?of f is defined by . The signed domination number of a digraph D is . Let Cm × Cn denotes the cartesian product of directed cycles of length m and n. In this paper, we determine the exact values of gs(Cm × Cn) for m = 8, 9, 10 and arbitrary n. Also, we give the exact value of gs(Cm × Cn) when m, ?(mod 3) and bounds for otherwise. 展开更多
关键词 Directed GRAPH Directed CYCLE CARTESIAN Product SIGNED dominating function SIGNED DOMINATION NUMBER
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Distribution pattern of macrobenthic assemblages along a salinity gradient in the Hangzhou Bay and its adjacent waters
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作者 Runxuan Yan Xiaobo Wang +1 位作者 Songyao Peng Qingxi Han 《Acta Oceanologica Sinica》 SCIE CAS CSCD 2023年第9期79-89,共11页
It is widely acknowledged that the distribution of macrobenthos is affected by salinity, but the degree of influence varies in different areas. To explore the distribution pattern of macrobenthic assemblages in the Ha... It is widely acknowledged that the distribution of macrobenthos is affected by salinity, but the degree of influence varies in different areas. To explore the distribution pattern of macrobenthic assemblages in the Hangzhou Bay,12 stations were sampled to collect macrobenthos and the corresponding bottom water. Changes in the general characteristics of macrobenthos along the salinity gradient in the Hangzhou Bay and its adjacent waters were considered. Three dominant species were identified, including the polychaetes Sternaspis chinensis, the crustacea Oratosquilla oratoria and the echinoderm Ophiuroglypha kinbergi. And the macrobenthic assemblages showed a zonal distribution along with the salinity change. The correlation analyses showed that salinity, depth,temperature, suspended solids and dissolved oxygen had concurrent significant correlations with carnivorous group, Margalef species richness(d), Brillouin index(H) and Shannon-Wiener diversity index(H'). In light of the strong correlation between salinity and Changjiang River diluted water, which produces considerable disturbances by freshwater inflows, the deposition of suspended solids and the resuspension of seabed sediments,the combined environmental disturbances, instead of salinity alone, should be adopted to explain the zonation distribution pattern of macrobenthic assemblages. 展开更多
关键词 MACROBENTHOS dominant species functional groups environmental disturbances
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Comparison of Carbon Dynamics among Three Cool-Temperate Forests (<i>Quercus serrata, Larix kaempferi</i>and <i>Pinus densiflora</i>) under the Same Climate Conditions in Japan
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作者 Mitsutoshi Tomotsune Yohei Suzuki +5 位作者 Yuki Kato Rina Masuda Nobuhiko Suminokura Yuta Koyama Yoshiaki Sakamaki Hiroshi Koizumi 《Journal of Environmental Protection》 2019年第7期929-941,共13页
To understand the role of forest ecosystems in the global carbon cycle, it is important to clarify the factors affecting the carbon balance of forest ecosystems. However, little is known about the direct effect of for... To understand the role of forest ecosystems in the global carbon cycle, it is important to clarify the factors affecting the carbon balance of forest ecosystems. However, little is known about the direct effect of forest types, especially dominant species, on their different carbon dynamics. To clarify the effect of difference in forest types, an experiment was conducted in three forests, which were located in the same place and exposed to the same climate conditions. These forests were middle-aged (40 - 45 years) and dominated by Quercus serrata (Q forest), Larix kaempferi (L forest) and Pinus densiflora (P forest). Net primary production (NPP), heterotrophic respiration (HR) and net ecosystem production (NEP) were estimated in each forest, using a biometric method over one year. For NPP estimated from the annual growth of tree biomass (ΔB) and amount of litter (LF), P forest NPP (5.3 MgC·ha-1·yr-1) was higher than Q and L forest NPP (4.6 and 3.2 MgC·ha-1·yr-1). The difference was affected by a significant difference in ΔB (p = 0.032) and LF (p -1·yr-1) was higher than L and P forest (2.3 and 2.1 MgC·ha-1·yr-1). This difference could result from the amount of litter (respiration substrate) and chemical properties of litter (lability of decomposition). The NEP, which was calculated from the difference between NPP and HR, varied widely among the forest types (0.5, 0.9 and 3.2 MgC·ha-1·yr-1 in Q, L and P forests, respectively). The range of values among the forest types was comparable to those among age sequences and climate zones in previous studies. These results suggest that the difference in forest types (especially dominant species) can potentially lead to a large variation in carbon dynamics, in ecosystems located in the same place. 展开更多
关键词 Dominant Species functional Type HETEROTROPHIC RESPIRATION NET Ecosystem PRODUCTION NET Primary PRODUCTION
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The Generalization of Signed Domination Number of Two Classes of Graphs
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作者 Xia Hong Guoyan Ao Feng Gao 《Open Journal of Discrete Mathematics》 2021年第4期114-132,共19页
Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16... Let <img src="Edit_092a0db1-eefa-4bff-81a0-751d038158ad.png" width="58" height="20" alt="" /> be a graph. A function <img src="Edit_b7158ed5-6825-41cd-b7f0-5ab5e16fc53d.png" width="79" height="20" alt="" /> is said to be a Signed Dominating Function (SDF) if <img src="Edit_c6e63805-bcaa-46a9-bc77-42750af8efd4.png" width="135" height="25" alt="" /> holds for all <img src="Edit_bba1b366-af70-46cd-aefe-fc68869da670.png" width="42" height="20" alt="" />. The signed domination number <img src="Edit_22e6d87a-e3be-4037-b4b6-c1de6a40abb0.png" width="284" height="25" alt="" />. In this paper, we determine the exact value of the Signed Domination Number of graphs <img src="Edit_36ef2747-da44-4f9b-a10a-340c61a3f28c.png" width="19" height="20" alt="" /> and <img src="Edit_26eb0f74-fcc2-49ad-8567-492cf3115b73.png" width="19" height="20" alt="" /> for <img src="Edit_856dbcc1-d215-4144-b50c-ac8a225d664f.png" width="32" height="20" alt="" />, which is generalized the known results, respectively, where <img src="Edit_4b7e4f8f-5d38-4fd0-ac4e-dd8ef243029f.png" width="19" height="20" alt="" /> and <img src="Edit_6557afba-e697-4397-994e-a9bda83e3219.png" width="19" height="20" alt="" /> are denotes the <em>k</em>-th power graphs of cycle <img src="Edit_27e6e80f-85d5-4208-b367-a757a0e55d0b.png" width="21" height="20" alt="" /> and path <img src="Edit_70ac5266-950b-4bfd-8d04-21711d3ffc33.png" width="18" height="20" alt="" />. 展开更多
关键词 Signed Domination function Signed Domination Numbers Graphs Cn style="margin-left:-7px ">k Graphs Pn style="margin-left:-7px ">k
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Dominating functions with integer values in graphs a survey 被引量:2
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作者 康丽英 单而芳 《Journal of Shanghai University(English Edition)》 CAS 2007年第5期437-448,共12页
For an arbitrary subset P of the reals, a function f : V →P is defined to be a P-dominating function of a graph G = (V, E) if the sum of its function values over any closed neighbourhood is at least 1. That is, fo... For an arbitrary subset P of the reals, a function f : V →P is defined to be a P-dominating function of a graph G = (V, E) if the sum of its function values over any closed neighbourhood is at least 1. That is, for every v ∈ V, f(N[v]) ≥ 1. The definition of total P-dominating function is obtained by simply changing ‘closed' neighborhood N[v] in the definition of P-dominating function to ‘open' neighborhood N(v). The (total) P-domination number of a graph G is defined to be the infimum of weight w(f) = ∑v ∈ V f(v) taken over all (total) P-dominating function f. Similarly, the P-edge and P-star dominating functions can be defined. In this paper we survey some recent progress on the topic of dominating functions in graph theory. Especially, we are interested in P-, P-edge and P-star dominating functions of graphs with integer values. 展开更多
关键词 P-dominating function signed domination signed total domination minus domination minus total domination.
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Rock burst laws in deep mines based on combined model of membership function and dominance-based rough set 被引量:1
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作者 刘浪 陈忠强 王李管 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第9期3591-3597,共7页
Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressiv... Rock bursts are spontaneous, violent fracture of rock that can occur in deep mines, and the likelihood of rock bursts occurring increases as depth of the mine increases. Rock bursts are also affected by the compressive strength, tensile strength, tangential strength, elastic energy index, etc. of rock, and the relationship between these factors and rock bursts in deep mines is difficult to analyze from quantitative point. Typical rock burst instances as a sample set were collected, and membership function was introduced to process the discrete values of these factors with the discrete factors as condition attributes and rock burst situations as decision attributes. Dominance-based rough set theory was used to generate preference rules of rock burst, and eventually rock burst laws analysis in deep mines with preference relation was taken. The results show that this model for rock burst laws analysis in deep mines is more reasonable and feasible, and the prediction results are more scientific. 展开更多
关键词 deep mine rock burst membership function dominance relation rough set
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Training of Multi-layered Neural Network for Data Enlargement Processing Using an Activity Function 被引量:1
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作者 Betere Job Isaac Hiroshi Kinjo +1 位作者 Kunihiko Nakazono Naoki Oshiro 《Journal of Electrical Engineering》 2019年第1期1-7,共7页
In this paper, we present a study on activity functions for an MLNN (multi-layered neural network) and propose a suitable activity function for data enlargement processing. We have carefully studied the training perfo... In this paper, we present a study on activity functions for an MLNN (multi-layered neural network) and propose a suitable activity function for data enlargement processing. We have carefully studied the training performance of Sigmoid, ReLu, Leaky-ReLu and L & exp. activity functions for few inputs to multiple output training patterns. Our MLNNs model has L hidden layers with two or three inputs to four or six outputs data variations by BP (backpropagation) NN (neural network) training. We focused on the multi teacher training signals to investigate and evaluate the training performance in MLNNs to select the best and good activity function for data enlargement and hence could be applicable for image and signal processing (synaptic divergence) along with the proposed methods with convolution networks. We specifically used four activity functions from which we found out that L & exp. activity function can suite DENN (data enlargement neural network) training since it could give the highest percentage training abilities compared to the other activity functions of Sigmoid, ReLu and Leaky-ReLu during simulation and training of data in the network. And finally, we recommend L & exp. function to be good for MLNNs and may be applicable for signal processing of data and information enlargement because of its performance training characteristics with multiple teacher training patterns using original generated data and hence can be tried with CNN (convolution neural networks) of image processing. 展开更多
关键词 DATA ENLARGEMENT PROCESSING MLNN ACTIVITY function multi teacher TRAINING signals BP NN CNN
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Communicating with the non-dominant hemisphere:Implications for neurological rehabilitation 被引量:2
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作者 Fabricio Ferreira de Oliveira Sheilla de Medeiros Correia Marin Paulo Henrique Ferreira Bertolucci 《Neural Regeneration Research》 SCIE CAS CSCD 2013年第13期1236-1246,共11页
Aphasic syndromes usually result from injuries to the dominant hemisphere of the brain. Despite the fact that localization of language functions shows little interindividual variability, several brain areas are simult... Aphasic syndromes usually result from injuries to the dominant hemisphere of the brain. Despite the fact that localization of language functions shows little interindividual variability, several brain areas are simultaneously activated when language tasks are undertaken. Mechanisms of language recovery after brain injury to the dominant hemisphere seem to be relatively stereotyped, including activations of perilesional areas in the acute phase and of homologues of language areas in the non-dominant hemisphere in the subacute phase, later returning to dominant hemisphere activation in the chronic phase. Plasticity mechanisms reopen the critical period of language development, more specifically in what leads to disinhibition of the non-dominant hemisphere when brain lesions affect the dominant hemisphere. The non-dominant hemisphere plays an important role during recovery from aphasia, but currently available rehabilitation therapies have shown limited results for efficient language improvement. Large-scale randomized controlled trials that evaluate well-defined interventions in patients with aphasia are needed for stimulation of neuroplasticity mechanisms that enhance the role of the non-dominant hemisphere for language recovery. Ineffective treatment approaches should be replaced by more promising ones and the latter should be evaluated for proper application. The data generated by such studies could substantiate evidence-based rehabilitation strategies for patients with aphasia. 展开更多
关键词 neural regeneration reviews linguistics APHASIA language speech non-dominant hemisphere disability evaluation prognosis CEREBRUM function grants-supported paper neuroregeneration
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Ecological function transitions of land use in the Beibu Gulf Economic Zone from the perspective of production-living-ecological space
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作者 ZHOU Guipeng LONG Hualou +1 位作者 JIANG Yanfeng TU Shuangshuang 《Journal of Geographical Sciences》 SCIE CSCD 2024年第11期2212-2238,共27页
The ecological function of land use is the basis for developing an ecological civilization and realizing sustainable development.This paper may help guide the coordination of economic development and ecological develo... The ecological function of land use is the basis for developing an ecological civilization and realizing sustainable development.This paper may help guide the coordination of economic development and ecological development in China’s coastal border areas.Based on theoretical analysis,this paper studies the spatiotemporal evolution of the functional spaces and the ecological function transitions of land use in the Beibu Gulf Economic Zone(BGEZ)by analyzing patterns,processes,and factors by applying eco-environmental quality index,grid subdivision,kriging interpolation,barycenter model,and Geodetector.This paper constructs a theoretical framework of ecological function transitions of land use based on the research idea of“system-pattern-process-factor”,and carries out empirical research.Some conclusions can be drawn as follows:(1)The ecological space in the BGEZ has continuously decreased,converting mainly into agricultural production space and industrial-mining production space.The production space has expanded slowly.The area of living space in the BGEZ has increased rapidly.(2)The ecological function of land use in the BGEZ has continued to weaken,especially in the southern part of the BGEZ.The“high-sub-high”quality zones of ecological function are retreating to the north.(3)There were more deterioration transition areas than optimization transition areas of ecological function in the BGEZ.The former were mostly located in the central and southern urbanized areas of the BGEZ,whereas the latter were mostly located in the edge zones of district and county units.(4)As for the driving factors of the deterioration transitions of land use ecological function in the BGEZ,the significant trend of“de-ecologization”of the land cover/land use structure was the dominant driving factor;the interactions among the“natural-socioeconomic-managerial”systems were the main recessive factor.The natural system played a fundamental role,and the driving force of natural factors was the strongest.The industrialization,urbanization,and GDP increment in the socioeconomic system and the policy positioning of development intensity in the managerial system played a significant role.The interactions among natural factors,road construction,and industrial non-agricultural transformation had a“fuze”effect on stimulating driving forces. 展开更多
关键词 land use transitions ecological function eco-environmental quality production-living-ecological spaces dominant and recessive factors Beibu Gulf
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An Analysis on Functions of Interruptions in Specific Conversational Situations
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作者 许幼青 《海外英语》 2012年第23期259-260,267,共3页
The functional analysis of interruption is of great necessity in carrying out a smooth conversation.By exemplifying interruptions in specific conversational situations identified in Friends,the paper has explored the ... The functional analysis of interruption is of great necessity in carrying out a smooth conversation.By exemplifying interruptions in specific conversational situations identified in Friends,the paper has explored the relative,interactive,pluralistic and situational characteristics of functions of interruptions. 展开更多
关键词 INTERRUPTION function CONVERSATIONAL SITUATION DOM
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Signed total domatic number of a graph 被引量:1
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作者 管梅 单而芳 《Journal of Shanghai University(English Edition)》 CAS 2008年第1期31-34,共4页
Let G = (V, E) be a graph, and let f : V →{-1, 1} be a two-valued function. If ∑x∈N(v) f(x) ≥ 1 for each v ∈ V, where N(v) is the open neighborhood of v, then f is a signed total dominating function on ... Let G = (V, E) be a graph, and let f : V →{-1, 1} be a two-valued function. If ∑x∈N(v) f(x) ≥ 1 for each v ∈ V, where N(v) is the open neighborhood of v, then f is a signed total dominating function on G. A set {fl, f2,… fd} of signed d total dominating functions on G with the property that ∑i=1^d fi(x) ≤ 1 for each x ∈ V, is called a signed total dominating family (of functions) on G. The maximum number of functions in a signed total dominating family on G is the signed total domatic number on G, denoted by dt^s(G). The properties of the signed total domatic number dt^s(G) are studied in this paper. In particular, we give the sharp bounds of the signed total domatic number of regular graphs, complete bipartite graphs and complete graphs. 展开更多
关键词 signed total domatic number signed total dominating function signed total domination number
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Roman Domination Number and Domination Number of a Tree 被引量:1
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作者 SONG Xiao-xin WANG Xiao-feng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第3期358-367,共10页
A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weig... A Roman dominating function on a graph G = (V, E) is a function f : V→{0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V) = Σu∈Vf(u). The minimum weight of a Roman dominating function on a graph G, denoted by γR(G), is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR(T) = γ(T) + 3. 展开更多
关键词 Roman dominating function Roman dominating number dominating number healthy spider wounded spider
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Auditory cerebral activation patterns of Chinese English learners by fMRI
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作者 SHEN Tong HU Zi-cheng LI Yong ZHANG Yong XIE Peng LV Fa-jin LUO Tian-you MU Jun 《重庆医科大学学报》 CAS CSCD 2008年第z1期55-59,共5页
Objective:To identify the cerebral activation patterns associated with the processes that occur during viewing Chinese and English words in native Chinese English learners. Methods:12 right-handed Chinese English lear... Objective:To identify the cerebral activation patterns associated with the processes that occur during viewing Chinese and English words in native Chinese English learners. Methods:12 right-handed Chinese English learners were divided into two groups equally,namely English majors and non-English majors,and took semantic judgement tasks of both English and Chinese words, for whom the fMRI images were collected.Results:To various degrees, all subjects demonstrated activation of associated cerebral regions in both hemispheres and the left hemisphere activation was more significant for most subjects. Except for classical regions involved in language processing,such as Wernicke areas and Broca areas,there were other activated cerebral regions, including cerebellum, limbic system and basal ganglia nucleus, etc. To sum up,there were apparent overlap for cerebral activation distribution and no specific processing areas for both tasks. The analysis of ROI(region of interest)suggested that subjects in specialized group were more dependent on right hemisphere to perform English words task. Conclusion:Language cognition is dominated by left hemisphere,which is also shared by the right hemisphere to various degrees and thus two hemispheres work by ways of both dissociation and coordination. It is possible that working strategy of the right hemisphere in English task is related to proficiency of the second language. A variety of distinctions are shared by each subject for language cognitive patterns. 展开更多
关键词 English LEARNERS functional magnetic resonance imaging(fMRI) DOMINANCE CEREBRAL activation PATTERNS
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Impacts of Improved Supplemental Irrigation on Farm Income, Productive Efficiency and Risk Management in Dry Areas
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作者 Tamer El-Shater Yigezu A. Yigezu +1 位作者 Kamil Shideed Aden Aw-Hassan 《Journal of Water Resource and Protection》 2017年第13期1709-1720,共12页
This paper provides empirical evidence that improved supplemental irrigation (ISI) can be justified on both environmental and economic grounds. Results of a stochastic frontier model which explicitly and simultaneousl... This paper provides empirical evidence that improved supplemental irrigation (ISI) can be justified on both environmental and economic grounds. Results of a stochastic frontier model which explicitly and simultaneously accounts for technical inefficiency and production risk applied to data collected from 513 wheat farms in the rainfed areas of Syria show that the typical adopter farmer obtained yield and productive efficiency gains of 6% and 7% respectively. A stochastic dominance criterion also showed that the adopter farmers got 10% and 13% reductions in risk of obtaining yield levels below 4 tons/ha and 3 tons/ha respectively. Given its adoption level of 22.3% in 2010, ISI led to the production of 52 thousand metric tons (6%), more wheat and conservation of 120 million cubic meters of water (10%). ISI has the potential to reduce total irrigation water use by upto 45% and for further increases in yield if accompanied with sprinklers and other improved agronomic practices, thereby enhancing food security and environmental sustainability in the country. An important policy implication of these findings is that wider dissemination of ISI along with other complementary agronomic practices in postwar Syria could be a viable option to be considered by national and international efforts for the restoration and rehabilitation of agriculture in the country. 展开更多
关键词 Supplemental IRRIGATION Wheat Yield Technical INEFFICIENCY PRODUCTION Risk STOCHASTIC FRONTIER PRODUCTION function STOCHASTIC DOMINANCE
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Do Almost All Trees Have No Perfect Dominating Set?
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作者 Bill Quan Yue 《Open Journal of Discrete Mathematics》 2018年第1期1-13,共13页
A graph G is said to have a perfect dominating set S if S is a set of vertices of G and for each vertex v of G, either v is in S and v is adjacent to no other vertex in S, or v is not in S but is adjacent to precisely... A graph G is said to have a perfect dominating set S if S is a set of vertices of G and for each vertex v of G, either v is in S and v is adjacent to no other vertex in S, or v is not in S but is adjacent to precisely one vertex of S. A graph G may have none, one or more than one perfect dominating sets. The problem of determining if a graph has a perfect dominating set is NP-complete. The problem of calculating the probability of an arbitrary graph having a perfect dominating set seems also difficult. In 1994 Yue [1] conjectured that almost all graphs do not have a perfect dominating set. In this paper, by introducing multiple interrelated generating functions and using combinatorial computation techniques we calculated the number of perfect dominating sets among all trees (rooted and unrooted) of order n for each n up to 500. Then we calculated the average number of perfect dominating sets per tree (rooted and unrooted) of order n for each n up to 500. Our computational results show that this average number is approaching zero as n goes to infinity thus suggesting that Yue’s conjecture is true for trees (rooted and unrooted). 展开更多
关键词 TREE dominating GRAPH GENERATING function
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On Signed Domination of Grid Graph
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作者 Mohammad Hassan Muhsin Al Hassan Mazen Mostafa 《Open Journal of Discrete Mathematics》 2020年第4期96-112,共17页
Let <em>G</em>(<em>V</em>, <em>E</em>) be a finite connected simple graph with vertex set <em>V</em>(<em>G</em>). A function is a signed dominating function ... Let <em>G</em>(<em>V</em>, <em>E</em>) be a finite connected simple graph with vertex set <em>V</em>(<em>G</em>). A function is a signed dominating function <em>f </em>: <em style="white-space:normal;">V</em><span style="white-space:normal;">(</span><em style="white-space:normal;">G</em><span style="white-space:normal;">)</span><span style="white-space:nowrap;">→{<span style="white-space:nowrap;"><span style="white-space:nowrap;">&minus;</span></span>1,1}</span> if for every vertex <em>v</em> <span style="white-space:nowrap;">∈</span> <em>V</em>(<em>G</em>), the sum of closed neighborhood weights of <em>v</em> is greater or equal to 1. The signed domination number <em>γ</em><sub>s</sub>(<em>G</em>) of <em>G</em> is the minimum weight of a signed dominating function on <em>G</em>. In this paper, we calculate the signed domination numbers of the Cartesian product of two paths <em>P</em><sub><em>m</em></sub> and <em>P</em><sub><em>n</em></sub> for <em>m</em> = 6, 7 and arbitrary <em>n</em>. 展开更多
关键词 Grid Graph Cartesian Product Signed dominating function Signed Domination Number
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