research article collaboration and evolution of e-commerce...

Research ArticleCollaboration and Evolution of E-Commerce andExpress Delivery Industry Supply Chain

Ying Xu1 Xuemei Zhang12 Jian Cao23 Ya Chen24 and Xuhong Ye2

1College of Economic Commerce Ningbo Dahongying University Ningbo 315175 China2College of Economics amp Management Zhejiang University of Technology Hangzhou 310023 China3Department of Civil amp Environmental Engineering The University of Iowa Iowa City IA 52242 USA4Zhejiang Technical Institute of Economics Hangzhou 310018 China

Correspondence should be addressed to Jian Cao jcaozjuteducn

Received 5 June 2016 Accepted 15 November 2016

Academic Editor Paolo Renna

Copyright copy 2016 Ying Xu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Considering the contradictions between the electronic commerce (e-commerce) and its matching express delivery service thispaper investigates a supply chain regarding e-commerce and express delivery industry in which collaborative operations ofenterprises are discussed The profitability and collaboration capability acting as order parameters and the rest of the influentialresources including logistics fund information and commodity are selected with their interrelations being examined based onservo theory of synergetics Besides evolutionary model of the e-commerce and express delivery industry is established andanalyzed according to self-organization method of system dynamic theory to illustrate order parametersrsquo role in system evolutionand numerical analyses emerged to intuitively demonstrate the solutions We conclude the work along with its results of significantreferences for investigating resource integrations by combining the two closely related businesses in an entire cooperative supplychain and providing guidelines for e-commerce and express delivery enterprises and industries in effective collaboration and systemevolution

1 Introduction

In company with the acceleration of economic globalizationand regional integration electronic commerce (e-commerce)industry has been thriving during the past few decadesDeveloped countries Europe in particular have enjoyede-commerce booming with a market size of $426 billionaccounting for 35 of e-commerce market share globally in2012 followed by 331 with a number of $389 billion inNorth America market [1] Asia-Pacific has witnessed persis-tent development of e-commerce at an unprecedented rapidspeed since 2013 with an average growth rate of 23 whileChina and Indonesia stand out as the two fastest-increasede-commerce regions that hold a year-on-year growth of 65and 71 respectively [2] Specifically as middle class inChina has become more web-savvy in recent years onlinebusiness in the country driven by technological innovationas well remains prosperous

To e-commerce industry logistics service is of vital signif-icance for regular operations as well as further innovationsand breakthroughs to better satisfy customers While e-commerce industry has progressed and improved constantlycontradictions have arisen between e-commerce and itsmatching express delivery service that needs to be betterregulated and standard simultaneously Statistics and surveyshave proved however that the express system in Chinahas got low flow rate of efficiency limited managementarea and poor corresponsive ability for market changeswhich have inevitably inhibited further development of e-commerce industry [3] As a response to this new challengecoordination and cooperation between e-commerce andexpress delivery enterprises should be attained for win-windevelopment In fact the rapid expansion of e-commercehas indeed brought about dramatic opportunities for expressindustry which in turn determines the quality and efficiencyof e-commerce undertakings Therefore study of synergistic

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2016 Article ID 3452037 12 pageshttpdxdoiorg10115520163452037

2 Discrete Dynamics in Nature and Society

model along with its evolutionary process of the so-called ldquoe-commerce and express industry supply chainrdquo in this papercomes into notice

In this paper a supply chain considering e-commerceand express delivery enterprises is taken into account Servotheory of synergetics and self-organizationmethod of systemdynamics theory are employed to investigate the intra-and interrelations among influential elements impactingthe collaborative undertakings of e-commerce and expressdelivery industry across the supply chain Besides relevantnumerical analyses emerged to corroborate and supplementthe theoretical exploration

2 Literature Review

To our knowledge existing literatures mostly concern prac-tical issues on supply chain collaborative management suchas the significance of synergy among supply chain members[4 5] the advantage of resource integration and interaction ofchannelmembers [6ndash8] strategies or incentives for successfulcooperation and coordination in the system [9ndash12] andmodeselections and practices of joint operations [13ndash15] Amongthese considerable attention has been paid to collaborativesupply chain of single industry while relevant researchesconveying two or more industries are few and channelcooperation under e-commerce environment has not beenmentioned yet

Since the conceptually prospective ideas on supply chaincollaboration under e-commerce background have beenproposed relating studies are believed to be highly significantin promoting management innovation of logistics systemsfor further breakthroughs of e-commerce development [16ndash19] Channel adaption and member behaviors of a supplychain consisting of the manufacturer and retailer under e-commerce environment are considered in [20] Reference[21] figures out that win-win development of e-commerceandprivate courier is becoming tendencywith correspondingrecommendations provided Reference [22] declares thatsupply chainmanagement of circulation fruits and vegetablescould be better implemented with the e-commerce ser-vice platform equipped with advanced IT applications B2B(Business-to-Business) e-commerce technology adoption oforganizations within the grocery industry supply chain isexamined in [23] Reference [24] analyzes the integrationcapabilities of B2B e-commerce from the perspective ofcapital and market operations and production and demanduncertainty in the supply chain as an influential factor Ref-erence [25] explores the role of e-commerce environmentalmanagement in improving support abilities of collaborativeoperations through confirmatory factor analysis Reference[26] investigates the relations between supply chain man-agement and e-commerce operation in automobile industryto illustrate the feasibility and necessity of managing theindustrial chain taking advantage of e-commerce superiorityIn sum there are two prevailing topics of supply chaincollaboration under e-commerce platform (i) supply chainmanagement innovations in the face of challenges and oppor-tunities brought by the booming e-commerce industry and(ii) collaborative e-commerce supply chain management to

attain a win-win status Both research orientations howevertend to overlook a potentially crucial role of influential factorswithin the channel that virtually should not be ignored inthe collaboration and cooperation across the entire supplychain In fact profitability and interoperability along with thecirculation of commodity fund information and logistics areof vital importance in supply chain operations In this paperwe further investigate supply chain coordination along withits evolutionary process of e-commerce and express deliveryindustry considering horizontal collaborations among vari-ous resource elements that combine the two closely relatedbusinesses in an entire cooperative supply chain

As is known to all that the circulation of commoditylogistics information and fund is the basis and premisefor e-commerce initiatives researches on their connotationsand interrelations have been prolific [27ndash29] Besides itis insufficient to merely cooperate one resource elementbetween two nodes vertically for supply chain collaborationhorizontal collaboration that various factors are jointly con-sidered should be emphasized even more That is to saythe entire synergy could be attained only if the cooperativeinteractions are fulfilled among all influences both longitu-dinally and transversely [30] In recent years naturally anincreasing number of scholars examine issues of coordinativeresource elements on supply chain operations For example[31] figures out that product and capital turnover reflected oninformation transmission constitute the basis for cooperativemode of agriculture product circulation Reference [32]presents a brand-new 5F research model that introducesbusiness flow and work flow as additional elements com-pared with traditional physical fund and information flowfor resource integration and consolidation Reference [33]addresses a collaborative supply chain system in which theflows of capital goods and information are optimized toenhance service innovation capabilities

Previous approaches applied in supply chain collabora-tion are diverse while mathematical models involving theconfirmatory factor analysis structural model formulationmixed integer programming and game theory methods [34ndash36] are proved to be applicable under specific assumptionsand limitations Meanwhile adoptions of servo theory ofsynergetic and system dynamics methods which belong tomechanical discipline initially have taken place dramati-cally in supply chain collaboration [37ndash39] Servo theoryillustrates that the resource and operation elements shouldwork externally and internally so that a well-regulated systemcould be accomplished [40] Additionally though the orderparameters occupy a relatively smaller rate compared with adiversity of the rest of the elements in the supply chain theymake the entire system stable in its transition fromdisorderedto ordered condition and the progress of low-ordered stateconverting to a high-ordered one [41ndash43] The principle ofself-organization of system dynamic [44ndash49] is employed inour work to present interrelations between order parametersand other resource elements through differential equationsformulation and calculation

As such our objective is to take a sound look at the inter-actions and connectedness among all influential factors of e-commerce and express delivery supply chain particularly the

Discrete Dynamics in Nature and Society 3

decisive role of order parameters in attaining well-regulatedcollaborations of the entire system Order parameters alongwith influential elements selections based on servo theoryare accomplished with reference to previous studies [50 51]Differential equations according to self-organization methodof system dynamic theory are established to demonstrateevolutionary process toward a state of cooperative systemstability

3 Collaboration Model

With the deepening of technological innovation competitionamong corporations is replaced with that among supplychains and supply chain management has become a popularagenda of many enterprises Among these the collaborationcapability is regarded as the core competence for accomplish-ing profit maximization and market share increase

In practical terms enterprises in a collaborative supplychain are required to cooperate with each other for win-win development by integrating and optimizing resourcesinvolving logistics fund information and commodity whichare of great concern in the e-commerce and express deliveryindustry Logistics conveying the process of procurementdistribution warehousing packaging and so forth is partof the transaction between supply chain enterprises andcustomers and ultimately reflects the value of goods andservice The flow of commodity in the trade process showsthe ownership transition of the goods from the e-commerceenterprise to customers while the capital flows are in anopposite direction Last but not least flow of informationreferring to the processes of information collection transmis-sion storage retrieval and analysis is the basis for regularfunctions of logistics and capital flow All in all the infor-mation flow provides accurate messages on the supply chainand the circulation of fund achieves value form transfer ofthe product while the flow and logistics complete commoditytransfer eventually Apparently the four main elements worktogether to have an impact on the collaborative ability andprofitability ability of the e-commerce and express deliveryindustry supply chain

Taking synergetics as the guiding ideology this sectionanalyzes the considering supply chain collaboration fromthe perspective of resource synergy within the channel forall membersrsquo consolidated goal of profit maximization andmarket share increase In this case two order parametersof profitability and interoperability are incurred in pre-dominating the process of resource integration and channelevolution

31 Problem Characteristics and Assumptions Profitabilityand collaboration capabilities along with the circulationof commodity fund information and logistics of the e-commerce and express delivery industry should be takentogether for accomplishing a collaborative supply chainAmong these profitability and collaboration capability areorder parameters that are key to system evolution whilethe rest of the resources involving logistics information

commodity and capital are also regarded as indispensablefactors for proper functioning119875 is considered as the profitability of e-commerce andexpress enterprises while 119862 represents the collaborationabilities Logistics fund information and commodity factorsare expressed as 119871 119865 119868 and 119861 respectively Thus theoperational systems of enterprises denoted as 119876 could beobtained

119876119864 = 119875119864 119862119864 119871119864 119865119864 119868119864 119861119864 119876119863 = 119875119863 119862119863 119871119863 119865119863 119868119863 119861119863

(1)

where the subscripts of 119864 and 119863 signify the e-commerceenterprise and express delivery enterprise separately

Logic algebramethod is connected tomodel calculationswhere ldquo0rdquo and ldquo1rdquo are applied for demonstrating relationsamong resource elements of the e-commerce and expressdelivery industry supply chain Specifically if there existinteractions between different features the result comes tobe ldquo1rdquo and otherwise the solution of ldquo0rdquo would be putforward Consequently matrix model illustrating relationsamong factors could be expressed as

119875119863 119862119863 119871119863 119865119863 119868119863 119861119863119875119864119862119864119871119864119865119864119868119864119861119864

[[[[[[[[[[[[[[

119886111198862111988631119886411198865111988661

119886121198862211988632119886421198865211988662

119886131198862311988633119886431198865311988663

119886141198862411988634119886441198865411988664

119886151198862511988635119886451198865511988665

119886161198862611988636119886461198865611988666

]]]]]]]]]]]]]]

(2)

where 119886119894119895 = 0 1 119894 119895 = 1 2 3 4 5 6 119886119894119895 = 0 when elementsunder observation are unrelatedwith each other while 119886119894119895 = 1could be obtained from a contrary result

32 Model Formulation In this part interactions of prof-itability and collaboration capability that act as order parame-ters and remaining influences regarding logistics fund infor-mation and commodity which are treated as a whole areinvestigated through a diverse of matrix model formulationsand calculations

Firstly we deem 1198721198771 as the interaction of profitabilitybetween e-commerce and express delivery enterprises while1198721198772 is interrelations of enterprisesrsquo collaboration capabilitiesand 1198721198773 is shown as self-feedback status of logistics fundinformation and commodity resources Combining the givenparameters and assumptions with (2) we have


1198721198771 =

[[[[[[[[[[[[

1 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198772 =

[[[[[[[[[[[[

0 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198773 =

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

]]]]]]]]]]]]

(3)

1198721198774 is defined as interactions between profitability and inter-operability of e-commerce and express delivery enterprisesthen 1198721198775 signifies the relations between profitability andother resource elements as a whole while 1198721198776 states theinfluences of collaboration ability and resource elementssimilarly Moreover 1198721198777 is introduced to show the internalrelations among factors of logistics fund information andcommodity resources

1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198775 =

[[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

1198721198776 =[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]

1198721198777 =[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 0 1 1 10 0 1 0 1 10 0 1 1 0 10 0 1 1 1 0

]]]]]]]]]]]

(4)

33 Model Calculation and Investigation According to thematrix models established in Section 32 relations of prof-itability and collaboration ability along with the rest of theresources in the e-commerce and express delivery industrysupply chain could be acknowledged by model computing

Proposition 1 119872119877119894times119872119877119894 = 119872119877119894 119894 isin 1 2 3 Self-feedback oforder parameters and other resource elements have no impacton system transaction that is interrelations within one singlefactor would not cause system evolution Mere collaborationsof profitability interoperability or resource elements with thechannel would not help to accomplish synergy across the entirechannel

Proposition 2 119872119877119894 times 119872119877119895 = 0 when 119894 119895 isin 1 2 3 and119894 = 119895 Analogously interactions would not occur betweenself-feedbacks of order parameters and resource elementsProfitability collaboration capability and other resources couldbe cooperated only if all factors are related with each other

Proposition 3 1198721198771 times 1198721198777 = 1198721198777 times 1198721198771 = 0 1198721198772 times1198721198777 = 1198721198777 times 1198721198772 = 0 shows that it is insufficient forthe order parameters and resources to exert influences on eachother when logistics fund information and commodity are notjointly considered In other words only collaborative operationsof resource elements could affect enterprisesrsquo profitability andinteroperability within the channel

Further calculations to analyze the impacts on resourceelements allocated by the order parameters are conducted wehave1198721198778 and1198721198779 shown as follows

1198721198778 = 1198721198771 times1198721198775 = 1198721198775 times1198721198773 = 1198721198775 times11987211987773

=[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]



=

[[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

(5)

Proposition 4 1198721198778 and 1198721198779 regarded as the impacts ofprofitability and interoperability put on resources respectivelyindicate that influences of order parameters self-feedback areexerted on resource elements and profitability and interoper-ability are affecting the circulation of logistics fund informa-tion and commodity Thus the order parameters in the supplychain are acting as dominant factors for the evolution of otherresources

Thefollowing considerations of1198721198771011987211987711 and11987211987712 aretaken into account to demonstrate the strong power of orderparameters influencing other resources

11987211987710 = 1198721198771 +1198721198774 =

[[[[[[[[[[[[

1 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987711 = 1198721198772 +1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987712 = 11987211987710 times1198721198775 = 11987211987711 times1198721198776

=

[[[[[[[[[[[[

0 0 1 1 1 10 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

= 1198721198778 +1198721198779

(6)

where 11987211987710 and 11987211987711 describe the interrelations within theparameters while11987211987712 is resolved as influences on resourceelements exerted by cooperative order parameters

Proposition 5 When there exist interactions between the twoparameters it would function better for promoting resourceelementsrsquo collaborative operations

Correspondingly resources elementsrsquo effects on prof-itability and collaboration capability are discussed expressedas11987211987713 and11987211987714 respectively


=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

(7)


=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

(8)

Proposition 6 Interrelations of order parameters andresources elements would have an impact on order parametersin their role of channel collaboration Reactions of logisticsfund information and commodity occur in the face ofprofitability and interoperability of the e-commerce andexpress delivery industry supply chain

11987211987715 is introduced to further analyze resource elementsrsquocounteractions on order parameters (10) and (11) acquiredaccordingly show enhanced influences exerted on orderparameters

11987211987715 = 1198721198773 +1198721198777 =

[[[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 1 1 10 0 1 1 1 10 0 1 1 1 10 0 1 1 1 1

]]]]]]]]]]]]]]

(9)


11987211987715 times1198721198775 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

= 411987211987713 (10)

11987211987715 times1198721198776 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

= 411987211987714 (11)

Proposition 7 Intensive effects of order parameters onresources reflected as 411987211987713 and 411987211987714 could be attainedthrough closely related resource elements11987211987715 Counteractionsof resources involving logistics fund information and com-modity would be enhanced to expedite the progress toward acooperative direction of the e-commerce and express deliverysupply chain of which profitability and collaboration capabilityare improved certainly

4 Evolutionary Model

41 Model Formulation The evolution of the supply chainfrom disordered to ordered state is associated with theinterrelations of channel members and factors within thesystem along with external stochastic fluctuations Mutualinfluences between resources along with system changescould be expressed by the following functions [35]

119889119883119889119905 = minus1198861119883 + 1198871 (119884 119885 119877) + 119865 (119905)119889119884119889119905 = minus1198862119884 + 1198872 (119883 119885 119877) + 119865 (119905)119889119885119889119905 = minus1198863119885 + 1198873 (119883 119884 119877) + 119865 (119905)119889119877119889119905 = minus1198864119877 + 1198874 (119883 119884 119885) + 119865 (119905)

(12)

where 119883 119884 119885 119877 represent resource elements and 1198861 11988621198863 1198864 reflect the factorsrsquo change rate which is affected byinterrelationship of resources expressed as 1198871 1198872 1198873 1198874 119865(119905)is regarded as the stochastic fluctuation which is the functionof time 119905

In the e-commerce and express delivery industry supplychain similarly the circulation of logistics fund informa-tion and commodity holding intricate relations with each

other are considered as main resource elements of the chan-nel for system progress so that we have the correspondingself-organizing dynamic equation shown as


(13)

where 119871 119865 119868 119861 represent resource elements regardinglogistics fund information and commodity respectivelyand the rest of the parameters share the same meaning withequations (12)

In the process of evolution from disordered to an orderedstatus order parameters play a decisive role in the structureformulation of the entire system The order parameters andother resource elements are depending on each other as wellas interacting with each other leading to the emerging ofa new order with self-organized procedure [52] Taking thedominant function of the order parameters into accountit is adequate to merely analyze the evolution law of theprofitability and interoperability for getting an idea of thesupply chainrsquos evolutionary mechanism

42 Model Analysis Define 119875 and 119862 regarded as the prof-itability and collaboration ability respectively as the orderparameters and 119878 signifies the resource elementsrsquo systemthat deems the remaining factors involving logistics fundinformation and commodity as a whole 119903 means the profitparameters 1205791 and 1205792 represent the damping coefficients of 119875and 119862 respectively 1205721 is the interaction force of profitabilityand interoperability 1205722 denotes the influence coefficientsof 119862 and 119875 and 1205723 indicates resource elementsrsquo impacton collaboration capability 120601 stands for the attenuationcoefficient of profitability and 1205731 and 1205732 are influentialfactors of resource elements affected by profitability andinteroperability separately while 1205733 states the self-feedbackparameter of resources and 1205734 is expressed as the combinedeffect of profitability and collaboration ability exerted onresource factors According to the self-organization principleof synergetics the evolutionary process of the e-commerceand express delivery supply chain immediately impacted bythe order parameters could be obtained as follows

119889119875119889119905 = (119903 minus 1205791) 119875 minus 1206011198752 + 1205721119875119862 + 119865 (119905)119889119862119889119905 = minus1205792119862 + 12057221198752 + 1198863119878119889119878119889119905 = 1205731119875 + 1205732119862 + 1205733119878 + 1205734119875119862

(14)

where the first two equations in the above equation set signifythe decisive role of the parameters in the system evolution


C

P

S

001

002

003

004

005

006

007

4035302520151050Time t

(a) The system is stable and 119891(119905) = 0

C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007

(b) The system is stable and 119891(119905) = 0001

Figure 1 Variation trends of parameters and resource elements under system stability

sequentially while the last one is introduced to illustrate theorder parametersrsquo impact on resource elements

During the progressive process of the e-commerce andexpress industry supply chain the system remains stableunder the conditions that the order parameters that isprofitability and interoperability stay unchanged and otherresources are also invariableThebalance point turns out to be(0 0 0) accordingly where 119889119875119889119905 = 0 119889119862119889119905 = 0 119889119878119889119905 = 0and the feature matrix accordingly could be attained as

119869 = [[[

119903 minus 1205791 minus 2120601119875 + 1205721119862 1205721119875 021205722119875 minus1205792 1205723

1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)

Then the feature matrix in the balance point could beexpressed as

119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

120582 minus (119903 minus 1205791) 0 00 120582 + 1205792 minus1205723

minus1205731 minus1205732 120582 minus 1205733

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)

Based on (16) the characteristic roots could be calculatedto be 1205821 = 119903minus1205791 and 12058223 = [1205733minus1205792plusmnradic(1205792 + 1205733)2 + 412057231205732]2The balance point of the system would be stable only if allcharacteristic roots are negative according to the principle ofdifferential equation

Proposition 8 (1) When 119903 lt 1205791 and 1205733 minus 1205792 +radic(1205792 + 1205733)2 + 412057231205732 lt 0 are satisfied the system turns outto be steady However the e-commerce and express industrysupply chain is under a low level of stable circumstance thatresources have not been fully integrated and cooperated leadingto incomplete collaboration which is lack of strength to bringabout channel transition

(2) Conversely when 119903 ge 1205791 or 1205733 minus 1205792 +radic(1205792 + 1205733)2 + 412057231205732 ge 0 occurs the supply chain would sufferfrom instability At this moment external random fluctuationwould take effect to make the system evolved withthe accompanied with the self-organization evolutionforming a more stable structure In particular therewould be a demarcation point arising if 119903 = 1205791 or1205733 minus 1205792 + radic(1205792 + 1205733)2 + 412057231205732 = 0 is fulfilled and thewhole channel stands ready to make a difference if affected byeven a minor change Additionally when the characteristicroots 120582 = 0 119903 gt 1205791 or 1205733 minus 1205792 + radic(1205792 + 1205733)2 + 412057231205732 gt 0should be attained and the system collaboration graduallyenhanced for system transition to accomplish sophisticatedorder

43 Numerical Analysis We concluded from Proposition 8that 119903 1205791 1205792 1205723 1205732 1205733 are of vital significance of attainingsystem stability Thence numerical analysis in this sectiontakes diverse values of the parameters under various condi-tions aiming at providing an intuitive idea of the results

431 System Stability Analysis Proposition 8 has illustratedthat under the condition of 119903 lt 1205791 and 1205733 minus 1205792 +radic(1205792 + 1205733)2 + 412057231205732 lt 0 the supply chain system staysunchanged with a relatively low level of ordered state Rele-vant parameters affecting the system stability are deemed asfollows 119903 = 01 1205791 = 03 1205792 = 04 1205721 = 12 1205722 = 091205723 = 08 120601 = 06 1205731 = 08 1205732 = 06 1205733 = minus2 1205734 =15 and corresponding simulation curves of profitabilitycollaboration capability and resource integration of the e-commerce and express delivery industry supply chain couldbe obtained by MATLAB application

Figure 1(a) reflects the factorsrsquo various conditions in theabsence of the stochastic fluctuation while Figure 1(b) shows


P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6

(a) The system is stable and 1205723 = minus2

C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5

(b) The system is stable and 1205723 = 15

Figure 2 Variation trends of parameters and resource elements under the influence of resource integration

that when 119891(119905) = 0001 Apparently whether the externalfluctuation exists or not the variation trends of all variableskeep inclining to zero generally when 119903 lt 1205791 and 1205733 minus 1205792+radic(1205792 + 1205733)2 + 412057231205732 lt 0 are satisfied Specifically eventhough a minor change externally could make the curvesdrift off the courses in Figure 1(b) eventually the solutionsgradually round toward zero with the increase of 119905 as timegoes on

Influences on collaboration ability exerted by resourceelements are given numerically as well Solution curves underdifferent values of 1205723 which indicates resource elementsrsquoimpact on collaboration capability are shown as Figures 2(a)and 2(b)

Figure 2(a) shows that under the situation that 1205723 =minus2 lt 0 when resource elements have a negative impacton interoperability it suggests inadequate resources integra-tion of the supply chain which result in poor profitabilityinevitability and the collaboration ability even suffers fromminus at the very beginning With the increase of 119905 theorder parameters have strengthened their power in leadingthe system positively so that the collaboration capabilitygradually tends to evolve and keep steady since then Onthe other hand when 1205723 rises from minus2 to 15 in Figure 2(b)interoperability is constantly under active guidance and isenhanced as a result

432 System Instability Analysis The e-commerce and exp-ress delivery industry supply chain demonstrates unstabilitywhen 119903 ge 1205791 or 1205733 minus 1205792 +radic(1205792 + 1205733)2 + 412057231205732 ge 0 is satisfiedTaking 119903 gt 1205791 into account firstly we have Figures 3(a) and3(b)

Figure 3(a) suggests a growth of profitability of the supplychain when the profit parameter is bigger than the dampingcoefficients that is 119903 gt 1205791 With time extending the prof-itability and interoperability acting as order parameters that

are dominant in the process of system evolutionwork activelyin guiding the whole channel toward a steady status alongwith the smoothly varied curves In Figure 3(b) howeverthere are tiny effects of external random fluctuation existingwhen 119891(119905) = 00001 and great change has taken placein all the three solution curves with the order parameterslosing their function in improving the coordination andcooperation of the supply chain and the entire system isat the brink of a disordered condition Hence alternativesother than profitability and collaboration capability shouldbe put forward to replace the original order parameters forthe efficient evolution of the e-commerce and express deliveryindustry supply chain

The process of system evolution under condition 1205733 minus1205792 + radic(1205792 + 1205733)2 + 412057231205732 gt 0 is discussed subsequently withparameter setting being presented as 119903 = 01 1205791 = 031205792 = 12 1205721 = 12 1205722 = 09 1205723 = 08 120601 = 06 1205731 = 081205732 = 2 1205733 = minus2 1205734 = 15

Figure 4(a) describes the tendency of system evolu-tion of all factors involving the profitability interoperabil-ity and other resource elements of the e-commerce andexpress delivery industry supply chain when 1205733 minus 1205792 +radic(1205792 + 1205733)2 + 412057231205732 gt 0 is fulfilled As 1205792 and 1205732 hold ahigh value so that the damping coefficient increases with thedecrease of the collaboration ability leading to a decrementof its influence on resource elements Figure 4(b) is drawnup when there exists external stochastic fluctuation thatis 119891(119905) = 00001 the order parameters have functionedactively in guiding the system progressed and it workseventually as all factors within the channel evolved withall solution curves going smoothly over time In additioncompared with Figure 4(a) values of the same points ofcurves in Figure 4(b) turn out to be higher which implies asystem transition with a higher level of ordered status of thesupply chain ultimately


p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001

Figure 3 Variation trends of parameters and resource elements under system instability (when 119903 gt 1205791)

P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001

Figure 4 Variation trends of parameters and resource elements under system instability (when 1205733 minus 1205792 + radic(1205792 + 1205733)2 + 412057231205732 gt 0)

5 Conclusions and Future Research

This paper investigates the e-commerce and express deliveryindustry supply chain based on servo theory of synergeticsSelf-organization principle of system dynamics method isintroduced to analyze the intra- and interrelations of allinfluential elements in system evolution Among these prof-itability and collaboration ability acting as order parametersaccording to servo theory have played a decisive role in thesystem evolution Interactions of order parameters and therest of the resource elements are discussed and the orderparametersrsquo function in channel transition is emphasizedFurthermore numerical analysis is employed to give anillustrative idea of the results Main concluding remarks aresummarized as follows

(1) The profitability and collaboration capability of thee-commerce and express delivery industry supply chain

work efficiently only if the rest of the resource elementsregarding logistics fund information and commodity arecoordinated Similarly the resource factors could affect theorder parameters on the premise of their own collaboration(Propositions 1 2 and 3)

(2) Order parameters of profitability and interoperabil-ity exert influences on resource elements which in turnhave reactions on order parameters as well While theorder parameters keep the dominant role in the supplychain enhanced logistics fund information and commodityresources have strong reflections on the profitability andcollaboration ability resulting in the regular operation andcooperative development of the entire channel (Propositions4 5 6 and 7)

(3) In the initial stage of e-commerce and express deliveryindustry collaborative operations the interoperability has


been so week to bring about supply chain transitions and thesystem stays in a relatively low level of stability and externalstochastic fluctuations have no impact on system balance(Proposition 8 Figure 1) With the enhancement of resourceintegration the collaboration capability transition occurswhen other resource elements present closer cooperative andcoordinated relations (Figure 2)

(4) External stochastic fluctuation works to generatestructural changes of the system leading to the disorderedstatus of the supply chain The profitability and collaborationcapability what is worse lose their advantage when acting asorder parameters to guide the system (Figure 3) While theinteroperability enhanced the supply chain is available for anevolution toward a higher ordered state under the influenceof external stochastic fluctuation (Proposition 8 Figure 4)

This paper focuses on the collaboration and evolutionof the e-commerce and express delivery industry supplychain Existing researches accounting intra- and interrela-tions among resources of a supply chain conveying twoor more industries are rare which makes our study apath-breaking attempt of e-commerce and express deliveryindustry resource elementsrsquo relations investigation throughtheoretical models We have indeed investigated horizontalcollaborations among various elements and proved that allresources are mutually interacted by combining the twoclosely related businesses in an entire cooperative supplychain

In practical it is imperative for e-commerce and expressdelivery enterprises to accomplish coordinated developmentas both industries are interdependent on each other Toillustrate 60 of express delivery business in China isderived from online shopping in 2013 and the proportion wasreported to increase to 80 in the following year Howeverwhile e-commerce stands out as an innovative industry thatfacilitate the interaction of logistics fund information andcommodity it comes to a halt due to the low efficiencyand unqualified technique level of express delivery as thecomplaint rates of express delay and unfavourable deliveryservice in 2015 were reported to have a growth of 128and 658 respectively In terms of current contradictionsbetween the e-commerce and express delivery industry thatcause the whole channel failing to collaborate efficientlywe conclude our work along with its results of significantreferences for e-commerce and express delivery enterprisesand industries with similar experiences in integrating andoptimizing resources

There is still room for further extensions and improve-ments for system evolution As our work mainly focuses onthe cooperation and coordination of e-commerce and expressdelivery enterprises within the supply chain external inter-ferences involving governmental policies market demandcustomer preferences and loyalty are somewhat overlookedwhich indeed mean a lot to the collaborative supply chainfor instance when governmental involvement via financialinstruments functions on either member of the supply chainthe relations and interaction of profitability and collabora-tion capability within the chain would be interfered as well asthe process of channel evolution Further more appropriateand comprehensive collaboration and evolutionarymodels of

e-commerce and express delivery industry supply chain areworth discussing in the future works

Competing Interests

The authors declare that they do not have any commercialor associative interests that represent a conflict of interests inconnection with this work

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (71172182 71302122 U1509220) theHumanities and Social Sciences Research Project of Min-istry of Education (14YJC630154) the National Natural Sci-ence Foundation of Ningbo (2014A610174) the ElectronicCommerce Research of Ningbo Dahongying University(1320151003) and the Soft Science Foundation of Ningbo(2016A10059)

References

[1] China Electronic Commerce Center Global Cross-Border Elec-tronic Commerce Report 2013 China Electronic CommerceCenter 2014 httpwww100eccndetailndash6181892html

[2] D Y Zhang E-Commerce Development Index of ChinaRanks Chinese Electronics News 2014 httpepapercenacomcncontent2014-0812content 342510htm

[3] H C Wang and H Q Sun ldquoRe-engineering of enterprise phys-ical distribution system under e-commerce environmentrdquo Chi-nese Journal of Management Science vol 8 pp 797ndash802 2000

[4] Y X Yang and G G Zhou ldquoA quantifying synergy modelfor closed loop supply chain network integrationrdquo Journal ofIndustrial Engineering and EngineeringManagement vol 26 no4 pp 112ndash118 2012

[5] K Xu Y Dong and Y Xia ldquolsquoToo littlersquo or lsquoToo latersquo the timingof supply chain demand collaborationrdquo European Journal ofOperational Research vol 241 no 2 pp 370ndash380 2015

[6] Y P Li and S H Ma ldquoResearch on multi-supplier horizontallysynchronization based on space-constrained construction sup-ply chainrdquo Chinese Journal of Management Science vol 21 no 1pp 111ndash117 2013

[7] Y S Wu ldquoEvolution model of low carbon supply chain collabo-rative operationrdquoOperations Research andManagement Sciencevol 23 no 2 pp 124ndash132 2014

[8] D Luzzini E Brandon-Jones A Brandon-Jones and G SpinaldquoFrom sustainability commitment to performance the role ofintra- and inter-firm collaborative capabilities in the upstreamsupply chainrdquo International Journal of Production Economicsvol 165 article no 6023 pp 51ndash63 2015

[9] H Akkermans P Bogerd and J Van Doremalen ldquoTravailtransparency and trust a case study of computer-supportedcollaborative supply chain planning in high-tech electronicsrdquoEuropean Journal of Operational Research vol 153 no 2 pp445ndash456 2004

[10] C J Corbett and P R Kleindorfer ldquoEnvironmental manage-ment and operations management introduction to the thirdspecial issuerdquo Production and Operations Management vol 12no 3 pp 287ndash289 2003

[11] L M Ascencio R G Gonzalez-Ramırez L A Bearzotti N RSmith and J F Camacho-Vallejo ldquoA collaborative supply chain


management system for amaritime port logistics chainrdquo Journalof Applied Research and Technology vol 12 no 3 pp 444ndash4582014

[12] U Ramanathan and A Gunasekaran ldquoSupply chain collabora-tion impact of success in long-termpartnershipsrdquo InternationalJournal of Production Economics vol 147 pp 252ndash259 2014

[13] H Yu and F P Chen ldquoOperation mode selection of automotiveinbound logistics based on supply chain collaborationrdquo SystemEngineering-Theory amp Practice vol 31 no 7 pp 1231ndash1239 2011

[14] C Eksoz S A Mansouri and M Bourlakis ldquoCollaborativeforecasting in the food supply chain a conceptual frameworkrdquoInternational Journal of Production Economics vol 158 pp 120ndash135 2014

[15] Z R David A Nait-Sidi-Moh D Durand and F JeromeldquoUsing Internet of Things Technologies for a collaborativesupply chain application to tracking of pallets and containersrdquoProcedia Computer Science vol 56 pp 550ndash557 2015

[16] E Rabinovich A M Knemeyer and C M Mayer ldquoWhy doInternet commerce firms incorporate logistics service providersin their distribution channels the role of transaction costs andnetwork strengthrdquo Journal of Operations Management vol 25no 3 pp 661ndash681 2007

[17] J P Qiu and E M Song ldquoInnovation of logistics managementin electronic businessrdquo China Soft Science vol 4 pp 107ndash1102002

[18] Z D Gnimpieba N S Ahmed and D Durand ldquoUsing Internetof things technologies for a collaborative supply chain applica-tion to tracking of pallets and containersrdquo Procedia ComputerScience vol 56 pp 550ndash557 2015

[19] C Araneda-Fuentes L J Lustosa and SMinner ldquoA contract forcoordinating capacity decisions in a business-to-business (B2B)supply chainrdquo International Journal of Production Economicsvol 165 article no 6035 pp 158ndash171 2015

[20] Q Lu and N Liu ldquoEffects of e-commerce channel entry ina two-echelon supply chain a comparative analysis of single-and dual-channel distribution systemsrdquo International Journal ofProduction Economics vol 165 pp 100ndash111 2015

[21] Y Y Yang Electronic commerce and the private express logisticswin-win development mode research [MS thesis] Dalian Mar-itime University 2012

[22] L W Bao Y C Huang Z J Ma J Zhang and Q C LvldquoOn the supply chain management supported by E-commerceservice platform for agreement based circulation of fruits andvegetablesrdquo Physics Procedia vol 33 pp 1957ndash1963 2012

[23] S Kurnia R J Karnali and M M Rahim ldquoA qualitative studyof business-to-business electronic commerce adoption withinthe Indonesian grocery industry a multi-theory perspectiverdquoInformation amp Management vol 52 no 4 pp 518ndash536 2015

[24] K N S Iyer R Germain and C Claycomb ldquoB2B e-commercesupply chain integration and performance a contingency fitperspective on the role of environmentrdquo Information amp Man-agement vol 46 no 6 pp 313ndash322 2009

[25] J W Zhong J N Wu and S Mei ldquoApplication capability of e-business theory development and empirical validationrdquo Journalof Management Science in China vol 13 no 12 pp 61ndash75 2010

[26] T J Feng andG H Gong ldquoResearch on electronic commercial-ized SCM of automobile industryrdquoChina Soft Science vol 2 pp105ndash107 2001

[27] C JWang ldquoManagingmaterial and information flows in supplychainrdquo Chinese Journal of Management Science vol 8 no 4 pp16ndash23 2000

[28] X DWang and T Zhou ldquoAbout interaction among informationflow logistics and fund flow of electronic businessrdquo Science ampTechnology Progress and Policy vol 4 pp 136ndash138 2002

[29] S B Xu ldquoThe theory of commoditymaterial flowrdquoManagementWorld vol 7 pp 1ndash9 2009

[30] S Z Bai andW LWang Research on Resource Flow of ComplexAdaptive System in Supply Chain Science Press Beijing China2009

[31] R H Deng X J Chen and P H Liu ldquoCollaborative modelsresearch on collaboration systems in farm-produce circulationrdquoSystem EngineeringmdashTheory amp Practice vol 7 pp 59ndash65 2006

[32] L Z Tong andCMGu ldquoResearch on 5Fmodel in supply chainmanagementrdquoManagement World vol 6 pp 184ndash185 2013

[33] Q Xu ldquoThe integrative and collaborative services innovationmanagement of supply chain logistics financerdquoChinese Businessand Market vol 8 pp 29ndash32 2009

[34] A Soylu C Oruc M Turkay K Fujita and T AsakuraldquoSynergy analysis of collaborative supply chain management inenergy systems using multi-period MILPrdquo European Journal ofOperational Research vol 174 no 1 pp 387ndash403 2006

[35] X-W Huang and M-S He ldquoSelf-organization evolution modelof supply chain resources synergyrdquo Journal of Nanjing Universityof Science and Technology vol 34 no 1 pp 36ndash39 2010

[36] M Cao and Q Zhang ldquoSupply chain collaboration impacton collaborative advantage and firm performancerdquo Journal ofOperations Management vol 29 no 3 pp 163ndash180 2011

[37] H Haken Synergetic The Mysteries of Nature vol 97 ShanghaiTranslation Publishing House Shanghai China 2001

[38] H Haken ldquoSynergetics of brain functionrdquo International Journalof Psychophysiology vol 60 no 2 pp 110ndash124 2006

[39] M M Huang ldquoEvolutionary game analysis of cooperationmechanism for collaborative product development in supplychainrdquo Chinese Journal of Management Science vol 18 no 6pp 155ndash162 2010

[40] M Nakano ldquoCollaborative forecasting and planning in supplychains the impact on performance in Japanese manufacturersrdquoInternational Journal of Physical Distribution amp Logistics Man-agement vol 39 no 2 pp 84ndash105 2009

[41] Z T Fan ldquoAnalysis of the internal coordination process ofthe formation of core competencerdquo Science and TechnologyManagement Research vol 3 pp 25ndash28 2000

[42] V B Kreng and F-T Chen ldquoThe benefits of a cross-dockingdelivery strategy a supply chain collaboration approachrdquo Pro-duction Planning amp Control vol 19 no 3 pp 229ndash241 2008

[43] B K Bahinipati A Kanda and S G Deshmukh ldquoHorizontalcollaboration in semiconductor manufacturing industry supplychain an evaluation of collaboration intensity indexrdquo Comput-ers amp Industrial Engineering vol 57 no 3 pp 880ndash895 2009

[44] H Haken Information and Self-Organization A MacroscopicApproach to Complex System vol 40 of Springer Series inSynergetics Springer New York NY USA 1988

[45] T Wu Self-Organization Methodology Research Tsinghua Uni-versity Press Beijing China 2001

[46] H C Co and F Barro ldquoStakeholder theory and dynamics insupply chain collaborationrdquo International Journal of Operationsamp Production Management vol 29 no 6 pp 591ndash611 2009

[47] M Cedillo-Campos and C Sanchez-Ramırez ldquoDynamic self-assessment of supply chains performance an emerging marketapproachrdquo Journal of Applied Research and Technology vol 11no 3 pp 338ndash347 2013


[48] J Wilson J Hill M Kersula et al ldquoCostly information and theevolution of self-organization in a small complex economyrdquoJournal of Economic Behavior amp Organization vol 90 pp S76ndashS93 2013

[49] L Biggiero and P P Angelini ldquoHunting scale-free propertiesin RampD collaboration networks self-organization power-lawand policy issues in the European aerospace research areardquoTechnological Forecasting and Social Change vol 94 no 5 pp21ndash43 2015

[50] Q R Xu and Z X Xie ldquoStudy of firmrsquos innovation synergy andthe evolvement modelrdquo Studies In Science of Science vol 22 no3 pp 327ndash332 2004

[51] P J Daugherty R G Richey S E Genchev and H ChenldquoReverse logistics superior performance through focusedresource commitments to information technologyrdquoTransporta-tion Research Part E Logistics and Transportation Review vol41 no 2 pp 77ndash92 2005

[52] H Haken ldquoSynergetics of brain functionrdquo International Journalof Psycho Physiology vol 60 no 2 pp 110ndash124 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


model along with its evolutionary process of the so-called ldquoe-commerce and express industry supply chainrdquo in this papercomes into notice

In this paper a supply chain considering e-commerceand express delivery enterprises is taken into account Servotheory of synergetics and self-organizationmethod of systemdynamics theory are employed to investigate the intra-and interrelations among influential elements impactingthe collaborative undertakings of e-commerce and expressdelivery industry across the supply chain Besides relevantnumerical analyses emerged to corroborate and supplementthe theoretical exploration

2 Literature Review

To our knowledge existing literatures mostly concern prac-tical issues on supply chain collaborative management suchas the significance of synergy among supply chain members[4 5] the advantage of resource integration and interaction ofchannelmembers [6ndash8] strategies or incentives for successfulcooperation and coordination in the system [9ndash12] andmodeselections and practices of joint operations [13ndash15] Amongthese considerable attention has been paid to collaborativesupply chain of single industry while relevant researchesconveying two or more industries are few and channelcooperation under e-commerce environment has not beenmentioned yet

Since the conceptually prospective ideas on supply chaincollaboration under e-commerce background have beenproposed relating studies are believed to be highly significantin promoting management innovation of logistics systemsfor further breakthroughs of e-commerce development [16ndash19] Channel adaption and member behaviors of a supplychain consisting of the manufacturer and retailer under e-commerce environment are considered in [20] Reference[21] figures out that win-win development of e-commerceandprivate courier is becoming tendencywith correspondingrecommendations provided Reference [22] declares thatsupply chainmanagement of circulation fruits and vegetablescould be better implemented with the e-commerce ser-vice platform equipped with advanced IT applications B2B(Business-to-Business) e-commerce technology adoption oforganizations within the grocery industry supply chain isexamined in [23] Reference [24] analyzes the integrationcapabilities of B2B e-commerce from the perspective ofcapital and market operations and production and demanduncertainty in the supply chain as an influential factor Ref-erence [25] explores the role of e-commerce environmentalmanagement in improving support abilities of collaborativeoperations through confirmatory factor analysis Reference[26] investigates the relations between supply chain man-agement and e-commerce operation in automobile industryto illustrate the feasibility and necessity of managing theindustrial chain taking advantage of e-commerce superiorityIn sum there are two prevailing topics of supply chaincollaboration under e-commerce platform (i) supply chainmanagement innovations in the face of challenges and oppor-tunities brought by the booming e-commerce industry and(ii) collaborative e-commerce supply chain management to

attain a win-win status Both research orientations howevertend to overlook a potentially crucial role of influential factorswithin the channel that virtually should not be ignored inthe collaboration and cooperation across the entire supplychain In fact profitability and interoperability along with thecirculation of commodity fund information and logistics areof vital importance in supply chain operations In this paperwe further investigate supply chain coordination along withits evolutionary process of e-commerce and express deliveryindustry considering horizontal collaborations among vari-ous resource elements that combine the two closely relatedbusinesses in an entire cooperative supply chain

As is known to all that the circulation of commoditylogistics information and fund is the basis and premisefor e-commerce initiatives researches on their connotationsand interrelations have been prolific [27ndash29] Besides itis insufficient to merely cooperate one resource elementbetween two nodes vertically for supply chain collaborationhorizontal collaboration that various factors are jointly con-sidered should be emphasized even more That is to saythe entire synergy could be attained only if the cooperativeinteractions are fulfilled among all influences both longitu-dinally and transversely [30] In recent years naturally anincreasing number of scholars examine issues of coordinativeresource elements on supply chain operations For example[31] figures out that product and capital turnover reflected oninformation transmission constitute the basis for cooperativemode of agriculture product circulation Reference [32]presents a brand-new 5F research model that introducesbusiness flow and work flow as additional elements com-pared with traditional physical fund and information flowfor resource integration and consolidation Reference [33]addresses a collaborative supply chain system in which theflows of capital goods and information are optimized toenhance service innovation capabilities

Previous approaches applied in supply chain collabora-tion are diverse while mathematical models involving theconfirmatory factor analysis structural model formulationmixed integer programming and game theory methods [34ndash36] are proved to be applicable under specific assumptionsand limitations Meanwhile adoptions of servo theory ofsynergetic and system dynamics methods which belong tomechanical discipline initially have taken place dramati-cally in supply chain collaboration [37ndash39] Servo theoryillustrates that the resource and operation elements shouldwork externally and internally so that a well-regulated systemcould be accomplished [40] Additionally though the orderparameters occupy a relatively smaller rate compared with adiversity of the rest of the elements in the supply chain theymake the entire system stable in its transition fromdisorderedto ordered condition and the progress of low-ordered stateconverting to a high-ordered one [41ndash43] The principle ofself-organization of system dynamic [44ndash49] is employed inour work to present interrelations between order parametersand other resource elements through differential equationsformulation and calculation

As such our objective is to take a sound look at the inter-actions and connectedness among all influential factors of e-commerce and express delivery supply chain particularly the









119876119864 = 119875119864 119862119864 119871119864 119865119864 119868119864 119861119864 119876119863 = 119875119863 119862119863 119871119863 119865119863 119868119863 119861119863

(1)



119875119863 119862119863 119871119863 119865119863 119868119863 119861119863119875119864119862119864119871119864119865119864119868119864119861119864

[[[[[[[[[[[[[[

119886111198862111988631119886411198865111988661

119886121198862211988632119886421198865211988662

119886131198862311988633119886431198865311988663

119886141198862411988634119886441198865411988664

119886151198862511988635119886451198865511988665

119886161198862611988636119886461198865611988666

]]]]]]]]]]]]]]

(2)





1198721198771 =

[[[[[[[[[[[[

1 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198772 =

[[[[[[[[[[[[

0 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198773 =

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

]]]]]]]]]]]]

(3)


1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198775 =

[[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

1198721198776 =[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]

1198721198777 =[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 0 1 1 10 0 1 0 1 10 0 1 1 0 10 0 1 1 1 0

]]]]]]]]]]]

(4)







=[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]



=

[[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

(5)



11987211987710 = 1198721198771 +1198721198774 =

[[[[[[[[[[[[

1 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987711 = 1198721198772 +1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987712 = 11987211987710 times1198721198775 = 11987211987711 times1198721198776

=

[[[[[[[[[[[[

0 0 1 1 1 10 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

= 1198721198778 +1198721198779

(6)





=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

(7)


=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

(8)



11987211987715 = 1198721198773 +1198721198777 =

[[[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 1 1 10 0 1 1 1 10 0 1 1 1 10 0 1 1 1 1

]]]]]]]]]]]]]]

(9)


11987211987715 times1198721198775 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

= 411987211987713 (10)

11987211987715 times1198721198776 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

= 411987211987714 (11)





(12)





(13)





(14)



C

P

S

001

002

003

004

005

006

007

4035302520151050Time t


C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007





119869 = [[[


1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)


119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816



100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)








P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra

















119876119864 = 119875119864 119862119864 119871119864 119865119864 119868119864 119861119864 119876119863 = 119875119863 119862119863 119871119863 119865119863 119868119863 119861119863

(1)



119875119863 119862119863 119871119863 119865119863 119868119863 119861119863119875119864119862119864119871119864119865119864119868119864119861119864

[[[[[[[[[[[[[[

119886111198862111988631119886411198865111988661

119886121198862211988632119886421198865211988662

119886131198862311988633119886431198865311988663

119886141198862411988634119886441198865411988664

119886151198862511988635119886451198865511988665

119886161198862611988636119886461198865611988666

]]]]]]]]]]]]]]

(2)





1198721198771 =

[[[[[[[[[[[[

1 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198772 =

[[[[[[[[[[[[

0 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198773 =

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

]]]]]]]]]]]]

(3)


1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198775 =

[[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

1198721198776 =[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]

1198721198777 =[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 0 1 1 10 0 1 0 1 10 0 1 1 0 10 0 1 1 1 0

]]]]]]]]]]]

(4)







=[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]



=

[[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

(5)



11987211987710 = 1198721198771 +1198721198774 =

[[[[[[[[[[[[

1 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987711 = 1198721198772 +1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987712 = 11987211987710 times1198721198775 = 11987211987711 times1198721198776

=

[[[[[[[[[[[[

0 0 1 1 1 10 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

= 1198721198778 +1198721198779

(6)





=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

(7)


=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

(8)



11987211987715 = 1198721198773 +1198721198777 =

[[[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 1 1 10 0 1 1 1 10 0 1 1 1 10 0 1 1 1 1

]]]]]]]]]]]]]]

(9)


11987211987715 times1198721198775 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

= 411987211987713 (10)

11987211987715 times1198721198776 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

= 411987211987714 (11)





(12)





(13)





(14)



C

P

S

001

002

003

004

005

006

007

4035302520151050Time t


C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007





119869 = [[[


1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)


119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816



100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)








P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1198721198771 =

[[[[[[[[[[[[

1 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198772 =

[[[[[[[[[[[[

0 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198773 =

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 0 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1

]]]]]]]]]]]]

(3)


1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

1198721198775 =

[[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

1198721198776 =[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]

1198721198777 =[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 0 1 1 10 0 1 0 1 10 0 1 1 0 10 0 1 1 1 0

]]]]]]]]]]]

(4)







=[[[[[[[[[[[

0 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]



=

[[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

(5)



11987211987710 = 1198721198771 +1198721198774 =

[[[[[[[[[[[[

1 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987711 = 1198721198772 +1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987712 = 11987211987710 times1198721198775 = 11987211987711 times1198721198776

=

[[[[[[[[[[[[

0 0 1 1 1 10 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

= 1198721198778 +1198721198779

(6)





=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

(7)


=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

(8)



11987211987715 = 1198721198773 +1198721198777 =

[[[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 1 1 10 0 1 1 1 10 0 1 1 1 10 0 1 1 1 1

]]]]]]]]]]]]]]

(9)


11987211987715 times1198721198775 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

= 411987211987713 (10)

11987211987715 times1198721198776 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

= 411987211987714 (11)





(12)





(13)





(14)



C

P

S

001

002

003

004

005

006

007

4035302520151050Time t


C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007





119869 = [[[


1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)


119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816



100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)








P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











=

[[[[[[[[[[[[

0 0 0 0 0 00 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

(5)



11987211987710 = 1198721198771 +1198721198774 =

[[[[[[[[[[[[

1 1 0 0 0 01 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987711 = 1198721198772 +1198721198774 =

[[[[[[[[[[[[

0 1 0 0 0 01 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

11987211987712 = 11987211987710 times1198721198775 = 11987211987711 times1198721198776

=

[[[[[[[[[[[[

0 0 1 1 1 10 0 1 1 1 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 0

]]]]]]]]]]]]

= 1198721198778 +1198721198779

(6)





=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

(7)


=

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

(8)



11987211987715 = 1198721198773 +1198721198777 =

[[[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 0 1 1 1 10 0 1 1 1 10 0 1 1 1 10 0 1 1 1 1

]]]]]]]]]]]]]]

(9)


11987211987715 times1198721198775 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

= 411987211987713 (10)

11987211987715 times1198721198776 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

= 411987211987714 (11)





(12)





(13)





(14)



C

P

S

001

002

003

004

005

006

007

4035302520151050Time t


C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007





119869 = [[[


1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)


119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816



100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)








P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










11987211987715 times1198721198775 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 01 0 0 0 0 0

]]]]]]]]]]]]

= 411987211987713 (10)

11987211987715 times1198721198776 = 4 times

[[[[[[[[[[[[

0 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 00 1 0 0 0 0

]]]]]]]]]]]]

= 411987211987714 (11)





(12)





(13)





(14)



C

P

S

001

002

003

004

005

006

007

4035302520151050Time t


C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007





119869 = [[[


1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)


119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816



100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)








P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










C

P

S

001

002

003

004

005

006

007

4035302520151050Time t


C

P

S

5 10 15 20 25 30 35 400Time t

001

002

003

004

005

006

007





119869 = [[[


1205731 + 1205734119862 1205732 + 1205734119875 1205733]]] (15)


119860 =100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816



100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816= 0 (16)








P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










P

S

C

5 10 15 20 25 30 35 400Time t

times10minus5

minus4

minus2

0

2

4

6


C

P

S

5 10 15 20 25 30 35 400Time t

1

2

3

4

5

6times10minus5












p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










p

C

S

5 10 15 20 25 30 35 400Time t

002

004

006

008

01

012

014

(a) 119891(119905) = 0

p

C

S

5 10 15 20 25 30 35 400Time t

005

01

015

02

025

03

035

04

045

(b) 119891(119905) = 00001


P

C

S

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5times10minus3

(a) 119891(119905) = 0

P

C

S

times10minus3

5 10 15 20 25 30 35 400Time t

05

1

15

2

25

3

35

4

45

5

(b) 119891(119905) = 00001















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Competing Interests


Acknowledgments


References































































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




























































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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