• 沒有找到結果。

A novel architecture for dense wavelength-division multiplexing/subcarrier multiplexing networks

N/A
N/A
Protected

Academic year: 2021

Share "A novel architecture for dense wavelength-division multiplexing/subcarrier multiplexing networks"

Copied!
6
0
0

加載中.... (立即查看全文)

全文

(1)

REFERENCES

1. K.K. Mei, One of the differential equations of thin wire struc-tures, 1999 Asia Pacific Microwave Conf, Dec. 1999, vol. 2, pp. 393᎐396.

2. Y.W. Liu, K.K. Mei, and J.S. Hong, Radiation extraction for transmission-line interconnects, 2001 IEEE AP-S Int Symp and USNCrURSI Nat Radio Sci Meeting, session 29, Diverse wave-guiding structures.

3. K.S. Yee, Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans

Ž .

Antennas Propagat AP-14 1966 , 302᎐307.

4. J.X. Zheng, IE3D 6.0 software, Zeland Software, Inc., 48890 Milmont Dr., 105D, Fremont, CA 94538.

5. Y. Qian, S. Iwata, and E. Yamashita, Characterization of the perturbation effect of a probe head using the FD-TD method,

Ž .

IEEE Microwave Guided Wave Lett 4 1994 , 317᎐319. 6. A. Zhao and V. Raisanen, Application of a simple and efficient

source excitation technique to the FDTD analysis of waveguide and microstrip circuits, IEEE Trans Microwave Theory Tech 44 Ž1996 , 1535. ᎐1539.

7. G. Mur, Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field

equa-Ž .

tions, IEEE Trans Electromag Compat EMC-23 1981 , 77᎐382. 8. K.K. Mei and J. Fang, SuperabsorptionᎏA method to improve absorbing boundary conditions, IEEE Trans Antennas Propagat

Ž .

43 1995 , 1460᎐1463.

9. F. Giannini, G. Bartolucci, and M. Ruggieri, Equivalent circuit models for computer aided design of microstrip rectangular

Ž .

structures, IEEE Trans Microwave Theory Tech 40 1992 . 10. C.J. Railton and T. Rozzi, The rigorous analysis of cascaded step

discontinuities in microstrip, IEEE Trans Microwave Theory

Ž .

Tech 36 1988 .

11. J.C. Rautio, An experimental investigation of the microstrip step

Ž .

discontinuity, IEEE Trans Microwave Theory Tech 37 1989 . 12. X.L. Zhang and K.K. Mei, Time-domain finite-difference

ap-proach to the calculation of the frequency-dependent character-istics of microstrip discontinuities, IEEE Trans Microwave

The-Ž .

ory Tech 36 1988 , 1775᎐1787. 䊚 2001 John Wiley & Sons, Inc.

A NOVEL ARCHITECTURE FOR

DENSE WAVELENGTH-DIVISION

MULTIPLEXING ///// SUBCARRIER

MULTIPLEXING NETWORKS

Wen-Piao Lin,1Ming-Seng Kao,2and Sien Chi1 1Institute of Electro-Optical Engineering

National Chiao Tung University Hsin Chu 30056, Taiwan, R.O.C. 2

Department of Communication Engineering National Chiao Tung University

Hsin Chu 30056, Taiwan, R.O.C.

Recei¨ed 2 July 2001

ABSTRACT: We propose and demonstrate a new sur¨i¨able dense (

wa¨elength-di¨ision multiplexingrsubcarrier multiplexing DWDMr

) ( )

SCM network based on the star᎐bus᎐ring architecture SBRA . This architecture ensures an OBI-free optical network, and can ser¨e tremen-dous subscribers. In addition, remote nodes and bidirectional wa¨elength

( )

addrdrop multiplexers B᎐WADMs are designed by using simple opti-cal switches to reconfigure the network under link failure. We further set up an experimental network to demonstrate the feasibility of the proposed architecture.䊚 2001 John Wiley & Sons, Inc. Microwave Opt Technol

Lett 32: 51᎐56, 2002.

Key words: dense wa¨elength-di¨ision multiplexingrsubscarrier

multi-( ) ( )

plexing DWDMrSCM ; star᎐bus᎐ring architecture SBRA ; optical

( )

beat interference OBI ; bidirectional wa¨elength addrdrop multiplexing

(B᎐WADM ; cascade addrdrop transcei) ¨er CAT( ) DOI 10.1002r mop.10089

I. INTRODUCTION

Owing to the inherent flexibility in simultaneously carrying analog and digital messages, as well as the capability to finely use the available modulation bandwidth of laser sources, the

Ž .

subcarrier multiplexing SCM based on a passive optical

Ž .

network PON is a promising approach for future subscriber networks to accommodate advanced broadband services. A critical limitation imposed on the SCM network is the optical

Ž .

beat interference OBI problem, which would limit the

num-w x

ber of subscribers served by the network 1᎐3 . The authors of this paper had proposed a modified star᎐ring architecture ŽMSRA by adopting a cascade add. rdrop transceiver CATŽ . structure in the lower level rings to offer an OBI-free SCM

w x

network 4 . However, the MSRA could not provide abundant bandwidth to serve the dramatic rise in the applications of

Ž .

high-speed multimedia, video on demand VOD , and future advanced services. Therefore, a new broadband architecture is desirable.

The DWDMrSCM network is currently being developed to transmit video as well as advanced Internet applications to

w x

serve users needing a large channel capacity 5 . Here, we propose a novel DWDMrSCM network, which employs a properly designed three-level star᎐bus᎐ring architecture ŽSBRA having a star subnet on the upper level, several bus. subnets on the middle level, along with many ring subnets on the lower level. The star subnet establishes a high-capacity infrastructure for the network, whereas the bus subnets offer broadband channels for multiwavelength signals to and from the lower level ring subnets. In the ring subnets, we adopt the

Ž .

cascade addrdrop transceiver CAT structure at each optical

Ž .

network unit ONU to overcome the OBI problem. The use of DWDMrSCM technology combined with all-optical

wave-Ž .

length addrdrop multiplexing WADM is able to accommo-w x date future growth in broadband subscriber networks 6 .

Since the network accommodates a large number of sub-scribers, any service outage due to link failure will translate into tremendous loss for service providers. Therefore, the design of a self-healing function to recover from failure in

w x

real time is very important 7 . In this paper, we propose a simple surviving scheme based on two protected stages in the SBRA. Consequently, the SBRA is a reliable broadband network architecture.

II. THE DWDM ///// SCM STAR–BUS–RING ARCHITECTURE Figure 1 shows the configuration of the SBRA based on a DWDMrSCM network. A star subnet on the upper level

Ž . Ž .

connects many remote nodes RNs to a central office CO using two fibers for each link. This provides a high-capacity optical path between the CO and each RN. A dual-fiber bus connects two neighboring RNs. Many ring subnets are at-tached to the bus via bidirectional wavelength addrdrop

Ž .

multiplexers B᎐WADM , with each ring subnet serving a number of ONUs.

In the star subnet, we design two distinct wavelength

 4  4

groups ␭ , ␭ , . . . , ␭A1 A 2 A n and ␭ , ␭ , . . . , ␭B1 B 2 B n in the al-ternate links. Each group consists of many ITU-T standard wavelength signals, being used in both upstream and down-stream directions. This arrangement will ease the network reconfiguration under link failure. The function of the RN is to properly transfer multiwavelength signals between the CO

(2)

Figure 1 DWDMrSCM star᎐bus᎐ring architecture

and the corresponding fiber bus. Downstream signals are delivered from the CO to the fiber bus via the RN, and upstream signals from the fiber bus are forwarded to the CO through the RN as well. The RN can perform a self-healing function if link failure occurs in the star or bus subnet.

The two fibers in the fiber bus carry downstream and upstream multiwavelength signals, respectively. Downstream signals are dropped to the lower level ring subnets via B᎐WADM. Each B᎐WADM drops a specific wavelength

Ž .

signal e.g., ␭A1 from the downstream wavelength group Že.g.,␭ . This downstream wavelength signal contains manyA4. SCM signals to serve those ONUs belonging to the ring subnet of interest. A special cascade addrdrop transceiver ŽCAT is employed at each ONU to drop the desired down-. stream SCM signal and to add the local upstream SCM signal as well. The use of a CAT structure can eliminate the OBI

problem, and compensate the branch loss at each ONU. The last ONU in the ring subnet transmits the upstream signal

Ž .

with a specific wavelength e.g.,␭B1 in the other wavelength  4

group ␭ , being carried by another fiber of the fiber bus.B The fiber bus gathers all upstream wavelength signals coming from the attached ring subnets, and then forwards them to the CO via the corresponding RN.

( )

A. The Bidirectional WADM B᎐WADM . In order to ensure

excellent reliability, a B᎐WADM making use of simple opti-cal components is designed to alter the signal flow if the corresponding fiber bus is cut. We employ the multilayer dielectric interference filter to implement the B᎐WADM due to its bidirectional property. This filter can be designed to add or drop a specific wavelength signal within a group of multiwavelength signals.

Ž . Ž . Ž .

Figure 2 Configurations of a bidirectional wavelength drop multiplexing B᎐WDM , b bidirectional wavelength add multiplexing ŽB᎐WAM.

(3)

Figure 3 Block diagram of bidirectional wavelength addrdrop

mul-Ž .

tiplexing B᎐WADM

Ž .

Figure 2 a demonstrates a bidirectional wavelength drop

Ž . Ž .

multiplexing B᎐WDM via a 2 = 1 optical switch OS . It can drop a specific wavelength ␭B j from a group of

wave- 4 Ž .

lengths ␭B in both directions. Figure 2 b demonstrates a

Ž .

bidirectional wavelength add multiplexing B᎐WAM , which can add a specific wavelength ␭Ak within a group of

wave- 4

lengths ␭ . Finally, we design the B᎐WADM to be used inA the SBRA, as shown in Figure 3. It is composed of a B᎐WAM and a B᎐WDM, which can addrdrop a specific wavelength signal in the dual-fiber bus in both directions by controlling the states of optical switches. As will be clear later, the B᎐WADM will alter signal flow in the fiber bus if link failure occurs.

( )

B. The Remote Node RN . Figure 4 shows the configuration

of an RN under normal conditions. Each RN contains four 1= 2 optical switches and two 1 = 2 couplers. Refer to Figure 1 to better understand the signal flow. The switch states are arranged such that downstream wavelength signals coming from the CO are forwarded through a 1= 2 coupler,

Ž .

Figure 4 Configuration of remote node RN under normal condi-tion

Ž .

and then sent to a fiber in the fiber bus Fdr located on the right of the RN. On the other hand, upstream wavelength signals coming from the bus located on the left of the RN ŽFul. are directed to a 1= 2 coupler, and then sent to the star link. The switch states of the RN can be modified to redirect signal flow in case a fiber cut occurs in the star or bus subnets.

( )

C. The Cascade Addr Drop Transcei¨er CAT Structure. As

shown in Figure 5, a ring subnet drops a specific wavelength

Ž .

signal e.g.,␭A j from the downstream wavelength group, and

Ž .

we adopt the cascade addrdrop transceiver CAT structure at each ONU. The CAT consists of a p-i-n detector, an electrical addrdrop module, and a laser transmitter. In the

Ž .

first ONU ONU , the downstream SCM signal coming from1 the CO is first converted to electrical by the p-i-n module. This signal is forwarded to an addrdrop module in which the

Ž .

upstream signal S1 is added and the message destined to

Ž . Ž .

the ONU1 C1 is dropped. A Fabry᎐Perot FP laser

trans-Ž .

(4)

Ž .

Figure 6 a Reconfiguration of RN under link failure in the star. Ž .b Virtual connection of RN and the configuration of B᎐WADM under link failure in the star

mits the output of the addrdrop module, which contains the downstream signal from the CO and the upstream signal of the ONU , to the next ONU. The same operation is per-1 formed in the following ONUs in a cascade manner. Finally,

Ž .

the last ONU ONUk converts the upstream signals into a

Ž .

specific wavelength signal ␭ , and forwards it to theB j B᎐WADM. Thus, all downstream signals are received by destined ONUs, and all upstream signals can be transferred to the B᎐WADM and then to the CO via the corresponding RN. Only an ITU-T standard DFB laser transmitter should be used in the last ONU.

D. Self-Healing Functions. The SBRA can offer survivable

functions under link failure by reconfiguring the RN and the B᎐WADM. If a fiber cut occurs in a star link, the switch states of the corresponding RN are modified as shown in

Ž .

Figure 6 a ; thereby, the virtual configuration of the network Ž .

is as shown in Figure 6 b . In this case, traffic originally Ž

supported by the failed link e.g., uprdownstream wave- 4.

lengths ␭B is managed by two neighboring RNs. Note that the assignment of distinct wavelength groups for alternate links in the star subnet eases reconfiguration without affect-ing the signal flow in the bus and raffect-ing subnets. If a fiber cut occurs in the bus subnet, we can modify signal flow by reconfiguring the corresponding B᎐WADM and RNs as shown in Figure 7. In this case, uprdownstream signals in the ring subnets are redirected to avoid the breakpoint, and the switch states of RNs are rearranged such that up rdown-stream signals are adequately transferred between the CO and those ring subnets.

III. EXPERIMENTAL SETUP AND RESULTS

To demonstrate the feasibility of the SBRA, we set up an experimental network as shown in Figure 8. In the downstream direction, four ITU-T standard DFB lasers Ž␭ , ␭ , ␭ , ␭ with center wavelengths of 1547.72, 1549.32,1 2 3 4. 1550.92, and 1552.52 nm are directly modulated with

subcar-Figure 7 Reconfiguration of RN and B᎐WADM under bus link failure

rier multiplexed signals covering the 550᎐1000 MHz band. These four optical signals are multiplexed by a DWDM multiplexer, and sent to the RN through a 2.2 km single-mode fiber. The four signals are forwarded to a dual-fiber bus via

Ž .

the RN, and the 1549.32 nm ␭ as well as the 1550.92 nm2 Ž␭ signals are dropped by B᎐WADM to two ring subnets,3. respectively. There are four ONUs in each ring subnet, which can receive desired downstream signals and transmit up-stream signals as well.

In the upstream direction, the signals generated at the ring subnet are linked to the CO via B᎐WADM and the RN. Two ITU-T standard DFB lasers with center wavelengths of

Ž . Ž .

1554.12 nm ␭ and 1558.92 nm ␭ are used in the last5 8 ONU of two ring subnets, respectively. Low-cost 1.5␮m FP lasers are used in the other ONUs, being directly modulated by several 3 Mbitrs FSK subcarrier signals. The upstream FSK subcarrier channel spacing is 6 MHz, ranging from 80 to 500 MHz. The 3 Mbitrs data signal can be converted into an FSK signal through a VCO module, and then directly modu-lates the laser. In this work, the upstream subcarrier channels were chosen from 94 to 136 MHz, and the 106 MHz channel ŽONU3 was monitored. In the downstream direction, the. subcarrier channels were chosen from 550 to 562 MHz, and the 556 MHz subcarrier channel was monitored. The total optical loss through the 2.2 km single-mode fiber is 0.43 dB at 1549.32 nm. The end-to-end optical loss of the system of the downstream 1549.32 nm signal is 6.53 dB, and it is 7.33 dB for the upstream 1554.12 nm signal.

Figure 9 shows the measured BER of the 556 MHz downstream channel versus the received optical power at the

(5)

Figure 9 Measured BER curves for downstream transmission at

ONU1.' with the 556 MHz SCM channel only, with two adjacent downstream SCM channels, B with eight upstream SCM channels and two adjacent downstream SCM channels

output of the p-i-n module in ONU1. It is monitored under .

three conditions: 1 transmit the 556 MHz channel only,

. .

2 add two adjacent downstream SCM channels, and 3 add two adjacent downstream SCM channels and eight upstream SCM channels. For the 1549.32 nm DFB laser at the CO, the transmitted optical power isy0.2 dBm, and a BER of 10y9 is obtained at a received optical power ofy29.9 dBm in case 1. There is a 0.4 dB power penalty due to the eight upstream channels in case 3. Thus, the downstream channel optical

Ž .

power margin is 22.77 dB y0.2 y 6.53 y 0.4 q 29.9 in case 3.

In Figure 10, the 106 MHz upstream channel is monitored .

under the following three cases: 1 transmit the 106 MHz .

SCM channel only, 2 add seven adjacent upstream SCM .

channels, and 3 add three downstream SCM channels and seven adjacent upstream SCM channels. For the 1554.12 nm DFB laser in ONU4, the transmitted optical power isy0.2 dBm, and a BER of 10y9 is obtained at a received optical power of y28.7 dBm in case 1. There is a 0.5 dB power penalty with three downstream SCM channels and seven adjacent SCM channels in case 3. Thus, the optical power

Ž .

margin is 20.67 dB y0.2 y 7.33 y 0.5 q 28.7 in case 3. IV. DISCUSSION

In the SBRA, two distinct wavelength groups are repeatedly used in alternate links of the upper level star subnet for uprdownstream transmission. Each wavelength signal in the group can carry many SCM signals to serve a ring subnet. If there are N wavelengths in each group, each link of the star subnet can support N ring subnets. Thus, each star link can support a total of N⭈ k nodes, where k is the number of ONUs in a ring subnet. As there is no limit on the number of

Figure 10 Measured BER curves for upstream transmission at CO.

' with the 106 MHz SCM channel only, with seven adjacent upstream SCM channels, B with three downstream SCM channels and seven adjacent upstream SCM channels

links in the star subnet, the network capacity of the SBRA is virtually unlimited.

While bandwidth is the salient advantage of star networks, the inherent weakness in reliability should be adequately addressed. In the SBRA, we design two distinct wavelength groups in alternate star links cooperating with RNs with self-healing functions to overcome the weakness of the star subnet. We further design B᎐WADM to manage fiber cut occurrences in the bus subnet. In practice, some signaling schemes should be included in order to recover failures promptly, but are omitted in this paper.

From our CAT structure, the RIN is a critical factor concerned with the maximum number of ONUs in the ring subnet. However, the RIN is indeed not the only critical parameter in the system if the number of active ONUs is large. In this scenario, the nonlinear distortion induced by

w x laser clipping should be taken into consideration 8 . More-over, laser modulation bandwidth is also a dominant factor for the maximum number of ONUs. In this study, we use commercial FP laser diodes with a modulating bandwidth of about 1 GHz in each ONU. Thus, the downstream signal frequency bandwidth is chosen from 550 MHz to 1.0 GHz, and the upstream signal frequency bandwidth ranges from 80 to 500 MHz, respectively. If 6 MHz is assigned to each subcarrier, more than 70 subcarrier channels are available both in the upstream and downstream directions according to our simulated results.

V. CONCLUSIONS

We have proposed and demonstrated a feasible and flexible architecture for DWDMrSCM passive optical networks with very high capacity and excellent reliability. The SBRA is a three-level network having a star subnet on the upper level to

(6)

offer virtually unlimited bandwidth, bus subnets on the mid-dle level to transfer multiwavelength signals, and ring subnets on the lower level to link a number of ONUs. We adopt a CAT structure in the ring subnet to eliminate the OBI problem and compensate branch loss. The SBRA demon-strates to be a good combination of those three popular network topologies, being able to support tremendous broad-band users. Self-healing functions are designed to overcome fiber cuts in the star and bus subnets to ensure good network reliability. We have further set up an experimental network to demonstrate the feasibility of SBRA. From the results, we believe that the proposed SBRA is a promising architecture for future high-capacity broadband subscriber networks. REFERENCES

1. C. Desem, Optical interference in subcarrier multiplexed system with multiple optical carriers, IEEE J Select Areas Commun 3 Ž1990 , 1290. ᎐1295.

2. S.L. Woodward, X. Lu, T.E. Darcie, and G.E. Bodeep, Reduction of optical-beat interference in subcarrier networks, IEEE Photon

Ž .

Technol Lett 8 1996 , 649᎐696.

3. W.-P. Lin, Reducing multiple optical carries interference in broadband passive optical networks, IEEE Photon Technol Lett 9 Ž1997 , 368. ᎐370.

4. W.-P. Lin, M.-S. Kao, and S. Chi, The modified star-ring architec-ture for high capacity subcarrier multiplexed passive optical

net-Ž .

works, J Lightwave Technol 19 2001 , 32᎐39.

5. J. Nishikido et al., Multiwavelength securely-authenticated broad-cast network, Proc 23nd European Conf Opt Commun, 1997, pp. 17᎐20.

Ž .

6. A. Mariconda et al., An optical add-drop multiplexer OADM node architecture in a fully transparent self healing ring network, Proc 22nd European Conf Opt Commun, 1996, pp. 4.139᎐4.142. 7. T.-H. Wu, Fiber network service survivability, Artech House, New

York, 1992.

8. N.J. Frigo, M.R. Phillips, and G.E. Bodeep, Clipping distortion in lightwave CATV systems: Models, simulations, and measurement,

Ž .

J Lightwave Technol 11 1993 , 138᎐146. 䊚 2001 John Wiley & Sons, Inc.

OPEN-HEXAGON TILTED PATCH

ANTENNA FOR TERRESTRIAL DIGITAL

TV RECEPTION

Javier Yague Mondelo,¨ 1Mercedes Sanchez Varela,´ 1 Inigo Cuinas,˜ ˜ 1Manuel Garcıa Sanchez,´ ´ 1and Antonio Garcıa Pino´ 1

1Departamento de Teorıa do Sinal e Comunicacions´ ´ Universidade de Vigo

E36200 Vigo, Spain

Recei¨ed 17 July 2001

ABSTRACT: Some specific situations for digital TV reception need

¨ertically polarized transmission, and so,¨ertically polarized antennas. This letter presents a new open-hexagon suspended tilted patch antenna. This element pro¨ides medium gain and directi¨ity in a compact format and small size. The proposed antenna is an open-hexagonal patch, tilted 45⬚ relati¨e to the ground plane. The radiation pattern is end fire, and the polarization is orthogonal to the ground plane. This design has been analyzed, built, and measured, showing good performance for the in-tended use.䊚 2001 John Wiley & Sons, Inc. Microwave Opt Technol

Lett 32: 56᎐60, 2002.

Key words: digital terrestrial tele¨ision; patch antenna; antenna design; antenna radiation pattern

DOI 10.1002r mop.10090

INTRODUCTION

Digital television broadcasting has several advantages if com-pared to analog technology, such as baseband efficiency, flexibility, and RF performance. Therefore, all broadcasts will eventually fall to the digital wave.

A major catalyst of the digital era is the Digital Video

Ž . w x

Broadcasting DVB project 1, 2 . It is a collaborative project that began in Europe, but now involves a large number of organizations from around the world. Not only has DVB scaled technical heights in digital television systems develop-ment, but it has also taught us much about working together to achieve standardization. The DVB has three different

Ž . Ž .

specifications: the DVB-T terrestrial , the DVB-C cable ,

Ž .

and the DVB-S satellite .

Both analogical and digital terrestrial TV broadcasting signals are usually transmitted in horizontal polarization. Nevertheless, some broadcast transmitting stations use verti-cal polarization in order to avoid loverti-cal critiverti-cal situations such as interference or high attenuation.

A typical case is that found in shadowed areas with no visibility to the transmitting station. A nonexpensive solution is the installation of a retransmitter located in a line-of-sight place, with its receiving horizontally polarized antenna pointed to the transmitter, and its transmitting vertically polarized antenna pointed to the possible subscribers of the service. In this way, a pseudomicrocell is performed.

Another special situation where a vertically polarized an-tenna is often used is the domestic gap filler. Such a system, which can be defined as an indoor retransmitter, avoids cabling a house or a building. In this case, it is used as a base station for a wireless indoor network. The basis is the use of a

Ž .

typical antenna horizontally polarized for outdoor recep-tion, and the installation of a vertically polarized antenna indoors, to provide the signal distribution.

For both situations, the microcell and the domestic gap filler, the proposed hexagonal antenna is intended for use.

數據

Figure 1 DWDM rSCM star᎐bus᎐ring architecture
Figure 4 Configuration of remote node RN under normal condi- condi-tion
Figure 7 Reconfiguration of RN and B ᎐WADM under bus link failure
Figure 9 Measured BER curves for downstream transmission at

參考文獻

相關文件

Understanding and inferring information, ideas, feelings and opinions in a range of texts with some degree of complexity, using and integrating a small range of reading

Writing texts to convey information, ideas, personal experiences and opinions on familiar topics with elaboration. Writing texts to convey information, ideas, personal

• Introduction of language arts elements into the junior forms in preparation for LA electives.. Curriculum design for

• Content demands – Awareness that in different countries the weather is different and we need to wear different clothes / also culture. impacts on the clothing

• Examples of items NOT recognised for fee calculation*: staff gathering/ welfare/ meal allowances, expenses related to event celebrations without student participation,

 At the junior secondary level, schools are expected to offer a broad and balanced TE curriculum which nurtures students’ capability for understanding various

Writing texts to convey simple information, ideas, personal experiences and opinions on familiar topics with some elaboration. Writing texts to convey information, ideas,

We propose a primal-dual continuation approach for the capacitated multi- facility Weber problem (CMFWP) based on its nonlinear second-order cone program (SOCP) reformulation.. The