1910 Tiroler SK (Innsbruck) 1919/20 qualification for championship 1920/21 1920/21 Innsbrucker Turnverein 1922 Innsbrucker Turnverein 1922/23 SV Innsbruck 1923/24 SV Innsbruck 1924/25 SV Innsbruck 1925/26 SV Innsbruck 1927 Innsbrucker AC 1928 FC Veldidena Innsbruck 1928/29 Innsbrucker AC 1929/30 Innsbrucker AC 1930/31 Innsbrucker AC 1931/32 SV Hötting 1932/33 Innsbrucker AC 1933/34 SV Hötting 1934/35 Innsbrucker SK 1935/36 Innsbrucker AC 1936/37 Innsbrucker AC 1937/38 Innsbrucker SK 1938/39 tournament abandoned 1940 tournament abandoned 1940/41 FC Wacker 1941/42 Reichsbahn 1942/43 tournament abandoned 1944 SV Innsbruck 1944/45 no tournament 1946 Innsbrucker AC Tiroler Landesliga 1946/47 SV Innsbruck 1947/48 Innsbrucker SK 1948/49 SK Kufstein 1949/50 Polizei SV Innsbruck 1950/51 Innsbrucker SK 1951/52 Polizei SV Innsbruck 1952/53 Innsbrucker AC 1953/54 Innsbrucker SK 1954/55 SV Wattens 1955/56 Innsbrucker SK 1956/57 ESV Austria Innsbruck 1957/58 SV Wattens 1958/59 Innsbrucker SK 1959/60 FC Wacker Innsbruck 1960/61 FC Wacker Innsbruck 1961/62 FC Wacker Innsbruck 1962/63 SV Wattens 1963/64 FC Wacker Innsbruck 1964/65 SV Wattens 1965/66 SV Wattens 1966/67 SV Wattens 1967/68 WSG Wattens 1968/69 Innsbrucker AC 1969/70 ESV Austria Innsbruck 1970/71 SV Hall 1971/72 SV Innsbruck 1972/73 SC Kufstein 1973/74 SV Hall 1974/75 SPG Innsbruck 1975/76 WSG Wattens 1976/77 WSG Wattens 1977/78 SV Absam 1978/79 SC Schwaz 1979/80 SK Rum 1980/81 SC Kufstein 1981/82 SV Hall 1982/83 SV Hall Tiroler Liga 1983/84 SVG Mayrhofen 1984/85 SV Fügen 1985/86 SV Axams 1986/87 SV Haiming 1987/88 SV Axams 1988/89 SC Kundl 1989/90 SV Fügen 1990/91 SK Rum 1991/92 SV Wörgl Regionalliga Tirol 1992/93 SV Wörgl 1993/94 SV Kundl 1994/95 SV Hall 1995/96 SV Hall Tiroler Liga 1996/97 SV Kirchbichl 1997/98 SVg Reichenau 1998/99 SVg Jenbach 1999/00 SV Axams 2000/01 SV Hall 2001/02 SK Rum 2002/03 SV Axams 2003/04 SV Wörgl/Amateure 2004/05 WSG Wattens 2005/06 Innsbrucker AC 2006/07 SC KUndl 2007/08 SC Schwaz UPC Tirol-Liga 2008/09 FC Wacker Innsbruck II 2009/10 SPG Reichenau/Union Innsbruck II 2010/11 SV Hall 2011/12 SVG Reichenau 2012/13 SC Schwaz 2013/14 FC Kitzbühel 2014/15 SVG Reichenau 2015/16 SV Wörgl 2016/17 FC Kitzbühel 2017/18 SVG Reichenau 2018/19 SV Hall
The following league tables refer to the second level league for teams from Tirol until 1949/50 (although promotion to the national championship was not possible). For most of the period, this league was restricted to the capital Innsbruck, and only isolated data from the other regions of Tirol are available.
A tournament for teams from Tirol and Vorarlberg was played. Final Ranking Tirol 1.Fußball Innsbruck 1 2.Fußball Innsbruck 2 3.Realschüler Final Tirol/Vorarlberg [Oct 24] Fußball Innsbruck 1 3-2 FC Lustenau
NB: as only one club, Tiroler SK, registered for the championship, they were declared
champions without playing.
Qualification Tournament for Championship 1920/21
Participating Teams (8):
ATuS Innsbruck (Arbeiter Turn- und Sportklub)
Germania Innsbruck
Innsbrucker SV II
Rapid Innsbruck II
Studenten FC Innsbruck (Mittelschüler)
Wacker Innsbruck II
Wacker Innsbruck III
Veldidena Innsbruck
Round 1 [Sep 14]
Studenten 3-0 Wacker III
Wacker II 8-0 ATuS
Innsbrucker SV II 9-1 Germania
Rapid II 2-1 Veldidena
Round 2 [Sep 21]
Wacker II 3-1 Innsbrucker SV II [aet]
Rapid II 4-3 Studenten
NB: Innsbrucker SV II successfully protested against the homologation of the result
against Wacker II and entered the 1920/21 A-Liga.
Round 1 [Sep 19] FC Wacker 1-1 FC Rapid 1.Innsbrucker SV 8 7 1 0 31- 7 13 2.FC Wacker 8 5 2 1 28- 7 12 3.Innsbrucker SV II 8 4 0 4 22-24 8 4.FC Rapid 8 2 1 5 19-19 5 5.FC Rapid II 8 0 0 8 5-48 0 B-Liga [Oct 9] Wacker II 4-0 ATV [Jun 5] Akademischer FV 4-2 FC Veldidena [Jul 3] FC Veldidena - Haller TV Promoted: Veldidena
1.Innsbrucker Turnverein 3 3 0 0 7- 0 6
2.FC Rapid 3 2 0 1 5- 2 4
3.FC Veldidena 3 1 0 2 4- 7 2
4.FC Wacker 3 0 0 3 0- 7 0
NB: no secondary league (B-Liga) was organised, due to the
amount of protests in the B-Liga in the previous season.
NB: FC Wacker were relegated but saved themselves by a merger with
FC Rapid to FC Sturm.
Promoted: ATV
1.SV Innsbruck 6 6 0 0 22- 5 12
2.Arbeiter TV Innsbruck 6 2 2 2 18-14 6
3.FC Sturm 6 2 2 2 6-13 6 [*]
4.FC Veldidena 6 0 0 6 6-20 0
[*] FC Sturm were a temporary merger of FC Rapid and FC Wacker;
the merger was dissolved after one season due to disagreements.
B-Liga
Last Round [Jul 8]
Christlich-D. TV 3-1 SC Tirol
Champions and promoted: Christlich-Deutscher Turnverein Innsbruck
1.SV Innsbruck 6 5 1 0 29- 9 11 2.Arbeiter TV Innsbruck 6 4 1 1 22- 9 9 3.Chr.-dtsch. TV Innsbruck 6 1 0 5 9-21 2 4.FC Veldidena 6 1 0 5 6-27 2 Relegated Promoted: AC Tirol and ATV Pradl
1.SV Innsbruck 8 7 1 0 30- 6 15 2.Arbeiter TV Innsbruck 8 5 1 2 23-11 11 3.Chr.-dtsch. TV Innsbruck 8 4 0 4 18-30 8 4.SC Tirol 8 3 0 5 24-26 6 5.ATV Pradl 8 0 0 8 3-25 0 B-Klasse [Jul 12] FC Veldidena 3-1 FC Wacker Innsbruck Champions and promoted: FC Veldidena Other participants included FC Wacker (finished 3rd), SV Hötting, ASC Olympia
1.SV Innsbruck 8 7 1 0 25- 7 15
2.FC Veldidena 8 5 1 2 27-12 11
3.Innsbrucker AC 8 4 2 2 27-13 8
4.Chr.-dtsch. TV Innsbruck 8 2 0 6 11-31 4 [*]
5.SC Tirol 8 0 0 8 3-30 0 [*]
[*] both the Christlich-deutscher Turnverein Innsbruck and
SC Tirol withdrew during the season.
B-Klasse
Champions and promoted: FC Wacker
1.Innsbrucker AC 6 5 1 0 30- 5 11 2.FC Wacker 6 2 1 3 15-15 5 3.FC Veldidena 6 2 1 3 12-24 5 4.SV Innsbruck 6 1 1 4 12-25 3 Champions B-Liga 1926/27: SC Hötting (promoted) Cup 1927 Round 1 FC Wacker Innsbruck 7-1 SC Lichtwerke Innsbruck Semifinals Veldidena Innsbruck 5-0 FC Wacker Innsbruck Final Innsbrucker AC 3-1 FC Veldidena
1.FC Veldidena 10 8 0 2 44-16 16 2.SV Hötting 10 8 0 2 34-17 16 3.Innsbrucker AC 10 6 0 4 35-23 12 4.FC Wacker 10 5 0 5 32-36 10 5.SV Innsbruck 10 3 0 7 24-37 6 6.SC Lichtwerke 10 0 0 10 1-41 0
1.Innsbrucker AC 8 6 0 2 37-15 12 2.FC Veldidena 8 5 0 3 26-25 10 3.FC Wacker 8 5 0 3 27-25 10 4.SV Innsbruck 8 4 0 4 20-26 8 5.SV Hötting 8 0 0 8 10-31 0 NB: overall goal difference -2 Innsbrucker AC qualified for Amateur Championship 1929. Cup 1929 Round 1 FC Wacker Innsbruck 4-2 SV Hötting Semifinals Innsbrucker AC 6-2 FC Wacker Innsbruck Final Innsbrucker AC 6-1 SV Innsbruck
1.Innsbrucker AC 6 5 0 1 28- 7 10 2.FC Veldidena 6 5 0 1 13- 9 10 3.FC Wacker 6 1 1 4 6-17 3 4.SV Innsbruck 6 0 1 5 5-19 1 Innsbrucker AC qualified for Amateur Championship 1930. B-Liga 2.SV Kufstein [promoted to A-Klasse] Also promoted: SC Lichtwerke Innsbruck and SV Hötting Cup 1930 Round 1 [Aug 9] FC Wacker Innsbruck 3-0 SV Innsbruck [Aug 10] SV Hötting 6-3 SC Lichtwerke Innsbrucker AC 3-2 FC Veldidena Round 2 [Aug 15] FC Veldidena 6-2 SC Lichtwerke SV Innsbruck bye Round 3 [Aug 17] SV Innsbruck 1-0 FC Veldidena Semifinals [Aug 16] Innsbrucker AC 6-2 SV Hötting [Aug 31] FC Wacker Innsbruck 2-0 SV Innsbruck Final [Sep 28] Innsbrucker AC 1-1 FC Wacker Innsbruck [aet] Final Replay [Oct 11] FC Wacker Innsbruck 1-1 Innsbrucker AC [aet] NB: cup shared
1.Innsbrucker AC 12 10 1 1 44-15 21 2.FC Veldidena 12 7 1 4 31-23 15 3.FC Wacker 12 6 1 5 33-31 13 4.SV Hötting 12 6 0 6 41-26 12 5.SV Innsbruck 12 5 2 5 24-30 12 6.SC Lichtwerke 12 2 2 8 13-32 6 7.SV Kufstein 12 2 1 9 9-38 5 Innsbrucker AC qualified for Amateur Championship 1931.
1.SV Hötting 6 4 1 1 15- 9 9 2.Innsbrucker AC 6 4 0 2 22-13 8 3.FC Wacker 6 3 1 2 20-15 7 4.Fc Veldidena 6 0 0 6 7-27 0 SV Hötting qualified for Amateur Championship 1932.
1.Innsbrucker AC 12 9 1 2 33-15 19 2.SV Hötting 12 8 1 3 45-19 17 3.SV Hall 12 6 0 6 29-34 12 4.FC Veldidena 12 5 1 6 21-19 11 5.FC Wacker 12 5 0 7 12-24 10 6.SV Innsbruck 12 4 1 7 12-21 9 7.Pfadfinder 12 3 0 9 16-36 6 Innsbrucker AC qualified for Amateur Championship 1933.
1.SV Hötting 12 8 3 1 42-14 19 2.Innsbrucker AC 12 7 2 3 48-20 16 3.FC Veldidena 12 7 0 5 34-28 14 4.Heeres SV Innsbruck 12 4 3 5 26-31 11 5.FC Wacker 12 3 4 5 23-30 10 6.SC Tirol 12 3 2 7 27-54 8 7.SV Hall 12 2 2 8 17-40 6 SV Hötting qualified for Amateur Championship 1934. Meisterschaft Unterland (second edition): 1.SV Kufstein (also winners first edition (1932/33?)) 2.SV Rattenberg 3.SV Wörgl 4.SC Wattens 5.SV Schwaz 6.FC Kitzbühel Oberland-Cup winners: SV Silz
1.Innsbrucker SK 12 10 0 2 49-10 20 [*] 2.Innsbrucker AC 12 9 0 3 35-15 18 3.Heeres SV Innsbruck 12 8 1 3 39-31 17 4.FC Wacker 12 5 2 5 28-26 14 5.FC Veldidena 12 3 1 8 23-37 7 6.SV Innsbruck 12 1 2 9 21-47 4 7.SC Tirol 12 2 0 10 15-44 4 [*] SV Hötting were renamed Innsbrucker SK in Sep 1934 Innsbrucker SK qualified for Amateur Championship 1935. B-Klasse Top Final Standings: 1.FC Hall (promoted) 2.SC Pfadfinder Innsbruck 3.Österreichische Jugendkraft Oberland Champions: FC Imst
1.Innsbrucker AC 12 8 4 0 47-11 20 2.Heeres SV Innsbruck 12 8 2 2 56-15 18 3.Innsbrucker SK 12 6 3 3 28-19 15 4.FC Veldidena 12 5 2 5 18-40 12 5.SV Innsbruck 12 2 3 7 14-32 7 6.SV Hall 12 2 3 7 15-40 7 7.FC Wacker 12 1 3 8 18-39 5 Innsbrucker AC qualified for Amateur Championship 1936. B-Klasse Champions and promoted: Österreichische Jugendkraft (ÖJK) Innsbruck
1.Innsbrucker AC 12 9 3 0 37-10 21 2.Heeres SV Innsbruck 12 9 2 1 51-24 20 3.Innsbrucker SK 12 8 1 3 44-14 17 4.SV Hall 12 4 0 8 18-32 8 5.FC Veldidena 12 3 2 7 21-38 8 6.SV Innsbruck 12 3 1 8 17-39 7 7.Österr. Jugendkraft 12 1 1 10 10-41 3 Innsbrucker AC qualified for Amateur Championship 1937. Unterland champions: FC Kitzbühel Oberland champions: FC Reutte 'Countryside Championship Playoff' FC Reutte 10-2 FC Kitzbühel B-Klasse 1.FC Wacker Innsbruck 10 9 0 1 43-13 18 2.Bundesbahn SVG Innsbruck 10 7 1 2 46-12 15 3.Sturm Hall 10 6 1 3 26-17 13 3.SC Pfadfinder Innsbruck 10 3 1 6 22-35 7 4.SK Wilten 10 2 0 8 19-38 4 5.SV Mühlau 10 1 1 8 13-54 3
1.Innsbrucker SK 12 10 1 1 35-11 21 2.Innsbrucker AC 12 8 0 4 42-10 16 3.SV Hall 12 3 0 9 13-41 6 4.Heeres SV Innsbruck 12 2 1 9 12-40 5 NB: HSVI were dissolved mid-May 1938. B-Klasse Champions and promoted: FC Wacker
1.FC Wacker 7 5 0 2 17-18 10 2.Innsbrucker AC 9 4 1 4 28-23 9 3.SV Innsbruck 9 3 2 4 21-15 8 4.DTSG Hall 9 3 2 4 21-31 8 5.Innsbrucker SK 5 2 1 2 21-10 5 6.FC Wattens 4 2 0 2 6-19 4 7.Reichsbahn 3 1 0 2 10- 8 2 NB: league abandoned and no championship awarded.
Known results SV Innsbruck 2-1 FC Wacker SV Innsbruck 4-4 DTSG Hall Reported Table (at abandonment Jul 30): 1.Reichsbahn SV Innsbruck 4 3 1 0 15- 8 7 2.SV Innsbruck 5 2 1 2 11-11 5 3.Innsbrucker AC 4 1 2 1 4- 3 4 4.DTSG Wattens 3 2 0 1 7- 7 4 5.Innsbrucker SK 3 1 1 1 4- 7 3 6.FC Wacker Innsbruck 5 0 1 4 6-12 1 NB: total goal difference -1
1.FC Wacker 8 7 1 0 41-16 15
2.SV Innsbruck 6 2 1 3 22-15 5
3.Innsbrucker AC 5 2 1 2 12-10 5
4.Reichsbahn 6 2 1 3 13-19 5
5.Innsbrucker SK 7 2 1 4 10-23 5
6.DTSG Wattens 6 2 1 3 16-31 5
NB: two more wins than losses; league was abandoned,
FC Wacker declared champions.
1.Reichsbahn 6 5 1 0 22- 7 11 2.SV Innsbruck 7 4 0 3 27-15 8 3.BSG Heinkel Jenbach 5 3 0 2 16-23 6 4.Innsbrucker SK 4 1 0 3 8-13 2 5.FC Wacker 6 0 1 5 12-27 1 NB: league abandoned, Reichsbahn declared champions.
1.Gebirgs-Artillerie Hall 3 3 0 0 17- 2 6 2.Reichsbahn 3 2 0 1 12- 2 4 3.SV Innsbruck 3 1 0 2 6-15 2 4.FC Wacker 3 0 0 3 6-22 0 NB: league abandoned after fall season, no championship awarded.
1.SV Innsbruck 3 3 0 0 16- 4 6 2.Reichsbahn 3 1 0 2 14-15 2 3.WM Schwaz 2 1 0 1 6-14 2 4.BSG Heinkel Jenbach 2 0 0 2 4-11 0 NB: overall goal difference -4; championship played as single round.
Innsbruck 1.Innsbrucker AC 5 4 1 0 24- 4 9 Qualified 2.Innsbrucker SK 5 3 2 0 16- 7 8 3.SK Rot-Weiß 5 2 1 2 10-23 5 4.Polizei SV Innsbruck 5 2 0 3 11-12 4 5.SV Hall 5 1 1 3 8-14 3 6.SV Innsbruck 5 0 1 4 11-20 1 Oberland 1.ATV Landeck/Zams 6 5 1 0 31- 5 11 Qualified 2.TS Imst 6 3 0 3 11-26 6 3.FC Reutte 6 2 1 3 12-13 5 4.SV Silz 6 1 0 5 5-15 2 Unterland 1.FC Wörgl 6 5 1 0 35- 3 11 Qualified 2.SK Kufstein 6 5 0 1 37- 4 10 3.SC Kitzbühel 6 4 0 2 16-10 8 4.FC Schwaz 6 3 0 3 17- 9 6 5.FC Wattens 6 2 1 3 8-16 5 6.ATV Jebach 6 1 0 5 8-26 2 7.ATV Kirchbichl 6 0 0 6 4-57 0 Championship Playoff 1.Innsbrucker AC 4 4 0 0 21- 3 8 2.FC Wörgl 4 1 0 3 10-10 2 3.ATV Landeck/Zams 4 1 0 3 4-22 2
1.SV Innsbruck 18 13 3 2 63-29 29
2.Innsbrucker SK 18 11 3 4 54-29 25
3.FC Wörgl 18 11 1 6 47-28 23
4.Polizei SV Innsbruck 18 10 3 5 59-37 23
5.Innsbrucker AC 18 9 3 6 47-21 21
6.SK Kufstein 18 6 5 7 38-39 17
7.SV Hall 18 4 5 9 26-34 13
8.ATV Landeck 18 3 5 10 41-61 11
9.SV Reutte 18 4 2 12 21-57 10
10.SC Rot-Weiß 18 2 2 14 15-76 6
NB: 2 more losses than wins; presumably one match awarded 0-0 loss against
both teams.
Second Level
B-Klasse Ober-Inntal
1.FC Wacker Innsbruck 14 9 3 2 46-19 21 Promoted
2.Innsbrucker SK 1b 14 7 3 4 44-19 17
3.Eisenbahner-SV Innsbruck 14 8 1 5 39-21 17
4.FC Peter-Mayer-Sport Ibk. 14 6 4 4 51-37 16
5.FC Imst 14 6 3 5 36-34 15
6.SV Telfs 14 5 3 6 29-44 13
7.SV Silz 14 3 5 6 39-47 11
8.ASV Kematen 14 0 2 12 15-78 2
1.Innsbrucker SK 18 13 2 3 52-16 28 2.SK Kufstein 18 11 4 3 45-21 26 3.Innsbrucker AC 18 9 3 6 53-45 21 4.Polizei SV Innsbruck 18 8 3 7 51-27 19 5.AC Wörgl 18 8 2 8 34-29 18 6.SV Innsbruck 18 8 1 9 41-40 17 7.ATV Landeck 18 6 3 9 33-71 15 8.FC Schwaz 18 6 1 11 31-49 13 9.SV Hall 18 4 4 10 23-38 12 10.FC Wacker 18 4 3 11 29-56 11 B-Klasse Final Standings: 1.SC Rot-Weiß Innsbruck 2.Eisenbahner-SV Innsbruck 3.Peter-Mayer-Sport Innsbruck 4.Zollwache-SVG Innsbruck 5.Innsbrucker SK 1b 6.SK Wilten Innsbruck 7.ASV Kematen
1.SK Kufstein 18 14 2 2 53-16 30 2.Innsbrucker AC 18 14 2 2 57-19 30 3.SV Innsbruck 18 14 1 3 62-24 29 4.Innsbrucker SK 18 12 2 4 44-23 26 5.Polizei SV Innsbruck 18 8 3 7 36-30 19 6.AC Wörgl 18 7 2 9 40-34 16 7.FC Schwaz 18 5 3 10 38-51 13 8.ESV Austria 18 3 4 11 35-51 10 9.SVG Jenbach 18 2 1 15 15-54 5 10.ATV Landeck 18 1 0 17 11-89 2 B-Klasse - Innsbruck-Stadt Reported Final Table: 1.FC Wacker Innsbruck 14 12 1 1 64-20 25 2.Eisenbahner-SV Innsbruck 14 10 1 2 51-25 21 [?!] 3.Peter-Mayer-Bund I'bruck 14 5 3 5 31-29 13 [?!] 4.ASV Kematen 14 6 0 8 36-42 12 5.Zollwache Innsbruck 7 3 3 1 17-14 9 6.SK Wilten Innsbruck 14 4 1 6 24-34 9 [?!] 7.SK Sturm Hall 13 4 1 8 21-32 9 8.FC Veldidena Innsbruck 12 3 1 8 20-39 7 9.Postsport SV Innsbruck 7 0 0 7 1-30 0 NB: odd number of matches, draws and points, various inconsistencies in Pd-W-D-L records
1.Polizei SV Innsbruck 14 11 0 3 44-13 22 Promotion Playoff
2.SV Innsbruck 14 10 1 3 47-30 21 Qualified
3.Innsbrucker SK 14 8 1 5 44-26 17 Qualified
4.SK Kufstein 14 8 0 6 40-28 16 Qualified
5.SC Schwaz 14 6 1 7 23-30 13 [*] Qualified
6.Innsbrucker AC 14 5 0 9 31-38 10 Qualified
7.AC Wörgl 14 5 0 9 24-37 10 Qualified
8.ESV Austria 14 1 1 12 10-61 3
[*] apparently FC Schwaz changed name to SC Schwaz.
NB: Polizei SV qualified for promotion playoff to first level but failed to
obtain promotion; instead they entered the new Staatsliga B 1950/51
while the teams finishing 2nd to 7th qualified for the new Arlbergliga,
together with the 6 best teams of the Vorarlberger Liga.
1. Klasse
Reported Final Table:
1.SV Hall 14 11 2 1 47-15 24
2.SpVgg Jenbach 14 9 4 1 59-26 22
3.FC Wacker Innsbruck 14 8 2 4 43-24 18
4.SV Wattens 14 6 3 5 42-28 15
5.FC Reutte 14 6 3 5 35-34 15
6.SV Landeck 14 4 2 8 32-56 10
7.ESV Austria Innsbruck 14 2 1 11 13-44 5
8.SV Silz 14 1 1 12 11-57 3
NB: total goal difference -2
2. Klasse Oberland
1.SV Ötztal
2.SV Zams
3.FC Imst
4.SV Telfs
5.ASV Kematen
6.FC Vils
7.SK Wilten Innsbruck
8.FC Veldidena Innsbruck
Sources: [ÖFB 78], [Gra 96], [DaS 13], www.fc-wacker-innsbruck.at, Innsbrucker Nachrichten
Prepared and maintained by Hans Schöggl and Markus Dayer for the Rec.Sport.Soccer Statistics Foundation
Authors: Hans Schöggl and Markus Dayer
Last updated: 10 Jan 2020
(C) Copyright Hans Schöggl, Markus Dayer and RSSSF 2002/20
You are free to copy this document in whole or part provided that proper
acknowledgement is given to the authors. All rights reserved.