SQL*Plus: Release 10.2.0.1.0 - Production on Fri Jun 21 21:10:41 2013

Copyright (c) 1982, 2005, Oracle.  All rights reserved.

Connected to an idle instance.

SQL> startup nomount pfile=initstanddb.ora
ORA-27123: unable to attach to shared memory segment
Linux Error: 13: Permission denied

standdb.__db_cache_size=79691776
standdb.__java_pool_size=4194304
standdb.__large_pool_size=4194304
standdb.__shared_pool_size=75497472
standdb.__streams_pool_size=0
*.audit_file_dest='/u01/ora10g/db_1/admin/standdb/adump'
*.background_dump_dest='/u01/ora10g/db_1/admin/standdb/bdump'
*.compatible='10.2.0.1.0'
*.control_files='/u01/ora10g/oradata/standdb/control01.ctl','/u01/ora10g/oradata/standdb/control02.ctl','/u01/ora10g/oradata/standdb/control03.ctl'
*.core_dump_dest='/u01/ora10g/db_1/admin/standdb/cdump'
*.db_block_size=8192
*.db_domain=''
*.db_file_multiblock_read_count=16
*.db_name='proddb'
*.db_recovery_file_dest='/u01/ora10g/db_1/flash_recovery_area'
*.db_recovery_file_dest_size=3221225472
*.dispatchers='(PROTOCOL=TCP) (SERVICE=proddbXDB)'
*.fal_client='PRODDB'
*.fal_server='STANDDB'
*.job_queue_processes=10
*.log_archive_config='DG_CONFIG=(proddb, standby)'
*.log_archive_dest_1='location=/u02/archive VALID_FOR=(ALL_LOGFILES, ALL_ROLES) DB_UNIQUE_NAME=standdb'
*.log_archive_dest_2='service=prodddb LGWR ASYNC VALID_FOR=(ONLINE_LOGFILES, PRIMARY_ROLES) DB_UNIQUE_NAME=proddb'
*.log_archive_dest_state_1='ENABLE'
*.log_archive_dest_state_2='ENABLE'
*.open_cursors=300
*.pga_aggregate_target=16777216
*.processes=150
*.remote_login_passwordfile='EXCLUSIVE'
*.sga_target=167772160
*.standby_file_management='AUTO'
*.undo_management='AUTO'
*.undo_tablespace='UNDOTBS1'
*.user_dump_dest='/u01/ora10g/db_1/admin/standdb/udump'
*.db_unique_name=standdb
*.db_file_name_convert=('/u01/ora10g/oradata/proddb', '/u01/ora10g/oradata/standdb')
*.log_file_name_convert=('/u01/ora10g/oradata/proddb', '/u01/ora10g/oradata/standdb')

calhost dbs]$ cd $ORACLE_HOME/bin
[standdb@localhost bin]$ chmod 6751 oracle
[standdb@localhost bin]$ cd ../dbs/
[standdb@localhost dbs]$ sqlplus / as sysdba

SQL*Plus: Release 10.2.0.1.0 - Production on Fri Jun 21 21:44:36 2013

Copyright (c) 1982, 2005, Oracle.  All rights reserved.

Connected to an idle instance.

SQL> startup nomount pfile=initstanddb.ora
ORA-27123: unable to attach to shared memory segment
Linux Error: 13: Permission denied

http://exploreoracle.wordpress.com/2008/12/29/ora-27123-unable-to-attach-to-shared-memory-segment/

Solution of The Problem:
------------------
You need to change the "umask" to the required 022, set the proper permission on $ORACLE_HOME, $ORACLE_HOME/bin directories. In my computer, I ran the following.

1)Log on as root and change permission.
bash-3.00$ su
Password:
# umask 022
# cd $ORACLE_HOME
# chmod 755 *
# cd $ORACLE_BASE/admin/$ORACLE_SID
# chmod 755 *
# cd $ORACLE_HOME/bin
# chmod 6751 oracle
# exit

2)Log on normal user and log on to database.
bash-3.00$ sqlplus / as sysdba

SQL*Plus: Release 10.2.0.1.0  Production on Wed May 14 23:40:12 2008

Copyright (c) 1982, 2005, Oracle. All rights reserved.

Connected to:
Oracle Database 10g Enterprise Edition Release 10.2.0.1.0  Production
With the Partitioning, OLAP and Data Mining options