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Fixed bug Stack overflow with imagefilltoborder. CVE Fixed bug imagecreatefromwebm shifts colors. Fixed bug imagewebp doesn't pad to even length. Fixed bug imagerotate by degrees truncates image by 1px. Fixed bug imagescale Fixed bug imagescale segfault with palette based image. Fixed bug Zero-height rectangle has whiskers. Fixed bug imagecrop add a black line when cropping.

Fixed bug copy 'n paste error. Fixed bug PHP segfaults in imagexbm. CVE Phar: Improved fix for bug Fixed bug Files extracted from archive may be placed outside of destination directory. Fixed bug can induce segmentation fault with basic php code. Fixed bug Windows 10 reported as Windows 8. Fixed bug finally in generator yield swallows exception in iteration. Fixed bug phpinfo does not report many Windows SKUs.

GD: Fixed bug imagegammacorrect function loses alpha channel. Fixed bug PDO-pgsql fails to connect if password contains a leading single quote. Fixed bug Conditional jump or move depends on uninitialised value in extension trait. Fixed bug OS command injection vulnerability in escapeshellarg. Mail: Fixed bug mail does not have mail header injection prevention for additional headers. Opcache: Fixed bug Memory leak with opcache.

Phar: Fixed bug phar symlink in binary directory broken. CVE Sqlite3: Upgrade bundled sqlite to 3. Fixed bug "use statement [ Fixed bug segmentation fault in destructor. Fixed bug Returning compatible sub generator produces a warning. Fixed bug CVE fix regressions in 5. CVE Fixed bug heap buffer overflow in unpack. Fixed bug out of memory with sage odbc driver. Additional fix for bug Type confusion vulnerability in exception::getTraceAsString. Fixed bug serialize function return corrupted data when sleep has non-string values.

Fixed bug Segmentation fault when using a generator in combination with an Iterator. Fixed bug Missing null byte checks for paths in various PHP extensions. Enchant: Fixed bug Enchant broker plugins are in the wrong place in windows builds.

Fixed bug Use After Free. Fixed bug Crypto servers should send client CA list. Fixed bug Phar::mapPhar fails for Phars inside a path containing ". Fixed bug Buffer Over-read in unserialize when parsing Phar. Fixed bug Upgrade bundled libsqlite to 3. Fixed bug SQLite prepared statement use-after-free. Fixed bug Exception with invalid character causes segv. Fixed bug Missing arguments in reflection info for some builtin functions. Ereg: Fixed bug heap overflow vulnerability in regcomp.

Opcache: Fixed bug Opcache causes problem when passing a variable variable to a function. Fixed bug Array numeric string as key. Fixed bug , , , encrypted streams don't observe socket timeouts. Fixed bug RecursiveDirectoryIterator::seek 0 broken after calling getChildren. Fixed bug getClosure returns somethings that's not a closure.

Fixed bug Use after free vulnerability in unserialize with DateTimeZone. Added NULL byte protection to exec, system and passthru. Dba: Fixed bug useless comparisons. Fixed bug Bundled libmagic 5. Fixed bug core dump when webserver close the socket. Fixed bug Reading 4 byte floats with Mysqli and libmysqlclient has rounding errors.

Phar: Fixed bug use after free. Fixed bug Empty session IDs do still start sessions. Standard: Fixed bug flock out parameter not set correctly in windows. Fixed bug Request may get env. Streams: Fixed bug which caused call after final close on streams filter. Fixed bug unlink bug with some files path. Fixed bug Inside trait, self::class!

Fixed bug pack for 64bits integer is broken on bigendian. Fixed bug errors spawn MessageBox, which blocks test automation. Fixed bug Application Popup provides too few information. Fixed bug localeconv broken in TS builds. Fixed bug setting locale randomly broken. Fixed bug Crash in timeout thread. Fixed bug Constructor from trait conflicts with inherited constructor.

Fixed bug Explicit Double Free. CVE Fileinfo: Fixed bug msooxml matches too many archives. Fixed bug invalid free in libmagic. Fixed bug incorrect expression in libmagic. Removed readelf. Fixed bug fileinfo out-of-bounds memory access. Fixed bug listen. Fixed bug Memory leak when using "continue 2" inside two foreach loops. Fixed bug Added escape parameter to SplFileObject::fputcsv. SQLite: Fixed bug Update bundled libsqlite to 3. Streams: Fixed bug convert. Fixed bug Segfault while pre-evaluating a disabled function.

Fixed bug "Inconsistent insteadof definition. Fixed bug Inconsistency in example php. Fixed bug NULL pointer dereference in unserialize. Fixed bug Array constant not accepted for array parameter default. Fixed bug Use after free vulnerability in unserialize. Fixed bug access. Fixed bug php-fpm man page is oudated.

Implemented FR Change pm. Implemented FR php-fpm conf files loading order. Mcrypt: Fixed possible read after end of buffer and use after free.

GMP: Fixed bug build error with gmp 4. Session: Fixed bug Session custom storage callable functions not being called. Fixed bug A foreach on an array returned from a function not doing copy-on-write. Fixed bug Windows 8. Fileinfo: Fixed bug libmagic: don't assume char is signed.

Fixed bug fileinfo: out-of-bounds read in elf note headers. Implemented FR listen and listen. GD: Fixed bug imagescale fails without height param. Mysqli: Fixed bug linker error on some OS X machines with fixed width decimal support.

Fixed bug Segmentation fault on statement deallocation. Reflection: Fixed bug Duplicate entry in Reflection for class alias. Fixed bug Segfault when extending interface method with variadic. Fixed bug Incorrect last used array index copied to new array after unset.

Fixed bug New Posthandler Potential Illegal efree vulnerability. Fileinfo: Fixed bug finfo::file returns invalid mime type for binary files. GD: Made fontFetch's path parser thread-safe. MySQLi: Fixed bug mysqli does not handle 4-byte floats correctly.

Added dedicated syntax for variadic functions. Added support for argument unpacking to complement the variadic syntax. Added phpdbg SAPI. Added unified default encoding. Added use function and use const.. Added a function for timing attack safe string comparison. Added gost-crypto CryptoPro S-box hash algorithm. Stream wrappers verify peer certificates and host names by default in encrypted client streams.

Uploads equal or greater than 2GB in size are now accepted. Core: Fixed bug incorrect push to the empty array. Removed inconsistency regarding behaviour of array in constants at run-time.

Fixed bug eval with parse error causes segmentation fault in generator. Fixed bug strtr with empty array crashes. Fixed bug Incorrect behavior with nested "finally" blocks. Implemented FR ucwords and Title Case. Fixed bug make install fails to install libphp5. Fixed bug Memory leak with immediately dereferenced array in class constant.

Fixed bug iptcparse out-of-bounds read. Fixed bug printf out-of-bounds read. Implemented FR Differentiate between member function call on a null and non-null, non-objects. Fixed bug Autoloader isn't called if two method definitions don't match. Fixed bug Closures do not correctly capture the late bound class static:: in some cases. Fixed bug insecure temporary file use in the configure script.

CVE Fixed bug dtrace breaks argument unpack. Fixed bug header 'Location: foo' will override a response code. Fixed bug putenv with empty variable may lead to crash. Improved empty string handling. Now ZE uses an interned string instead of allocation new empty string each time. Fixed bug Segfault with finally. Fixed bug copy arginfo has changed starting from 5. Fixed bug exit in stream filter produces segfault.

Fixed bug fpassthru broken. Fixed bug Unexpected array indexing in class's static property. Fixed bug Update reflection information for unserialize function. Fixed bug Composer.

Fixed bug getimagesize should recognize BMP files with negative height. Fixed bug Echoing unserialized "SplFileObject" crash. Fixed bug Remove reference to Windows Fixed bug Empty header causes PHP built-in web server to hang. Fixed bug built-in web-server segfaults on startup. Check for openssl. Remove cURL close policy related constants as these have no effect and are no longer used in libcurl.

Date: Fixed bug Heap buffer over-read in DateInterval. Fixed bug Serialize of DateTime truncates fractions of second. Fixed regression in fix for constructor can't be called twice. Fixed bug DateTime constructor crash with invalid data. Embed: Fixed bug php5embed. Fileinfo: Fixed bug Segfault in cdf. CVE Fixed bug extensive backtracking in rule regular expression. CVE Fixed bug fileinfo: mconvert incorrect handling of truncated pascal string size. CVE Upgraded to libmagic CVE Fixed bug out-of-bounds memory access in fileinfo.

CVE Fixed bug fileinfo: extensive backtracking in awk rule regular expression. Fixed bug Solaris 10 is missing strcasestr and needs substitute.

Fixed bug Fileinfo crashes with powerpoint files. Fixed bug php links to systemd libraries without using pkg-config. Fixed bug syslog cannot be set in pool configuration. Fixed bug Fix Apache 2. Fixed bug unknown entry 'priority' in php-fpm. CVE Fixed bug imageaffinematrixget missing check of parameters. Fixed imagettftext to load the correct character map rather than the last one. Fixed bug Heap Overflow Vulnerability in imagecrop. CVE Fixed bug Invalid 2nd argument crashes imageaffinematrixget.

Fixed bug imagescale - poor quality of scaled image. Fixed bug imagescale segfault. Fixed bug imagescale ignore method argument. Moved GMP to use object as the underlying structure and implemented various improvements based on this. Michael M Slusarz. Fixed bug Locale::parseLocale Double Free. Fixed issue with null bytes in LDAP bindings. Mbstring: Upgraded to oniguruma 5. Milter: Fixed bug php-milter does not build and crashes randomly.

Added a new fetching mode to mysqlnd. Added support for gb from MySQL 5. Fixed broken build against OpenSSL older than 0. Fixed bug Subject altNames doesn't support wildcard matching. Fixed bug certificates validity parsing does not work past New openssl.

Added certificate fingerprint support. Added explicit TLSv1. Fallback to Windows CA cert store for peer verification if no openssl. The openssl. Fixed bug "cafile" SSL context option now supports stream wrappers. Encrypted stream wrappers now disable TLS compression by default. Crypto methods for encrypted client and server streams now use bitwise flags for fine-grained protocol support. Added new tlsv1.

Encrypted client streams now enable SNI by default. Encrypted streams now prioritize ephemeral key agreement and high strength ciphers by default.

Encrypted stream servers now automatically mitigate potential DoS vector arising from client-initiated TLS renegotiation. Fixed memory leak in windows cert verification on verify failure. Peer certificate capturing via SSL context options now functions even if peer verification fails. Fixed bug Fix broken build when extension built separately.

Added script level constant replacement optimization pass. Added information about interned strings usage. Upgraded to PCRE 8. Added 64bit large object support for PostgreSQL 9. Fixed bug Cannot build against libpq 7. Fixed bug readline feature not enabled when build with libedit. Fixed issue 94 List behavior is inconsistent. Fixed issue 97 The prompt should always ensure it is on a newline. Fixed issue 98 break if does not seem to work. Fixed issue 99 register function has the same behavior as run.

Fixed bug which caused phpdbg to fail immediately on startup in non-debug builds. Added watchpoints watch command. According to the release notes that means 8. Fixed bug Redirection loop on nginx with FPM. Fixed bug Save command history when exiting interactive shell with control-c.

Fixed bug session. Fixed bug ArrayIterator use-after-free due to object change during sorting. Fixed bug Segmentation fault with ArrayObject unset. Implemented FR Allow to unserialize empty data. Zip: update libzip to version 0. PHP doesn't use any ilibzip private symbol anymore.

Mike Fixed bug chained zlib filters silently fail with large amounts of data. GD: Fixed bug Stack overflow with imagefilltoborder. Fixed bug temp. PCRE: Upgraded pcrelib to 8. Fixed bug Wrong checked for the interface by using Trait. Fixed bug User exceptions not properly handled in streams.

Fixed bug Upgrade bundled sqlite to 3. Fixed bug Fail to push to the empty array with the constant value defined in class scope.

Opcache: Fixed bug Array numeric string as key. OpenSSL: Fixed bug , , , encrypted streams don't observe socket timeouts. Removed support for multi-line headers, as they are deprecated by RFC Date: Fixed bug strtotime incorrectly interprets SGT time zone. CVE Fileinfo: Fixed bug incorrect expression in libmagic.

CVE Removed readelf. FPM: Fixed bug listen. Opcache: Fixed bug Memory leak when using "continue 2" inside two foreach loops. OpenSSL: Fixed bug use case-insensitive cert name matching. Fixed bug cannot cast SplFileInfo to boolean. Fixed bug Change pm. Fixed bug php-fpm conf files loading order. Fixed bug Integer overflow in unserialize bits only. OpenSSL: Revert regression introduced by fix of bug Date: Fixed bug memory leaks in DateTime constructor.

Fixed bug Some timezones are no longer valid in PHP 5. Fixed bug First uppercase letter breaks date string parsing. Fixed bug extension won't build if openssl compiled without SSLv3.

Zlib: Fixed bug chained zlib filters silently fail with large amounts of data. Fixed bug internal corruption phar error. Fileinfo: Fixed bug extensive backtracking in rule regular expression. CVE Fixed bug Segfault in cdf. FPM: Fixed bug php links to systemd libraries without using pkg-config. CVE Fixed bug Null byte injection possible with imagexxx functions. Core: Fixed bug header 'Location: foo' will override a response code.

Fixed bug syslog cannot be set in pool configuratio. OPCache: Fixed bug php-cgi work with opcache, may be segmentation fault happen. Core: Fixed bug Closures do not correctly capture the late bound class static:: in some cases. Date: Fixed bug Serialize of DateTime truncates fractions of second. Fixed regression in fix for bug constructor can't be called twice. Fixed bug mconvert incorrect handling of truncated pascal string size. OpenSSL: Fixed bug certificates validity parsing does not work past Fixed bug Segfault in recursiveDirectoryIterator.

Fixed bug Missing element after ArrayObject::getIterator. Core: Fixed bug copy doesn't work when destination filename is created by tempnam. Date: Fixed bug DateTime constructor crash with invalid data. Fileinfo: Fixed bug Fileinfo crashes with powerpoint files.

GD: Fixed bug imageaffinematrixget missing check of parameters. Fixed bug getimagesize should recognize BMP files with negative heighty. FPM: Fixed bug unknown entry 'priority' in php-fpm. Fixed bug possible privilege escalation due to insecure default configuration. SQLite: Fixed bug Updated bundled libsqlite to 3. Fix compilation on libcurl versions between 7.

Fileinfo: Fixed bug fileinfo: extensive backtracking in awk rule regular expression. GD: Fixed bug imageconvolution breakage.

Fixed bug Invalid 2nd argument crashes imageaffinematrixget. Intl: Fixed bug A reproductible crash in UConverter when given invalid encoding. SQLite: Updated bundled libsqlite to 3. Fixed bug out-of-bounds memory access in fileinfo CVE OPCache: Fixed bug Optimizer bug in constant string to boolean conversion.

Fixed bug PHP crashes if opcache. Session: Fixed bug Session module is sending multiple set-cookie headers when session. Standard: Fixed bug basename function doesn't remove drive letter. Added validation of class names in the autoload process.

Fixed bug list fails to unpack yielded ArrayAccess object. Fixed bug DateTimeImmutable::diff does not work. Filter: Fixed bug GD: Fixed bug Use freetype-config for determining freetype2 dir s. Fixed issue "opcache. Fixed bug Inconsistent results with require return value.

Fixed bug Opcache: cache not cleared if changes occur while running. Fixed bug basename is no more working after fgetcsv in certain situation. Fixed bug Space before ";" breaks php.

Fixed bug dangling context pointer causes crash. FPM: Changed default listen backlog to OPCache: Increased limit for opcache. Fixed issue path issue when using phar. Fixed issue Phar mount points not working with OPcache enabled. Fixed bug compile time errors won't trigger auto loading. Fixed bug By-ref foreach on property access of string offset segfaults. CLI Server: Fixed bug built-in server treat some http headers as case-sensitive. Fixed bug Segfault with built-in webserver and chunked transfer encoding.

Fixed bug Comparison for DateTimeImmutable doesn't work. GD: Ensure that the defined interpolation method is used with the generic scaling methods. IMAP: Fixed bug configure script broken in 5. Fixed bug Exception not properly caught when opcache enabled. Fixed bug 5. Fixed issue segfault in interned strings if initial memory is too low. Added support for GNU Hurd. Standard: Fixed bug content-type must appear at the end of headers for Location to work in http.

Fixed bug XMLReader does not suppress errors. Build system: Fixed bug Race condition in shtool's mkdir -p implementation. Fixed bug 'make test' crashes starting with 5. Improved fputcsv to allow specifying escape character. Fixed bug quoted-printable encode stream filter incorrectly encoding spaces.

Fixed bug Pointer aliasing issue results in miscompile on gcc4. Datetime: Fixed bug createFromFormat broken when weekday name is followed by some delimiters. Session: Fixed bug Session ID is not initialized properly when strict session is enabled. Found via static analysis by cjones. Fixed bug solaris sed has no -i switch. Fixed bug CGI mode - make install don't work. OPcache: Added opcache.

Added support for glob symbols in blacklist entries? Phar: Fixed bug Phar::buildFromDirectory creates corrupt archives for some specific contents. Fixed possible buffer overflow under Windows. Note: Not a security fix. Changed session. Streams: Fixed bug select implementation uses outdated tick API. Fixed bug chroot does not get enabled.

CGI: Fixed bug Missing php-cgi man page. CLI server: Fixed bug Cli server not responsive when responding with http status code. DateTime: Fixed bug strftime returns insufficient-length string under multibyte locales.

GD: Fixed bug bgcolor does not use the same format as the input image with imagerotate. Fixed bug imagecreatefrom Their further promotions will be in their own parent Department. Clerks in scale Rs. For promotion against this quota, candidate will be required to possess a typing speed of 30 w. Promotions may however, be allowed on provisional basis and the concerned staff given two years time from the date of promotion to qualify the prescribed typewriting test; and if they fail to qualify the prescribed typewriting test within the said period, they will be liable to be reverted.

Shortfall, if any, against this quota will be added to direct recruitment quota at 4 i above. Note : Graduate Typists in grade Rs. The minimum percentage of marks will not apply to those candidates who possess Qualifications higher than Matriculation. After such directly recruited candidates join the Railway service they should be asked to pick up English typewriting also within a specified period.

For direct recruitment qualification etc. Those Stenographers who pass the examination in English and dictation in shorthand and transcription at w.

Those Stenographers who pass the examination in Hindi and dictation in shorthand and transcription at w. Stenographer Gr. PB-2 Rs.

Private Secretary-II. Those Stenographers, who pass the examination in English and dictation in shorthand and transcription at w. I in PB-1 Rs. Those Stenographers, who pass the examination in Hindi and dictation in shorthand and transcription at w.

I in PB-2 Rs. RBE No. Master's degree of a recognized University or equivalent in any subject other than Hindi or English, with Hindi or English medium and English or Hindi as a compulsory or elective subject or as a medium of examination at degree level;. Master's degree of a recognized University or equivalent in any subject other than Hindi or English, with Hindi and English as a compulsory or elective subjects of either of the two as medium of examination and other as a compulsory or elective subject at degree level.

Senior Translator. Basic Grade. Senior Grade. Service in the senior Gr. Group, Manual Instructor Asstt. Instructor , Instructor for Workshop. Service in senior Gr. The qualifications etc. As for Post Graduate Teachers. Science, History, Agriculture. As for Trained Graduate Teachers Rly. Two years diploma certificate of training in the trade concerned from ITI or any other recognized Institution. Two years professional experience in any Govt.

Institution or a concern of repute. Agriculture from a recognized University. Degree in teaching from a recognized University,. Graduate from a recognised University with Diploma in Physical Training from a recognised Institution.

ED, from a recognised University and Hr. Domestic Science Teacher. Degree with Music, as one of the subject from a recognized University. Higher Secondary with any one of the following :�. Degree in Dance from a recognised University' 4 years Course. Diploma in Dance, from a recognised institution 5 years. Its equivalent oriental Degree in Sanskrit, and. Knowledge of Hindi essential. Desirable :- At least 2 years Teachers Training Course from a recognized institution.

Note: The condition of II class in Bachelor's Degree can be relaxed in respect of promotee candidates who have at least 5 years experience as Primary Teachers. Higher Sec. Intermediate with JBT 1 year or its equivalent. Senior Sec. Authority Rly Board's Letter No. Authority : No. Note: Such of the staff as have worked satisfactorily for two years as Data Entry Operators need not be subjected to Aptitude Test, if they are otherwise eligible for consideration for posting, promotion on ex cadre basis, as Sr.

Data Entry Operator. Note: such of the staff as had worked satisfactorily in the computer centre in these units for a period of three years prior to the qualification of graduation need not be insisted upon for reinduction into the streams covered by sub- paras 1 , 2 and 3 of this para.

The following procedure shall apply in respect of recruitment of Group D railway servants [other than Rakshaks Sainiks employed in the Railway Protection Force who are governed by the provisions of Railway Protection Force Act, and the Rules framed there under. Recruitment for each category will be made separately.

If necessary, there may be more than one unit for recruitment in a Division. The notices should also be sent to Special Employment Exchanges and the Vocational Rehabilitation Centres in the case of vacancies reserved for physically handicapped and to the Director General Resettlement and the Rajya and the Zila Sanik Boards in the case of vacancies reserved for ex-servicemen.

Copies of these notices should also be exhibited on notice boards outside railway offices etc. Note : Notification of vacancies to the Employment Exchanges should conform to provisions of Compulsory Notification of Vacancies Act, and Rules made thereunder. These may be limited in proportion to the total vacancies available in the recruitment unit concerned. In other cases, where literacy is not required for competence in the job and is not prescribed, applicants applying directly to the Railway Administration should also be considered and registration at an Employment Exchange should not be made obligatory.

They should be got registered in an Employment Exchange by deputing a Welfare Inspector, if necessary, for this purpose and will thereafter be eligible for consideration along with others. It is not necessary that their names should be nominated by the Employment Exchange concerned. In cases where the Employment Exchanges do not accept applications from such candidates and they require the candidate concerned to appear before them in person for registration of his application such applicants may be considered without their getting registered at the Employment Exchange.

At the time of selection no discrimination can be made between a candidate applying direct to the administration and the one nominated by the Employment Exchange and only the most suitable ones will be selected for appointment.

No member of the Committee shall be directly subordinate to any of the other members. The application will be screened by a Personnel Officer or any other Officer or a committee of officers nominated for this purpose and not by the selection board. Non-Officials whenever co-opted as members of the Interview Board should not be repeated in every Board. The non-official member may be issued a free first class railway return journey pass and also permitted the free use of railway rest house, if available.

Note : �All inclusive remuneration of Rs. The list will contain as many names as are likely to be needed against the bare anticipated vacancies in the course of six months or one year following the selection, depending on the frequency of recruitment No allowance should be made for medically unfit candidates etc. The currency of the panels should be normally one year. In exceptional circumstances it can be extended by one year with the personal approval of the Chief Personnel Officer [No.

The percentages of reservation for Scheduled Castes and Scheduled Tribes should be observed in recruitment to temporary or permanent vacancies. Such of the workmen as join service before attaining the age of 28 years may be allowed relaxation of maximum age limit prescribed for Group 'D' posts to the extent of their total service, which may be either continuous or broken periods. The names should be recorded strictly in the order of their taking up casual appointment at the initial stage and for the purpose of empanelment for regular Group 'D' posts, they should as far as possible, be selected in the order maintained in the aforesaid registers.

In showing preference to casual labour over other outsiders due consideration and weightage should be given to the knowledge and experience gained by them. Other conditions being equal, total length of service as casual labour , either continuous or in broken periods, irrespective of whether they have attained the temporary status or not, should be taken into account so as to ensure that casual labour who are senior by virtue of longer service are not left out.

Special instructions issued in this regard from time to time will also apply. Group 'D' vacancies in workshops should be filled up in the manner indicated below:. The Railway servants concerned should be suitable in all respects i. Transportation Traffic and Commercial Deptt. Applications should be invited from amongst categories eligible for promotion from both the branches. All Railway servants who apply will be considered.

An adhoc seniority list will be prepared on the basis of length of Continuous service in the grade and suitable men selected and placed on a panel for training. Systematic and adequate training and examinations or tests must precede actual promotions.

Civil Engineering Deptt : � Trolly men, gatemen and chowkidars should be grouped with gangmen and be eligible for promotion as keymen and mates. These persons should be required to render a minimum of three years service as gangmen but it is not necessary that they should work as gangmen in rotation. Gangmen who are disabled and cannot work as Gangmen will, of course, not be eligible for promotion.

Medical Deptt. For this purpose the eligible railway servants should be screened by holding a suitability test to determine whether they are educationally up to the required standard and have the necessary aptitude. The Railway servants considered suitable should be given training as may be necessary which they should successfully complete before they art finally promoted.

This provision will continue to remain in force till there are no non-matriculate Hospital Attendants Level-1 on Zonal Railways. The Railway servants considered suitable should be given training as may be necessary which they they should successfully complete before they are finally promoted. Signal and Telecommunication Engineering Deptt. Systematic training should also be given to semiskilled artisans for promotion to skilled categories.

The period of training may be prescribed by the individual railway administrations. In individual cases the period of training may be reduced. Mechanical Engineering Deptt. No category shall be excluded from such consideration and there need to be no sub grouping within the respective branches. Unskilled staff in running sheds should also be eligible for consideration for transfer to posts of cleaners upto the age of 30 years, relaxable upto 35 years in the case of persons belonging to scheduled castes and scheduled tribes, subject to their being otherwise eligible for such consideration but on two occasions only and their having the necessary aptitude and satisfying the medical and educational qualifications.

Electrical Engineering Department. Promotion of Safaiwalas or Sanitary cleaners in other Departments. In the case of posts which are in the normal avenue of promotion to Group 'D' railway servants, promotion should be made from amongst the railways servants of the Deptt. The quota for promotion of Group 'D' staff in the Accounts Deptts.

Promotion to Group 'C' will be subject to the following conditions: -. There should be written tests to assess the educational attainments of candidates. Group 'C' categories referred to above should be suitably linked with specified categories in the lower grades on broad affinity of work to form groups for promotion but it should be ensured that the prospects are made equal in the different groups.

The test should be correlated to the standards of proficiency that can reasonably be expected from railway servants who are generally non-matriculates. The aim of the examiners should be to assess the general suitability of the Group 'D' railway servants offering themselves for promotion to Group 'C' posts from the point of view of their knowledge of English and their general standard of intelligence.

The factors of selection and their relative weight will be as indicated below Maximum Marks. Written Test. Record of Service. Note: 1. Written test should consist of one paper of 3 hours duration divided into two parts - Part 'A' to test the working knowledge of the Railway servant of the English language and Part 'B' his general standard of intelligence and proficiency through questions in Arithmetic, General Knowledge mainly pertaining to Railway matters and matters immediately pertaining to the work he has been acquainted with during his Railway service.

In drawing up the questions it must be ensured that they are not set as such a standard as to make it impracticable for a Group 'D' railway servant of average intelligence and normal standards of efficiency to qualify in the test. However, in cases where incumbency of more than 3 years is prescribed, the same shall continue. Promotions may, however, be allowed on provisional basis and the concerned staff given two year's time from the date of promotion, to qualify the prescribed typewriting test; and if they fail to qualify the typewriting test within the said period, they will be liable to be reverted.

During the period of their training they would get as stipend the pay that they would have normally drawn on promotion to Group 'C'. All allowances like Dearness, Compensatory and House Rent Allowances will be allowed to them at the scales applicable, had the stipend been treated as pay. Note: Employees in lower Group 'C' scale of Rs. This will apply to the categories of staff who have been recruited from the open market against the vacancies reserved for recruitment of physically handicapped and the staff who acquire disability during service and are absorbed in suitable alternative employment as per provisions contained in Chapter-XIII.

One month At the Railway Staff College , Vadodara for orientation course whenever the same is arranged. Determination of Seniority of Group 'A' Probationers of Different Services in Junior Scale after their Confirmation The performance of Group 'A' probationers during the probationary training and during their posting against working post will be evaluated and marks will be awarded for each item of probationary training and for the performance while working against working posts.

Departmental Examinations All the Departmental Examinations will be conducted by the Institutes where the probationary training has been centralised. E Engg. Sub-Section II - Procedure Fitter B. Electrician C.

Instrument Mechanic D. Electronics Mechanic G. Mechanic Motor Vehicle H. Wireman I. There are a number of direct consequences of the vector space axioms. Further properties follow by employing also the distributive law for the scalar multiplication, for example a v equals 0 if and only if a equals 0 or v equals 0. Vector spaces stem from affine geometry , via the introduction of coordinates in the plane or three-dimensional space.

Bellavitis introduced the notion of a bipoint, i. In , Cayley introduced the matrix notation which allows for a harmonization and simplification of linear maps. He envisaged sets of abstract objects endowed with operations. Actually Grassmann's work exceeds the framework of vector spaces, since his considering multiplication, too, led him to what are today called algebras. Italian mathematician Peano was the first to give the modern definition of vector spaces and linear maps in An important development of vector spaces is due to the construction of function spaces by Henri Lebesgue.

This was later formalized by Banach and Hilbert , around The simplest example of a vector space over a field F is the field itself, equipped with its standard addition and multiplication. More generally, all n -tuples sequences of length n. The various axioms of a vector space follow from the fact that the same rules hold for complex number arithmetic. More generally, field extensions provide another class of examples of vector spaces, particularly in algebra and algebraic number theory : a field F containing a smaller field E is an E -vector space, by the given multiplication and addition operations of F.

Many notions in topology and analysis, such as continuity , integrability or differentiability are well-behaved with respect to linearity: sums and scalar multiples of functions possessing such a property still have that property. They are studied in greater detail using the methods of functional analysis , see below.

Systems of homogeneous linear equations are closely tied to vector spaces. They form a vector space: sums and scalar multiples of such triples still satisfy the same ratios of the three variables; thus they are solutions, too. Matrices can be used to condense multiple linear equations as above into one vector equation, namely. In a similar vein, the solutions of homogeneous linear differential equations form vector spaces.

For example,. Bases allow one to represent vectors by a sequence of scalars called coordinates or components. Linear independence means that the coordinates a k are uniquely determined for any vector in the vector space. The corresponding coordinates x 1 , x 2 , � , x n are just the Cartesian coordinates of the vector.

Every vector space has a basis. This follows from Zorn's lemma , an equivalent formulation of the Axiom of Choice.

Dimension theorem for vector spaces. If the space is spanned by finitely many vectors, the above statements can be proven without such fundamental input from set theory. The dimension of the coordinate space F n is n , by the basis exhibited above. The dimension of the polynomial ring F [ x ] introduced above [ clarification needed ] is countably infinite , a basis is given by 1 , x , x 2 , � A fortiori , the dimension of more general function spaces, such as the space of functions on some bounded or unbounded interval, is infinite.

These two functions are linearly independent over R , so the dimension of this space is two, as is the degree of the equation. A field extension over the rationals Q can be thought of as a vector space over Q by defining vector addition as field addition, defining scalar multiplication as field multiplication by elements of Q , and otherwise ignoring the field multiplication.

Thus, C is a two-dimensional R -vector space and, as any field, one-dimensional as a vector space over itself, C. The relation of two vector spaces can be expressed by linear map or linear transformation.

They are functions that reflect the vector space structure, that is, they preserve sums and scalar multiplication:. Equivalently, f is both one-to-one injective and onto surjective. For example, the "arrows in the plane" and "ordered pairs of numbers" vector spaces in the introduction are isomorphic: a planar arrow v departing at the origin of some fixed coordinate system can be expressed as an ordered pair by considering the x - and y -component of the arrow, as shown in the image at the right.

Conversely, given a pair x , y , the arrow going by x to the right or to the left, if x is negative , and y up down, if y is negative turns back the arrow v. It is an isomorphism, by its very definition. Another way to express this is that any vector space is completely classified up to isomorphism by its dimension, a single number. In particular, any n -dimensional F -vector space V is isomorphic to F n.

The freedom of choosing a convenient basis is particularly useful in the infinite-dimensional context; see below. Matrices are a useful notion to encode linear maps. Any m -by- n matrix A gives rise to a linear map from F n to F m , by the following. The determinant det A of a square matrix A is a scalar that tells whether the associated map is an isomorphism or not: to be so it is sufficient and necessary that the determinant is nonzero.

The vector space V may or may not possess an eigenbasis , a basis consisting of eigenvectors. This phenomenon is governed by the Jordan canonical form of the map. To achieve the spectral theorem , the corresponding statement in the infinite-dimensional case, the machinery of functional analysis is needed, see below.

In addition to the above concrete examples, there are a number of standard linear algebraic constructions that yield vector spaces related to given ones. In addition to the definitions given below, they are also characterized by universal properties , which determine an object X by specifying the linear maps from X to any other vector space.

A nonempty subset W of a vector space V that is closed under addition and scalar multiplication and therefore contains the 0 -vector of V is called a linear subspace of V , or simply a subspace of V , when the ambient space is unambiguously a vector space. The intersection of all subspaces containing a given set S of vectors is called its span , and it is the smallest subspace of V containing the set S.

Expressed in terms of elements, the span is the subspace consisting of all the linear combinations of elements of S. A linear subspace of dimension 1 is a vector line.

A linear subspace of dimension 2 is a vector plane. A linear subspace that contains all elements but one of a basis of the ambient space is a vector hyperplane. In a vector space of finite dimension n , a vector hyperplane is thus a subspace of dimension n � 1. The counterpart to subspaces are quotient vector spaces. This concept also extends to linear differential equations.

The direct product of vector spaces and the direct sum of vector spaces are two ways of combining an indexed family of vector spaces into a new vector space. If the index set I is finite, the two constructions agree, but in general they are different. The tensor product is a particular vector space that is a universal recipient of bilinear maps g , as follows. It is defined as the vector space consisting of finite formal sums of symbols called tensors.

From the point of view of linear algebra, vector spaces are completely understood insofar as any vector space is characterized, up to isomorphism, by its dimension. However, vector spaces per se do not offer a framework to deal with the question�crucial to analysis�whether a sequence of functions converges to another function. Likewise, linear algebra is not adapted to deal with infinite series , since the addition operation allows only finitely many terms to be added.

Therefore, the needs of functional analysis require considering additional structures. Ordered vector spaces , for example Riesz spaces , are fundamental to Lebesgue integration , which relies on the ability to express a function as a difference of two positive functions.

Vector spaces endowed with such data are known as normed vector spaces and inner product spaces , respectively. Coordinate space F n can be equipped with the standard dot product :. In R 2 , this reflects the common notion of the angle between two vectors x and y , by the law of cosines :. An important variant of the standard dot product is used in Minkowski space : R 4 endowed with the Lorentz product.

Singling out the fourth coordinate� corresponding to time , as opposed to three space-dimensions�makes it useful for the mathematical treatment of special relativity.

Convergence questions are treated by considering vector spaces V carrying a compatible topology , a structure that allows one to talk about elements being close to each other. In such topological vector spaces one can consider series of vectors. The infinite sum. For example, the f i could be real or complex functions belonging to some function space V , in which case the series is a function series.

The mode of convergence of the series depends on the topology imposed on the function space. In such cases, pointwise convergence and uniform convergence are two prominent examples. A way to ensure the existence of limits of certain infinite series is to restrict attention to spaces where any Cauchy sequence has a limit; such a vector space is called complete.

Roughly, a vector space is complete provided that it contains all necessary limits. For example, the vector space of polynomials on the unit interval [0,1], equipped with the topology of uniform convergence is not complete because any continuous function on [0,1] can be uniformly approximated by a sequence of polynomials, by the Weierstrass approximation theorem.

Banach and Hilbert spaces are complete topological vector spaces whose topologies are given, respectively, by a norm and an inner product. Their study�a key piece of functional analysis �focuses on infinite-dimensional vector spaces, since all norms on finite-dimensional topological vector spaces give rise to the same notion of convergence.

In the infinite-dimensional case, however, there will generally be inequivalent topologies, which makes the study of topological vector spaces richer than that of vector spaces without additional data. From a conceptual point of view, all notions related to topological vector spaces should match the topology.

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