Record Citations :: Library Catalog

APA (7th ed.) Citation

Gao, Y., & Xu, H. (2026). MacNeille completions of parabolic quotients.

Chicago Style (17th ed.) Citation

Gao, Yibo, and Hanlin Xu. MacNeille Completions of Parabolic Quotients. 2026.

MLA (9th ed.) Citation

Gao, Yibo, and Hanlin Xu. MacNeille Completions of Parabolic Quotients. 2026.

Warning: These citations may not always be 100% accurate.

Whoops! There was an error.

Whoops \ Exception \ ErrorException (E_WARNING)

fopen(/var/lib/vufind/sessions/sess_9e1f8060596e11b3f7dbd2211e2cdabb): Failed to open stream: No space left on device

Whoops\Exception\ErrorException thrown with message "fopen(/var/lib/vufind/sessions/sess_9e1f8060596e11b3f7dbd2211e2cdabb): Failed to open stream: No space left on device" Stacktrace: #5 Whoops\Exception\ErrorException in /usr/local/vufind/module/VuFind/src/VuFind/Session/File.php:159 #4 fopen in /usr/local/vufind/module/VuFind/src/VuFind/Session/File.php:159 #3 VuFind\Session\File:saveSession in /usr/local/vufind/module/VuFind/src/VuFind/Session/AbstractBase.php:192 #2 VuFind\Session\AbstractBase:write in [internal]:0 #1 session_write_close in /usr/local/vufind/vendor/laminas/laminas-session/src/SessionManager.php:242 #0 Laminas\Session\SessionManager:writeClose in [internal]:0

Application frames (0) All frames (6)

Whoops\Exception\ErrorException

…/module/VuFind/src/VuFind/Session/File.php159

fopen

…/module/VuFind/src/VuFind/Session/File.php159

VuFind\Session\File saveSession

…/module/VuFind/src/VuFind/Session/AbstractBase.php192

VuFind\Session\AbstractBase write

[internal]0

session_write_close

…/vendor/laminas/laminas-session/src/SessionManager.php242

Laminas\Session\SessionManager writeClose

[internal]0

Open: /usr/local/vufind/module/VuFind/src/VuFind/Session/File.php

            if (filemtime($filename) + $maxlifetime < time()) {
                unlink($filename);
                $count++;
            }
        }
        return $count;
    }
 
    /**
     * A function that is called internally when session data is to be saved.
     *
     * @param string $sessId The current session ID
     * @param string $data   The session data to write
     *
     * @return bool
     */
    protected function saveSession($sessId, $data): bool
    {
        $sessFile = $this->path . '/sess_' . $sessId;
        if ($handle = fopen($sessFile, 'w')) {
            $return = false;
            // Lock the file for exclusive access to avoid issues with multiple
            // processes writing session simultaneously:
            if (flock($handle, LOCK_EX)) {
                $return = fwrite($handle, $data);
                // Make sure that there's no trailing data by truncating the file to
                // the correct length:
                ftruncate($handle, strlen($data));
                fflush($handle);
                flock($handle, LOCK_UN);
            }
            fclose($handle);
            if ($return !== false) {
                return true;
            }
        }
        // If we got this far, something went wrong with the file output...
        // It is tempting to throw an exception here, but this code is called
        // outside of the context of exception handling, so all we can do is
        // echo a message.

Arguments

              "fopen(/var/lib/vufind/sessions/sess_9e1f8060596e11b3f7dbd2211e2cdabb): Failed to open stream: No space left on device"

          

Open: /usr/local/vufind/module/VuFind/src/VuFind/Session/File.php

            if (filemtime($filename) + $maxlifetime < time()) {
                unlink($filename);
                $count++;
            }
        }
        return $count;
    }
 
    /**
     * A function that is called internally when session data is to be saved.
     *
     * @param string $sessId The current session ID
     * @param string $data   The session data to write
     *
     * @return bool
     */
    protected function saveSession($sessId, $data): bool
    {
        $sessFile = $this->path . '/sess_' . $sessId;
        if ($handle = fopen($sessFile, 'w')) {
            $return = false;
            // Lock the file for exclusive access to avoid issues with multiple
            // processes writing session simultaneously:
            if (flock($handle, LOCK_EX)) {
                $return = fwrite($handle, $data);
                // Make sure that there's no trailing data by truncating the file to
                // the correct length:
                ftruncate($handle, strlen($data));
                fflush($handle);
                flock($handle, LOCK_UN);
            }
            fclose($handle);
            if ($return !== false) {
                return true;
            }
        }
        // If we got this far, something went wrong with the file output...
        // It is tempting to throw an exception here, but this code is called
        // outside of the context of exception handling, so all we can do is
        // echo a message.

Open: /usr/local/vufind/module/VuFind/src/VuFind/Session/AbstractBase.php

        // Anecdotal testing Today and Yesterday seems to indicate destroy()
        //   is called by the garbage collector and everything is good.
        // Something to keep in mind though.
        return 0;
    }
 
    /**
     * Write function that is called when session data is to be saved.
     *
     * @param string $sessId The current session ID
     * @param string $data   The session data to write
     *
     * @return bool
     */
    public function write($sessId, $data): bool
    {
        if ($this->writesDisabled) {
            return true;
        }
        return $this->saveSession($sessId, $data);
    }
 
    /**
     * A function that is called internally when session data is to be saved.
     *
     * @param string $sessId The current session ID
     * @param string $data   The session data to write
     *
     * @return bool
     */
    abstract protected function saveSession($sessId, $data): bool;
}

Open: [internal]

Open: /usr/local/vufind/vendor/laminas/laminas-session/src/SessionManager.php

     *
     * @return void
     */
    public function writeClose()
    {
        // The assumption is that we're using PHP's ext/session.
        // session_write_close() will actually overwrite $_SESSION with an
        // empty array on completion -- which leads to a mismatch between what
        // is in the storage object and $_SESSION. To get around this, we
        // temporarily reset $_SESSION to an array, and then re-link it to
        // the storage object.
        //
        // Additionally, while you _can_ write to $_SESSION following a
        // session_write_close() operation, no changes made to it will be
        // flushed to the session handler. As such, we now mark the storage
        // object isImmutable.
        $storage = $this->getStorage();
        if (! $storage->isImmutable()) {
            $_SESSION = $storage->toArray(true);
            session_write_close();
            $storage->fromArray($_SESSION);
            $storage->markImmutable();
        }
    }
 
    /**
     * Attempt to set the session name
     *
     * If the session has already been started, or if the name provided fails
     * validation, an exception will be raised.
     *
     * @param  string $name
     * @return SessionManager
     * @throws Exception\InvalidArgumentException
     */
    public function setName($name)
    {
        if ($this->sessionExists()) {
            throw new Exception\InvalidArgumentException(
                'Cannot set session name after a session has already started'

Open: [internal]

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"en"
VUFIND_SESSION	"9e1f8060596e11b3f7dbd2211e2cdabb"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790851000.6244 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "9e1f8060596e11b3f7dbd2211e2cdabb" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
SessionHelper	Laminas\Stdlib\ArrayObject {#1360}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=en; VUFIND_SESSION=9e1f8060596e11b3f7dbd2211e2cdabb; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"39195"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2604_26502/Cite """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2604_26502/Cite"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790851000.6147
REQUEST_TIME	1790851000

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Cannot write session to /var/lib/vufind/sessions/sess_9e1f8060596e11b3f7dbd2211e2cdabb Whoops! There was an error.

Whoops \ Exception \ ErrorException (E_WARNING)

session_write_close(): Failed to write session data using user defined save handler. (session.save_path: /var/lib/php/sessions, handler: VuFind\Session\File::write)

Whoops\Exception\ErrorException thrown with message "session_write_close(): Failed to write session data using user defined save handler. (session.save_path: /var/lib/php/sessions, handler: VuFind\Session\File::write)" Stacktrace: #2 Whoops\Exception\ErrorException in /usr/local/vufind/vendor/laminas/laminas-session/src/SessionManager.php:242 #1 session_write_close in /usr/local/vufind/vendor/laminas/laminas-session/src/SessionManager.php:242 #0 Laminas\Session\SessionManager:writeClose in [internal]:0

Application frames (0) All frames (3)

Whoops\Exception\ErrorException

…/vendor/laminas/laminas-session/src/SessionManager.php242

session_write_close

…/vendor/laminas/laminas-session/src/SessionManager.php242

Laminas\Session\SessionManager writeClose

[internal]0

Open: /usr/local/vufind/vendor/laminas/laminas-session/src/SessionManager.php

     *
     * @return void
     */
    public function writeClose()
    {
        // The assumption is that we're using PHP's ext/session.
        // session_write_close() will actually overwrite $_SESSION with an
        // empty array on completion -- which leads to a mismatch between what
        // is in the storage object and $_SESSION. To get around this, we
        // temporarily reset $_SESSION to an array, and then re-link it to
        // the storage object.
        //
        // Additionally, while you _can_ write to $_SESSION following a
        // session_write_close() operation, no changes made to it will be
        // flushed to the session handler. As such, we now mark the storage
        // object isImmutable.
        $storage = $this->getStorage();
        if (! $storage->isImmutable()) {
            $_SESSION = $storage->toArray(true);
            session_write_close();
            $storage->fromArray($_SESSION);
            $storage->markImmutable();
        }
    }
 
    /**
     * Attempt to set the session name
     *
     * If the session has already been started, or if the name provided fails
     * validation, an exception will be raised.
     *
     * @param  string $name
     * @return SessionManager
     * @throws Exception\InvalidArgumentException
     */
    public function setName($name)
    {
        if ($this->sessionExists()) {
            throw new Exception\InvalidArgumentException(
                'Cannot set session name after a session has already started'

Arguments

              "session_write_close(): Failed to write session data using user defined save handler. (session.save_path: /var/lib/php/sessions, handler: VuFind\Session\File::write)"

          

Open: /usr/local/vufind/vendor/laminas/laminas-session/src/SessionManager.php

     *
     * @return void
     */
    public function writeClose()
    {
        // The assumption is that we're using PHP's ext/session.
        // session_write_close() will actually overwrite $_SESSION with an
        // empty array on completion -- which leads to a mismatch between what
        // is in the storage object and $_SESSION. To get around this, we
        // temporarily reset $_SESSION to an array, and then re-link it to
        // the storage object.
        //
        // Additionally, while you _can_ write to $_SESSION following a
        // session_write_close() operation, no changes made to it will be
        // flushed to the session handler. As such, we now mark the storage
        // object isImmutable.
        $storage = $this->getStorage();
        if (! $storage->isImmutable()) {
            $_SESSION = $storage->toArray(true);
            session_write_close();
            $storage->fromArray($_SESSION);
            $storage->markImmutable();
        }
    }
 
    /**
     * Attempt to set the session name
     *
     * If the session has already been started, or if the name provided fails
     * validation, an exception will be raised.
     *
     * @param  string $name
     * @return SessionManager
     * @throws Exception\InvalidArgumentException
     */
    public function setName($name)
    {
        if ($this->sessionExists()) {
            throw new Exception\InvalidArgumentException(
                'Cannot set session name after a session has already started'

Open: [internal]

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"en"
VUFIND_SESSION	"9e1f8060596e11b3f7dbd2211e2cdabb"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790851000.6244 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "9e1f8060596e11b3f7dbd2211e2cdabb" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
SessionHelper	Laminas\Stdlib\ArrayObject {#1360}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=en; VUFIND_SESSION=9e1f8060596e11b3f7dbd2211e2cdabb; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.147"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"39195"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2604_26502/Cite """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2604_26502/Cite"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790851000.6147
REQUEST_TIME	1790851000

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler