Record Citations :: Library Catalog

APA (7th ed.) Citation

Xue, H. (2026). A Frankel type theorem in Euclidean and hyperbolic spaces.

Chicago Style (17th ed.) Citation

Xue, Haotian. A Frankel Type Theorem in Euclidean and Hyperbolic Spaces. 2026.

MLA (9th ed.) Citation

Xue, Haotian. A Frankel Type Theorem in Euclidean and Hyperbolic Spaces. 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_7dd7ed76b555219493f724d59c3a43e8): Failed to open stream: No space left on device

Whoops\Exception\ErrorException thrown with message "fopen(/var/lib/vufind/sessions/sess_7dd7ed76b555219493f724d59c3a43e8): 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_7dd7ed76b555219493f724d59c3a43e8): 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"
ui	"standard"
VUFIND_SESSION	"7dd7ed76b555219493f724d59c3a43e8"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790827062.8596 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "7dd7ed76b555219493f724d59c3a43e8" ]`]
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; ui=standard; VUFIND_SESSION=7dd7ed76b555219493f724d59c3a43e8"
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	"11539"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2605_19679/Cite """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2605_19679/Cite"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790827062.8551
REQUEST_TIME	1790827062

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Cannot write session to /var/lib/vufind/sessions/sess_7dd7ed76b555219493f724d59c3a43e8 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"
ui	"standard"
VUFIND_SESSION	"7dd7ed76b555219493f724d59c3a43e8"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790827062.8596 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "7dd7ed76b555219493f724d59c3a43e8" ]`]
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; ui=standard; VUFIND_SESSION=7dd7ed76b555219493f724d59c3a43e8"
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	"11539"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2605_19679/Cite """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2605_19679/Cite"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790827062.8551
REQUEST_TIME	1790827062

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler