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Increased expression of glucose transporter 3 in gerbil brains following magnesium sulfate treatment and focal cerebral ischemic injury.
Glucose is the primary energy substrate for neurons. Glucose transporter 3 (Glut3) localizes at the neuronal cellular membrane, which transports glucose from the extracelluar space into neurons. Ischemia results in an increased energy demand that is associated with profound changes in brain energy metabolism. Magnesium sulfate (MgSO(4)) ameliorates ischemia-induced neuronal death in the rat and gerbil model. We investigated the effects of MgSO(4) administration on the expression of Glut3 in cortex and hippocampus of gerbils during ischemia. The focal cerebral ischemia was produced by unilateral occlusion of the right common carotid artery and right middle cerebral artery. Following ischemia, Glut3 expression increased significantly versus non-ischemic (contra-lateral) cortex and hippocampus. MgSO(4) treatment significantly increased the level of Glut3 expression in the non-ischemic and ischemic cortex and hippocampus. We found that the MgSO(4)-induced increase in Glut3 expression was not reversed by administration of U0126, a MEK kinase inhibitor. These results suggest that other factors may function to modulate the MgSO(4)-induced Glut3 response. In all, our data showed that MgSO(4) increases the expression of Glut3 in the cortex and hippocampus of gerbil brains both in non-ischemia and ischemia status. However, the MEK signaling pathway might not be involved in MgSO(4)-induced Glut3 expression following focal ischemia.
|
2023-11-10T01:26:51.906118
|
https://example.com/article/3259
|
In connection with future legal specifications with regard to the nitrogen emissions of motor vehicles, a corresponding exhaust gas treatment is required. In order to reduce the NOx emission (NOx removal) of internal combustion engines, especially diesel engines with chronologically predominant lean, i.e. oxygen rich, exhaust gas, the so called selective catalytic reduction (SCR) process can be deployed. In this process a defined amount of a selectively active reduction agent is added to the exhaust gas. This can, for example, be in the form of ammonia, which is metered directly as a gas, or can also be derived from a precursor substance in the form of urea or from a urea-water-solution (HWL).
In the German patent DE 10139142 A1 an emission control system of an internal combustion engine is, for example, described, in which an SCR catalytic converter is deployed to reduce the NO emission which reduces the nitro en oxides contained in the exhaust as to nitrogen with the reagent substance ammonia. The ammonia is derived from a urea-water-solution (HWL) in a hydrolysis catalytic converter disposed upstream in front of the SCR-catalytic converter. The hydrolysis catalytic converter converts the urea contained in the HWL to ammonia and carbon dioxide. In a second step the ammonia reduces the nitrogen oxides to nitrogen, whereby water is produced as a byproduct. The exact mechanism has been adequately described in the trade literature (cf. WEISSWELLER in CIT (72), pages 441-449, 2000). The HWL is supplied in a reagent substance tank.
In the German patent DE 19739848 A1 a procedural approach is described, with which the NO emissions of the internal combustion engine before the catalytic converter can be calculated at least approximately from known operating parameters. The point of origin is an engine characteristic map, which is constructed from the load and rotational speed of the internal combustion engine. Additionally, provision can be made for corrections, for example, as a function of the air number lambda.
From the patent EP 1024254 A2 an exhaust gas treatment system of an internal combustion engine is made known, in which an SCR-catalytic converter is likewise deployed to reduce the NOx emissions. Provision is made again for ammonia to be the reagent substance which is derived from a urea-water-solution (HWL) in the exhaust gas tract. The reagent substance rate is established using the amount of fuel injected, the engine rotational speed as well as using at least one parameter of the exhaust gas, for example, the exhaust gas temperature.
In the patent EP 697062 B1 a procedure and a mechanism are described for the controlled introduction of a reagent substance into an exhaust gas containing nitrogen oxide. Provision is likewise made for a SCR-catalytic converter, which requires ammonia as a reagent substance, which is derived from a reagent substance introduced into the exhaust gas tract upstream from the SCR-catalytic converter. At least one parameter of the exhaust gas relevant to the operation, at least one parameter of a catalytic converter relevant to the operation and if need be a parameter of the internal combustion engine relevant to the operation are acquired to determine the NOx emissions before the catalytic converter of the internal combustion engine. Corresponding to the NOx emissions before the catalytic converter, an intermediate value is determined for a reagent substance rate to be specified. This intermediate value is reduced by a reagent substance rate desorbed by the catalytic converter or increased by a reagent substance rate adsorbed by the catalytic converter.
This characteristic of the SCR-catalytic converter, to be able to at least partially store ammonia, can or must be used depending upon catalytic converter type and metering strategy in order to optimize the NOx conversion rates. Additionally, the ammonia storage capability must be known in order to avoid ammonia breaches, as they can occur during dramatic temperature increases. The background for that is that with increasing temperature the ammonia storage capacity of the catalytic converter sinks. An uncontrolled release of stored ammonia resulting from this leads to offensive smells. To monitor an ammonia breach, ammonia sensors are meanwhile known in context with SCR-catalytic converters. On the basis of zeolite layers, these sensors change their electrical conductivity with the ammonia concentration in the gas surrounding them.
As a rule the ammonia storage capability of a catalytic converter is known when new and can be deposited in a liquid level characteristic curve as a function of temperature. The reduction of the ammonia storage capability with the life of the system (deterioration) is, however, not known.
It is, therefore, the task of the invention, to provide a procedure to monitor the performance capability of a catalytic converter, especially its capability to store reduction agents.
It is additionally the task of the invention, to provide a corresponding device.
|
2023-12-18T01:26:51.906118
|
https://example.com/article/2823
|
Development and evaluation of a reverse transcription-insulated isothermal polymerase chain reaction (RT-iiPCR) assay for detection of equine arteritis virus in equine semen and tissue samples using the POCKIT™ system.
Equine arteritis virus (EAV) is the causative agent of equine viral arteritis (EVA), a respiratory and reproductive disease of horses. Most importantly, EAV induces abortion in pregnant mares and can establish persistent infection in up to 10-70% of the infected stallions, which will continue to shed the virus in their semen. The objective of this study was to develop and evaluate a reverse transcription insulated isothermal polymerase chain reaction (RT-iiPCR) for the detection of EAV in semen and tissue samples. The newly developed assay had a limit of detection of 10 RNA copies and a 10-fold higher sensitivity than a previously described real-time RT-PCR (RT-qPCR). Evaluation of 125 semen samples revealed a sensitivity and specificity of 98.46% and 100.00%, respectively for the RT-qPCR assay, and 100.00% and 98.33%, respectively for the RT-iiPCR assay. Both assays had the same accuracy (99.2%, k=0.98) compared to virus isolation. Corresponding values derived from testing various tissue samples (n=122) collected from aborted fetuses, foals, and EAV carrier stallions are as follows: relative sensitivity, specificity, and accuracy of 88.14%, 96.83%, and 92.62% (k=0.85), respectively for the RT-qPCR assay, and 98.31%, 92.06%, and 95.08% (k=0.90), respectively for the RT-iiPCR assay. These results indicate that RT-iiPCR is a sensitive, specific, and a robust test enabling detection of EAV in semen and tissue samples with very considerable accuracy. Even though the RT-qPCR assay showed a sensitivity and specificity equal to virus isolation for semen samples, its diagnostic performance was somewhat limited for tissue samples. Thus, this new RT-iiPCR could be considered as an alternative tool in the implementation of EAV control and prevention strategies.
|
2024-06-24T01:26:51.906118
|
https://example.com/article/9542
|
// Copyright © 2016 Sidharth Kshatriya
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
package engine
import (
"bufio"
"encoding/json"
"fmt"
"github.com/chzyer/readline"
"github.com/cyrus-and/gdb"
"github.com/fatih/color"
"github.com/kr/pty"
"io"
"io/ioutil"
"log"
"net"
"os"
"os/exec"
"os/user"
"path"
"path/filepath"
"strconv"
"strings"
"sync"
"time"
)
const (
numFilesSentinel = "//&&& Number of Files:"
maxStackDepthSentinel = "//&&& Max Stack Depth:"
phpFilenameSentinel = "//###"
levelSentinel = "//$$$"
// @TODO improve this
gHelpText = `
h display this help text
q quit
r debug in reverse mode
f debug in forward (normal) mode
t toggle between reverse and forward modes
v toggle between verbose and quiet modes
n toggle between showing and not showing gdb notifications
<enter> will tell you whether you are in forward or reverse mode
Debugging in reverse mode can be confusing but here is a cheat sheet:
The buttons in your PHP IDE debugger will have the following new (and opposite) meanings in reverse debugging mode:
step-into becomes: step-into a PHP statement in the reverse direction
step-over becomes: step-over one PHP statement backwards. As usual, stop if you encounter
a breakpoint while doing this operation.
step-out becomes: run backwards until you come out of the current function and are about to enter it.
As usual, stop if you encounter a breakpoint while doing this operation.
run/continue becomes: run backwards until you hit a breakpoint
run to cursor becomes: run backwards until you hit the cursor (need to place cursor before current line)
Expert Usage:
* For commands to be sent to GDB-MI prefix command with "-" e.g. -thread-info
* For dbgp commands to be sent to PHP, prefix command with "#" e.g. #stack_get -i 0
Note: only a subset of dbgp commands may issued in this way.
`
)
type snapInfo struct {
snapRRTraceDir string
snapRootDir string
origDocrootOrScript string
}
func getSnapInfoFromUser() (snapInfo, bool) {
currentUser, err := user.Current()
fatalIf(err)
rrHome := currentUser.HomeDir + "/.local/share/rr"
snapshotDirsGlob := fmt.Sprintf("%v/*/dontbug-snapshot*", rrHome)
matches, err := filepath.Glob(snapshotDirsGlob)
fatalIf(err)
traceDirAr := make([]snapInfo, 0, 20)
fmt.Println("Saved Snapshots (created with flag --take-snapshot in `dontbug record`)")
fmt.Println("-----------------------------------------------------------------------")
fmt.Println("A snapshot comprises PHP sources at a point in time along with an rr execution trace")
i := 0
for _, v := range matches {
if strings.Contains(v, "latest-trace") {
continue
}
metaDataBytes, err := ioutil.ReadFile(v)
fatalIf(err)
if strings.TrimSpace(string(metaDataBytes)) == "" {
continue
}
info, err := os.Stat(v)
fatalIf(err)
modTime := info.ModTime().Format("2006-01-02 15:04:05")
traceDir := path.Dir(v)
metaData := string(metaDataBytes)
rootDir := strings.Split(metaData, ":")[0]
origDocrootOrScript := strings.Split(metaData, ":")[1]
fmt.Printf("[%v] Snapshot for %v Date: %v rr trace: %v\nPHP sources stored at: %v\n", i, origDocrootOrScript, modTime, traceDir, rootDir)
i++
traceDirAr = append(traceDirAr, snapInfo{
snapRRTraceDir: traceDir,
snapRootDir: rootDir,
origDocrootOrScript: origDocrootOrScript,
})
}
if i == 0 {
fmt.Println("\nNo saved snapshots")
os.Exit(0)
}
for {
// @TODO commands like delete
var snapShotSel string
fmt.Print("Snapshot number to replay> ")
fmt.Scanln(&snapShotSel)
snapShotSel = strings.TrimSpace(snapShotSel)
snapShotNum, err := strconv.Atoi(snapShotSel)
if err != nil || snapShotNum < 0 || snapShotNum >= i {
fmt.Println("Please enter a valid snapshot number")
continue
}
return traceDirAr[snapShotNum], true
}
}
func DoReplay(installLocation, replayArg, rrPath, gdbPath string, replayHost string, replayPort int, targetExtendedRemotePort int) {
extAbsNoSymDir := getAbsNoSymExtDirAndCheckInstallLocation(installLocation)
bpMap, levelAr, maxStackDepth := constructBreakpointLocMap(extAbsNoSymDir)
rrTraceDir := "" // This corresponds to the latest trace
snapInfo := snapInfo{}
if replayArg == "snaps" {
var ok bool
snapInfo, ok = getSnapInfoFromUser()
if ok {
rrTraceDir = snapInfo.snapRRTraceDir
}
}
if rrTraceDir != "" {
color.Yellow("dontbug: Using snapshot %v corresponding to rr trace: %v", snapInfo.snapRootDir, rrTraceDir)
} else {
color.Yellow("dontbug: Using latest trace")
}
engineState := startReplayInRR(
rrTraceDir,
rrPath,
gdbPath,
bpMap,
levelAr,
maxStackDepth,
targetExtendedRemotePort,
)
debuggerLoop(engineState, replayHost, replayPort)
}
func startReplayInRR(traceDir string, rrPath, gdbPath string, bpMap map[string]int, levelAr []int, maxStackDepth int, targetExtendedRemotePort int) *engineState {
rrCmdAr := []string{
rrPath,
"replay",
"-s", strconv.Itoa(targetExtendedRemotePort),
traceDir,
}
// Start an rr replay session
replayCmd := exec.Command(rrCmdAr[0], rrCmdAr[1:]...)
Verbosef("dontbug: Issuing command: %v\n", strings.Join(rrCmdAr, " "))
f, err := pty.Start(replayCmd)
fatalIf(err)
color.Green("dontbug: Successfully started replay session")
// Abort if we are not able to get the gdb connection string within 5 sec
cancel := make(chan bool, 1)
go func() {
time.Sleep(5 * time.Second)
select {
case <-cancel:
return
default:
log.Fatal("Could not find gdb connection string that is given by rr")
}
}()
// Get hardlink filename which will be needed for gdb debugging
buf := bufio.NewReader(f)
for {
line, err := buf.ReadString('\n')
if strings.Contains(line, "target extended-remote") {
cancel <- true
close(cancel)
fmt.Print(line)
go io.Copy(os.Stdout, f)
slashAt := strings.Index(line, "/")
hardlinkFile := strings.TrimSpace(line[slashAt:])
return startGdbAndInitDebugEngineState(
gdbPath,
hardlinkFile,
bpMap,
levelAr,
maxStackDepth,
f,
replayCmd,
targetExtendedRemotePort,
)
}
if err != nil {
log.Fatal("Could not find gdb connection string that is given by rr")
}
fmt.Print(line)
}
}
// Starts gdb and creates a new DebugEngineState object
func startGdbAndInitDebugEngineState(gdbExecutable string, hardlinkFile string, bpMap map[string]int, levelAr []int, maxStackDepth int, rrFile *os.File, rrCmd *exec.Cmd, targetExtendedRemotePort int) *engineState {
gdbArgs := []string{
gdbExecutable,
"-l", "-1",
"-ex", fmt.Sprintf("target extended-remote :%v", targetExtendedRemotePort),
"--interpreter", "mi",
hardlinkFile,
}
Verboseln("dontbug: Issuing command: ", strings.Join(gdbArgs, " "))
var gdbSession *gdb.Gdb
var err error
stopEventChan := make(chan string)
started := false
gdbSession, err = gdb.NewCmd(gdbArgs,
func(notification map[string]interface{}) {
if ShowGdbNotifications {
jsonResult, err := json.MarshalIndent(notification, "", " ")
fatalIf(err)
fmt.Println(string(jsonResult))
}
id, ok := breakpointStopGetID(notification)
if ok {
// Don't send the very first stopped notification
if started {
stopEventChan <- id
}
started = true
}
})
fatalIf(err)
go io.Copy(os.Stdout, gdbSession)
// This is our usual steppping breakpoint. Initially disabled.
miArgsAr := []string{"-f", "-d", "--source", "dontbug.c", "--line", strconv.Itoa(dontbugCstepLineNum)}
result := sendGdbCommand(gdbSession, "break-insert", miArgsAr...)
// Note that this is a temporary breakpoint, just to get things started
miArgsAr = []string{"-t", "-f", "--source", "dontbug.c", "--line", strconv.Itoa(dontbugCstepLineNumTemp)}
sendGdbCommand(gdbSession, "break-insert", miArgsAr...)
// Unlimited print length in gdb so that results from gdb are not "chopped" off
sendGdbCommand(gdbSession, "gdb-set", "print", "elements", "0")
// Should break on line: dontbugCstepLineNumTemp of dontbug.c
sendGdbCommand(gdbSession, "exec-continue")
result = sendGdbCommand(gdbSession, "data-evaluate-expression", "filename")
payload := result["payload"].(map[string]interface{})
filename := payload["value"].(string)
properFilename, err := parseGdbStringResponse(filename)
fatalIf(err)
es := &engineState{
gdbSession: gdbSession,
breakStopNotify: stopEventChan,
featureMap: initFeatureMap(),
entryFilePHP: properFilename,
status: statusStarting,
reason: reasonOk,
sourceMap: bpMap,
lastSequenceNum: 0,
levelAr: levelAr,
rrCmd: rrCmd,
maxStackDepth: maxStackDepth,
breakpoints: make(map[string]*engineBreakPoint, 10),
rrFile: rrFile,
}
// "1" is always the first breakpoint number in gdb
// Its used for stepping
es.breakpoints["1"] = &engineBreakPoint{
id: "1",
lineno: dontbugCstepLineNum,
filename: "dontbug.c",
state: breakpointStateDisabled,
temporary: false,
bpType: breakpointTypeInternal,
}
return es
}
func debuggerLoop(es *engineState, replayHost string, replayPort int) {
defer func() {
es.rrFile.Close()
err := es.rrCmd.Wait()
fatalIf(err)
}()
defer es.gdbSession.Exit()
reverse := false
mutex := &sync.Mutex{}
closeConChan := make(chan bool, 1)
defer func() {
closeConChan <- true
}()
go debuggerIdeLoop(es, closeConChan, mutex, &reverse, replayHost, replayPort)
fmt.Print("(dontbug) ") // prompt
currentUser, err := user.Current()
fatalIf(err)
historyFile := currentUser.HomeDir + "/.dontbug.history"
rdline, err := readline.NewEx(
&readline.Config{
Prompt: "(dontbug) ",
HistoryFile: historyFile,
})
fatalIf(err)
defer rdline.Close()
color.Yellow("h <enter> for help. If the prompt does not display press <enter>")
for {
userResponse, err := rdline.Readline()
if err == io.EOF || err == readline.ErrInterrupt {
color.Yellow("Exiting.")
return
} else if err != nil {
log.Fatal(err)
}
if strings.HasPrefix(userResponse, "t") {
mutex.Lock()
reverse = !reverse
mutex.Unlock()
if reverse {
color.Red("In reverse mode")
} else {
color.Green("In forward mode")
}
} else if strings.HasPrefix(userResponse, "r") {
mutex.Lock()
reverse = true
mutex.Unlock()
color.Red("In reverse mode")
} else if strings.HasPrefix(userResponse, "f") {
mutex.Lock()
reverse = false
mutex.Unlock()
color.Green("In forward mode")
} else if strings.HasPrefix(userResponse, "-") {
command := strings.TrimSpace(userResponse[1:])
result := sendGdbCommand(es.gdbSession, command)
jsonResult, err := json.MarshalIndent(result, "", " ")
fatalIf(err)
fmt.Println(string(jsonResult))
} else if strings.HasPrefix(userResponse, "v") {
VerboseFlag = !VerboseFlag
if VerboseFlag {
color.Red("Verbose mode")
} else {
color.Green("Quiet mode")
}
} else if strings.HasPrefix(userResponse, "n") {
ShowGdbNotifications = !ShowGdbNotifications
if ShowGdbNotifications {
color.Red("Will show gdb notifications")
} else {
color.Green("Wont show gdb notifications")
}
} else if strings.HasPrefix(userResponse, "#") {
command := strings.TrimSpace(userResponse[1:])
// @TODO blacklist commands that are handled in gdb or dontbug instead
xmlResult := recoverableDiversionSessionCmd(es, command)
fmt.Println(xmlResult)
} else if strings.HasPrefix(userResponse, "q") {
color.Yellow("Exiting.")
return
} else if strings.HasPrefix(userResponse, "h") {
fmt.Println(gHelpText)
} else {
if reverse {
color.Red("In reverse mode")
} else {
color.Green("In forward mode")
}
}
}
}
func debuggerIdeLoop(es *engineState, closeConnChan chan bool, mutex *sync.Mutex, reverse *bool, replayHost string, replayPort int) {
color.Yellow("dontbug: Trying to connect to debugger IDE")
conn, err := net.Dial("tcp", fmt.Sprintf("%v:%v", replayHost, replayPort))
if err != nil {
log.Fatalf("%v: Is your IDE listening for debugging connections from PHP?", err)
}
es.ideConnection = conn
defer func() {
color.Yellow("dontbug: Closing connection to IDE")
conn.Close()
es.ideConnection = nil
fmt.Print("(dontbug) ")
}()
// send the init packet
payload := fmt.Sprintf(gInitXMLResponseFormat, es.entryFilePHP, os.Getpid())
packet := constructDbgpPacket(payload)
_, err = conn.Write(packet)
fatalIf(err)
color.Green("dontbug: Connected to PHP IDE debugger")
buf := bufio.NewReader(conn)
go func(closeChan chan<- bool) {
defer func() {
r := recover()
if r != nil {
fmt.Println(r)
fmt.Println("Recovering from panic....")
color.Yellow("dontbug: Initiating shutdown of IDE connection. The dontbug prompt will be still operable")
}
closeChan <- true
}()
for es.status != statusStopped {
command, err := buf.ReadString(byte(0))
command = strings.TrimRight(command, "\x00")
if err == io.EOF {
Verboseln("dontbug: EOF Received on tcp connection to IDE")
break
} else if err != nil {
Verboseln("dontbug: IDE TCP connection was terminated")
break
}
if VerboseFlag {
color.Cyan("\nide -> dontbug: %v", command)
}
mutex.Lock()
reverseVal := *reverse
mutex.Unlock()
payload = dispatchIdeRequest(es, command, reverseVal)
conn.Write(constructDbgpPacket(payload))
if VerboseFlag {
continued := ""
if len(payload) > 300 {
continued = "..."
}
color.Green("dontbug -> ide:\n%.300v%v", payload, continued)
fmt.Print("(dontbug) ")
}
}
}(closeConnChan)
<-closeConnChan
}
func dispatchIdeRequest(es *engineState, command string, reverseMode bool) string {
dbgpCmd := parseCommand(command, reverseMode)
es.lastSequenceNum = dbgpCmd.seqNum
switch dbgpCmd.command {
case "feature_set":
return handleFeatureSet(es, dbgpCmd)
case "feature_get":
return handleFeatureGet(es, dbgpCmd)
case "status":
return handleStatus(es, dbgpCmd)
case "breakpoint_set":
return handleBreakpointSet(es, dbgpCmd)
case "breakpoint_remove":
return handleBreakpointRemove(es, dbgpCmd)
case "breakpoint_update":
return handleBreakpointUpdate(es, dbgpCmd)
case "step_into":
return handleStepInto(es, dbgpCmd)
case "step_over":
return handleStepOverOrOut(es, dbgpCmd, false)
case "step_out":
return handleStepOverOrOut(es, dbgpCmd, true)
case "eval":
return handleInDiversionSessionWithNoGdbBpts(es, dbgpCmd)
case "stdout":
return handleStdFd(es, dbgpCmd, "stdout")
case "stdin":
return handleStdFd(es, dbgpCmd, "stdin")
case "stderr":
return handleStdFd(es, dbgpCmd, "stderr")
case "property_set":
return handlePropertySet(es, dbgpCmd)
case "property_get":
return handleInDiversionSessionWithNoGdbBpts(es, dbgpCmd)
case "context_get":
return handleInDiversionSessionWithNoGdbBpts(es, dbgpCmd)
case "run":
return handleRun(es, dbgpCmd)
case "stop":
color.Yellow("IDE sent 'stop' command")
return handleStop(es, dbgpCmd)
// All these are dealt with in handleInDiversionSessionStandard()
case "stack_get":
return handleInDiversionSessionStandard(es, dbgpCmd)
case "stack_depth":
return handleInDiversionSessionStandard(es, dbgpCmd)
case "context_names":
return handleInDiversionSessionStandard(es, dbgpCmd)
case "typemap_get":
return handleInDiversionSessionStandard(es, dbgpCmd)
case "source":
return handleInDiversionSessionStandard(es, dbgpCmd)
case "property_value":
return handleInDiversionSessionStandard(es, dbgpCmd)
default:
es.sourceMap = nil // Just to reduce size of map dump to stdout
fmt.Println(es)
panicIf(fmt.Errorf("Unimplemented command: %v", command))
}
return ""
}
func constructBreakpointLocMap(extensionDir string) (map[string]int, []int, int) {
absExtDir := getAbsNoSymlinkPath(extensionDir)
dontbugBreakFilename := absExtDir + "/dontbug_break.c"
Verboseln("dontbug: Looking for dontbug_break.c in", absExtDir)
file, err := os.Open(dontbugBreakFilename)
fatalIf(err)
defer file.Close()
Verboseln("dontbug: Found", dontbugBreakFilename)
bpLocMap := make(map[string]int, 1000)
buf := bufio.NewReader(file)
level := 0
lineno := 0
line, err := buf.ReadString('\n')
lineno++
fatalIf(err)
indexNumFiles := strings.Index(line, numFilesSentinel)
if indexNumFiles == -1 {
log.Fatal("Could not find the sentinel: ", numFilesSentinel)
}
numFiles, err := strconv.Atoi(strings.TrimSpace(line[indexNumFiles+len(numFilesSentinel):]))
fatalIf(err)
line, err = buf.ReadString('\n')
lineno++
fatalIf(err)
indexMaxStackDepth := strings.Index(line, maxStackDepthSentinel)
if indexMaxStackDepth == -1 {
log.Fatal("Could not find the marker: ", maxStackDepthSentinel)
}
maxStackDepth, err := strconv.Atoi(strings.TrimSpace(line[indexMaxStackDepth+len(maxStackDepthSentinel):]))
fatalIf(err)
levelLocAr := make([]int, maxStackDepth)
for {
line, err := buf.ReadString('\n')
lineno++
if err == io.EOF {
break
} else if err != nil {
log.Fatal(err)
}
indexB := strings.Index(line, phpFilenameSentinel)
indexL := strings.Index(line, levelSentinel)
if indexB != -1 {
filename := strings.TrimSpace("file://" + line[indexB+dontbugCpathStartsAt:])
_, ok := bpLocMap[filename]
if ok {
log.Fatal("dontbug: Sanity check failed. Duplicate entry for filename: ", filename)
}
bpLocMap[filename] = lineno
}
if indexL != -1 {
levelLocAr[level] = lineno
level++
}
}
if len(bpLocMap) != numFiles {
log.Fatal("dontbug: Consistency check failed. dontbug_break.c file says ", numFiles, " files. However ", len(bpLocMap), " files were found")
}
Verboseln("dontbug: Completed building association of filename => linenumbers and levels => linenumbers for breakpoints")
return bpLocMap, levelLocAr, maxStackDepth
}
|
2024-06-06T01:26:51.906118
|
https://example.com/article/3980
|
Enhancement of glucose uptake in muscular cell by soybean charged peptides isolated by electrodialysis with ultrafiltration membranes (EDUF): activation of the AMPK pathway.
Soy peptides consumption has been associated with beneficial effects in type 2 diabetes patients. However, the peptide fractions responsible for these effects, and their mechanisms of action, have not been identified yet. In this study, we have isolated soybean peptides by electrodialysis with an ultrafiltration membrane (EDUF) at 50 V/100 kDa, and tested them for their capacity to improve glucose uptake in L6 muscle cells. We observed that these fractions were able to significantly enhance glucose uptake in the presence of insulin. The reported bioactivity would be due to the low molecular weight peptides (300-500 Da) recovered. Moreover, we observed that an enhancement of glucose uptake was correlated to the activation of the AMPK enzyme, well known for its capacity to increase glucose uptake in muscle cells. To our knowledge, this is the first time that bioactive peptides with glucose uptake activity have been isolated from a complex soy matrix, and that the implication of AMPK in it is demonstrated.
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2023-12-14T01:26:51.906118
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https://example.com/article/9853
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1. Field of the Invention
The present invention generally relates to electromagnetic transponder systems and, more specifically, to electromagnetic transponders that do not have their own power supply, but rather which extract the power required for the operation of the electronic circuits comprised therein from an electromagnetic field radiated by a read and/or read/write terminal.
An example of application of the present invention relates to electronic tags (TAG) comprising an electronic chip and a radio-frequency field reception antenna.
2. Discussion of the Related Art
FIG. 1 is a schematic block diagram illustrating an example of an electromagnetic transponder system of the type to which the present invention applies. An electronic tag 1 forming an electromagnetic transponder is based on an oscillating circuit 10 formed, for example, of an inductive element 11 in parallel with a capacitive element 12 between two terminals 13 and 14 of circuit 10. Terminals 13 and 14 are connected to an electric circuit 15 (IC), generally a single integrated circuit, intended to exploit the voltage sampled across oscillating circuit 10 when tag 1 is a radio-frequency field radiated by a terminal 2 (READER) or read or read/write terminal. Terminal 2 comprises an oscillating circuit 20 based on an inductive element 21 forming an antenna, for example, in series with a capacitive element 22 and a resistive element 26 between two terminals 23 and 24 of an electronic circuit 25 (ICS). Circuit 25 comprises one or several integrated circuits for exciting the oscillating circuit and interpreting possible transmissions coming from electronic tag 1.
The operation of such a system is based on the coupling of oscillating circuits 20 and 10 of terminal 2 and of transponder 1. On the side of terminal 2, circuit 25 generates a high-frequency excitation signal (typically with a carrier at a frequency on the order of 13.56 MHz or on the order of 125 kHz according to applications). This signal is applied to antenna 21 of generation of an electromagnetic field in the vicinity of the terminal. When a transponder 1 is in the field of the terminal, its antenna 11 collects the power radiated by the terminal and resonant circuit 10 develops between its terminals 13 and 14 a voltage exploitable by circuit 15. Oscillating circuits 10 and 20 are generally tuned to a same resonance frequency approximately corresponding to the carrier frequency of the signal transmitted by the terminal. Generally, circuit 15 has no autonomous power supply and samples the power necessary for its operation from the field radiated by the terminal. Circuit 15 integrates so-called back-modulation means for modifying the load formed by transponder 1 in the field of the terminal to enable a communication in the transponder-to-terminal direction. On the side of terminal 2, the voltage across capacitive element 22 is for example measured, the interconnection point between antenna 21 and capacitor 22 being connected (connection 27) to circuit 25 to enable demodulation of transponder-to-terminal transmissions. According to applications, the high-frequency carrier generated by terminal 2 may also be modulated to transmit information to the transponder.
FIG. 2 very schematically shows, in top view, an example of an electronic tag 1 of the type to which the present invention more specifically applies. Such a tag is formed of a plate 16 (flexible or rigid) on which is deposited a metal 11 in the form of a planar winding of concentric spirals to form the antenna, the two ends of track 11 being connected to terminals of circuit 15, here assumed to integrate capacitor 12.
A tag 1 such as illustrated in FIG. 2 is generally associated with an object or an element, for example, for identification purposes. These may be products (for example, products for sale in a store), smart cards in access-control applications, etc. More generally, an electronic tag may be associated with any object or system (for example, a vehicle) for identification, counting, or other purposes.
FIG. 3 shows an example of an object 30 on which (for example glued) a tag 1 of the type illustrated in FIG. 2 is placed. Product 30 is assumed to be made of an insulating material (DIEL), for example, cardboard, plastic matter, etc. When the planar antenna (not visible in FIG. 3) of tag 1 is close to a reader (represented in FIG. 3 by its antenna 21), the electric field of antenna 21 is likely to be sensed by product 1, field lines EF crossing plate 16 (FIG. 2) of tag 1 and object 30 by passing through the center of planar winding 11.
A problem is however posed in the case where tag 1 is placed on a metal object at least at the surface thereof. Indeed, the electromagnetic field is disturbed by this object that it cannot cross. Further, this causes a detuning of the oscillating circuits of the terminal and of the transponder, which adversely affects the remote supply of the tag and the information transmission.
FIG. 4 very schematically shows a first known example of a solution for placing a planar-antenna electronic tag 1 on a metal object 40 (METAL). This solution consists of interposing a spacer 41 formed of an insulating block between tag 1 and object 40. A disadvantage is the bulk of spacer 41, the thickness of which must in practice be greater than 5 millimeters to enable field lines EF to come out through the lateral surfaces of this spacer.
FIG. 5 very schematically shows a second conventional example of a solution for placing an electronic tag 1 on a metal object 40. In this solution, a ferrite spacer 43 is interposed between metal object 40 and electronic tag 1. The use of a ferrite spacer enables reducing the thickness of this spacer, the ferromagnetic material conducting the field to enable looping back of the field lines and avoid the metal disturbance. A disadvantage of ferrite or another ferromagnetic material is that such materials are expensive, in practice incompatible with the low costs desired for electronic tag systems.
The problem of the disturbance created by a metal object on the operation of a transponder system is all the more critical as the carrier frequency is high. Indeed, the higher the frequency, the smaller the number of turns of planar winding 11 of the antenna (typically from 1 to 3 turns for a 13.56-MHz frequency). Now, the smaller the number of turns, the lower the coupling and the more the system is sensitive to disturbances.
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2023-08-14T01:26:51.906118
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https://example.com/article/4866
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BIG thanks to Hi-Torque Publications for
allowing
me to use the articles from Dirtwheels and 3&4 Wheel Action. If
you'd
like to subscribe, please check out their website!
---------------------------------------------------------------------------
I'd also like to thank Bruce Simurda for allowing
me to post articles from 3wheeling magazine. This was later renamed to
ATV Sports before going out of business in the early 90s (shoulda kept
the trike name guys!).
Please be patient while loading, some of these tests
are
4 pages or more. I've tried to reduce the file size as much as possible
without compromising the readability and quality of the scans. However,
by necessity some are VERY large. So go get a cold beverage of your
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use the bathroom, and by the time you're done they may be loaded. Trust
me, they're worth the wait.
All articles from Dirtwheels and 3&4Wheel Action are copyright
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2024-05-21T01:26:51.906118
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https://example.com/article/1281
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Will Paul Ryan Go the Way of Palin, Edwards and Lieberman? The past three V.P. candidates have faded from public soon after their losses.
Nov. 7, 2012 -- Paul Ryan may have been on the losing ticket with running mate Mitt Romney, but he was a winner in Wisconsin where he once again was elected to serve as U.S. congressman.
Ryan won his eighth consecutive term as the representative for Wisconsin's 1st District, a position which helped him rise to national prominence as the chairman of the House Budget Committee during his last term.
Check out full coverage of Election 2012 from ABC News.
Now, when he returns to Congress in 2013, many political watchers will be wondering where Ryan goes from here. Will his run as a vice presidential candidate boost his stature in the House, or will he follow the path of recent Veep candidates whose stature within their parties was significantly altered after their losses, including Sarah Palin, John Edwards, and the soon-to-be-retired Joe Lieberman?
All three V.P. candidates were once at the top of their parties, but after suffering losses at the national level, fell from their parties' pedestals rather quickly.
In the 2000 election, Lieberman lost alongside Al Gore on the presidential ticket against George Bush and Dick Cheney in the famous recount election. In 2006, he was forced to leave his own party after a Democratic challenger won the Senate primary. Lieberman still won his seat as an Independent and then threw his support behind 2008 Republican presidential candidate John McCain. Lieberman announced plans in 2011 to retire from national politics at the end of this term.
Read President Obama's Acceptance Speech from Tuesday Night
John Edwards and Sarah Palin both lost on their bids for vice president, Edwards alongside John Kerry in 2004 and Palin alongside John McCain in 2008, and watched as their political careers were swallowed by tabloid fascination with their personal lives.
Shortly after Edwards' bid for the presidency in 2008, he was indicted on campaign finance crime charges and was the subject of a National Enquirer story about his affair with a campaign worker that resulted in Edwards having a secret love child. The scandal, which erupted while Edwards was running for president, ended his political career despite the fact that he was eventually found not guilty in a headline grabbing trial.
Palin rose to fame as McCain's running mate in 2008, but shortly after their loss she resigned from her post as Alaska governor and became a political consultant to Fox News. She was featured in a reality show on TLC, and her daughter was a featured performer on Dancing With the Stars. But Palin decided against running for president this year and it's not clear that she is a viable candidate in the future.
Stu Rothenberg, a political commentator who writes the Rothenberg Report online each week, said he doubts Ryan will fare the same way his most recent predecessors have.
"That is a conclusion based on a ridiculously small sample," he said.
"I suppose he'll get more media attention that will make him one of the party's spokesman over the next couple of years," Rothenberg said. "Without the White House, there's no obvious party spokesman other than Boehner, so who's going to be on the Sunday morning shows and doing interviews? I would think Ryan will definitely be in the mix."
Ryan, who is heading back to Wisconsin today, released a statement saying he looked forward to going back to Congress next year.
"I am immensely proud of the campaign we ran, and I remain grateful to Gov. Romney for the honor of being his running mate," he said. "I look forward to spending some time with my family in the coming days and then continuing my responsibilities as chairman of the House Budget Committee and representative of Wisconsin's First Congressional District."
Ryan drew praise as the HBC chair after introducing his budget proposal, which became a controversial part of the Romney campaign when Ryan was announced as his running mate in August.
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2023-09-26T01:26:51.906118
|
https://example.com/article/1276
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In recent years, especially in the area of avionics, multiple dissimilar general purpose microprocessor architectures have been used to attain a high level of assurance of integrity of general purpose microprocessor performance. These multiple processors are used in parallel, and their outputs are compared to reduce the likelihood of an undetected processor failure.
While these multiple dissimilar microprocessor architectures have been used extensively in the past, they do have some drawbacks. First of all, these architectures often use commercially available general purpose processors because of their relatively high performance and low cost. However, these processors, with their ever-increasing size, have increased capacity for bugs or defects. Therefore, with each increase in microprocessor size, which is heralded by the PC community, there is an actual reduction in assurance level. Additionally, when attempting to run the same program on dissimilar processors for avionics equipment, it is necessary to compile and maintain, over the service life of the product (which can often be in excess of thirty years), distinct versions for each of the dissimilar processors. This can be expensive.
Yet another drawback of dissimilar processors is the level of complexity typically involved in achieving communication between the dissimilar processors.
Consequently, there exists a need for economically efficient improved methods and systems for providing enhanced microprocessor integrity without the need for maintaining multiple versions of each of the various applications which run on the multiple processor system.
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2023-10-24T01:26:51.906118
|
https://example.com/article/8672
|
/* This file is part of the MicroPython project, http://micropython.org/
* The MIT License (MIT)
* Copyright (c) 2019 Damien P. George
*/
#ifndef MICROPY_INCLUDED_STM32WBXX_HAL_CONF_H
#define MICROPY_INCLUDED_STM32WBXX_HAL_CONF_H
// Oscillator values in Hz
#define HSE_VALUE (32000000)
#define LSE_VALUE (32768)
#define EXTERNAL_SAI1_CLOCK_VALUE (48000)
// Oscillator timeouts in ms
#define HSE_STARTUP_TIMEOUT (100)
#define LSE_STARTUP_TIMEOUT (5000)
#include "boards/stm32wbxx_hal_conf_base.h"
#endif // MICROPY_INCLUDED_STM32WBXX_HAL_CONF_H
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2024-07-06T01:26:51.906118
|
https://example.com/article/2862
|
Rs 12-crore Collectorate complex to be inaugurated tomorrow
The city has been spruced up for the visit of Chief Minister M. Karunanidhi on September 8. Arrangements being made by the district administration and the police authorities for the Chief Minister's functions have reached a feverish pitch.
The Chief Minister who will arrive here from Chennai by train on September 8 will inaugurate the Rs. 12 crore new integrated Collectorate complex, and the taluk office building constructed along the Bharathidasan Salai close to the Tiruchi Corporation office. He will also distribute welfare assistance of over Rs. 8 crore to more than 7,000 beneficiaries and lay foundation for various projects .
In the evening, Mr. Karunanidhi will unveil the statue of late DMK leader Anbil Dharmalingam installed at Karur By Pass Road and address a public meeting at the military ground in Mannarpuram. The City Police authorities have prepared detailed bandobust scheme for the visit of the Chief Minister and police personnel from other districts have also been drafted for security duty in addition to the local police. Police sources said over 1,500 police personnel would be deployed at various places in the city as part of the security arrangement. Ten Superintendents of Police, 10 Additional Superintendents of Police, 40 Deputy Superintendents of Police, Inspectors and over 1,000 policemen of other ranks form part of the security scheme.
At an advanced security liaison meeting held here on Monday, senior officials from various departments including police, revenue, public works and fire and rescue services, and the Tiruchi Corporation took part.
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2023-12-01T01:26:51.906118
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https://example.com/article/5425
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605 So.2d 694 (1992)
Gregory VICKERS, Plaintiff-Appellant,
v.
Tanya Vickers WELLBRINK, Defendant-Appellee.
No. 23916-CA.
Court of Appeal of Louisiana, Second Circuit.
September 23, 1992.
Blackwell, Chambliss, Hobbs & Henry by Sam O. Henry, IV, for plaintiff-appellant.
Geary S. Aycock, for defendant-appellee.
Before SEXTON, VICTORY and BROWN, JJ.
VICTORY, Judge.
Gregory Vickers appeals a trial court judgment awarding $300 per month in child support to his ex-wife, Tanya Vickers Wellbrink, for two of their three minor children. In granting this award, the trial judge chose to deviate from the child support guidelines, LSA-R.S. 9:315 et seq. Mr. Vickers argues that the entire income of Mrs. Wellbrink's second spouse should have been considered and applied to the guidelines, which would have resulted in Mrs. Wellbrink actually owing him a small amount of support. Finding that the award is appropriate, but noting that the procedure used to deviate was inadequate, we affirm.
FACTS
Gregory Vickers and Tanya Wellbrink were married on October 21, 1979 and three children were born during the marriage: Derek, Amber and Chad. This marriage ended in divorce on February 12, 1985, with both parties remarrying soon thereafter.
*695 Following the divorce, the parties entered a joint custody plan in which Mr. Vickers was named the primary domiciliary parent of all three children. This plan did not award child support to either parent. In January 1987, custody was temporarily transferred to the children's maternal grandparents until December 1987, when custody was transferred back to Mr. Vickers who had by this time moved to Tennessee. Once again, no support was awarded to either parent.
In 1989 and 1990 respectively, Derek and Amber moved back to Louisiana to live with their mother and her husband, Neal Wellbrink. The third child, Chad, continued to live with his father in Tennessee. On April 19, 1991, the parties filed a joint motion to modify custody whereby Mrs. Wellbrink was made the domiciliary parent of Derek and Amber, while Mr. Vickers maintained his status as the domiciliary parent of Chad.
On June 13, 1991, Mrs. Wellbrink filed a rule for child support for Derek and Amber. In response, on August 1, 1991, Mr. Vickers petitioned the court for support for Chad. These reciprocal rules were consolidated for a September 3, 1991 evidentiary hearing, which resulted in a ruling in favor of Mrs. Wellbrink awarding her $150 per month, per child, or $300 per month, in support for Derek and Amber. Mr. Vickers was allowed to file a tax exemption for Derek and Chad, while Mrs. Wellbrink was given the exemption for Amber. All anticipated medical, dental and orthodontic expenses of the children, which appear to be substantial, were ordered to be paid by the domiciliary parent of the respective children.
DISCUSSION
The child support guidelines contained in LSA-R.S. 9:315 et seq. are to be used in any proceeding to establish or modify child support filed on or after October 1, 1989. The guidelines provide that a "basic child support obligation" for one or more children is calculated on the basis of several factors, including the "combined adjusted gross monthly income" of the parents. If a party is voluntarily unemployed or underemployed, child support shall be calculated based on a determination of income earning potential unless the party is physically or mentally incapacitated, or is caring for a child of the parties under the age of five years. LSA-R.S. 9:315.9. The guidelines further provide in the definition of income, that the court may also consider as income the benefits a party derives from remarriage, expense sharing or other sources. LSA-R.S. 9:315(6)(c).[1]
After combining the adjusted gross monthly income of the parties, each party is to contribute to the basic child support obligation by the percentage of his or her proportionate share. Once the basic obligation has been established, the total child support obligation is determined by adding to the basic obligation, if necessary, net child care costs, health insurance premiums, extraordinary medical expenses, and other extraordinary expenses incurred on behalf of the child. LSA-R.S. 9:315.3, 9:315.4, 9:315.5, 9:315.6. There is a rebuttable presumption that the amount of child support calculated under the guidelines is the proper amount of child support to be awarded. LSA-R.S. 9:315.1(A); State v. Flintroy, 599 So.2d 331 (La.App. 2d Cir. 1992).
If the court finds that the application of the guidelines would not be in the best interest of the child or would be inequitable to the parties, it may deviate from the guidelines. LSA-R.S. 9:315.1(B). The statute mandates that the court give oral or *696 written reasons for the deviation and that these reasons be made a part of the record of the proceedings. Montgomery v. Waller, 571 So.2d 765 (La.App. 2d Cir.1990). LSA-R.S. 9:315.1(C)(1 through 7) provides an illustrative list of factors which may be considered by a court in determining whether to deviate from the guidelines:
(1) That the combined adjusted gross income of the parties is not within the amounts shown on the schedule in LSA-R.S. 9:314.14. If the combined adjusted gross income of the parties is less than the lowest sum shown on the schedule, the court shall determine an amount of child support based on the facts of the case. If the combined adjusted gross income of the parties exceeds the highest sum shown on the schedule, the provisions of LSA-R.S. 9:315.10(B) shall apply.
(2) The legal obligation of a party to support dependents who are not the subject of the action before the court and who are in that party's household.
(3) The extraordinary medical expenses of a party, or extraordinary medical expenses for which a party may be responsible, not otherwise taken into consideration under the guidelines.
(4) An extraordinary community debt of the parties.
(5) The need for immediate and temporary support for a child when a full hearing on the issue of support is pending but cannot be timely held. In such cases, the court at the full hearing shall use the provisions of this part and may redetermine support without the necessity of a change of circumstances being shown.
(6) The permanent or temporary total disability of a spouse to the extent such disability diminishes his present and future earning capacity, his need to save adequately for uninsurable future medical costs, and other additional costs associated with such disability, such as transportation and mobility costs, medical expenses, and higher insurance premiums.
(7) Any other consideration which would make application of the guidelines not in the best interest of the child or children or inequitable to the parties.
Here, in choosing to deviate from the guidelines the trial court stated that although the guidelines would have imposed a greater award for Mrs. Wellbrink, only $300 per month was appropriate because of the Vickers' diminished income in comparison to the Wellbrinks' income. He noted that the Vickers have a combined gross annual income of $30,000, that Neal Wellbrink makes an annual base salary of $40,000, although he made substantial overtime in previous years, and that Mrs. Wellbrink could have made $900 per month if she were employed. In addition, the trial judge stated that it was justified in deviating from the guidelines for the following reasons:
"the actual gross income of all parties; the number of children involved in both households; and the financial obligations of all parties including child support for the children by previous marriages and large anticipated medical expenses of both households."
Other facts surrounding this case mentioned by the trial judge include the somewhat unusual situation presented because physical custody of the three children is split between the parents.[2] The judge recognized that the Wellbrinks have a five-year-old daughter, and that Neal Wellbrink has a son by a prior marriage for whom he pays child support. The trial judge also mentioned the large anticipated orthodontic expenses for all of the children.
When a trial judge decides deviation is appropriate, he should fully explain what the support would be if he were not deviating, why he is deviating, and how much he has allowed for each factor of deviation. The proper procedure would be to calculate child support under the guidelines by stating the amount of income attributed to each party, including the amount of second spouse income considered, in reaching the basic support obligation under the guidelines. *697 Any additional expenses provided for under the guidelines, such as net child care costs and extraordinary medical expenses incurred on behalf of the child(ren), should be added to the basic support obligation to reach the total obligation. Once this total is determined, the judge may deviate from the guidelines, giving a specific amount of deviation for each factor used in the deviation. Utilizing and explaining fully the deviation gives an appellate court a basis to review the appropriateness of the deviation.
Although deviation in this case was within the trial judge's discretion, he failed to state what figures he used for the parties' income, what he believed the guidelines would have provided if he had not deviated, and what amount he deviated for each factor. Nevertheless, we find that the $300 monthly award in this case was proper.[3] Under all reasonable scenarios, including different combinations of considering extraordinary medical expenses, child support from previous marriages, net child care costs (if Mrs. Wellbrink was working), and up to one-half of second spouse income, the award would be $300 or more. The only scenario in which the award would be less than $300 is if all or most of Neal Wellbrink's income is considered, which we do not find is appropriate in this case.
Mr. Vickers cites Goodall v. Goodall, 561 So.2d 867 (La.App. 2d Cir.1990) in support of his argument that the entire income of Neal Wellbrink should have been used to calculate Mrs. Wellbrink's gross monthly income. Although Goodall does state that it is proper to consider the earnings of a second spouse, it does not state that second spouse income must be considered in its entirety. Consideration of second spouse income is discretionary. LSA-R.S. 9:315(6)(c); Crockett v. Crockett, 575 So.2d 942 (La.App. 2d Cir.1991).
In conclusion, we find no error by the trial judge in ordering Mr. Vickers to pay child support of $150 per month, per child, or $300 total. If anything, he deviated from the guidelines downward, which is favorable to appellant. We cannot conclude that he abused his discretion in refusing to use all or most of Mr. Wellbrink's income.
DECREE
For the forgoing reasons, the judgment of the trial court is affirmed.
AFFIRMED.
NOTES
[1] LSA-R.S. 9:315(6)(c) was recently amended by Art. 854 of the 1991 Regular Session, effective September 6, 1991, three days after the evidentiary hearing on this rule for child support, and now reads:
(c) The court may also consider as income the benefits a party derives from expense-sharing or other sources; however, in determining the benefits of expense-sharing, the court shall not consider the income of another spouse, regardless of the legal regime under which the remarriage exists, except to the extent that such income is used directly to reduce the cost of a party's actual expenses.
The amended article changes the law by limiting the extent to which second spouse income may be considered, if the judge chooses to consider it.
[2] We are not called upon to rule whether split custody is appropriate in this case, but we note that it is not favored in the law absent extraordinary circumstances.
[3] Mr. Vickers was also allowed to deduct two children for tax purposes, when he only has custody of one. See LSA-R.S. 9:315.7.
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2024-06-14T01:26:51.906118
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https://example.com/article/9724
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Details
Description
This superb Coastal inspired family home design by Don Stevenson and built by Midwest Developers, LLC is the best value in the heart of Olde Naples and only a short walk to restaurants and shopping and across the street from the boat launch to Naples Bay. Refined elegance with a comfortable yet classic feel welcomes you as you step through the front door. The open layout, natural light and inviting hues utilized throughout the home fused with modern building advancements make this single family residence truly exceptional. The main house has 3 generous sized en-suite bedrooms, a powder bath on the first floor, study with temperature controlled wine vault, security system, an elevator and a spacious living and dining room opening up to the kitchen. There is a full, detached guest suite and rooftop sundeck above the garage. The exterior living area comprises of a covered outdoor lanai with remote control screens, a natural gas fireplace, outdoor kitchen with private pool, spa and sundeck. The oversized garage is capable of accommodating 2 cars with access at the rear of the property. The guest house has its own private entry and would be perfect for visitors or in-home caretaker.
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2023-12-11T01:26:51.906118
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https://example.com/article/7050
|
A journalist called Kellyanne Conway 'the darkness' in 'Democracy dies in darkness'
WATCH | Here's the moment of truth.
The comment drew laughs from the audience. Conway responded, "Just because someone says something doesn't make it true."
The "Democracy dies in darkness" motto is far older than Conway's time in the limelight. It became the Post's official slogan in February, but reporter Bob Woodward was fond of the phrase and used it frequently, The Hill reported.
15 times recent Trump has criticized the media on Twitter
Check the full list
A journalist called Kellyanne Conway 'the darkness' in 'Democracy dies in darkness'
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2023-11-14T01:26:51.906118
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https://example.com/article/5900
|
906-ADB Honeywell Microswitch
Stock Qty: 5 (in stock)
We accept Visa, Mastercard and American Express on domestic orders (USA and Canada)
Description
CMC SERIES
About
The Honeywell part 906-ADB is distributed by Electrol. The product that you are looking to replace may be brand labeled Microswitch, Hobbs, Honeywell, Data Instruments, Pepperl-Fuchs, Sensym, Senasys, Sensotec or Honeywell-Yamatake, all of which are trade names or previous joint ventures between Honeywell and other partners. The Micro Switch brand is a trade name of Honeywell Sensing & Control headquartered in Freeport Illinois and with manufacturing facilities worldwide including the USA, Mexico, France, Germany, the UK, China and Korea. Electrol has been a distributor of Micro Switch products since 1970.
Honeywell Sensing & Control is a world leader in electro-mechanical switching devices for industry, aerospace, medical and defense. The product line up now also includes sensors for pressure, force, humidity and temperature. Electrol stocks a broad range of Honeywell products for immediate shipment including switching devices for hazardous locations, hermetically sealed switches, pressure transducers and wide range of limit switches for virtually every application.
Frequently viewed with this item...
9002AW2 SQUARE D
9003EN8B MICRO
Sealed switch. Honeywell MICRO SWITCH EN Series limit switches are bushing mount designed, manufactured, and qualified to MIL-PRF-8805 standards. These products provide a durable switch for commercial and military aircraft as well as commercial and military ground-based equipment. Other applications include off-road equipment where severe environments are encountered. The EN Series of switches have proven to deliver consistent and reliable operation in harsh environments on critical applications for more than 65 years.
9003EN11B MICRO
Sealed switch. Honeywell MICRO SWITCH EN Series limit switches are bushing mount designed, manufactured, and qualified to MIL-PRF-8805 standards. These products provide a durable switch for commercial and military aircraft as well as commercial and military ground-based equipment. Other applications include off-road equipment where severe environments are encountered. The EN Series of switches have proven to deliver consistent and reliable operation in harsh environments on critical applications for more than 65 years.
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2023-09-22T01:26:51.906118
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https://example.com/article/9900
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Non-transformable mutants of Bacillus subtilis defective in the penetration of DNA into the cell.
Four non-transformable mutants of Bacillus subtilis 168 defective in the penetration of DNA into the recipient cell were isolated. All mutants were fully non-transformable with mutation in genes influencing irreversible binding of the donor DNA by the recipient cell.
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2024-05-01T01:26:51.906118
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https://example.com/article/1725
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Is My CBD Legal? An Informative Article to Help You Make Sure You’reUsing Legal, High Quality CBD
Is My CBD Legal?
By now, everyone is starting to notice CBD – not only because its been so closely associated with THC, but because of the countless benefits people have claimed to receive from it. Because of this, not only is CBD attracting the attention of consumers from around the world, it is also attracting the attention of the DEA. Now, lets address the elephant in the room – there is a lot of talk out there about CBD being illegal, unsafe, and so forth. While this is partially true under circumstances when CBD oil is not manufactured properly or contains traces of THC, thus indeed making that CBD Oil illegal; it is not the case when CBD oils are manufactured in certified lab environments, and are tested to contain 0% THC (such as the CBD oil products we sell here at Koi). With that being said, CBD is legal in all 50 States, but how are consumers to know how to make sure they are using legal, high quality CBD Oil? Simple, you shop at KoiCBD! We’re kidding (partially)… All joking aside, we understand that there are a wide range of CBD products out there, and we wrote this article to help you make sure you make sure you’re using CBD products that are 100% legal and high quality. Lets get to it then!
How to Make Sure You’re Using Legal, High Quality CBD
So you’re not a chemist or mixologist with a full-scale laboratory to test a product before you use it right? Don’t worry, you don’t have to be! So how do you make sure you’re using legal, high quality CBD then? Simple, you look at the resources! Follow this simple checklist to make sure you’re using legal CBD products:
Look at the Company’s Lab Results
First, and most importantly, you must ensure that the company you are considering buying a CBD product from has lab results from a certified lab for each of their products in question. The results must show (lab location, lab certificate number, etc.)? If the company does not have lab results for their products readily available on their website, then this is a huge red flag. If you’re still interested in their product, email their support team and request copies of their lab results. If they do not respond, this is another red flag, and we high recommend that you do not engage in business with this company.
Look for a THC-FREE Seal or Guarantee
The next item to check off is if the company displays a clear statement that their product(s) is free of any THC. Typically this statement would be shown on their product and/or website in the form of a seal or banner. Now, If the company does not visibly state that their CBD product is not THC-free, this doesn’t necessarily mean that product contains THC, but if their product was THC-free why wouldn’t they proudly be displaying it all over the place? Again, you can always reach out to the company and simply ask them if their product is THC-free. If they don’t respond, again, this is a huge red flag.
Look at the Company’s Track Record
Lastly, you want to look at a company’s track record. This is an important process to do to not only determine if the CBD oil you are considering is legal and high-quality, but also if the company that’s selling it is a good business who values you as a customer. Important questions that you want to ask when examining a company’s track record include:
How long has the company been in business?
What are customers saying about their experience with using their products, or are does the company have any testimonials at all?
Does the company have negative feed back on their marketplaces or social profiles?
Does the company talk about their passion for being in the industry and that they believe in offering quality product?
These are important questions that will help validate the company’s credibility, and whether or not the product you are considering purchasing is legal and high quality. Because the industry is so new, and there is a lot of political activity happening around CBD, you want to make sure that you are as careful as possible when buying CBD so that you are able to spend your hard earned money on the best quality product. More importantly, you want to make sure that you are engaging in legal activity.
Once you do find a company who provides a product that passes all these tests, we recommend that you stick with them; and if you’re exploring new products, always make sure to go through our simple checklist to make sure you’re getting the best product for your money.
We truly hope that this article helped relieve some unsettled thoughts in the back of your minds. When manufactured and properly tested, CBD is legal in all 50 states, making it available to everyone and anyone. At Koi CBD, we are very passionate about providing high-quality CBD to our customers because many of us have experienced the benefits of the amazing substance ourselves, and want to help the rest of the world experience the wonders of CBD.
Customer
This product is not for use by or sale to persons under the age of 18. This product should be used only as directed on the label. It should not be used if you are pregnant or nursing. Consult with a physician before use if you have a serious medical condition or use prescription medications. A Doctor's advice should be sought before using this product. These statements have not been evaluated by the FDA. This product is not intended to diagnose, treat, cure or prevent any disease. By using this website, you agree to follow the Privacy Policy and all Terms & Conditions printed on this site. Void Where Prohibited by Law.
|
2024-05-03T01:26:51.906118
|
https://example.com/article/2070
|
Relationships between parenting and adolescent adjustment over time: genetic and environmental contributions.
The predictive association between parenting and adolescent adjustment has been assumed to be environmental; however, genetic and environmental contributions have not been examined. This article represents one effort to examine these associations in which a genetically informative design was used. Participants were 395 families with adolescent siblings who participated in the Nonshared Environment in Adolescent Development (D. Reiss et al., 1994) project at 2 times of assessment, 3 years apart. There were 5 sibling types in 2 types of families: 63 identical twins, 75 fraternal twins, and 58 full siblings in nondivorced families and 95 full, 60 half, and 44 genetically unrelated siblings in stepfamilies. Results indicate that the cross-lagged associations between parental conflict-negativity and adolescent antisocial behavior and depressive symptoms can be explained primarily by genetic factors. These findings emphasize the need to recognize and examine the impact that adolescents have on parenting and the contribution of genetic factors to developmental change.
|
2024-02-05T01:26:51.906118
|
https://example.com/article/6195
|
Q:
XCODE 5+ ... how to stop text in a TextView from jumping to just above keyboard when second line added?
Relative newbie question: text entered in my textView is positioned at the top of the textview area until the text goes onto the second line at which point it jumps to the line just above the keyboard and then scrolls upwards as new lines are added. But I want the text to remain at the top of the textview until the text reaches the line above the keyboard and then scroll upwards. I can't figure out what to do to fix this.
I have spent some time searching and not found a simple example. Any suggestions are appreciated.
A:
In the end, I downloaded the Apple Keyboard Accessory app and changed my code to match and it works now.
Here is the working code - but it is not meant to be an example of elegant code as I am an amateur:
#import "CREWGenericNotesVC.h"
@interface CREWGenericNotesVC ()
@property (nonatomic, weak) IBOutlet UIBarButtonItem *doneButton;
@property (nonatomic, weak) IBOutlet UITextView *textView;
// the height constraint we want to change when the keyboard shows/hides
@property (weak, nonatomic) IBOutlet NSLayoutConstraint *constraintToAdjust;
// @property(nonatomic) CGSize contentSize;
@end
@implementation CREWGenericNotesVC
#define VIEW_NAME @"CREWGenericNotesVC" // need the name of the view that calls this
#define VIEW_DESCRIPTION @"Generic notes"
#define RETURN_NC @"NCEmergencyKitsList" // where to return to when complete processing
- (void)viewDidLoad {
[super viewDidLoad];
// [_textView addObserver:self forKeyPath:@"contentSize" options: (NSKeyValueObservingOptionNew) context:NULL];
// load saved notes into textView
NSUserDefaults *defaults = [NSUserDefaults standardUserDefaults];
self.navigationItem.title = [defaults objectForKey:@"VCtitle"];
self.navigationItem.rightBarButtonItem = self.doneButton;
[self initializeView];
}
// create and load entity and notes
- (void) initializeView
{
NSUserDefaults *defaults = [NSUserDefaults standardUserDefaults];
NSString *viewName = [defaults objectForKey:@"VCname"]; // parameter to specify which view is calling notes and
CREWAppDelegate *appDelegate = [[UIApplication sharedApplication]delegate];
NSManagedObjectContext *context = [appDelegate managedObjectContext];
NSEntityDescription *entityDesc = [NSEntityDescription entityForName:@"Notes" inManagedObjectContext:context];
NSFetchRequest * request = [[NSFetchRequest alloc] init];
[request setEntity:entityDesc];
NSPredicate *pred = [NSPredicate predicateWithFormat:@"(viewName = %@)", VIEW_NAME];
[request setPredicate:pred];
NSError *error = nil;
NSArray * objects = [context executeFetchRequest:request error:&error];
if ([objects count] == 0) { // create new notes instance if not already created
[self newNotes:viewName]; // create a new empty note object
} else {
self.textView.text = [self getNotes:viewName]; // load existing notes
}
} // end of initializeView
// create a new empty Notes record
- (void) newNotes:(NSString*)viewName
{
NSError *error = nil;
CREWAppDelegate *appDelegate = [[UIApplication sharedApplication]delegate];
NSManagedObjectContext *context = [appDelegate managedObjectContext];
NSManagedObject * newNotes;
newNotes = [NSEntityDescription insertNewObjectForEntityForName:@"Notes" inManagedObjectContext:context];
[newNotes setValue:viewName forKey:@"viewName"];
[newNotes setValue:nil forKey:@"viewNotes"];
if (! [context save:&error])
NSLog(@"newNotes Couldn't save new data! Error:%@", [error description]);
} // end of newNotes
// read existing notes
- (NSString*) getNotes:(NSString*)viewName// get stored notes
{
CREWAppDelegate *appDelegate = [[UIApplication sharedApplication]delegate];
NSManagedObjectContext *context = [appDelegate managedObjectContext];
NSEntityDescription *entityDesc = [NSEntityDescription entityForName:@"Notes" inManagedObjectContext:context];
NSFetchRequest * request = [[NSFetchRequest alloc] init];
[request setEntity:entityDesc];
NSPredicate *pred = [NSPredicate predicateWithFormat:@"(viewName = %@)", viewName];
[request setPredicate:pred];
// Execute Fetch Request
NSManagedObjectContext * matches = nil;
NSError *fetchError = nil;
NSArray *objects = [appDelegate.managedObjectContext executeFetchRequest:request error:&fetchError];
if (fetchError) {
NSLog(@"getNotes Fetch error:%@", fetchError);
};
NSString *viewNotes;
if (! [objects count] == 0) {
matches = objects [0];
viewNotes = [matches valueForKey : @"viewNotes"];
}
return viewNotes;
} // end of getNotes
- (void)saveNotes:(NSString*)viewName toValue:(NSString*)newNotes // to get stored notes and update them
{
CREWAppDelegate *appDelegate = [[UIApplication sharedApplication]delegate];
NSManagedObjectContext *context = [appDelegate managedObjectContext];
NSEntityDescription *entityDesc = [NSEntityDescription entityForName:@"Notes" inManagedObjectContext:context]; // get notes entity
NSFetchRequest * request = [[NSFetchRequest alloc] init];
[request setEntity:entityDesc];
NSPredicate *pred = [NSPredicate predicateWithFormat:@"(viewName = %@)", viewName ];
[request setPredicate:pred];
NSManagedObject *matches = nil;
NSError *error = nil;
NSArray * objects = [context executeFetchRequest:request error:&error];
if (![objects count] == 0) {
matches = objects[0];
}
[matches setValue:newNotes forKey:@"viewNotes"];
if (! [context save:&error]) NSLog(@"newNotes Couldn't save notes! Error:%@", [error description]);
} // end of saveSwitch
// keyboard stuff
- (void)viewDidAppear:(BOOL)animated {
// observe keyboard hide and show notifications to resize the text view appropriately
[[NSNotificationCenter defaultCenter] addObserver:self
selector:@selector(keyboardWillShow:)
name:UIKeyboardWillShowNotification
object:nil];
[[NSNotificationCenter defaultCenter] addObserver:self
selector:@selector(keyboardWillHide:)
name:UIKeyboardWillHideNotification
object:nil];
// start editing the UITextView (makes the keyboard appear when the application launches)
[self editAction:self];
}
- (void)viewDidDisappear:(BOOL)animated {
[[NSNotificationCenter defaultCenter] removeObserver:self
name:UIKeyboardWillChangeFrameNotification
object:nil];
[[NSNotificationCenter defaultCenter] removeObserver:self
name:UIKeyboardWillHideNotification
object:nil];
}
- (void)didRotateFromInterfaceOrientation:(UIInterfaceOrientation)fromInterfaceOrientation {
[self adjustSelection:self.textView];
}
#pragma mark - Actions
- (IBAction)doneAction:(id)sender {
// user tapped the Done button, release first responder on the text view
[self.textView resignFirstResponder];
NSUserDefaults *defaults = [NSUserDefaults standardUserDefaults];
NSString *viewName = [defaults objectForKey:@"VCname"]; // parameter to specify where to save notes
// NSString *stringNC = [defaults objectForKey:@"NCname"]; // parameter to specify which navigation controller to return to
[self saveNotes:viewName toValue: self.textView.text]; // save notes
[defaults stringForKey:@"NCname"];
UIViewController *viewController = [[UIStoryboard storyboardWithName:@"Main" bundle:nil] instantiateViewControllerWithIdentifier:[defaults stringForKey:@"NCname"]];
[self presentViewController:viewController animated:YES completion:nil];
}
- (IBAction)editAction:(id)sender {
// user tapped the Edit button, make the text view first responder
[self.textView becomeFirstResponder];
}
#pragma mark - UITextViewDelegate
- (BOOL)textViewShouldBeginEditing:(UITextView *)aTextView {
}
self.navigationItem.rightBarButtonItem = self.doneButton;
return YES;
}
- (BOOL)textViewShouldEndEditing:(UITextView *)aTextView {
[aTextView resignFirstResponder];
return YES;
}
- (void)adjustSelection:(UITextView *)textView {
// workaround to UITextView bug, text at the very bottom is slightly cropped by the keyboard
if ([textView respondsToSelector:@selector(textContainerInset)]) {
[textView layoutIfNeeded];
CGRect caretRect = [textView caretRectForPosition:textView.selectedTextRange.end];
caretRect.size.height += textView.textContainerInset.bottom;
[textView scrollRectToVisible:caretRect animated:NO];
}
}
- (void)textViewDidBeginEditing:(UITextView *)textView {
[self adjustSelection:textView];
}
- (void)textViewDidChangeSelection:(UITextView *)textView {
[self adjustSelection:textView];
}
#pragma mark - Responding to keyboard events
- (void)adjustTextViewByKeyboardState:(BOOL)showKeyboard keyboardInfo:(NSDictionary *)info {
/*
Reduce the size of the text view so that it's not obscured by the keyboard.
Animate the resize so that it's in sync with the appearance of the keyboard.
*/
// transform the UIViewAnimationCurve to a UIViewAnimationOptions mask
UIViewAnimationCurve animationCurve = [info[UIKeyboardAnimationCurveUserInfoKey] unsignedIntegerValue];
UIViewAnimationOptions animationOptions = UIViewAnimationOptionBeginFromCurrentState;
if (animationCurve == UIViewAnimationCurveEaseIn) {
animationOptions |= UIViewAnimationOptionCurveEaseIn;
}
else if (animationCurve == UIViewAnimationCurveEaseInOut) {
animationOptions |= UIViewAnimationOptionCurveEaseInOut;
}
else if (animationCurve == UIViewAnimationCurveEaseOut) {
animationOptions |= UIViewAnimationOptionCurveEaseOut;
}
else if (animationCurve == UIViewAnimationCurveLinear) {
animationOptions |= UIViewAnimationOptionCurveLinear;
}
[self.textView setNeedsUpdateConstraints];
if (showKeyboard) {
UIDeviceOrientation orientation = self.interfaceOrientation;
BOOL isPortrait = UIDeviceOrientationIsPortrait(orientation);
NSValue *keyboardFrameVal = [info objectForKey:UIKeyboardFrameEndUserInfoKey];
CGRect keyboardFrame = [keyboardFrameVal CGRectValue];
CGFloat height = isPortrait ? keyboardFrame.size.height : keyboardFrame.size.width;
// adjust the constraint constant to include the keyboard's height
self.constraintToAdjust.constant += height;
}
else {
self.constraintToAdjust.constant = 0;
}
NSTimeInterval animationDuration = [[info objectForKey:UIKeyboardAnimationDurationUserInfoKey] doubleValue];
[UIView animateWithDuration:animationDuration delay:0 options:animationOptions animations:^{
[self.view layoutIfNeeded];
} completion:nil];
// now that the frame has changed, move to the selection or point of edit
NSRange selectedRange = self.textView.selectedRange;
[self.textView scrollRangeToVisible:selectedRange];
}
- (void)keyboardWillShow:(NSNotification *)notification {
/*
Reduce the size of the text view so that it's not obscured by the keyboard.
Animate the resize so that it's in sync with the appearance of the keyboard.
*/
NSDictionary *userInfo = [notification userInfo];
[self adjustTextViewByKeyboardState:YES keyboardInfo:userInfo];
}
- (void)keyboardWillHide:(NSNotification *)notification {
/*
Restore the size of the text view (fill self's view).
Animate the resize so that it's in sync with the disappearance of the keyboard.
*/
NSDictionary *userInfo = [notification userInfo];
[self adjustTextViewByKeyboardState:NO keyboardInfo:userInfo];
}
@end
|
2024-07-06T01:26:51.906118
|
https://example.com/article/3656
|
Believe it or not, it wasn't a spilled drink or relationship troubles that caused a fight at a Key West bar.
The Miami Herald reports that two couples got into a tussle last week at Sloppy Joe's Bar after someone tooted.
One couple told police they were having a drink with friends when the girlfriend traded words (allegedly over the fart) with an unidentified woman in what police called "an aggressive manner."
|
2024-06-26T01:26:51.906118
|
https://example.com/article/7563
|
You are here
The Education Gadfly Show
Mike and Dara tear themselves away from round-the-clock royal baby coverage to bring you commentary on ESEA renewal, the cost of PARCC’s tests, and special-education vouchers. Amber throws down OECD statistics.
Tanned and refreshed, Mike’s back in the saddle, this time joined by Fordham media relations and outreach manager Michelle Gininger to talk Common Core tests, Wisconsin’s Act 10, and school accountability in the Sunshine State. Amber digs into the statistics on child well-being.
Dara and Daniela—covering for Mike “Never-Returning-from-the-Beach-Because-These-Fruity-Drinks-Are-Too-Good” Petrilli—throw down on NYC’s transfer high schools, California’s potential NGSS adoption, and MOOCs in K–12 education. Amber is upbeat about early-college high schools.
With Mike beaching it in an undisclosed location, Dara and Daniela take on some big topics: If affirmative action were to end, how could colleges maintain diversity? Do teachers need convincing to use technology? All things considered, is college worth it? Amber charts a course to charter quality.
Mike and Dara discuss NCLB reauthorization, NYC’s teacher evaluations, and the relationship between poverty and educational outcomes. Amber revels in the glory of having finally gotten Fordham’s epic pensions out the door.
Can wonky Mike and data-loving Dara come to an agreement on Texas’s education reforms, Illinois’s rebuff of online learning, and a moratorium on Common Core–related stakes? Amber joins the number-cruncher brigade with a study on the effect of career and technical education on math achievement.
While discussing UFT pandering, Algebra 2 mandates, and Common Core consortia, Mike and Andy try very, very hard not to say the two magic words that rain down the wrath of the IRS (hint: they begin with T and P). Amber sorts through teacher sorting—but can she really do it in under a minute? Listen to find out!
About the Education Gadfly Show
For more than eight years, the Fordham Institute has been hosting a weekly podcast, The Education Gadfly Show. Each week, you’ll get three lively, entertaining discussions of recent education news, usually featuring Fordham’s Mike Petrilli, with questions read by Ellen Alpaugh. Then the wise Amber Northernwill recap a recent research study.
Download the podcast using the link to the left or subscribe via iTunes.
|
2023-10-28T01:26:51.906118
|
https://example.com/article/9132
|
[A few remarks on the subject of correct planning of epidemiologic studies].
The paper presents some problems on the planning of epidemiological studies. The definition of epidemiology is related to medicine, statistics, sociology, demography and other branches of science. Different types of epidemiological studies are enumerated (descriptive, analytical and experimental epidemiology, retrospective and prospective analysis). In the plan of epidemiological studies fifteen stages are distinguished and described. Special attention is given to the aim and object of research, sources of data, methods and techniques of evaluation, presentation and the analysis of results. The consequences of working without plan or with incomplete and wrong plan are presented. The authors suggest how to develop modern epidemiology in Poland.
|
2024-05-10T01:26:51.906118
|
https://example.com/article/9638
|
Q:
HTML Image Problem
I am trying to make my own website and only know some basic HTML, I've searched the web for a bit and can't seem to figure out how to place text under an image and on the left of the image.
So pretty much:
[image] [text]
[text]
would pretty much be my layout of the web page. At the moment I can only float the image or align it to the left making the text wrap around the image, which I don't want. Can someone help me?
A:
<div style="width:400px; clear:both;">
<img src="http://media.techworld.com/cmsdata/news/3246520/1998_google.jpg" style="width:300px; float:left;" />
<div style="width:100px; float:left;">
text beside image
</div>
</div>
<div style="clear:both;">
text beneath image
</div>
http://jsfiddle.net/Tw2v7/
|
2024-07-31T01:26:51.906118
|
https://example.com/article/1187
|
Adaptive transmission controls are, for example, known from U.S. Pat. No. 5,157,609 and German patent publication 4,136,613 as well as from the articles from xe2x80x9cAutomobiltechnische Zeitschriftxe2x80x9d 94 (1992) 9, starting at page 428 and from xe2x80x9cAutomobiltechnische Zeitschriftxe2x80x9d 95 (1993) 9, starting at page 420. In automatic transmissions, the transmission changes are, in general, determined in dependence upon the vehicle longitudinal speed and the engine load (throttle flap angle). This takes place by means of a characteristic field. In adaptive transmission control systems, the characteristic field can be adapted to the behavior of the driver (driver type), the traffic situation and/or to the driving situation to which the vehicle is subjected. The transmission ratio changes are determined by means of the characteristic field. In setting the behavior of the driver, it is generally evaluated whether the driver adheres more to a driving-power orientated driving manner or more to a fuel optimized driving manner. In the evaluation of the traffic and driving situation, it can be distinguished, for example, whether the vehicle is in city traffic, ahead of or in a curve, on a hill or in overrun operation. Depending upon the evaluation of the above-mentioned points, the particular characteristic line which is suitable is selected from a number of different characteristic lines. Furthermore, a shifting of the base shifting characteristic field, as described in U.S. Pat. No. 5,857,161, can be provided.
In the known state of the art, for recognizing the type of driver, it is suggested to arrive at different types of estimation of the instantaneously present type of driver by means of different algorithms (for example, start-up evaluation, gradient evaluation). These estimates are then collected and processed to an instantaneous valid type of driver, for example, via maximum formation, weighted and/or sliding sum formation. In this processing, the above-mentioned various types of estimation are prioritized differently.
Reference can also be made to U.S. Pat. No. 6,216,077.
Furthermore, a hierarchially structured control of the elements of the drive train of a motor vehicle is known from U.S. Pat. No. 5,351,776. The drive train includes, for example, the engine, clutch/torque converter, transmission.
In electronic transmission controls (GS), it is therefore conventional to make the selection of the particular gear to be engaged in a stepped automatic transmission (AT) or in an automated shift transmission (ASG) on the basis of a plurality of criteria. The in part contradictory requirements of the criteria (for example, minimizing of the fuel consumption in contrast to high Dower reserve) can be considered via a prioritization which is dependent upon the driving state, driver command and the driving situation. Furthermore, situation-caused shifting restraints have to be considered. Here, a series of problems results. Accordingly, it is difficult to integrate new criteria because this brings with it a change of the already existing program code. The prioritization is partially directly hidden in the code. For this reason, it is difficult to adapt the prioritization to continuously changing requirements. In this way, the overview is missing which is needed for applying the prioritization.
The invention relates to an advantageous breakdown of the criteria in individual aspects and the sequence of the gear selection which results therefrom. This gear selection avoids the disadvantages and is a partial result of an object orientated analysis of the transmission control.
The system of the invention for adjusting a transmission ratio in a transmission built into a motor vehicle includes: at least two transmission criteria with which first transmission ratios are determined on the basis of at least two different determination modi; and, first means by means of which a second transmission ratio is selected in accordance with a pregivable prioritization from the determined first transmission ratios. The transmission ratio is then adjusted in dependence upon the selected second transmission ratio.
In an advantageous embodiment of the invention, second means are provided with which the second transmission ratio is modified in accordance with a pregivable strategy. The transmission ratio is then adjusted in dependence upon the modified second transmission ratio.
In a further embodiment of the invention, with the second means: a change of the adjusted transmission ratio is determined in dependence upon the instantaneous adjusted transmission ratio and the selected second transmission ratio; a check is made in accordance with a pregivable strategy as to whether the determined change is permitted; and, an adjustment of the transmission ratio in accordance with the determined change (HSV, REV, DHSV, DRSV) is only then undertaken when this change is permissible.
Here, it can be provided that the modification or the check of the permissibility of the change takes place in dependence upon the transmission ratio criterion which forms the selected second transmission ratio.
The determined changes can be upshifting operations, downshifting operations, double upshifting operations and/or double downshifting operations and/or pregivable multiple upshifting and/or multiple downshifting operations.
Furthermore, it can be provided that at least one transmission ratio criterion contains at least two shift characteristic lines which can be distinguished via pregivable codes.
In an especially advantageous embodiment of the invention, it is provided that the transmission ratio criteria and the first means for transmitting the first transmission ratios communicate via a criteria administrator. This affords a very simple applicability. Here, the first means communicate with the transmission ratio criteria by means of the criteria administrator via pregiven identification codes.
|
2024-07-28T01:26:51.906118
|
https://example.com/article/5220
|
[Cataract extraction combined with trabeculotomy (author's transl)].
In this paper we report on a series of 56 eyes which underwent a combined cataract-trabeculotomy operation. After a follow-up of at least 6 months. 63% of the eyes had normal intraocular pressure while 34% of them required further medication to achieve the same. No serious complications were observed.
|
2024-06-07T01:26:51.906118
|
https://example.com/article/4191
|
Devasom Hua Hin Resort
Devasom Hua Hin Resort
Devasom Hua Hin Resort
About the Hotel
Property LocationWith a stay at Devasom Hua Hin Resort in Cha-am, you'll be in the historical district and close to FN Factory Outlet and Mrigadayavan Palace. This 4-star resort is within the vicinity of Wat Bo Fai and Royal Queen's Park.
AmenitiesRelax on the private beach or enjoy other recreational amenities such as an outdoor pool.
DiningSatisfy your appetite at the resort's restaurant, which serves breakfast, lunch, and dinner, or stay in and take advantage of room service (during limited hours). Quench your thirst with your favorite drink at a bar/lounge.
Business, Other AmenitiesThe front desk is staffed during limited hours.
|
2024-04-16T01:26:51.906118
|
https://example.com/article/7097
|
The I-65/I-70 North Split interchange was built nearly 50 years ago, is operating at full capacity and is at the end of its useful life. INDOT reconstructed the mainline pavement between the North and South splits – dubbed HyperFix – in 2003. Other projects near the North Split addressed specific ramps or bridges that needed immediate repair. This is the first project to completely reconstruct the interchange, bridges and pavement along the North Split since it was built in 1968.
|
2024-02-06T01:26:51.906118
|
https://example.com/article/4072
|
The purpose of this project is a detailed investigation at the molecular level of the mechanism of action of vitamin D and its most biologically active metabolite 1,25-dihydroxy-vitamin D3(1,25-(OH)2-D3). The major thesis of the study is that in terms of its chemical structure and postulated mode of action the seco-steroid vitamin D (calciferol) is similar to that of other classical steroid hormones. The kidney is postulated to be the endocrine gland which produces in a physiologically regulated fashion small amounts of 1,25-(OH)2-D3. After systemic transport, this steroid interacts in the target tissues, the intestinal mucosa and bone to generate the usual biological response attributed to vitamin D. Also the biochemical and biological properties of other vitamin D metabolites and analogs, e.g. 25-hydroxy-vitamin D3, 24,25-dihydroxy-vitamin D3, 1 alpha-hydroxy-vitamin D3, 3-deoxy-1 alpha-hydroxy-vitamin D3 and 25-hydroxy-5,6-transvitamins D3 will be evaluated in this framework. The specific studies proposed include: (a) identification of the biochemical steps in the target intestinal mucosa as 1,25-(OH)2-D3 interacts with cytoplasmic, then nuclear receptors, to stimulate new genetic information required for stimulation of messenger RNA and protein biosynthesis (including calcium-binding-protein); (b) elucidation of the molecular aspects of the regulation of the renal production of 1,25-(OH)2-D3 via studies on the biochemical properties of this mitochondrial enzyme as well as changes in its rate of biosynthesis and biodegradation; (c) evaluation of the uptake of specific vitamin D metabolites by bone and/or cartilage tissue and identification of possible subcellular receptors as well as possible consequences on calcium and collagen metabolism; and (d) a detailed assessment of how changes in the chemical structure and conformation of the vitamin D steroid nucleus may be related to biological activity in specific target tissues so that the structure requirements of differentially acting D-analogs or an antivitamin may be identified.
|
2023-09-20T01:26:51.906118
|
https://example.com/article/7057
|
671 So.2d 781 (1995)
Jimmie Randall CHILDS
v.
STATE.
CR-94-98.
Court of Criminal Appeals of Alabama.
May 26, 1995.
Rehearing Denied July 28, 1995.
Phyllis Logsdon, Dothan, for Appellant.
Jeff Sessions, Atty. Gen., and Gregory O. Griffin, Sr., Asst. Atty. Gen., for Appellee.
TAYLOR, Presiding Judge.
The appellant, Jimmie Randall Childs, was convicted of unlawful possession of marijuana in the first degree, a violation of § 13A-12-213, Code of Alabama 1975. He was sentenced to five years in the penitentiary.
The state's evidence tended to show that on February 10, 1994, the appellant possessed 1.72 grams of marijuana and that he had previously been convicted of unlawful possession of marijuana for personal use. Officer Kenny Horn of the Dothan Police Department testified that at 6:30 p.m. he was driving down West Powell Street in a marked patrol car. He stated that the area was known to have a high amount of drug activity and that he had personally made many drug arrests in that area. He said that as he was driving he saw a small brown Chevrolet Monza station wagon being driven by the appellant stopped in front of a house. A black man was leaning into the window on the passenger's side of the car talking to the appellant. Horn testified that he pulled his patrol car parallel to the car to see what the men were doing. Horn said that the appellant started to drive away so he turned on the blue lights on his patrol car. The appellant drove 10 or 15 feet and then stopped. Horn testified that he walked up to the driver's side window and asked the appellant for his driver's license. He then asked him what he was doing. The appellant told Horn that he had been talking to a friend. Horn testified that he told the appellant that they were in a high drug activity area and that he *782 thought the appellant might have been involved in a drug transaction. He then asked the appellant if he could search the car. The appellant refused. Scott Heath, a K-9 officer with the Dothan Police Department, arrived. Officer Heath's trained drug-detection dog sniffed the outside of the appellant's car. Heath testified that the dog pawed at the passenger's side door of the car, which indicates that drugs were present.
Horn testified that he again asked the appellant for permission to search the car and that the appellant then consented. On the front passenger's seat Horn found a black 35-millimeter film canister containing a green leafy substance. The substance later proved to be marijuana.
The appellant raises two issues on appeal.
I
The appellant contends that the trial court erred by denying his motion to suppress the marijuana seized by Officer Horn. Specifically, he contends that the initial stop and resulting seizure of drugs by Officer Horn violated his rights pursuant to the Fourth Amendment to the United States Constitution and Terry v. Ohio, 392 U.S. 1, 88 S.Ct. 1868, 20 L.Ed.2d 889 (1968).
The appellant contends that the initial stop by police was illegal because, he says, the police did not have a reasonable suspicion to believe he was involved in criminal activity, as required by Terry. In Worthy v. State, 473 So.2d 634, 636 (Ala.Cr.App.1985), this court summarized the standards required by Terry and subsequent cases.
"In Terry, it was held that
"`where a police officer observes unusual conduct which leads him reasonably to conclude in light of his experience that criminal activity may be afoot and that the persons with whom he is dealing may be armed and presently dangerous, where in the course of investigating this behavior he identifies himself as a policeman and makes reasonable inquiries, and where nothing in the initial stages of the encounter serves to dispel his reasonable fear for his own or other's safety, he is entitled for the protection of himself and others in the area to conduct a carefully limited search of the outer clothing of such persons in an attempt to discover weapons which might be used to assault him.' 392 U.S. at 30, 88 S.Ct. at 1884-85.
"In order to justify the brief investigatory detention of an individual, a police officer does not have to have probable cause to arrest the person for a crime. Terry, 392 U.S. at 27, 88 S.Ct. at 1883; Spradley v. State, 414 So.2d 170, 173 (Ala.Cr.App. 1982). Although there is `no simple shorthand verbal formula which can adequately express the grounds for a Terry stop', 3 LaFave, [Search and Seizure] at § 9.3, p. 40, 1985 Pocket Part, `the essence of all that has been written is that the totality of the circumstancesthe whole picture must be taken into account. Based upon that whole picture the detaining officers must have a particularized and objective basis for suspecting the particular person stopped of criminal activity.' United States v. Cortez, 449 U.S. 411, 417-18, 101 S.Ct. 690, 695, 66 L.Ed.2d 621 (1981)."
473 So.2d at 636-37. (Emphasis added.)
Officer Horn's testimony revealed that his only basis for stopping the appellant was that the appellant was in an area known for drug activity and that someone was leaning into the window of the appellant's car. He testified that, based on his previous experience, this behavior often indicated that a drug transaction was taking place. The appellant contends that these facts were not sufficient to give police a reasonable suspicion that he was involved in criminal activity. We agree.
This court has held that similar facts were not sufficient to give police a reasonable suspicion that criminal activity was afoot. Gaskin v. State, 565 So.2d 675 (Ala.Cr.App.1990); State v. Bodereck, 549 So.2d 542 (Ala.Cr.App. 1989). In Bodereck, police were patrolling an area known for a high amount of drug activity and observed a black man leaning into the passenger's side window of a parked Cadillac automobile bearing an out-of-state license plate. As the police drove by, the black man ducked behind the Cadillac. Based on these facts, the police decided to investigate. This *783 court held that these facts were not sufficient "to satisfy the `reasonable suspicion' requirement for a valid investigatory stop under Terry." Bodereck, 549 So.2d at 546.
In Gaskin, police observed a pickup truck parked in an alley. One occupant was in the truck. A person was standing near the driver's side of the truck, but the officer could not tell if that person and the person in the truck were talking. He did not see them exchange anything. The area was "notorious for drug transactions." Again, this court held that a vehicle parked in a high crime area with persons both inside and outside the vehicle engaged in conversation does not justify a Terry stop under the totality of the circumstances. Gaskin, 565 So.2d at 676-78.
This case is controlled by Bodereck and Gaskin. The facts of those cases are virtually indistinguishable from the facts in this case. This court has no choice but to reverse the judgment of the lower court. The appellant's motion to suppress should have been granted.
II
In the interest of judicial economy, we address the appellant's second issue because it could be an issue in a future proceeding.
The appellant contends that the trial court erred by allowing a scale seized from his car to be received into evidence. Specifically, he contends that the scale was irrelevant and prejudicial because he was indicted for possession of marijuana only.
We do not need to address the merits of this issue because the seizure of the scale was a result of the illegal stop and resulting search of the appellant's car. As such, it is a "fruit of the poisonous tree" and is also due to be suppressed. Wong Sun v. United States, 371 U.S. 471, 83 S.Ct. 407, 9 L.Ed.2d 441 (1963).
For the foregoing reasons, the judgment in this case is reversed and the cause remanded to the Houston Circuit Court for proceedings not inconsistent with this opinion.
REVERSED AND REMANDED.
All the Judges concur, except LONG, J., who dissents with opinion.
LONG, Judge (dissenting).
I respectfully dissent. In my opinion, the officer's actions in approaching and stopping the appellant's vehicle were fully justified under the rule established in Terry v. Ohio, 392 U.S. 1, 88 S.Ct. 1868, 20 L.Ed.2d 889 (1968). In light of the officer's testimony regarding his knowledge that the area was one of high drug-sale activity, his testimony regarding his experience and his training in the methods frequently used in drug transactions, and his testimony about his observations of the appellant and the man seen leaning into the appellant's car, I believe the officer had a "particularized and objective basis for suspecting the particular person stopped of criminal activity." United States v. Cortez, 449 U.S. 411, 418, 101 S.Ct. 690, 695, 66 L.Ed.2d 621 (1981). "`[I]t is important to recall that a trained law enforcement agent may be "able to perceive and articulate meaning in given conduct which would be wholly innocent to the untrained observer." (quoting Brown v. Texas, 443 U.S. [47,] 52 n. 2, 99 S.Ct. [2637,] 2641 n. 2 [, 61 L.Ed.2d 357 (1979)].)'" Pianzio v. State, 423 So.2d 258, 266 (Ala.Cr.App.1981) (DeCarlo, J., dissenting).
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2024-03-06T01:26:51.906118
|
https://example.com/article/9289
|
Exposure to air pollution and noise from road traffic and risk of congenital anomalies in the Danish National Birth Cohort.
Ambient air pollution has been associated with certain congenital anomalies, but few studies rely on assessment of fine-scale variation in air quality and associations with noise from road traffic are unexplored. Among 84,218 liveborn singletons (1997-2002) from the Danish National Birth Cohort with complete covariate data and residential address history from conception until birth, we identified major congenital anomalies in 4018 children. Nitrogen dioxide (NO2) and noise from road traffic (Lden) burden during fetal life was modeled. Outcome and covariate data were derived from registries, hospital records and questionnaires. Odds ratios (ORs) for eleven major anomaly groups associated with road traffic pollution during first trimester were estimated using logistic regression with generalized estimating equation (GEE) approach. Most of the associations tested did not suggest increased risks. A 10-µg/m3 increase in NO2 exposure during first trimester was associated with an adjusted ORs of 1.22 (95% confidence interval: 0.98-1.52) for ear, face and neck anomalies; 1.14 0.98-1.33) for urinary anomalies. A 10-dB increase in road traffic noise was also associated with these subgroups of anomalies as well as with an increased OR for orofacial cleft anomalies (1.17, 0.94-1.47). Inverse associations for several both air pollution and noise were observed for atrial septal defects (0.85, 0.68-1.04 and 0.81, 0.65-0.99, respectively). Residential road traffic exposure to noise or air pollution during pregnancy did not seem to pose a risk for development of congenital anomalies.
|
2024-03-19T01:26:51.906118
|
https://example.com/article/6371
|
Q:
How to identify polylines with multiple end/starting points?
I'm looking for a way to programmatically identify polyline features which do not represent a 'simple' line from A to B but instead have several starting and/or end points. These are called complex network edges when working with geometric networks.
Why am I asking this? Because I have a geometric network with a feature class that is defined as only having simple network edges. But it somehow occurred that there are some 'bad' (i.e. complex) edges in there as well and I need to sort them out. Checking if the interface IComplexEdgeFeature is implemented doesn't work on the feature objects because by definition all features within that class are simple edges.
A:
Try finding all polylines where IGeometryCollection.GeometryCount > 1.
I think the example for calculating vertex count could be adapted to do this with the field calculator.
|
2024-05-07T01:26:51.906118
|
https://example.com/article/8489
|
The ejector-loop fermenter: Description and performance of the apparatus.
A novel fermentation unit, the ejector-loop fermenter (ELF), consisting of an outer-loop tower fermenter, a centrifugal pump, a plate-heat exchanger, and a gas-liquid ejector, was designed and constructed. Aeration was achieved by continuously recirculating the fermentation medium through two different nozzle devices instead of using the traditional expensive air compressor. By carrying out a whey fermentation with Kluyveromyces fragilis as the test organism, either in the ELF or in conventional stirred fermenter, it was possible to confirm that the high sheat streses and mixing shock occurring in the ejector nozzle and diffuser sections did not affect microbial growth. Within the range of experimental power consumption per unit volume (-0.1-5 kW/m(3)), the oxygen transfer capability of the ELF per unit power input was found to vary from 1 to 2.5 kg O(2) kW(-1)h(-1). Moreover, it is shown that there is suficient room for improvement in the performance of the ELF unit by care fully designing the aeration device. In fact, at constant volumetric oxygen transfer coefficient, the power consumpotion per unit volume in a 4-mm nozzle was found to be about 40% less than that in a 6-mm nozzle.
|
2024-04-16T01:26:51.906118
|
https://example.com/article/2079
|
Having studied evolutionary psychology and sociobiology which seems to right now be the dominant explanation of the nature of biological human life and thus existence, it seems to me like erotic sadism is the driving force behind existence. We are besieged by Schopenhauer's hegehog's dilemma. We hedgehogs have a need to be close to one another for warmth, and yet our point pricks ensure that we cause pain whenever in contact. Do our selfish-genes need us to be happy? Look at the immense misery of domestic cattle, who exist only to feed man. Their brief knowledge of life is simply a long torture. Yet they can not will themselves out of existence. From the point of view of the data contained in their genes, they are very successful. Humans will take great care to ensure that they survive and reproduce. And so from the perspective of evolution, farm animals are far more successful than wild animals. And that is also the human condition. We are bred to survive, and however miserable we might be, we also serve to further the gene.
What is the nature of woman? It was simpler to view them from only the blank slatist feminist doctrine that they are simply men. To accept evopsych and its various offshoots on the uniqueness of woman, makes life more complicated. Do women simply exist for pain? Like farm animals, their condition might always be miserable as mere playthings and meat for men, but they would still propagate their selfish genes under such conditions. Are women driven by an emotional desire to be dominated and hurt by dominant men?
What kind of world is this? This brutal Darwinian struggle, red in tooth and claw, and how does one live in it? Should we hate our parents for forcing us to be born, merely to satisfy their selfish-genes? Am I just a robot for my parent's inferior genes?
Why do you ask? The question of identity doesn't really occur in the electrochemical world itself - there are too many and none! You have to deal with this purely in the context of logic or metaphysics - where you appear to be anyway. Confusion sets in the moment a person is first defined as some mechanical entity in a mechanical context and then afterwards questioned what it's doing there or what it's supposed to be. It's a bit like first killing God and then wonder: "does he really exist?" or "did he ever".
schopen84 wrote:Having studied evolutionary psychology and sociobiology which seems to right now be the dominant explanation of the nature of biological human life and thus existence, it seems to me like erotic sadism is the driving force behind existence. We are besieged by Schopenhauer's hegehog's dilemma. We hedgehogs have a need to be close to one another for warmth, and yet our point pricks ensure that we cause pain whenever in contact. Do our selfish-genes need us to be happy? Look at the immense misery of domestic cattle, who exist only to feed man. Their brief knowledge of life is simply a long torture. Yet they can not will themselves out of existence. From the point of view of the data contained in their genes, they are very successful. Humans will take great care to ensure that they survive and reproduce. And so from the perspective of evolution, farm animals are far more successful than wild animals. And that is also the human condition. We are bred to survive, and however miserable we might be, we also serve to further the gene.
What is the nature of woman? It was simpler to view them from only the blank slatist feminist doctrine that they are simply men. To accept evopsych and its various offshoots on the uniqueness of woman, makes life more complicated. Do women simply exist for pain? Like farm animals, their condition might always be miserable as mere playthings and meat for men, but they would still propagate their selfish genes under such conditions. Are women driven by an emotional desire to be dominated and hurt by dominant men?
What kind of world is this? This brutal Darwinian struggle, red in tooth and claw, and how does one live in it? Should we hate our parents for forcing us to be born, merely to satisfy their selfish-genes? Am I just a robot for my parent's inferior genes?
schopen84 wrote:1 We are besieged by Schopenhauer's hegehog's dilemma. We hedgehogs have a need to be close to one another for warmth, and yet our point pricks ensure that we cause pain whenever in contact.
2 Do our selfish-genes need us to be happy?
1 Not all of us are "hedgehogs"... ;-) 2 No.
Look at the immense misery of domestic cattle, who exist only to feed man. Their brief knowledge of life is simply a long torture. Yet they can not will themselves out of existence. From the point of view of the data contained in their genes, they are very successful. Humans will take great care to ensure that they survive and reproduce. And so from the perspective of evolution, farm animals are far more successful than wild animals. And that is also the human condition. We are bred to survive, and however miserable we might be, we also serve to further the gene.
What are you, but a snowflake in the endless, timeless snowstorm? Genes will record your experiance for posterity. Be happy that you are here given this chance.
What is the nature of woman? It was simpler to view them from only the blank slatist feminist doctrine that they are simply men. To accept evopsych and its various offshoots on the uniqueness of woman, makes life more complicated. Do women simply exist for pain? Like farm animals, their condition might always be miserable as mere playthings and meat for men, but they would still propagate their selfish genes under such conditions. Are women driven by an emotional desire to be dominated and hurt by dominant men?
They are the ying of the yang. etc. etc. They have their own agendas. Not too complicated at the root. You seem a little misserable... too bad. Go talk to them.
What kind of world is this? This brutal Darwinian struggle, red in tooth and claw, and how does one live in it? Should we hate our parents for forcing us to be born, merely to satisfy their selfish-genes? Am I just a robot for my parent's inferior genes?
The reason for life is to fertilise the soil... ehehWe are here to experiance this reality. Your mind makes hell out of this amazing paradise we see before us. Blah, blah ... wake up, quit smoking and smell the roses... darky. :-D
Maybe its trite, but I guess I'm just wondering what the point of it all is. Well actually if life is pointless and meaningless, I'm ok with it. I'm ok with the 0. The problem is the -negative. From Evopsych and Dawkins it seems like life does have a point. To dominate males, conquer females, and spread your genes. A brutal sadistic Nietzschean struggle to be the strongest, toughest, baddest ape on the mountain of skulls. When I was a younger man, I sucked up the warrior ethos. So maybe I'm just bitter as I age. I like Nietzsche, even though I read him from "slave morality". He does a good job of exposing the envy and resentment of the strong, the powerful, the superior Masters, that inspires my crypto-Christian whining.
TheAbsolute has a bunch of quotes about the nature of woman. And I guess for me that plays a big part in it to. That women are the prizes to be won in this game of life. Show your sadism, dominance and cruelty and win a girl.
I don't know I guess it just seems useless to me to wake up in the morning for 70 years, show up to work for some alphamale boss, grovel before him. Get paid, go home, and use my wages to subsistence my meaningless submission to dominance for nearly a century.
schopen84 wrote:Maybe its trite, but I guess I'm just wondering what the point of it all is.
No kidding... :-D
Well actually if life is pointless and meaningless, I'm ok with it. I'm ok with the 0.
Not much choice there.
The problem is the -negative. From Evopsych and Dawkins it seems like life does have a point. To dominate males, conquer females, and spread your genes. A brutal sadistic Nietzschean struggle to be the strongest, toughest, baddest ape on the mountain of skulls.
Survival is the name of the game? Adapt or perish. Big apes are big targets for poachers. So... wrong there. :-P
When I was a younger man, I sucked up the warrior ethos. So maybe I'm just bitter as I age. I like Nietzsche, even though I read him from "slave morality". He does a good job of exposing the envy and resentment of the strong, the powerful, the superior Masters, that inspires my crypto-Christian whining.
I have never read any of his writings. Christians are sweet, naive, fools for the most part. Church prays on the lost with corupted truth.
TheAbsolute has a bunch of quotes about the nature of woman. And I guess for me that plays a big part in it to. That women are the prizes to be won in this game of life. Show your sadism, dominance and cruelty and win a girl.
There are exceptions if that is what you after. Try love, care and compassion... you never know, it might work. =)
I don't know I guess it just seems useless to me to wake up in the morning for 70 years, show up to work for some alphamale boss, grovel before him. Get paid, go home, and use my wages to subsistence my meaningless submission to dominance for nearly a century.
No argument here. This place is screwed up, but at least we know what the problem is. That's a start. Don't be afraid of changes.
schopen84 wrote:Maybe its trite, but I guess I'm just wondering what the point of it all is. Well actually if life is pointless and meaningless, I'm ok with it. I'm ok with the 0. The problem is the -negative. From Evopsych and Dawkins it seems like life does have a point. To dominate males, conquer females, and spread your genes. A brutal sadistic Nietzschean struggle to be the strongest, toughest, baddest ape on the mountain of skulls. When I was a younger man, I sucked up the warrior ethos. So maybe I'm just bitter as I age. I like Nietzsche, even though I read him from "slave morality". He does a good job of exposing the envy and resentment of the strong, the powerful, the superior Masters, that inspires my crypto-Christian whining.
TheAbsolute has a bunch of quotes about the nature of woman. And I guess for me that plays a big part in it to. That women are the prizes to be won in this game of life. Show your sadism, dominance and cruelty and win a girl.
I don't know I guess it just seems useless to me to wake up in the morning for 70 years, show up to work for some alphamale boss, grovel before him. Get paid, go home, and use my wages to subsistence my meaningless submission to dominance for nearly a century.
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2023-08-29T01:26:51.906118
|
https://example.com/article/7022
|
In a communication system including a communication apparatus and an external apparatus, a technology for establishing wireless connection between the communication apparatus and the external apparatus has been known.
|
2023-09-07T01:26:51.906118
|
https://example.com/article/8598
|
The present invention relates to improvements in a reciprocating hydraulic motor. More specifically, the present invention relates to a hydraulic pump coupled to a hydraulic motor employing a reciprocating piston. One use for such motors is to supply slurries of paint, or other coating compositions, to the several spray heads of an airless paint sprayer system.
Hydraulic motors employing reciprocating pistons for airless paint sprayers have been used in the past. One known manufacturer of such a hydraulic motor is The Speeflo Division of Titan Tool, Inc. of Roslyn, N.Y. Other known manufacturers of hydraulic motors for airless paint sprayer systems include Graco, Inc. of Minneapolis, Minn., Durotech Co. of Moorpark, Calif. and Airlessco of Orange, Calif.
Hydraulic pumps can also be used for a variety of other purposes. For example, they can be used in connection with plastic injection molding machines, fork lifts, punch presses, log splitters, and the like. In all such uses, a hydraulically driven device, which is supplied with hydraulic fluid by a hydraulic pump, is preferably moved into position quickly but does its work at the end of the stroke: In such a device, what is required is a high volume of hydraulic fluid at a low pressurexe2x80x94when the device is being moved into positionxe2x80x94and a low volume of hydraulic fluid at a high pressurexe2x80x94when the device does its work.
The function of the hydraulic pump needs to be regulated in all such devices in order to enable the pump to move a high volume of hydraulic fluid at a low pressure and a low volume of hydraulic fluid at a high pressure. The current control circuits for operating such pumps have not been found to be optimum. In current hydraulic pump designs for airless paint sprayers, as the pressure increases, the pump has a tendency to chatter and deliver cyclical amounts of fluid instead of a smooth, steady stream thereof. Most control circuits are also external to the housing of the pump and are thus more susceptible to leakage.
Accordingly, it is desirable to develop a new and improved hydraulic pump which would overcome the foregoing difficulties and others while providing better and more advantageous overall results.
In one embodiment of the present invention, a control circuit for a variable displacement pump is provided.
In this embodiment of the invention, the control circuit comprises a pressure compensator valve in fluid communication with an input of an associated variable displacement pump and a first piston which selectively exerts a first force on a swashplate of the associated variable displacement pump. Also provided is a second piston which selectively exerts a second force on the first piston, and hence on the swashplate of the associated variable displacement pump wherein the second force is in opposition to the first force.
Another embodiment of the present invention relates to a combination pump and control circuit.
In accordance with this embodiment of the invention, a variable displacement pump is provided having a swashplate, an input line and an output line. A pressure compensator valve is in fluid communication with the output line of the variable displacement pump. A first piston has a first end operatively connected to the swashplate wherein the first piston selectively exerts a first force on the swashplate of the variable displacement pump. A second piston is also provided. The second piston selectively contacts the first piston and exerts a second force on a swashplate wherein the second force is in the same direction as the first force. A first biasing element exerts a third force on the swashplate, wherein the third force is in opposition to the first force. A second biasing element is operatively associated with the second piston. The second biasing element exerts a fourth force on the second piston. The fourth force is in opposition to the second force.
In accordance with still another embodiment of the present invention, a combination pump and a control circuit for the pump is provided.
More particularly, in accordance with this embodiment of the invention, the combination comprises a housing and a variable displacement pump having a swashplate, an input line and an output line wherein the variable displacement pump is positioned in the housing. A pressure compensator valve is in fluid communication with the output line of the variable displacement pump. The pressure compensator valve is positioned in the housing. A first piston has a first end operatively connected to the swashplate, wherein the first piston selectively exerts a first force on the swashplate of the variable displacement pump. The first piston is located in the housing. A second piston selectively exerts a second force on the swashplate wherein, the second force is in the same direction as the first force. The second piston is also located in the housing.
One advantage of the present invention is the provision of a new and improved hydraulic pump. The pump is particularly adapted for use with a reciprocating hydraulic motor of an airless paint sprayer system. However, the pump could also be used to power punch presses, log splitters, fork lifts, plastic injection molding machines, and the like.
Another advantage of the present invention is the provision of a hydraulic pump which is regulated by a pressure compensator valve. In this design, a piston is employed to move the swashplate of the pump. The piston is regulated by fluid pressure from the pressure compensator valve.
Still another advantage of the present invention is the provision of a hydraulic pump in which the maximum volume output is controlled by a relationship between a first piston, which adjusts the position of a swashplate of the pump, and a second piston, which adjusts the position of the first piston. By setting the ratio of these two pistons, one can control the fluid pressure at which the two pistons respectively act on the swashplate.
Yet another advantage of the present invention is the provision of a hydraulic pump employing first and second pistons to control the position of a swashplate and a spring mounted adjacent to the second piston to preset the pressure at which the second piston will begin to move in relation to the first piston, thereby controlling the pressure point at which the first piston moves the swashplate and lowers the output volume of the hydraulic pump.
Yet still another advantage of the present invention is the provision of a hydraulic pump which eliminates the hysteresis, or lag time, of the response of a first piston that controls a swashplate position of the hydraulic pump as soon as a pressure drop is detected. This feature decreases xe2x80x9cdead bandxe2x80x9d and the response time of the hydraulic circuit.
A further advantage of the present invention is the provision of a hydraulic pump having a new and improved hydraulic feedback loop to adjust the position of a swashplate of the hydraulic pump. As pressure increases, the effect is to lower the volume demanded of the pump which makes it easier for the pump to meet the demand for hydraulic fluid. To the user, the effect is a smoother, steadier supply of the pumped product, especially at high pressures.
A still further advantage of the present invention is the provision of a hydraulic pump in which pulsations in the output of the hydraulic pump are damped.
A yet further advantage of the present invention is the provision of a hydraulic pump with a control circuit which optimizes the pressurized fluid flow output of a hydraulic pump to a given horsepower input, thus allowing a use of lower horsepower motors to power the hydraulic pump. This reduces the manufacturing cost of the system and also the amount of energy consumed.
An additional advantage of the present invention is the provision of a hydraulic pump which is more compact and lighter in weight for a given output volume of hydraulic fluid and operating pressure.
Yet another advantage of the present invention is the provision of a hydraulic pump with an internal hydraulic control circuit thereby eliminating external piping and possible hazardous leakage points due to external hydraulic connections.
Still other benefits and advantages of the present invention will become apparent to those skilled in the art upon a reading and understanding of the following detailed specification.
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2024-05-06T01:26:51.906118
|
https://example.com/article/3829
|
Q:
Getting SIGSEGV (segmentation error) for the given problem. (Finding LCA of a generic tree)
So, I was trying to solve the below problem using the most basic method i.e. storing the paths and finding LCA.
My code is working fine on VSCode and giving the right output. But when submitting on SPOJ, it gives runtime error (SIGSEGV).
Problem Link: https://www.spoj.com/problems/LCA/
Problem Description:
A tree is an undirected graph in which any two vertices are connected by exactly one simple path. In other words, any connected graph without cycles is a tree. - Wikipedia
The lowest common ancestor (LCA) is a concept in graph theory and computer science. Let T be a rooted tree with N nodes. The lowest common ancestor is defined between two nodes v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself). - Wikipedia
Your task in this problem is to find the LCA of any two given nodes v and w in a given tree T.
Sample Input:
1
7
3 2 3 4
0
3 5 6 7
0
0
0
0
2
5 7
2 7
Sample Output:
Case 1:
3
1
My Code:
#include <iostream>
#include <vector>
#include <cmath>
#include <cstring>
using namespace std;
vector<vector<int>> edges;
bool storepath(int s, int d, vector<int>& path, vector<bool>& visited) {
if(s == d)
{
path.push_back(d);
return true;
}
else if(edges[s].size() == 1) {
if(s != d)
{
for(int i = 0; i < path.size(); i++)
if(path[i] == s) {
path.erase(path.begin() + i);
}
}
return false;
}
visited[s] = true;
path.push_back(s);
for(auto e: edges[s])
{
if(visited[e] == false)
{
bool ans = storepath(e, d, path, visited);
if(ans)
break;
}
}
}
int LCA(int a, int b)
{
if(a == b)
return a;
vector<int> path1, path2;
vector<bool> visited(edges.size(), false);
storepath(1, a, path1, visited);
visited.assign(edges.size(), false);
storepath(1, b, path2, visited);
int n = path1.size();
int m = path2.size();
int i = 0,j = 0;
while(i < n && j < m && path1[i] == path2[j]) {
i++;
j++;
}
return path1[i-1];
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);cout.tie(0);
int t;
cin >> t;
int Case = 1;
while(t--)
{
int n;
cin >> n;
edges.resize(n+1);
for(int i = 1; i <= n; i++)
{
int size, val;
cin >> size;
while(size--)
{
cin >> val;
edges[i].push_back(val);
edges[val].push_back(i);
}
}
int q;
cin >> q;
cout << "Case "<< Case << ":" << endl;
while(q--)
{
int a, b;
cin >> a >> b;
cout << LCA(a, b) << endl;
}
Case++;
edges.clear(); //added after igor's comment (forgot to add before but used while submitting)
}
return 0;
}
I think I'm not accessing any out of scope element so SIGSEGV should not occur.
Please tell me how can I fix and improve my code.
A:
Some bugs are easy to find, when you know how to find them. The tools every programmer should know about are valgrind and -fsanitize. Remember to always compile with warnings enabled and fix them. Compiling your code with:
g++ -Wall -Wextra -fsanitize=undefined 1.cpp && ./a.out </tmp/2
results in a helpful warning:
1.cpp:38:1: warning: control reaches end of non-void function [-Wreturn-type]
38 | }
| ^
and a runtime error:
1.cpp:9:6: runtime error: execution reached the end of a value-returning function without returning a value
Your storepath doesn't return value.
|
2023-08-24T01:26:51.906118
|
https://example.com/article/7757
|
One of the North Carolina men’s basketball players’ favorite ways to tease their new teammate, graduate transfer guard Cameron Johnson, is to show highlights from UNC’s 80-78 last-season win over Pitt.
Johnson, who was then playing for the Panthers, scored 24 points in the game, but because the Tar Heels won, his new UNC teammates embrace their bragging rights.
They also like to remind Johnson about the second time the two teams played — when North Carolina again won, this time 85-67.
That’s just one of the ways junior guard Kenny Williams, Johnson’s roommate, likes to mess with him. Besides bringing up last season, Williams calls the 6-8, 210-pound Johnson, “little body.”
“He’s smaller than me,” Williams said with a smile. Williams is 6-4, 185 pounds, but he said he beats Johnson in the “muscle department.”
After living with now-Sacramento Kings rookie Justin Jackson for two years, Williams and junior forward Luke Maye started rooming with Johnson when he transferred to UNC from Pitt this season. The three grew close quickly.
Maye said it was their shared values – both have three brothers – while Williams pointed to Johnson’s funny, down-to-earth demeanor. An ideal companion for watching TV, going out to eat or hanging out as the hours slip by unnoticed.
But on the court, Johnson is trying to replace Jackson. The two have already drawn comparisons with their lanky frames and prowess on the perimeter.
UNC coach Roy Williams hasn’t seen enough of Johnson to know how he compares to Jackson in play style, but he does know one thing: Johnson can shoot. Last season at Pitt, he averaged 11.9 points per game and made 41.5 percent of his 3-point attempts. But Johnson, whom Maye called an unselfish player, at first hesitated to shoot during UNC’s practices.
“Cam, you’re one of the best shooters on the team,” Williams said to Johnson on the second team practice. “Why are you not shooting the ball?”
That’s not a problem anymore. Whether it be at practice or Late Night With Roy, Johnson has shown off his talent for making shots. During one practice last week, Johnson made every shot he took.
Rebounding is not the reason UNC was drawn to Johnson, but the Tar Heels will need him to build that skill. North Carolina led the nation last season with a 12.3 rebounding margin. Last season’s top three rebounders – starting forwards Kennedy Meeks and Isaiah Hicks and off-the-bench big man Tony Bradley – are all gone. This season, North Carolina’s rebounding capabilities remain a mystery.
Williams said none of the freshmen forwards are ready to start, so that leaves Maye and Johnson tasked to take over the rebounding effort down low. Johnson averaged 4.5 rebounds for Pitt last season and said he has improved.
Johnson’s experience will expedite his transition into UNC basketball, but so have the bonds he’s already made with Maye, Kenny Williams and the rest of the Tar Heels, despite the “little body” nickname and incessant Pitt-UNC highlight reels.
|
2023-10-21T01:26:51.906118
|
https://example.com/article/5071
|
Screenplays (eventually) and the Meanderings of a Complex Mind
Month: August 2016
She has been the matriarch of our household pets for the last ten years even though we’ve had her longer. Up until then it was only her. She traveled well and was low maintenance.
Later, when we moved and lived in Alabama, she would be joined by others. A hard thing for the “old” gal to accept.
The first of the interlopers, was Thomas the Ally Cat, a small Calico stray kitten we found quaking under the house. He managed to endear himself to her for awhile and the two would romp and bounce around the house. For awhile she got to be a kitten again, that is until we adopted Abby, another stray that found it’s way under my husband’s truck and riding 30 miles under the carriage without getting killed. We resisted adopting her, but she slowly wormed her way into our lives. Abby didn’t mew but made this cute chirping sound as she walked.
Chloe managed to make them tow the line and would whop them if they didn’t. In a way it was sad to see how the relationship changed once Abby came on the scene. Mostly because the two kittens had each other to play with and there was no room for her in their play. The old gal got shut out and Chloe got cranky and at times she’d attack Abby in reprisal.
Chloe, Abby & Thomas
As if that wasn’t enough, then came cute, bouncy Ferguson, our little “Dog in the Wind”, who landed on our doorstep after a big tornado. The kittens took to him fine until Chloe sauntered in and gave him a big whollop, sending him whimpering and cowering across the room. The other two took that as their cue to follow suit and proceeded to gang up on him. Cat logic? Thankfully, it only happened one other time and that was it.
Eventually things settled and they made peace of sorts.
When we moved to California, my sister Diana kept the two youngun’s and we brought Chloe and Ferg with us.
Just so you know, Chloe hadn’t always been our cat. In fact, she changed hands more than once.
In 2002, or thereabouts my third grandson had just been born.
What possessed my daughter to do this I have no clue, but shortly thereafter, Jack being only two or three months old at the time, she and her sister (my other daughter) had gone to the mall and fell in love with this scrawny little thing. They were told she was six weeks old, but I highly doubted that and here she was. She barely fit in their cupped hands. Her legs were spindly and still wobbly. She hopped around like most kittens do and then would fall back on her haunches. She wasn’t a cute kitten and kittens are generally cute. I looked on and shook my head.
In my opinion, my daughter Tina( and her husband) do not do well with pets. She(they) get them and ignore them. They already had this beautiful, imported, enormous German Shepard, they had special ordered and imported from Germany. They spent thousands on this highly trained dog, name Dach that they hardly interacted with and now a kitten? I know they cared for him, but… Well, this isn’t about Dach.
Chloe and Dach did however, get along beautifully. There were times we’d find the kitten curled up with him, the two of them finding comfort in one another. Smart kitten that she was, she stayed close to Dach because my daughter’s second child, Matt would seek her out and torment her. He was four.
Fortunately for Chloe, that would change a year later at Christmas.
She came to us in a box at Christmas in 2003. I believe it was the following year. The box the kids brought in, held gingerly, was highly suspect. My grandson Matt the tormentor was chomping at the bit. “Hurry grandma, poppa, open your present, it’s gray and it, it moves!!!” he announced.
The cat’s out of the box.
There she was. We didn’t want another pet, having lost the last one to, I suspect, coyotes.
Never fear. Chloe was unlike her predecessor.
First of all, Chloe is NOT a lap cat, although on rare occasions she’d sit on my sister’s lap or on my husband’s tummy, she was not a cuddler. She also loves to play rough in a nice way and manages to always keeps her claws sheathed.(I stopped declawing cats when I learned how and what they do to them – NEVER again) Her teeth on the other hand, being razor sharp are the only lethal weapons to watch out for, not because she means to hurt you, because she never clamps down hard, EVER , but because they are sooo vampire sharp.
Over the years she has brought home, lizards, gophers, a sundry of birds, snakes, mice and bugs. She eats giant grasshoppers and palmetto’s (in AL) with relish, so no photos.
Chloe is also wise and resourceful and will be celebrating her 14th birthday this fall.
Long ago, we realized she would be fine against any predator and has had carte blanche coming and going. She knows where home is. Truly.
When we gave her to mother a few years back, thinking she would have a good home after her 23 year old cat died and that perhaps she would be good company for her, she disappeared. Mother didn’t even know who she was. She called her Ashes and sometimes the “New Ashes”, her old kitty’s name. When mom’s husband died and the paramedics came, Chloe flew the coop. (Keep in mind that was before we realized how bad mother’s Alzheimer’s was) Two months later as I’m packing mother’s stuff, I hear a scratchin’ and a meowin’ at the front door and there she was. She saunters in like she’d been out on an afternoon stroll. I can only imagine what an adventure she must’ve had. That was ten years ago.
One day I watched her as she assessed the possibility of her getting into and on the top shelf of a linen closet. The door to the closet was open maybe 1/2 inch if that, when she saw it. She jumped on the edge of the tub to check it out, she looked this way and that, then got back on the floor and looked again, then back to the tub, thoroughly calculating. I really didn’t know what she was about to do, but when she was done, she leaped from the floor, used her paw to fling the door open and landed on the top shelf. This was like a 6 foot jump! It was truly amazing.
Chloe’s Den
I found her in the above self made “den” one day. Fortunately, she has the perfect coat for camouflage.
Chloe is quite enterprising and has traveled across these United States. Twice. She started out in Colorado, flew to Nashville, which didn’t go well. She relieved herself from Grand Junction to Denver, howling all the way, much to the dismay of the passengers, got washed in Denver and did fine the rest of the way. She then moved from Nashville to Alabama and rode like a champ, by car, cross country to California, visiting several states in between.
She has braved the coyotes and puma’s of Colorado, survived the farm in Alabama with it’s many predators, coyotes, hawks, owls and snakes, not to mention the vicious dogs next door and now in California with more hawks, a lone eagle and coyotes. She knows how to make herself flat and invisible. She can hug the walls of the house and run like hell and howl at our door when danger is present.
Today, I take her to the vet. She’s getting very skinny for no apparent reason and losing patches of her coat. She seems fine otherwise, lounging and hunting. But I want to be sure.
Sometimes Russ and I talk about how nice it would be not to have pets to be responsible for, but as soon as one of them isn’t seen for a time, we panic. I took Ferguson (the Papillon) to the vet this morning for his 6 month check, did some shopping and really missed him running to me when I came home. If anything happened to them, we would surely be sad. It’s amazing how they can be so much a part of us.
Isn’t she gorgeous? Her with Al Pacino.
Love you Chloe-bird.
***Update on Chloe: She had lost two pounds. Thyroid and liver function were a little higher than normal but still within range, for her age she is doing fine. A little change in diet and more wet food which is easier to digest was the recommendation. No meds!!!
Milton Farbin dreamt he was “the Fast-moving Man.” It was a recurring dream, part of a campaign to promote particular products and services. The Fast-moving Man and the Alluring Woman were cultural icons, pop stars with the highest appeal-rating according to the new, Trump Index. They were loved and adored. They slipped into people’s dreams by means of a new phone app given out for free. The glorious couple demonstrated new, American-made merchandise that was on sale for bargain prices.
In the dream, Milton was a charismatic leader with blistering eyes and orange hair, a man of wealth and power. When he awoke he was penniless and depressed having spent all his money on goods and services he did not need or want. Once he left the Virtual Dream, Milton was a rag man, no longer capable of keeping a regular job. In the past he was a beautician. He…
Welcome to Online Website Reviews! Where you can get free online website reviews from real customers. The kind of reviews that you will find on our site is to. Business sites, web hosting sites, payment gateway sites, and even mystical websites. We also offer job search, phone services, blog reviews, electronics reviews, jewelry reviews, psychic reading reviews, and spell casting reviews.
|
2024-04-27T01:26:51.906118
|
https://example.com/article/8376
|
John Mercer (Australian pastoralist)
John Henry Mercer (4 January 1823 – 8 December 1891) was a landowner, pastoralist and politician in colonial Victoria (Australia).
Mercer born in Midlothian, Scotland, the son of George Dempster Mercer and Frances Charlotte Reid.
Mercer was a pastoralist with his brother George Duncan Mercer and cousin William Drummond Mercer in properties near Geelong.
Mercer was elected to the district of Grant in the inaugural Victorian Legislative Council on 16 September 1851.
Mercer left the Council in December 1852, he became commissioner of insolvent estates and chairman of the water commission. In 1857 Mercer had the Gheringhap freehold mapped as the Dryden estate. Mercer later returned to Scotland where he married Anne Catherine Anstruther on 11 December 1861. Mercer died in Huntingtower, Perthshire on 8 December 1891.
References
Category:1823 births
Category:1891 deaths
Category:Members of the Victorian Legislative Council
Category:19th-century Australian politicians
|
2023-11-30T01:26:51.906118
|
https://example.com/article/5113
|
Luigi’s Mansion: Dark Moon Coming Soon
The wait will soon be over Luigi fans. On March 24th, 2013, Luigi's Mansion: Dark Moon is coming to the Nintendo 3DS. Teased last year during Nintendo's E3 press conference, little has been seen or heard about the game since. Even though there still isn't much new information about the sequel to the Gamecube classic, at least we can take some solace in knowing when we can play Dark Moon.
Luigi will get to explore a few new mansions with his trusty new Poltergust 5000, which he'll use to capture ghosts and treasure along the way. And that's basically all we know. Hopefully Nintendo will reveal some more details about the game before its March release.
|
2024-07-12T01:26:51.906118
|
https://example.com/article/6405
|
---
abstract: 'Spin injection in metallic normal/ferromagnetic junctions is investigated taking into account the anisotropic magnetoresistance occurring in the ferromagnetic layer. On the basis of a generalized two-channel model, it is shown that there is an interface resistance contribution due to anisotropic scattering, besides spin accumulation and giant magnetoresistance. The corresponding expression of the thermoelectric power is derived and compared with the expression accounting for the thermoelectric power produced by the giant magnetoresistance. Measurements of anisotropic magneto-thermoelectric power are presented in electrodeposited Ni nanowires contacted with Ni, Au, and Cu. It is shown that this thermoelectric power is generated at the interfaces of the nanowire. The results of this study indicate that, while the giant magnetoresistance and the corresponding thermoelectric power indicate the role of spin-flip scattering, the observed anisotropic magneto-thermoelectric power might be the fingertint of interband s-d relaxation mechanisms.'
author:
- 'J.-E. Wegrowe, Q. Anh Nguyen, M. Al-Barki, J.-F. Dayen, T.L. Wade, and H.-J. Drouhin'
title: 'Anisotropic Magneto-Thermopower: the Contribution of Interband Relaxation'
---
Introduction
============
In order to explain the high resistance and the high thermoelectric power observed in transition metals, Mott introduced the concept of spin-polarized current and suggested that s-d interband scattering plays an essential role in the conduction properties [@Mott]. This approach, in terms of two conduction bands, explained the existence of a spin-polarized current in the 3d ferromagnetic materials, and was used for the description of anisotropic magnetoresistance (AMR) [@Potter0; @Potter], and thermoelectric power [@Handbook]. With the discovery of giant magnetoresistance (GMR) [@GMR] and related effects, the development of spintronics focused the discussion on spin-flip scattering occurring between spin-polarized conducting channels. The two-channel model, which describes the conduction electrons with majority and minority spins, is applied with great efficiency to GMR and spin injection effects [@Johnson; @VanSon; @Valet; @Zhang; @PRBThermo], including metal/semiconductor [@Molenkamp] and metal/supraconductor interfaces [@JedemaSupra]. In this context, it is sufficient to describe the diffusion process in terms of spin-flip scattering without the need to invoke interband s-d scattering.
Magneto-thermoelectric power (MTEP) experiments in GMR structures [@MTEP; @piraux; @Shi; @Shi2; @Tsymbal; @Gravier; @Gravier2] however point out the need for a deeper understanding of the dissipative mechanism responsible for the giant magnetothermopower related to GMR. The problem of s-d electronic relaxation at the interface was also put forward in the context of current induced magnetization reversal mechanisms in various systems exhibiting AMR [@BergerDW; @Derek; @JulieDW; @Marcel; @cond-mat]. However, the interface contribution to the resistance in relation to AMR has so far not been investigated. The aim of the present work is to study the non-equilibrium contribution of a normal/ferromagnetic (N/F) interface to both the resistance and the thermoelectric power.
For our purpose, it is convenient to generalize the two spin channel approach to any relevant transport channels, i.e. to any distinguishable electron populations $\alpha$ and $\gamma$ [@hybride]. The local out-of-equilibrium state near the junction is then described by a non-vanishing chemical-potential difference between these two populations: $\Delta
\mu_{\alpha \gamma}¥ = \mu_{\alpha}-\mu_{\gamma} \neq 0$ [@PRBThermo]. Corollarilly, assuming that the presence of a junction induces a deviation from the local equilibrium, the $\alpha$ and $\gamma$ populations can be [*defined by the $\alpha
\rightarrow \gamma$ relaxation mechanism*]{} itself, that allows the local equilibrium to be recovered in the bulk material ($lim_{z
\rightarrow \pm \infty}¥\Delta \mu(z) = 0$). In this context [@PRBThermo; @cond-mat], the basic idea we develop here is that, beyond spin-flip relaxation, interband s-d relaxation also plays a crucial role in the interface magnetoresistance of magnetic nanostructures. Though similar ideas have been suggested in previous spintronics studies [@Mott; @Potter0; @Potter; @Suzuki; @Tsymbal; @Baxter], the originality of this work is to deal with interband relaxation on an equal footing with spin-flip relaxation [@cond-mat] in the framework of a [*thermokinetic approach*]{}. For this purpose, the two spin-channel model is generalized, with the introduction of the corresponding transport coefficients: the conductivities $\sigma_{\alpha}$ and $\sigma_{\gamma}$ of each channel define the total conductivity $\sigma_{t}=¥\sigma_{\alpha} +
\sigma_{\gamma}$ and the conductivity asymmetry $\beta =
(\sigma_{\alpha}- \sigma_{\gamma}) /\sigma_{t}$; the relaxation between both channels is described by the parameter $L$ (or equivalently, the relevant relaxation times $\tau_{\gamma
\leftrightarrow \alpha}$). It is shown that this two-channel model can be applied straightforwardly to the description of MTEP, by introducing an extra transport parameter which is nothing but the derivative of $\beta$ with respect to the energy. The predictions of the model are compared with experimental results of anisotropic MTEP measured in electrodeposited nanowires.
The article is structured as follows: General expressions of the interface contributions of resistance (Sec. II) and thermoelectric power (Sec. III) are derived, and applied to the case of AMR and GMR systems (Sec. IV), and to the corresponding MTEP (Sec. V). It is shown that a contribution of the interface resistance related to AMR and the corresponding MTEP should be expected. The experimental study performed on single-contacted Ni nanowires (Sec. VI) confirms the presence of an anisotropic MTEP, which is produced by the interfaces.
Out-of-equilibrium resistance
=============================
In the framework of the two conducting-channel model, which includes relaxation from one channel to the other, it is possible to show, on the basis of the entropy variation [@PRBThermo], that the kinetics are described by the following Onsager equations:
$$\begin{array} {lll}
J_{\alpha} = -\frac{\sigma_{\alpha }}{e} \frac{\partial
\mu_{\alpha}}{\partial z}\\
J_{\gamma} = -\frac{\sigma_{\gamma}}{e} \frac{\partial \mu_{\gamma}}{\partial z}\\
\dot{\Psi}_{\alpha \gamma}¥ = L \left ( \mu_{\alpha}-\mu_{\gamma} \right )
\end{array}
\label{Onsager0}$$
Where $\dot{\Psi}_{\alpha \gamma}$ describes the relaxation from the channel $\alpha$ to the other channel $\gamma$ in terms of velocity of the reaction $\alpha
\rightarrow \gamma$. The Onsager coefficient $L$ is inversely proportional to the relaxation times $\tau_{\alpha
\leftrightarrow \gamma}$ :
$$L \propto \left ( \frac{1}{\tau_{\alpha \rightarrow
\gamma}} + \frac{1}{\tau_{\gamma \rightarrow \alpha}}\right )$$
The out-of-equilibrium configuration is quantified by the chemical affinity $\Delta \mu = \mu_{\alpha} - \mu_{\gamma}$, i.e. the chemical potential difference of the reaction.
Furthermore, in the case of a stationary regime, the conservation laws lead to :
$$\begin{array} {ll}
\frac{d J_{\alpha}}{dt}\, = \,-\frac{\partial J_{\alpha}}{\partial
z} - \, \dot{\Psi} = 0 \\
\frac{dJ_{\gamma}}{dt}\, = \,-\frac{\partial J_{\gamma}}{\partial z} + \, \dot{\Psi} = 0\\
\end{array}
\label{con}$$
The total current $J_{t}$ is constant:
$$J_{t} = J_{\alpha} + J_{\gamma} = -\frac{1}{e} \frac{\partial
}{\partial z} \left (\sigma_{\alpha } \mu_{\alpha}+
\sigma_{\gamma } \mu_{\gamma } \right )$$
The expression of Ohm’s law, $J_{t}= -\sigma_{t} \frac{\partial \Phi}{\partial
z}$, is recovered by introducing the measured electric potential $\Phi$ and the total conductivity $\sigma_{t}=\sigma_{\alpha}+ \sigma_{\gamma}$ [@Constantes] :
$$e \Phi= \frac{1}{\sigma_{t}}( \sigma_{\alpha} \mu_{\alpha} +
\sigma_{\gamma} \mu_{\gamma})$$
Let us assume that the two channels collapse to a unique conduction channel for a specific configuration, the reference, which is a local equilibrium situation: $\Delta \mu_{eq}=0$. The out-of-equilibrium contribution to the resistance, $R^{ne}$, is calculated through the relation:
$$-J_{t}e \, R^{ne} = \int_{A}^{B} \frac{\partial }{ \partial z}
(\mu_{\alpha} - e \Phi(z))dz = \int_{A}^{B} \frac{\partial }{ \partial z}
(\mu_{\gamma} - e \Phi(z))dz$$
so that
$$R^{ne}= -\frac{1}{J_{t}e} \int_{A}^{B}
\frac{\sigma_{\alpha} - \sigma_{\gamma}}{2 \sigma_{t}} \frac{\partial
\Delta \mu}{ \partial z}dz
\label{Res}$$
where the measurement points $A$ and $B$ are located far enough from the interface (inside the bulk) so that $\Delta
\mu (A)=\Delta \mu (B) =0$. The derivative is only calculated in the intervals where $\Phi$ is continuous. The above relation allows the out-of-equilibrium resistance at a simple junction between two layers (composed by the layers $I$ and $II$) to be easily calculated. If the junction is set at $z=0$ and the conductivities are respectively $\sigma_{i}^{I}$ and $\sigma_{i}^{II}$ ($i=\{\alpha, \gamma \}$), we have:
$$-J_{T}e \, R^{ne} = \int_{A}^{0}
\frac{\sigma^{I}_{\alpha} - \sigma^{I}_{\gamma}}{2 \sigma_{T}} \frac{\partial
\Delta \mu^{I}}{ \partial z}dz + \int_{0}^{B}
\frac{\sigma^{II}_{\alpha} - \sigma^{II}_{\gamma}}{2 \sigma_{T}} \frac{\partial
\Delta \mu^{II}}{ \partial z}dz
\label{ResJunct}$$
The equilibrium is recovered in the bulk, so that:
$$R^{ne} = \left (
\frac{\sigma^{I}_{\alpha} - \sigma^{I}_{\gamma}}{\sigma^{I}_{t}} -
\frac{\sigma^{II}_{\alpha} - \sigma^{II}_{\gamma}}{\sigma^{II}_{t}}
\right )
\frac{\Delta \mu(0)}{2 J_{t}e}
\label{Result}$$
The chemical potential difference $\Delta \mu(z)$, which accounts for the pumping force opposed to the relaxation $\alpha \rightarrow
\gamma$, is obtained by solving the diffusion equation deduced from Eqs. (\[Onsager0\]) and (\[con\]) [@Johnson; @VanSon; @Valet; @Zhang; @PRBThermo]:
$$\frac{\partial^{2}¥\Delta \mu(z)}{\partial z^{2}}= \frac{\Delta \mu(z)}{l_{diff}^{2}}
\label{DiffEq}$$
where $$l_{diff}^{-2}= eL(\sigma_{\alpha}^{-1}+\sigma_{\gamma}^{-1})
\label{ldiff}$$
is the diffusion length related to the $\alpha \rightarrow \gamma$ relaxation.
At the interface ($z=0$), the continuity of the currents for each channel writes: $$J_{\alpha}(0)=-\frac{\sigma_{\alpha} \sigma_{\gamma}}{e
\sigma_{t}} \frac{\partial \Delta \mu}{\partial
z}+\frac{\sigma_{\alpha}}{\sigma_{t}} J_{t}=J_{\gamma}(0)
\label{currentcon}$$
which leads to the general relation:
$$\Delta \mu (0)= \left ( \frac{\sigma^{I}_{\alpha}}{\sigma^{I}_{t}} -
\frac{\sigma^{II}_{\alpha}}{\sigma^{II}_{t}} \right
) \, \left ( \frac{\sigma^{I}_{\alpha} \sigma^{I}_{\gamma}}{\sigma^{I}_{t} l_{diff}}+
\frac{\sigma^{II}_{\alpha}\sigma^{II}_{\gamma}}{\sigma^{II}_{t}
l^{II}_{diff}} \right )^{-1}\, \, eJ_{T}
\label{DeltaMu0}$$
Inserting Eq. (\[DeltaMu0\]) into Eq. (\[Result\]), we obtain the general expression for the out-of-equilibrium resistance (per unit area) produced by the $\alpha \rightarrow
\gamma$ relaxation mechanism at a junction:
$$R^{ne} = \left (
\frac{\sigma^{I}_{\alpha} - \sigma^{I}_{\gamma}}{2 \sigma^{I}_{t}} -
\frac{\sigma^{II}_{\alpha} - \sigma^{II}_{\gamma}}{2 \sigma^{II}_{t}}
\right )\, \left ( \frac{\sigma^{I}_{\alpha}}{\sigma^{I}_{t}} -
\frac{\sigma^{II}_{\alpha}}{\sigma^{II}_{t}} \right
) \, \left ( \sqrt{\frac{\sigma^{I}_{\alpha}
\sigma^{I}_{\gamma}eL^{I}}{\sigma^{I}_{t}}} + \sqrt{\frac{\sigma^{II}_{\alpha}
\sigma^{II}_{\gamma}eL^{II}}{\sigma^{II}_{t}}}\right )^{-1}
\label{Rout}$$
It is convenient to describe the conductivity asymmetry by a parameter $\beta$ such that $\sigma_{\alpha}= \sigma_{t} (1+\beta)/2$ and $\sigma_{\gamma}=\sigma_{t}(1-\beta)/2$. The out-of-equilibrium contribution to the resistance then takes the following form:
$$R^{ne} = \frac{1}{2}
\frac{(\beta_{I} - \beta_{II})^{2}}{\sqrt{eL^{I}\sigma_{t}^{I}(1-\beta_{I}^{2})}+
\sqrt{eL^{II}\sigma_{t}^{II}(1-\beta_{II}^{2})}}
\label{Rbeta}$$
where the diffusion length $l_{diff}$ now writes:
$$l_{diff}^{-1}= 2 \sqrt{\frac{eL}{\sigma_{t}¥(1-\beta^{2})}}$$
giant magnetoresistance vs. anisotropic magnetoresistance
=========================================================
Giant Magnetoresistance
-----------------------
The most famous example of the out-of-equilibrium resistance described in the preceding section, is the giant magnetoresistance (GMR) [@GMR] occurring near a junction composed of two ferromagnetic layers $F_{1}/F_{2}$ made out of the same metal. The electronic populations are the spin-polarized carriers quantized along the ferromagnetic order parameter $\alpha = \uparrow$, $\gamma= \downarrow $. The diffusion length is the spin-diffusion length $l_{diff}=l_{sf}$. The $\alpha
\rightarrow \gamma$ relaxation is the spin-flip relaxation, and tends to balance the deviation from the local equilibrium. This process leads to a spin-accumulation described by the generalized force $\Delta \mu = \mu_{\uparrow}-\mu_{\downarrow}$. The local equilibrium ($\Delta \mu = 0 $) is recovered in the bulk ferromagnet, at the voltage probes, or equivalently in the case of two parallel magnetic configurations. When the magnetization of the two layers are parallel, we have indeed: $\sigma_{\uparrow}^{I}=\sigma_{\uparrow}^{II}$ and $\sigma_{\downarrow}^{I}=\sigma_{\downarrow}^{II}$, and $R^{ne}=0$. In contrast, for an antiparallel configuration $\sigma_{\uparrow}^{I}=\sigma_{\downarrow}^{II}$ and $\sigma_{\downarrow}^{I}=\sigma_{\uparrow}^{II}$. In terms of conductivity asymmetry $\beta_{s}$, we have $\sigma_{\uparrow}= \sigma_{t} (1+\beta_{s})/2$ and $\sigma_{\downarrow}=\sigma_{t}(1-\beta_{s})/2$ (the subscript $s$ refers to the $s$ type - possibly $s d$ hybridized - conduction band). The out-of-equilibrium resistance writes:
$$R_{GMR}^{\uparrow \downarrow } = \frac{
\beta_{s}^{2}}{\sigma_{t}¥(1-\beta_{s}^{2})} \, l_{sf} =
\frac{\beta_{s}^{2}}{\sqrt{eL\sigma_{t}(1-\beta_{s}^{2})}}
\label{RGMR}$$
This expression is the well-known giant magnetoresistance [@Johnson; @VanSon; @Valet; @Zhang; @PRBThermo; @Jedema; @George] measured in various $F_{1}¥/N/F_{2}$ devices. It is usually presented as the normalized ratio
$$\frac{R_{GMR}^{\uparrow \downarrow }}{R_{0}} =
\frac{\beta_{s}^{2}}{1-\beta_{s}^{2}} \, \frac{l_{sf}}{\Lambda}
\label{GMRStandard}$$
measured on a layer of thickness $\Lambda$, where $R_{0} = R^{\uparrow
\uparrow} = R^{\downarrow \downarrow} = \Lambda / \sigma_{t}$ is the overall resistance of the layers (also per surface units).
In the case of a single $N/F$ junction, we have $\sigma_{\alpha}^{I}=\sigma_{\gamma}^{I}$ in the normal metal and $\sigma_{\alpha}^{II} \neq \sigma_{\gamma}^{II}$ in the ferromagnetic metal. The out of equilibrium resistance writes:
$$R_{GMR}^{N-F} = \frac{1}{2}
\frac{\beta^{2}_{s}}{\sqrt{eL^{N}\sigma^{N}_{t}}+\sqrt{eL^{F}\sigma^{F}_{t}(1-\beta^{2}_{s})}}$$
This is the out-of-equilibrium resistance arising in a single magnetic layer. It is worth pointing out that, in spite of the existence of spin accumulation and non-vanishing out-of-equilibrium resistance, it is not possible to measure a deviation of $R_{GMR}^{N-F}$ from a reference state because the resistance does not vary with the magnetic configurations, or with any well-controled external parameters (except in the case of domain wall scattering, discussed e.g. in reference [@DWS]). In other words, $R_{GMR}$ is present but there is nevertheless no analyzer, or probe, to detect it. Although the GMR results are well known, the more general Eq. (\[Rout\]) allows one to push the discussion about non-equilibrium resistances beyond GMR effects.
Out-of-equilibrium anisotropic magnetoresistance
------------------------------------------------
From our generalized approach one should predict the existence of a [**non-equilibrium anisotropic magnetoresistance**]{} (NeAMR). The anisotropic magnetoresistance (AMR) is characterized by a conductivity $\sigma_{t}(\theta)$ which depends on the angle $\theta
= (\vec{I},\vec{M})$ between [*the direction of the current and the magnetization*]{}. In single-domain structures, the angle $\theta$ is tuned with the applied magnetic field which modifies the magnetization direction. In contrast to GMR ($\uparrow \,
\downarrow$ relaxation), AMR is a bulk effect that necessarily involves at least one anisotropic relaxation channel $\alpha
\rightarrow \gamma (\theta)$ which is controlled by the direction of the magnetization (and is hence related to spin-orbit coupling) [@Potter]. Although generated by spin-dependent electronic relaxations, the $\alpha \rightarrow \gamma (\theta)$ relaxation channel does not necessarily involve spin-flip scattering. It is generally assumed that [*the relaxation from the isotropic $s$ minority channel $\alpha = s \downarrow$ to the anisotropic $d$ minority channels $\gamma = d \downarrow$ is the main contribution to AMR in $3d$ ferromagnets* ]{} [@Mott; @Potter0; @Potter; @Note2; @cond-mat]. In the [*normal metal*]{} (here normal means with no d band effect), the conductivity of the (minority) $d$ channel is vanishing, so that $\beta_{sd}^{N}=1$. The out of equilibrium magnetoresistance is then a function of $\theta(\vec{M})$ defined by:
$$R^{N-F}_{AMR}(\theta) = \frac{1}{2} \frac{\left ( 1-\beta_{sd}(\theta) \right )^{2}}{
\sqrt{eL_{sd}(\theta) \, \sigma_{t}(\theta)(1-\beta_{sd}¥^{2}(\theta))}}
\label{RAMR}$$
where $\beta_{sd} (\theta)$ is the conductivity asymmetry corresponding the AMR relaxation channels; $\sigma_{\alpha}(\theta)=
\sigma_{t}(\theta)(1+\beta_{sd}(\theta))/2$ and $\sigma_{\gamma}(\theta)= \sigma_{t}(\theta)(1-\beta_{sd}(\theta))/2$ in the ferromagnet. In terms of diffusion length and normalized to the bulk AMR $R_{0}(\theta)$, the Ne-AMR writes :
$$\frac{R^{N-F}_{AMR}(\theta) }{R_{0}(\theta)}=
\left ( \frac{1-\beta(\theta)}{1+\beta(\theta)} \right ) \frac{l_{diff}(\theta)}{
\Lambda}¥$$
However, the contribution of $R^{N-F}_{AMR}(\theta)$ is difficult to measure because $l_{diff}$ is expected to be small (nanometric or below), and the direct bulk contribution of the AMR dominates in usual configurations (see however references [@Jedema; @George] for a possible contribution in $F_{1}¥/N/F_{2}$ devices).
Out-of-equilibrium magnetothermopower
=====================================
Since, in metallic structures, the heat transfer is carried by the conduction electrons, it is possible to study the electronic transport coefficients by performing thermoelectric (TEP) measurements while applying a temperature gradient to the sample. TEP is usually characterized through the bulk Seebeck coefficients, while imposing a temperature gradient under zero electric current (open circuit). In the same manner as for GMR, TEP is composed of a bulk contribution and an out-of-equilibrium contribution due to the interfaces (see next sub-section). Surprisingly, anisotropic MTEP in bulk ferromagnets has not been reported although extensive investigations about TEP had been performed on Ni, Fe and Co based materials since the work of Mott [@RqueTEP]. Thus, a vanishing bulk MTEP can be expected, that would favor the measurements of out-of-equilibrium interface MTEP. Previous investigations about the interface contribution to the magneto-thermoelectric power (MTEP) have been performed exclusively in GMR structures, with typical sizes of the magnetic layers below the spin-diffusion length (spin-valve structures) [@MTEP; @piraux; @Shi; @Shi2; @Tsymbal; @Gravier; @Gravier2]. In this very case, the experimental results show that the spin-dependent thermopower is nearly proportional to the GMR. As will be shown below, the situation is similar in the case of single ferromagnetic layers exhibiting AMR.
In the following, the temperature gradient is assumed to be uniform : $ \nabla T = \frac{\Delta
T}{\Lambda}$, where $\Lambda$ is the length of the wire, and $\Delta T $ is the temperature difference between the two terminals. This simplifying assumption allows us to recover the diffusion equation, Eq. (\[DiffEq\]). The Onsager relations follow, by adding the heat flows $J^{Q}_{\alpha \gamma}¥$ of the two channels:
$$\begin{array} {lllll}
J_{\alpha} = -\frac{\sigma_{\alpha }}{e} \frac{\partial
\mu_{\alpha}}{\partial z} + S_{\alpha} \sigma_{\alpha} \frac{\partial
T}{\partial z}\\
J_{\gamma} = -\frac{\sigma_{\gamma}}{e} \frac{\partial \mu_{\gamma}}{\partial
z} + S_{\gamma} \sigma_{\gamma} \frac{\partial
T}{\partial z}\\
J^{Q}_{\alpha} = \lambda_{\alpha}¥ \frac{\partial
T}{\partial z} -\pi_{\alpha}¥ \frac{\partial
\mu_{\alpha}}{\partial z}\\
J^{Q}_{\gamma} = \lambda_{\gamma}¥ \frac{\partial
T}{\partial z} -\pi_{\gamma}¥ \frac{\partial \mu_{\gamma}}{\partial z}\\
\dot{\Psi}_{\alpha \gamma} = L¥ \left ( \mu_{\alpha}-\mu_{\gamma} \right )
\end{array}
\label{OnsagerTEP}$$
where $S_{i}$, $\lambda_{i}$, and $\pi_{i}$, $i=\{\alpha,\gamma \}$, are respectively the Seebeck, the Fourier, and the Pelletier coefficients of each channel.
Hereafter, we will not study the channel dependent heat flow $J^{Q}_{\alpha \gamma}¥$. The thermopower is deduced from Eqs (\[OnsagerTEP\]) following step-by-step the method developed in the previous section, and incorporating the condition $J_{t}=0$. In the bulk metal, the local equilibrium condition leads to the relation:
$$J_{t}(\infty)= -\sigma_{t} \, \frac{\partial
\Phi}{\partial z}(\infty) \, + \, S_{t} \sigma_{t} \frac{\Delta
T}{\Lambda} = 0$$
which yields,
$$\frac{\partial \Phi}{\partial
z}(\infty) = S_{t} \frac{\Delta T}{\Lambda}
\label{CurrentTEP}$$
Where
$$S_{t}= \frac{\sigma_{\alpha}¥S_{\alpha} +
\sigma_{\gamma}¥S_{\gamma}}{\sigma_{\alpha}+\sigma_{\gamma}¥}
\label{SRef0}$$
is the [*the reference thermopower*]{} corresponding to the bulk, or the equilibrium TEP. The effective current (analogous to the total current in the GMR calculation) $J_{eff} = -S_{t} \sigma_{t} \frac{\Delta T}{\Lambda}$ is [*different*]{} in both sides of the junction (like the conductivity, $\sigma_{t}$, the Seebeck coefficient, $S_{t}$, is discontinuous at the interface).
From Eqs. (\[OnsagerTEP\]) and (\[currentcon\]), the continuity of the currents $J^{I}_{\alpha}(0)=J^{II}_{\alpha}(0)$ leads to the following chemical-potential splitting at the interface:
$$\Delta \mu (0)= \left ( \sigma^{I}_{\alpha} \, (S^{I}_{\alpha} -
S^{I}_{t} ) \, - \,
\sigma^{II}_{\alpha} \, ( S^{II}_{\alpha} -
S^{II}_{t}) \right ) \, \left ( \sqrt{\frac{\sigma^{I}_{\alpha}
\sigma^{I}_{\gamma}eL^{I}}{\sigma^{I}_{t}}} + \sqrt{\frac{\sigma^{II}_{\alpha}
\sigma^{II}_{\gamma}eL^{II}}{\sigma^{II}_{t}}} \right )^{-1}
\, e \frac{\Delta T}{\Lambda}¥
\label{Deltamu}$$
The chemical-potential splitting, $\Delta \mu (0)$, is analogous to that calculated in Sec. II, Eq. (\[DeltaMu0\]) for the GMR, after introducing the effective current $J_{eff} = -S_{t} \sigma_{t}
\frac{\Delta T}{\Lambda}$ :
$$\Delta \mu (0)= e \left ( J^{I}_{eff}¥\frac{\sigma^{I}_{\alpha} -
\sigma^{I}_{\gamma}}{\sigma^{I}_{t}}
\frac{\sigma^{I}_{\alpha}¥}{\sigma^{I}_{t}} \frac{\sigma^{I}_{\gamma}¥}{\sigma^{I}_{t}}
- J^{II}_{eff}¥\frac{\sigma^{II}_{\alpha} -
\sigma^{II}_{\gamma}}{\sigma^{II}_{t}}
\frac{\sigma^{II}_{\alpha}¥}{\sigma^{II}_{t}} \frac{\sigma^{II}_{\gamma}¥}{\sigma^{II}_{t}} \right )
\left ( \sqrt{\frac{\sigma^{I}_{\alpha}
\sigma^{I}_{\gamma}eL^{I}}{\sigma^{I}_{t}}} + \sqrt{\frac{\sigma^{II}_{\alpha}
\sigma^{II}_{\gamma}eL^{II}}{\sigma^{II}_{t}}} \right )^{-1}
\label{DeltamuBIS}$$
Here again (see Eq. (\[Res\])), the out-of-equilibrium thermopower $\Sigma ^{ne}$ can be defined from the reference corresponding to local equilibrium condition, $\Delta \mu_{eq}¥ =
0$ and $J_{\alpha}=J_{\gamma}=0$:
$$\Sigma^{ne} \frac{\Delta T}{\Lambda} = \frac{1}{e} \int_{A}^{B} \left (
\frac{\partial \mu_{\alpha}}{\partial z} - e S_{t} \frac{\partial
T}{ \partial z} \right ) dz= \frac{1}{e} \int_{A}^{B} \left (
\frac{\partial \mu_{\alpha}}{\partial z} - e \frac{\partial
\Phi}{ \partial z} \right ) dz
\label{RefTEP}$$
where $A$ (resp. $B$) is located in the layer I (II), at a distance $\Lambda^{I}$ ($\Lambda^{II}$), far enough from the interface (inside the bulk). This is the same expression as that calculated for the out-of-equilibrium resistance in Eq. (\[Result\]). We obtain
$$\Sigma^{ne} \frac{\Delta T}{\Lambda} = -\left (
\frac{\sigma^{I}_{\alpha} - \sigma^{I}_{\gamma}}{ \sigma^{I}_{t}} -
\frac{\sigma^{II}_{\alpha} - \sigma^{II}_{\gamma}}{ \sigma^{II}_{t}}
\right )
\frac{\Delta \mu(0)}{2e}
\label{MTEP}$$
Making use of Eq. (\[Deltamu\]) we deduce the out-of-equilibrium TEP :
$$\begin{aligned}
\Sigma^{ne} = - \frac{1}{2} \left (
\frac{\sigma^{I}_{\alpha} - \sigma^{I}_{\gamma}}{\sigma^{I}_{t}} -
\frac{\sigma^{II}_{\alpha} - \sigma^{II}_{\gamma}}{\sigma^{II}_{t}}
\right )
\left ( \frac{\sigma^{I}_{\alpha} \sigma^{I}_{\gamma}}{\sigma^{I}_{t}}
\, (S^{I}_{\alpha} - S^{I}_{\gamma} ) \, - \,
\frac{\sigma^{II}_{\alpha} \sigma^{II}_{\gamma}}{\sigma^{II}_{t}}
\, ( S^{II}_{\alpha} - S^{II}_{\gamma}) \right ) \nonumber \\
\left ( \sqrt{\frac{\sigma^{I}_{\alpha}
\sigma^{I}_{\gamma}eL^{I}}{\sigma^{I}_{t}}} + \sqrt{\frac{\sigma^{II}_{\alpha}
\sigma^{II}_{\gamma}eL^{II}}{\sigma^{II}_{t}}}\right )^{-1}
\label{ResultMTEP}\end{aligned}$$
Let us define the parameters, $\mathcal
S_{+}=(S_{\alpha}+S_{\gamma})/2$ and $ \mathcal
S_{-}=(S_{\alpha}-S_{\gamma})/2$. We see that $S_{t}= \frac{1}{2}
\left ( (1+\beta) S_{\alpha} + (1-\beta) S_{\gamma} \right ) $, so that the overall Seebeck coefficient rewrites: $$S_{t} = \mathcal S_{+} + \beta \mathcal S_{-}$$ The out of equilibrium interface thermopower takes the form:
$$\Sigma^{ne} = -(\beta^{I}-\beta^{II})
\frac{\sigma_{t}^{I} \left (1- (\beta^{I})^{2}¥ \right ) \,
\mathcal S_{-}^{I} -
\sigma_{t}^{II} \left (1-(\beta^{II})^{2} \right ) \mathcal S_{-}^{II}
}{\sqrt{eL^{I}\sigma_{t}^{I}(1-(\beta^{I})^{2})}+
\sqrt{eL^{II}\sigma_{t}^{II}(1-(\beta^{II})^{2})}}
\label{Sbeta}$$
This is the general expression of the out-of-equilibrium MTEP. In the following, it will be expressed in terms of transport-coefficient asymmetry $\beta$. It is possible to investigate further this relation by using the microscopic Mott’s relation (valid for a spherical energy band and assuming a local thermal equilibrium) [@Mott]:
$$S_{\alpha \gamma}¥=
\frac{a}{\sigma_{\alpha \gamma}¥} \left ( \frac{\partial
\sigma_{\alpha \gamma}}{\partial \epsilon} \right
)_{\epsilon_{F}}$$
where $a= \frac{\pi^{2} k_{B}^{2}T}{3e}$, $\epsilon$ is the electron energy, and $\epsilon_{F}$ is the Fermi energy.
$$\begin{aligned}
\mathcal S_{+} =S_{t} - a \frac{ \beta \beta'}{1-\beta^{2}¥} \nonumber\\
\mathcal S_{-}¥ = a \frac{\beta'}{1-\beta^{2}}
\label{SRef}\end{aligned}$$
and $$S_{t}=\frac{a}{\sigma_{t}} \left ( \frac{\partial
\sigma_{t}}{\partial \epsilon} \right )_{\epsilon_{F}}
\label{Stotal}$$
is the [*the reference thermopower*]{} defined in Eq. (\[SRef0\]), and $\beta' = \frac{\partial \beta}{\partial\epsilon})_{\epsilon_{F}}$ is the derivative of the asymmetry conductivity coefficient $\beta$ taken at the Fermi level. Eq. (\[Sbeta\]) rewrites :
$$\Sigma^{ne} =
-\frac{a ¥(\beta^{I}-\beta^{II}) \left ( \sigma_{t}^{I} \,
\beta'^{I} -
\sigma_{t}^{II} \, \beta'^{II} \right )
}{\sqrt{eL^{I}\sigma_{t}^{I}(1-(\beta^{I})^{2})}+
\sqrt{eL^{II}\sigma_{t}^{II}(1-(\beta^{II})^{2})}}
\label{Sbeta2}$$
Magnetothermopower corresponding to GMR and NeAMR
-------------------------------------------------
In the case of spin-valve structures (i.e. junctions consisting of layers with parallel or antiparallel magnetization), and considering identical ferromagnetic layers, we have $\beta_{s} =
\beta^{I} =-\beta^{II}$ and also $\beta'_{s} =
\beta'^{I} =-\beta'^{II}$ :
$$\Sigma_{GMR}^{\uparrow \downarrow} =
- 2 a \sigma_{t} ¥\left ( \frac{\beta'}{\beta} \right ) \, R_{GMR}^{\uparrow \downarrow}
\label{SGMRGen}$$
As discussed in Ref. [@Shi], the MTEP associated to GMR vanishes if the parameter $\beta' $ is zero, i.e. if the conductivity asymmetry is not energy dependent. The proportionality between $R^{GMR}/R_{0}$ and $\Sigma^{GMR}/(\Lambda S_{t})$ was observed experimentally [@Gravier; @Gravier2; @Shi; @MTEP] and the proportionality factor $\mathcal P_{GMR}¥= - \frac{2 a}{S_{t}}¥\frac{\beta'}{\beta}$ was found to be of the order of one to ten in usual experimental conditions.
Besides, the out-of-equilibrium contribution due to the AMR in a Normal/Ferromagnetic junction is deduced by taking into account the relevant s-d relaxation channels: $\beta^{N}_{sd}=1$ (Sec. III.B) and $\beta'^{N}_{sd} = 0$ :
$$\Sigma^{N-F}_{AMR} = 2 a \sigma^{F}(\theta) \, \left (
\frac{\beta'(\theta)}{1-\beta(\theta)} \right )
R^{N-F}_{AMR}(\theta)
\label{SAMR}$$
The expression $\Sigma^{ne}_{AMR}/S_{t} = \mathcal P_{AMR}
(R^{N-F}/R_{0})$ (where $R_{0} = \sigma_{t}(\theta)/ \Lambda$) shows that a simple relation simmilar to that of GMR reltates the NeAMR and MTEP. The proportionality factor $\mathcal P_{AMR}¥= \frac{2
a}{S_{t}¥} \frac{\beta'}{1-\beta}$ (refer to AMR/MTEP ratio in the next section) can be measured providing that the NeAMR, described in Sect. III.B., Eq. (\[RAMR\]), is measured independently (e.g. with the configuration proposed in references [@Jedema; @George]). The relevance of the picture proposed above, which is based on the differentiation between two well-separated relaxation channels (spin-flip or s-d scattering) can now be compared to experimental facts.
Measuring MTEP
--------------
It is important to point out that the measurements of interface TEP necessarily involve the measurement of the TEP of the bulk materials contacted to the voltmeter through reference wires (see Fig. 1). In our experiments, a temperature difference $\Delta T = T_{B} - T_{A}$ is maintained between the extremities A and B of the junction (located at the J point), whereas the voltmeter with the terminals of the reference wires are maintained at temperature $ T_{0}$. Referring to the TEP of the reference contact as $S_{t}$, the total voltage difference measured in the open circuit consists of the bulk TEP and an interface TEP:
$$V_{TEP}¥ = \Delta T \left ( \frac{(AJ) S^{I}_{t} + (JB) S^{II}_{t}}{AB}
- S_{r} \right) + \Sigma^{ne} \left ( \frac{\partial T}{\partial z} \right )_{J}¥
\label{TotalMTEP}$$
As already pointed out, and according to the literature, the bulk term appears to be independent on the magnetic configuration (i.e. independent on $ \theta$). Such a situation occurs under the following weakly restrictive condition: $\sigma_{t}(\epsilon, \theta) = g(\theta) \sigma_{t}(\epsilon)$ (see Eq. (\[Stotal\])), where $g(\theta)$ is any function accounting for the conductivity anisotropy. In contrast, the out-of-equilibrium term is still $\theta$ dependent through the parameter $\beta(\theta)$, or $l_{sd}(\theta$). In consequence, we expect that a MTEP contribution can be measured as a function of the external magnetic field, and that this MTEP is produced by the out-of-equilibrium interface term only. On the other hand, the amplitude of the non-equilibrium interface effect depends on the amplitude of the temperature gradient at the junction $\left ( \frac{\partial
T}{\partial z} \right )_{J}$. The effect is then larger in case of a non-homogeneous temperature gradient, if the junction is placed in a region where there is a sharp temperature variation, i.e. near the interface with the heat source or cryostat. In contrast, if the junction is placed far away from the interface with the heat source or cryostat, the effect is expected to be smaller.
As for AMR, the $\theta$ dependence of the TEP (the MTEP) is defined as the ratio:
$$\frac{\Delta V}{V} = \frac{Max\{V(\theta)\}-Min\{V(\theta)
\}}{Min\{V(\theta)\}}$$
In the next section, the quantity $V(\theta)$ is measured as a function of the amplitude and direction of the applied magnetic field $\vec H$.
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![ \[fig:SetUp\] The structure consists of two metallic layers of length AJ and JB with a typical temperature gradiant $\Delta T / AB $. It is contacted through two reference wires connected to a voltmeter at temperature $T_{0}$](Weg1.eps "fig:"){height="6cm"}
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Experiments
===========
As already mentioned, the nearly linear relation between the GMR ($\Delta R/R$) and the corresponding MTEP ($\Delta V/V$) has been observed in various spin-valve systems [@MTEP; @piraux; @Shi; @Shi2; @Tsymbal; @Gravier; @Gravier2]. The GMR/MTEP ratio is of the order of one to ten in GMR samples consisting of about 150 electrodeposited Co/Cu bilayers where both the GMR and the MTEP are of the order of 10 % [@Gravier]. The present study focuses on MTEP in single Ni nanowires by pointing out the role of the contacts. The results presented hereafter have been measured near room temperature. All nanowires contain two contacts N/F and F/N, and a bulk ferromagnetic (F) region. The results presented in Sec. IV predict that an anisotropic out-of-equilibrium interface magnetoresistance, and corresponding MTEP, should be present at the junctions.
This experimental section is composed as follows. The samples are described in subsection A. The magnetic configurations of the nanowire are discussed in subsection B on the basis of recent AMR measurements and of previous reports. Subsection C reports on the anisotropic nature of the measured MTEP. Section D evidences that the measured MTEP is an interface effect. Subsection E describes the magnetic configurations of the Ni contact that allow the MTEP profiles to be understood.
Samples
-------
The samples are prepared by electrodeposition in porous polycarbonate track-etched membranes. This technique has been used extensively in order to study the micromagnetic configurations inside the wires [@Travis; @Fert; @IEEE; @Schoen; @Yvan; @PRL; @Meyer]. The pores are 6-micrometer length and 40 to 25-nm diameter. A gold layer is deposited on the bottom and top of the membrane and fixed to the electrode. By applying the potential in the electrolytic bath, the Ni nucleates at the bottom of the pores, grows through the membrane and reaches the top Au layer. Then, a single nanowire can be contacted inside the electrolytic bath, by controlling the potential between the two sides of the membrane during the electrodeposition and stopping the process when the potential drops to zero [@IEEE]. The single contact can be performed either with the same material as that of the wire (Ni) or with a different material (for instance non-ferromagnetic like Cu or Au), by changing the electrolytic bath before performing the contact (see Fig. 2). The contact has the shape of a mushroom on top of the membrane [@IEEE; @Yvan; @Schoen].
The electrodeposited Ni nanowire consists of nanometric nanocrystallites with random orientations: the magnetocrystalline anisotropy is averaged out at the nanometer scale [@Meyer; @Yvan; @Derek; @PRL]. Only a strong uniaxial shape anisotropy remains present (anisotropy field $H_{a}= 2 \pi M_{S} \approx 0.6$ T, where $ M_{s}$ is the magnetization at saturation). It has been shown that the Ni nanowires are uniformly magnetized for all stable states [@PRL; @Yvan]. Furthermore, due to the high aspect ratio, the spatial distribution of the current density $\vec{J}$ is well defined along the wire axis: the angle $(\vec{J}, \vec{M}) $ between the current and the magnetization $\vec{M}$ coincides with the angle $\theta$ of the magnetization of the wire (see Fig. 2).
It is expected that a ferromagnetic contact localized on the top of the membrane (the Ni mushroom) changes the interface properties for two reasons: due to the non uniform spin-polarized current density [@Otani], and due to the presence of specific magnetic configurations that do not exist inside the wire. Note that the problem related to the spin-accumulation and GMR generated by magnetic domain walls has been studied in detail in such electrodeposited samples [@DWS]. [*The conditions that are necessary to obtain a GMR-like contribution, the presence of a highly-constrained magnetic domain wall, are not fullfilled*]{} in the present case. Here we report on a comparative study between samples with different contacts for a significant number of samples (a few tens).
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![ \[fig:SetUp\] Geometry and contacts of the two kinds of single contacted nanowires. The heat resistance at the bottom is driven by an AC voltage generator at frequency f.](Weg2.eps "fig:"){height="9cm"}
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Magnetic characterization through AMR
-------------------------------------
Due to the uniform magnetization and to the homogeneous current density, the magnetic field dependence of the AMR is directly linked to the magnetic hysteresis loop of the Ni nanowire. A quadratic dependence is observed [@Potter]:
$$R(\theta)=R_{0}+ \Delta R_{AMR} \, \, cos^{2}( \theta )
\label{AMRexp}$$
The magnetoresistance (Fig. 3) is measured with an external magnetic field applied at a given angle $\Psi$ with respect to the wire axis. Except for some few samples were domain walls can be observed (not shown), the hysteresis loop corresponds to a uniform rotation of the magnetization with a precision of two to three percents [@PRL; @Yvan; @Marcel]. The magnetic configurations are described by the well-known profile (see e.g. the Stoner-Wohlfarth model) [@Aharoni]. At large angles ($\Psi \approx 90 (deg)$), the magnetization states follow a reversible rotation from the wire axis $\theta = 0$ to the angle of the external field $\Psi $ while increasing the magnetic field from zero to the saturation field (see Fig. 2): intermediate states ($\theta \in [0,90]$) are stable and correspond to the profile of the AMR curve (Fig. 3). In contrast, for small angles (around $\Psi \approx 10$ deg) the magnetoresistance profile as a function of the applied field (Fig. 3) is flat because the magnetization is pinned along the wire axis : there are no stable positions between $\theta \approx 10$ and $\theta \approx 170$ deg. There is no fundamental change if contacting the nanowire with Cu or Au [@Marcel].
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![ \[fig:AMR\] The AMR is plotted at different angles of the external field: (a) Ni wire contacted with Ni; (b) Ni wire contacted with Cu.](Weg3.eps "fig:"){height="10cm"}
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
MTEP is anisotropic
-------------------
The thermoelectric measurements are performed with a compact resistive heater (5 Ohms), placed on the bottom of the membrane and contacted to a voltage generator of 5 to 7 Volts (Fig. 2). A sine wave of frequency of the order of f=0.05 Hz is injected in the heater. At this frequency, a stationary thermal regime is reached, and the output thermopower signal is detected at 2f = 0.1Hz. The amplitude of the 2f signal gives the TEP $\Sigma^{ne} \Delta T/ \Lambda$. With our experimental configuration, the amplitude of the TEP ranges between five to fifty $\mu V$, which corresponds to $\Delta T \approx 1 K$, with $S_{T}^{Ni} \approx -13$ $\mu$ V/K and $S^{Cu}_{t} \approx 1.8
\mu $ V/K, so that the temperature gradient is $\frac{\Delta
T}{\Lambda} \approx 3 \, 10^{5} K/m$. These values are close to that measured in electrodeposited Co/Cu/Co multilayered spin-valves [@Gravier; @Gravier2].
A MTEP signal is obtained by measuring the voltage at zero current, as a function of the applied field. The MTEP signal does not originate directly from the magnetic field, but is related to the ferromagnetic configurations: the [*anisotropic nature of the MTEP*]{} is observed in Fig. 4, by measuring the TEP voltage as a function of the angle of the applied saturation field (at saturation field, the magnetization aligns with the field : $\theta = \Phi$). The anisotropic MTEP, with a $\Delta V / V$ variation of about 13 %, can be compared to the corresponding AMR (1.3 % amplitude, fitted with a $cos^{2}
\theta$ law) in Fig. 4. The MTEP profile is not very regular, and varies slighly from one sample to the other.
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
![ \[fig:angles\] Comparison of magnetothermopower (left) and AMR (right) for a single Ni nanowire with a Ni contact measured as a function of the angle of the external field with a saturating field ($\theta = \Psi$) of 1.2 T.](Weg4.eps "fig:"){height="8cm"}
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
The typical MTEP signal of Ni nanowires contacted with Ni, measured as a function of the external field, is shown in Fig. 5 for the sample characterized in Fig. 3 (a). A variation larger than that of the AMR signal is seen (depending on the samples, the MTEP amplitude ranges from about $\Delta
V/V = 3 $ % up to 30 %) and is of the same order that the MTEP produced in GMR devices composed of 150 bilayers [@Gravier]. The overall shape is surprising, since the profile as a function of the external field $\vec{H}_{ext}$ at small angles $\Psi$ shows the maximum variation (while the magnetization is fixed along the wire axis), and inversely, the profile at large angle $\Psi$ is approximately flat (while the magnetization rotates from zero to 90 deg). Note that the MTEP minimum at small angles corresponds to the zone of switching field (see Fig. 3), and that the high-field profile shows an approach to saturation corresponding to the anisotropy field of the wire. Such curves are systematically observed on all measured samples with small diameters (about 15 samples of diameter about 40 nm) [@LastMeas].
MTEP is not a bulk effect
-------------------------
The MTEP profile is not a function of the angle $\theta$ between the magnetization of the Ni nanowire and the wire axis and the variations observed should be related to another parameter. The most likely hypothesis is that the variations are produced by the magnetization states confined at the interface close to the Ni contact. [*In contrast to the AMR which is a bulk effect, the MTEP appears as an interface out-of-equilibrium process*]{}.
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![ \[fig:3\] Thermoelectric power as a function of the external field in Ni nanowires contacted with Ni for different directions of the external field. The magnetic configurations of the Ni contact are represented with arrows for $\Psi \approx 2$ deg.](Weg5.eps "fig:"){height="10cm"}
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
This hypothesis can easily be checked by comparing the Ni nanowires contacted with Ni to those contacted with Cu or Au (See Fig. 2). In these last samples, the ferromagnetic/normal interfaces are located inside the nanowire where electric current, temperature gradient, and magnetization are homogeneous. We observe that the MTEP signal vanishes with Cu and Au contacts (the TEP measured as a function of the angles $\Psi$ is constant). The two curves measured as a function of the applied field are compared in Fig. 6 (concerning the two samples characterized in Fig. 3), for $\Psi=0$. These measurements first confirm that the effect is due to the interface, and second, that the role played by the Ni contact is essential for the observation of MTEP processes. Note that a similar role of the Ni contact has been observed in experiments of spin-injection induced magnetization switching [@Marcel], were irreversible magnetization reversal provoked by the current was observed with ferromagnetic contacts, but not with Cu contacts.
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![ \[fig:Contacts\] Magnetothermopower of Ni nanowires with Ni, Au and Cu contacts, measured with external field $\Psi \approx 0$ deg (a): Ni with Ni contacts (left scale) compared with Au contact (right scale), MTEP $\approx 0.3 \%$ for about $6 \mu $V TEP; (b) Ni with Ni contactss compared with Cu contacts, MTEP $\approx 3.3 \%$, for TEP about 38 $\mu$V](Weg6.eps "fig:"){height="10cm"}
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These observations corroborate the analysis performed in Sec. IV. B where the amplitude of the effect is shown to be proportional to $\Sigma^{ne} \Delta T/AB$. In the case of an interface localized near the mushroom, the ratio $l_{diff}/AB$ is very large. In contrast, in the case of Cu or Au contacted wires, where the ferromagnetic/normal junction is localized inside the wire, the ratio $l_{diff}/AB$ is expected to be much smaller.
MTEP is related to the magnetic configurations of the Ni contact
----------------------------------------------------------------
It is possible to relate the observed MTEP to the AMR if we consider that the relevant angle is the angle $\theta_{N/F}=(\vec{I}_{N/F},\vec{M}_{N/F}¥)$ between the local current $I$ and the magnetization $M$ at the nanoscopic scale near the $N/F$ interface. With Cu and Au contacts, both the current density and the magnetization direction are well defined, and the angles coincide with that of the AMR: $\theta_{N/F}=(\vec{I}_{N/F}¥,\vec{M}_{N/F})= \theta$. However, with the Ni contact, the interface is located near the Ni mushroom. The direction of the current is no longer along the wire axis, and the magnetic configurations do not follow that measured with AMR inside the wire (see Fig. 5). The relevant angle $\theta_{N/F}¥ $ is defined by the current direction in the Ni mushroom, probably near the plane of the contact (if the current were uniform). The MTEP variations can then be reproduced assuming that the magnetization of the mushroom rotates following the total magnetic field $\vec{H}_{T}
= \vec{H}_{a} + \vec{H} + \vec{H}_{perp}$ where $\vec{H}_{a}$ is the dipole field due to the wire (which is of the order of the shape anisotropy of the wire) and $\vec{H}$ is the applied field. The field $\vec{H}_{perp}$ is the shape anisotropy of the mushroom. It is produced by the dipole field of the mushroom, probably interacting with the other vicinity mushrooms in the plane of the membrane (it plays the role of the anisotropy field of a thin layer). Thus the case of large and small angles have to be distinguished : i) The application of the external fields at large angles fixes the magnetization of all mushrooms in the plane perpendicular to the wire axis so that the configuration with the magnetization of the mushroom along the wire axis is expected only near zero applied field where $H_{a}$ dominates. ii) In the case of an external magnetic field applied at small angles $\Psi \le $ 10 $^{o} $ ( see schemes of Fig. 5), the magnetization of the mushroom is along the wire axis for nearly zero field ($H_{a}$ dominates) and for saturation fields ($H$ dominates). At intermediate fields, the magnetization of the wire switches to the opposite direction: a domain wall should be present between the wire and the mushroom. The transverse field $\vec{H}_{perp}$ dominates. The above scenario describes well the curves observed at different angles: the minima correspond to the MTEP with the magnetization of the mushroom perpendicular to the wire axis. The maximal value of MTEP corresponds to the magnetization of the mushroom parallel to the wire axis. The whole behavior is similar to that of AMR (see Fig. 4).
conclusion
==========
The well-known two-spin-channel model has been extended to the general case of an interface between two layers in the relaxation time approximation. A general expression of the thermoelectric power is derived. Like giant magnetoresistance (GMR), a non-equilibrium interface resistance contribution due to the anisotropic magnetoresistance (AMR) is predicted in a ferromagnetic/normal interface due to s-d interband relaxation. The corresponding magnetothermopower (MTEP) is derived, and is found to be proportional to $ l_{diff} \left ( \frac{\partial T}{\partial z} \right )_{J}¥$ where $ l_{diff}$ is the relevant diffusion length, and $\left ( \frac{\partial T}{\partial z} \right )_{J}$ is the temperature gradient at the junction (see Fig. 1). The MTEP associated to GMR is proportional to the magnetoresistance with the proportionality coefficient $\mathcal
P_{GMR}¥ =- \frac{2 a}{S_{t}}¥\beta' / \beta$ and the MTEP associated to AMR is proportional to the out of equilibrium AMR, with the coefficient $\mathcal P_{AMR}¥ = \frac{2 a}{S_{t}} \beta' /
(1-\beta)$. In the case of GMR, the experimental value of $\mathcal
P_{GMR}$ is close to one [@Gravier] (the MTEP is of the same order as the GMR) for many junctions in series.
In complement to the experiments with multilayered systems (Co/Cu/Co) [@Gravier], measurements of MTEP in electrodeposited Ni nanowires are presented. This signal presents three striking features: (i) A large MTEP signal of several $\mu V$ for about 1K temperature variation is measured (3 to 30% of the TEP); (ii) This MTEP is anisotropic; (iii) The measured MTEP signal is produced by a local magnetic configuration (at nanometric range) near the interface only. However, in contrast to transport experiments in GMR systems where both the magnetoresistance and the magnetothermopower are measured, the out-of-equilibrium AMR is not accessible in our two-point measurements in Ni nanowires. Accordingly, the interpretation of anisotropic MTEP due to GMR (where $ MTEP \propto l_{sf}/AB$) produced by magnetic inhomogeneities (i.e. domain-wall scattering effects) cannot be directly rule-out. But the interpretation of domain wall TEP is not realistic because DWS is very weak (below 0.1 % if any, according to previous studies [@DWS]) so that an important anisotropic MTEP could be measured only with a huge proportionality coefficient ($\ge
100$), which is in contradiction with the known GMR coefficient ($\mathcal P_{GMR} \approx 1$ for 150 junctions) measured in GMR structures.
The results of this study hence show that, while GMR and associated thermopower indicates spin-flip diffusion at the interface, the observed interface anisotropic MTEP should indicate interband s-d relaxation associated with ferromagnetism in Ni (where $MTEP \propto
l_{sd}/AB$). The amplitude of the effect suggests that the corresponding sd-diffusion length is sizable (e.g. of the order of the spin-flip length $l_{sf}$¥). Within this framework, further experiments allowing direct measurements of non-equilibrium AMR would probe and clarify the role played by the two kinds of relaxation processes.
Acknowledgement
===============
HJD thanks the Délégation Générale pour l’Armement for support.
N. F. Mott and H. Jones, [*Theory of the properties of metal and alloys*]{}, Oxford University Press, 1953. R. Potter, Phys. Rev. B [**10**]{}, 4626 (1974). T. R. McGuire and R. I. Potter, IEEE Trans. vol [**Mag-11**]{}, 1018 (1975). F. J. Blatt, P. A. Schroeder, C. L. Foiles, and D. Greig, [*Termoelectric power of metals*]{}, Plenum Press, 1976, Chap. 5. M. N. Baibich, J. M. Broto, A. Fert, F. Ngyen Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Phys. Rev. Lett. [**61**]{}, 2472 (1988) and G. Binasch, P. Grunberg, F. Saurenbach, and W. Zinn, Phys. Rev. B [**39**]{}, 4828 (1989). T. Valet and A. Fert, Phys. Rev. B, [**48**]{}, 7099 (1993). M. Johnson and R.H. Silsbee Phys. Rev. B [**35**]{}, 4959 (1987); M. Johnson and R. H. Silsbee, Phys. Rev. B [**37**]{}, 5312 (1988). P. C. van Son, H. van Kempen, and P. Wyder, Phys. Rev Lett. [**58**]{}, 2271 (1987). P. M. Levy, H. E. Camblong, S. Zhang, J. Appl. Phys. [**75**]{}, 7076 (1994). J. -E. Wegrowe, Phys. Rev. B [**62**]{}, 1067 (2000). G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, and B. J. van Wees, Phys. Rev. B [**62**]{}, R4790 (2000). F. J. Jedema, B. J. van Wees, B. H. Hoving, A. T. filip, and T. M. Klapwijk, Phys. Rev. B [**60**]{}, 16549 (1999). J. Sakurai, M. Horie, S. Araki, H. Yamamoto, and T. Shinjo, J. Phys. Soc. Jpn. [**60**]{}, 2522 (1991). L. Piraux, A. Fert, P. A. Schroeder, R. Laloee, and P. Etienne, J. Magn. Magn. Mat. [**110**]{}, L247 (1993). J. Schi, S. S. P. Parkin, L. Xing, M. B. Salamon, J. Appl. Phys. [**73**]{}, 5524 (1993). J. Schi, K. Pettit, E. Kita, S. S. P. Parkin, R. Nakatani, M. B. Salamon, Phys. Rev. B,[**54**]{}, 15273 (1996). E. Y. Tsymbal, D. G. Pettifor, J. Shi, M. B. Salamon, Phys. Rev. B [**59**]{}, 8371 (1999). L. Gravier, J. -E. Wegrowe, T. Wade, A. Fabian, J. -Ph. Ansermet, IEEE Trans. Mag. Mat. [**38**]{}, 2700 (2002). L. Gravier, A. Fabian, A. Rudolf, A. Cachin, J. -E. Wegrowe, J. -Ph. Ansermet, J. Magn. Magn. Mater. [**271**]{},153 (2004) and L. Gravier, S. Serrano-Guisan, and J. -Ph. Ansermet, J. Appl. Phys. [**97**]{}, 10C501 (2005). L. Berger, J. appl. Phys. [**55**]{}, 1954 (1984), P. P. Freitas and L. Berger, J. Appl. Phys. [**57**]{}, 1266 (1985). J. Grollier, D. Lacour, V. Cros, A. Hamzic, A. Vaures, and A. Fert, J. Appl. Phys. [**92**]{} 4825 (2002). D. Kelly, J. -E. Wegrowe, Trong-kha Truong, X. Hoffer, Ph. Guittienne, and J. -Ph. Ansermet. Phys. Rev. B [**68**]{} 134425 (2003). J. -E. Wegrowe, M. Dubey, T. Wade, H. -J. Drouhin, and M. Konczykowski, J. Appl. Phys. [**96**]{} 4490 (2004). J. -E. Wegrowe, H. -J. Drouhin, Proc. SPIE Quantum Sensing and Nanophotonic Devices II Vol. 5732, 498 (2005), and J. -E. Wegrowe and H. -J. Drouhin, cond-mat/0408410 (2005). The case of up and down spin electrons is obvious. In the case of $s$ and $d$ channel, band hybridization was often invoked against this distinction. However, even when dealing with hybridized states, it is still possible to separate conduction channels with a dominant $s$ character from conduction channnels originating from states with a stronger $d$ contribution.
Motofumi Suzuki and Yasunori Taga, Phys. Rev. B, [**52**]{}, 361 (1995). R. J. Baxter, D. G. Pettifor, E. Y. Tsymbal, D. Bozec, J. A. D. Matthew, and S. D. Thomson, J. Phys. : Condens. Matter [**15**]{}, L695 (2003). In all these calculations, the channel parameters $\sigma_{\alpha \gamma}$, $\beta$, and $L$ are considered as constant in space. It can be shown that taking into account the gradient only introduces vanishingly small corrections. F. J. Jedema, A. T. Filip, B. J. van Wees, Nature [**410**]{}, 345 (2001) J. -M. George, G. Faini and A. Fert, Phys. Rev. B [**67**]{}, 012410 (2003).
J. -E. Wegrowe, A. Comment, Y. Jaccard, J.- Ph. Ansermet, N. M. Dempsey, and J. -Ph. Nozières, Phys. Rev B, [**61**]{} 12216 (2000). It is clear that the corresponding model should include four channels that take into account the two spin channels for each $s$ and $d$ band. This more involved description is performed elsewhere ([@cond-mat]). For the sake of simplicity, we limit here the discussion to two independent models, with two spin-polarized channels on one hand, and $s$ and $d$ bands with one minority spin channel on the other hand.
Measurements of magnetic field depence of TEP in bulk iron are reported in F.J. Blatt, Can. J. Phys., [**50**]{}, 2836 (1972). The study is performed in the context of the Sondheimer theory of thermopower. AMR is not invoked.
T. L. Wade and J. -E. Wegrowe, Eur. Phys. J. Appl. Phys. [**29**]{} 3 (2005). A. Fert, L. Piraux, J. Magn. Magn. Mat [**200**]{}, 338 (1999). J. -E. Wegrowe, S. E. Gilbert, V. Scarani, D. Kelly, B. Doudin, J. -Ph. Ansermet, IEEE Trans. Magn. [**34**]{}, 903 (1998). C. Schoenenberger, B. M. I. van der Zande, L. G. J. Fokkink, M. Henny, M. Krueger, A. Bachtold, R. Huber, H. Birk, and U. Staufer, C. Schmid, J. Chem. B [**101**]{}, 5497 (1997). Y. Jaccard, P. Guittienne, D. Kelly, J. -E. Wegrowe, J. -Ph. Ansermet, Phys. Rev. B [**62**]{}, 1141 (2000). J. -E. Wegrowe, D. Kelly, A. Franck, S. E. Gilbert, and J. -Ph. Ansermet, Phys. Rev. Lett. [**82**]{}, 3681 (1999). J. Meier, B. Doudin, and J. -Ph. Ansermet, J. Appl. Phys. [**79**]{} 6010 (1996). J. Hamrle, T. Kimura, T. Yang, and Y. Otani, Phys. Rev. B [**71**]{}, 094434 (2005). A. Aharoni, [*Introduction to the Theory of Ferromagnetism*]{}, Clarandon Press, Oxford, 1996. Some nanowires with very high AMR (about 3 %) and large diameter show a MTEP profil as a function of the magnetic field that follows the AMR profile: these samples have a very low contact resistance, and no mushroom effects.
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2024-04-10T01:26:51.906118
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https://example.com/article/7710
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---
abstract: 'It is shown that the $AdS_3$ gravity action with boundary terms is non invariant under diffeomorphisms and that its Lie derivative has the form of the Weyl anomaly in two dimensions. This variation is compensated by a Weyl transformation of the boundary metric when the radial derivative of the metric on the boundary is expressed in terms of the stress tensor of a Liouville field. The obtained invariance of the action under the combined transformation of a diffeomorphism and a Weyl transformation allows to interpret the computed Lie derivative as minus the Weyl anomaly of the two-dimensional effective action.'
---
-1.2cm 21.5cm 0.375cm
ULB–TH–99/25\
October 1999
[Diffeomorphisms and Weyl tranformations\
in $AdS_3$ gravity]{}[^1]
[Karin Bautier]{}[^2]
\
[*Université Libre de Bruxelles, Campus Plaine, C.P.231*]{}\
[*Boulevard du Triomphe, B-1050 Bruxelles, Belgium*]{}\
Brown and Henneaux have shown [@brown] that the asymptotic symmetry group of anti-de Sitter gravity in three dimensions is the conformal group in two dimensions with a central charge $c=3l/2G$. We are interested in understanding this central charge as the Weyl anomaly of the two-dimensional effective action. This anomaly has been calculated in [@skenderis] by means of a regularization procedure and for a constant Weyl parameter[^3]. Here we will relate it to the non invariance of the action under diffeomorphisms. We compute the Lie derivative of the $AdS_3$ on-shell action and show that it has the form of the Weyl anomaly in two dimensions with the value of the Brown-Henneaux central charge. However the variation of the action can be compensated by a Weyl transformation on the boundary, provided that the radial derivative of the metric on the boundary is expressed in terms of the stress tensor of a Liouville field. Moreover the Liouville equation and the Einstein equation are shown to be satisfied at the same time. Therefore the invariance of the action under the combined transformation of the diffeomorphism and the Weyl transformation is established and the Lie derivative of the action can be interpreted as minus the Weyl anomaly of the two-dimensional effective action. In this way, the relation between $AdS_3$ gravity and Liouville theory [@vandriel] is recovered at the level of the Weyl transformations properties and of the equations of motion. The work presented here was done in collaboration with F. Englert, M. Rooman and P. Spindel, and a extended version of these results will be published separately [@papier].
The action considered is the Einstein-Hilbert action for three-dimensional gravity with a negative cosmological constant, improved by the Gibbons-Hawking surface term and a constant surface term: $$S=\frac{1}{16\pi G} \int_M \sqrt{-^{(3)}g}(^{(3)}R+\frac{2}{l^2})d^3x
+\frac{1}{8\pi G} \int_{\partial M} \sqrt{-^{(3)}g}
(2D_{\mu} n^{\mu}+\frac{1}{l})d^2x.$$ The constant term makes the Lie derivative of the action finite. The Gibbons-Hawking term gets rid of the second derivatives of the metric and makes the action stationary on the equations of motion for small variations of the metric that keep it fixed on the boundary. Here, because of the cosmological constant in the Einstein equations, the metric diverges at spatial infinity and the boundary metric is ill-defined. Yet a conformal class of boundary metrics can be builded by multiplying the metric by an arbitrary function (which is called the defining function) that vanishes on the boundary and taking the value of this product on the boundary as the boundary metric. As this metric changes by a conformal transformation when the defining function is changed, a conformal equivalence class of boundary metrics has been defined.
According to Fefferman and Graham [@fefferman], a suitable choice of coordinates allows to put any solution of the Einstein equations in the form: $$^{(3)}g_{\mu\nu}dx^\mu dx^\nu
=\frac{l^2}{4y^2}dy^2+\frac{1}{y}g_{ij}(y,x)dx^i dx^j,
\label{metric}$$ where $y=0$ on the boundary. The metric $g_{ij}$ appearing in (\[metric\]) can be expanded order by order in the radial coordinate $y$, leading to the following development: $$^{(3)}g_{\mu\nu}dx^\mu dx^\nu
=\frac{l^2}{4y^2}dy^2+(\frac{1}{y}g_{(0)ij}+g_{(2)ij})dx^i dx^j
+{\cal O}(y),
\label{metric2}$$ where $g_{(0)ij}=g_{ij}(y=0,x)$ is a representative of the conformal class of boundary metrics and $g_{(2)ij}$ is the first radial derivative of $g_{ij}$ on the boundary. The Einstein equations constraint the metric $g_{ij}$ order by order in $y$. The equations of motion for $g_{(2)}$ are given by: $$\begin{aligned}
Tr(g_{(0)}^{-1} g_{(2)}) = -\frac{l^2}{2}R(g_{(0)}),& &\label{einstein1}\\
D_i(g_{(0)}^{-1ik} g_{(2)kj}) - D_j (g_{(0)}^{-1ik}g_{(2)ik}) &=& 0.
\label{einstein2}\end{aligned}$$ We see that, unlike in higher dimensions where $g_{(2)}$ is uniquely determined by the Einstein equations, there is an equation of motion for its trace-free part. When $g_{(2)}$ is chosen, the rest of the solution is determined. This shows that the on-shell action depends on the boundary metric $g_{(0)}$ and on the trace-free part of $g_{(2)}$.
We consider now diffeomorphisms that keep the metric in the form (\[metric\]), i.e. such that $\delta_{diff}{}^{(3)}g_{yy}
=\delta_{diff}{}^{(3)}g_{yi}=0$. They are given by: $$\begin{aligned}
\delta_{diff}y &=& 2\delta\sigma(x) y, \\
\delta_{diff}x^i &=& -\frac{l^2}{4}\int_0^y g^{ij}(x,y')
\delta\sigma_{,j} dy',\end{aligned}$$ and induce on $g_{(0)}$ and $g_{(2)}$ the following transformations: $$\begin{aligned}
\delta_{diff}g_{(0)ij} &=& -2\delta\sigma g_{(0)ij},
\label{diff1} \\
\delta_{diff}g_{(2)ij} &=& -l^2 D_i \partial_j \delta\sigma.
\label{diff2}\end{aligned}$$ This diffeomorphism keeps $g_{(0)}$ in its conformal class (which is unique in two dimensions). Yet the Lie derivative of the action on the equations of motion gives: $$\delta_{diff}S=\frac{l}{16\pi G} \int_{\partial M}
\sqrt{-g_{(0)}}R(g_{(0)})\delta\sigma d^2x,\label{anomaly}$$ showing that the action is not invariant under the diffeomorphism.
To restore the invariance, we would like to compensate the above diffeomorphism by a Weyl transformation on the boundary: $$\delta_W g_{(0)}=2\delta\sigma g_{(0)},$$ which clearly cancels the tranformation (\[diff1\]) induced by the diffeomorphism on $g_{(0)}$. We recall that the on-shell action depends not only on the boundary metric $g_{(0)}$ but also on the trace-free part of $g_{(2)}$ because there correspond different $g_{(2)}$’s solutions for the same $g_{(0)}$. During the Weyl transformation, this further degree of freedom needs to be controlled to ensure that we are back to the initial solution, i.e. the transformation properties of $g_{(2)}$ must be specified in order to compensate exactly its variation (\[diff2\]) under the diffeomorphism. To induce this transformation, we note that the dependence of the action on the trace-free part of $g_{(2)}$ can be expressed in terms of a field $\phi$ living on the boundary. We take for $\phi$ the following conformal weight: $$\delta_W\phi=-\delta\sigma,$$ and look for an expression for $g_{(2)}$ as a functional of $g_{(0)}$ and $\phi$.
We can check that the relation for $g_{(2)}$ in terms of $g_{(0)}$ and $\phi$ that implies the correct transformation for $g_{(2)}$ under the Weyl transformation is given by the following expression: $$g_{(2)ij}=l^2[-D_i\partial_j\phi+\partial_i\phi\partial_j\phi
+g_{(0)ij}(\lambda e^{2\phi}-\frac{1}{2}\partial^k\phi\partial_k\phi)].
\label{phi1}$$ It can be written more compactly in terms of the on-shell Liouville stress tensor $T_{ij}$: $$\frac{1}{l^2}g_{(2)ij}=\frac{8\pi G}{l}T_{ij}-\frac{1}{2}g_{(0)ij}R,
\label{phi2}$$ where $T_{ij}$ is derived from the Liouville action: $$S=\frac{l}{8\pi G}\int(\frac{1}{2}\sqrt{-g_{(0)}} g_{(0)}^{ij}
\partial_i\phi \partial_j\phi +\frac{1}{2}\sqrt{-g_{(0)}}R\phi +\lambda
\sqrt{-g_{(0)}} e^{2\phi})d^2x.$$ The constants in front of the action and $T_{ij}$ have been adjusted to match the value of the Weyl anomaly that will be computed below.
Under the Weyl transformations of $g_{(0)}$ and $\phi$, $$\begin{aligned}
\delta_W g_{(0)} &=& 2\delta\sigma g_{(0)},\label{weyl1}\\
\delta_W\phi &=& -\delta\sigma \label{weyl2},\end{aligned}$$ equation (\[phi1\]) implies the searched-for transformation for $g_{(2)}$: $$\delta_W g_{(2)ij}=l^2 D_i \partial_j \delta\sigma.$$ Moreover, we see that the field $\phi$ satisfies the Liouville equation when the Einstein equation (\[einstein1\]) on the trace of $g_{(2)}$ is satisfied: $$Tr(g_{(0)}^{-1} g_{(2)})+\frac{l^2}{2}R
=l^2(-\Box\phi+\frac{1}{2}R+2\lambda e^{2\phi})=0.
\label{liouville}$$ The Einstein equation (\[einstein2\]) on the trace-free part of $g_{(2)}$ is then automatically verified: $$D_i(g_{(0)}^{-1ik}g_{(2)kj}) - D_j (g_{(0)}^{-1ik}g_{(2)ik})
= l^2 \partial_j\phi(\Box\phi-\frac{1}{2}R-2\lambda e^{2\phi})=0,
\label{conservation}$$ and expresses the conservation of the Liouville stress tensor. Indeed it can be written, with the use of (\[liouville\]), as: $$l^2 \frac{8\pi G}{l} D_i T^i_{\ j}=0.$$
After doing the diffeomorphism (\[diff1\],\[diff2\]) and the Weyl transformation (\[weyl1\],\[weyl2\]), we are back to the initial solution and the action is invariant under this combined transformation: $$(\delta_{diff}+\delta_W)S=0.$$ The value of the Weyl anomaly of the two-dimensional effective action can then be deduced from expression (\[anomaly\]): $$\delta_W S=-\delta_{diff}S=-\int_{\partial M}\sqrt{-g_{(0)}}
A\delta\sigma,$$ with $$A=\frac{3l}{2G}\frac{R}{24\pi}.$$ We recover in this way the central charge of the Brown-Henneaux asymptotic algebra [@brown].
Acknowledgements {#acknowledgements .unnumbered}
----------------
I would like to thank my collaborators on the work which was the subject of this talk, F. Englert, M. Rooman and P. Spindel. This work has been partly supported by the “Actions de Recherche Concert[é]{}es" of the “Direction de la Recherche Scientifique - Communaut[é]{} Fran[ç]{}aise de Belgique" and by IISN - Belgium (convention 4.4505.86). The author is “Chercheur F.R.I.A.” (Belgium).
[99]{}
J.D. Brown and M. Henneaux, [*Central charge in the canonical realization of asymptotic symmetries : an example from three-dimensional gravity*]{}, Commun. Math. Phys. [**104**]{} (1986) 207. M. Henningson and K. Skenderis, [*The holographic Weyl anomaly*]{}, JHEP [**9807**]{} (1998) 023, hep-th/9806087. K. Skenderis and S.N. Solodukhin, [*Quantum effective action from the AdS/CFT correspondence*]{}, hep-th/9910023. O. Coussaert, M. Henneaux and P. van Driel, [*The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant*]{}, Class. Quant. Grav. [**12**]{} (1995) 2961, gr-qc/9506019. K. Bautier, F. Englert, M. Rooman and P. Spindel, [*to appear*]{}. C. Fefferman and C.R. Graham, [*Conformal invariants*]{}, in [*Elie Cartan et les Mathématiques d’aujourd’hui*]{}, Astérisque (1985) 95.
[^1]: Presented at the TMR European program meeting “Quantum aspects of gauge theories, supersymmetry and unification”, ENS, Paris, France, 1-7 September 1999.
[^2]: E-mail: kbautier@ulb.ac.be
[^3]: In a recent paper, the anomaly has been obtained for arbitrary Weyl parameters by computing the boundary effective action [@skenderis2].
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2024-05-02T01:26:51.906118
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https://example.com/article/9801
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Not applicable.
Not applicable.
1. Field of the Invention
The present invention relates to suspended luminaires designed to use linear fluorescent lamps to provide general lighting by illuminating the ceiling, and also provide a large luminous lens when viewed from below.
2. Background Art
With the recent proliferation of Video Display Terminals (VDTs) in the office environment, lighting designers have identified high contrast overhead lighting as a source of glare and reflection on VDT screens. Such glare and reflection is an undesirable effect which impacts worker comfort and productivity. Thus, the need has arisen for efficient low contrast illumination of the work environment.
Indirect linear fluorescent overhead lighting has been determined to be the most efficient means of illuminating a large office environment while providing low contrast illumination of the work area. Such lighting is accomplished by positioning linear fluorescent fixtures below the plane of the ceiling and directing light upward toward the ceiling. The light is then reflected off of the ceiling downward toward the room. Uniform illumination of the ceiling will provide low contrast lighting. Reflectors are used to produce wide distributions and permit short suspension distances.
Additionally, designers have found that eliminating glare does not in itself result in a pleasant environment. An appropriate perceived brightness has been found to be necessary to create comfort and a sense of well-being. Thus, lighting designers desire indirect luminaires having large luminous lens areas. Such large luminous lens areas are said to give the luminaire a xe2x80x98chandelierxe2x80x99 look.
A problem with prior art lumianires is that even illumination of large luminous lens areas has precluded the use of optical control elements, such as outboard kick reflectors, which may create shadows on the lens areas. Thus, the performance of the indirect component of such fixtures has suffered to provide the aesthetic benefit of the large luminous lens areas.
It is an object of the present invention to provide a suspended indirect linear fluorescent luminaire with a large luminous lens area having a wide optical distribution for a short suspension distance.
It is a further object of the present invention to provide a suspended indirect linear fluorescent luminaire having even illumination of large luminous lens areas and utilizing outboard kick reflectors, which does not have kick reflector shadows on the lens areas.
It is yet a further object of the present invention to provide a suspended indirect linear fluorescent luminaire having even illumination of large luminous lens areas and utilizing outboard kick reflectors which utilizes a parabolic reflector assembly under the tubular lamp to focus light toward the kick reflectors and toward the lens areas behind the kick reflectors.
These and other objects are achieved through the use of a suspended indirect linear fluorescent luminaire having a linear fluorescent lamp defining a central longitudinal axis for the optical system of the luminaire, or at least lamp sockets for such a lamp. The luminaire further has a parabolic reflector assembly having a pair of elongated reflectors, with each reflector having a substantially parabolic shaped cross section and being joined to form an apex parallel to and directly under the longitudinal axis of the lamp. The luminaire still further has a pair of lens members which are symmetrically arranged on either side of the longitudinal axis, with each lens member having an upper section inner portion longitudinal edge. Further still, the luminaire utilizes a pair of elongated kick reflector members, with each kick reflector member being supported along a different one of the lens member upper section inner portion longitudinal edges such that each of the substantially parabolic shaped reflectors redirects a portion of the light emitted by the underside of the linear fluorescent lamp toward the corresponding kick reflector member and toward the corresponding lens member upper section. Thus, the lenses may be illuminated in the shadow area behind the kick reflector members, and also have a wide optical distribution for a short suspension distance from the ceiling.
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2023-10-24T01:26:51.906118
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https://example.com/article/6702
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To support the newly created Oaks and Prairies Joint Venture between the states of Oklahoma and Texas, and through this partnership, to promote and expand all-bird conservation in central Oklahoma by developing conservation strategies to reverse or...
The Oklahoma State Legislature passed a concurrent resolution on April 12, 2011 that directed the Secretary of Environment and the Oklahoma Department of Wildlife Conservation (ODWC) to develop the Oklahoma Lesser Prairie-Chicken Conservation Plan...
The Endangered Species and Economic Development Task Force was created by Senate Bill 603 of the 1st Session of the 53rd legislature to assist agencies in providing policy and technical assistance regarding compliance with endangered species laws.;...
Hackberry Flat was built and is managed to mimic the seasonal wet and dry cycles of the mixed grass prairie region. This provides a mosaic of microhabitats, which attracts a diverse group of species and outdoor enthusiasts from across Oklahoma. It...
Valuable information on hunting in Oklahoma; where to look for licensing information; a handy reference to the more than 54 ranches and farms offering lodges, cabins or guided hunts and more; and a fold-out map, are just some of what you’ll find in...
This high-quality regulation guide is offered to you by the Oklahoma Department of Wildlife Conservation through its unique partnership with J.F. Griffin Publishing, LLC.; The following are brief descriptions of regulation changes for the 2013-2014...
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This time of the year is known for reflecting and sharing radition. And this winter, the Wildlife Department asks you to start (or continue) the tradition of giving back to wildlife by participating in the 2013 Winter Bird Feeder Survey.; A Sleepy...
This report was prepared in response to Section 314(a) of the Clean Water Act (P.L. 92-500) of 1977 which, upon election to participate, requires each state to trophically classify, diagnose, and restore their
publicly owned freshwater lakes. The...
The 2013 Oklahoma Legislative Session convened on January 8, 2013, for its biennial organizational day, and then reconvened in regular session on February 4 and adjourned sine die on May 24, 2013, a week earlier than the constitutionally mandated...
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2023-08-26T01:26:51.906118
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https://example.com/article/6786
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Articles in the Indianapolis Colts Category
Last year at this time I drove down to Indianapolis twice to see the Colts in the playoffs. This year was no exception except for the fact they were playing on Wild Card weekend rather than later in the playoffs. This worked out for my schedule since the Chicago Bears are now playing on the Divisional Playoff weekend. For this road trip, I was able to get a babysitter so I was set to drive to Indianapolis for the evening.
Pre-Game Dining
I arrived in Indianapolis early to give myself plenty of …
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Obtaining TicketsOn Saturday morning, I emailed a guy on craigslist.org about …
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Booking the HotelWhen I got …
After sprinting to Lucas Oil Stadium, my ticket was scanned and I entered the stadium. I heard over the speakers there was 12:39 left in the first quarter. I left the Pacers game with 2:24 left and I was in Lucas Oil Stadium after 2:21 – pretty much as even as I could have hoped. 30 seconds later I was looking at the scoreboard as I stood in the concourse overlooking the end zone where Matt Stover kicked his first field goal with 10:44 left in the first quarter.
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All week I planned to attend the Indianapolis Colts AFC Divisional Playoff game versus the Baltimore Ravens. Since that game did not start until 8:15 ET I wondered if there was another game I could attend earlier in the day. There was. The Pacers game had been rescheduled to 6 pm because of the playoff game at Lucas Oil Stadium. However, I knew that NBA games normally last between 2 hours and 15 minutes and 2 hours and 30 minutes. Thus, I did not think …
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Pre Game DiningWe arrived in Indianapolis around 2:00 pm and parked in a downtown parking lot for $20. We wandered around downtown for a bit before settling down at the Ugly Monkey located at 373 S. Illinois St. Surprisingly, the Ugly Monkey was a fun bar between the free shots …
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2024-07-07T01:26:51.906118
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https://example.com/article/6924
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Q:
How to configure portlet in liferay 6.1 programmatically?
How to set specific options of different portlets programmatically? For example how to set view in "Web Content Display" portlet to specific JournalArticle.
A:
This one might be a bit difficult because there will be some discovery involved. First you'll need to figure out which preference key you'd like to over write. The difficult lies that the developer can use any key for example some of Liferay's are portlet-setup-show-borders.
But to set a Web Content Display, you can use something like:
PortletPreferences portletSetup =
PortletPreferencesFactoryUtil.getLayoutPortletSetup(
layout, portletId);
portletSetup.setValue("groupId", String.valueOf(layout.getGroupId()));
portletSetup.setValue("articleId", articleId);
portletSetup.store();
|
2024-02-15T01:26:51.906118
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https://example.com/article/6551
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---
abstract: |
We propose two basic assumptions, under which the rate of convergence of the augmented Lagrange method for a class of composite optimization problems is estimated. We analyze the rate of local convergence of the augmented Lagrangian method for a nonlinear semidefinite nuclear norm composite optimization problem by verifying these two basic assumptions. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to $1/c$, where $c$ is the penalty parameter that exceeds a threshold $\overline{c}>0$. The analysis is based on variational analysis about the proximal mapping of the nuclear norm and the projection operator onto the cone of positively semidefinite symmetric matrices.
12 true pt **Key words**: Composite optimization, nonlinear semidefinite nuclear norm composite optimization, rate of convergence, the augmented Lagrangian method, variational analysis.
author:
- 'Liwei Zhang[^1],Yule Zhang[^2],and Jia Wu[^3]'
title: 'The Rate of Convergence of the Augmented Lagrangian Method for a Nonlinear Semidefinite Nuclear Norm Composite Optimization Problem[^4]'
---
Introduction
============
Nuclear norm optimization problems have seen many applications in engineering and science. They arise from the convex relaxation of a rank minimization problem with noisy data in many machine learning and compressed sensing applications such as dimensionality reduction, matrix classification, multi-task learning and matrix completion, as well as in theoretical applications from mathematics ([@Fazel2002],[@BAStephen2011], [@Srebro2004],[@CTao2009],[@LLRabinovich1995]). A proximal point algorithmic framework was developed in [@Liu2012] for solving convex nuclear norm optimization problems and numerical results show that the proposed proximal point algorithms perform quite well in comparison to several recently proposed state-of-the-art algorithms. For non-convex nonlinear programming and non-convex semidefinite programming, related to proximal point algorithms, the augmented Lagrange method is regarded as an effective numerical method. It is quite natural to consider the augmented Lagrange method for the non-convex nuclear norm composite optimization problem and study its theoretical properties. In the general setting, the augmented Lagrangian method can be used to solve the following composite optimization problem
(COP) $$\min \ f(x) + \theta (F(x)) \quad {\rm s.t.} \quad h(x)=0,\,\, g(x) \in K\, ,$$where $f:\Re^n\mapsto \Re$,$F: \Re^n \mapsto {\cal Z}$, $h:\Re^n \mapsto \Re^m$ and $g:\Re^n \mapsto {\cal Y}$ are twice continuously differentiable mappings, $\theta: {\cal Z} \rightarrow \Re \cup \{+\infty\}$ is a proper lower semicontinuous convex function, ${\cal Z}$ and ${\cal Y}$ are finite-dimensional real Hilbert spaces equipped with scalar product $\langle \cdot, \cdot \rangle$ and induced norm $\|\cdot\|$, and $K$ is a closed convex cone in ${\cal Y}$.
Let $c>0$ be a parameter. The augmented Lagrangian function with the penalty parameter $c$ for problem (COP) is defined as (with no composite term, see [@RW98 Section 11.K]) $$\label{al}
\begin{array}{ll}
L_c(x,Y, \mu,\lambda):= & f(x)+ \theta_c (F(x)+Y/c)-\displaystyle\frac{\|Y\|^2}{2c}\\[8pt]
& +\langle \mu, h(x) \rangle+\displaystyle \frac{c}{2}\|h(x)\|^2+ \frac{1}{2c}\left[ \|
\Pi_{K^*}(\lambda-c g(x))\|^2-\|\lambda\|^2\right]\, ,
\end{array}$$ where $(x,Y,\mu, \lambda) \in \Re^n \times {\cal Z} \times \Re^m\times {\cal Y}$ and $\Pi_{K^*}(\cdot)$ denotes the metric projection operator onto the set $K^*$($K^*$ is the dual cone of $K$), $\theta_c=e_{1/c}\theta$ and $[e_{\tau}\theta](\cdot)$ is the Moreau-Yosida regularization of $\theta$ defined by $$\label{eq:morea}
[e_{\tau}\theta](Z)=\inf_{Z' \in \mathbb {\cal Z}} \left\{\theta(Z')+\displaystyle \frac{1}{\tau}\|Z'-Z\|^2\right\}.$$
The augmented Lagrangian method for solving (COP) can be stated as follows. Let $c_0>0$ be given. Let $(Y^0, \mu^0,\lambda^0) \in {\cal Z} \times \Re^m \times K^*$ be the initial estimated Lagrange multiplier. At the $k$th iteration, determine $ x^k$ by minimizing $L_{c_k}(x,Y^k,\mu^k,\lambda^k)\, $, compute $(Y^{k+1},\mu^{k+1},\lambda^{k+1})$ by $$\left \{ \begin{array}{l}
Y^{k+1}:={\rm D}\theta_{c_k}(F(x^k)+Y^k/c)^*,\\[4pt]
\mu^{k+1}:=\mu^k +c h(x^k),\\[4pt]
{\lambda}^{k+1}:=\Pi_{K^*}({\lambda}^k-c_kg(x^k))\, ,
\end{array}
\right.$$ and update $c_{k+1} $ by $$c_{k+1} :=c_k \quad {\rm or} \quad c_{k+1}:=\kappa c_k$$ according to certain rules, where $\kappa >1$ is a given positive number. In the case when the sequence of parameters $\{c_k\}$ satisfies $c_k\rightarrow +\infty$, the global convergence of the augmented Lagrangian method can be discussed similarly as in [@B82]. In this paper, instead of considering global convergence properties, we consider the rate of convergence of the augmented Lagrangian method for (COP) when $c_k$ has a finite limit, namely the case in which $c_k \equiv c$ for all sufficient large $k$. For simplicity in our analysis, for $k$ sufficiently large, we choose $x^k$ as an exact local solution of $L_{c}(\cdot,Y^k,\mu^k,\lambda^k)$.
The augmented Lagrangian method was proposed by Hestenes [@H69] and Powell [@P72] for solving equality constrained nonlinear programming problems and was generalized by Rockafellar [@R73a] to nonlinear programming problems with both equality and inequality constraints. For convex programming, Rockafellar [@R73a] established a saddle point theorem in terms of the augmented Lagrangian and Rockafellar [@R73b] proved the global convergence of the augmented Lagrangian method for any positive penalty parameter.
For nonlinear programming, the study about the rate of convergence of the augmented Lagrangian method is quite complete. For the equality constrained problem, Powell offered a proof in [@P72] showing that if the linear independence constraint qualification and the second-order sufficient condition are satisfied, then the augmented Lagrangian method can converge locally at a linear rate. Bertsekas [@B82 Chapter 3] established an important result on the linear rate of convergence of the augmented Lagrangian method for nonlinear programming when the strict complementarity condition is assumed, in which the ratio constant is proportional to $1/c$. On the other hand, without assuming the strict complementarity condition, Conn et al. [@CGToint91], Contesse-Becker[@Contesse-Becker93], and Ito and Kunisch [@IKunisch90] derived linear convergence rate for the augmented Lagrangian method.
For nonlinear semidefinte programming, without requiring strict complementarity, Sun et al. [@SSZhang2008] proved that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence of the augmented Lagrangian method is linear and the ratio constant is proportional to $1/c$, where $c$ is the penalty parameter that exceeds a threshold $\overline{c}>0$. Moreover, Sun et al. [@SSZhang2008] used a direct way to derive the same linear rate of convergence under the strict complementarity condition.
The main objective of this paper is to study, without assuming the strict complementarity, the rate of convergence of the augmented Lagrangian method for solving the nonlinear semidefinite nuclear norm composite optimization problem
(SDNOP) $$\min \ f(x) + \theta(F(x))\quad
{\rm s.t.} \quad h(x)=0\, ,
\ g(x) \in {\cal
S}^p_+\, ,$$ where $\theta (X)=\|X\|_*$ is the nuclear norm function of $X \in {\cal S}^q$ (for simplicity, here we only consider the nuclear norm of a symmetric matrix), ${\cal S}^p_+$ is the cone of all positive semidefinite matrices in ${\cal S}^p$, the linear space of all $p$ by $p$ symmetric matrices in $\Re^{p\times p}$.
The organization of this paper is as follows. In Section \[general-discussions\], we develop a general theory on the rate of convergence of the augmented Lagrangian method for a class of composite optimization problems under two basic assumptions. In Section \[preliminaries\], we discuss variational properties of the projection over the cone of symmetric positively semidefinite matrices and the proximal mapping of the nuclear norm, and the second-order optimality conditions for nonlinear semidefinite nuclear norm composite optimization problem. Section \[NLSDP-case\] is devoted to applying the theory developed in Section \[general-discussions\] to nonlinear semidefinite nuclear norm composite optimization problem. Finally, we give our conclusions in Section \[final-section\].
General discussions on the rate of convergence {#general-discussions}
==============================================
In this section, we always assume that the cone $K$ presented in the optimization problem (COP) is a closed convex cone and that $\Pi_{K^*}(\cdot)$ is semismooth everywhere, where $K^*$ is the dual cone of $K$, i.e., $$K^*:=\{v \in {\cal Y} \,|\, \langle v, z \rangle \geq 0, \ \ \forall\, z
\in K\}.$$ The cones $\Re^p_+$, ${\cal S}_+^p$, $\mbox{epi}\|\cdot\|_2$ and $\mbox{epi}\|\cdot\|_*$ satisfy these assumptions, where $\|\cdot\|_2$ and $\|\cdot\|_*$ stand for the spectral norm of a matrix and the nuclear norm of a matrix, respectively. Moreover we always assume that ${\rm D}\theta_c(\cdot)$ is semismooth everywhere, where $\theta_c(\cdot)=e_{1/c}\theta(\cdot)$ and $[e_{\tau}\theta](\cdot)$ is the Moreau-Yosida regularization of $\theta$ defined by (\[eq:morea\]).
A feasible point $x\in \Re^n$ to (COP) is called a stationary point if there exists $(Y,\mu,\lambda)\in {\cal Z} \times \Re^m \times {\cal Y}$ such that the following Karush-Kuhn-Tucker (KKT) condition is satisfied at $(x, Y,\mu, \lambda)$: $$\label{eq:stationarity}
\nabla _x L(x,Y,\mu, \lambda) =0,\, Y \in \partial \theta (F(x)), h(x)=0, g(x)\in
K,\, \lambda \in K^*\, {\rm and} \, \langle
g(x),\lambda \rangle =0,$$ where the Lagrangian function $L: \Re^n \times {\cal Z} \times \Re^m \times {\cal Y} \mapsto \Re$ is defined as $$L(x, Y,\mu, \lambda): = f(x) +\langle Y, F(x) \rangle +\langle \mu, h(x) \rangle-\langle
\lambda, g(x)\rangle.$$ Any point $(x, Y, \mu,\lambda)\in \Re^n \times {\cal Z} \times \Re^m \times {\cal Y}$ satisfying (\[eq:stationarity\]) is named as a KKT point and the corresponding point $(Y, \mu,\lambda)$ is called a Lagrange multiplier at $x$. Let ${\cal M}(x)$ be the set of all Lagrangian multipliers at $x$.
Let $c>0$ and $\overline{ x} $ be a stationary point of (COP), namely ${\cal M}(\overline{x})\ne \emptyset$. Since $f, F,
h$, and $g$ are assumed to be twice continuously differentiable, we know from (\[al\]), [@Zarantonello71] and Chapter 2 of [@RW98] that the augmented Lagrangian function $L_c( \cdot)$ is continuously differentiable and for any $(x, Y,\mu,\lambda)\in \Re^n \times {\cal Z} \times \Re^m
\times {\cal Y}$, $$\label{compFx}
\begin{array}{ll}
\nabla_x L_c(x,Y,\mu,\lambda)= & \nabla f(x) + {\rm D}F(x)^*{\rm D} \theta_c(F(x)+Y/c)^*\\[4pt]
& +{\cal J} h(x)^T (\mu+ch(x)) - {\rm D} g(x)^* \Pi_{K^*}(\lambda-c g(x)).
\end{array}$$ Therefore, from (\[eq:stationarity\]), we have $\nabla_x L_c(\overline{x},Y,\mu,\lambda)=0$ for any $(Y,\mu,\lambda) \in {\cal M} (\overline{x})$.
For any $(x, Y,\mu,\lambda) \in \Re^n \times {\cal Z} \times \Re^m \times {\cal Y}$, let $$\begin{array}{l}
\Phi_c(x,Y,\mu,\lambda):={\rm D}F(x)^*{\rm D} \theta_c(F(x)+Y/c)^*,\\[4pt]
\Psi_c(x,Y,\mu,\lambda):= {\rm D}g(x)^* \Pi_{K^*}(\lambda-cg(x)).\end{array}$$ Let $(x, Y,\mu,\lambda) \in \Re^n \times {\cal Z} \times \Re^m \times {\cal Y}$. Then from the semismoothness of ${\rm D}\theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ we obtain that for any $(\Delta x, \Delta Y,\Delta \mu, \Delta \lambda) \in \Re^n \times {\cal Z} \times \Re^m\times {\cal Y}$, $$\label{composite2-app}
\begin{array}{l}
\quad \partial_B\Phi_c(x,Y,\mu,\lambda) (\Delta x, \Delta Y, \Delta \mu,
\Delta \lambda)
\\[2mm]
= {\rm D}^2 F(x) (\Delta x) {\rm D} \theta_c(F(x)+Y/c)^*+ {\rm D}F(x)^*
\partial_B [{\rm D} \theta_c]^*(F(x)+Y/c)({\rm D}F(x)\Delta x+\Delta Y/c),\\[2mm]
\quad \partial_B\Psi_c(x,Y,\mu,\lambda) (\Delta x, \Delta Y, \Delta \mu,
\Delta \lambda)
\\[2mm]
= {\rm D}^2 g(x) (\Delta x) \Pi_{K^*}(\lambda-cg(x)) + {\rm D}g(x)^*
\partial_B \Pi_{K^*} (\lambda-cg(x))(\Delta \lambda-c {\rm D}g(x) \Delta x).
\end{array}$$ From (\[compFx\]) and the definition of $\Psi_c(\cdot)$ we know that $$\begin{array}{l}
\partial_B (\nabla_x L_c)(x,Y,\mu,\lambda)= \\[2mm]
(\nabla^2 f(x),0, 0,0)+\left(\displaystyle\sum_{i=1}^m
(\mu_i+ch_i(x))
\nabla^2 h_i(x)+c {\cal J} h(x)^T{\cal J}h(x), 0, {\cal J} h(x)^T,0\right)\\[4mm]
+\partial_B \Phi_c(x,Y,\mu,\lambda)
\partial_B \Psi_c(x,Y,\mu,\lambda),
\end{array}
$$
which implies that for any $\Delta x \in \Re^n$,
\begin{equation}\label{comequation3.14}
\begin{array}{l}
\left( \pi_x \partial_B (\nabla_x L_c)
(x,Y,\mu,\lambda) \right) (\Delta x)\\[2mm]
= \nabla^2_{xx} L(x,{\rm D} \theta_c(F(x)+Y/c)^*,
\mu+ch(x), \Pi_{K^*}(\lambda-c g(x))) (\Delta x)
\\[2mm]
\quad +{\rm D}F(x)^*
\partial_B [{\rm D} \theta_c]^*(F(x)+Y/c){\rm D}F(x)(\Delta x)\\[2mm]
\quad + c {\cal J} h(x)^T{\cal J} h(x) (\Delta x)
+c {\rm D}g(x)^* \partial_B \Pi_{K^*}(\lambda-c g(x)){\rm D} g(x) (\Delta x)\, ,
\end{array}
\end{equation}
where
\[
\begin{array}{l}
\nabla^2_{xx} L(x,{\rm D} \theta_c(F(x)+Y/c)^*,
\mu+ch(x), \Pi_{K^*}(\lambda-c g(x))) (\Delta x)\\[4pt]
=\nabla^2 f(x)(\Delta x)+{\rm D}^2F(x)(\Delta x){\rm D} \theta_c(F(x)+Y/c)^*\\[4pt]
\quad +
{\rm D}^2h(x)(\Delta x)(\mu+ch(x))
-{\rm D}^2g(x)(\Delta x)\Pi_{K^*}(\lambda-c g(x)).
\end{array}$$ Let $(\overline{Y},\overline{\mu},\overline{\lambda}) \in {\cal M}(\overline{x})$ be a Lagrange multiplier at $\overline{x}$. For any linear operators $W_1:{\cal Z} \mapsto {\cal Z}$, $W_2: {\cal Y}
\mapsto {\cal Y}$, let $$\label{comac}
\begin{array}{ll}
{\cal A}_c(\overline{Y},\overline{\mu},\overline{\lambda},W_1,W_2):= & \nabla^2_{xx}
L(\overline{x},\overline{Y},\overline{\mu},\overline{\lambda})
+{\rm D}F(\overline x)^*W_1{\rm D}F(\overline x)\\[6pt]
& + c {\cal J}h(\overline{x})^T{\cal J} h(\overline{x})
+c {\rm D}g(\overline{x})^*W_2{\rm D}g(\overline{x}).
\end{array}$$ Then for any $\Delta x \in \Re^n$, $$\label{compix}
\begin{array}{l}
\left( \pi_x \,\partial_B (\nabla_x
L_c)(\overline{x},\overline{Y},\overline{\mu},\overline{\lambda}\right) (\Delta
x) \\[10pt]
=\left\{{\cal A}_c(\overline{Y},\overline{\mu},\overline{\lambda},W_1,W_2) (\Delta x):
\begin{array}{l}
W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)\\[4pt]
W_2 \in
\partial_B \Pi_{K^*}(\overline{\lambda}-c g(\overline{x}))
\end{array}
\right\}.
\end{array}$$
7 true pt Next, we make two basic assumptions for the constrained optimization composite optimization problem (COP). The first one is about the positive definiteness of ${\cal A}_c(\overline{Y},\overline{\mu},\overline{\lambda},\cdot,\cdot)$.
7 true pt [**Assumption B1**]{}. We assume that $(\overline{Y},\overline{\mu},\overline{\lambda})$ is the unique Lagrange multiplier at $\overline{x}$, i.e., ${\cal
M}(\overline{x})=\{(\overline{Y},\overline{\mu},\overline{\lambda})\}$ and that there exist two positive numbers $c_0$ and $\underline{\eta}$ such that for any $c \geq c_0$ and any $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$, $W_2 \in \partial_B
\Pi_{K^*}(\overline{\lambda}-c g(\overline{x}))$, $$\left\langle d ,
{\cal A}_{c}(\overline{Y},\overline{\mu},\overline{\lambda},W_1,W_2) d\right\rangle
\geq\underline{\eta}\left\langle d ,d \right\rangle, \quad \forall \, d \in
\Re^n.$$
Assumption B1 is related to the sufficient optimality conditions for the constrained composite optimization problem (COP). It will be shown in Proposition \[pronlsdp\] that, under the constraint nondegeneracy condition and the strong second order sufficient condition (they will be clarified in Section \[preliminaries\]), Assumption B1 is valid for (SDNOP).
7 true pt Let $\overline{y}:=(\overline{Y},\overline{\mu},\overline{\lambda})$. Then $\nabla_x
L_c(\overline{x}, \overline{y})=0$. Let $c_0$ and $\underline{\eta}$ be two positive numbers defined in Assumption B1 and $c\ge c_0$ be a positive number. Since by (\[compix\]) and Assumption B1, every element in $\pi_x
\partial_B(\nabla_x L_c)(\overline{x}, \overline{y})$ is positive definite, we know from the implicit function theorem for semismooth functions developed in [@S01], that there exist an open neighborhood ${\cal O}_{\overline y}$ of $\overline{y}$ and a locally Lipschitz continuous function $x_c(\cdot)$ defined on ${\cal O}_{\overline y}$ such that for any $y\in {\cal O}_{\overline y}$, $\nabla_x L_c( x_c(y), y)=0$. Furthermore, since ${\rm D} \theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are assumed to be semismooth everywhere, $x_c(\cdot)$ is semismooth (strongly semismooth if $\nabla^2f, {\rm D}^2F, {\rm D}^2 g$, and ${\rm D}^2 h$ are locally Lipschitz continuous, and both ${\rm D} \theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are strongly semismooth everywhere) at any point in ${\cal O}_{\overline y}$. Moreover, there exist two positive numbers $\varepsilon >0$ and $\delta_0>0$ (both depending on $c$) such that for any $x \in
\mathbb{B}_{\varepsilon}(\overline{x})$ and $y\in
\mathbb{B}_{\delta_0} (\overline{y}) :=\{y\in {\cal Z}\times \Re^m \times {\cal Y}\, | \,
\|y-\overline{y}\|< \delta _0\} \subset {\cal O}_{\overline y}$, every element in $\pi_x
\partial_B (\nabla_x L_c)(x,y)$ is positive definite. Thus, for any $y\in \mathbb{B}_{\delta_0} (\overline{y})$, $x_c(y)$ is the unique minimizer of $L_c(\cdot,y)$ over $\mathbb{B}_{\varepsilon}(\overline{x})$, i.e., $$\label{def-xc}
\{x_c(y)\} = \argmin \Big\{ L_c(x,y) \,|\, x \in
\mathbb{B}_{\varepsilon}(\overline{x}) \Big \}.$$ Summarizing the above discussions, we obtain the following proposition.
\[prop:general-discussions\] Suppose that Assumption B1 is satisfied. Let $c\ge c_0$. Then there exist two positive numbers $\varepsilon >0$ and $\delta_0>0$ $($both depending on $c$$)$ and a locally Lipschitz continuous function $x_c(\cdot)$, given by (\[def-xc\]), defined on the open ball $\mathbb{B}_{\delta_0}(\overline{y})$ such that the following conclusions hold:
(i)
: The function $x_c(\cdot)$ is semismooth at any point in $\mathbb{B}_{\delta_0}(\overline{y})$.
(ii)
: If $\nabla^2f, {\rm D}^2F, {\rm D}^2 g$, and ${\rm D}^2 h$ are locally Lipschitz continuous, ${\rm D} \theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are strongly semismooth everywhere, then $x_c(\cdot)$ is strongly semismooth at any point in $\mathbb{B}_{\delta_0}(\overline{y})$.
(iii)
: For any $x \in
\mathbb{B}_{\varepsilon}(\overline{x})$ and $y\in
\mathbb{B}_{\delta_0} (\overline{y})$, every element in $\pi_x
\partial_B (\nabla_x L_c)(x,y)$ is positive definite.
(iv)
: For any $y\in \mathbb{B}_{\delta_0}
(\overline{y})$, $x_c(y)$ is the unique optimal solution to $$\min \ L_c(x, y)
\quad {\rm s.t.} \ x\in {\mathbb B}_{\varepsilon}(\overline{x})\, .$$
Let $\vartheta_c:{\cal Z} \times \Re^m \times {\cal Y} \mapsto \Re$ be defined as $$\label{dual}
\vartheta_c(Y,\mu,\lambda):=\min_{x \in
\mathbb{B}_{\varepsilon}(\overline{x})} L_c(x,Y,\mu,\lambda), \quad
(Y,\mu,\lambda)\in {\cal Z} \times \Re^m \times {\cal Y}\, .$$ Since for each fixed $x\in X$, $L_c(x, \cdot)$ is a concave function, we have that $\vartheta_c(\cdot)$ is also a concave function. By using the fact that for any $y\in \mathbb{B}_{\delta_0}
(\overline{y})$, $x_c(y)$ is the unique minimizer of $L_c(\cdot,y)$ over $\mathbb{B}_{\varepsilon}(\overline{x})$, we have $$\vartheta_c(y)=L_c(x_c(y),y) \, , \quad y\in
\mathbb{B}_{\delta_0} (\overline{y})\, .$$For any $y\in \mathbb{B}_{\delta_0} (\overline{y})$ with $y=(Y,\mu,\lambda)\in {\cal Z} \times \Re^m \times {\cal Y}$, let $$\label{comnota1}
\left(\begin{array}{c}
Y_c(y)\\
\mu_c(y)
\\
\lambda_c(y)
\end{array} \right):=
\left(\begin{array}{c}
{\rm D} \theta_c(F(x_c(y))+Y/c)^*\\
\mu+ch(x_c(y)) \\
\Pi_{K^*}(\lambda-c g(x_c(y)))\end{array}\right) \, .$$ Then we have $$\label{comnabla0}
\nabla_x L(x_c(y),Y_c(y),\mu_c(y),\lambda_c(y)) =\nabla_x
L_c(x_c(y),y)=0\, , \quad y\in \mathbb{B}_{\delta_0}
(\overline{y})\, .$$
\[comdcproperty1\] Suppose that Assumption B1 is satisfied. Let $c\ge c_0$. Then the concave function $\vartheta_c(\cdot)$ defined by $(\ref{dual})$ is continuously differentiable on $\mathbb{B}_{\delta_0}
(\overline{y})$ with $$\label{comdcjacobi}
{\rm D}\vartheta_c (y)^*=\left (
\begin{array}{c}
-c^{-1}Y+c^{-1}{\rm D}\theta_c(F(x_c(y))+Y/c))^*\\
h(x_c(y))\\
-c^{-1}\lambda+c^{-1}\Pi_{K^*}(\lambda-c g(x_c(y)))
\end{array}
\right )\, , \quad y =(Y,\mu,\lambda) \in \mathbb{B}_{\delta_0}
(\overline{y})\, .$$ Moreover, ${\rm D}\vartheta_c (\cdot)$ is semismooth at any point in $\mathbb{B}_{\delta_0} (\overline{y})$. It is strongly semismooth at any point in $\mathbb{B}_{\delta_0}(\overline{y})$ if $\nabla^2f, {\rm D}^2F, {\rm D}^2 g$, and ${\rm D}^2 h$ are locally Lipschitz continuous, and ${\rm D} \theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are strongly semismooth everywhere.
[**Proof.**]{} Let $y =(Y,\mu,\lambda) \in
\mathbb{B}_{\delta_0} (\overline{y})$. Then from (\[comnabla0\]) and [@C83 Theorem 2.6.6] we have for any $(\Delta Y,\Delta\mu,
\Delta\lambda)\in {\cal Z} \times \Re^m \times {\cal Y}$ that $$\begin{array}{ll}
\partial \vartheta_c(y)(\Delta Y,\Delta\mu,
\Delta\lambda)&=
{\cal J}_x L_c(x_c(y),y)(\partial
x_c(y)(\Delta Y,\Delta\mu,
\Delta\lambda))\\
&\\
& \quad +{\rm D}_{Y}L_c(x_c(y),y)(\Delta Y)+
{\cal
J}_{\mu}L_c(x_c(y),y)(\Delta\mu)+{\rm D}_{\lambda}L_c(x_c(y),y)(\Delta \lambda)\\
&\\
&=
\langle -c^{-1}Y,\Delta Y \rangle +c^{-1}{\rm D}\theta_c(F(x_c(y))+Y/c)(\Delta Y)\\
&\\
& \quad +\langle h(x_c(y)), \Delta\mu \rangle -c^{-1} \langle \lambda,
\triangle\lambda \rangle+\langle c^{-1} \Pi_{K^*}(\lambda-c
g(x_c(y))),\Delta\lambda\rangle\, .
\end{array}$$ Thus, $\partial \vartheta_c (y)(\Delta Y,\Delta\mu,
\Delta\lambda)$ is a singleton for each $(\Delta Y,\Delta\mu,
\Delta\lambda)\in {\cal Z} \times \Re^m \times {\cal Y}$. This implies that $\partial \vartheta_c(y)$ is a singleton. Therefore, $ \vartheta_c(\cdot)$ is Fréchet-differentiable at $y$ and ${\rm D} \vartheta_c(y)$ is given by (\[comdcjacobi\]). The continuity of ${\rm D}
\vartheta_c(\cdot)$ follows from the continuity of $x_c(\cdot)$.
The properties on the (strong) semismoothness of ${\rm D}
\vartheta_c (\cdot)$ at $y$ follows directly from (\[comdcjacobi\]) and Proposition \[prop:general-discussions\].
7 true pt For any $c\ge c_0$ and $\Delta y :=(\Delta Y,\Delta\mu,
\Delta\lambda)\in {\cal Z}\times \Re^m \times {\cal Y}$, define $$\label{comcalV}
\begin{array}{l}
\overline{{\cal V}}_c(\Delta y):=\\[8pt]
\left\{\left
[
\begin{array}{c}
c^{-1}W_1{\rm D}F(\overline x)\\
{\cal J} h (\overline{x})\\
-W_2{\rm D}g(\overline{x})
\end{array}
\right
]\right.{\cal A}_c(\overline{y},W_1,W_2)^{-1}\left[-c^{-1}{\rm D}F(\overline x)^*W_1(\Delta Y)\right.\\[5mm]
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad\quad \left.-{\cal J}
h(\overline{x})^T\Delta\mu+{\rm D}g(\overline{x})^*W_2(\Delta\lambda)\right]\\[6mm]
+\left.\left
(
\begin{array}{c}
-c^{-1}\Delta Y+c^{-2}W_1(\Delta Y)\\
0\\
-c^{-1}\Delta \lambda+ c^{-1}W_2( \Delta \lambda)\end{array} \right
) \, \Big |\, \begin{array}{l}
W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)\\[4pt]
W_2 \in
\partial_B \Pi_{K^*}(\overline{\lambda}-c g(\overline{x}))
\end{array}\right\}.
\end{array}$$ Since by Assumption B1, ${\cal A}_c(\overline{y},W_1,W_2)$ is positive definite for any $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$,$W_2 \in
\partial_B \Pi_{K^*}(\overline{\lambda}-c g(\overline{x}))$, $\overline{{\cal V}}_c(\cdot)$ is well defined. The next proposition shows that $\overline{{\cal V}}_c(\cdot)$ is an outer approximation to $\partial_B [{\rm D}
\vartheta_c]^*(\overline{y})(\cdot)$.
\[comthta\] Suppose that Assumption B1 is satisfied. Let $c\ge c_0$. Then for any $\Delta y :=(\Delta Y,\Delta\mu,
\Delta\lambda)\in {\cal Z}\times \Re^m \times {\cal Y}$, $$\label{combdiff}
\partial_B[{\rm D} \vartheta_c]^*(\overline{y}) (\Delta y )\subseteq
\overline{{\cal V}}_c (\Delta y)\, .$$
[**Proof.**]{} Choose $\Delta y :=(\Delta Y,\Delta\mu,
\Delta\lambda)\in {\cal Z}\times \Re^m \times {\cal Y}$. From Proposition \[comdcproperty1\], we know that ${\rm D}\vartheta_c(\cdot)$ is semismooth at any point $y \in
\mathbb{B}_{\delta_0}(\overline{y})$. Let ${\cal
D}_{{\rm D}\vartheta_c}$ denote the set of all Fréchet-differentiable points of ${\rm D}\vartheta_c(\cdot)$ in $\mathbb{B}_{\delta_0}(\overline{y})$. Then for any $y=(Y,\mu,\lambda) \in {\cal D}_{{\rm D}\vartheta_c}$, we have $$\label{comgrad}
\begin{array}{l}
{\rm D}^2 \vartheta_c(y)(\Delta y)\\[6mm]
= \left (
\begin{array}{c}
-c^{-1}\Delta y+c^{-1}[{\rm D}\theta_c]^*(F(x_c(y))+Y/c); {\rm D}F(x_c(y))(x_c)'(y;\Delta y)+\Delta Y/c)\\[6pt]
{\cal J} h(x_c(y)) (x_c)'(y;\Delta y)
\\[6pt]
-c^{-1}\Delta\lambda+c^{-1}\Pi^\prime_{K^*}\Big(\lambda-cg(x_c(y));\Delta\lambda-c
{\rm D} g(x_c(y))(x_c)'(y;\Delta y)\Big)
\end{array}
\right )\, .
\end{array}$$
Let $y\in \mathbb{B}_{\delta_0}(\overline{y})$. Now, we derive the formula for $(x_c)^\prime(y;\Delta y)$. From (\[comnabla0\]) and (\[comnota1\]) we have $$\label{comdiff0}
\begin{array}{lcl}
0&=& \nabla^2_{xx}
L(x_c(y),Y_c(y),\mu_c(y),\lambda_c(y))(x_c)^\prime(y;\Delta y) +c{\cal J}
h(x_c(y))^T{\cal J} h(x_c(y))(x_c)^\prime(y;\Delta y)\\[2mm]
& & +{\cal J}h(x_c(y))^T (\Delta\mu) -{\rm D}g(x_c(y))^*
\Pi^\prime_{K^*}\Big(\xi-cg(x_c(y));\Delta\xi-c{\rm D}
g(x_c(y))(x_c)^\prime(y;\Delta y)\Big)\\[2mm]
&&+{\rm D}F(x_c(y))^*[{\rm D}\theta_c]^{*\prime}(F(x_c(y))+Y/c;{\rm D}F(x_c(y))(x_c)^\prime(y;\Delta y)+\Delta Y/c).
\end{array}$$ Since ${\rm D}\theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are semismooth everywhere, there exist $\widehat{W}_1\in
\partial_B [{\rm D}\theta_c]^*(F(x_c(y))+Y/c)$ and $\widehat{W}_2\in
\partial_B \Pi_{K^*}(\lambda-cg(x_c(y)))$ such that $$\label{comderiv}
\begin{array}{l}
[{\rm D}\theta_c]^{*\prime}(F(x_c(y))+Y/c;{\rm D}F(x_c(y))(x_c)^\prime(y;\Delta y)+\Delta Y/c)\\[3mm]
\quad \quad \quad \quad \quad \quad=\widehat{W}_1({\rm D}F(x_c(y))(x_c)^\prime(y;\Delta y)+\Delta Y/c),\\[3mm]
\Pi^\prime_{K^*}\Big(\lambda-cg(x_c(y));\Delta\lambda-c{\cal J} g(x_c(y))
(x_c)^\prime(y;\Delta y)\Big)\\[3mm]
\quad \quad \quad \quad \quad \quad=\widehat{W}_2 (\Delta\lambda-c {\rm D}
g(x_c(y)) (x_c)^\prime(y;\Delta y)).
\end{array}$$ For any $W_1\in
\partial_B [{\rm D}\theta_c]^*(F(x_c(y))+Y/c)$ and $W_2 \in
\partial_B \Pi_{K^*}(\lambda-cg(x_c(y)))$, let $$\begin{array}{lcl}
{\cal A}_c(y,W_1,W_2):&= & \nabla^2_{xx} L(x_c(y),Y_c(y),\mu_c(y),\lambda_c(y))
+ {\rm D}F(x_c(y))^*W_1{\rm D}F(x_c(y))\\[2mm]
& & +c {\cal J}h(x_c(y))^T{\cal J}
h(x_c(y))+c {\rm D}g(x_c(y))^*W_2{\rm D} g(x_c(y))\, .
\end{array}$$ From (\[comequation3.14\]) and the definition of ${\delta_0}$, ${\cal A}_c(y,W_1,W_2)$ is positive definite for any $W_1\in
\partial_B [{\rm D}\theta_c]^*(F(x_c(y))+Y/c)$ and $W_2 \in
\partial_B \Pi_{K^*}(\lambda-cg(x_c(y)))$. Then from (\[comdiff0\]) and (\[comderiv\]) we obtain that $$\label{comxderi}
\begin{array}{ll}
(x_c)'(y;\Delta y) & ={\cal A}_c(y,\widehat{W}_1,\widehat{W}_2 )^{-1}\left(-{\rm D}F(x_c(y))^*\widehat W_1(\Delta Y/c)\right.\\[6mm]
& \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \left. -{\cal J}
h(x_c(y))^T (\Delta\mu)+{\rm D}g(x_c(y))^*
\widehat{W}_2(\Delta\lambda)\right).
\end{array}$$ Therefore, we have from (\[comxderi\]) and (\[comgrad\]) that for any $y=(Y,\mu,\lambda) \in {\cal D}_{{\rm D}\vartheta_c}$,
$$\begin{array}{l}
{\rm D}^2 \vartheta_c(y) (\Delta y) \in
\left\{\left
[
\begin{array}{c}
c^{-1}W_1{\rm D}F(x_c(y))\\
{\cal J} h (x_c(y))\\
-W_2{\rm D}g(x_c(y))
\end{array}
\right
]\right.{\cal A}_c(y,W_1,W_2)^{-1}\left[-c^{-1}{\rm D}F(x_c(y))^*W_1(\Delta Y)\right.\\[4mm]
\quad \quad \quad \quad \quad\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \left.
-{\cal J}
h(x_c(y))^T\Delta\mu+{\rm D}g(x_c(y))^*W_2(\Delta\lambda)\right]\\[6mm]
\quad \quad \quad \quad \quad \quad \quad +\left.\left
(
\begin{array}{c}
-c^{-1}\Delta Y+c^{-2}W_1\Delta Y\\
0\\
-c^{-1}\Delta \lambda+ c^{-1}W_2( \Delta \lambda)\end{array} \right
) \, \Big |\, \begin{array}{l}
W_1\in \partial_B [{\rm D} \theta_c]^*(F(x_c(y))+ Y/c)\\[4pt]
W_2 \in
\partial_B \Pi_{K}(\lambda-c g(x_c(y)))
\end{array}\right\}.
\end{array}$$ which, together with the continuity of $x_c(\cdot)$ and the upper semicontinuity of $\partial_B \Pi_{K^*}(\cdot)$, implies that $V(\Delta y) \in
\overline{{\cal V}}_c (\Delta y)$ for any $V \in
\partial_B [{\rm D} \vartheta_c]^*(\overline{y})$. Consequently, (\[combdiff\]) holds.
The second basic assumption required in this section is stated as below.
[**Assumption B2**]{}. There exist positive numbers $\overline{c}\ge c_0$, $\mu_0>0$, $\varrho_0>0$, and $\gamma>1$ such that for any $c \geq {\overline{c}}$ and $\Delta y\in {\cal Z} \times \Re^m \times {\cal Y}$, $$\label{eq:direction-added}
\|(x_c)^\prime(\overline{y};\Delta y)\|\le \varrho_0 \|\Delta
y\|/c$$ and $$\label{comimport110}
\left \langle V(\Delta y)+c^{-1} \Delta y, \, \Delta y \right
\rangle \in \mu_0 \left[-1, 1\right]\| \Delta y\|^2/c^{\gamma}\,
\quad \forall\, V( \Delta y ) \in \overline{{\cal V}}_c(\Delta
y)\, .$$ It will be shown in Proposition \[thdcnlsdp\] that Assumption B2 is valid for (SDNOP) when the constraint nondegeneracy condition and the strong second order sufficient condition are satisfied.
Let $C$ be a closed convex set in ${\cal Y}$. It follows from [@Zarantonello71] that the metric projector $\Pi_C(\cdot)$ is Lipschitz continuous with the Lipschitz modulus $1$. Then for any $y\in {\cal Y}$, $\partial \Pi_C(y)$ is well defined and it has the following variational properties.
\[Lem:projector-pros\] [[@MSZhao05 Proposition 1]]{} Let $C\subseteq {\cal Y}$ be a closed convex set. Then, for any $y\in {\cal Y}$ and $V \in \partial \Pi_C(y)$, it holds that
[(i)]{}
: $V$ is self-adjoint.
[(ii)]{}
: $\langle d, Vd \rangle \geq 0, \quad \forall \, d
\in {\cal Y}$.
[(iii)]{}
: $\langle Vd, d - Vd \rangle \geq 0, \quad \forall
\, d \in {\cal Y}.$
Under Assumptions B1 and B2, we are ready to give the main result on the rate of convergence of the augmented Lagrangian method for the composite optimization problem (COP).
\[comthconv1\] Suppose that $K$ is an nonempty closed convex cone and that ${\rm D} \theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are semismooth everywhere. Let Assumptions B1 and B2 be satisfied. Let $c_0,$ $\underline{\eta},$ $\overline{c}$, $ \mu_0$, $\varrho_0$, and $\tau$ be the positive numbers defined in these assumptions. Define $$\varrho_1:= 2\varrho_0 \quad {\rm and} \quad \varrho_2:=4\mu_0.$$ Then for any $c \geq {\overline{c}}$, there exist two positive numbers $\varepsilon$ and $\delta $ $($both depending on $c$$)$ such that for any $(Y,\mu, \lambda)
\in\mathbb{B}_{\delta}(\overline Y, \overline{\mu}, \overline{\lambda})$, the problem $$\label{Problem-op}
\min \ L_c(x, Y,\mu, \lambda)
\quad {\rm s.t.} \ x\in {\mathbb{B}}_{\varepsilon}(\overline{x})\,$$ has a unique solution denoted $x_c(Y,\mu, \lambda)$. The function $x_c(\cdot,\cdot, \cdot)$ is locally Lipschitz continuous on $\mathbb{B}_{\delta}(\overline Y, \overline{\mu}, \overline{\lambda})$ and is semismooth at any point in $\mathbb{B}_{\delta}(\overline Y, \overline{\mu}, \overline{\lambda})$, and for any $(Y,\mu, \lambda) \in
\mathbb{B}_{\delta}(\overline Y, \overline{\mu}, \overline{\lambda})$, we have $$\label{comest111}
\|x_c(Y,\mu, \lambda)-\overline{x}\| \leq \varrho_1 \|(Y,\mu,
\lambda)-(\overline Y, \overline{\mu}, \overline{\lambda})\|/{c}$$ and $$\label{comest112}
\|(Y_c(Y, \mu, \lambda), \mu_c(Y, \mu, \lambda), \lambda_c(Y, \mu, \lambda))- (\overline Y, \overline{\mu}, \overline{\lambda})\| \leq \varrho_2 \|(Y,\mu,
\lambda)-(\overline Y, \overline \mu, \overline \lambda)\|/{c^{\gamma-1}}\, ,$$ where $Y_c(Y, \mu, \lambda)$, $\mu_c(Y, \mu, \lambda)$ and $\lambda_c(Y, \mu, \lambda)$ are defined by $(\ref{comnota1})$, i.e., $$\begin{array}{lll}
Y_c(Y, \mu, \lambda)&=&{\rm D} \theta_c(F(x_c(y))+Y/c)^*,\\
\mu_c(Y, \mu, \lambda)&=&\mu+ch(x_c(y)),
\\
\lambda_c(Y, \mu, \lambda)&=&\Pi_{K^*}(\lambda-c g(x_c(y))).
\end{array}$$
[**Proof.**]{} Let $c\ge {\overline{c}}$. From Proposition \[prop:general-discussions\] we have already known that there exist two positive numbers $\varepsilon >0$ and $\delta_0>0$ (both depending on $c$) and a locally Lipschitz continuous function $x_c(\cdot, \cdot,\cdot)$ defined on $\mathbb{B}_{\delta_0}(\overline Y, \overline{\mu}, \overline{\lambda})$ such that the function $x_c(\cdot,\cdot, \cdot)$ is semismooth at any point in $\mathbb{B}_{\delta_0}(\overline Y, \overline{\mu}, \overline{\lambda})$ and for any $(Y, \mu,\lambda)\in \mathbb{B}_{\delta_0} (\overline Y, \overline{\mu}, \overline{\lambda})$, $x_c(Y,\mu, \lambda)$ is the unique solution to (\[Problem-op\]).
Denote $y:=(Y, \mu, \lambda)\in {\cal Z} \times \Re^m\times {\cal Y}$. Since $x_c(\cdot)$ is locally Lipschitz continuous on $\mathbb{B}_{\delta_0}(\overline{y})$ and is directionally differentiable at $\overline{y}$, by [@Shapiro90] we know that $x_c(\cdot)$ is Bouligand-differentiable at $\overline{y}$, i.e., $x_c(\cdot)$ is directionally differentiable at $\overline{y}$ and $$\lim _{y\to \overline{y}} \frac{\|x_c(y)-x_c(\overline{y})
-(x_c)^\prime(y;y-\overline{y}) \|}{\|y-\overline{y}\|} =0\, .$$ By Proposition \[comdcproperty1\], ${\rm D}
\vartheta_c(\cdot)$ is semismooth at $\overline{y}$, and thus is also Bouligand-differentiable at $\overline{y}$. Then there exists $\delta \in (0, \delta_0]$ such that for any $y \in
\mathbb{B}_{\delta}(\overline{y})$, $$\label{comest113-A}
\|x_c(y)-x_c(\overline{y})-(x_c)^\prime(\overline{y};y-\overline{y})\|
\leq\varrho_0 \|y-\overline{y}\|/{c}$$ and $$\label{comest113-B}
\|{\rm D} \vartheta_c(y)-{\rm D} \vartheta_c(\overline{y})-({\rm D}
\vartheta_c)^\prime(\overline{y};y-\overline{y})\|\leq
\mu_0\|y-\overline{y}\|/c^{\gamma}\, .$$
Let $y:=(Y,\mu, \lambda)\in \mathbb{B}_{\delta}(\overline{y})$ be an arbitrary point. From (\[eq:direction-added\]), (\[comest113-A\]), and the fact that $x_c(\overline{y})
=\overline{x}$, we have $$\|x_c(y)-\overline{x}\| \leq
\|(x_c)^\prime(\overline{y};y-\overline{y})\|+\varrho_0\|y-\overline{y}\|
{c} = \varrho_1 \|y-\overline{y}\|/{c}\, ,$$ which, shows that (\[comest111\]) holds.
Since ${\rm D} \vartheta_{c}(\cdot)$ is semismooth at $\overline{y}$, there exists an element $V
\in
\partial_B [{\rm D} \vartheta_{c}]^*(\overline{y})$ such that $({\rm D}
\vartheta_{c})^{*\prime}(\overline{y};y-\overline{y})=V(y-\overline{y})$. By using the fact that $V$ is self-adjoint (see Lemma \[Lem:projector-pros\]), we know from (\[comimport110\]) in Assumption B2 and Proposition \[comthta\] that $$\label{eq:squareroot}
\|V(y-\overline{y})+c^{-1} (y-\overline{y}) \|
\le 3 \mu_0\|y-\overline{y}\|/{c^\gamma} \, .$$ Therefore, we have from (\[comest113-B\]) and (\[eq:squareroot\]) $$\begin{array}{l}
\quad \|y+c({\rm D}\vartheta_{c})^*(y)-\overline{y}\|
\\[2mm]
= c \| ({\rm D}\vartheta_{c})^*(y)-({\rm D}\vartheta_{c})^*(\overline{y})-({\rm D}\vartheta_{c})^{*\prime}(\overline{y};y-\overline{y}) + ({\rm D}\vartheta_{c})^{*\prime}(\overline{y};y-\overline{y})+{c}^{-1}(y-\overline{y})\|
\\[2mm]
\le {c} \|({\rm D}\vartheta_{c})^*(y)-({\rm D}\vartheta_{c})^*(\overline{y})-({\rm D}\vartheta_{c})^{*\prime}(\overline{y};y-\overline{y})\|
+c\|V(y-\overline{y})+c^{-1} (y-\overline{y})\|\\[2mm]
\leq \mu_0 \|y-\overline{y}\|/c^{\gamma-1} +
3{\mu_0}\|y-\overline{y}\|/c^{\gamma-1} =
{\varrho_2}\|y-\overline{y}\|/c^{\gamma-1}\, ,
\end{array}$$ which, together with (\[comdcjacobi\]) and the definitions of $Y_c(Y,\mu,\lambda)$, $\mu_c(Y,\mu,\lambda)$ and $\lambda_c(Y,\mu,\lambda)$, proves (\[comest112\]). The proof is completed.
7 true pt Under Assumptions B1 and B2, Theorem \[comthconv1\] shows that if for all $k$ sufficiently large with $c_k\equiv c$ larger than a threshold and if $(x^k,Y^k,
\mu^k,\lambda^k)$ is sufficiently close to $(\overline{x},\overline Y, \overline \mu,
\overline \lambda)$, then the augmented Lagrangian method can locally be regarded as the gradient ascent method applied to the dual problem $$\max \ \vartheta_c(Y,\mu,\lambda)
\quad
{\rm s.t.}\
(Y,\mu,\lambda)\in {\cal Z}\times \Re^m \times {\cal Y}\,$$ with a constant step-length $c$, i.e., for all $k$ sufficiently large $$\left(
\begin{array}{c}
y^{k+1}\\
\mu^{k+1} \\
\lambda^{k+1} \end{array}\right)
= \left(
\begin{array}{c}
Y^k\\
\mu^{k} \\
\lambda^{k} \end{array}\right) + c{\rm D}
{\vartheta_c}(Y^k, \mu^k,\lambda^k)^*.$$ In Section \[NLSDP-case\], we shall check, under what kind of conditions, Assumptions B1 and B2 imposed in this section can be satisfied by the nonlinear semidefinite nuclear norm composite optimization problem.
Variational analysis for SDNOP {#preliminaries}
==============================
For studying the rate of convergence of the augmented Lagrange method for the nonlinear semidefinite nuclear norm composite optimization problem (SDNOP), we have to provide some variational properties of $\Pi_{{\cal S}^p_+}(\cdot)$ and $\|\cdot\|_*$, and the second-order optimality conditions for (SDNOP).
Variational properties of $\Pi_{{\cal S}^p_+}(\cdot)$ and $\|\cdot\|_*$
-----------------------------------------------------------------------
Since there exists an nonlinear semidefinite constraint in Problem (SDNOP), we need more properties about the tangent cone of the cone ${\cal S}^p_+$ and the B-subdifferential of the metric projector $\Pi_{{\cal S}_+^p}(\cdot)$ over ${\cal S}_+^p$. Let ${\cal O}^p$ be the set of all $p\times p$ orthogonal matrices. For a given matrix $M\in\mathcal{S}^p$, there exists $P\in\mathcal{O}^p$ such that $$\label{spec-11}
M=P\Lambda(M)P^T,$$ where $\Lambda(M)={\rm
diag}(\lambda_1(M),\lambda_2(M),\ldots,\lambda_p(M))$ and $\lambda_1(M)\geq\lambda_2(M)\geq\ldots\geq\lambda_p(M)$ are eigenvalues of $M$. We denote the set of such $P$ in the eigenvalue decomposition by ${\cal O}(M)$. Let $\overline{M}\in {\cal S}^p$ and $\overline{M}_+:=
\Pi_{{\cal S}_+^p}(\overline{M})$. Suppose that $\overline{M}$ has the following spectral decomposition $$\label{eq:orthogonal-decomposition}
\overline{M} = \overline{P} \Lambda \overline{P} ^T,$$ where $P\in {\cal O}(\overline M)$ and $\Lambda $ is the diagonal matrix of eigenvalues of $\overline{Z}$. Then $$\overline{M}_+ = P \Lambda_+P ^T,$$ where $\Lambda_+$ is the diagonal matrix whose diagonal entries are the nonnegative parts of the respective diagonal entries of $\Lambda$ [@Higham88; @Tseng98]. Define three index sets of positive, zero, and negative eigenvalues of $\overline{M}$, respectively, as $$\alpha := \{ i \, | \, \lambda_i > \, 0 \}, {\hspace{1pc}}\beta := \{
i \, | \, \lambda_i \, = \, 0 \}, {\hspace{1pc}}\gamma := \{ i \, | \,
\lambda_i \, < \, 0 \}.$$ Write $$\Lambda = \left[ \begin{array}{ccc} \Lambda_{\alpha} & 0 & 0 \\
[5pt] 0 & 0 & 0 \\ [5pt] 0 & 0 & \Lambda_{\gamma}
\end{array} \right] {\hspace{1pc}}\mbox{and} {\hspace{1pc}}P = [ \begin{array}{ccc}P_{\alpha} &
P_{\beta} & P_{\gamma}
\end{array} ]$$ with $P_{\alpha} \in \Re^{p \times |\alpha|}$, $P_{\beta} \in \Re^{p \times |\beta|}$, and $P_{\gamma} \in \Re^{p \times |\gamma| }$. Let $\Theta $ be any matrix in ${\cal S}^p$ with entries $$\label{eq:Theta-form}
\left\{ \begin{array}{ll}
\Theta_{ij} =\displaystyle
{\frac{\max\{\lambda_i,0\} + \max\{\lambda_j,0\}}{ | \, \lambda_i
\, | +| \, \lambda_j \, |}}& {\rm if}\ (i, j) \notin \beta\times
\beta\, ,
\\[2mm]
\Theta_{ij} \in [0,1] & {\rm if}\ (i, j) \in
\beta\times \beta\, .
\end{array} \right.$$ The projection operator $\Pi_{{\cal S}^p_+}(\cdot)$ is directionally differentiable everywhere in ${\cal S}^p$ [@BCS99] and is a strongly semismooth matrix-valued function [@SS02]. For any $ H\in {\cal S}^p$, we have $$\label{eq:dd-projection}
\Pi_{{\cal S}_+^p} ^{ \prime}(\overline{M};H) = P
\left[
\begin{array}{ccc}
P_\alpha^T HP_ {\alpha} &
P_\alpha^T HP_ {\beta} & \Theta_{\alpha
\gamma} \circ P_\alpha^T HP_ {\gamma}
\\ [7pt]
P_\beta^T HP_ {\alpha} & \Pi_{{\cal
S}_+^{|\beta|}} ( P_\beta^T HP_ {\beta} )
& 0 \\ [7pt]
P_\gamma^T HP_ {\alpha} \circ {\Theta}_{\gamma \alpha} & 0 & 0
\end{array}
\right] P^T\, ,$$ where $``\circ"$ denotes the Hadamard product [@SS02]. When $\beta =\emptyset$, $\Pi_{{\cal S}^p_+}(\cdot)$ is Fréchet-differentiable at $\overline{M}$ and (\[eq:dd-projection\]) reduces to the classical result: $$\label{eq:fd-projection}
{\cal J} \Pi_{{\cal S}_+^p} (\overline{M})H = P \left[
\begin{array}{cc}
P_\alpha^T HP_ {\alpha} & \Theta_{\alpha
\gamma} \circ P_\alpha^T HP_ {\gamma}
\\ [7pt]
P_\gamma^T HP_ {\alpha} \circ {\Theta}_{\gamma \alpha} & 0
\end{array}
\right] P^T\, \quad \forall \, H\in {\cal S}^p\, .$$ The tangent cone of ${\cal S}_+^p$ at $\overline{M}_+$, denoted ${\cal
T}_{{\cal S}_+^p} (\overline{M}_+)$, can be completely characterized as follows $${\cal T}_{{\cal S}_+^p} (\overline{M}_+) =\{B\in {\cal S}^p\, |
\, B = \Pi_{{\cal S}_+^p} ^{ \prime}(\overline{M}_+;B)\} =\{B\in
{\cal S}^p\, |\, [P_\beta \ P_\gamma]^T B
[P_\beta \ P_\gamma] \succeq 0\}\, .$$ The lineality space of ${\cal T}_{{\cal
S}_+^p} (\overline{M}_+)$, i.e., the largest linear space in ${\cal T}_{{\cal S}_+^p} (\overline{M}_+)$, denoted by ${\rm lin}
\left ({\cal T}_{{\cal S}_+^p} (\overline{M}_+)\right)$, takes the following form: $${\rm lin} \left ( {\cal T}_{{\cal S}_+^p} (\overline{M}_+)
\right) =\{B\in {\cal S}^p\, |\, [P_\beta \
P_\gamma]^T B [P_\beta \
P_\gamma] =0\}\, .$$The critical cone of ${\cal S}^p_+$ at $\overline{M} \in {\cal
S}^p$ associated with the problem of finding the metric projection of $\overline{M}$ onto ${\cal S}^p_+$ (i.e., $\overline{M}_+$) is defined as [@BS00 Section 5.3] $${\cal C}_{{\cal S}_+^p}(\overline{M}) \, : = \, {\cal T}_{{\cal
S}_+^p} (\overline{M}_+) \cap \{B \in {\cal S}^p\, |\, \langle B,
\overline{M}_+-\overline{M}\rangle =0\}\, .$$ Thus, it holds that $${\cal C}_{{\cal S}_+^p}(\overline{M}) \, = \, \left\{ B \in {\cal
S}^p \, \Big{|} \, P_{\beta}^T B P_{\beta} \succeq
0, \ P_{\beta }^TB P_{\gamma} = 0, \
P_{\gamma }^T B P_{\gamma } = 0 \right \}.$$The affine hull of ${\cal C}_{{\cal S}_+^p}(\overline{M})$, denoted by ${\rm aff}({\cal C}_{{\cal S}_+^p}(\overline{M}))$, can then be written as $$\label{eq:aff-critical-cone}
{\rm aff}\left({\cal C}_{{\cal S}_+^p}(\overline{M})\right)=\left\{
B \in {\cal S}^p \, | \, P_{\beta }^T B
P_{\gamma} = 0, \ P_{\gamma}^T
BP_{\gamma } = 0 \right\}.$$
The following lemma on $\partial _B\Pi_{{\cal S}_+^p}
(\overline{M})$ is part of [@S05 Proposition 4], which is based on [@PSS03 Lemma 11].
\[lemma:projector-Jacobian-cone-pre\] Let $\Theta\in {\cal S}^p$ satisfy $(\ref{eq:Theta-form})$. Then $W \in
\partial _B\Pi_{{\cal S}_+^p} (\overline{M})$ if and only if there exists $W_0 \in
\partial _B\Pi_{{\cal S}_+^{|\beta|}} (0)$ such that $$W(H)=
P
\left[
\begin{array}{ccc}
P_\alpha^T HP_ {\alpha} &
P_\alpha^T HP_ {\beta} & \Theta_{\alpha
\gamma} \circ P_\alpha^T HP_ {\gamma}
\\ [7pt]
P_\beta^T HP_ {\alpha} & W_0(
P_\beta^T HP_ {\beta} )
& 0 \\ [7pt]
P_\gamma^T HP_ {\alpha} \circ {\Theta}_{\gamma \alpha} & 0 & 0
\end{array}
\right] P^T
\quad \forall \, H\in {\cal S}^p\, .$$
From the definition of $\partial _B\Pi_{{\cal
S}_+^{|\beta|}} (0)$ and (\[eq:fd-projection\]) we know that if $W_0\in \partial _B\Pi_{{\cal S}_+^{|\beta|}}
(0)$, then there exist matrices $Q\in {\cal O}^{|\beta|}$ and $\Omega\in
{\cal S }^{|\beta|}$ with entries $\Omega_{ij}\in [0,1]$ such that $$W_0 (D)= Q(\Omega \circ (Q^T DQ)) Q^T \quad \forall\, D \in {\cal
S}^{|\beta|}\, .$$ For an extension to the above result, see [@CQT03 Lemma 4.7]. By using Lemma \[lemma:projector-Jacobian-cone-pre\] we obtain the following useful lemma, which does not need further explanation.
\[lemma:projector-Jacobian-cone\] For any $W\in \partial
_B\Pi_{{\cal S}_+^p} (\overline{M})$, there exist two matrices $P\in {\cal O}(\overline{M})$ and $\Theta \in {\cal S}^p$ satisfying $(\ref{eq:Theta-form})$ such that $$W(H) = P\left( \Theta \circ (P^THP)\right )P^T\quad \forall \, H
\in {\cal S}^p\, .$$
For discussions on the nuclear norm function we need more properties about the first and second-order directional derivatives of $\theta$ and the sub-differential of its proximal mapping. For a given matrix $X\in\mathcal{S}^q$, there exists $Q\in\mathcal{O}^q$ such that $$\label{X-spec}
X=Q\Lambda(X)Q^T,$$ where $\Lambda(X)={\rm
diag}(\lambda_1(X),\lambda_2(X),\ldots,\lambda_q(X))$ and $\lambda_1(X)\geq\lambda_2(X)\geq\ldots\geq\lambda_q(X)$ are eigenvalues of $X$. We denote the set of such $Q$ in the eigenvalue decomposition by ${\cal O}(X)$.
Let $\varpi_1>\varpi_2>\ldots>\varpi_r$ be the distinct eigenvalues of $X$. Define $$\begin{array}{l}
a_k:=\{i\,|\,\lambda_i(X)=\varpi_k\},\quad k=1,\ldots,r.
\end{array}$$ Partition $Q$ as $Q=[Q_{a_1}\,\,\,Q_{a_2}\,\,\,\ldots\,\,\,Q_{a_r}]$, where $Q_{a_k}=(q_i:i \in a_k)$ and $Q_{a_k}\in\Re^{q\times |a_k|}$, $k=1,\ldots,r$.
For a given $H\in\mathcal{S}^q$ and $k\in\{1,\ldots,r\}$, suppose that $Q^T_{a_k}HQ_{a_k}\in\Re^{|a_k|\times|a_k|}$ has the following spectral decomposition: $$(Q^k)^T(Q^T_{a_k}HQ_{a_k})Q^k=\diag(\xi^k_1,\ldots,\xi^k_{|a_k|}),$$ where $ Q^k\in\mathcal{O}^{|a_k|}(Q^T_{a_k}HQ_{a_k})$ and $\xi^k_i=\lambda_{i}(Q^T_{a_k}HQ_{a_k})$, $i=1,\ldots,|a_k|$. Let $\eta^k_1,\ldots,\eta^k_{n_k}$ be the distinct eigenvalues of $Q^T_{a_k}HQ_{a_k}$ and define $$\begin{array}{l}
b^k_j:=\{i\,|\,\xi^k_i=\eta^k_j,\quad i=1,\ldots,|a_k|\}, \quad
j=1,\ldots,n_k.
\end{array}$$ For simplicity, we denote $\displaystyle
\kappa_i:=\sum^{i}_{j=1}|a_j|$ $(\kappa_0:=0)$, $\displaystyle \kappa^{(k)}_i=\sum^{i}_{j=1}|b^k_j|$ ($\kappa^{(k)}_{0}:=0$), and define the following mappings: $$\begin{array}{lll}
&& \nu:\{1,\ldots,n\}\rightarrow\{1,\ldots,r\},\quad
\nu(i)=k,\,\,\, {\rm if} \,\,\,i\in a_k, \\
& & l:\{1,\ldots,n\}\rightarrow\mathbb{N},\quad
l(i)=i-\kappa_{\nu(i)-1}, \\
&& \omega: \{1,\ldots,n\}\rightarrow\mathbb{N},\quad
\omega(i)=j,\,\,\,{\rm if} \,\,\,l(i)\in b^{\nu(i)}_j, \\
&& l':\{1,\ldots,n\}\rightarrow\mathbb{N},\quad
l'(i)=l(i)-\kappa^{\nu(i)}_{\mu(i)-1}.
\end{array}$$ Then, for $i'\in b^k_j$, its corresponding index $i \in \{1,\ldots,q\}$ is expressed as $i=\kappa^{(k)}_{j-1}+i'+\kappa_{k-1}$. Define $$\begin{array}{l}
\widehat Q_{a_ka_k}=Q_{a_k}^THQ_{a_k},k=1,\ldots, r,\\[4pt]
\widehat V_k(H,W)=Q_{a_k}^T[W-2H(X-\varpi_k I)^{\dag}H]Q_{a_k},k=1,\ldots, r.
\end{array}$$ Then we have from [@ZZX2013 Theorem 3.1] that $$\begin{array}{l}
\lambda_i'(X;H)=\lambda_{l(i)}(\widehat H_{a_{\nu(i)}a_{\nu(i)}}),\, i=1,\ldots,q,\\[4pt]
\lambda_i''(X;H,W)=\lambda_{l'(i)}\left({Q^{\nu(i)}_{b^{\nu(i)}_{\omega(i)}}}^T\widehat V_{\nu(i)}(H,W)Q^{\nu(i)}_{b^{\nu(i)}_{\omega(i)}}\right),\, i=1,\ldots,q.
\end{array}$$ Assume that there exists an integer $s_0$ satisfying $1 \leq s_0 \leq N_s$ and $\eta^s_{s_0}=0$. Let $b^s_+=b^s_1\cup \cdots\cup b^s_{s_0-1}$, $b^s_0=b^s_{s_0}$ and $b^s_-=b^s_{s_0+1}\cup \cdots\cup b^s_{N_s}$. Then we obtain the following proposition about the directional derivative and the second-order directional derivative of $\theta (X)$.
\[1-2-dd\] Under the above notations, one has he directional derivative of $\theta$ at $X$ along $H$ is expressed as $$\label{eq:1d}
\theta'(X;H)=\displaystyle \sum_{i=1}^{s-1}{\rm Tr}(\widehat H_{a_ia_i})-
\displaystyle \sum_{i=s+1}^r{\rm Tr}(\widehat H_{a_ia_i})+\|\widehat H_{a_sa_s}\|_*.$$ and the second-order directional derivative of $\theta$ at $X$ along $(H,W)$ is expressed as $$\label{eq:2d}
\begin{array}{ll}
\theta''(X;H,W)
&=\displaystyle \sum_{i=1}^{s-1}{\rm Tr}(\widehat V_i(H,W))-
\displaystyle \sum_{i=s+1}^r{\rm Tr}(\widehat V_i(H,W))+{\rm Tr}({Q^s_{b^s_+}}^T\widehat V_s(H,W)Q^s_{b^s_+})\\[4pt]
& \quad -
{\rm Tr}({Q^s_{b^s_-}}^T\widehat V_s(H,W)Q^s_{b^s_-})
+
\|{Q^s_{b^s_0}}^T\widehat V_s(H,W)Q^s_{b^s_0}\|_*.
\end{array}$$
[**Proof**]{}. For $\theta(X)=\|X\|_*$, the nuclear norm of a symmetric matrix in $X \in {\cal S}^q$, it is the spectral function corresponding to the symmetric function $$\varsigma (z)=\sum_{j=1}^q |z_i|, z=(z_1,\ldots, z_q)^T \in \Re^q,$$ namely $\theta(X)=\|X\|_*=[\varsigma \circ \lambda](X)$.
Let $\overline z \in \Re^q$. We define $$I_+(\overline z)=\{i: \overline z_i >0\},\, I_0(\overline z)=\{i:\overline z=0\},\,
I_-(\overline z)=\{i: \overline z_i <0\}$$ and $$\begin{array}{l}
I_{0+}(\overline z,\Delta z)=\{i \in I_0(\overline z): \Delta z_i >0\},\\[4pt]
I_{00}(\overline z,\Delta z)=\{i \in I_0(\overline z): \Delta z_i =0\},\\[4pt]
I_{0-}(\overline z,\Delta z)=\{i \in I_0(\overline z): \Delta z_i<0\}.
\end{array}$$ Then the directional derivative of $\varsigma$ at $\overline z$ along $\Delta z$ is $$\varsigma'(\overline z;\Delta z)=\displaystyle \sum_{i \in I_+(\overline z)} \Delta z_i-\displaystyle \sum_{i \in I_-(\overline z)} \Delta z_i +\displaystyle \sum_{i \in I_0(\overline z)}| \Delta z_i |$$ and the second-order parabolic directional derivative at $\overline z$ along $\Delta z$ and $\Delta w$ is $$\varsigma''(\overline z;\Delta z,\Delta w)=\displaystyle \sum_{i \in I_+(\overline z)\cup I_{0+}(\overline z,\Delta z)} \Delta w_i-\displaystyle \sum_{i \in I_-(\overline z)\cup I_{0-}(\overline z,\Delta z)} \Delta w_i +\displaystyle \sum_{i \in I_{00}(\overline z,\Delta z)}| \Delta w_i |.$$ Then, from the chain rules of directional derivatives (see Chapter 2 of [@BS00]), we obtain $$\theta'(X;H)=\varsigma'(\lambda (X);\lambda'(X;H))=\displaystyle \sum_{i=1}^{s-1}{\rm Tr}(\widehat H_{a_ia_i})-
\displaystyle \sum_{i=s+1}^r{\rm Tr}(\widehat H_{a_ia_i})+\|\widehat H_{a_sa_s}\|_*$$ and $$\begin{array}{ll}
\theta''(X;H,W) &=\varsigma'(\lambda (X);\lambda'(X;H),\lambda''(X;H,W))\\[6pt]
&=\displaystyle \sum_{i=1}^{s-1}{\rm Tr}(\widehat V_i(H,W))-
\displaystyle \sum_{i=s+1}^r{\rm Tr}(\widehat V_i(H,W))+{\rm Tr}({Q^s_{b^s_+}}^T\widehat V_s(H,W)Q^s_{b^s_+})\\[4pt]
& \quad -
{\rm Tr}({Q^s_{b^s_-}}^T\widehat V_s(H,W)Q^s_{b^s_-})
+
\|{Q^s_{b^s_0}}^T\widehat V_s(H,W)Q^s_{b^s_0}\|_*.
\end{array}$$ The proof is completed.$\Box$\
By direct calculation, we may obtain the following conclusion.
\[prop-psi\] Let $\psi (W)=\theta''(X;H,W)$, then $$\label{eq:conj}
\begin{array}{l}
\psi^*(Y)=\\[10pt]
\left
\{
\begin{array}{ll}
\begin{array}{l}
2\displaystyle \sum_{i=1}^{s-1} {\rm Tr}(Q_{a_i}^TH(X-\varpi_iI)^{\dag}HQ_{a_i})\\
+2\displaystyle \sum_{i=s+1}^{r} {\rm Tr}(Q_{a_i}^TH(X-\varpi_iI)^{\dag}HQ_{a_i})\\[4pt]
+ 2{\rm Tr}({Q^s_{b^s_+}}^TQ_{a_s}^THX^{\dag}HQ_{a_s}Q^s_{b^s_+})\\[4pt]
+2{\rm Tr}({Q^s_{b^s_-}}^T Q_{a_s}^THX^{\dag}HQ_{a_s}Q^s_{b^s_-})\\[4pt]+2\langle
{Q^s_{b^s_0}}^T\widehat Y_{a_sa_s}Q^s_{b^s_0}, {Q^s_{b^s_0}}^TQ_{a_s}^THX^{\dag}HQ_{a_s}Q^s_{b^s_0}
\rangle
\end{array} & \mbox{if} \left(\begin{array}{l}
\widehat Y_{a_ia_i}=I_{|a_i|},\\
\quad \quad \mbox{for } 1\leq i\leq s-1, \\
\widehat Y_{a_ia_i}=-I_{|a_i|},\\
\quad \quad \mbox{for } s+1\leq i\leq r,\\
{Q^s_{b^s_+}}^T \widehat Y_{a_sa_s}Q^s_{b^s_+}=I_{|b^s_+|},\\
{Q^s_{b^s_-}}^T \widehat Y_{a_sa_s}Q^s_{b^s_-}=I_{|b^s_-|},\\
\|{Q^s_{b^s_0}}^T\widehat Y_{a_sa_s}Q^s_{b^s_0}\|_2\leq 1,
\end{array}\right.\\[26pt]
0 & \mbox{otherwise}.
\end{array}
\right.
\end{array}$$
Now we characterize elements in $\partial \theta (X)$ for $X \in {\cal S}^q$. If follows from Page 121 of Borwin and Lewis (2006) [@BLewis2006], for the given $X \in {\cal S}^q$ with the spectral decomposition (\[X-spec\]), that $Y \in \partial [\varsigma \circ \lambda]( X)$, or $Y \in \partial \theta (X)$ if and only if there exists $w \in \partial \varsigma (\lambda ( X))$ $$Y=Q{\rm Diag}\,(w) Q^T,$$ where $X$ has the spectral decomposition $ X=Q{\rm Diag}(\lambda ( X))Q^T$. Define the following three index sets: $$a=\{i: \lambda_i( X)>0\},\,\, b=\{i: \lambda_i( X)=0\},\,\, c=\{i: \lambda_i( X)<0\},$$ or alternatively $a=a_1 \cup\cdots\cup a_{s-1}$, $b=a_s$ and $c=a_{s+1}\cup \cdots\cup a_r$. Then, $w \in \partial \varsigma (\lambda (X))$ has the following property $$w_a =\textbf{1}_{|a|}, w_{c}=-\textbf{1}_{|c|} \mbox{ and } -\textbf{1}_{|b|}\leq w_{b}\leq \textbf{1}_{|b|},$$ and $$Y=Q{\rm Diag}\,(w) Q^T=Q_{a}Q_{a}^T+Q_{b}{\rm Diag}\,(w_{b}) Q^T_{b}-Q_{c}Q_{c}^T.$$ For the index set $b$, we partition it as follows $b=b_L \cup b_S \cup b_U$: $$b_L=\{i\in b: w_i=-1\}, b_S=\{i\in b: -1< w_i< 1\},b_U=\{i\in b: w_i=1\}.$$ Then $Y \in \partial \theta (X)$ can be expressed as $$\label{eq:dec-Y}
Y=Q{\rm Diag}\,(w) Q^T=Q_{a\cup_{b_U}}Q_{a\cup_{b_U}}^T+Q_{b_S}{\rm Diag}\,(w_{b_S}) Q^T_{b_S}-Q_{c\cup_{b_L}}Q_{c\cup_{b_L}}^T$$ and for $Z=X+Y$, $$\label{eq:cDecop}
Z=[Q_a\,Q_{b_U}\,Q_{b_S}\,Q_{b_L}\,Q_{c}]\left
[
\begin{array}{ccccc}
\Lambda_a+I_{|a|} &&&&\\[4pt]
& I_{|b_U|} &&&\\[4pt]
&&{\rm Diag}\,(w_{b_S})&&\\[4pt]
&&&-I_{|b_L|}&\\[4pt]
&&&&\Lambda_c-I_{|c|}
\end{array}
\right
]\left
[\begin{array}{c}
Q_a^T\\[4pt]
Q_{b_U}^T\\[4pt]
Q_{b_S}^T\\[4pt]
Q_{b_L}^T\\[4pt]
Q_{c}^T
\end{array}
\right].$$ The critical cone of $\theta$ at $Z$ associated with $Y \in \partial \theta (X)$ is defined by $$\label{eq:directional-c}
{\cal C}_\theta(Z)=\{H \in {\cal S}^q: \theta'(X;H)= \langle Y, H\rangle\}.$$ The next lemma gives an characterization of the critical cone ${\cal C}_\theta$.
\[lem:critic-char\] Let $X,Y,Z \in {\cal S}^q$, $Z=X+Y$ satisfies $Y \in \partial \theta (X)$. Then $H \in {\cal C}_\theta (Z)$ if and only if $$\label{eq:critical-Prox}
{\cal C}_{\theta}(Z)=\left\{H \in {\cal S}^q:\begin{array}{l}
Q^{T}_{b_S}H[Q_{b}]=0,
Q^{T}_{b_U}H[Q_{b_L}]=0\\[4pt]
Q^{T}_{b_U}HQ_{b_U}\in {\cal S}^{|b_U|}_+,
Q^{T}_{b_L}HQ_{b_L}\in {\cal S}^{|b_L|}_-
\end{array}
\right
\}.$$
[**Proof.**]{} Noting that $$\partial \theta (X)=\{Q_{a}Q_{a}^T+Q_{b}W_{b} Q^T_{b}-Q_{c}Q_{c}^T:W_{b} \in {\cal S}^{|b|}, \|W_b\|_2 \leq 1\},$$ where $\|W_b\|_2$ denotes the spectral norm of $W_b$. And the directional derivative of $\theta$ at $X$ along $H$ is $$\theta'(X;H)=\langle Q_{a}Q_{a}^T-Q_{c}Q_{c}^T, H \rangle+\|Q_{b}^T[H] Q_{b}\|_*.$$ Noting that $B$ has the expression $$B=Q_{a}Q_{a}^T+Q_{b}{\rm Diag}\, (w_{b}) Q^T_{b}-Q_{c}Q_{c}^T$$ where $w_b \in \Re^{|b|}$ satisfies $\|w_b\|_{\infty} \leq 1$. Then $\theta'(A;H)= \langle B, H\rangle$ is equivalent to $$\label{eq:hlp10}
\|Q_{b}^T[H] Q_{b}\|_*=\langle Q_{b}^T[H] Q_{b},{\rm Diag}\, (w_{b}) \rangle.$$ From Fan’s inequality one has $$\langle Q_{b}^T[H] Q_{b},{\rm Diag}\, (w_{b}) \rangle
\leq \lambda (Q_{b}^T[H] Q_{b})^Tw_{b},$$ which implies, from (\[eq:hlp10\]), for $\lambda (Q_{b}^T[H] Q_{b})=(\lambda_1 (Q_{b}^T[H] Q_{b}),\ldots, \lambda_{|b|} (Q_{b}^T[H] Q_{b}))^T$ with $\lambda_1 (Q_{b}^T[H] Q_{b})\geq \cdots \geq \lambda_{|b|} (Q_{b}^T[H] Q_{b})$, that $$\langle Q_{b}^T[H] Q_{b},{\rm Diag}\, (w_{b}) \rangle
= \lambda (Q_{b}^T[H] Q_{b})^Tw_{b}=\|Q_{b}^T[H] Q_{b}\|_*.$$ Then $Q_{b}^T[H] Q_{b}$ and ${\rm Diag}\, (w_{b})$ admit a simultaneous ordered eigenvalue decomposition, and thus we can check that $H$ satisfies $$\begin{array}{l}
Q^{T}_{b_S}H[Q_{b}]=0,
Q^{T}_{b_U}H[Q_{b_L}]=0,
Q^{T}_{b_U}HQ_{b_U}\in {\cal S}^{|b_U|}_+,
Q^{T}_{b_L}HQ_{b_L}\in {\cal S}^{|b_L|}_-.
\end{array}$$ The proof is completed. $\Box$\
\[coro-an-equality\] Let $X,Y,Z \in {\cal S}^q$, $Z=X+Y$ satisfies $Y \in \partial \theta (X)$. Then $H \in {\cal C}_\theta (Z)$ if and only if $$\|Q_{a_s}^THQ_{a_s}\|_*=\langle Q_{a_s}^TYQ_{a_s}, Q_{a_s}^THQ_{a_s} \rangle.$$
\[prop-sigmaterm\] Let $X,Y,Z,H \in {\cal S}^q$, $Z=X+Y$ satisfies $Y \in \partial \theta (X)$ and $H \in {\cal C}_{\theta}(Z)$. Then $$\label{eq:conj1}
\begin{array}{ll}
\psi^*(Y)= &
2\displaystyle \sum_{i=1}^{s-1} {\rm Tr}(Q_{a_i}^TH(X-\varpi_iI)^{\dag}HQ_{a_i})
+2\displaystyle \sum_{i=s+1}^{r} {\rm Tr}(Q_{a_i}^TH(X-\varpi_iI)^{\dag}HQ_{a_i})\\[14pt]
& + 2{\rm Tr}[(Q_{b_U}^THX^{\dag}HQ_{b_U})]
+2{\rm tr}[(Q_{b_L}^THX^{\dag}HQ_{b_L})]+2 \langle Q_{b_S}^T YQ_{b_S},Q_{b_S}^THX^{\dag}HQ_{b_S} \rangle.
\end{array}$$
[**Proof**]{}. Since $H \in {\cal C}_{\theta}(Z)$, we have from (\[eq:critical-Prox\]) that there exist $\widehat Q^s_U \in
{\cal O}(Q^{T}_{b_U}HQ_{b_U})$ and $\widehat Q^s_L \in
{\cal O}(Q^{T}_{b_L}HQ_{b_L})$ such that $$Q^s=\left
[
\begin{array}{ccc}
\widehat Q^s_U & 0 &0\\[2pt]
0 & I_{|b_S|} & 0\\[2pt]
0 & 0 & \widehat Q^s_L
\end{array}
\right
].$$ Then $Q^s_{b^k_+}$ and $Q^s_{b^k_+}$ can be expressed as $$Q^s_{b^k_+}=\left
[
\begin{array}{c}
\widehat Q^s_U\\
0\\
0
\end{array}
\right
] \mbox{ and } Q^s_{b^k_-}=\left
[
\begin{array}{c}
0\\
0\\
\widehat Q^s_L
\end{array}
\right
].$$ Then we obtain (\[eq:conj1\]) from (\[eq:conj\]). $\Box$
\[coro-simple-version\] Let $X,Y,Z,H \in {\cal S}^q$, $Z=X+Y$ satisfies $Y \in \partial \theta (X)$ and $H \in {\cal C}_{\theta}(Z)$. Then $$\label{eq:conj1n}
\psi^*(Y)
=2\displaystyle \sum_{i=1}^{r} \langle Q^T_{a_i}YQ_{a_i}, Q_{a_i}^TH(X-\varpi_iI)^{\dag}HQ_{a_i} \rangle,$$ or alternatively $$\label{eq:conj1ns}
\psi^*(Y)
=2\displaystyle \sum_{i \ne s}\displaystyle \frac{1}{\varpi_i} \langle Q^T_{b_s}YQ_{b_s}-I_{|b_s|}, Q_{b_s}^THQ_{a_i}Q_{a_i}^THQ_{b_s} \rangle.$$
We now discuss the differential of $[e_{\tau}\theta](X)$ for $\theta(X)=\|X\|_*$, where $[e_{\tau}\theta](X)$ is the Moreau-Yosida regularization defined by (\[eq:morea\]). Let proximal mapping of $\theta$ be defined by $$[{\cal P}_{\tau}\theta] (X)={\rm argmin}_{X' \in {\cal S}^q} \left\{\theta(X')+\displaystyle \frac{1}{\tau}\|X'-X\|^2\right\}.$$ For simplicity, we use ${\cal P}\theta$ to denote ${\cal P}_1\theta$. Then $[e_{\tau}\theta](X)$ is the spectral function corresponding to the Moreau-Yosida regularization $e_{\tau}\varsigma$, namely $$[e_{\tau}\theta](X)=[e_{\tau}\varsigma \circ \lambda](X).$$ It follows from [@Lewis95] or [@WDSun14] that $$[{\cal P}_{\tau}\theta](X)=P{\rm Diag}\,([{\cal P}_{\tau}\varsigma](\lambda(X)))P^T$$ or $[{\cal P}_{\tau}\theta]( X)$ is the Löwner operator associated with $p_{\tau}(t)=[t-\tau]_+-[-t-\tau]_+$, namely $$[{\cal P}_{\tau}\theta]( X)=Q{\rm Diag}\left(p_{\tau}(\lambda_1( X)),\cdots,p_{\tau}(\lambda_q( X))\right) Q^T.$$ Let $X$ have $r$ distinct eigenvalues, among them there are $r_1$ positive distinct eigenvalues and $r-r_1$ negative distinct eigenvalues and zero eigenvalues: $$\varpi_1>\varpi_2 > \cdots > \varpi_{r_1}>\varpi_{r_1+1}=0> \varpi_{r_1+2} > \cdots > \varpi_r.$$ Define $$a_k=\{i: \lambda_i(X)=\varpi_k\},\,\, k=1,\ldots, r$$ and the first divided difference matrix at $X$ along $H \in{\cal S}^q$ as follows for $k,l=1,\ldots, r$, $$\label{eq:ptdir}
(p_{\tau}^{[1]}(\Lambda (X), Q^THQ))_{a_ka_l}:=
\left
\{
\begin{array}{ll}
\displaystyle \frac{p_{\tau}(\varpi_k)-p_{\tau}(\varpi_l)}{\varpi_k-\varpi_l} Q_{a_k}^THQ_{a_l} & \mbox{if } k \ne l,\\[16pt]
\Psi_k(Q_{a_k}^THQ_{a_k}) & \mbox{if }k = l.
\end{array}
\right.$$ where $\Psi_k (\cdot)$ is the Löwner operator with respect to $\psi_k (\cdot)=p_{\tau}'(\varpi_k;\cdot)$. Then the directional derivative of ${\cal P}_{\tau}\theta$ at $X$ along $H \in{\cal S}^q$ is expressed as $$\label{eq:drD-prox}
[{\cal P}_{\tau}\theta]'(X;H)=Q [p_{\tau}^{[1]}(\Lambda (X), Q^THQ)]Q^T.$$
\[lem:proxSub\] Let $X,Y,Z,H \in {\cal S}^q$, $Z_{\tau}=X+\tau Y$ satisfies $Y \in \partial \theta (X)$. Then ${\cal P}_{\tau}\theta$ is strongly semismooth at $Z_{\tau}$ and for $W\in \partial {\cal P}_{\tau}\theta (Z_{\tau})$, there exist $W_{b_U}\in \partial \Pi_{{\cal S}^{|b_U|}_+}(0)$ and $W_{b_L}\in \partial \Pi_{{\cal S}^{|b_L|}_-}(0)$ such that $$\label{eq:VH}
\begin{array}{l}
W(H)=\\[8pt]
Q\left
[
\begin{array}{ccccc}
\widehat H_{aa} & \widehat H_{ab_U} & \widehat H_{ab_S} \circ (\Omega_{\tau})_{ab_S}
&\widehat H_{ab_L} \circ (\Omega_{\tau})_{ab_L} & \widehat H_{ac} \circ (\Omega_{\tau})_{ac}\\[8pt]
\widehat H_{b_Ua} & W_{b_U}(\widehat H_{b_Ub_U}) & 0 & 0 & \widehat H_{b_Uc} \circ (\Omega_{\tau})_{b_Uc}\\[8pt]
\widehat H_{b_Sa} \circ (\Omega_{\tau})_{b_Sa} & 0 & 0 & 0 & \widehat H_{b_Sc} \circ (\Omega_{\tau})_{b_Sc}\\[8pt]
\widehat H_{b_La}\circ (\Omega_{\tau})_{b_La} & 0 & 0 & W_{b_L}(\widehat H_{b_Lb_L})& \widehat H_{b_Lc} \\[8pt]
\widehat H_{ca}\circ (\Omega_{\tau})_{c a} & \widehat H_{cb_U}\circ (\Omega_{\tau})_{c b_U} & \widehat H_{cb_S}\circ (\Omega_{\tau})_{c b_S} & \widehat H_{cb_L}& \widehat H_{cc}
\end{array}
\right
]Q^T,
\end{array}$$ where $\widehat H=Q^THQ$, $$(\Omega_{\tau})_{ij}=[p_{\tau}^{[1]}(\Lambda (Z_{\tau}))]_{ij}, (i,j) \in a \times [b_S \cup b_L \cup c]
\mbox{ or } (i,j) \in c \times [ b_U \cup b_S].$$ In other words, $\nabla e_{\tau}\theta$ is strongly semismooth at $Z_{\tau}$ and for $V \in \partial \nabla e_{\tau}\theta (Z_{\tau})$, there exist $V_{b_U}\in \partial \Pi_{{\cal S}^{|b_U|}_-}(0)$ and $V_{b_L}\in \partial \Pi_{{\cal S}^{|b_L|}_+}(0)$ such that $$\label{eq:VH}
\begin{array}{l}
\tau V(H)=\\[8pt]
Q\left
[
\begin{array}{ccccc}
0 & 0 & \widehat H_{ab_S} \circ (\Delta_{\tau})_{ab_S}
&\widehat H_{ab_L} \circ (\Delta_{\tau})_{ab_L} & \widehat H_{ac} \circ (\Delta_{\tau})_{ac}\\[8pt]
0 & V_{b_U}(\widehat H_{b_Ub_U}) & \widehat H_{b_Ub_S} & \widehat H_{b_Ub_L} & \widehat H_{b_Uc} \circ (\Delta_{\tau})_{b_Uc}\\[8pt]
\widehat H_{b_Sa} \circ (\Delta_{\tau})_{b_Sa} &\widehat H_{b_Sb_U} & \widehat H_{b_Sb_S} & \widehat H_{b_Sb_L} & \widehat H_{b_Sc} \circ (\Delta_{\tau})_{b_Sc}\\[8pt]
\widehat H_{b_La}\circ (\Delta_{\tau})_{b_La} & \widehat H_{b_Lb_U} & \widehat H_{b_Lb_S} & V_{b_L}(\widehat H_{b_Lb_L})& 0 \\[8pt]
\widehat H_{ca}\circ (\Delta_{\tau})_{c a} & \widehat H_{cb_U}\circ (\Delta_{\tau})_{c b_U} & \widehat H_{cb_S}\circ (\Delta_{\tau})_{c b_S} & 0 & 0
\end{array}
\right
]Q^T,
\end{array}$$ where $\widehat H=Q^THQ$, $$\label{eq:Delta}
(\Delta_{\tau})_{ij}=1-[p_{\tau}^{[1]}(\Lambda (Z_{\tau}))]_{ij}, (i,j) \in a \times [b_S \cup b_L \cup c]
\mbox{ or } (i,j) \in c \times [ b_U \cup b_S].$$
Optimality conditions for (SDNOP)
---------------------------------
This subsection is devoted to studying optimality conditions for the following nonlinear semidefinite nuclear norm composite optimization problem (SDNOP) $$ \min \ f(x)+\theta (F(x))\quad
{\rm s.t.} \ h(x)=0\, ,
\ g(x) \in {\cal S}^p_+\, ,$$ where $\theta (X)=\|X\|_*$ is the nuclear norm function of $X \in {\cal S}^q$, $f:\Re^n\mapsto \Re$, $F: \Re^n \mapsto {\cal S}^q$, $h:\Re^n \mapsto \Re^m$ and $g:\Re^n \mapsto {\cal S}^p$ are twice continuously differentiable functions. Obviously, Problem (SDNOP) is a special case of (COP) with ${\cal Z}:={\cal S}^q$, $\theta (X):=\|X\|_*$, ${\cal Y}:={\cal S}^p$ and $K:={\cal S}^p_+$. The Lagrange function for (SDNOP) is $$L(x,Y,\mu,\Gamma)=f(x)+\langle Y, F(x)\rangle+
\langle \mu, h(x)\rangle- \langle \Gamma, g(x)\rangle\,\, (x,
Y,\mu, \Gamma)\in \Re^n \times {\cal S}^q \times \Re^m \times {\cal S}^p.$$ Then for any $(x, Y,\mu, \Gamma)\in \Re^n \times {\cal S}^q \times \Re^m \times {\cal
S}^p$, $$\nabla_xL(x,Y,\mu,\Gamma) =\nabla f(x) +{\rm D}F(x)^*Y+ {\cal J} h(x)^T\mu
-{\rm D}g(x)^* \Gamma.$$ If $x$ is a stationary point, the set of Lagrange multipliers at $x$ is defined by $$\Lambda (x)=\left\{(Y,\mu, \Gamma)\in {\cal S}^q \times \Re^m \times {\cal
S}^p:\begin{array}{l}
\nabla_x L(x,Y,\mu,\Gamma)=0, \\
Y \in \partial \theta(F(x)), \Gamma \in -{\cal N}_{{\cal S}^p_+}(g(x))
\end{array}
\right\}.$$ When discussing optimality conditions, we need some constraint qualifications. We say that Robinson constraint qualification holds at $\overline{x}$ if $$\left(\begin{array}{c}
{\cal J}h(\overline{ x})
\\
{\rm D}g(\overline{ x})
\end{array} \right)\Re^n
+\left(\begin{array}{c}
\{0\}
\\
\left({\cal T}_{ {\cal S}^p_+}(g(\overline{ x})) \right)
\end{array}\right) = \left(\begin{array}{c}
\Re^m\\
{\cal S}^p
\end{array}
\right).$$
The critical cone of Problem (SDNOP) at $x$ is defined by $${\cal C}(x)=\{d\in {\cal T}_{\Phi}(x): \nabla f(x)^Td+\theta'(F(x);{\rm D}F(x)d)\leq 0\}.$$ We can easily derive the following necessary optimality conditions and second-order sufficient optimality conditions.
\[nec-th\] If $\overline x \in \Phi$ is a local minimizer around which $f,F,h$ and $g$ are twice continuously differentiable and Robinson constraint qualification holds at $\overline x$. Then
- $\Lambda (\overline x)$ is non-empty, compact and convex.
- For any $d \in {\cal C}(\overline x)$, $$\displaystyle \sup_{y \in \Lambda (\overline x)} \left\{\left\langle d, \nabla^2_{xx}L(\overline{x},y)d \right \rangle-\psi^*(\overline Y)+
2\left \langle \overline \Gamma,[{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle\right\}
\geq 0,$$ where $\psi (W)=\theta''(F(\overline x);{\rm D}F(\overline x)d,W)$.
\[suf-th\] Let $\overline x$ be a feasible point around which $f,F,h$ and $g$ are twice continuously differentiable. Suppose the following conditions hold:
- $\Lambda (\overline x)$ is non-empty;
- For any $d \in {\cal C}(\overline x)\setminus \{0\}$, $$\displaystyle \sup_{y \in \Lambda (\overline x)}\left \{\left\langle d, \nabla^2_{xx}L(\overline{x},y)d \right \rangle-\psi^*(\overline Y)+
2\left \langle \overline \Gamma,[{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle\right\}
> 0,$$ where $\psi (W)=\theta''(F(\overline x);{\rm D}F(\overline x)d,W)$.
Then the second-order growth condition holds at $\overline x$.
Now we list our two assumptions for Problem (SDNOP), which will be used in the next section to derive Assumptions B1 and B2.\
[**Assumption (sdnop-A1)**]{}[@CDing2017]. The constraint nondegeneracy condition holds at $\overline{x}$: $$\label{eq:nondegeracy-SDP}
\left(\begin{array}{c}
{\rm D}F(\overline x)\\
{\cal J}h(\overline{ x})
\\
{\rm D}g(\overline{ x})
\end{array} \right)\Re^n
+\left(\begin{array}{c}
{\cal T}^{{\rm lin}}(F(\overline x))\\
\{0\}
\\
{\rm lin} \left({\cal T}_{ {\cal S}^p_+}(g(\overline{ x})) \right)
\end{array}\right) = \left(\begin{array}{c}
{\cal S}^q\\
\Re^m\\
{\cal S}^p
\end{array}
\right),$$ where $$\label{eq:Tlin}
{\cal T}^{{\rm lin}}(\overline X)=\{H \in {\cal S}^q: \theta'(\overline X;H)=-\theta'(\overline X;-H)\}=\{H \in {\cal S}^q: Q_{b}^THQ_{b}=0\}.$$
Assumption (sdnop-A1) is the analogue to the linear independence constraint qualification for nonlinear programming, which implies that ${\cal
M}(\overline{x})$ is a singleton [@BS00 Proposition 4.50].
[**Assumption (sdnop-A2)**]{} The strong second order sufficient condition holds at $\overline{x}$ : $$\left \langle d, \nabla^2_{xx}L(\overline{x},\overline Y,
\overline{\mu},\overline{\Gamma})d \right \rangle-\psi^*(\overline Y)+
2\left \langle \overline \Gamma, [{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle
>0, \quad \forall \, d \in {\rm app}(\overline Y,\overline{\mu},\overline{\Gamma}) \setminus \{0\}\, ,$$where $\psi (W)=\theta''(F(\overline x);{\rm D}F(\overline x)d,W)$ and $$\label{equation3.5}
\mbox{app} (\overline Y, \overline{\mu},\overline{\Gamma}):=\l\{d\in \Re^n:
\begin{array}{l} {\cal
J} h(\overline{x})d=0, \, {\rm D}F(\overline x)d \in \mbox{aff}({\cal C}_{\theta}(F(\overline x)+\overline Y))\\
{\rm D} g(\overline{x})d \in \mbox{aff}({\cal C}_{\S^p_+}(g(\overline{x})-\overline{\Gamma}))
\end{array}\r\}.$$ From the expressions ${\cal C}_{\theta}$ and ${\cal C}_{\S^p_+}$, we obtain the following expression of ${\rm app }(\overline Y, \overline{\mu},\overline{\Gamma})$: $$\label{equation3.5a}
{\rm app }(\overline Y, \overline{\mu},\overline{\Gamma})=\left\{d\in \Re^n:
\begin{array}{l}
Q_{b_S}^T({\rm D}F(\overline x)d)Q_b=0, Q_{b_U}^T({\rm D}F(\overline x)d)Q_{b_L}=0\\[6pt]
{\overline P}_{\alpha}^T({\cal J}
g(\overline{x})d){\overline P}_{\alpha}=0, {\overline
P}_{\alpha}^T({\cal J} g(\overline{x})d){\overline P}_{\beta}=0,{\cal J}
h(\overline{x}) d =0
\end{array}
\right\}.$$ 7 true pt At the end of this subsection, we list two technical results coming from [@SSZhang2008], which will be used in the next section.
\[lemma3.2nlp\][@SSZhang2008 Lemma 7] Let $\phi: {\cal X} \mapsto \Re$ be continuous and positive homogeneous of degree two: $$\phi (t d)=t^2 \phi (d), \quad \forall \, t \geq 0 \ {\rm and} \ d
\in {\cal X} \, .$$ Suppose that there exists a positive number $\eta_0>0$ such that for any $d$ satisfying ${\cal L}d=0$, one has $\phi (d) \geq \eta_0
\|d\|^2$, where ${\cal L}: {\cal X} \mapsto {\cal Y} $ is a given linear operator. Then there exist positive numbers $\underline{\eta} \in (0, \eta_0]$ and $c_0
>0$ such that $$\phi (d)+c_0 \langle {\cal L}d, {\cal L}d\rangle \geq
\underline{\eta} \langle d, d\rangle, \quad \forall \, d \in {\cal X} \, .$$
\[phiineq\][@SSZhang2008 Lemma 8] Let $a,b,c,$ and $c_0$ be four positive scalars with $c\ge c_0$. Let $$\label{phicom}
\psi(t;c,a,b,c_0):=a- \frac{1}{c}t+\frac{t^2}{b+(c-c_0)t}\, ,
\quad t \in [0,1]\, .$$ Then, for any $c \geq \max \big\{c_0,(b-c_0)^2/c_0\big\}$, $\psi (\cdot;c,a,b,c_0)$ is a convex function on $[0,1]$, $$\label{k4com}
\min_{t \in [0,1]} \psi(t;c,a,b,c_0)=a-\frac{1}{c}
\frac{b}{(\sqrt{c}+\sqrt{c_0})^2}\, ,$$ and $$\label{u4com}
\max_{t \in [0,1]} \psi(t;c,a,b,c_0)= \max
\Big\{\psi(0;c,a,b,c_0), \, \psi(1; c,a,b,c_0)\Big\} \, .$$
On the augmented Lagrange method for SDNOP {#NLSDP-case}
============================================
This section is devoted to studying the rate of convergence of the augmented Lagrange method for Problem (SDNOP). Let $(\overline{x}, \overline Y, \overline{\mu},
\overline{\Gamma}) \in \Re^n \times {\cal S}^q \times \Re^m \times {\cal S}^p$ be a given KKT point. Then, $(\overline{x},\overline Y, \overline{\mu},
\overline{\Gamma})$ satisfies $$\label{nlsdp:KKT}
\nabla_xL(\overline{x},\overline Y, \overline{\mu},
\overline{\Gamma})=0, \ \overline Y \in \partial \theta (F(\overline x),\ h(\overline{x})=0, \ \overline{\Gamma} \succeq 0,
\ g(\overline{x})\succeq 0\,\, {\rm and}\,\, \langle
\overline{\Gamma}, g(\overline{x})\rangle =0.$$ Let $\overline X=F(\overline x)$ and $\overline Y\in \partial \theta (\overline X)$. Define the following three index sets: $$a=\{i: \lambda_i(\overline X)>0\},\,\, b=\{i: \lambda_i(\overline X)=0\},\,\, c=\{i: \lambda_i(\overline X)<0\},$$ then $$\overline X=Q \left[ \begin{array}{ccc} \Lambda_a & 0 & 0 \\
[5pt] 0 & 0 & 0 \\ [5pt] 0 & 0 & \Lambda_c
\end{array} \right]Q^T {\hspace{1pc}}\mbox{and } Q \in {\cal O}(\overline X) \mbox{ with }
Q \, = \, [ \begin{array}{ccc}Q_a &
Q_{b} & Q_{c}
\end{array} ]$$ with $Q_{a} \in \Re^{q \times |a|}$, $Q_{b} \in \Re^{q \times |b|}$, and $Q_{c} \in \Re^{q \times |c|}$. Then there exists $w \in \partial \varsigma (\lambda (\overline X))$ satisfying $\overline Y=Q{\rm Diag}(w)Q^T$ and $w$ has the following relations $$w_a =\textbf{1}_{|a|}, w_{c}=-\textbf{1}_{|c|} \mbox{ and } -\textbf{1}_{|b|}\leq w_{b}\leq \textbf{1}_{|b|}.$$ For the index set $b$, we partition it as follows $b=b_L \cup b_S \cup b_U$: $$b_L=\{i\in b: w_i=-1\}, b_S=\{i\in b: -1< w_i< 1\},b_U=\{i\in b: w_i=1\}.$$ Then $\overline Y$ can be expressed as follows: $$\label{eq:dec-Ya}
\overline Y=
\left (Q_{a\cup_{b_U}} \quad Q_{b_S} \quad Q_{c\cup_{b_L}} \right)
\left[ \begin{array}{ccc}
I_{|a\cup_{b_U}|} & 0& 0\\
0 & {\rm Diag}\,(w_{b_S}) & 0 \\
0 & 0 & I_{|c\cup_{b_L}|}
\end{array}
\right
]
\left
(
\begin{array}{c}
Q_{a\cup_{b_U}}^T\\[4pt]
Q^T_{b_S}\\[4pt]
Q_{c\cup_{b_L}}^T
\end{array}
\right)$$ with $Q_{a\cup_{b_U}} \in \Re^{q \times |a\cup_{b_U}|}$, $Q_{b_S} \in \Re^{q \times |b_S|}$, and $Q_{c\cup_{b_L}} \in \Re^{q \times |c\cup_{b_L}|}$.
Let $\overline{M}: =\overline{\Gamma}-g(\overline{x})$. Suppose that $\overline{M}$ has the spectral decomposition as in (\[eq:orthogonal-decomposition\]), i.e, $\overline{M} = P \Lambda
P^T$. Define three index sets of positive, zero, and negative eigenvalues of $\overline{M} $, respectively, as $$\alpha := \{ i \, | \, \lambda_i > \, 0 \}, {\hspace{1pc}}\beta := \{
i \, | \, \lambda_i \, = \, 0 \}, {\hspace{1pc}}\gamma := \{ i \, | \,
\lambda_i \, < \, 0 \}.$$ Write $$\Lambda = \left[ \begin{array}{ccc} \Lambda_{\alpha} & 0 & 0 \\
[5pt] 0 & 0 & 0 \\ [5pt] 0 & 0 & \Lambda_{\gamma}
\end{array} \right] {\hspace{1pc}}\mbox{and} {\hspace{1pc}}P \, = \, [ \begin{array}{ccc} P_{\alpha} &
P_{\beta} & P_{\gamma}
\end{array} ]$$ with $P_{\alpha} \in \Re^{p \times |\alpha|}$, $P_{\beta} \in \Re^{p \times |\beta|}$, and $P_{\gamma} \in \Re^{p \times |\gamma| }$. From (\[nlsdp:KKT\]), we know that $\overline{\Gamma} g(\overline{x}) =
g(\overline{x}) \overline{\Gamma}=0$. Thus, we have $$\overline{\Gamma} = P
\left[
\begin{array}{ccc} \Lambda_{\alpha} & 0 & 0 \\ [5pt] 0 & 0 & 0 \\
[5pt] 0 & 0 & 0
\end{array} \right] P^T \, , \quad
g(\overline{x}) = P \left[ \begin{array}{ccc} 0& 0 & 0
\\ [5pt] 0 & 0 & 0
\\ [5pt] 0 & 0 & -\Lambda_{\gamma}
\end{array} \right] P^T$$ $$\label{eq:Zc}
\overline{\Gamma}- t g(\overline{x}) =P\left[
\begin{array}{ccc} \Lambda_{\alpha} & 0 & 0 \\ [5pt] 0 & 0 & 0 \\
[5pt] 0 & 0 & t\Lambda_{\gamma}
\end{array} \right] P^T \, .$$ For $\overline X=F(\overline x)$, let $$\label{eq:two-nus}
\begin{array}{ll}
\underline{\nu}_{a,b_S} :=\displaystyle\min_{i\in a, 1\leq j\leq |b_S|}\displaystyle \frac{1-(w_b)_j}{\lambda_i(\overline X)}
& \overline{\nu}_{\alpha,\gamma} :=\max_{i\in a, 1\leq j\leq |b_S|} \displaystyle \frac{1-(w_b)_j}{\lambda_i(\overline X)};\\[4mm]
\underline{\nu}_{a,b_L} :=\displaystyle \min_{i\in a} \displaystyle \frac{2}{\lambda_i(\overline X)}
& \overline{\nu}_{a,b_L} :=\max_{i\in a} \displaystyle \frac{2}{\lambda_i(\overline X)};\\[4mm]
\underline{\nu}_{a,c} :=\displaystyle\min_{i\in a, j\in c}\displaystyle \frac{2}{\lambda_i(\overline X)-\lambda_j(\overline X)}
& \overline{\nu}_{a,c} :=\max_{i\in a, j\in c}\displaystyle \frac{2}{\lambda_i(\overline X)-\lambda_j(\overline X)};\\[4mm]
\underline{\nu}_{c,b_U} :=\displaystyle\min_{i\in c}\displaystyle \frac{2}{-\lambda_i(\overline X)}
& \overline{\nu}_{c,b_U} :=\displaystyle\max_{i\in c}\displaystyle \frac{2}{-\lambda_i(\overline X)};\\[4mm]
\underline{\nu}_{c,b_S} :=\displaystyle\min_{i\in c, 1\leq j\leq |b_S|}\displaystyle \frac{1+(w_{b_S})_j}{-\lambda_i(\overline X)}
& \overline{\nu}_{c,b_U} :=\displaystyle\max_{i\in c, 1\leq j\leq |b_S|}\displaystyle \frac{1+(w_{b_S})_j}{-\lambda_i(\overline X)};\\[4mm]
\underline{\nu}_{\alpha,\gamma} :=\displaystyle \min_{i\in\alpha, j\in \gamma} \lambda_i
/|\lambda_j| & \overline{\nu}_{\alpha,\gamma} :=\displaystyle \max_{i\in\alpha, j\in
\gamma} \lambda_i / |\lambda_j|
\end{array}$$ and $$\label{nu0}
\begin{array}{l}
\underline{\nu}_0=\min\{\underline{\nu}_{a,b_S},\underline{\nu}_{a,b_L},\underline{\nu}_{a,c},
\underline{\nu}_{c,b_U},\underline{\nu}_{c,b_S},\underline{\nu}_{\alpha,\gamma}\};\\[4mm]
\overline{\nu}_0=\min\{\overline{\nu}_{a,b_S},\overline{\nu}_{a,b_L},\overline{\nu}_{a,c},
\overline{\nu}_{c,b_U},\overline{\nu}_{c,b_S},\overline{\nu}_{\alpha,\gamma}\}.
\end{array}$$
For a given symmetric matrix $M$, we use ${\rm vec}(M)$ to denote the vector obtained by stacking up all the columns of a given matrix $M$ and ${\rm svec}(M)$ to denote the vector obtained by stacking up all the columns of the upper triangular part of $M$.
Let $Q\in {\cal O}(\overline X)$ with $Q=[Q_a\,\, Q_{b_U}\,\, Q_{b_S} \,\, Q_{b_L} \,\, Q_c]$. For index sets $\chi, {\chi'} \in \{a, b_U,b_S,b_L,c\}$, let $$B_{(\chi,\chi')}(Q):=\Big(\mbox{vec}(Q_{\chi}^T{\cal J}_{x_1}
F(\overline{x})Q_{\chi'}) \,\, \cdots \,\,
\mbox{vec}(Q_{\chi}^T{\cal J}_{x_n}
F(\overline{x})Q_{\chi'})\Big)\,$$and $${\widehat B}_{(\chi,\chi)}(Q):=\Big(\mbox{svec}(Q_{\chi}^T{\cal
J}_{x_1} F(\overline{x})Q_{\chi} )\,\, \cdots \,\,
\mbox{svec}(Q_{\chi}^T{\cal J}_{x_n} F(\overline{x})Q_{\chi}
)\Big).$$ Let $P\in {\cal O}(g(\overline x))$ with $
P=[ P_\alpha\ P_\beta \
P_\gamma]$. For index sets $\chi, {\chi'} \in \{\alpha,\beta,\gamma\}$, let $$C_{(\chi,\chi')}(P):=\Big(\mbox{vec}(P_{\chi}^T{\cal J}_{x_1}
g(\overline{x})P_{\chi'}) \,\, \cdots \,\,
\mbox{vec}(P_{\chi}^T{\cal J}_{x_n}
g(\overline{x})P_{\chi'})\Big)\,$$and $${\widehat C}_{(\chi,\chi)}(P):=\Big(\mbox{svec}(P_{\chi}^T{\cal
J}_{x_1} g(\overline{x})P_{\chi} )\,\, \cdots \,\,
\mbox{svec}(P_{\chi}^T{\cal J}_{x_n} g(\overline{x})P_{\chi}
)\Big).$$ Define $$n_1:=m+|b|(|b|+1)/2 \, , \
n_2:=n_1+(|\alpha|+|\beta|)(|\alpha|+|\beta|+1)/2 \, , \ n_3:=n-n_2\,
,$$ and $$A(Q,P):=\left ( \begin{array}{c}
{\cal J} h(\overline{x})\\
{\widehat B}_{(b_U,b_U)}(Q)\\
B_{(b_U,b_S)}(Q)\\
B_{(b_U,b_L)}(Q)\\
{\widehat B}_{(b_S,b_S)}(Q)\\
B_{(b_S,b_L)}(Q)\\
{\widehat B}_{(b_L,b_L)}(Q)\\
-{\widehat C}_{(\alpha,\alpha)}(P)\\
-{\widehat C}_{(\beta,\beta)}(P)\\
- C_{(\alpha,\beta)}(P)
\end{array}
\right
)\, .$$ Suppose that Assumption (sdnop-A1) holds. Then by (\[eq:nondegeracy-SDP\]) in Assumption (sdnop-A1) we know that $A(Q,P)$ is of full row rank. Let $A(Q,P)$ have the following singular value decomposition: $$\label{singvalu}
A(Q,P)=U[\Sigma (Q,P)\,\,\,\,\, 0]R^T\, ,$$ where $U \in \Re^{n_2 \times n_2}$ and $R \in \Re^{n \times n}$ are orthogonal matrices, $\Sigma(Q,P)=\mbox{Diag}
\Big(\sigma_1(A(Q,P)),\cdots,$ $ \sigma_{n_2}(A(Q,P))\Big)$, and $\sigma_1(A(Q,P))\geq \sigma_2(A(Q,P)) \geq $ $ \cdots $ $\geq
\sigma_{n_2}(A(Q,P))>0$ are the singular values of $A(Q,P)$. It should be pointed out here that $U$ and $R$ also depend on $(Q,P)$. But for the sake of notational simplification, we drop the argument $(Q,P)$ from $U$ and $R$ in our analysis below.
Let $$\underline{\sigma}:=\min\left\{1, \min_{Q \in {\cal O}(\overline X),P \in {\cal O}(\overline M)} \min_{1
\leq i \leq n_2} \sigma_i^{-2}(A(Q,P))\right\}$$ and $$\overline{\sigma}:=\max\left\{1, \max_{Q \in {\cal O}(\overline X),P \in {\cal O}(\overline M)} \max_{1
\leq i \leq n_2}\sigma_i^{-2}(A(Q,P))\right \}\, .$$Then, since ${\cal O}(\overline X)$ and ${\cal O}(\overline M)$ are compact sets and $\Sigma(Q,P)$ changes continuously with respect to $(Q,P)$, both $\underline{\sigma}$ and $\overline{\sigma}$ are finite positive numbers. Define $$C=\left
[
\begin{array}{c}
B_{(a,b_S)}\\
B_{(a,b_L)}\\
B_{(a,c)}\\ B_{(c,b_U)}\\
B_{(c,b_S)}\\
- C_{(\alpha,\gamma)}\\
\end{array}
\right].$$ Thus there exist numbers $\underline{\nu} \geq 0$ and $\overline{\nu}>0$ such that for any $Q\in {\cal O}(\overline X)$, $P\in {\cal O}(\overline M)$ and $s\in \Re^{|a||b_S|+|a||b_L|+|a||c|+|c||b_U|+|\alpha||\gamma|}$, $$\label{eq:nu-lower-upper}
\underline{\nu} \|s\|^2 \leq \max\left\{ \left\langle s,
\widetilde{C}(Q,P)(\widetilde{C}^{\,
T}(Q,P)) s \right\rangle, \left\langle s,
C C^Ts \right\rangle
\right\}
\le \overline{\nu}\|s\|^2\, ,$$ where $$\widetilde{C}(Q,P):=C\widetilde{R}
\quad {\rm and} \quad \widetilde{R}:=R\left [
\begin{array}{cc}
\Sigma(Q,P)^{-1}U^T & 0 \\ 0 & I_{n_3}
\end{array}
\right ].$$ When no ambiguity arises, we often drop $Q$ and $P$ from $A(Q,P)$, $B_{(\chi,\chi')}(Q)$, $\widehat{B}_{(\alpha,\gamma)}(Q)$. $C_{(\chi,\chi')}(Q)$, and $\widehat{C}_{(\alpha,\gamma)}(P)$. Let $c>0$ and $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$, there exist matrices $Q\in {\cal O}(F(\overline x))$ and $\Delta_{1/c} \in {\cal S}^q$ such that $$\label{eq:w1h}
W_1(H_1)= Q\left( \Delta_{1/c} \circ (Q^TH_1Q)\right )Q^T,\quad \forall \, H_1
\in {\cal S}^q\, .$$ with the entries of $\Delta_{\tau}$ being given by $$\label{Shc}
\left\{ \begin{array}{ll}
(\Delta_{\tau})_{ij} =1-[p_{\tau}^{[1]}(\Lambda (Z_{\tau}))]_{ij}, & (i,j) \in a \times [b_S \cup b_L \cup c]
\mbox{ or } (i,j) \in c \times [ b_U \cup b_S]
\\[2mm]
(\Delta_{\tau})_{ij} \in [0,1], & (i, j) \in
b_U\times b_U \mbox{ or } (i,j) \in b_L\times b_L.
\end{array} \right.$$ It can be easily verified, for $\overline X=F(\overline x)$, that $$\label{eq:dDeltac}
[{\Delta_{1/c}}]_{ij}=\left
\{
\begin{array}{ll}
\quad \quad 0 & (i,j)\in (a\times a \cup b_U)\cup (c \times b_L\cup c),\\[12pt]
\displaystyle \frac{c^{-1}(1-(w_{b_S})_j)}{\lambda_i(\overline X)+c^{-1}(1-(w_{b_S})_j)} & (i,j)\in a\times \{1,\ldots,|b_S|\},\\[12pt]
\displaystyle \frac{2c^{-1}}{\lambda_i(\overline X)+2c^{-1}} & (i,j)\in a\times b_L,\\[12pt]
\displaystyle \frac{2c^{-1}}{\lambda_i(\overline X)-\lambda_j(\overline X)+2c^{-1}} & (i,j)\in a\times c,\\[12pt]
\displaystyle \frac{2c^{-1}}{-\lambda_j(\overline X)+2c^{-1}} & (i,j)\in b_U\times c,\\[12pt]
\displaystyle \frac{c^{-1}((w_{b_S})_i+1)}{c^{-1}((w_{b_S})_i+1)-\lambda_j(\overline X)} & (i,j)\in \{1,\ldots,|b_S|\}\times c.
\end{array}
\right.$$ Let $c>0$ and $W_2 \in \partial_B \Pi_{{\cal
S}^p_+}(\overline{\Gamma}-cg(\overline{x}))$. Define $\lambda_c \in
\Re^p$ as $$(\lambda_c)_i := \left\{
\begin{array}{ll} \lambda_i & {\rm if} \
i\in \alpha \cup \beta\, ,
\\
c \lambda_i & {\rm if} \ i\in \gamma\, .
\end{array} \right.$$ Then it follows from Lemma \[lemma:projector-Jacobian-cone\] that there exist two matrices $Q\in {\cal O}(\overline M)$ and $\Theta_c \in {\cal S}^p$ such that $$\label{wh}
W_2(H_2) = P\left( \Theta_c \circ (P^TH_2P)\right )P^T,\quad \forall \, H_2
\in {\cal S}^p\,$$ with the entries of $\Theta_c$ being given by $$\label{Sh}
\left\{ \begin{array}{ll}
(\Theta_c)_{ij} =\displaystyle
{\frac{\max\{(\lambda_c)_i,0\} + \max\{(\lambda_c) _j,0\}}{ | \,
(\lambda_c)_i \, | + | \, (\lambda_c)_j \, |}}& {\rm if}\ (i, j)
\notin \beta\times \beta\, ,
\\[2mm]
(\Theta_c)_{ij} \in [0,1] & {\rm if}\ (i, j) \in
\beta\times \beta\, .
\end{array} \right.$$ For index sets $\chi, {\chi'} \in \{a,b_U,b_S,b_L,c\}$, we introduce the following notation: $$(\Delta_{\tau})_{(\chi,\chi')}=\mbox{Diag} \left
(\mbox{vec}((\Delta_{\tau})_{\chi\chi'} )\right)\, , \ \ (\widehat
\Delta_{\tau})_{(\chi,\chi)}=\mbox{Diag} \left
(\mbox{svec}((\Delta_{\tau})_{\chi\chi} \circ E_{\chi\chi})\right),$$ where $``\circ"$ is the Hadamard product and $E$ is a matrix in ${\cal S}^q$ with entries being given by $$E_{ij} :=\left \{
\begin{array}{ll}
1 & {\rm if} \ i=j\, ,
\\
{2} & {\rm if} \ i\ne j\, .
\end{array}
\right.$$ For index sets $\chi, {\chi'} \in \{\alpha,\beta,\gamma\}$, we introduce the following notation: $$(\Theta_c)_{(\chi,\chi')}=\mbox{Diag} \left
(\mbox{vec}((\Theta_c)_{\chi\chi'} )\right)\, , \ \ ({\widehat
\Theta}_c)_{(\chi,\chi)}=\mbox{Diag} \left
(\mbox{svec}((\Theta_c)_{\chi\chi} \circ E'_{\chi\chi})\right)\, ,$$ where $E'$ is a matrix in ${\cal S}^p$ with entries being given by $$E'_{ij} :=\left \{
\begin{array}{ll}
1 & {\rm if} \ i=j\, ,
\\
{2} & {\rm if} \ i\ne j\, .
\end{array}
\right.$$ Let $$ D_c:=\left [
\begin{array}{ccccc}
I_{m} & 0 & 0 & 0 &0\\
0 & \Sigma_c & 0 & 0 &0\\
0 & 0 &({\widehat \Theta_c})_{(\alpha,\alpha)} & 0 & 0\\
0 & 0& 0& ({\widehat \Theta_c})_{(\beta,\beta)} &0 \\
0 & 0 & 0& 0& 2I_{|\alpha||\beta|}
\end{array}
\right ],$$ where $$\Sigma_c=\left
[
\begin{array}{ccc}(\widehat \Delta_{1/c})_{b_Ub_U} & 0 & 0\\
0 & 2I_{m_0} & 0\\
0 & 0 & ( \widehat \Delta_{1/c})_{b_Lb_L}
\end{array} \right ]$$ with $m_0=|b_U|(|b_S|+|b_L|)+|b_S|((|b_S|+1)/2+|b_L|)$.\
Let ${\cal A}_c(\overline Y,\overline{\mu}, \overline{\Gamma},W_1,W_2)$ be defined as (\[comac\]) for the semidefinite nuclear norm composite optimization problem (SDNOP), i.e, $$\begin{array}{ll}
{\cal A}_c(\overline Y,\overline{\mu}, \overline{\Gamma},W_1,W_2)=& \nabla^2_{xx}
L(\overline{x},\overline Y,\overline{\mu}, \overline{\Gamma})\\[3mm]
&+c {\cal J}
h(\overline{x})^T{\cal J} h(\overline{x}) +{\rm D}F(\overline x)^*W_1{\rm D}F(\overline x)+
c{\rm D}g(\overline{x})^*W_2{\rm D} g(\overline{x}).
\end{array}$$ A compact formula for ${\cal A}_c(\overline Y,\overline{\mu}, \overline{\Gamma},W_1,W_2)$ is given in the next lemma.
\[acpres\] The matrix ${\cal A}_c(\overline Y,\overline{\mu}, \overline{\Gamma},W_1,W_2)$ can be expressed equivalently as $$\label{acy}
\begin{array}{ll}{\cal A}_c(\overline Y,\overline{\mu}, \overline{\Gamma},W_1,W_2) =& \nabla^2_{xx}
L(\overline{x},\overline Y,\overline{\mu}, \overline{\Gamma})+c \left( {\cal J} h(\overline{x})^T
{\cal J} h(\overline{x})+2 B_{(b_U,b_S)}^{\, T} B_{(b_U,b_S)}\right.\\[2mm]
& \left.+2 B_{(b_U,b_L)}^{\, T} B_{(b_U,b_L)}
+\widehat B_{(b_S,b_S)}^{\, T}\widehat B_{(b_S,b_S)}+2 B_{(b_S,b_L)}^{\, T} B_{(b_S,b_L)}\right.\\[2mm]
&\left.+\widehat B_{(b_U,b_U)}^{\, T}(\widehat \Delta_{1/c})_{(b_U,b_U)}\widehat B_{(b_U,b_U)}+\widehat B_{(b_L,b_L)}^{\, T}(\widehat \Delta_{1/c})_{(b_L,b_L)}\widehat B_{(b_L,b_L)}\right.\\[2mm]
&\left.+2 B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)} B_{(a,b_S)}+2 B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)} B_{(a,b_L)}\right.\\[2mm]
&\left. +2 B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)} B_{(a,c)}+2 B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} B_{(c,b_U)}\right.\\[2mm]
&\left.+2 B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)} B_{(c,b_S)}+{\widehat C}^{\, T}
_{(\alpha,\alpha)}({\widehat
\Theta}_c)_{(\alpha,\alpha)}{\widehat C}_{(\alpha,\alpha)}\right. \\[2mm]
& \left. +2C_{(\alpha,\beta)}^{\, T} C_{(\alpha,\beta)} + 2
C_{(\alpha,\gamma)}^{\, T}
(\Theta_c)_{(\alpha,\gamma)}C_{(\alpha,\gamma)} +{\widehat
C}_{(\beta,\beta)}^{\, T} ({\widehat
\Theta}_c)_{(\beta,\beta)}{\widehat C}_{(\beta,\beta)}
\right)\, .
\end{array}$$
Lemma \[acpres\] shows that ${\cal
A}_c(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2)$ can be written as $$\label{acyy}
\begin{array}{l}
{\cal
A}_c(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2) = \nabla^2_{xx}
L(\overline x,\overline Y,\overline{\mu},\overline{\Gamma})+cA^TD_cA\\[2mm]
\quad \, +2c B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)} B_{(a,b_S)}+2c B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)} B_{(a,b_L)}\\[2mm]
\quad \, +2c B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)} B_{(a,c)}+2c B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} B_{(c,b_U)}\\[2mm]
\quad \,+2c B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)} B_{(c,b_S)}
+2cC_{(\alpha,\gamma)}^{\, T}
(\Theta_c)_{(\alpha,\gamma)}C_{(\alpha,\gamma)}\, .
\end{array}$$ For any $c^\prime, c>0$, let $$\label{eq:B-form}
\begin{array}{l}
{\cal B}_{c^\prime, c}(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2) = \nabla^2_{xx}
L(\overline x,\overline Y,\overline{\mu},\overline{\Gamma})+c'A^TD_cA\\[2mm]
\quad \, +2c B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)} B_{(a,b_S)}+2c B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)} B_{(a,b_L)}\\[2mm]
\quad \, +2c B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)} B_{(a,c)}+2c B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} B_{(c,b_U)}\\[2mm]
\quad \,+2c B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)} B_{(c,b_S)}
+2cC_{(\alpha,\gamma)}^{\, T}
(\Theta_c)_{(\alpha,\gamma)}C_{(\alpha,\gamma)}\, .
\end{array}$$
The following proposition shows that, under Assumptions (sdnop-A1) and (sdnop-A2), the basic Assumption B1 made in Section \[general-discussions\] is satisfied by nonlinear semidefinite nuclear norm composite optimization problem.
\[pronlsdp\] Suppose that Assumptions (sdnop-A1) and (sdnop-A2) are satisfied. Then there exist two positive numbers $c_0 $ and $\underline{\eta} $ such that for any $c \geq c_0$ and $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$, $W_2 \in
\partial_B \Pi_{{\cal S}^p_+}(\overline{\Gamma}-c g(\overline{x}))$, $$\left \langle d,{\cal
A}_c(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2)
d\right\rangle\ge \left \langle d,{\cal B}_{c_0,
c}(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2) d\right\rangle \geq
\underline{\eta}\langle d, d\rangle, \quad \forall \, d\in \Re^n\, .$$
[**Proof.**]{} It follows from Assumption (sdnop-A2) that there exists $\eta_0 >0$ such that $$\label{secnlp9-secnlp9}
\left \langle d, \nabla^2_{xx}L(\overline{x},\overline Y,
\overline{\mu},\overline{\Gamma})d \right \rangle-\psi^*(\overline Y)+
2\left \langle \overline \Gamma, [{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle
\geq \eta_0 \|d\|^2$$ for all $d \in {\rm app}(\overline Y,\overline{\mu},\overline{\Gamma}) \setminus \{0\}$. By (\[equation3.5\]), we obtain $$\label{equation3.20}
\begin{array}{ll}
\mbox{app }(\overline Y,\overline{\mu},\overline{\Gamma})
&=\left\{d \in \Re^n: \begin{array}{l}
{\cal J} h(\overline{x}) d =0,
B_{(b_U,b_S)}(Q)d=0,
B_{(b_U,b_L)}(Q)d=0\\[4pt]
{\widehat B}_{(b_S,b_S)}(Q)d=0,
B_{(b_S,b_L)}(Q)d=0\\[4pt]
{\widehat C}_{(\alpha,
\alpha)}(P)d=0 \, , \ C_{(\alpha, \beta)} (P)d = 0
\end{array}
\right\}\, .
\end{array}$$ Since (\[secnlp9-secnlp9\]) and (\[equation3.20\]) hold, by using Lemma \[lemma3.2nlp\] with $\phi$ and ${\cal L}$ being defined by $$\phi (d):=\langle d, \nabla^2_{xx}L(\overline{x},
\overline Y,\overline{\mu},\overline{\Gamma})d \rangle-\psi^*(\overline Y)+
2\left \langle \overline \Gamma, [{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle$$ and $${\cal L}(d):=({\cal J} h(\overline{x})d;B_{(b_U,b_S)}(Q)d;
B_{(b_U,b_L)}(Q)d;
{\widehat B}_{(b_S,b_S)}(Q)d;
B_{(b_S,b_L)}(Q)d;{\widehat C}_{(\alpha,
\alpha)}(P)d;C_{(\alpha, \beta)}(P)d),$$ for any $d\in
\Re^n$, respectively, we know that there exist two positive numbers $c_1$ and $\underline{\eta} \in (0, \eta_0/2]$ such that for any $c\ge c_1$, $$\label{eq:upgrade}
\begin{array}{l}
\left \langle d, \nabla^2_{xx}L(\overline{x},\overline Y,
\overline{\mu},\overline{\Gamma})d \right \rangle-\psi^*(\overline Y)+
2\left \langle \overline \Gamma, [{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle
\\[2mm]
\quad +c\|B_{(b_U,b_S)}(Q)d\|^2+c\|B_{(b_U,b_L)}(Q)d\|^2+c\|{\widehat B}_{(b_S,b_S)}(Q)d\|^2+c\|B_{(b_S,b_L)}(Q)d\|^2
\\[2mm]
\quad +c\|{\cal J} h(\overline{x}) d\|^2 +c \|{\widehat
C}_{(\alpha, \alpha)}(P)d\|^2 + c \|C_{(\alpha,
\beta)}(P)d\|^2
\geq
2 \underline{\eta} \|d\|^2,\quad \forall \, d \in \Re^n\, .
\end{array}$$
Let $c_0 \ge c_1$ be such that for any $c \geq c_0$, $$\label{equation3.21}
\begin{array}{l}
\displaystyle \max_{1 \leq l \leq n} \|{\cal J}_{x_l} F(\overline{x})\|^2
\sum_{i \in a, 1\leq j \leq |b_S|} \frac{c^{-1}(1-(w_{b_S})_j)^2}{\lambda_i(F(\overline x))(\lambda_i(F(\overline x))+c^{-1}(1-(w_{b_S})_j))} \leq \underline{\eta}/4,\\
\displaystyle \max_{1 \leq l \leq n} \|{\cal J}_{x_l} g(\overline{x})\|^2
\sum_{i \in \gamma, j \in \alpha} \frac{\lambda_j^2}{|\lambda_i|
(\lambda_j+c |\lambda_i|)} \leq \underline{\eta}/4.
\end{array}$$ Let $c\ge c_0$ and $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$, $W_2 \in
\partial_B \Pi_{{\cal S}^p_+}(\overline{\Gamma}-c g(\overline{x}))$. Then there exist two matrices $Q\in {\cal O}(F(\overline x))$ and $P\in {\cal O}(g(\overline x))$ and $\Delta_{1/c} \in {\cal S}^q$ satisfying (\[Shc\]) and $\Theta_c \in {\cal S}^p$ satisfying (\[Sh\]) such that $$W_1(H_1)= Q\left( \Delta_{1/c} \circ (Q^TH_1Q)\right )Q^T,\quad \forall \, H_1
\in {\cal S}^q\, .$$ and $$W_2(H_2) = P\left( \Theta_c \circ (P^TH_2P)\right )P^T,\quad \forall \, H_2
\in {\cal S}^p\, .$$ It is easy to see from (\[equation3.21\]) that for any $c
\ge c_0$ and $d\in \Re^n$ we have for $H_1={\rm D}F(\overline x)d$ and $\widehat H_1=Q^TH_1Q$ that $$\begin{array}{l}
-\psi^*(\overline Y)-2c \langle d, [ B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)} B_{(a,b_S)}]d \rangle\\[2mm]
=2\displaystyle \sum_{i \ne s}\displaystyle \frac{1}{\varpi_i} \langle I_{|b_s|}-Q^T_{b_s}YQ_{b_s}, Q_{b_s}^TH_1Q_{a_i}Q_{a_i}^THQ_{b_s} \rangle-2c \langle d, [ B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)} B_{(a,b_S)}]d \rangle\\[2mm]
=2 \displaystyle \sum_{i\ne s}\sum_{j=1}^{|b_S|}\frac{1-(w_{b_S})_j}{\varpi_i}\|Q_{a_i}^TH_1(Q_{b_S})_j\|^2-2c \displaystyle \sum_{i=1}^{s-1}\langle Q_{a_i}^TH_1Q_{b_S}\circ \Delta_{a_ib_S},Q_{a_i}^TH_1Q_{b_S} \rangle\\[2mm]
\leq 2\displaystyle \sum_{i=1}^{s-1}\sum_{j=1}^{|b_S|}\frac{1-(w_{b_S})_j}{\varpi_i}\|Q_{a_i}^TH_1(Q_{b_S})_j\|^2-2c \displaystyle \sum_{i=1}^{s-1}\langle Q_{a_i}^TH_1Q_{b_S}\circ \Delta_{a_ib_S},Q_{a_i}^TH_1Q_{b_S} \rangle\\[2mm]
=2\displaystyle \sum_{i=1}^{s-1}\sum_{j=1}^{|b_S|}\frac{1-(w_{b_S})_j}{\varpi_i}\|Q_{a_i}^TH_1(Q_{b_S})_j\|^2-2\displaystyle \sum_{i=1}^{s-1}\sum_{j=1}^{|b_S|}\frac{1-(w_{b_S})_j}{\varpi_i+c^{-1}(1-(w_{b_S})_j)}\|Q_{a_i}^TH_1(Q_{b_S})_j\|^2\\[2mm]
=2\displaystyle \sum_{i\in a}\sum_{j=1}^{|b_S|}\frac{c^{-1}(1-(w_{b_S})_j)^2}{\lambda_i(F(\overline x))(\lambda_i(F(\overline x)+c^{-1}(1-(w_{b_S})_j))}\|Q_i^T[{\rm D}F(\overline x)d](Q_{b_S})_j\|^2\end{array}$$ $$\begin{array}{l}
=2\displaystyle \sum_{i\in a}\sum_{j=1}^{|b_S|}\frac{c^{-1}(1-(w_{b_S})_j)^2}{\lambda_i(F(\overline x))(\lambda_i(F(\overline x)+c^{-1}(1-(w_{b_S})_j))}\displaystyle \sum_{l=1}^n[Q_i^T[{\cal J}_{x_l}F(\overline x)](Q_{b_S})_jd_l]^2\\[2mm]
\leq 2\displaystyle \sum_{i\in a}\sum_{j=1}^{|b_S|}\frac{c^{-1}(1-(w_{b_S})_j)^2}{\lambda_i(F(\overline x))(\lambda_i(F(\overline x)+c^{-1}(1-(w_{b_S})_j))}\displaystyle \sum_{l=1}^n\|Q_i\|^2\|[{\cal J}_{x_l}F(\overline x)]\|^2\|(Q_{b_S})_j\|^2d_l^2\\[2mm]
\leq \displaystyle \max_{1 \leq l \leq n} \|{\cal J}_{x_l} F(\overline{x})\|^2
\sum_{i \in a, 1\leq j \leq |b_S|} \frac{c^{-1}(1-(w_{b_S})_j)^2}{\lambda_i(F(\overline x))(\lambda_i(F(\overline x))+c^{-1}(1-(w_{b_S})_j))}\|d\|^2\\
\leq \underline{\eta}
\|d\|^2/2.
\end{array}$$ Similarly, we have from (\[equation3.21\]) that for any $c
\ge c_0$ and $d\in \Re^n$ that $$\begin{array}[b]{l}
\quad 2\left \langle \overline \Gamma, [{\rm D}g(\overline x)d]g(\overline x)^\dag [{\rm D}g(\overline x)d]\right
\rangle -2c \left\langle d, C^{\, T}_{(\alpha,\gamma)}
(\Theta_c)_{(\alpha,\gamma)}C_{(\alpha,\gamma)} d \right\rangle
\\[2mm]
\displaystyle
= 2 \left\langle \overline{\Gamma}, [{\rm D}g(\overline{x})d]
g(\overline{x})^{\dagger}[{\rm D}g(\overline{x})d] \right\rangle
-2c \left\langle d, C^{\, T}_{(\alpha,\gamma)}
(\Theta_c)_{(\alpha,\gamma)}C_{(\alpha,\gamma)} d \right\rangle
\\[2mm]
\displaystyle
= 2 \sum_{i \in \gamma, j \in
\alpha} \frac{\lambda_j}{ |\lambda_i| } \left(\sum_{l=1}^n P_i^T
{\cal J}_{x_l} g(\overline{x}) P_j d_l\right)^2 -2 c \sum_{i \in
\gamma, j \in \alpha} \frac{\lambda_j}{\lambda_j+c |\lambda_i| }
\sum_{l=1}^n \left(P_i^T {\cal J}_{x_l} g(\overline{x}) P_j
d_l\right)^2
\\[2mm]\displaystyle
\leq 2\sum_{i \in \gamma, j \in
\alpha}\left[\frac{\lambda_j^2}{|\lambda_i|(\lambda_j+c
|\lambda_i|)}\sum_{l=1}^n \|{\cal J}_{x_l} g(\overline{x})\|^2
\|P_i\|^2\|P_j\|^2d_l^2\right]
\\[2mm]\displaystyle
\leq 2 \max_{1 \leq l \leq n}\|{\cal J}_{x_l}
g(\overline{x})\|^2\sum_{i \in \gamma, j \in
\alpha}\frac{\lambda_j^2}{|\lambda_i|(\lambda_j+c
|\lambda_i|)} \|d\|^2\\[2mm] \displaystyle\leq \underline{\eta}
\|d\|^2/2\, ,
\end{array}$$ Therefore, we have from (\[eq:upgrade\]), for any $c\ge c_0$, that $$\label{eq:eta-one-form}
\begin{array}{l}
\langle d, \nabla^2_{xx}L(\overline{x},\overline Y,
\overline{\mu},\overline{\Gamma})d \rangle+2c \langle d, [ B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)} B_{(a,b_S)}]d \rangle\\[2mm]
\quad +c_0\|B_{(b_U,b_S)}(Q)d\|^2+c_0\|B_{(b_U,b_L)}(Q)d\|^2+c_0\|{\widehat B}_{(b_S,b_S)}(Q)d\|^2\\[2mm]
+c_0\|B_{(b_S,b_L)}(Q)d\|^2
+2c \left\langle d,
C_{(\alpha,\gamma)}^{\, T}
(\Theta_c)_{(\alpha,\gamma)}C_{(\alpha,\gamma)} d \right\rangle
\\[2mm]
\quad +c_0\|{\cal J} h(\overline{x}) d\|^2 +c_0 \|{\widehat
C}_{(\alpha, \alpha)}(P)d\|^2 + c_0 \|{C}_{(\alpha,
\beta)}(P)d\|^2
\geq
\underline{\eta} \|d\|^2, \quad \forall \, d \in \Re^n\, .
\end{array}$$ In view of the expression $(\Delta_{1/c})_{ij}$ from (\[eq:dDeltac\]) for $(i,j) \in (a \times b_L)\cup (a\times \{1,\ldots,|b_S|\})\cup (a \times c)\cup (b_U \times c)\cup (\{1,\ldots,|b_S|\} \times c)$, we obtain $$\begin{array}{rl}
B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)} B_{(a,b_L)}\succeq 0, &
B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)} B_{(a,c)}\succeq 0,\\[2mm]
B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} B_{(c,b_U)}\succeq 0,&
B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)} B_{(c,b_S)}\succeq 0,\\[2mm]
\widehat B_{(b_U,b_U)}^{\, T}(\widehat \Delta_{1/c})_{(b_U,b_U)}\widehat B_{(b_U,b_U)} \succeq 0,& \widehat B_{(b_L,b_L)}^{\, T}(\widehat \Delta_{1/c})_{(b_L,b_L)}\widehat B_{(b_L,b_L)}\succeq 0.
\end{array}$$ From this and the fact that ${\widehat
C}_{(\beta,\beta)}^{\, T} ({\widehat
\Theta}_c)_{(\beta,\beta)}{\widehat C}_{(\beta,\beta)} \succeq 0$, we can see that for any $c\ge c_0$, $$\left\langle d, {\cal B}_{c_0, c}(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2)d \right\rangle \ge \underline{\eta} \|d\|^2,\quad \forall
\, d \in \Re^n\, .$$ By noting the fact that $${\cal A}_{c}(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2) ={\cal B}_{c_0, c}(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2) +(c-c_0)A^TD_cA\, ,$$ we complete the proof.
Let Assumptions (sdnop-A1) and (sdnop-A2) be satisfied. Let the two positive numbers $c_0$ and $\underline{\eta}$ be defined as in Proposition \[pronlsdp\]. Let $c\ge c_0$. Then, by Propositions \[prop:general-discussions\] and \[pronlsdp\] and the fact that ${\rm D} \theta_c(\cdot)$ and $\Pi_{{\cal S}^p_+} (\cdot)$ are strongly semismooth everywhere, there exist two positive numbers $\varepsilon >0$ and $\delta_0>0$ (both depending on $c$) and a locally Lipschitz continuous function $x_c(\cdot, \cdot,\cdot)$ defined on $\mathbb{B}_{\delta_0}(\overline Y,\overline{\mu},\overline{\Gamma})$ such that for any $(Y,\mu, \Gamma)\in \mathbb{B}_{\delta_0}(\overline Y,\overline{\mu},\overline{\Gamma})$, $x_c(Y,\mu, \Gamma)$ is the unique minimizer of $L_c(\cdot, Y,\mu, \Gamma)$ over $\mathbb{B}_{\varepsilon}(\overline{x})$ and $x_c(\cdot,\cdot, \cdot)$ is semismooth at $(Y,\mu, \Gamma)$. Let $\vartheta_c: {\cal S}^q \times \Re^m \times {\cal
S}^p\mapsto \Re$ be defined as (\[dual\]), i.e., $$\vartheta_c(Y,\mu,\Gamma):=\min_{x \in
\mathbb{B}_{\varepsilon}(\overline{x})} L_c(x,Y,\mu,\Gamma), \quad
(Y, \mu,\Gamma)\in {\cal S}^q \times \Re^m \times {\cal S}^p\, .$$ Then it holds that $$\vartheta_c(Y,\mu,\Gamma)= L_c (x_c(Y,\mu, \Gamma),Y, \mu, \Gamma)\, , \quad (Y,\mu, \Gamma)
\in \mathbb{B}_{\delta_0}(\overline Y,\overline{\mu},\overline{\Gamma})\, .$$ Furthermore, it follows from Propositions \[comdcproperty1\] and \[pronlsdp\] that the concave function $\vartheta_c(\cdot, \cdot,\cdot)$ is continuously differentiable on $\mathbb{B}_{\delta_0}(\overline Y,\overline{\mu},\overline{\Gamma})$ with $${\rm D}\vartheta_c (Y,\mu, \Gamma)^*=\left (
\begin{array}{c}
-c^{-1}Y+c^{-1}{\rm D}\theta_c(F(x_c(Y,\mu, \Gamma))+Y/c))^*\\[2mm]
h(x_c(Y,\mu, \Gamma))\\[2mm]
-c^{-1}\Gamma+c^{-1}\Pi_{{\cal S}^p_+}(\Gamma-c g(x_c(Y,\mu, \Gamma)))
\end{array}
\right ), \,y =(Y,\mu,\Gamma) \in \mathbb{B}_{\delta_0}
(\overline Y,\overline{\mu},\overline{\Gamma})\, .$$For any $(\Delta Y,\Delta \mu, \Delta \Gamma) \in {\cal S}^q \times \Re^m \times {\cal S}^p$, let $\overline{{\cal V}}_c (\Delta Y,\Delta \mu, \Delta \Gamma)$ be defined as in (\[comcalV\]). By Propositions \[comthta\] and \[pronlsdp\], we have for any $(\Delta Y,\Delta \mu, \Delta \Gamma) \in {\cal S}^q \times \Re^m \times {\cal S}^p$ that $$\partial_B(\nabla \vartheta_c)(\overline Y,\overline{\mu}, \overline{\Gamma})(\Delta Y,\Delta \mu, \Delta \Gamma)
\subseteq \overline{{\cal V}}_c (\Delta Y,\Delta \mu, \Delta \Gamma)\, .$$Since when $c \rightarrow \infty$, $$c[{\Delta_{1/c}}]_{ij}=\left
\{
\begin{array}{clll}
\quad \quad 0 && & (i,j)\in (a\times a \cup b_U),\\[12pt]
\quad \quad 0 && & (i,j)\in (c \times b_L\cup c),\\[12pt]
\displaystyle \frac{1-(w_{b_S})_j}{\lambda_i(\overline X)+c^{-1}(1-(w_{b_S})_j)}
& \rightarrow& \displaystyle \frac{1-(w_{b_S})_j}{\lambda_i(\overline X)}
& (i,j)\in a\times \{1,\ldots,|b_S|\},\\[12pt]
\displaystyle \frac{2}{\lambda_i(\overline X)+2c^{-1}}& \rightarrow&
\displaystyle \frac{2}{\lambda_i(\overline X)}
& (i,j)\in a\times b_L,\\[12pt]
\displaystyle \frac{2}{\lambda_i(\overline X)-\lambda_j(\overline X)+2c^{-1}} & \rightarrow&
\displaystyle \frac{2}{\lambda_i(\overline X)-\lambda_j(\overline X)}
& (i,j)\in a\times c,\\[12pt]
\displaystyle \frac{2}{-\lambda_j(\overline X)+2c^{-1}} & \rightarrow&
\displaystyle \frac{2}{-\lambda_j(\overline X)} & (i,j)\in b_U\times c,\\[12pt]
\displaystyle \frac{(w_{b_S})_i+1}{c^{-1}((w_{b_S})_i+1)-\lambda_j(\overline X)} & \rightarrow&
\displaystyle \frac{(w_{b_S})_i+1}{-\lambda_j(\overline X)}
& (i,j)\in \{1,\ldots,|b_S|\}\times c.
\end{array}
\right.$$ where $\overline X=F(\overline x)$, and $$\lim_{c\to \infty} c (\Theta_c)_{ij} =\lim_{c\to \infty}
c
\frac{\lambda_i}{\lambda_i+c|\lambda_j|}=\frac{\lambda_i}{|\lambda_j|},
\forall \, (i, j)\in \alpha \times \gamma\, ,$$ we know that there exists a positive number $\overline{\eta}$ such that $$\label{mu1nlsdp}
\left\langle d, {\cal B}_{c_0, c}(\overline Y,\overline{\mu},\overline{\Gamma},W_1, W_2)d \right\rangle \le \overline{\eta} \langle d, d\rangle
\quad \begin{array}{l}
\forall\, d\in \Re^n, c\ge c_0 \,{\rm and}\,\\
W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c),\\
W_2 \in
\partial_B \Pi_{S^p_+}(\overline{\Gamma}-c g(\overline{x})).
\end{array}$$
Let $c\ge c_0$, $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$ and $W_2 \in
\partial_B \Pi_{S^p_+}(\overline{\Gamma}-c g(\overline{x}))$. Then there exist two matrices $Q\in {\cal O}(F(\overline x)$ with $ P\in {\cal O}(g(\overline x))$ and $\Delta_{1/c}$ satisfying (\[Shc\]) such that (\[eq:w1h\]) holds, $\Theta_c \in {\cal S}^p$ satisfying (\[Sh\]) such that (\[wh\]) holds. Let $A(Q,P)$ have the singular value decomposition as in (\[singvalu\]), i.e., $$\label{eq:singvalu-rep}
A(Q,P)=U[\Sigma (Q,P)\,\,\,\,\, 0]R^T\, .$$ Let $\overline{y}:=(\overline Y, \overline{\mu}, \overline{\Gamma})$. Then we have the following result for ${\cal A}_c(\overline{y}, W_1,W_2)$.
\[le2\] Let $c> c_0$ and $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$ and $W_2 \in
\partial_B \Pi_{{\cal S}^p_+}(\overline{\Gamma}-c g(\overline{x}))$. Suppose that Assumptions (sdnop-A1) and (sdnop-A2) are satisfied. Then we have $$\label{ac-2-101}
\begin{array}{l}
{\cal A}_c(\overline{y},W_1,W_2)^{-1} \preceq R\left [
\begin{array}{cc}
\Sigma^{-1}U^T\Big({\underline{\sigma}}\underline{\eta}I_{n_2}+(c-c_0)D_c\Big)^{-1}U \Sigma^{-1} & 0\\
0 & {\underline{\sigma}}^{-1}\underline{\eta}^{-1} I_{n_3}
\end{array}\right
]R^T,
\end{array}$$ $$\label{ac-1-101}
\begin{array}{l}
{\cal A}_c(\overline{y},W_1,W_2)^{-1} \succeq R\left [
\begin{array}{cc}
\Sigma^{-1}U^T \Big(\overline{\sigma}\overline{\eta}I_{n_2}+(c-c_0)D_c\Big)^{-1}U\Sigma^{-1} & 0\\
0 & {\overline{\sigma}}^{-1}\overline{\eta}^{-1} I_{n_3}
\end{array}\right]R^T\, ,
\end{array}$$ and $$\label{ac-1-101a}
\|{\cal A}_c(\overline{y},W_1,W_2)^{-1}A^TD_c u\| \leq \sqrt{2}\left(
\overline{\sigma} + ( \underline{\sigma} \underline{\eta} )^{-2}
(\overline{\sigma} \overline{\eta} )^2\right) \|u\|/(c-c_0),\ \,
\forall\, u \in \Re^{n_2},$$ where $\Sigma: =\Sigma(Q,P)$.
[**Proof.**]{} Let $\hat{c}:=c-c_0$. By (\[acyy\]), (\[eq:B-form\]), and the singular value decomposition (\[eq:singvalu-rep\]) of $A:=A(P)$, we have $$\label{calnlp}
\begin{array}[b]{l}
\quad {\cal A}_c(\overline{y},W_1,W_2)^{-1}=\Big({\cal B}_{c_0,
c}(\overline{y},W_1,W_2)+\hat{c}A^TD_cA \Big)^{-1}
\\[2mm]
=\left({\cal B}_{c_0,c}(\overline{y},W_1,W_2)+\hat{c}R[\Sigma \quad
0]^TU^TD_cU[\Sigma \quad 0]R^T\right)^{-1}
\\[2mm]
=R \left(R^T{\cal B}_{c_0,c}(\overline{y},W_1,W_2)R+\hat{c}\left [
\begin{array}{cc}
\Sigma & 0\\
0 & I_{n_3}
\end{array}\right
]\left [
\begin{array}{cc}
U^T D_cU & 0
\\
0 & 0
\end{array}\right
]\left [
\begin{array}{cc}
\Sigma & 0\\
0 & I_{n_3}
\end{array}\right
]\right)^{-1}R^T
\\[2mm]
=R \left [
\begin{array}{cc}
\Sigma^{-1} & 0
\\
0 & I_{n_3}
\end{array}\right
] \left({\cal G}_{c_0,c}(\overline{y},W_1,W_2)+\hat{c} \left [
\begin{array}{cc}
U^TD_cU & 0\\
0 & 0
\end{array}\right
]\right)^{-1} \left [
\begin{array}{cc}
\Sigma^{-1} & 0\\
0 & I_{n_3}
\end{array}\right
]R^T,
\end{array}$$ where $${\cal G}_{c_0,c}(\overline{y},W_1,W_2):=\left [
\begin{array}{cc}
\Sigma^{-1} & 0\\
0 & I_{n_3}
\end{array}\right
]R^T{\cal B}_{c_0,c}(\overline{y},W_1,W_2)R\left [
\begin{array}{cc}
\Sigma^{-1} & 0\\
0 & I_{n_3}
\end{array}\right
]\, .$$ It follows from Proposition \[pronlsdp\], the definitions of ${\underline{\sigma}}$ and $\overline{\sigma}$, and (\[mu1nlsdp\]) that $$\label{eq:G-lower-bound}
{\cal G}_{c_0,c}(\overline{y},W_1,W_2) \succeq \underline{ \eta} \left [
\begin{array}{cc}
\Sigma^{-1} & 0\\
0 & I_{n_3}
\end{array}\right
]^2 \succeq {\underline{\sigma}}\underline{\eta} I_{n}$$ and $$\label{eq:G-upper-bound}
{\cal G}_{c_0,c}(\overline{y},W_1,W_2) \preceq \overline{\eta} \left [
\begin{array}{cc}
\Sigma^{-1} & 0\\
0 & I_{n_3}
\end{array}\right
]^2 \preceq \overline{\sigma} \overline{\eta} I_{n}\, .$$ Therefore, (\[ac-2-101\]) and (\[ac-1-101\]) follow from (\[calnlp\]).
15 true pt Now we turn to the proof of (\[ac-1-101a\]). Let $$\overline{{\cal G}}_{c_0,c}(\overline{y},W_1,W_2):= \left [
\begin{array}{cc}
U & 0\\
0 & I_{n_3} \end{array}\right ] {\cal G}_{c_0,c}(\overline{y},W_1,W_2)
\left [
\begin{array}{cc}
U^T & 0\\
0 & I_{n_3} \end{array}\right ]$$ and $${\overline {\cal
H}}_{c_0}(\overline{y},W_1,W_2) := \overline{{\cal
G}}_{c_0}(\overline{y},W_1,W_2)^{-1}\, .$$ Partition $ {\overline{\cal H}}_{c_0,c}(\overline{y},W_1,W_2)$ as $$ \_[c\_0,c]{}(,W\_1,W\_2)= with $H_{1}(W_1,W_2)\in {\cal S}^{n_2}$, $H_{2}(W_1,W_2)\in
\Re^{n_3 \times n_2}$, and $H_{3}(W_1,W_2)\in {\cal S}^{n_3}.$ Then, it follows from (\[eq:G-lower-bound\]) and (\[eq:G-upper-bound\]) that $$\label{eq:H12-form}
\begin{array}{l}
\|H_{1}(W_1,W_2)\|_2 \le (\underline{\sigma}\underline{\eta})^{-1}\, , \
\ \|H_{1}(W_1,W_2)^{-1}\|_2 \le \overline{\sigma}\overline{\eta}\\[2mm]
{\rm and} \ \ \|H_2(W_1,W_2)H_{1}(W_1,W_2)^{-1}\|_2 \leq (\underline{\sigma}
\underline{\eta} )^{-1} \overline{\sigma}\overline{\eta}\, .
\end{array}$$ For any $\varepsilon>0$, let $$D_{c,\varepsilon}:=D_c+\varepsilon I_{n_2}, \quad {\cal
A}_{c,\varepsilon}(\overline{y},W_1,W_2):={\cal
B}_{c_0,c}(\overline{y},W_1,W_2)+\hat{c}A^TD_{c,\varepsilon}A.$$ Let $\varepsilon >0$. By referring to (\[calnlp\]), we obtain $$\begin{array}{l}
{\cal A}_{c, \varepsilon}(\overline{y},W_1,W_2)^{-1}
\\[2mm]
=R
\left [
\begin{array}{cc}
\Sigma^{-1}U^T & 0
\\
0 & I_{n_3}
\end{array}\right]
\left(\overline{{\cal G}}_{c_0,c}(\overline{y},W_1,W_2)+\hat{c} \left [
\begin{array}{cc}
D_{c, \varepsilon} & 0\\
0 & 0
\end{array}\right
]\right)^{-1} \left [
\begin{array}{cc}
U\Sigma^{-1} & 0\\
0 & I_{n_3} \end{array}\right ]R^T\, ,
\end{array}$$ which, together with (\[eq:singvalu-rep\]) and the Sherman-Morrison-Woodbury formula (cf. [@GVanLoan96 Section 2.1]), implies $$\begin{array}{l}
{\cal A}_{c,\varepsilon}(\overline{y},W_1,W_2)^{-1}A^TD_{c,\varepsilon}\\[2mm]
=
R \left [
\begin{array}{ll}
\Sigma^{-1}U^T &0\\[2mm]
0& I_{n_3}
\end{array}
\right ] \left [
\begin{array}{c}
\left ( {H}_{1}(W_1,W_2)^{-1}+\hat{c}D_{c,\varepsilon} \right)^{-1}D_{c,\varepsilon}\\[2mm]
{H}_{2}(W_1,W_2) {H}_{1}(W_1,W_2)^{-1}\left
({H}_{1}(W_1,W_2)^{-1}+\hat{c}D_{c,\varepsilon}\right )^{-1}
D_{c,\varepsilon}\end{array} \right ]\, .
\end{array}$$ Since, it follows from the Sherman-Morrison-Woodbury formula that $$\begin{array}{l}
\left({H}_{1}(W_1,W_2)^{-1}+\hat{c}D_{c,\varepsilon}\right)^{-1}D_{c,\varepsilon}\\[1.2mm]
=\left(\hat{c}I_{n_2}+ D_{c,\varepsilon}^{-1}
{H}_{1}(W_1,W_2)^{-1}\right)^{-1}\\[1.2mm]
=\hat{c}^{-1}I_{n_2}-\hat{c}^{-2} D_{c,\varepsilon}^{-1} \left
(I_{n_2}+\hat{c}^{-1} {H}_{1}(W_1,W_2)^{-1} D_{c,\varepsilon}^{-1}
\right)^{-1}{H}_{1}(W_1,W_2)^{-1}\\[1.2mm]
=\hat{c}^{-1}I_{n_2}-\hat{c}^{-1}\left(\hat{c}D_{c,\varepsilon}+
{H}_{1}(W_1,W_2)^{-1}\right)^{-1}{H}_{1}(W_1,W_2)^{-1},
\end{array}$$ we have $$\begin{array}{l}
\quad {\cal A}_c(\overline{y},W_1,W_2)^{-1}A^TD_c =\displaystyle
\lim_{\varepsilon \downarrow 0} {\cal
A}_{c,\epsilon}(\overline{y},W_1,W_2)^{-1}A^TD_{c,\epsilon}\\[1.2mm]
= R \left [
\begin{array}{c}
\Sigma^{-1}U^T \\
{H}_{2}(W_1,W_2) {H}_{1}(W_1,W_2)^{-1}
\end{array}
\right ]\left(
\hat{c}^{-1}I_{n_2}-\hat{c}^{-1}\left(\hat{c}D_c+{H}_{1}(W_1,W_2)^{-1}\right)^{-1}{H}_{1}(W_1,W_2)^{-1}
\right )\, .
\end{array}$$ Therefore, from the definition of $\overline{\sigma}$ and (\[eq:H12-form\]) we have for any $u \in \Re^{n_2}$ that $$\begin{array}{l}
\quad \|{\cal A}_c(\overline{y},W_1,W_2)^{-1}A^TD_cu\|^2\\[1.5mm]
\leq \left( \overline{\sigma} + ( \underline{\sigma}
\underline{\eta} )^{-2} (\overline{\sigma} \overline{\eta} )^2
\right)
\left\|\left(\hat{c}^{-1}I_{n_2}-\hat{c}^{-1}\left(\hat{c}D_c+{H}_{1}(W_1,W_2)^{-1}\right)^{-1}{H}_{1}(W_1,W_2)^{-1}\right)u\right\|^2\\[1.5mm]
\leq \left( \overline{\sigma} + ( \underline{\sigma}
\underline{\eta} )^{-2} (\overline{\sigma} \overline{\eta} )^2
\right) \left(
\hat{c}^{-1}\|u\|+\hat{c}^{-1}\left\| \left(
\hat{c}D_c+{H}_{1}(W_1,W_2)^{-1} \right )^{-1}\right \|_2
\|{H}_{1}(W_1,W_2)^{-1}\|_2 \|u\|\right)^2
\\[1.5mm]
\leq \left( \overline{\sigma} + ( \underline{\sigma}
\underline{\eta} )^{-2} (\overline{\sigma} \overline{\eta} )^2
\right)\hat{c}^{-2}\left(1+\|{H}_{1}(W_1,W_2)\|_2
\|{H}_{1}(W_1,W_2)^{-1}\|_2\right)^2\|u\|^2\\[1.5mm]
\leq \left( \overline{\sigma} + ( \underline{\sigma}
\underline{\eta} )^{-2} (\overline{\sigma} \overline{\eta} )^2
\right) \hat{c}^{-2} \left(1+ ( \underline{\sigma}
\underline{\eta} )^{-1} (\overline{\sigma} \overline{\eta} )
\right)^2\|u\|^2\, ,
\end{array}$$ which, together with the fact that $\overline{\sigma}\ge 1$, proves (\[ac-1-101a\]).
7 true pt Let $$\label{eq:barc-sdp}
\overline{c}:=\max\left \{(2+\sqrt{2})c_0, \, (\overline{\sigma}
\overline{\eta}-c_0)^2/c_0, \ (\underline{\sigma}
\underline{\eta}/2-c_0)^2/c_0\right\} \,$$ and
$$\label{varrho0-sdp}
\varrho_0:= \left( \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2}
\underline{\eta}^{-2}\max \left
\{8\overline \nu_1^2,16\overline \nu_2^2,32\overline \nu_3^2,64\overline \nu_4^2,128\overline \nu_5^2,128\overline{\nu}_0^2, \ 4
\kappa_0^2\right\}\right)^{1/2}
\, .$$
where ($\overline X=F(\overline x)$) $$\begin{array}{l}
\overline \nu_1=\displaystyle \left (\max_{i \in a, j \in \{1,\ldots,|b_S|\}}\displaystyle \frac{1-(w_{b_S})_j}{\lambda_i(\overline X)}\right)\\[2mm]
\overline \nu_2=\displaystyle \left (\max_{i \in a, j \in b_L}\displaystyle \frac{2}{\lambda_i(\overline X)}\right)\\[2mm]
\overline \nu_3=\displaystyle \left (\max_{i \in a, j \in c}\displaystyle \frac{2}{\lambda_i(\overline X)-\lambda_j(\overline X)}\right)\\[2mm]
\overline \nu_4=\displaystyle \left (\max_{i \in b_U, j \in c}\displaystyle \frac{2}{-\lambda_j(\overline X)}\right)\\[2mm]
\overline \nu_5=\displaystyle \left (\max_{i \in \{1,\ldots,|b_S|\},j \in c}\displaystyle \frac{(w_{b_S})_i+1}{-\lambda_j(\overline X)}\right)
\end{array}$$ and $$\kappa_0:=\sqrt{2}\left( \overline{\sigma} + (
\underline{\sigma} \underline{\eta} )^{-2} (\overline{\sigma}
\overline{\eta} )^2\right)\, .$$
\[thdcnlsdp\] Suppose that Assumptions (sdnop-A1) and (sdnop-A2) are satisfied. Then there exists a positive number $\mu_0$ such that for any $c \geq {\overline{c}}$ and $\Delta y
\in {\cal S}^q \times \Re^m \times {\cal S}^p$, $$\label{eq:direction-added-sdp}
\|(x_c)^\prime(\overline{y};\Delta y)\|\le \mu_0 \|\Delta
y\|/c$$ and $$\label{import11}
\left \langle V(\Delta y)+c^{-1}\Delta y, \Delta y \right \rangle
\in \mu_0[-1, 1] \| \Delta y\|^2/c^{2},\quad \forall \, V(\Delta y)
\in \overline{{\cal V}}_c(\Delta y)\, .$$
[**Proof.**]{} Let $c\ge {\overline{c}}$. Let $\Delta y:=
(\Delta Y,\Delta\mu, \Delta\Gamma) \in {\cal S}^q \times \Re^m \times {\cal S}^p$. From the proof of Proposition \[comthta\] we know that there exist $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$ and $W_2 \in
\partial_B \Pi_{S^p_+}(\overline{\Gamma}-c g(\overline{x}))$ such that $$\label{comxderrii-sdp}
(x_c)'(\overline y;\Delta y)={\cal A}_c(\overline y,W_1,W_2 )^{-1}\left(-{\rm D}F(\overline x)^* W_1(\Delta Y/c)-{\cal J}
h(\overline x)^T (\Delta\mu)+{\rm D}g(\overline x)^*
W_2(\Delta\Gamma)\right).$$ For this $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$, there exist matrices $Q\in {\cal O}(F(\overline x))$ and $\Delta_{1/c} \in {\cal S}^q$ satisfying (\[eq:dDeltac\]) such that $$W_1(H_1)= Q\left( \Delta_{1/c} \circ (Q^TH_1Q)\right )Q^T,\quad \forall \, H_1
\in {\cal S}^q\, .$$ For this $W_2 \in
\partial_B \Pi_{{\cal S}^p_+}(\overline{\Gamma}-cg(\overline{x}))$, there exist two matrices $P \in {\cal O}(\overline X)$ and $\Theta_c\in {\cal S}^p$ satisfying (\[Sh\]) such that $$W_2(H_2) = P\left( \Theta_c \circ (P^TH_2P)\right )P^T,\quad \forall \, H_2
\in {\cal S}^p\, .$$ Let $A: =A(Q,P)$ have the singular value decomposition as in (\[singvalu\]), i.e., $$\label{singvalue-in}
A=U[\Sigma \,\,\,\,\, 0]R^T\, ,$$ where $\Sigma:=\Sigma(Q,P)$.\
For any two index sets $\chi, \chi' \in \{b_U,b_S,b_L\}$, let $$\xi_{(\chi,\chi')}:={\rm vec}(Q_{\chi}^{\, T}\Delta Y
Q_{\chi'})\, , \quad {\widehat \xi}_{(\chi,\chi)}:={\rm
svec}(Q_{\chi}^{\, T}\Delta Y Q_{\chi})\, .$$
For any two index sets $\chi, \chi' \in \{\alpha, \beta, \gamma\}$, let $$\omega_{(\chi,\chi')}:={\rm vec}(P_{\chi}^{\, T}\Delta\Gamma
P_{\chi'})\, , \quad {\widehat \omega}_{(\chi,\chi)}:={\rm
svec}(P_{\chi}^{\, T}\Delta\Gamma P_{\chi})\, .$$ Define $$\Delta d_0:= \left ( \begin{array}{l}
\Delta\mu\\
{\widehat \xi}_{(b_U,b_U)}\\
\xi_{(b_U,b_S)}\\
\xi_{(b_U,b_L)}\\
{\widehat \xi}_{(b_S,b_S)}\\
\xi_{(b_S,b_L)}\\
{\widehat \xi}_{(b_L,b_L)}\\
{\widehat \omega} _{(\alpha,\alpha)}\\
{\widehat \omega}_{(\beta,\beta)}\\
\omega _{(\alpha,\beta)}
\end{array}\right)\, , \quad
\Delta d: =\left ( \begin{array}{l} \Delta d_0\\
\xi_{(a,b_S)}\\
\xi_{(a,b_L)}\\
\xi_{(a,c)}\\
\xi_{(c,b_U)}\\
\xi_{(c,b_S)}\\
\omega_{(\alpha,\gamma)}
\end{array}
\right )\, .$$ Then, from (\[comxderrii-sdp\]), we have $$\begin{array}{ll}
(x_c)^\prime(\overline{y};\Delta y) =&
-{\cal
A}_c(\overline{y},W_1,W_2)^{-1}
[A^T D_c\Delta d_0+2 B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}\\
&+2 B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+2 B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\
&+2 B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ 2 B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\\
& -2C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]
\end{array}$$ and $$\label{Ahh-0}
\begin{array}[b]{l}
\quad \left \langle (x_c)^\prime(\overline{y};\Delta y),
(x_c)^\prime(\overline{y};\Delta y)\right\rangle
\\[2mm]
\le2 \left \langle A^TD_c\Delta d_0, {\cal
A}_c(\overline{y},W_1,W_2)^{-2}A^TD_c \Delta d_0\right \rangle
\\[2mm]
+16 \left \langle B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)} \right \rangle\\[2mm]
+32\left \langle B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)} \right \rangle\\[2mm]
+64 \left \langle B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)} \right \rangle\\[2mm]
+128\left \langle B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)}\xi_{(c,b_U)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)}\xi_{(c,b_U)} \right \rangle\\[2mm]
+256 \left \langle B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)} \right \rangle\\[2mm]
+256 \left \langle C^{\, T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}\right
\rangle\, .
\end{array}$$ From (\[ac-1-101a\]), we have for $c \geq \overline{c} \quad
(\geq (2+\sqrt{2})c_0)$ that $$\label{anup-1-add0}
\begin{array}{l}
\quad \left\langle A^TD_c \Delta d_0, {\cal
A}_c(\overline{y},W_1,W_2)^{-2}A^TD_c \Delta d_0 \right\rangle
\\[2mm]
=\|{\cal A}_c(\overline{y},W_1,W_2)^{-1}A^TD_c \Delta d_0\|^2
\\[2mm]
\le \kappa_0^2{\hat c}^{-2} \left(\|\Delta d_0 \right\|)^2
\\[2mm]
\le \kappa_0^2{\hat c}^{-2} (\|(\Delta\mu, \xi_{(b_U,b_U)},
\xi_{(b_S,b_S)},
\xi_{(b_L,b_L)}, { \omega}_{(\alpha,\alpha)}, {
\omega}_{(\beta,\beta)})\|^2\\[2mm]
\quad + 2 \|( \xi_{(b_U,b_S)}, \xi_{(b_S,b_L)},
\xi_{(b_U,b_L)}, \omega_{(\alpha,\beta)})\|^2
)
\\[2mm]
\le \displaystyle \frac{1}{2}\varrho_0^2
c^{-2}(\|(\Delta\mu, \xi_{(b_U,b_U)},
\xi_{(b_S,b_S)},
\xi_{(b_L,b_L)}, { \omega}_{(\alpha,\alpha)}, {
\omega}_{(\beta,\beta)})\|^2\\[2mm]
\quad + 2\|( \xi_{(b_U,b_S)}, \xi_{(b_S,b_L)},
\xi_{(b_U,b_L)}, \omega_{(\alpha,\beta)})\|^2 )\, .
\end{array}$$ Let $$\underline{{\cal E}}_c:= \left(\overline{\sigma} \overline{\eta}
I_{n_2} +(c-c_0)D_c\right )^{-1}\, , \quad \overline{{\cal
E}}_c:=\left(\underline{\sigma}\underline{\eta}I_{n_2}
+(c-c_0)D_c\right)^{-1}$$and $$\label{eu1-A}
\underline{{\cal H}}_c := \left[
\begin{array}{cc}
\underline{{\cal E}}_c & 0
\\
0 &{\overline{\sigma}}^{-1} \overline{\eta}^{-1}I_{n_3}
\end{array}\right]\, , \quad
\overline{{\cal H}}_c := \left[
\begin{array}{cc}
\overline{{\cal E}}_c & 0
\\
0 &{\underline{\sigma}}^{-1} \underline{\eta}^{-1}I_{n_3}
\end{array}\right]\, .$$ We know from Lemma \[le2\], (\[eu1-A\]), (\[eq:nu-lower-upper\]), and (\[eq:two-nus\]) that $$\begin{array}[b]{l}
\quad \left\langle C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)},
{\cal A}_c(\overline{y},W_1,W_2)^{-2}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}
\right\rangle
\\[2mm]
=\left\langle {\cal A}_c(\overline{y},W_1,W_2)^{-1/2}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)},
{\cal A}_c(\overline{y},W_1,W_2)^{-1}{\cal
A}_c(\overline{y},W_1,W_2)^{-1/2}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}
\right\rangle
\\[2mm]
\leq \left\langle {\cal A}_c(\overline{y},W_1,W_2)^{-1/2}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)},
{\widetilde{R}} \overline{{\cal H}}_c {\widetilde{R}} ^T{\cal
A}_c(\overline{y},W_1,W_2)^{-1/2}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}
\right\rangle\\[2mm]
\leq \overline{\sigma} {\underline{\sigma}}^{-1}
\underline{\eta}^{-1} \left\langle C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)},
{\cal A}_c(\overline{y},W_1,W_2)^{-1}C^{\,
T}_{(\alpha,\gamma)}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}
\right\rangle
\\[2mm]
\leq \overline{\sigma}{\underline{\sigma}}^{-2}
\underline{\eta}^{-2} \left\langle {\widetilde{C}}^{\,
T}_{(\alpha,\gamma)}
(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)},
{\widetilde{C}}^{\, T}_{(\alpha,\gamma)}
(\Theta_c)_{(\alpha,\gamma)} \omega_{(\alpha,\gamma)}
\right\rangle\\[2mm]
\leq
\overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\|(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}\|^2
\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2}
\underline{\eta}^{-2} \displaystyle \left (\max_{i \in \alpha, j \in
\gamma}\lambda_i/(\lambda_i+c|\lambda_j|)\right)^2 \|
\omega_{(\alpha,\gamma)}\|^2
\end{array}$$ $$\label{ineq2-add0}
\begin{array}{l}
\leq \overline{\nu}\overline{\sigma} {\underline{\sigma}}^{-2}
\underline{\eta}^{-2} \overline{\nu}_0^2 (\overline{\nu}_0+c)^{-2}
\| \omega_{(\alpha,\gamma)}\|^2\,
\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2}
\underline{\eta}^{-2} \overline{\nu}_0^2 c^{-2} \|
\omega_{(\alpha,\gamma)}\|^2\,
\\[2mm]
\leq \displaystyle \frac{1}{256}\varrho_0^2c^{-2} (2\|
\omega_{(\alpha,\gamma)}\|^2).\,
\end{array}$$ Similarly, we obtain $$\label{eq:est1}
\begin{array}{l}
\left \langle B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)} \right \rangle\\[2mm]
\leq
\overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\|(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}\|^2\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\overline \nu_1=\displaystyle \left (\max_{i \in a, j \in \{1,\ldots,|b_S|\}}\displaystyle \frac{1-(w_{b_S})_j}{c\lambda_i(\overline X)}\right)^2 \|\xi_{(a,b_S)}\|^2\\[2mm]
\leq
\displaystyle \frac{1}{16}\varrho_0^2c^{-2} (2 \|\xi_{(a,b_S)}\|^2);\,
\end{array}$$ $$\label{eq:est2}
\begin{array}{l}
\left \langle B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)} \right \rangle\\[2mm]
\leq
\overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\|(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\|^2\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\overline \nu_2=\displaystyle \left (\max_{i \in a, j \in b_L\}}\displaystyle \frac{2}{c\lambda_i(\overline X)}\right)^2 \|\xi_{(a,b_L)}\|^2\\[2mm]
\leq
\displaystyle \frac{1}{32}\varrho_0^2c^{-2} (2 \|\xi_{(a,b_L)}\|^2);
\end{array}$$ $$\label{eq:est3}
\begin{array}{l}
\left \langle B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)} \right \rangle\\[2mm]
\leq
\overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\|(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\|^2\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\overline \nu_3=\displaystyle \left (\max_{i \in a, j \in c\}}\displaystyle \frac{2}{c(\lambda_i(\overline X)-\lambda_j(\overline X))}\right)^2 \|\xi_{(a,c)}\|^2\\[2mm]
\leq
\displaystyle \frac{1}{64}\varrho_0^2c^{-2} (2 \|\xi_{(a,c)}\|^2);
\end{array}$$ $$\label{eq:est4}
\begin{array}{l}
\left \langle B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)}\xi_{(c,b_U)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)}\xi_{(c,b_U)} \right \rangle\\[2mm]
\leq
\overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\|(\Delta_{1/c})_{(c,b_U)}\xi_{(c,b_U)}\|^2\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\overline \nu_4=\displaystyle \left (\max_{i \in b_U, j \in c\}}\displaystyle \frac{2}{-c\lambda_j(\overline X)}\right)^2 \|\xi_{(b_U,c)}\|^2\\[2mm]
\leq
\displaystyle \frac{1}{128}\varrho_0^2c^{-2} (2 \|\xi_{(b_U,c)}\|^2)
\end{array}$$ and $$\label{eq:est5}
\begin{array}{l}
\left \langle B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}, {\cal
A}_c(\overline{y},W_1,W_2)^{-2} B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)} \right \rangle\\[2mm]
\leq
\overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\|(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\|^2\\[2mm]
\leq \overline{\nu} \overline{\sigma}{\underline{\sigma}}^{-2} \underline{\eta}^{-2}
\overline \nu_5=\displaystyle \left (\max_{i \in \{1,\ldots,|b_S|\},j \in c}\displaystyle \frac{(w_{b_S})_i+1}{-c\lambda_j(\overline X)}\right)^2 \|\xi_{(b_S,c)}\|^2\\[2mm]
\leq
\displaystyle \frac{1}{256}\varrho_0^2c^{-2} (2 \|\xi_{(b_S,c)}\|^2).
\end{array}$$ Combining (\[eq:est1\])-(\[eq:est5\]) with (\[Ahh-0\]) and (\[anup-1-add0\]), we obtain $$ \left \langle (x_c)^\prime(\overline{y};\Delta y),
(x_c)^\prime(\overline{y};\Delta y)\right\rangle \le
\varrho_0^2\|\Delta y\|^2 /c^2.$$ Thus (\[eq:direction-added-sdp\]) holds for $\mu_0\geq \varrho_0$.
Now we prove (\[import11\]) for some $\mu_0\geq \varrho_0$. Let $V(\Delta y) \in \overline{{\cal V}}_c(\Delta y)$. Then from the definition of $\overline{{\cal V}}_c(\Delta y)$, there exist $W_1\in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c)$ and $W_2 \in
\partial_B \Pi_{{\cal S}^p_+}(\overline{\Gamma}-c g(\overline{x}))$ such that $$\begin{array}{l}
V(\Delta y)\\[6pt]
= \left
[
\begin{array}{c}
c^{-1}W_1{\rm D}F(\overline x)\\
{\cal J} h (\overline{x})\\
-W_2{\rm D}g(\overline{x})
\end{array}
\right
]{\cal A}_c(\overline{y},W_1,W_2)^{-1}\left[-c^{-1}{\rm D}F(\overline x)^*W_1(\Delta Y)-{\cal J}
h(\overline{x})^T\Delta\mu+{\rm D}g(\overline{x})^*W_2(\Delta\Gamma)\right]\\[8mm]
\quad \quad \quad \quad \quad \quad\quad \quad \quad \quad \quad \quad \quad \quad \quad +\left
(
\begin{array}{c}
-c^{-1}\Delta Y+c^{-2}W_1\Delta Y\\
0\\
-c^{-1}\Delta \Gamma+ c^{-1}W_2( \Delta \Gamma)
\end{array}
\right
).
\end{array}$$ For notational convenience, we assume that $(W_1,W_2) \in \partial_B [{\rm D} \theta_c]^*(F(\overline x)+\overline Y/c) \times
\partial_B \Pi_{{\cal S}^p_+}(\overline{\Gamma}-cg(\overline{x}))$ is the same as in (\[comxderrii-sdp\]). After direct calculations, we obtain $$\label{Ahh}
\begin{array}{l}
\quad -\left\langle V(\Delta y), \Delta y \right \rangle=
\\[2mm]
[A^T D_c\Delta d_0+2 B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}\\[2mm]
+2 B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+2 B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
+2 B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ 2 B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\\[2mm]
-2C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]^{\,
T}{\cal
A}_c(\overline{y},W_1,W_2)^{-1}
[A^T D_c\Delta d_0+2 B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}\\[2mm]
+2 B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+2 B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
+2 B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ 2 B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-2C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]\\[4mm]
+c^{-1}\|\Delta Y\|^2-c^{-2}\left \langle W_1\Delta Y, \Delta Y \right \rangle
+ {c}^{-1}\|\Delta\Gamma\|^2 -c^{-1}\left\langle
\Delta\Gamma, W_2(\Delta\Gamma) \right \rangle\,
\end{array}$$
Next, we estimate the lower and upper bounds of the right hand side of (\[Ahh\]). By using (\[singvalue-in\]) and Lemma \[le2\] we obtain $$\underline{{\cal E}}_c \preceq
A {\cal A}_c(\overline{y},W_1,W_2)^{-1}A^T
\preceq\overline{{\cal E}}_c\, .$$Thus, for $l_U=|b_U|(|b_U|+1)/2$, $l_L=|b_L|(|b_L|+1)/2$ and $l_\beta= |\beta|(|\beta|+1)/2$, we have $$\begin{array}[b]{l}
\quad \left\langle A^TD_c \Delta d_0, {\cal
A}_c(\overline{y},W_1,W_2)^{-1}A^TD_c \Delta d_0 \right\rangle \geq
\left\langle D_c \Delta d_0,\underline{{\cal E}}_c D_c \Delta d_0
\right\rangle
\\[2mm]
\ge
\left({\overline{\sigma}}\overline{\eta}+(c-c_0)\right)^{-1}\|(\Delta\mu,\xi_{(b_S,b_S)},{
\omega}_{(\alpha,\alpha)})\|^2\\[2mm]
\quad + {4}\left(
{\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1} \|(\xi_{(b_U,b_S)},\xi_{(b_U,b_L)},\xi_{(b_S,b_L)},\omega_{(\alpha,\beta)})\|^2
\\[2mm]
\, +\left\langle ({\widehat \Delta_{1/c}})_{(b_U,b_U)}{\widehat
\xi}_{(b_U,b_U)}, \left({\overline{\sigma}}\overline{\eta}
I_{l_U}+(c-c_0) ({\widehat
\Delta_{1/c}})_{(b_U,b_U)} \right )^{-1} ({\widehat
\Delta_{1/c}})_{(b_U,b_U)}{\widehat \xi}_{(b_U,b_U)}
\right\rangle\\[2mm]
\, +\left\langle ({\widehat \Delta_{1/c}})_{(b_L,b_L)}{\widehat
\xi}_{(b_L,b_L)}, \left({\overline{\sigma}}\overline{\eta}
I_{l_L}+(c-c_0) ({\widehat
\Delta_{1/c}})_{(b_L,b_L)} \right )^{-1} ({\widehat
\Delta_{1/c}})_{(b_L,b_L)}{\widehat \xi}_{(b_L,b_L)}
\right\rangle\\[2mm]
\, +\left\langle ({\widehat \Theta_c})_{(\beta, \beta)}{\widehat
\omega}_{(\beta,\beta)}, \left({\overline{\sigma}}\overline{\eta}
I_{l_\beta}+(c-c_0) ({\widehat
\Theta_c})_{(\beta,\beta)} \right )^{-1} ({\widehat
\Theta_c})_{(\beta,\beta)}{\widehat \omega}_{(\beta,\beta)}
\right\rangle
\end{array}$$ $$\label{anup-opposite}
\begin{array}{l}
\ge
\left({\overline{\sigma}}\overline{\eta}+(c-c_0)\right)^{-1}\|(\Delta\mu,\xi_{(b_S,b_S)},{
\omega}_{(\alpha,\alpha)})\|^2\\[2mm]
\quad + {4}\left(
{\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1} \|(\xi_{(b_U,b_S)},\xi_{(b_U,b_L)},\xi_{(b_S,b_L)},\omega_{(\alpha,\beta)})\|^2
\\[2mm]
\, +\left\langle ({\Delta_{1/c}})_{(b_U,b_U)}{
\xi}_{(b_U,b_U)}, \left({\overline{\sigma}}\overline{\eta}
I_{|b_U|}+(c-c_0) ({
\Delta_{1/c}})_{(b_U,b_U)} \right )^{-1} ({
\Delta_{1/c}})_{(b_U,b_U)}{\xi}_{(b_U,b_U)}
\right\rangle\\[2mm]
\, +\left\langle ({ \Delta_{1/c}})_{(b_L,b_L)}{
\xi}_{(b_L,b_L)}, \left({\overline{\sigma}}\overline{\eta}
I_{|b_L|}+(c-c_0) ({
\Delta_{1/c}})_{(b_L,b_L)} \right )^{-1} ({
\Delta_{1/c}})_{(b_L,b_L)}{ \xi}_{(b_L,b_L)}
\right\rangle\\[2mm]
\, +\left\langle ({ \Theta_c})_{(\beta, \beta)}{
\omega}_{(\beta,\beta)}, \left({\overline{\sigma}}\overline{\eta}
I_{|\beta|}+(c-c_0) ({ \Theta_c})_{(\beta,\beta)} \right )^{-1} ({
\Theta_c})_{(\beta,\beta)}{ \omega}_{(\beta,\beta)}
\right\rangle\,
\end{array}$$ and $$\label{anup-1}
\begin{array}[b]{l}
\quad \left\langle A^TD_c \Delta d_0, {\cal
A}_c(\overline{y},W_1,W_2)^{-1}A^TD_c \Delta d_0 \right\rangle \leq
\left\langle D_c \Delta d_0,\overline{{\cal E}}_c D_c \Delta
d_0\right\rangle
\\[2mm]
\le
\left({\underline{\sigma}}\underline{\eta}/2+(c-c_0)\right)^{-1}\|(\Delta\mu,\xi_{(b_S,b_S)},{
\omega}_{(\alpha,\alpha)})\|^2\\[2mm]
\quad + {4}\left(
{\underline{\sigma}}\underline{\eta}+2(c-c_0)\right)^{-1} \|(\xi_{(b_U,b_S)},\xi_{(b_U,b_L)},\xi_{(b_S,b_L)},\omega_{(\alpha,\beta)})\|^2
\\[2mm]
\, +\left\langle ({\widehat \Delta_{1/c}})_{(b_U,b_U)}{\widehat
\xi}_{(b_U,b_U)}, \left({\underline{\sigma}}\underline{\eta}
I_{l_U}+(c-c_0) ({\widehat
\Delta_{1/c}})_{(b_U,b_U)} \right )^{-1} ({\widehat
\Delta_{1/c}})_{(b_U,b_U)}{\widehat \xi}_{(b_U,b_U)}
\right\rangle\\[2mm]
\, +\left\langle ({\widehat \Delta_{1/c}})_{(b_L,b_L)}{\widehat
\xi}_{(b_L,b_L)}, \left({\underline{\sigma}}\underline{\eta}
I_{l_L}+(c-c_0) ({\widehat
\Delta_{1/c}})_{(b_L,b_L)} \right )^{-1} ({\widehat
\Delta_{1/c}})_{(b_L,b_L)}{\widehat \xi}_{(b_L,b_L)}
\right\rangle\\[2mm]
\, +\left\langle ({\widehat \Theta_c})_{(\beta, \beta)}{\widehat
\omega}_{(\beta,\beta)}, \left({\underline{\sigma}}\underline{\eta}
I_{l_\beta}+(c-c_0) ({\widehat
\Theta_c})_{(\beta,\beta)} \right )^{-1} ({\widehat
\Theta_c})_{(\beta,\beta)}{\widehat \omega}_{(\beta,\beta)}
\right\rangle
\\[2mm]
\le
\left({\underline{\sigma}}\underline{\eta}/2+(c-c_0)\right)^{-1}\|(\Delta\mu,\xi_{(b_S,b_S)},{
\omega}_{(\alpha,\alpha)})\|^2\\[2mm]
\quad + {4}\left(
{\underline{\sigma}}\underline{\eta}+2(c-c_0)\right)^{-1} \|(\xi_{(b_U,b_S)},\xi_{(b_U,b_L)},\xi_{(b_S,b_L)},\omega_{(\alpha,\beta)})\|^2
\\[2mm]
\, +\left\langle ({\Delta_{1/c}})_{(b_U,b_U)}{
\xi}_{(b_U,b_U)}, \left({\underline{\sigma}}\underline{\eta}
I_{|b_U|}+(c-c_0) ({
\Delta_{1/c}})_{(b_U,b_U)} \right )^{-1} ({
\Delta_{1/c}})_{(b_U,b_U)}{\xi}_{(b_U,b_U)}
\right\rangle\\[2mm]
\, +\left\langle ({ \Delta_{1/c}})_{(b_L,b_L)}{
\xi}_{(b_L,b_L)}, \left({\underline{\sigma}}\underline{\eta}
I_{|b_L|}+(c-c_0) ({
\Delta_{1/c}})_{(b_L,b_L)} \right )^{-1} ({
\Delta_{1/c}})_{(b_L,b_L)}{ \xi}_{(b_L,b_L)}
\right\rangle\\[2mm]
\, +\left\langle ({ \Theta_c})_{(\beta, \beta)}{
\omega}_{(\beta,\beta)}, \left({\underline{\sigma}}\underline{\eta}
I_{|\beta|}+(c-c_0) ({ \Theta_c})_{(\beta,\beta)} \right )^{-1} ({
\Theta_c})_{(\beta,\beta)}{ \omega}_{(\beta,\beta)}
\right\rangle.
\end{array}$$ By recalling that $$\widetilde{C}=C{\widetilde
R}\quad {\rm and}\quad {\widetilde R} =R \left [
\begin{array}{cc}
\Sigma^{-1}U^T & 0\\
0 & I_{n_3}
\end{array}
\right ]$$ and $$\underline{\nu} \|s\|^2 \leq \max\left\{ \left\langle s,
\widetilde{C}\widetilde{C}^{\,
T} s \right\rangle, \left\langle s,
C C^Ts \right\rangle
\right\}
\le \overline{\nu}\|s\|^2,\, \forall s,$$ from Lemma \[le2\], (\[eu1-A\]), (\[eq:nu-lower-upper\]), and (\[eq:two-nus\]) we know that $$\begin{array}[b]{l}
\displaystyle \langle [B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
\quad + B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}],\\[2mm]
{\cal
A}_c(\overline{y},W_1,W_2)^{-1}
[ B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\\[2mm]
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}\\[2mm]
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad+ B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}] \rangle
\end{array}$$ $$\label{ineq1}
\begin{array}{l}
\geq
\displaystyle \langle [\widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
\quad \, + \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-\widetilde C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}],\\[2mm]
\underline{{\cal H}}_c
[ \widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
\quad \, + \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-\widetilde C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}] \rangle\\[2mm]
\geq
\left(
{\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\displaystyle \langle [\widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\\[2mm]
\quad \, + \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\\[2mm]
\quad \, -\widetilde C_{(\alpha,\gamma)}^{\,T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}],
[ \widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\\[2mm]
\quad \,+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\\[2mm]
\quad \, -\widetilde C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}] \rangle\\[2mm]
\geq
\underline{\nu}\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\|[(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)},
(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)},(\Delta_{1/c})_{(a,c)}\xi_{(a,c)},\\[2mm]
\,\, \quad \quad \quad \quad \quad \quad
(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)},(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)},(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]\|^2
\\[2mm]
\ge \underline{\nu}\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1} \left [
\displaystyle \left (\min_{i \in a,1\leq j \leq |b_S|}\displaystyle \frac{1-(w_{b_S})_j}{c\lambda_i(\overline X)+(1-(w_{b_S})_j)}\right)^2 \|\xi_{(a,b_S)}\|^2\right.
\\[2mm]
+
\displaystyle \left (\min_{i \in a}\displaystyle \frac{2}{c\lambda_i(\overline X)+2}\right)^2 \|
\xi_{(a,b_L)}\|^2
+
\displaystyle \left (\min_{i \in a,j\in c}\displaystyle \frac{2}{c[\lambda_i(\overline X)-\lambda_i(\overline X)]+2}\right)^2 \|\xi_{(a,c)}\|^2
\\[2mm]
+
\displaystyle \left (\min_{i \in c, 1\leq j\leq |b_S|}\displaystyle \frac{(w_{b_S})_j+1}{((w_{b_S})_j+1)-c\lambda_i(\overline X )}\right)^2 \|\xi_{(c,b_S)}\|^2
\\[2mm]
\left. +
\displaystyle \left (\min_{i \in c}\displaystyle \frac{2}{-c\lambda_i(\overline X)+2}\right)^2 \|\xi_{(c,b_U)}\|^2+
\displaystyle \left (\min_{i \in \alpha, j \in
\gamma}\lambda_i/(\lambda_i+c|\lambda_j|)\right)^2 \|
\omega_{(\alpha,\gamma)}\|^2\right]
\\[2mm]
\ge
\underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\left[ \underline{\nu}_{a,b_S}^2 (\underline{\nu}_{a,b_S}+c)^{-2} \|
\xi_{(a,b_S)}\|^2+
\underline{\nu}_{a,b_L}^2 (\underline{\nu}_{a,b_L}+c)^{-2} \|
\xi_{(a,b_L)}\|^2\right.\\[2mm]
\quad\, +\underline{\nu}_{a,c}^2 (\underline{\nu}_{a,c}+c)^{-2} \|
\xi_{(a,c)}\|^2
+\underline{\nu}_{c,b_U}^2 (\underline{\nu}_{c,b_U}+c)^{-2} \|
\xi_{(c,b_U)}\|^2\\[2mm]
\quad \, \left.+\underline{\nu}_{c,b_S}^2 (\underline{\nu}_{c,b_S}+c)^{-2} \|
\xi_{(c,b_S)}\|^2
+\underline{\nu}_{\alpha,\gamma}^2 (\underline{\nu}_{\alpha,\gamma}+c)^{-2} \|
\omega_{(\alpha,\gamma)}\|^2\right]\\[2mm]
\geq \underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\underline{\nu}_0^2 (\underline{\nu}_0+c)^{-2}
\|(\xi_{(a,b_S)},\xi_{(a,b_L)},
\xi_{(a,c)},\xi_{(c,b_S)},
\omega_{(\alpha,\gamma)})\|^2.
\end{array}$$ Similarly, we get $$\begin{array}[b]{l}
\displaystyle \langle [B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
\quad \, + B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}],\\[2mm]
{\cal
A}_c(\overline{y},W_1,W_2)^{-1}
[ B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\\[2mm]
\quad \,\quad \,\quad \,\quad \, \quad \,\quad \,\quad \,\quad+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}\\[2mm]
\quad \,\quad \, \quad \,\quad \,\quad \,\quad \,\quad \,\quad + B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}] \rangle
\end{array}$$ $$\label{ineq2}
\begin{array}{l}
\leq
\displaystyle \langle [\widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
\quad \, + \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-\widetilde C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}],\\[2mm]
\overline{{\cal H}}_c
[ \widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[2mm]
\quad \, + \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-\widetilde C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}] \rangle\\[2mm]
\leq
\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \langle [\widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\\[2mm]
\quad \,+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\\[2mm]
\quad \, -\widetilde C_{(\alpha,\gamma)}^{\,T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}],
[ \widetilde B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+\widetilde B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}\\[2mm]
\quad \,+ \widetilde B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ \widetilde B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ \widetilde B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}\\[2mm]
\quad \, -\widetilde C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}] \rangle\\[2mm]
\leq
\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\|[(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)},
(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)},(\Delta_{1/c})_{(a,c)}\xi_{(a,c)},\\[2mm]
\,\, \quad \quad \quad \quad \quad \quad
(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)},(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)},(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]\|^2
\\[2mm]
\leq \overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \left (\max_{i \in a,1\leq j \leq |b_S|}\displaystyle \frac{1-(w_{b_S})_j}{c\lambda_i(F(\overline x))+(1-(w_{b_S})_j)}\right)^2 \|
\xi_{(a,b_S)}\|^2
\\[2mm]
\quad \,+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \left (\max_{i \in a}\displaystyle \frac{2}{c\lambda_i(F(\overline x))+2}\right)^2 \|
\xi_{(a,b_L)}\|^2
\\[2mm]
\quad \,+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \left (\max_{i \in a,j\in c}\displaystyle \frac{2}{c[\lambda_i(F(\overline x))-\lambda_i(F(\overline x))]+2}\right)^2 \|
\xi_{(a,c)}\|^2
\\[2mm]
\quad \,+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \left (\max_{i \in c}\displaystyle \frac{2}{-c\lambda_i(F(\overline x))+2}\right)^2 \|
\xi_{(c,b_U)}\|^2
\\[2mm]
\quad \,+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \left (\max_{i \in c, 1\leq j\leq |b_S|}\displaystyle \frac{(w_{b_S})_j+1}{((w_{b_S})_j+1)-c\lambda_i(F(\overline x))}\right)^2 \|
\xi_{(c,b_S)}\|^2
\\[2mm]
\quad \,+
\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\displaystyle \left (\max_{i \in \alpha, j \in
\gamma}\lambda_i/(\lambda_i+c|\lambda_j|)\right)^2 \|
\omega_{(\alpha,\gamma)}\|^2
\\[2mm]
\leq
\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_{a,b_S}^2 (\overline{\nu}_{a,b_S}+c)^{-2} \|
\xi_{(a,b_S)}\|^2
+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_{a,b_L}^2 (\overline{\nu}_{a,b_L}+c)^{-2} \|
\xi_{(a,b_L)}\|^2\\[2mm]
\quad \, +\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_{a,c}^2 (\overline{\nu}_{a,c}+c)^{-2} \|
\xi_{(a,c)}\|^2
+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_{c,b_U}^2 (\overline{\nu}_{c,b_U}+c)^{-2} \|
\xi_{(c,b_U)}\|^2\\[2mm]
\quad \, +\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_{c,b_S}^2 (\overline{\nu}_{c,b_S}+c)^{-2} \|
\xi_{(c,b_S)}\|^2
+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_{\alpha,\gamma}^2 (\overline{\nu}_{\alpha,\gamma}+c)^{-2} \|
\omega_{(\alpha,\gamma)}\|^2\\[2mm]
\leq \overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_0^2 (\overline{\nu}_0+c)^{-2} \|(\xi_{(a,b_S)},\xi_{(a,b_L)},
\xi_{(a,c)},\xi_{(c,b_S)},
\omega_{(\alpha,\gamma)})\|^2.
\end{array}$$ and $$\begin{array}[b]{l}
\displaystyle \| B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}
+B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\
\quad \, + B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}\|^2
\\[2mm]
\leq
\overline{\nu}
\|[(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)},
(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)},(\Delta_{1/c})_{(a,c)}\xi_{(a,c)},\\[3mm]
\,\, \quad \quad \quad \quad \quad \quad
(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)},(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)},(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]\|^2
\\[3mm]
\leq \overline{\nu}
\displaystyle \left (\max_{i \in a,1\leq j \leq |b_S|}\displaystyle \frac{1-(w_{b_S})_j}{c\lambda_i(F(\overline x))+(1-(w_{b_S})_j)}\right)^2 \|
\xi_{(a,b_S)}\|^2
\end{array}$$ $$\label{ineq2-added}
\begin{array}{l}
\, \quad +\overline{\nu}
\displaystyle \left (\max_{i \in a}\displaystyle \frac{2}{c\lambda_i(F(\overline x))+2}\right)^2 \|
\xi_{(a,b_L)}\|^2
\\[3mm]
\, \quad +\overline{\nu}
\displaystyle \left (\max_{i \in a,j\in c}\displaystyle \frac{2}{c[\lambda_i(F(\overline x))-\lambda_i(F(\overline x))]+2}\right)^2 \|
\xi_{(a,c)}\|^2
\\[3mm]
\, \quad +\overline{\nu}
\displaystyle \left (\max_{i \in c}\displaystyle \frac{2}{-c\lambda_i(F(\overline x))+2}\right)^2 \|
\xi_{(c,b_U)}\|^2
\\[3mm]
\, \quad +\overline{\nu}
\displaystyle \left (\max_{i \in c, 1\leq j\leq |b_S|}\displaystyle \frac{(w_{b_S})_j+1}{((w_{b_S})_j+1)-c\lambda_i(F(\overline x))}\right)^2 \|
\xi_{(c,b_S)}\|^2
\\[3mm]
\, \quad +
\overline{\nu}
\displaystyle \left (\max_{i \in \alpha, j \in
\gamma}\lambda_i/(\lambda_i+c|\lambda_j|)\right)^2 \|
\omega_{(\alpha,\gamma)}\|^2
\\[3mm]
\leq
\overline{\nu}
\overline{\nu}_{a,b_S}^2 (\overline{\nu}_{a,b_S}+c)^{-2} \|
\xi_{(a,b_S)}\|^2
+\overline{\nu}
\overline{\nu}_{a,b_L}^2 (\overline{\nu}_{a,b_L}+c)^{-2} \|
\xi_{(a,b_L)}\|^2\\[2mm]
+\overline{\nu}
\overline{\nu}_{a,c}^2 (\overline{\nu}_{a,c}+c)^{-2} \|
\xi_{(a,c)}\|^2
+\overline{\nu}
\overline{\nu}_{c,b_U}^2 (\overline{\nu}_{c,b_U}+c)^{-2} \|
\xi_{(c,b_U)}\|^2\\[2mm]
+\overline{\nu}
\overline{\nu}_{c,b_S}^2 (\overline{\nu}_{c,b_S}+c)^{-2} \|
\xi_{(c,b_S)}\|^2
+\overline{\nu}
\overline{\nu}_{\alpha,\gamma}^2 (\overline{\nu}_{\alpha,\gamma}+c)^{-2} \|
\omega_{(\alpha,\gamma)}\|^2\\[2mm]
\leq \overline{\nu}
\overline{\nu}_0^2 c^{-2}
\|(\xi_{(a,b_S)},\xi_{(a,b_L)},
\xi_{(a,c)},\xi_{(c,b_U)},\xi_{(c,b_S)},
\omega_{(\alpha,\gamma)})\|^2.
\end{array}$$ By using (\[anup-1-add0\]) and (\[ineq2-added\]) we have $$\label{eq:inequality003}
\begin{array}{l}
\displaystyle \Big|\Big\langle A^TD_c \Delta d_0, {\cal
A}_c(\overline{y},W_1,W_2)^{-1}[B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}\\[3mm]
\quad \, +B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}
+ B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}\\[3mm]
\quad \quad \quad \quad \quad \quad + B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]
\Big\rangle \Big|
\\[3mm]
\leq \| {\cal A}_c(\overline{y},W_1,W_2)^{-1}A^TD_c\Delta
d_0\|\, \|[B_{(a,b_S)}^{\, T}(\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)}\\[3mm]
\quad \, +B_{(a,b_L)}^{\, T}(\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)}
+ B_{(a,c)}^{\, T}(\Delta_{1/c})_{(a,c)}\xi_{(a,c)}\\[3mm]
\quad \,+ B_{(c,b_U)}^{\, T}(\Delta_{1/c})_{(c,b_U)} \xi_{(c,b_U)}
+ B_{(c,b_S)}^{\, T}(\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)}
-C_{(\alpha,\gamma)}^{\,
T}(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}]
\|
\\[3mm]
\leq \displaystyle \frac{\varrho_0}{\sqrt{2}}c^{-1}
(\|(\Delta\mu, \xi_{(b_U,b_U)},
\xi_{(b_S,b_S)},
\xi_{(b_L,b_L)}, { \omega}_{(\alpha,\alpha)}, {
\omega}_{(\beta,\beta)})\|^2\\[3mm]
\quad \quad \, + 2\|( \xi_{(b_U,b_S)}, \xi_{(b_S,b_L)},
\xi_{(b_U,b_L)}, \omega_{(\alpha,\beta)})\|^2
)^{1/2}\\[3mm]
\quad \quad \, \times\left( \overline{\nu}_0 \sqrt{\overline{\nu}} c^{-1} \|(\xi_{(a,b_S)},\xi_{(a,b_L)},
\xi_{(a,c)},\xi_{(c,b_L)},\xi_{(c,b_S)},
\omega_{(\alpha,\gamma)})\| \right)\,
\\[3mm]
\leq \displaystyle
\frac{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}{4}c^{-2}
(\|(\Delta\mu, \xi_{(b_U,b_U)},
\xi_{(b_S,b_S)},
\xi_{(b_L,b_L)}, { \omega}_{(\alpha,\alpha)}, {
\omega}_{(\beta,\beta)})\|^2\\[3mm]
\quad \quad \, \quad \, \quad \, \quad \,\quad \,+ 2\|( \xi_{(b_U,b_S)}, \xi_{(b_S,b_L)},
\xi_{(b_U,b_L)}, \omega_{(\alpha,\beta)})\|^2\\[3mm]
\, \quad \quad \,\quad \,\quad \,\quad \, \quad \,+2
\|(\xi_{(a,b_S)},\xi_{(a,b_L)},
\xi_{(a,c)},\xi_{(c,b_U)},\xi_{(c,b_S)},
\omega_{(\alpha,\gamma)})\|^2)\, .
\end{array}$$
By direct calculations we have $$\begin{array}{l}
\|\Delta Y\|^2-c^{-1}\left \langle W_1\Delta Y, \Delta Y \right \rangle\\[2mm]
=(\|\xi_{(a,a)}\|^2+2\|\xi_{(a,b_U)}\|^2+2\|\xi_{(c,b_L)}\|^2+\|\xi_{(c,c)}\|^2)\\[2mm]
+2(\|\xi_{(a,b_S)}\|^2-\langle \xi_{(a,b_S)}, (\Delta_{1/c})_{(a,b_S)}\xi_{(a,b_S)} \rangle)\end{array}$$ $$\label{ht2-1}
\begin{array}{l}
+2(\|\xi_{(a,b_L)}\|^2-\langle \xi_{(a,b_L)}, (\Delta_{1/c})_{(a,b_L)}\xi_{(a,b_L)} \rangle)\\[2mm]
+2(\|\xi_{(a,c)}\|^2-\langle \xi_{(a,c)}, (\Delta_{1/c})_{(a,c)}\xi_{(a,c)} \rangle)\\[2mm]
+2(\|\xi_{(c,b_U)}\|^2-\langle \xi_{(c,b_U)}, (\Delta_{1/c})_{(c,b_U)}\xi_{(c,b_U)} \rangle)\\[2mm]
+2(\|\xi_{(c,b_S)}\|^2-\langle \xi_{(c,b_S)}, (\Delta_{1/c})_{(c,b_S)}\xi_{(c,b_S)} \rangle)\\[2mm]
+(\|\xi_{(b_U,b_U)}\|^2-\langle \xi_{(b_U,b_U)}, (\Delta_{1/c})_{(b_U,b_U)}\xi_{(b_U,b_U)} \rangle)\\[2mm]
+(\|\xi_{(b_L,b_L)}\|^2-\langle \xi_{(b_L,b_L)}, (\Delta_{1/c})_{(b_L,b_L)}\xi_{(b_L,b_L)} \rangle)
\end{array}$$ and $$\label{ht2-2}
\begin{array}{l}
\|\Delta\Gamma \|^2-\langle \Delta\Gamma , W_2(\Delta\Gamma
)\rangle \\[2mm]
= \left(\|\omega_{(\gamma,\gamma)}\|^2
+2\|\omega_{(\beta,\gamma)}\|^2\right)
+2\left(\|\omega_{(\alpha,\gamma)}\|^2 -\langle
\omega_{(\alpha,\gamma)},(\Theta_c)_{(\alpha,\gamma)}\omega_{(\alpha,\gamma)}\rangle\right)
\\[2mm]
\quad \, + \left(\|\omega_{(\beta,\beta)}\|^2 -\langle
\omega_{(\beta,\beta)},(\Theta_c)_{(\beta,\beta)}\omega_{(\beta,\beta)}\rangle
\right)\, .
\end{array}$$ Now we are ready to estimate the lower and upper bounds of $-\langle V (\Delta y), \Delta y \rangle$. In light of (\[Ahh\]), (\[anup-opposite\]), (\[ineq1\]), (\[eq:inequality003\]), (\[ht2-1\]) and (\[ht2-2\]), we have $$\label{lb}
\begin{array}{lcl}
-\langle V(\Delta y), \Delta y \rangle &\geq&
{c}^{-1}(\|\xi_{(a,a)}\|^2+2\|\xi_{(a,b_U)}\|^2+2\|\xi_{(c,b_L)}\|^2+\|\xi_{(c,c)}\|^2)\\[2mm]
&& +{c}^{-1}\left(\|\omega_{(\gamma,\gamma)}\|^2+2
\|\omega_{(\beta,\gamma)}\|^2\right)
\\[2mm]
& & +\underline\kappa_1(c)\|(\Delta\mu,\xi_{(b_S,b_S)},\omega_{(\alpha,\alpha)})\|^2
+\underline\kappa_2(c)\|\xi_{(a,b_S)}\|^2\\[2mm]
&&+\underline \kappa_3(c)\|\xi_{(a,b_L)}\|^2 +\underline \kappa_4(c)\|\xi_{(a,c)}\|^2+\underline\kappa_5(c)\|\xi_{(b_U,b_U)}\|^2\\[2mm]
&& +\underline \kappa_6(c)\|\xi_{(b_U,b_S)}\|^2+\underline\kappa_7(c)\|\xi_{(b_U,b_L)}\|^2+\underline \kappa_8(c)\|\xi_{(b_U,c)}\|^2\\[2mm]
&& +\underline \kappa_9(c)\|\xi_{(b_S,b_L)}\|^2 +\underline \kappa_{10}(c)\|\xi_{(b_S,c)}\|^2+\underline\kappa_{11}(c)\|\xi_{(b_L,b_L)}\|^2\\[2mm]
& &
+\underline\kappa_{12}(c)\|\omega_{(\alpha,\beta)}\|^2+\underline\kappa_{13}(c)\|\omega_{(\alpha,\gamma)}\|^2+
\underline\kappa_{14}(c)\|\omega_{(\beta,\beta)}\|^2,
\end{array}$$ where $$\begin{array}{l}
\underline \kappa_1(c):=\left( \overline{\sigma}\overline{\eta}+(c-c_0)\right )^{-1}
-{\varrho_0 \overline{\nu}_0 \sqrt{\overline{\nu}}} c^{-2}\\[2mm]
\underline \kappa_2(c):=\underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\underline{\nu}_0^2 (\underline{\nu}_0+c)^{-2}-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
+\displaystyle \frac{\min_{i\in a}\lambda_i(F(\overline x))}{[c \min_{i\in a}\lambda_i(F(\overline x))+2]}\\[2mm]
\underline \kappa_3(c):=\underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\underline{\nu}_0^2 (\underline{\nu}_0+c)^{-2}-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
+\displaystyle \frac{\min_{i\in a}\lambda_i(F(\overline x))}{[c \min_{i\in a}\lambda_i(F(\overline x))+2]}\\[2mm]
\underline \kappa_4(c):=\underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\underline{\nu}_0^2 (\underline{\nu}_0+c)^{-2}-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}\\[2mm]
\quad \quad \quad \quad \quad \quad \quad \quad \quad +\displaystyle \frac{(\min_{i\in a}\lambda_i(F(\overline x))-\max_{j \in c}\lambda_j(F(\overline x)))}{ [c (\min_{i\in a}\lambda_i(F(\overline x))-\max_{j \in c}\lambda_j(F(\overline x)))+2]}\\[4mm]
\underline \kappa_{6}(c):=2\left(
\overline{\sigma}\overline{\eta}/2+(c-c_0)\right )^{-1}
-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
\\[3mm]
\underline \kappa_{7}(c):=\underline \kappa_{6}(c)\\[2mm]
\underline \kappa_{8}(c):=-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
+\displaystyle \frac{-\max_{j\in c}\lambda_j(F(\overline x))}{[-c \max_{j\in c}\lambda_j(F(\overline x))+2]}\\[2mm]
\underline \kappa_{9}(c):=\underline \kappa_{6}(c)
\end{array}$$ $$\begin{array}{l}
\underline \kappa_{10}(c):=\underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
\underline{\nu}_0^2 (\underline{\nu}_0+c)^{-2}-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
+\displaystyle \frac{-\max_{j\in c}\lambda_j(F(\overline x))}{[-c \max_{j\in c}\lambda_j(F(\overline x))+2]}\\[3mm]
\underline \kappa_{12}(c):=\underline \kappa_{6}(c)
\\[3mm]
\underline \kappa_{13}(c):=2 c^{-1}[1 -\overline{\nu}_0(\overline{\nu}_0+
c)^{-1}] +2\underline{\nu}
\left({\overline{\sigma}}\overline{\eta}+2(c-c_0)\right)^{-1}
{\underline{\nu}}_0^2 (\underline{\nu}_0+c)^{-2}
-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2} \, ,
\end{array}$$ and $$\underline \kappa_{5}(c)=\underline \kappa_{11}(c)=\underline \kappa_{14}(c): = \displaystyle \min_{t \in [0,1]}
\psi(t;c,a_c,b_c,c_0)$$ with $\psi(\cdot; \cdot)$ being defined as (\[phicom\]) in Lemma \[phiineq\] and $$a_c:={c}^{-1}-{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}\,
, \quad b_c:=\overline{\sigma}\overline{\eta}\, .$$ It follows from (\[k4com\]) in Lemma \[phiineq\] that for $c\ge {\overline{c}}$, $$\underline \kappa_{14}(c)=c^{-1}
-{\rho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2} -
\frac{\overline{\sigma}\overline{\eta}}{c(\sqrt{c}+\sqrt{c_0})^2}
\, .$$Thus, there exists a positive number $\underline \epsilon_1$ such that for $c\ge {\overline{c}}$ we have $$\min \left\{ \frac{1}{2} \min_{i \notin \{1,5,11,14\}} \{\underline \kappa_i(c) \}, \min_{i \in \{1,5,11,14\}} \{\underline \kappa_i(c) \} \right\}\ge
c^{-1}-\underline \epsilon_1{c^{-2}}\, .$$ Therefore, from (\[lb\]) we have $$\label{lbe}
-\langle V(\Delta y), \Delta y \rangle \geq ( c^{-1}-\underline \epsilon_1c^{-2}) \|\Delta y\|^2\, .$$ On the other hand, in light of (\[Ahh\]), (\[anup-1\]), (\[ineq2\]), (\[eq:inequality003\]), (\[ht2-1\]) and (\[ht2-2\]), we have
$$\label{ub}
\begin{array}{lcl}
-\langle V(\Delta y), \Delta y \rangle &\leq&
{c}^{-1}(\|\xi_{(a,a)}\|^2+2\|\xi_{(a,b_U)}\|^2+2\|\xi_{(c,b_L)}\|^2+\|\xi_{(c,c)}\|^2)\\[2mm]
&& +{c}^{-1}\left(\|\omega_{(\gamma,\gamma)}\|^2+2
\|\omega_{(\beta,\gamma)}\|^2\right)
\\[2mm]
& & +\overline\kappa_1(c)\|(\Delta\mu,\xi_{(b_S,b_S)},\omega_{(\alpha,\alpha)})\|^2
+\overline\kappa_2(c)\|\xi_{(a,b_S)}\|^2\\[2mm]
&&+\overline \kappa_3(c)\|\xi_{(a,b_L)}\|^2 +\overline \kappa_4(c)\|\xi_{(a,c)}\|^2+\overline\kappa_5(c)\|\xi_{(b_U,b_U)}\|^2\\[2mm]
&& +\overline \kappa_6(c)\|\xi_{(b_U,b_S)}\|^2+\overline\kappa_7(c)\|\xi_{(b_U,b_L)}\|^2+\overline \kappa_8(c)\|\xi_{(b_U,c)}\|^2\\[2mm]
&& +\overline \kappa_9(c)\|\xi_{(b_S,b_L)}\|^2 +\overline \kappa_{10}(c)\|\xi_{(b_S,c)}\|^2+\overline\kappa_{11}(c)\|\xi_{(b_L,b_L)}\|^2\\[2mm]
& &
+\overline\kappa_{12}(c)\|\omega_{(\alpha,\beta)}\|^2+\overline\kappa_{13}(c)\|\omega_{(\alpha,\gamma)}\|^2+
\overline\kappa_{14}(c)\|\omega_{(\beta,\beta)}\|^2,
\end{array}$$
where $$\begin{array}{l}
\overline \kappa_1(c):=\left(
\underline{\sigma}\underline{\eta}/2+(c-c_0)\right )^{-1}
+{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}\\
\overline \kappa_2(c):=2c^{-1}+\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_0^2 (\overline{\nu}_0+c)^{-2}+{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}\\
\overline \kappa_3(c)=\overline \kappa_4(c):=\overline \kappa_2(c)\\
\overline \kappa_{6}(c):=2\left(
\underline{\sigma}\underline{\eta}/2+(c-c_0)\right )^{-1}
+{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
\\
\overline \kappa_{7}(c):=\overline \kappa_{6}(c)\\
\overline \kappa_{8}(c):=2c^{-1}+{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}\\
\overline \kappa_{9}(c):=\overline \kappa_{6}(c)
\\
\overline \kappa_{10}(c):=\overline{\nu}\underline{\sigma}^{-1}\underline{\eta}^{-1}
\overline{\nu}_0^2 (\overline{\nu}_0+c)^{-2}+{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}\\
\overline \kappa_{12}(c):=\overline \kappa_{6}(c)
\\
\overline \kappa_{13}(c):=\overline \kappa_{2}(c)
\end{array}$$ and $$\overline \kappa_{5}(c)=\overline \kappa_{11}(c)=\overline \kappa_{14}(c): = \displaystyle \max_{t \in [0,1]} \psi(t;c,a'_c,b'_c,c_0)$$ with $$a^\prime_c:={c}^{-1}+{\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
\, , \quad b^\prime_c:=\underline{\sigma}\underline{\eta}/2\, .$$ It follows from (\[u4com\]) in Lemma \[phiineq\] that for $c\ge {\overline{c}}$, $$\label{u4c}
\begin{array}[b]{lcl}
\overline \kappa_{14}(c)&=&\max\{\psi(0;c,a^\prime_c,b^\prime_c,c_0),\psi(1;c,a^\prime_c,b^\prime_c,c_0)\}
\\[2mm]
&=& {\varrho_0\overline{\nu}_0\sqrt{\overline{\nu}}}c^{-2}
+\max\{{c}^{-1}, \left(
{\underline{\sigma}}\underline{\eta}/2+(c-c_0)\right)^{-1}\}\, .
\end{array}$$ Thus, there exists a positive number $\mu_0\geq \max \{\varrho_0,\underline \epsilon_1\}$ such that for $c\ge {\overline{c}}$ we have $$\max \left\{ \frac{1}{2} \max_{i \notin \{1,5,11,14\}} \{\overline \kappa_i(c) \}, \min_{i \in \{1,5,11,14\}} \{\overline \kappa_i(c) \} \right\}\le
c^{-1}+\mu_0 {c^{-2}}\, .$$ Therefore, from (\[ub\]) we have $$\label{ube}
-\langle V(\Delta y), \Delta y \rangle \leq ( c^{-1}+\mu_0c^{-2}) \|\Delta y\|^2\, .$$ By (\[lbe\]) and (\[ube\]), noting that $\mu_0\ge \underline \epsilon_1$, we obtain that $$\mu_0 c^{-2}\|\Delta y\|^2 \ge \langle V(\Delta y)+c^{-1} \Delta
y, \Delta y\rangle \ge -\mu_0 c^{-2}\|\Delta y\|^2 \, .$$This shows that (\[import11\]) holds. The proof is completed.
7 true pt
Now we are ready to state our main result on the rate of convergence of the augmented Lagrangian method for nonlinear semidefinite nuclear norm composite optimization.
\[thconv1nlsdp\] Suppose that Assumptions (sdnop-A1) and (sdnop-A2) are satisfied. Let ${c_0}$ and $\underline {\eta}$ be two positive numbers obtained by [Proposition \[pronlsdp\]]{}. Let $\overline{\eta}$, $\overline{c}$, and $\varrho_0$ be defined as in [(\[mu1nlsdp\])]{}, [(\[eq:barc-sdp\])]{}, and [(\[varrho0-sdp\])]{}, respectively. Let $\mu_0$ be obtained by [Proposition \[thdcnlsdp\]]{}. Define $$\varrho_1:=2\varrho_0 \quad {\rm and} \quad \varrho_2:=4\mu_0.$$ Then for any $c \geq {\overline{c}}$, there exist two positive numbers $\varepsilon$ and $\delta $ $($both depending on $c$$)$ such that for any $(Y,\mu, \Gamma)
\in\mathbb{B}_{\delta}(\overline{Y},\overline \mu, \overline{\Gamma})$, the problem $$ \min \ L_c(x, Y,\mu, \Gamma)
\quad {\rm s.t.} \ x\in {\mathbb {B}}_{\varepsilon}(\overline{x})\,$$has a unique solution denoted $x_c(Y,\mu, \Gamma)$. The function $x_c(\cdot, \cdot, \cdot)$ is locally Lipschitz continuous on $\mathbb{B}_{\delta}(\overline{Y},\overline \mu, \overline{\Gamma})$ and is semismooth at any point in $\mathbb{B}_{\delta}(\overline{Y},\overline \mu, \overline{\Gamma})$, and for any $(\zeta, \Xi) \in
\mathbb{B}_{\delta}(\overline{Y},\overline \mu, \overline{\Gamma})$, we have $$\|x_c(Y,\mu, \Gamma)-\overline{x}\| \leq \varrho_1 \|(Y,\mu,
\Gamma)-(\overline{Y},\overline \mu, \overline{\Gamma})\|/{{c}}$$and $$\|(Y_c(Y,\mu, \Gamma), {\mu}_c(Y,\mu, \Gamma),\Gamma_c(Y,\mu, \Gamma))- (\overline{Y},\overline \mu, \overline{\Gamma})\| \leq \varrho_2 \|(Y,\mu,
\Gamma)-(\overline{Y},\overline \mu, \overline{\Gamma})\|/{{c}},$$where $Y_c(Y,\mu, \Gamma)$, ${\mu}_c(Y,\mu, \Gamma)$ and $ {\Gamma}_c(Y,\mu, \Gamma)$ are defined as $$\begin{array}{rl}
Y_c(Y,\mu,\Gamma)&:={\rm D}\theta_c(F(x_c(Y,\mu,\Gamma))+Y/c)^*,\\[3mm]
\mu_c(Y,\mu,\Gamma)&:= \mu+ch(x_c(Y,\mu,\Gamma))\quad \rm{and} \\[2mm]
\quad \Gamma_c(Y,\mu,\Gamma)&:=\Pi_{{\cal S}^p_+}(\Gamma-c g(x_c(Y,\mu,\Gamma)))\, .
\end{array}$$
[**Proof.**]{} If Assumptions (sdnop-A1) and (sdnop-A2) are satisfied, then from Propositions \[pronlsdp\] and \[thdcnlsdp\] we know that both Assumption B1 and Assumption B2 (with $\gamma =2$) made in Section \[general-discussions\] are satisfied. Then the conclusions in this theorem follow from Theorem \[comthconv1\].
Conclusions {#final-section}
===========
This paper provides an analysis on the rate of convergence of the augmented Lagrangian method for solving the nonlinear semidefinite nuclear norm optimization problem. By assuming that $K$ is a closed convex cone, and that ${\rm D}\theta_c(\cdot)$ and $\Pi_{K^*}(\cdot)$ are semismooth everywhere, we first establish a general result on the rate of convergence of the augmented Lagrangian method for a class of general composite optimization problems. Then we apply this general result to the nonlinear semidefinite nuclear norm optimization problem under the constraint nondegeneracy condition and the strong second order sufficient condition. The methodology suggests us that we may verify Assumptions B1 and B2 to obtain the rate of convergence of the augmented Lagrange method for other optimization problems.
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[^1]: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China (e-mail:lwzhang@dlut.edu.cn).
[^2]: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China (e-mail:zyl@dlut.edu.cn).
[^3]: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China (e-mail:wujia@dlut.edu.cn).
[^4]: The research of Liwei Zhang is supported by the National Natural Science Foundation of China under project grant No.11571059, No.11731013 and No.91330206.
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2024-06-15T01:26:51.906118
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https://example.com/article/3747
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This article represents my own opinion and may contain affiliate links. Please read my disclosures for more information.
A better more efficient and odor eliminating homemade air purifier than just taping a 20x20x1 filter to a box fan. Sometimes you need to help clear the air in a dirty environment but don't want to use an expensive air purifier such as in a room after renovating and painting. Here's a cheap and easy way to build one.
What You'll Need
Materials
A pair of scissors or utility knife Quick Info About Filters The nice thing about this box fan filter setup is you can use any filters you want. If you are only concerned about large particles generated from something like cutting wood, you can use cheaper, lower MERV rated filters. If you're worried about finer particles from allergens such as mold, you can use a higher MERV rated filter. To understand more about what the MERV ratings mean have a look at Table 2 on this EPA article on residential air
I chose to go with the Filtrete Home Odor Reduction Filters which are a new type of filter from Filtrete. They contain a lot of activated carbon to help filter out odors and VOCs. They are rated MERV 11 and are equivalent to their 1000 MPR furnace filters. They should do a good job with even the fine drywall dust and the activated carbon will help a lot with odors. I bought a 4 pack for around $57 which gives me 2 sets of filters.
Filtrete Odor Reducing Air Filters The filtering power of these Filtrete Odor Reducing filters isn't listed on Filtrete's website or on Amazon but I contacted them and found out that these filters have a MERV 11 rating and filter 90% of particles between 1-10 microns which makes them more efficient than the I've been using in my air conditioning for the past few years. Plus Filtrete packs over 180 grams of activated carbon to help reduce odors.
After I go through both sets of carbon filters I'm probably going to switch to the which does a much better job of filtering small particles. If odors are a problem I'll get some and tape them over top of the Filtrete filters.
Okay, enough of the why, now for the how!
Step 1: Unbox The Filters You're thinking "OMG! He's actually describing how to open a cardboard box?!?!?!" The best deal I found for these filters were on
The box is sealed very well. Not only is it taped but the seams are also glued together. To get the filters out of the box I cut the top where it's perforated with a utility knife as shown.
Be careful not to cut too deep and damage the filters. Keep the box someplace safe to the side while we continue. The filtering power of these Filtrete Odor Reducing filters isn't listed on Filtrete's website or on Amazon but I contacted them and found out that these filters have a MERV 11 rating and filter 90% of particles between 1-10 microns which makes them more efficient than the Filtrete Micro Allergen Reduction Filters I've been using in my air conditioning for the past few years. Plus Filtrete packs over 180 grams of activated carbon to help reduce odors.After I go through both sets of carbon filters I'm probably going to switch to the Filtrete Elite Allergen Reduction Filter which does a much better job of filtering small particles. If odors are a problem I'll get some Cut-to-fit Carbon Prefilters and tape them over top of the Filtrete filters.Okay, enough of the why, now for the how!You're thinking "OMG! He's actually describing how to open a cardboard box?!?!?!" The best deal I found for these filters were on Amazon and with my Prime membership (or supersaver shipping) the shipping is free. Plus the packing box is going to be part of the filter so we need to keep in intact.The box is sealed very well. Not only is it taped but the seams are also glued together. To get the filters out of the box I cut the top where it's perforated with a utility knife as shown.Be careful not to cut too deep and damage the filters. Keep the box someplace safe to the side while we continue. Step 2: Hinge Filters
With the filters lined up, tape one of the short (20") edges of the filters to create a hinge between the two filters as shown.
I decided to go with white duck tape so it looks a little nicer but it makes it hard to see in the photos against the white cardboard filter frame.
Step 3: Tape Filters To Fan Start by taking 2 of the filters out of their plastic wrappers and lay them one on top of the other with the air flow arrows pointing towards each other. With the Odor Reducing Fitlers this means the black, carbon sides will be facing each other.With the filters lined up, tape one of the short (20") edges of the filters to create a hinge between the two filters as shown.I decided to go with white duck tape so it looks a little nicer but it makes it hard to see in the photos against the white cardboard filter frame.
Use a strip of duck tape to secure each side to the side of the fan.
Lay the box fan face down on a flat surface to mount the filters to the back making sure the bottom of the filters are about flush with the bottom of the fan and do not extend past the bottom.Use a strip of duck tape to secure each side to the side of the fan.
Step 4: Cut and Attach the Cardboard
Using a pencil, trace around the filters (while pressing down the cardboard so nothing moves) to mark where the cardboard needs to be cut.
Lift the cardboard up (the front piece of tape acts like a hinge) and cut along the lines to trim the sides. By the way, I really like these .
Repeat the process for the bottom cardboard. The other large piece from the box is seamed but it's taped and glued and very stiff so it shouldn't be an issue but you can run a strip of duck tape over the seem if it makes you feel better.
Also keep in mind that the bottom of the fan has feet. I positioned the cardboard underneath the feet and then pulled the feet out to tape.
After taping up the sides of the bottom cover to the filters, I added an extra strip of duck tape all the way around where the filters/cardboard meets the fan for added support. The rounded corners of the fan means there might still be an air gap there so check them and add extra duck tape if necessary. On the bottom there are also some holes, duck tape over those as well. Finally, replace the feet.
Step 5: Seal The Back Where the hinged filters meet the cardboard in the back, add another strip of duck tape for support and to seal any gaps.
Give another look around the seams to make sure there aren't any gaps. If you find any, tape them up.
When using the fan, I always make sure that the cord isn't underneath the cardboard and instead is under the metal fan chassis, just in case something goes wrong and the cord overheats. Can never be too safe. Replacing Filters Cut out one of the large sides of from the cardboard shipping box, place it over the top of the of the filters and secure it with a strip of tape to the top of the fan. Position it so that it's pretty even over both filters but it doesn't have to be perfect.Using a pencil, trace around the filters (while pressing down the cardboard so nothing moves) to mark where the cardboard needs to be cut.Lift the cardboard up (the front piece of tape acts like a hinge) and cut along the lines to trim the sides. By the way, I really like these Fiskars Cuts+More 5-in-1 Multi-Purpose Scissors Repeat the process for the bottom cardboard. The other large piece from the box is seamed but it's taped and glued and very stiff so it shouldn't be an issue but you can run a strip of duck tape over the seem if it makes you feel better.Also keep in mind that the bottom of the fan has feet. I positioned the cardboard underneath the feet and then pulled the feet out to tape.After taping up the sides of the bottom cover to the filters, I added an extra strip of duck tape all the way around where the filters/cardboard meets the fan for added support. The rounded corners of the fan means there might still be an air gap there so check them and add extra duck tape if necessary. On the bottom there are also some holes, duck tape over those as well. Finally, replace the feet.
When it's time to replace filters, use a utility knife to cut the filters free but leave the cardboard in place. Then just hinge and attach the new filters.
Air purifiers can be expensive and you've probably seen articles recommending to just put a 20" x 20" x 1" furnace filter on a cheap 20" box fan and POOF! instant cleaner air for not a lot of money. It really does clean the air pretty cheap.There's a problem with this though. These fans weren't designed to be run with a filter. The filter will restrict air flow which will put a higher strain on the motor causing it to use more electricity and in worse cases could be a fire hazard. The higher the MERV rating (cleaning efficiency) of the filter the more stress it will put on the fan Don't worry! You can still have youras long as the filter area is increased to decrease the effect of air resistance. Instead of using one 20x20x1 filter we'll use two 20x25x1 filters which increases the filter surface area over 250%. It's a little more expensive because you're using two filters instead of one but the increased filter surface area also helps the filter last longer before it gets clogged up and we're saving on energy use compared to a single filter.I can't take credit for the design, I found it via Marshall Hansen Design but I'm using different filters.I recently remodeled my basement and there's a lot of dust (including drywall dust and sawdust) and fumes from paint, cleaners and other building materials. It's an underground basement and mold has to always be a conern too. Because part of the space will be my home theater in the future I plan to get a more expensive air purifier that's smaller and quieter such as this Fellowes Quiet Air Purifier AP-300PH with True HEPA Filter because it has great reviews, is reasonably priced and the replacement filters aren't that expensive or a Sharp Plasmacluster True HEPA Air Purifier or Blueair HepaSilent Air-Purification System if I find some extra Benjamins in the couch cushions. But I don't want to put that in the dusty environment right away because I'll have to replace the more expensive filters fairly quickly because the air is so bad. I also don't want to spend the money right now but I do want cleaner air now.So I decided to get things going with athat has filters that not only clean the air of particulates but also. Even after I purchase an air purifier I'll still have an air purifier I can use for other purposes like when I'm painting or cutting wood.Also, don't forget to add more plants to your home. They're natures air purifiers. Not only do they convert carbon dioxide to oxygen but houseplants filter toxins and emit negative ions too!
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2024-02-27T01:26:51.906118
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https://example.com/article/1554
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Solo sequel? A Boba Fett Star Wars movie is in the works
It's been rumored for as long as Disney has had the rights to the Star Wars franchise, but we may be finally about to see a standalone Boba Fett film from the sci-fi galaxy far, far away.
According to the Hollywood Reporter, James Mangold, director of the fantastic X-Men spin-off movie Logan, is set to helm. It's also expected that he'll be joined by Simon Kinberg, who worked to co-write the Logan script with Mangold, in a both a writing and producing role. Simon Kinberg also wrote and created the superb Star Wars: Rebels animated series.
Logan, telling the story of an ageing Wolverine (Hugh Jackman), was a fantastic action film, earning Mangold an Oscar nod for best adapted screenplay.
Solo in his sights?
The news comes as Lucasfilm and Disney prepare to launch Solo: A Star Wars Story this week, the first of the current wave of Star Wars films to focus in on just one character for George Lucas's universe.
Could it be that the Boba Fett film would be a sequel to Solo? In the original trilogy (to which Solo is a prequel of sorts) the bounty hunter Boba Fett was Solo's nemesis, with Fett constantly looking to hunt down the owner of the Millennium Falcon. With Solo star Alden Ehrenreich reportedly contracted for two more movies, it'd make sense to see the two characters face off at some point.
Fett, originally played by British actor Jeremy Bulloch, originally appeared in 1980's Empire Strikes Back, and quickly became a fan favorite thanks to his cool composure and array of gadgets. The less said about his revival in Episodes I through III, however, the better.
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2024-05-02T01:26:51.906118
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https://example.com/article/5149
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KOTA KINABALU: An heir to the “Sulu sultanate” was asked to create trouble in Semporna by his uncle Agbimuddin Kiram (pic), who led the group of armed intruders at Kampung Tanduo in Lahad Datu three years ago, the High Court was told on Tuesday.
Businessman Amir Bahar Hushin Kiram, 53, said he refused to comply to with his uncle’s orders even though Agbimuddin was the “crown prince” of the sultanate.
“My uncle called me into a room and he asked me to convince our people to make problems in Semporna.
“I told him I respect him as my uncle but I must respect my father’s decision for me not to be involved in anything that goes against the Malaysian authorities,” he said, adding that Agbimuddin was angry with him.
He said Agbimuddin told him this after negotiations between Agbimuddin and top Special Branch officers at Kampung Tanduo on Feb 16, 2013.
Testifying before Justice Stephen Chung, Amir Bahar said among those at the negotiations were former Bukit Aman Special Branch deputy director Datuk Abdul Hamid Bador and former Sabah Special Branch deputy chief Asst Comm Zulkifli Abd Aziz.
Amir Bahar is among the key accused and the fourth defence witness in the trial of 19 individuals facing various charges, including waging war against the Yang di-Pertuan Agong, over the intrusion of Kampung Tanduo in February 2013.
To a question by defence counsel Majnah Abdullah, Amir Bahar said he lived in Jolo, southern Philippines, and was in Sabah on Feb 14, 2013 when he was called by an uncle, Datu Naufal, who lived in Likas, here.
He said Datu Naufal was a cousin of his father, Esmail Kiram, who had been “elected” Sulu sultan by the people there, though another brother, Jamallul Kiram, was also the sultan but lived in Manila.
Amir Bahar said Datu Naufar had called him on behalf of ACP and the Malaysian Government, who wanted him to arrange for his father Esmail Kiram to meet Agbimuddin.
According to Amir Bahar, his father was willing to come to Sabah to meet Agbimuddin, but Jamallul rejected the proposal, insisting that he was the rightful representative of the sultanate.
Amir Bahar said his father asked him to go to the negotiations at Kampung Tanduo where Hamid met Agbimuddin on Feb 16.
At that meeting, Hamid told Agbimuddin that Prime Minister Datuk Seri Najib Tun Razak had personally ordered him (Hamid) to get the gunmen to leave Tanduo.
Amir Bahar said Hamid had assured Agbimuddin that talks over the Sabah claim would begin when he and his men returned to the Philippines.
Agbimuddin was agreeable, provided the Government put in writing its willingness to negotiate the Sabah claim.
Majnah: Why did Agbimuddin tell Hamid Bador to tell the Prime Minister that this request must be put in writing?
Amir Bahar: Because Agbimuddin said the Government likes to promise things verbally, then they retract their promise.
The hearing continues.
|
2024-03-24T01:26:51.906118
|
https://example.com/article/9733
|
[The effect of high-frequency ventilation of the lungs on the pulmonary and systemic circulations in microembolism of the pulmonary artery].
The linear and volumetric blood flow velocity in the ascending aorta and pulmonary artery conus, right-left ventricular ejection balance, pulmonary and femoral arterial blood pressures, pulmonary microcirculation in fat pulmonary microembolism induced during the routine and high-frequency jet lung ventilation (HFJLV) were studied by ultrasonic techniques in acute experiments on cats with open chest under nembutal narcosis. Pulmonary microembolism was shown to resulted in 487 and 252% increases in pulmonary vascular resistance during the routine and HFJLVs, respectively. There were also 167 and 127% increases in mean pulmonary pressure and 60 and 34% decreases in the volumetric velocity of pulmonary blood flow. The linear velocity of pulmonary blood flow was unchanged with routine lung ventilation, whereas it decreased by 68% with HFJLV. Microembolism impaired the balance between right and left ventricular ejections with blood being redistributed into the greater circulation. The imbalance lasted 5-7 min during HFJLV, while with the routine lung ventilation it was preserved up to the end of the experiment, and systemic blood pressure and total peripheral vascular resistance decreased. Alveolar edema developed in interstitial pulmonary edema. The animals' death occurred 40-60 min later.
|
2024-07-28T01:26:51.906118
|
https://example.com/article/9198
|
base 10, what is -1014680 + -420?
-1015100
In base 13, what is c8b + -135?
b56
In base 16, what is -28d2d - -369?
-289c4
In base 8, what is -2 + -55230201?
-55230203
In base 2, what is -101110110100 + -100000101000101?
-100110011111001
In base 6, what is -24110 - -123223?
55113
In base 3, what is 1102 - 200120120211?
-200120112102
In base 4, what is -110332002231 - 2?
-110332002233
In base 6, what is 1351521405 - 1?
1351521404
In base 7, what is -35366 + 235336?
166640
In base 11, what is -18a0 - -1254a5?
123705
In base 6, what is -311234125 + -1?
-311234130
In base 2, what is 10000010000 + -1011111101?
100010011
In base 12, what is 8810a0 + 3?
8810a3
In base 15, what is 7a3 + 4c55?
5508
In base 3, what is -1002122002 - 102121?
-1010001200
In base 14, what is 75824 - -268?
75a8c
In base 6, what is -105311 - -12514?
-52353
In base 7, what is 12 + 6301654?
6301666
In base 7, what is -633 + 22354?
21421
In base 9, what is 42287 + 22125?
64423
In base 5, what is -10402231 - 220?
-10403001
In base 10, what is 112 + -556628?
-556516
In base 2, what is -10 + -10110101110110001010101100000?
-10110101110110001010101100010
In base 2, what is -1110111000111111010010 - 0?
-1110111000111111010010
In base 12, what is 160278 - 9?
16026b
In base 15, what is a7e69d - 5?
a7e698
In base 6, what is -40512540 + -10?
-40512550
In base 7, what is 350316541 + -2?
350316536
In base 12, what is -199ab1 - 42a?
-19a31b
In base 14, what is -dbc0239c + -3?
-dbc023a1
In base 15, what is 23 + -6e91be?
-6e919b
In base 10, what is 9222983 + -3?
9222980
In base 15, what is 1469c - -b2?
1475e
In base 5, what is -4 + 112233440330?
112233440321
In base 16, what is 1d - -669290?
6692ad
In base 14, what is -2406b2 - -c?
-2406a4
In base 16, what is 690 - 1afd8?
-1a948
In base 3, what is 12 + -1211010100220?
-1211010100201
In base 7, what is -10014 - 3154?
-13201
In base 13, what is -22a - 9513?
-9740
In base 15, what is 6d08 - a1?
6c57
In base 7, what is 4 - -234333531?
234333535
In base 10, what is -1043 + 1369?
326
In base 14, what is 0 + 14bb7ac4?
14bb7ac4
In base 6, what is -104 - -120052?
115544
In base 7, what is -405 - -65416?
65011
In base 16, what is -1ea - -9479?
928f
In base 4, what is -22 + -220120123?
-220120211
In base 14, what is 7 + 3162d06?
3162d0d
In base 6, what is 342301 - -115?
342420
In base 3, what is -2002002200 - 201111?
-2002211011
In base 9, what is -22483 - 24001?
-46484
In base 5, what is 12342 + 10012234?
10030131
In base 4, what is -132130231 + -11102?
-132201333
In base 2, what is -11000001011000010 + 1101011?
-11000001001010111
In base 12, what is -6153 - -6872?
71b
In base 15, what is 78 + -565d?
-55d5
In base 14, what is 15c + 3031?
318d
In base 2, what is -110011011000001 - -1011101001000?
-100111101111001
In base 11, what is 4 - 132a2a78?
-132a2a74
In base 5, what is -213243010 - -442?
-213242013
In base 10, what is -1 + 827571?
827570
In base 13, what is -7 - -10a0a96b?
10a0a964
In base 5, what is -421312330144 + 1?
-421312330143
In base 13, what is 6 - c311a6?
-c311a0
In base 5, what is -12 + -10441121?
-10441133
In base 3, what is 2011100 + -22011010?
-12222210
In base 14, what is -322 + -5b32?
-6054
In base 11, what is -a556aa7 - -3?
-a556aa4
In base 13, what is -588 - 43250?
-43808
In base 2, what is -100010000001000111010010 + -101?
-100010000001000111010111
In base 4, what is 1131 + 3000033?
3001230
In base 9, what is -228581013 + 2?
-228581011
In base 8, what is 4 + 5141035?
5141041
In base 12, what is -3 - 302119?
-302120
In base 4, what is -1302310 + -33031210?
-101000120
In base 12, what is -2 - -1a86909?
1a86907
In base 3, what is -122020 - 11110000102210?
-11110001002000
In base 6, what is -1024 - -20103302?
20102234
In base 14, what is 58 + -20034a?
-2002d2
In base 4, what is 1033323301202 + 10?
1033323301212
In base 9, what is -43254 - 3144?
-46408
In base 12, what is 1658 - -1b9a?
3636
In base 9, what is -363 - -2212305?
2211832
In base 2, what is 1000010101 - -110010101100010000?
110010110100100101
In base 13, what is -146 - 8946?
-8a8c
In base 5, what is 11224423 - -11332?
11241310
In base 6, what is 4005 - -1422110?
1430115
In base 6, what is -12434141001 + -1?
-12434141002
In base 9, what is 2511632 - 60?
2511562
In base 14, what is -2cc - 32bc?
-35aa
In base 13, what is 9440 - 895?
8878
In base 16, what is -139 - 33183?
-332bc
In base 13, what is 4274a13 - 4?
4274a0c
In base 16, what is 3 - -7de5b7?
7de5ba
In base 3, what is -111112222221 + -21111?
-111120021102
In base 2, what is -101100110111101001001000000 + -100?
-101100110111101001001000100
In base 3, what is -200212012 - 211010?
-201200022
In base 6, what is -11 - 10101353?
-10101404
In base 16, what is 2b + 109002?
10902d
In base 9, what is 5022 + -8285?
-3263
In base 11, what is 65991787 + -3?
65991784
In base 7, what is -1533215 - 146?
-1533364
In base 3, what is -10201020001221201 - 2?
-10201020001221210
In base 2, what is -101100110111 + -10001101000010010?
-10010010101001001
In base 16, what is 4 + 28b5760?
28b5764
In base 3, what is 11001100000021100012 + -11?
11001100000021100001
In base 6, what is 2201520 + 123410?
2325330
In base 8, what is 0 - 73760171?
-73760171
In base 2, what is -10 + -100011111011000001100?
-100011111011000001110
In base 16, what is -4 + 41997de?
41997da
In base 9, what is 362762 - -33?
362805
In base 4, what is -3130011112012 + 0?
-3130011112012
In base 8, what is 2 - -36267510?
36267512
In base 2, what is 110001111111010011010011101 + 101?
110001111111010011010100010
In base 5, what is 2341 + 11430421?
11433312
In base 4, what is 203 + 1300201123?
1300201332
In base 15, what is 737 + -69a?
8c
In base 2, what is 11 + 1101111010001110101100010?
1101111010001110101100101
In base 12, what is 0 + 64a873?
64a873
In base 2, what is 10 + 1001110100111011100?
1001110100111011110
In base 3, what is 21112011 - 1201101?
12210210
In base 5, what is -142 - 232444032?
-232444224
In base 10, what is 4367471 + -5?
4367466
In base 10, what is -840 + -308524?
-309364
In base 15, what is 3c20 + -30e0?
b30
In base 9, what is 14 + 1745874?
1745888
In base 9, what is 5 - -3084458?
3084464
In base 14, what is -29b1 - 14287?
-16c58
In base 16, what is -18c - 12471?
-125fd
In base 3, what is -221122102100 - -22120?
-221122002210
In base 11, what is 91277 + 72?
91339
In base 12, what is 1a94 + 7584?
9458
In base 6, what is -445313 - -132?
-445141
In base 13, what is -6 + 17ab68?
17ab62
In base 3, what is 2 + -1222122110202?
-1222122110200
In base 10, what is 19 + -2957?
-2938
In base 14, what is 120 + -5065d?
-5053d
In base 4, what is -20132131022030 - 10?
-20132131022100
In base 5, what is -102304110211 + 21?
-102304110140
In base 9, what is 0 - -150151511?
150151511
In base 4, what is 22211330312 - 13?
22211330233
In base 15, what is -2 - 170c34?
-170c36
In base 14, what is -94d + -454?
-da3
In base 12, what is a074a28 + 4?
a074a30
In base 10, what is 5 + -1797458?
-1797453
In base 7, what is -2 - 641641434?
-641641436
In base 7, what is -61 + 202105064?
202105003
In base 9, what is 1677805222 + 0?
1677805222
In base 12, what is -22418503 + 1?
-22418502
In base 6, what is -10124251 - 114?
-10124405
In base 10, what is 10 + 542921?
542931
In base 3, what is -1 + -10211222212102?
-10211222212110
In base 9, what is -6 + -853547?
-853554
In base 8, what is -574 - 1764261?
-1765055
In base 4, what is 13 + 3303313121?
3303313200
In base 6, what is 1221122335 + 13?
1221122352
In base 12, what is -3 - -1134874?
1134871
In base 8, what is -706 - 3327604?
-3330512
In base 10, what is -3870 + 908?
-2962
In base 10, what is 1 + -61534216?
-61534215
In base 4, what is -112011132 + 201?
-112010331
In base 3, what is 121112221211 - -10101?
121120002012
In base 10, what is -80833097 - 2?
-80833099
In base 10, what is 92127 + -105?
92022
In base 7, what is -21 + 4651454?
4651433
In base 14, what is 26623 - 1b5?
2644c
In base 6, what is 50223052 + -4?
50223044
In base 13, what is -6 - 895432?
-895438
In base 13, what is 171603 - -26?
171629
In base 10, what is -36136 + -31695?
-67831
In base 5, what is -22344 - -3113?
-14231
In base 9, what is -15 + -28618457?
-28618473
In base 12, what is 142201b2 - -2?
142201b4
In base 5, what is -1300 + 21313230?
21311430
In base 9, what
|
2023-10-04T01:26:51.906118
|
https://example.com/article/5232
|
In the NBA—a 30-franchise league where individual talent ultimately decides the fate of every team—losing a star in free agency tends to signal the end of an era, and a downshift into a new life cycle. It's impossible for even the most anticipatory front office to avoid the aftermath.
Earlier this month the Utah Jazz—an organically constructed, well-run franchise that's recently made a habit of making shrewd trades, brilliant draft picks, and systematic free agent signings—lost star player Gordon Hayward after having won 51 games and a playoff series in the cutthroat Western Conference.
It's an obvious gut punch to lose Hayward to the Boston Celtics. The Jazz scored a team-low 103.7 points per 100 possessions when Hayward was on the bench last year. He was their most talented all-around player and, at only 27 years old, a pillar Jazz GM Dennis Lindsey could build around.
But even though its short and long-term title odds took a massive hit at the same time numerous conference rivals got stronger, Utah isn't going anywhere. Hayward's points, athleticism, intelligence, and positional versatility are gone, but his departure will not fundamentally alter how the Jazz play. Their core identity remains intact, and without a go-to scorer to lean on, Utah will double down on a philosophy that made them so resilient in the first place.
Amazingly, instead of heading back toward the lottery, Utah will plow ahead with a roster that's simultaneously raw, experienced, talented, smart, versatile, and deep in ways that run parallel with the 2014-15 Atlanta Hawks, a star-less 60-win juggernaut that excelled on both ends; what they lacked in elite individual talent, the Hawks made up for with a selfless offense that was impossible to game-plan against, and consistently competent in every other area.
No Hawks player on that team averaged more than 17 points per game. But three averaged more than 15 points per game, and six players averaged in double figures. By comparison, last year two Jazz players averaged more than 15 points per game but only four averaged in double figures. That ratio figures to change after Hayward's departure.
Even if Utah's ultimate potential without Hayward is now lower, there's a benefit to unleashing lineups with no obvious weaknesses.
At the forefront is Rudy Gobert, a one-man Night's Watch whose presence singlehandedly guarantees a top-five defense. (Utah finished third in defensive rating last season, and Gobert finished first in Defensive Real Plus-Minus.) Even without Hayward's team-leading 21.9 points per game, Gobert's offensive improvement last year should splash a good amount of optimism onto a group that already uses his dominant rim protection as an automatic and unlimited bail bondsman.
Utah has surrounded Gobert with complementary two-way pieces that should sustain (if not improve) an imposing defensive unit without stripping too much off offensively.
Alongside the 2nd-team All-NBA center are reliable professionals who know how to play (Thabo Sefolosha, Jonas Jerebko, Ekpe Udoh, Joe Ingles, Joe Johnson), exciting young players (Donovan Mitchell, Dante Exum, Tony Bradley), and near-their-prime weapons (Ricky Rubio, Derrick Favors, Rodney Hood) who are all ready to make the jump to the next level.
Dante Exum appears fully recovered from 2016 ACL surgery. Photo by Kyle Terada - USA TODAY Sports
Rubio is a badger at the point of attack. He shreds through screens, irritates shooters, and takes charges with a grin, all while existing as an avant-garde opportunity maker. Rubio is slightly below average at his position, but that's more to do with the absurd depth at point guard than his own shortcomings.
That said, those weaknesses are well known, and fair or not, they are slightly exaggerated as a result of his reputation. Guards who don't force their man to fight over a screen, or let him sag down to the edge of the paint without worry, are an easy scapegoat for a struggling offense. Rubio's shot is welcomed by opposing coaches, and the only observers who wince when he shoots are his own team's fans.
But, the Minnesota Timberwolves boasted terrific offense with Rubio at the helm last year. He also made 40.8 percent of his catch-and-shoot threes after the All-Star break, and just about everyone on Utah's roster will enjoy having him around—even if George Hill was acceptable in the same role.
Gobert, who's emerged as one seriously savage lob threat, will benefit from his new teammate's creativity. According to Synergy Sports, only three players were more efficient than Rubio feeding roll men last year (minimum 200 possessions): Chris Paul, John Wall, and James Harden. Rubio was also a train wreck in transition, but that shouldn't be as problematic with the slow-poke Jazz.
And unlike in Minnesota, Rubio will always have at least one more playmaker flanking him on the wing. Johnson and Ingles are two Olympic-level archers who're plenty comfortable running a pick-and-roll or carving a defense up from the post, while Hood, Rubio's probable backcourt partner in the starting lineup, will stand in as a discounted insurance policy for Hayward.
Hood, who will be 25 in October, is injury prone and less consistent than his ex-All-Star teammate, but he owns similar traits and a nearly identical physical profile. Utah will politely ask him to increase his usage and efficiency this year, and it's very possible he obliges.
Whether that broadened responsibility will negatively impact Hood's defense is something to watch, as will Jazz head coach Quin Snyder's willingness to field smaller units that widen driving lanes for his perimeter-oriented pawns. Hood is crafty, poised, and deliberate, but he lacks the athletic burst around the rim that's shared by any run-of-the-mill first option. He attacks closeouts with confidence, can snake a pick-and-roll, and is dangerous with his feet set.
But, in part thanks to Utah's larger lineups, Hood too often settles for the inefficient pull-up jumpers that Utah will need him to ditch; a thicker free-throw rate from him would do wonders for this team.
Speaking of two-big units, Favors' role lingers as a question mark Snyder will need to answer sooner than later. Can a bulky forward share the floor with Gobert for extended stretches, or is Favors—when healthy—simply the best backup center in basketball? It's a contract year for the 26-year-old, and a trade deadline deal is conceivable given the increasingly uncomfortable offensive fit. On the other hand, defensively, a Favors and Gobert tandem are an unscalable mountain for any team that's slumping beyond the arc. Turning the restricted area into a moat can be pretty damn convenient in a seven-game series. (Lineups that featured Favors and Gobert without Hayward only played 57 minutes last season, according to NBAWowy.)
Elsewhere, the most thrilling variables both reside in the backcourt, where Mitchell and Exum function as inexperienced, high upside ball-handlers who have the potential to add a different dimension to Utah's attack. Their battle for minutes as Rubio's backup is something to keep an eye on. There were rumblings in Las Vegas that Exum, who's already extension eligible, played in those exhibitions primarily so the Jazz could showcase his rapidly decreasing physical limitations to the rest of the league after having had left ACL surgery in early 2016. He just turned 22, and once more appears to have that special line-drive quickness in his back pocket.
Off the bench, Sefolosha and Jerebko may be confused with window dressing, but each allows Snyder to tinker with more like-sized lineups without sacrificing too much spacing. Both can shoot, put it on the floor, and keep the ball moving in a hand-off-heavy scheme that prohibits a defense from focusing on just one or two primary threats. Udoh will replicate 75 percent of what Gobert provides for a dozen minutes every night.
|
2023-08-29T01:26:51.906118
|
https://example.com/article/1899
|
const EventEmitter = require('events');
const WorkerProcess = require('./worker/process');
const Sequence = require('./util/sequence');
const messages = require('./worker/message');
const ProcessRequest = messages.Request;
const ProcessResponse = messages.Response;
const workerSerial = new Sequence(1);
class Worker extends EventEmitter {
constructor({ srcFilePath, maxTasks, endurance, stopTimeout }) {
super();
this.id = workerSerial.nextValue();
this.calls = new Map();
this.tasksStarted = 0;
this.maxTasks = maxTasks;
this.endurance = endurance;
this.isTerminating = false;
this.isProcessAlive = false;
const process = this.process = new WorkerProcess(srcFilePath, { stopTimeout });
process.once('ready', () => {
this.isProcessAlive = true;
this.emit('ready');
});
process.on('message', data => {
const response = new ProcessResponse(data);
this.emit('data', response);
});
process.once('exit', code => {
this.exitCode = code;
this.isProcessAlive = false;
this.emit('exit', code);
});
}
/**
*
* @param {Task} task
*/
handle(task) {
this.calls.set(task.id, task);
this.tasksStarted += 1;
this.process.handle(new ProcessRequest({
callId: task.id,
workerId: this.id,
method: task.method,
args: task.args
}));
}
/**
* Gets all in-progress/unhandled calls from the worker.
*
* @returns {Array.<Task>}
*/
withdrawTasks() {
const unhandledCalls = Array.from(this.calls.values());
this.calls.clear();
return unhandledCalls;
}
/**
*
* @returns {number}
*/
get activeCalls() {
return this.calls.size;
}
/**
*
* @returns {boolean}
*/
isOperational() {
return this.isProcessAlive && !this.isTerminating;
}
/**
*
* @returns {boolean}
*/
isBusy() {
return this.activeCalls > 0;
}
/**
*
* @returns {boolean}
*/
canAcceptWork() {
return !this.isTerminating
&& this.activeCalls < this.maxTasks
&& this.tasksStarted < this.endurance;
}
/**
*
* @returns {boolean}
*/
isProcessAlive() {
return this.isProcessAlive;
}
/**
*
* @returns {boolean}
*/
isExhausted() {
return this.tasksStarted >= this.endurance;
}
/**
*
*/
stop() {
this.isTerminating = true;
this.process.exit();
}
/**
* @param {number} duration
*/
profiler(duration) {
this.process.handle({ cmd: 'profiler', data: { duration }});
}
/**
*
*/
takeSnapshot() {
const cmd = 'takeSnapshot';
this.calls.set(cmd, {
timer: null,
reject: () => {},
resolve: () => {},
});
this.process.handle({ cmd });
}
}
module.exports = Worker;
|
2024-04-27T01:26:51.906118
|
https://example.com/article/9233
|
The Best Gifts for the Best Dad
"License to Quill "is a page-turning James Bond-esque spy thriller starring William Shakespeare and Christopher Marlowe during history's real life Gunpowder Plot. The story follows the fascinating golden age of English espionage, the tumultuous cold war gripping post-Reformation Europe, the cloak-and-dagger politics of Shakespeare's England, and lastly, the mysterious origins of the Bard's most haunting play: "Macbeth." You won't want to miss this fast-paced historical retelling
"License to Quill "is a page-turning James Bond-esque spy thriller starring William Shakespeare and Christopher Marlowe during history's real life Gunpowder Plot. The story follows the fascinating golden age of English espionage, the tumultuous cold war gripping post-Reformation Europe, the cloak-and-dagger politics of Shakespeare's England, and lastly, the mysterious origins of the Bard's most haunting play: "Macbeth." You won't want to miss this fast-paced historical retelling
|
2024-07-08T01:26:51.906118
|
https://example.com/article/5022
|
Combate à Covid
Reações nos demais 5% não tiveram gravidade. 50 mil na China tomaram o imunizante, desenvolvido em parceria com o Instituto Butantan, de SP.
|
2024-02-17T01:26:51.906118
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https://example.com/article/4324
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Congress Controls Fates of Numerous Federal Health Programs
Community health centers, Medicare therapy caps at the forefront
With another government shutdown looming tomorrow (Thursday), the fates of several federal health programs hang in the balance of Congress’ decision.
A spending bill that passed the House Tuesday night is thought to be unlikely to make it through the Senate, but others such as Senator Chuck Schumer (D-NY) believe a deal is “closer than ever.”
Much as the Children’s Health Insurance Program (CHIP) was used as a bargaining chip last month, funding for over 1,400 community health care centers hang in the balance this time around. Additionally, previous limits imposed on Medicare spending on physical therapy, occupational therapy, and speech-language pathology could be prevented from implementation if Congress takes action.
Such measures are typically dependent upon being attached to another, larger item in a comprehensive spending bill—known as extenders, due to their ability to lengthen the period of time a measure is in effect.
Advocates are attempting to persuade lawmakers to keep these programs alive, foremost among the $3.6 billion provided annually to community health center that service about 27 million low-income Americans.
The aforementioned therapy caps are set at $2,010 for occupational therapy, and another $2,010 for the combination of physical therapy and speech-language pathology.
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2023-12-08T01:26:51.906118
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https://example.com/article/3205
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Transiently binding antibody fragments against Lewis x and sialyl-Lewis x.
Biomolecular recognition is often characterised by low affinity where many weak interactions work either alone or in concert, resulting in an inherent dynamic situation. For example the well-studied weak binding of cell-cell interactions is predominantly based on a range of carbohydrates that interact with numerous (protein) ligands. Finding appropriate binders to these carbohydrate structures may pave the way for new analytical strategies based on low affinity, and recombinant antibody technology is a promising approach to the development of such reagents. We have in the present study characterised two low affinity human single chain antibody fragments (scFv) by surface plasmon resonance for use in such applications. The two clones, LeX1 and sLeX10, had been selected from a naive phage display library against Lewis x (Le(x)) and sialyl Le(x) (sLe(x)), respectively. Both LeX1 and sLeX10 showed low affinity, with K(D) values of 3.5+/-0.7 x 10(-5) M for Le(x) and 2.6+/-0.7 x 10(-5) M for sLe(x), respectively. Kinetic studies revealed the scFvs to be associated with fast dissociation rates, with Kd values higher than 0.1 s(-1) for both LeX1 and sLeX10. Apart from the Lewis structures Le(x) and sLe(x), we investigated the conformational isomers Lewis a and sialyl-Lewis a together with the monosaccharide units of the Lewis structures, and both scFvs showed high specificity for their respective carbohydrate. Taking these observations together we have demonstrated that scFv with fast reaction kinetics and low affinity have the necessary characteristics for further development as specific tools in analytical strategies, e.g. differentiation of cells based on the various configurations of carbohydrate epitopes.
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2024-05-03T01:26:51.906118
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https://example.com/article/2608
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Ludwigshafen
Ludwigshafen am Rhein () is a city in Rhineland-Palatinate, Germany, on the river Rhine, opposite Mannheim. With Mannheim, Heidelberg, and the surrounding region, it forms the Rhine Neckar Area.
Known primarily as an industrial city, Ludwigshafen is the home of chemical giant BASF and other companies. Among its cultural facilities are the Staatsphilharmonie Rheinland-Pfalz. It is the birthplace of the former German chancellor Helmut Kohl and the philosopher Ernst Bloch.
The city is a global city with 'sufficiency' status.
History
Early history
In antiquity, Celtic and Germanic tribes settled in the Rhine Neckar area. During the 1st century B.C. the Romans conquered the region, and a Roman auxiliary fort was constructed near the present suburb of Rheingönheim.
The Middle Ages saw the foundation of some of Ludwigshafen's future suburbs, including Oggersheim, Maudach, Oppau, and Mundenheim. Most of the area, however, remained swampland, with its development hindered by seasonal flooding of the Rhine.
The Rheinschanze
The Rhine Neckar region was part of the territory of the Prince-elector of the Kurpfalz, or Electorate of the Palatinate, one of the larger states within the Holy Roman Empire. The foundation of the new capital of the Kurpfalz, Mannheim, was a decisive influence on the development of the area as a whole. Parallel to the foundation of Mannheim in 1606, a fortress (die Rheinschanze) was built by Frederick IV, Elector Palatine on the other side of the Rhine to protect the City of Mannheim, thus forming the nucleus of the City of Ludwigshafen itself.
In the 17th century the region was devastated and depopulated during the Thirty Years' War, and also in King Louis XIV of France’s wars of conquest in the later part of the century.
It was only in the 18th century that the settlements around the Rheinschanze began to prosper, profiting from the proximity of the capital Mannheim. Oggersheim in particular gained some importance, after the construction of both a small palace serving as secondary residence for the Elector, and the famous pilgrimage church, Wallfahrtskirche. For some weeks in 1782, the great German writer and playwright Friedrich Schiller lived in Oggersheim, on flight from his native Württemberg).
War returned to the Ludwigshafen area with the armies of the French Revolution. The palace at Oggersheim was burned down, Mannheim besieged several times, and all the area west of the Rhine annexed by France from 1798 to 1813. The Electorate of the Palatinate was split up. The eastern bank of the Rhine with Mannheim and Heidelberg was given to Baden, while the western bank (including the Ludwigshafen area) was granted to Bavaria, following the Wars of Liberation (1813-1815), in which the French were expelled. The Rhine had become a frontier and the Rheinschanze, cut off politically from Mannheim, lost its function as the neighbouring city's military bulwark.
Foundation of Ludwigshafen
In 1808, during the French occupation, Carl Hornig of Mannheim purchased the fortress from the French authorities and turned it into a way station for passing river traffic. Later, the Rheinschanze with its winter-proof harbour basin (created by a flood in 1824) was used as trading post. Hornig died in 1819, but Johann Heinrich Scharpff, a businessman from Speyer, continued Hornig's plans, which were then turned over to his son-in-law, Philipp Markus Lichtenberger, in 1830. Their activities marked the beginning of the civilian use of the Rheinschanze.
The year 1844 was the official birth of Ludwigshafen, when Lichtenberger sold this property to the state of Bavaria (Bayern), and the military title of the fortress was finally removed. The Bavarian king, Ludwig I, set forth plans to rename the settlement after himself and to start construction of an urban area as a Bavarian rival to Mannheim on the opposite bank.
During the failed German revolution of 1848 rebels captured Ludwigshafen, but they were bombarded from Mannheim (rumours said the Mannheimers didn't aim at the revolutionaries, but on the rival harbour's infrastructure), and Prussian troops quickly expelled the revolutionaries. On December 27, 1852, King Maximilian II granted Ludwigshafen am Rhein political freedom and as on November 8, 1859, the settlement gained city status.
Industry and growth of population
At its founding Ludwigshafen was still a very modest settlement with just 1,500 inhabitants. Real growth began with industrialization, and gained enormous momentum in Ludwigshafen due to its ideal transport facilities. In addition to its excellent position and harbor facilities on the Rhine, a railway connecting Ludwigshafen with the Saar coalfields was completed in 1849.
The year 1865 was an important date in the history of independent Ludwigshafen. After several discussions, BASF decided to move its factories from Mannheim to the Hemshof district, which belonged to Ludwigshafen. From then on, the city's rapid growth and wealth were linked to BASF's success and its expansion into becoming one of the world's most important chemical companies. Ludwigshafen also became home to several other rapidly growing chemical companies, including Friedrich Raschig GmbH, the Benckiser company (founded by Johann Benckiser), Giulini Brothers, Grünzweig&Hartmann AG, and .
With more jobs available, the population of Ludwigshafen increased rapidly. In 1899 the city was governing more than 62,000 residents (compared to 1,500 in 1852).
This population explosion looked quite “American” to contemporaries; it determined Ludwigshafen's character as a “worker's city”, and created problematic shortages of housing and real estate. The solution was the expansion of the municipal area and the incorporation of the two nearest villages, Friesenheim and Mundenheim, in the years 1892 and 1899. In the area between the city centre and those two suburbs new quarters (“North” and “South”) were built after (then) modern urban development plans. Because the ground was marshy and too low to be protected from Rhine floods, all the new houses were built on raised ground, sometimes as high as 5 metres above the original ground. Visitors can see the original ground level in many backyards of Ludwigshafen, which are sometimes two floors below street level.
World War I through World War II
During World War I (1914-1918), Ludwigshafen's industrial plants played a key role in Germany's war economy, producing chemical ingredients for munitions, as well as much of the poison gas used on the Western Front. This contributed to Ludwigshafen having the dubious honour, on May 27, 1915, of being the target of the world's first strategic aerial bombardment. French aircraft attacked the BASF plants, killing twelve people and setting the precedent for the age to come.
When the war was lost by Germany in 1918, the left bank of the Rhine was occupied by French troops, in accordance with the terms of the peace agreement. The French occupation lasted until 1930, and some of Ludwigshafen's most elegant houses were erected for the officers of the French garrison.
The economic recovery of the 1920s was marred by one of the worst industrial explosions in history when, on Sept. 21, 1921, a BASF storage silo in Oppau blew up, killing more than 500 people, injuring a further 2,000, and destroying countless buildings.
Despite this setback, Ludwigshafen reached a population of 100,000 in 1922, thus gaining “City” status. It prospered until the worldwide economic crisis of 1929, which brought unemployment, labor trouble, political strife, and the rise of the Nazis.
The Nazi party had few followers and votes in working-class-dominated Ludwigshafen, after 1933, when they had come to power in Germany, the Nazis succeeded in enforcing their policies in Ludwigshafen. Many small houses with gardens were built, especially in the Gartenstadt. Further, similar to Nazi plans in other cities (e.g. Hamburg), they aimed at creating a ”Greater Ludwigshafen” by agglomerating smaller towns and villages in the vicinity. Thus Oggersheim, Oppau, Edigheim, Rheingönheim, and Maudach became suburbs of Ludwigshafen, raising its population to 135,000. The Ludwigshafen synagogue was destroyed in 1938 and its Jewish population of 1,400 was deported in 1940.
During the Oil Campaign of World War II, the Allies conducted bombing of Ludwigshafen and Oppau. Thirteen thousand Allied bombers hit the city in 121 separate raids during the war, of which 56 succeeded in hitting the IG Farben plant. Those 56 raids dropped 53,000 bombs each containing 250 to 4,000 pounds of high explosives, plus 2.5 million 4-pound magnesium incendiary bombs (the bombers also dropped millions of leaflets warning the civilians to evacuate the city, plus counterfeit ration coupons). Repairs took longer and longer as spare parts became more difficult to find. By December 1944, so much damage had been done to vital utilities that output dropped to nearly zero. Follow-up raids every week ended production permanently. By war's end most dwellings were destroyed or damaged; 1,800 people had died, and 3,000 were injured.
The Allied ground advance into Germany reached Ludwigshafen in March 1945. The US 12th Armored Division and 94th Infantry Division captured Ludwigshafen against determined German resistance in house-to-house and block-to-block urban combat during 21–24 March 1945.
Post-war rebuilding
Post-war, Ludwigshafen was part of the French occupation zone, becoming part of the newly founded Bundesland (state) of Rheinland-Pfalz and thus part of the Federal Republic of Germany. Reconstruction of the devastated city and revival of the economy was supported by the Allies, especially by American aid. In 1948, the “Pasadena Shares Committee” sent packages of blankets, clothing, food, and medicines to help the residents of post-war Ludwigshafen. Many friendships started to form, so that in 1956, Ludwigshafen am Rhein and Pasadena, California became sister cities.
Large parts of the city were literally ruined, which were rebuilt in the architectural style of the 1950s and 1960s. The most important projects were the Hochstraßen (highways on stilts), the revolutionary new main station (then the most modern station in Europe), several tower blocks and a whole new suburb, the satellite quarter Pfingstweide north of Edigheim.
The city's economic wealth allowed social benefits and institutions to be introduced. The population number reached its all-time climax in 1970 with more than 180,000 inhabitants, thus surpassing even the capital of Rheinland-Pfalz, Mainz, for a while.
Financial crisis
In the early 1970s, a plan to reform the composition of the German Bundesländer, which would have created a new state around a united Mannheim-Ludwigshafen as capital with more than half a million inhabitants, failed.
Nevertheless, further ambitious projects were financed in Ludwigshafen, first of all the 15-floor city hall with its linked-up shopping centre (Rathaus Center). The last (up to now) new incorporated suburb was Ruchheim in 1974.
But then a process began that accelerated during the 1980s and 1990s and caused the financial near-collapse of Ludwigshafen. The enormous maintenance costs of the buildings and institutions introduced during the “fat time”, new tax regulations that cut down the trade tax profits from the local industries, and thousands of dismissals in BASF were the main causes for the city's crisis. Loss of population due to the loss of working places and general economic trends, such as the oil crises, further worsened Ludwigshafen's financial situation at the end of the 20th century.
The negative aspects of industrial success became obvious when examinations revealed the bad state of air and the Rhine due to pollution. There had always been some stench or dirt all over the city, caused by BASF and other plants, and as long as the industry had prospered, people had accepted it. Besides that, the concrete constructions that had been so modern after the war and had a formative influence on today's cityscape were increasingly considered as obsolete.
Contemporary Ludwigshafen
In recent years, many efforts have been made to enhance Ludwigshafen's image in the media. The city administration has cut down its deficit by cutting down social payments and maintenance, pollution has been (not least by BASF) restricted, the formerly rotten Hemshof quarter has been restored.
In 2008, a fire broke out in a building where many ethnic Turks lived. 9 people died, all of them Turks and 5 of them children. It was believed to be an arsonist attack, however this was found to be not true.
One of the most annoying faults of Ludwigshafen – at least for many of the city's inhabitants - was its comparative lack of high-quality shopping possibilities. It has attempted to repair this deficiency by creating a second large shopping mall on the southern tip of the city centre (the Walzmühle near Berliner Platz) with affiliated railway station (Ludwigshafen-Mitte). In addition, another shopping mall on the banks of the Rhine, the Rhein-Galerie, was completed in September 2010.
Ludwigshafen has enormous importance as an industrial city.
Districts
Centre
The city centre of Ludwigshafen is comparatively small and dominated by post-war buildings. Its northern and southern boundaries are the Hochstraßen (highways on stilts), the Rhine is in the East and the main station is located in the West of downtown Ludwigshafen, at a walking distance of about 15 minutes from the central pedestrian precinct Bismarckstraße that forms, together with the shopping mile Ludwigsstraße, the main North-South Axis, connecting the so-called “North Pole” with the Rathaus Center and the “South Pole” with Berliner Platz, the Walzmühle shopping centre and Ludwigshafen (Rhein) Mitte station. The main east–west connections are the Bahnhofsstraße and Kaiser-Wilhelm-Straße. The Pfalzbau, Staatsphilharmonie, Wilhelm-Hack-Museum and the half-destroyed monument Lutherkirche are main features of downtown Ludwigshafen.
South
The Südliche Innenstadt or “southern city centre” (ca. 29,000 inhabitants) includes the real city centre as described above and the Stadtteil Süd or “South” quarter. “South” has some of the most attractive residential areas, especially the Parkinsel area. Other sub-quarters of “South” are the Musikantenviertel or the Malerviertel. In a few years, there will be one more highly prized residential area (“Rheinufer Süd”) on the Rhine near the Walzmühle on former industrial estates.
North
The Nördliche Innenstadt (ca. 22,000 inhabitants) includes the Hemshof, “North” and “West” districts. Hemshof and “North” represent the “old town” of Ludwigshafen, they are known for their very high proportion of foreign inhabitants, making them culturally diverse. ”West” (also called Valentin-Bauer-Siedlung) is located between main station and main cemetery.
Friesenheim
Friesenheim (ca. 18,000 inhabitants) is located north of Hemshof and is one of the two (the other one being Mundenheim) “mother villages” of Ludwigshafen, because they were responsible for the administration of Ludwigshafen prior to its independence. Helmut Kohl was born in Friesenheim. Its western district, the Froschlache, boasts four impressive tower blocks.
Oppau
Oppau (ca. 10,000 inhabitants) in the North is dominated by the nearby BASF and had once been a town of its own prior to its incorporation into Ludwigshafen. In its history, it has been afflicted by several catastrophes like the explosion of 1921 and the flood of 1882.
Edigheim
Edigheim (ca. 9,000 inhabitants) had once been a part of Oppau in the South, today ist almost as large as Oppau.
The Pfingstweide (ca. 6,000 inhabitants) is Ludwigshafen's northernmost district; it is dominated by tower blocks and is located in close vicinity to Frankenthal.
Gartenstadt
The Gartenstadt (ca. 18,000 inhabitants), west of Mundenheim, is (as the name “garden city” suggests) a very green suburb, dominated by flat roofed houses and some tower blocks. Its sub-districts are Niederfeld, Hochfeld and Ernst-Reuter-Siedlung.
Mundenheim
Mundenheim (ca. 13,000 inhabitants) is a very old suburb, it boasts its own railway station, an extensive industrial area near the harbour. A sub-district is the Herderviertel in Mundenheim's North.
Oggersheim
Oggersheim (ca. 23,000 inhabitants) is one of the most important suburbs, being much like a town for itself (which it was in the Middle Ages). Helmut Kohl owned a bungalow in southern Oggersheim. The Wallfahrtskirche, a railway station, the important Unfallklinik (“accident hospital”), and several large residential blocks are to be found in Oggersheim. For the last few years, the northern subdistricts of Notwende and Melm have seen a large amount of building activities in their new housing estates.
Rheingönheim
Rheingönheim (ca 7,000 inhabitants), as the southernmost suburb of Ludwigshafen, is known mainly for its industry (Woellner) and its game enclosure Wildpark.
Maudach
Maudach (ca. 7,000 inhabitants), in Ludwigshafen's South-West, is a popular residential area, closely associated with the Maudacher Bruch park.
Ruchheim
Ruchheim (ca. 6,000 inhabitants), as the westernmost suburb, has long been a small agricultural village, but now it is growing rapidly due to new housing estates.
Transport
Although Ludwigshafen has no airfield, it is well connected with several airports in the region. There are small airfields near Speyer, Bad Dürkheim and Worms, a medium-sized regional airport in Mannheim, and the Frankfurt International Airport in about an hour's driving distance.
Ludwigshafen is the most important German harbour west of the Rhine. The local industry depends on shipping their raw materials and products on the river. The harbour of Ludwigshafen consists of several basins in the South of the city near Mundenheim (Luitpoldhafen, Kaiserwörthhafen, Mundenheimer Altrheinhafen), the wharfs along the river parallel to the city centre and the BASF, and, finally, of the Landeshafen basin in the North that connects the BASF.
Ludwigshafen has excellent Autobahn (motorway/highway) connections to all directions. Most important are the A 650 in west–east direction, the A 61 in north–south direction. But there are also A 6, A 65 and B 9 to be mentioned.
Ludwigshafen Hauptbahnhof is a huge station, its impressive pylon bridge pier serving as the city's landmark. The extraordinary architecture of the station complex is caused by the need to connect three joining tracks (to Frankenthal/Worms/Mainz, to Neustadt/Speyer and to Mannheim) and to work in the underground Straßenbahn station and the massive road bridge above the concourse. Other railway stations are at Oggersheim, Mundenheim, Rheingönheim, and, the new more central Ludwigshafen (Rhein) Mitte, near Berliner Platz. Since 2003, the S-Bahn Rhein-Neckar suburban train system runs successfully in the region.
Ludwigshafen's public transport system is run by the VBL (Verkehrsbetriebe Ludwigshafen) and the holding companies Rhein-Neckar-Verkehr (RNV) and VRN. There is an integrated Mannheim/Ludwigshafen tramway network; four tram lines (4,6,7,8) cross the Rhine bridges between the two cities and one other line (10) runs through Ludwigshafen only. In late 2008 Line 4 was extended and replaced Line 14 (also known as "Rhein-Haardt-Bahn"). Line 4 now serves as a long-distance line, which runs from Bad Dürkheim to Ludwigshafen, Mannheim and Heddesheim. The bus network consists of about ten municipal lines and further regional lines.
A rather strange feature of Ludwigshafen's public transport system is the existence of four underground tram stations (Rathaus, Danziger Platz (closed since late 2008), Hauptbahnhof, Hemshofstraße). They go back to the 1970s, when a common underground network in Mannheim and Ludwigshafen was planned. The rash construction of these first stations in Ludwigshafen became superfluous when Mannheim cancelled the project due to its enormous costs.
Region and neighbours
The twin cities of Mannheim and Ludwigshafen closely cooperate in many areas; although they are separated by the Baden-Württemberg/Rhineland Palatinate boundary, this frontier is mainly an administrative one. Many Ludwigshafeners shop and go out in Mannheim's inner city, as it is within easy reach. In the reverse case, some Mannheimers work in Ludwigshafen and many University of Mannheim students choose Ludwigshafen as residence because of its cheaper rents.
The surroundings of Ludwigshafen on the left bank of the Rhine are called Pfalz and are the easternmost part of the Palatinate region. The administrative district around Ludwigshafen is called Rhein-Pfalz-Kreis. North of Ludwigshafen, there is the industrial town of Frankenthal. In the western vicinity of Ludwigshafen, there are several villages producing enormous amounts of vegetables, thus securing the Rheinpfalz the title of “Germany's vegetable garden”. The district south of Ludwigshafen is dominated by the Rhine and the Altrhein arms (lakes marking the earlier course of the river) and the ancient town of Speyer with its magnificent imperial cathedral, a noteworthy and remarkable city.
The regions with some more distance to Ludwigshafen include the beautiful German Wine Route region with Germany's biggest coherent winegrowing area and the Palatinate forest, the biggest coherent forest of Europe in the West, the French region Alsace and the German Schwarzwald (Black Forest) hills in the South, Heidelberg and the Odenwald hills in the East and the Rhein-Main region with the city of Frankfurt about in the North.
Culture
The Pfalzbau is a theatre and concert hall with regional importance. The Staatsphilharmonie Rheinland-Pfalz keeps its own symphonic orchestra, and there is a production company that stages operas 25 nights per year. In the Hemshof district, there are smaller theatres playing regional dialect plays.
The Wilhelm-Hack-Museum is the municipal art museum, with collections spanning from ancient to contemporary art. It is known for the emblematic Miró mural covering an entire façade, called the "Miró Wall" (Miró-Wand in German). The mural is a work of art by the Spanish artist Joan Miró, with the collaboration of his long-time colleague, the ceramist, Joan Gardy Artigas, and is made of 7,200 ceramic tiles. It has been subject to degradation due to air pollution since it was installed in 1979.
Several small museums in Ludwigshafen focus on the city's history, first of all the Stadtmuseum in the Rathaus Center, but also the Schillerhaus Oggersheim, K.O. Braun-Museum in Oppau or the Frankenthaler Kanal Museum in the North.
The Fachhochschule Ludwigshafen (technical college) specialises in economics and has an affiliated Ostasieninstitut (East Asia Institute). There is also the Evangelische Fachhochschule Ludwigshafen, specialising in social sciences.
Economy
Although BASF is by far the most important industrial company in Ludwigshafen, there are many other firms. Trade and industry in Ludwigshafen have about 90,000 employees in total, with an annual total turnover of nearly 17 billion euros.
BASF is the world's leading chemical company, employing 110,000 people at all and about 35,000 (a few years ago, the employee total was about 55,000) of them in the Ludwigshafen plant, which is also the largest chemical plant in the world. The company's main products are fertilizers, dye, coolants and many other chemical substances.
Among the other chemical companies with plants in Ludwigshafen rank BK Giulini, Abbvie, Raschig and Benckiser.
Other important branches of industry are mechanical engineering, electrical engineering, IT and brewery (Mayerbräu Oggersheim).
Sports
Ludwigshafen is one of the German cities that has never had a professional football club. This is all the more surprising, because Ludwigshafen is a typical "workers' city" and has quite a large stadium, the Südweststadion, built from debris from World War II with a capacity of around 40,000. Several international matches and some Bundesliga matches when 1. FC Kaiserslautern or Waldhof Mannheim used it as alternative stadium during the past decades have been held there.
Huddersfield Town left-back Dominik Werling was born in Ludwigshafen.
Formerly the most successful Ludwigshafen football club was FSV Oggersheim, whose team experienced short-term success when gaining promotion to the Regionalliga (3rd Division) at the end of the 2006-07 season. However, the club found itself outclassed, and as the financial situation grew worse after two poor seasons, the club withdrew to 11th tier local level play in 2010-11.
, Arminia Ludwigshafen is the highest-classed football club from the city, competing in the Oberliga Rheinland-Pfalz/Saar (V).
An athletics hall has been constructed near the Stadium a few years ago.
The TSG Friesenheim plays in the German 1st handball division since summer 2010.
Nature
There are several municipal parks in Ludwigshafen: First of all the Ebertpark in the North quarter and Friesenheim. It was created for the South German Horticulture Exhibition in 1925 with the Friedrich-Ebert-Halle, a multi-purpose hall.
The official Stadtpark, or municipal park, is somewhat remote from the city centre (yet easy to reach by the #10 tram), because it is situated on the Parkinsel, or park island, on a bank of the Rhine.
The Friedenspark is closer to the city centre, being located just north of the main station and west of the city hall. It is the youngest of Ludwigshafen's parks, having been created on a former industrial area.
Further, there are numerous smaller parks that are just a bit larger than a towel in the suburbs, for example the Stadtpark Oggersheim, Riedsaumpark, Alwin-Mittasch-Platz and Friesenpark in Friesenheim, Stadtpark Oppau, Bürgerpark Pfingstweide or Zedtwitzpark Mundenheim.
The Maudacher Bruch in the West between Maudach, Gartenstadt and Oggersheim, is a very extensive, horse-shoe shaped area, including the Michaelsberg (126m), a mountain built of debris and wreckage after World War II. Due to excessive extraction of ground water from chemical companies the ground water level drops and the diversity of nature is no longer preserved.
The Kief´scher Weiher in the South is connected with the Rhine and serves as yacht harbour, being surrounded by weekend camping areas.
Notable natives
Nadiem Amiri (born 1996), association football player
Kurt Biedenkopf, politician (CDU), former Ministerpräsident of Saxony (1990–2002)
Max Clos (1925–2002), French journalist
William Dieterle, (1893-1972), Hollywood director
Gustav Ehrhart (1894-1971), chemist
Paul Ehmann, (born 1993), professional footballer
Barbara Eligmann (born 1963), television presenter
Wolfgang Güllich, (1960-1992), rock climber
Helmut Kohl, (1930-2017), German chancellor (1982–1998)
Robert Franz Schmidt (born 1932)
Christian Dissinger, (born 1991), handball player for THW Kiel
Richie Moller, (born 1977), former professional football player, football coach, previous German teacher at The John Carroll School
19th century
Ernst Bloch, (1885-1977), philosopher and writer
Ernst A. Lehmann, (1886-1937), airship captain and Zeppelin builder
William Dieterle, (1893-1972), film director, actor and Oscar-winner
Edgar Julius Jung, (1894-30.6 or 1.7 1934), lawyer, politician and journalist
20th century
1901-1920
Georg Gehring, (1903-1943), Olympic bronze medalist in 1928 and multiple European champion in wrestling
Ernst Gutting, (1919-2013) auxiliary bishop of Speyer
Klaus Gamber, (1919-1989), Catholic priest and liturgical historian
1921-1940
Rudolf Kortokraks, (1928-2014), painter
Waldemar Schreckenberger, (born 1929), lawyer, professor emeritus and secretary of state and head of the Bundeskanzleramt 1982-1984
Fanny Morweiser, (1940-2014), author
Lambert Hamel, (born 1940), television and film actor
1951-1970
Manfred Kaltz, (born 1953), former professional football player and offensive defender, football manager
Norbert Bolz, (born 1953), media scientist
Doris Barnett,(born 1953), politician (SPD), Member of Bundestag since 1994
Claudio Passarelli, (born 1965), wrestler and champion
Joachim Weickert, (born 1965), mathematician
1971-1990
Sanne Kurz, (born 1974), camera woman
Jan-Peter Peckolt, (born 1981), sailor (49er dinghy)
André Schürrle, (born 1990), footballer
International relations
Twin towns – sister cities
Ludwigshafen is twinned with:
Antwerp, Belgium
Dessau-Roßlau, Germany
Havering, United Kingdom
Lorient, France
Pasadena, California, United States
Sumqayit, Azerbaijan
Gaziantep, Turkey
References
External links
Official City Website
Wilhelm-Hack-Museum
Category:Cities in Rhineland-Palatinate
Category:Palatinate (region)
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2023-08-14T01:26:51.906118
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https://example.com/article/3464
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Q:
Php with AJAX Post - Return values JSON
I'm trying to get back values from php interacting with AJAX Post.
I've read that I should use JSON dataType but this is the first time for me doing it and I get "SyntaxError: JSON.parse: unexpected non-whitespace character after JSON data at line 1 column 72 of the JSON data".
My AJAX is the following:
function apfaddpost() {
var fd = new FormData($('#msform')[0]);
fd.append( "main_image", $('#main_image')[0].files[0]);
fd.append( "action", 'apf_addpost');
$('#form-container').hide();
$('#processing').show();
var postProject = $.ajax({
type: 'POST',
url: apfajax.ajaxurl,
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dataType: 'json',
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contentType: false,
});
postProject.done(function(data, textStatus, XMLHttpRequest) {
$('#processing').hide();
$('#confirm').show();
//elements where I should display success message and link
var success = '#success';
var projectlink = '#projectlink';
jQuery(success).html('');
jQuery(success).append(data.success);
$("#projectlink").attr("href", data.projectlink);
});
postProject.fail(function(MLHttpRequest, textStatus, errorThrown) {
alert(errorThrown);
});
}
My php
if ( $pid != 0 )
{
$message = 'Your post has been successfully added!';
$project_link = get_permalink($pid);
$result = array('success'=>$message,'projectlink'=>$projectlink);
echo json_encode($result);
}
else {
$message = 'Error occurred while adding the post';
$result = array('fail'=>$message);
echo json_encode($result);
}
My HTML where should be printed those values is:
<div id="confirm" class="row" style="display:none">
<div class="col-sm-12">
<h2 class="text-center"><?php _e("Thank you!","KleeiaDev") ?></h2>
<div class="text-center">
<p id="success"></p><!-- Here should go the success message -->
<p>
<a id="projectlink" href="">Link</a><!-- Here should go the link I'm getting as result -->
</p>
</div>
</div>
</div>
Where am I wrong?
A:
If your PHP is outputing something else after echo json_encode($result); it will lead to that error.
Make sure you have nothing else being output. If there is no more application logic after the json_encode use exit.
|
2023-08-02T01:26:51.906118
|
https://example.com/article/9443
|
<blockquote>''"West, North, and South the children of Men spread and wandered, and their joy was the joy of the morning before the dew is dry, when every leaf is green."
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{{quote|West, North, and South the children of Men spread and wandered, and their joy was the joy of the morning before the dew is dry, when every leaf is green.|''[[The Silmarillion]]'', [[Of Men]]}}
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''—[[The Silmarillion]]'': "[[Of Men]]"</blockquote>
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'''Men''' were one of the Kindreds of the [[Children of Ilúvatar]]. Men were called the Secondborn (or the Second Kindred<ref>{{PE|17}}, p. 89</ref>) by the [[Elves]], their [[Elves|Elder]] brethren, because they were the last of all the [[incarnate]] races to come into being. Though they were born after the other sentient races, Men were destined to inherit and [[Dominion of Men|rule]] [[Middle-earth]].
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'''Men''' (when written with a capital letter, this word refers to the human race and does not denote gender) were one of the Kindreds of the [[Children of Ilúvatar]]. Men were called the [[Secondborn]] by the [[Elves]], their [[Elder Children of Ilúvatar|Elder]] brethren, because they were the last of all the [[Mirröanwi|incarnate]] races to come into being. Though they were born after the other sentient races, Men were destined to inherit and [[Dominion of Men|rule]] [[Middle-earth]].
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==Origins and Nature==
==Origins and Nature==
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The race of Men is the second race of beings created by the Supreme God, [[Ilúvatar]]. Because they awoke at the start of the [[First Age]] of the Sun, while the [[Elves]] awoke three Ages before them, they are called the Secondborn ([[Quenya]]: ''Atani'', [[Sindarin]]: ''[[Edain]]'') by the Elves. Men awoke in a land located in the far east of Middle-earth called [[Hildórien]]. When the Sun rose for the first time in the far West, Men began to wander towards it, a journey which culminated in some of them reaching Beleriand centuries later.
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The race of Men is the second race of beings created by the Supreme God, [[Ilúvatar]]. Because they [[Awakening of Men|awoke]] at the start of the [[First Age]] of the Sun, while the [[Elves]] awoke three Ages before them, they are called the Secondborn ([[Quenya]]: ''Atani'', [[Sindarin]]: ''[[Edain]]'') by the Elves. Men awoke in a land located in the far east of Middle-earth called [[Hildórien]]. When the Sun rose for the first time in the far West, Men began to wander towards it, a journey which culminated in some of them reaching Beleriand centuries later.
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There is much evidence that, soon after their awakening, Morgoth came to Men and incited them to worship him and turn away from Ilúvatar, and that they complied. This makes Men the only race to have fallen completely under the Shadow, which may account for their propensity to do wrong. Though all were seduced by the Enemy, some Men repented and escaped; they were said to be the ancestors of the Edain.
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There is much evidence that, soon after their awakening, Morgoth came to Men and incited them to worship him and turn away from Ilúvatar, and that they complied. Though all were seduced by the Enemy, some Men repented and escaped; they were said to be the ancestors of the Edain.
Men bear the so-called ''[[Gift of Men]]'', mortality. Elves are immortal, in the sense that even if their bodies are slain, their spirits remain bound to the world, going to the [[Halls of Mandos]] to wait until they are released or the world ends. Elves are tied to the world for as long as it lasts. When Men die, they are released from [[Arda]] and the bounds of the world and have rest from its troubles. However, the influence of Morgoth has caused Men to fear their fate, and view Death as a Doom instead of a Gift.
Men bear the so-called ''[[Gift of Men]]'', mortality. Elves are immortal, in the sense that even if their bodies are slain, their spirits remain bound to the world, going to the [[Halls of Mandos]] to wait until they are released or the world ends. Elves are tied to the world for as long as it lasts. When Men die, they are released from [[Arda]] and the bounds of the world and have rest from its troubles. However, the influence of Morgoth has caused Men to fear their fate, and view Death as a Doom instead of a Gift.
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Although all Men are related to one another, there are many different groups with different cultures. The most important group in the tales of the [[First Age]] were the Edain. Although the word Edain technically refers to all Men, the Elves used it to distinguish those Men who fought with them in the First Age against [[Morgoth]] in [[Beleriand]]. The Edain were divided into three Houses.
Although all Men are related to one another, there are many different groups with different cultures. The most important group in the tales of the [[First Age]] were the Edain. Although the word Edain technically refers to all Men, the Elves used it to distinguish those Men who fought with them in the First Age against [[Morgoth]] in [[Beleriand]]. The Edain were divided into three Houses.
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The First House of the Edain was the [[House of Bëor]], and entered Beleriand in 305 FA and were granted the fief of [[Ladros]] in [[Dorthonion]] by [[Finrod Felagund]]. The Second House of the Edain, the [[Haladin]], was led by Haldad and later by his daughter Haleth and settled in the Forest of Brethil. The Third House, which became the greatest, was led by [[Marach]] and later his descendant [[Hador]], and they settled in [[Dor-lómin]]. This house was known both as the House of Marach and the [[House of Hador]].
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The First House of the Edain was the [[House of Bëor]], and entered Beleriand in 305 FA and were granted the fief of [[Ladros]] in [[Dorthonion]] by [[Finrod|Finrod Felagund]]. The Second House of the Edain, the [[Haladin]], was led by Haldad and later by his daughter Haleth and settled in the Forest of Brethil. The Third House, which became the greatest, was led by [[Marach]] and later his descendant [[Hador]], and they settled in [[Dor-lómin]]. This house was known both as the House of Marach and the [[House of Hador]].
Other Men did not cross the [[Misty Mountains]] or fight against Morgoth. However, some, such as the Easterlings, fought openly on his side. In later Ages, the Haradrim and Easterlings would fight on Sauron's side against the descendants of the Edain. Here below follow the short descriptions of the most important groups of Men in the First, Second and Third Ages.
Other Men did not cross the [[Misty Mountains]] or fight against Morgoth. However, some, such as the Easterlings, fought openly on his side. In later Ages, the Haradrim and Easterlings would fight on Sauron's side against the descendants of the Edain. Here below follow the short descriptions of the most important groups of Men in the First, Second and Third Ages.
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As the Men of the West increased in power and happiness, they came to resent the Gift of Men, Death. They wished to become immortal like the Elves and enjoy their possessions for all time. Most of the Númenóreans, including the line of the Kings, began to turn away from the Valar, and spoke against the Ban of the Valar that forbade them to sail west beyond sight of Númenor or to enter [[Valinor]]. The Númenóreans also became increasingly hostile to all Elvish influences in their realm, and in 2899 of the [[Second Age]], Ar-Adûnakhôr became the first king of Númenor to take his royal name in [[Adûnaic]], the language of Men, instead of [[Quenya]], the tongue of the Elves of Valinor.
As the Men of the West increased in power and happiness, they came to resent the Gift of Men, Death. They wished to become immortal like the Elves and enjoy their possessions for all time. Most of the Númenóreans, including the line of the Kings, began to turn away from the Valar, and spoke against the Ban of the Valar that forbade them to sail west beyond sight of Númenor or to enter [[Valinor]]. The Númenóreans also became increasingly hostile to all Elvish influences in their realm, and in 2899 of the [[Second Age]], Ar-Adûnakhôr became the first king of Númenor to take his royal name in [[Adûnaic]], the language of Men, instead of [[Quenya]], the tongue of the Elves of Valinor.
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During the early part of their rebellion, the Númenóreans became divided into two factions: the first, the [[King's Men]], enjoyed the support of the King and included the majority of the people. They wished to gain immortality and break away from their ancestral allegiance to the Valar. The King's Men also wanted to end relations with the Elves, and thus they favoured Adûnaic as the official language and eventually punished those who spoke the Elven tongues. The persecuted minority faction, the [[Faithful]], were led by the [[Lord of Andúnië|Lords of Andúnië]], the westernmost province of Númenor, and remained loyal to the Valar. They also tried to maintain friendship with the Elves.
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During the early part of their rebellion, the Númenóreans became divided into two factions: the first, the [[King's Men]], enjoyed the support of the King and included the majority of the people. They wished to gain immortality and break away from their ancestral allegiance to the Valar. The King's Men also wanted to end relations with the Elves, and thus they favoured Adûnaic as the official language and eventually punished those who spoke the Elven tongues. The persecuted minority faction, the [[Faithful]], were led by the [[Lords of Andúnië]], the westernmost province of Númenor, and remained loyal to the Valar. They also tried to maintain friendship with the Elves.
When Sauron was apparently defeated and taken to the Isle by the Númenórean army near the end of the Second Age, he took advantage of the pride of the Númenóreans. By teaching the Dúnedain many things and flattering the King, [[Ar-Pharazôn]], he worked his way into the King's counsels and won the hearts of the people. Ultimately, Sauron advised Ar-Pharazôn to attack Valinor and claim immortality. This he foolishly did, and as a punishment Númenor, the island of the Men of the West, sank into the Sea and only the Faithful escaped. When the Faithful returned to Middle-earth, they founded the twin kingdoms of [[Gondor]] and [[Arnor]].
When Sauron was apparently defeated and taken to the Isle by the Númenórean army near the end of the Second Age, he took advantage of the pride of the Númenóreans. By teaching the Dúnedain many things and flattering the King, [[Ar-Pharazôn]], he worked his way into the King's counsels and won the hearts of the people. Ultimately, Sauron advised Ar-Pharazôn to attack Valinor and claim immortality. This he foolishly did, and as a punishment Númenor, the island of the Men of the West, sank into the Sea and only the Faithful escaped. When the Faithful returned to Middle-earth, they founded the twin kingdoms of [[Gondor]] and [[Arnor]].
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===[[Black Númenóreans]] and [[Haradrim]]===
===[[Black Númenóreans]] and [[Haradrim]]===
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The Faithful weren't the only Númenóreans left on Middle-earth when Númenor sank. When Númenor grew in naval power, many Númenóreans founded colonies in Middle-earth. In the second millennium of the [[Second Age]] there was an exodus of Men from the overcrowded island. Many of the King's Men settled in Middle-earth because they wanted to conquer more lands, and the Faithful because they were persecuted by the Kings. The Faithful settled in [[Pelargir]], while the King's Men ruled the [[Haven of Umbar]] and other colonies in the South. From these colonies Sauron recruited men who would become some of the nine [[Ringwraiths]] in the second millennium of the Second Age. When Númenor was destroyed, the King's Men became known as the Black Númenóreans and remained hostile towards the Faithful of Gondor. Eventually, the Black Númenórean stronghold of Umbar was conquered by Gondor in 933 of the Third Age.
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The Faithful weren't the only Númenóreans left on Middle-earth when Númenor sank. When Númenor grew in naval power, many Númenóreans founded colonies in Middle-earth. In the second millennium of the [[Second Age]] there was an exodus of Men from the overcrowded island. Many of the King's Men settled in Middle-earth because they wanted to conquer more lands, and the Faithful because they were persecuted by the Kings. The Faithful settled in [[Pelargir]], while the King's Men ruled the [[Haven of Umbar]] and other colonies in the South. From these colonies Sauron recruited men who would become some of the nine [[Nazgûl|Ringwraiths]] in the second millennium of the Second Age. When Númenor was destroyed, the King's Men became known as the Black Númenóreans and remained hostile towards the Faithful of Gondor. Eventually, the Black Númenórean stronghold of Umbar was conquered by Gondor in 933 of the Third Age.
Further east of Umbar another group of Men lived, called the '''Haradrim''' or Southrons. They were dark skinned Men and waged war on great Oliphaunts or ''Mûmakil''. They too were hostile to Gondor, though they were subdued in 1050 of the Third Age by [[Hyarmendacil I]].
Further east of Umbar another group of Men lived, called the '''Haradrim''' or Southrons. They were dark skinned Men and waged war on great Oliphaunts or ''Mûmakil''. They too were hostile to Gondor, though they were subdued in 1050 of the Third Age by [[Hyarmendacil I]].
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===[[Easterlings]]===
===[[Easterlings]]===
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Most Men who fought in the armies of Morgoth and Sauron were Easterlings, who came from the region around the [[Sea of Rhûn]]. Some Easterlings offered their services to the Elvish kingdoms in Beleriand; among them were Bór and his sons, and Ulfang the Black and his sons. This proved to be disastrous for the Elves in the [[Nirnaeth Arnoediad]] when Ulfang and his clan switched sides and defected to Morgoth, though Bór and his sons died bravely fighting on the side of the [[Eldar]].
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Most Men who fought in the armies of Morgoth and Sauron were Easterlings, who came from the region around the [[Sea of Rhûn]]. Some Easterlings offered their services to the Elvish kingdoms in Beleriand; among them were [[Bór]] and his sons, and [[Ulfang the Black]] and his sons. This proved to be disastrous for the Elves in the [[Nirnaeth Arnoediad]] when Ulfang and his clan switched sides and defected to Morgoth, though Bór and his sons died bravely fighting on the side of the [[Eldar]].
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After Morgoth's defeat Sauron extended his influence over the Easterlings, and although Sauron was defeated by the [[Last Alliance of Elves and Men]] at the end of the Second Age, the Easterlings were the first enemies to attack Gondor again in 492 TA. They were soundly defeated by King [[Rómendacil I]], but they invaded again in 541 TA and took revenge by slaying King Rómendacil. Rómendacil's son [[Turambar]] took large portions of land from them.
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After Morgoth's defeat Sauron extended his influence over the Easterlings, and although Sauron was defeated by the [[Last Alliance of Elves and Men]] at the end of the Second Age, the Easterlings were the first enemies to attack Gondor again in 492 TA. They were soundly defeated by King [[Rómendacil I]], but they invaded again in 541 TA and took revenge by slaying King Rómendacil. Rómendacil's son [[Turambar (King of Gondor)|Turambar]] took large portions of land from them.
In the next centuries Gondor held sway over the Easterlings. When Gondor's power began to decrease in the twelfth century of the Third Age, the Easterlings took the complete eastern bank of the [[Anduin]] except [[Ithilien]] and crushed Gondor's allies, the Northmen.
In the next centuries Gondor held sway over the Easterlings. When Gondor's power began to decrease in the twelfth century of the Third Age, the Easterlings took the complete eastern bank of the [[Anduin]] except [[Ithilien]] and crushed Gondor's allies, the Northmen.
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===[[Northmen]]===
===[[Northmen]]===
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Not all the Men who remained east of the Blue Mountains and Misty Mountains during the First Age were tempted by Morgoth or Sauron, and they were joined after the War of Wrath by those of the Edain who did not wish to travel to Númenor. The Northmen who dwelt in [[Mirkwood|Greenwood the Great]] and other parts of [[Rhovanion]] were friendly to the Dúnedain, being for the most part their kin, and many of them became Gondorian subjects. The Men of [[Dale]] and [[Esgaroth]] were Northmen, as were the Woodsmen of Mirkwood, and the [[Éothéod]], who became the Rohirrim or Horse Lords.
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Not all the Men who remained east of the Blue Mountains and Misty Mountains during the First Age were tempted by Morgoth or Sauron, and they were joined after the War of Wrath by those of the Edain who did not wish to travel to Númenor. The Northmen who dwelt in [[Mirkwood|Greenwood the Great]] and other parts of [[Rhovanion (region)|Rhovanion]] were friendly to the Dúnedain, being for the most part their kin, and many of them became Gondorian subjects. The Men of [[Dale]] and [[Lake-town|Esgaroth]] were Northmen, as were the Woodsmen of Mirkwood, and the [[Éothéod]], who became the Rohirrim or Horse Lords.
===[[Dunlendings]] and [[Drúedain]]===
===[[Dunlendings]] and [[Drúedain]]===
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At the end of the Third Age a few Woses still lived in the Drúadan Forest. They held off [[Orcs]] with poisoned arrows and were vital in securing the aid of the Rohirrim in the Battle of the Pelennor Fields. King [[Aragorn|Elessar]] granted the Drúadan Forest to them "forever" in the [[Fourth Age]].
At the end of the Third Age a few Woses still lived in the Drúadan Forest. They held off [[Orcs]] with poisoned arrows and were vital in securing the aid of the Rohirrim in the Battle of the Pelennor Fields. King [[Aragorn|Elessar]] granted the Drúadan Forest to them "forever" in the [[Fourth Age]].
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===[[Hobbit]]s===
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===Hobbits===
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Hobbits were strictly a race of Men rather than a separate species. The origin of Hobbits is obscure; they first appeared in the records of other Men in the middle of the [[Third Age]].
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[[Hobbits]] were strictly a race of Men rather than a separate species. The origin of Hobbits is obscure; they first appeared in the records of other Men in the middle of the [[Third Age]].
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== Names ==
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== Names and Etymology ==
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The Elves called the race of Men '''[[Atani]]''' in [[Quenya]], literally meaning "Second People" (the [[Elves]] being the First), but also '''Hildor''' (Aftercomers), '''Fírimar''' (Mortals), '''Engwar''' (The Sickly), and many other names. The name ''Atani'' is cognate with [[Sindarin]] '''Edain''', but this term was later applied only to those Men who aided the Elves in their war with [[Morgoth]] in the [[First Age]].
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The Elves called the race of Men '''[[Atani]]''' in [[Quenya]], literally meaning "Second People" (the [[Elves]] being the First), but also '''[[Hildor]]''' (Aftercomers), '''[[Fírimar]]''' (Mortals), '''[[Engwar]]''' (The Sickly),<ref>{{S|Men}}</ref> and many other names. The name ''Atani'' is cognate with [[Sindarin]] '''[[Adan|Edain]]''', but this term was later applied only to those Men who aided the Elves in their war with [[Morgoth]] in the [[First Age]].
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==Notable Men==
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===First Age===
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*[[Bëor]] - leader of the [[First House of the Edain|First House]] of the [[Edain]] and the first of Men to come to [[Beleriand]]
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*[[Marach]] - leader of the [[Third House of the Edain]]
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*[[Haleth]] - led her people, the [[House of Haleth|Second House of the Edain]], to the [[Forest of Brethil]]
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*[[Hador Lórindol]] - patriarch of the [[House of Hador]]
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*[[Beren Erchamion]] - took a [[Silmaril]] from [[Morgoth]]'s crown; married [[Lúthien Tinúviel]]
*[[Tuor]] - came to [[Gondolin]] and married [[Idril]]; father of [[Eärendil]]
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===Second Age===
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*[[Elros Tar-Minyatur]] - son of Eärendil and first [[King of Númenor]]
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*[[Tar-Aldarion]] - sixth King of Númenor and founder of the [[Guild of Venturers]]
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*[[Ar-Pharazôn]] - twenty-fifth King of Númenor; humbled [[Sauron]]; caused the [[Downfall of Númenor]] by attacking [[Valinor]]
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*[[Elendil]] - escaped the Downfall of Númenor and founded the Kingdom of [[Arnor]]; helped defeat Sauron
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*[[Isildur]] - son of Elendil and cofounder of [[Gondor]]; cut the [[One Ring]] from Sauron's hand
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===Third Age===
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*[[Atanatar]] Alcarin - ruled Gondor at the height of its power
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*[[Mardil]] - first [[Steward of Gondor]]
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*[[Eorl]] - founder of [[Rohan]]
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*[[Denethor II]] - ruled Gondor at the time of the [[War of the Ring]]
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*[[Boromir II]] and [[Faramir son of Denethor II|Faramir]] - sons of Denethor II
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*[[Théoden]] - ruled Rohan at the time of the War of the Ring
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*[[Éomer]] - nephew and heir of Théoden; fought at the [[Battle of the Pelennor Fields]]
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*[[Éowyn]] - sister of Éomer; battled the [[Witch-king]]
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*[[Aragorn II]] - the [[Heir of Isildur]] and ruler of the [[Reunited Kingdom]]
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[[J.R.R. Tolkien|Tolkien]] employed a peculiar usage of the words ''Man'' and ''Mannish'': these terms came to replace the word "human" found in drafts of ''[[The Lord of the Rings]]''.<ref>{{PM|Languages}}, p. 61</ref> It has been suggested that Tolkien might have preferred ''Mannish'' over "human" since the former has Germanic roots (thus being closer to [[Old English]]), while the latter word has Latin roots.<ref>{{HM|RW}}, pp. 156-8</ref>
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{{references}}
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[[Category:Characters in The Hobbit]]
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[[Category:Men]]
[[Category:Races]]
[[Category:Races]]
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[[Category:Men]]
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[[Category:Characters in The Hobbit]]
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[[de:Menschen]]
[[de:Menschen]]
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[[fa:انسان]]
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[[fr:encyclo/peuples/hommes/hommes]]
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[[fi:Ihmiset]]
Revision as of 06:13, 27 October 2012
The name Men refers to more than one character, item or concept. For a list of other meanings, see Men (disambiguation).
Men were one of the Kindreds of the Children of Ilúvatar. Men were called the Secondborn (or the Second Kindred[2]) by the Elves, their Elder brethren, because they were the last of all the incarnate races to come into being. Though they were born after the other sentient races, Men were destined to inherit and ruleMiddle-earth.
Contents
Origins and Nature
The race of Men is the second race of beings created by the Supreme God, Ilúvatar. Because they awoke at the start of the First Age of the Sun, while the Elves awoke three Ages before them, they are called the Secondborn (Quenya: Atani, Sindarin: Edain) by the Elves. Men awoke in a land located in the far east of Middle-earth called Hildórien. When the Sun rose for the first time in the far West, Men began to wander towards it, a journey which culminated in some of them reaching Beleriand centuries later.
There is much evidence that, soon after their awakening, Morgoth came to Men and incited them to worship him and turn away from Ilúvatar, and that they complied. Though all were seduced by the Enemy, some Men repented and escaped; they were said to be the ancestors of the Edain.
Men bear the so-called Gift of Men, mortality. Elves are immortal, in the sense that even if their bodies are slain, their spirits remain bound to the world, going to the Halls of Mandos to wait until they are released or the world ends. Elves are tied to the world for as long as it lasts. When Men die, they are released from Arda and the bounds of the world and have rest from its troubles. However, the influence of Morgoth has caused Men to fear their fate, and view Death as a Doom instead of a Gift.
Groups and Alignments
Although all Men are related to one another, there are many different groups with different cultures. The most important group in the tales of the First Age were the Edain. Although the word Edain technically refers to all Men, the Elves used it to distinguish those Men who fought with them in the First Age against Morgoth in Beleriand. The Edain were divided into three Houses.
The First House of the Edain was the House of Bëor, and entered Beleriand in 305 FA and were granted the fief of Ladros in Dorthonion by Finrod Felagund. The Second House of the Edain, the Haladin, was led by Haldad and later by his daughter Haleth and settled in the Forest of Brethil. The Third House, which became the greatest, was led by Marach and later his descendant Hador, and they settled in Dor-lómin. This house was known both as the House of Marach and the House of Hador.
Other Men did not cross the Misty Mountains or fight against Morgoth. However, some, such as the Easterlings, fought openly on his side. In later Ages, the Haradrim and Easterlings would fight on Sauron's side against the descendants of the Edain. Here below follow the short descriptions of the most important groups of Men in the First, Second and Third Ages.
As a reward for their services and assistance rendered to the Elves and the Valar in the War of Wrath at the end of the First Age, the Edain received a new land of their own from the Valar, between Middle-earth and the Undying Lands. This was the land of Númenor, an island in the form of a five-pointed star that was far away from the troubles of Middle-earth.
They were led to this island by Elros with the help of his father Eärendil, who sailed the heavens as the bright star of the same name and guided the ships of the Edain to Númenor. Once they arrived, Elros became the first King of Númenor and took the name Tar-Minyatur. The Edain became known as the Númenóreans or Dúnedain (Sindarin for Men of the West). The kingdom of Númenor grew steadily in power, and the Dúnedain became the noblest and highest of all Men on Arda. In their early days, the Dúnedain remained allied to the Elves of Middle-earth, and aided them in battle against Morgoth's lieutenant Sauron.
As the Men of the West increased in power and happiness, they came to resent the Gift of Men, Death. They wished to become immortal like the Elves and enjoy their possessions for all time. Most of the Númenóreans, including the line of the Kings, began to turn away from the Valar, and spoke against the Ban of the Valar that forbade them to sail west beyond sight of Númenor or to enter Valinor. The Númenóreans also became increasingly hostile to all Elvish influences in their realm, and in 2899 of the Second Age, Ar-Adûnakhôr became the first king of Númenor to take his royal name in Adûnaic, the language of Men, instead of Quenya, the tongue of the Elves of Valinor.
During the early part of their rebellion, the Númenóreans became divided into two factions: the first, the King's Men, enjoyed the support of the King and included the majority of the people. They wished to gain immortality and break away from their ancestral allegiance to the Valar. The King's Men also wanted to end relations with the Elves, and thus they favoured Adûnaic as the official language and eventually punished those who spoke the Elven tongues. The persecuted minority faction, the Faithful, were led by the Lords of Andúnië, the westernmost province of Númenor, and remained loyal to the Valar. They also tried to maintain friendship with the Elves.
When Sauron was apparently defeated and taken to the Isle by the Númenórean army near the end of the Second Age, he took advantage of the pride of the Númenóreans. By teaching the Dúnedain many things and flattering the King, Ar-Pharazôn, he worked his way into the King's counsels and won the hearts of the people. Ultimately, Sauron advised Ar-Pharazôn to attack Valinor and claim immortality. This he foolishly did, and as a punishment Númenor, the island of the Men of the West, sank into the Sea and only the Faithful escaped. When the Faithful returned to Middle-earth, they founded the twin kingdoms of Gondor and Arnor.
The Faithful weren't the only Númenóreans left on Middle-earth when Númenor sank. When Númenor grew in naval power, many Númenóreans founded colonies in Middle-earth. In the second millennium of the Second Age there was an exodus of Men from the overcrowded island. Many of the King's Men settled in Middle-earth because they wanted to conquer more lands, and the Faithful because they were persecuted by the Kings. The Faithful settled in Pelargir, while the King's Men ruled the Haven of Umbar and other colonies in the South. From these colonies Sauron recruited men who would become some of the nine Ringwraiths in the second millennium of the Second Age. When Númenor was destroyed, the King's Men became known as the Black Númenóreans and remained hostile towards the Faithful of Gondor. Eventually, the Black Númenórean stronghold of Umbar was conquered by Gondor in 933 of the Third Age.
Further east of Umbar another group of Men lived, called the Haradrim or Southrons. They were dark skinned Men and waged war on great Oliphaunts or Mûmakil. They too were hostile to Gondor, though they were subdued in 1050 of the Third Age by Hyarmendacil I.
Both Umbar and the Harad were left unchecked by Gondor's waning power by the time of the War of the Ring, and presented grave threats from the south. Many Haradrim fought with Sauron's forces in Gondor in that War.
Most Men who fought in the armies of Morgoth and Sauron were Easterlings, who came from the region around the Sea of Rhûn. Some Easterlings offered their services to the Elvish kingdoms in Beleriand; among them were Bór and his sons, and Ulfang the Black and his sons. This proved to be disastrous for the Elves in the Nirnaeth Arnoediad when Ulfang and his clan switched sides and defected to Morgoth, though Bór and his sons died bravely fighting on the side of the Eldar.
After Morgoth's defeat Sauron extended his influence over the Easterlings, and although Sauron was defeated by the Last Alliance of Elves and Men at the end of the Second Age, the Easterlings were the first enemies to attack Gondor again in 492 TA. They were soundly defeated by King Rómendacil I, but they invaded again in 541 TA and took revenge by slaying King Rómendacil. Rómendacil's son Turambar took large portions of land from them.
In the next centuries Gondor held sway over the Easterlings. When Gondor's power began to decrease in the twelfth century of the Third Age, the Easterlings took the complete eastern bank of the Anduin except Ithilien and crushed Gondor's allies, the Northmen.
The Easterlings of the Third Age were divided in different tribes, such as the Wainriders and the Balchoth. The Wainriders were a confederation of Easterlings who were very active between 1856 and 1944 TA. They posed a serious threat to Gondor for many years, but were utterly defeated by Eärnil II in 1944.
When Gondor lost its royal dynasty in 2050 TA the Easterlings started to reorganize themselves, and a fierce group called the Balchoth became the most important tribe. In 2510 TA they invaded Gondor again and conquered much of Calenardhon, until they were defeated by the Éothéod who rode to Gondor's aid.
Not all the Men who remained east of the Blue Mountains and Misty Mountains during the First Age were tempted by Morgoth or Sauron, and they were joined after the War of Wrath by those of the Edain who did not wish to travel to Númenor. The Northmen who dwelt in Greenwood the Great and other parts of Rhovanion were friendly to the Dúnedain, being for the most part their kin, and many of them became Gondorian subjects. The Men of Dale and Esgaroth were Northmen, as were the Woodsmen of Mirkwood, and the Éothéod, who became the Rohirrim or Horse Lords.
When Elendil founded the Kingdom of Arnor, its borders were quickly extended towards the river Greyflood (Sindarin:Gwathló), and Gondor likewise extended up through Enedwaith. In Enedwaith and Minhiriath (Sindarin for Land between the Rivers) lived a group of Men related to those Men that became the House of Haleth, and they were known as the Dunlendings. They had lived in the great woods that covered most of Eriador, and when the Númenóreans started to chop these woods down to build their ships in the Second Age, they earned the hostility of the Dunlendings. The Dunlendings later became bitter enemies of Rohan, as they believed the Rohirrim had stolen their lands.
Because of their enmity with the Rohirrim, the Dunlendings served Saruman in the War of the Ring and fought against the Horse Lords in the Battle of the Hornburg.
Another group of Men were the Woses. They were small and stooped, and were always few in number and shortlived compared to other races of Men. They lived among the House of Haleth in the First Age, and were held as Edain by the Elves, who called them Drúedain (from Drûg, their own name for themselves, plus Edain).
At the end of the Third Age a few Woses still lived in the Drúadan Forest. They held off Orcs with poisoned arrows and were vital in securing the aid of the Rohirrim in the Battle of the Pelennor Fields. King Elessar granted the Drúadan Forest to them "forever" in the Fourth Age.
Hobbits
Hobbits were strictly a race of Men rather than a separate species. The origin of Hobbits is obscure; they first appeared in the records of other Men in the middle of the Third Age.
Names and Etymology
The Elves called the race of Men Atani in Quenya, literally meaning "Second People" (the Elves being the First), but also Hildor (Aftercomers), Fírimar (Mortals), Engwar (The Sickly),[3] and many other names. The name Atani is cognate with SindarinEdain, but this term was later applied only to those Men who aided the Elves in their war with Morgoth in the First Age.
Tolkien employed a peculiar usage of the words Man and Mannish: these terms came to replace the word "human" found in drafts of The Lord of the Rings.[4] It has been suggested that Tolkien might have preferred Mannish over "human" since the former has Germanic roots (thus being closer to Old English), while the latter word has Latin roots.[5]
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For the baguettes, place the flour, salt, yeast, olive oil and most of the water in a food mixer with a dough hook attached, taking care not to let the yeast touch the salt until you begin mixing.
Start mixing on a slow speed, gradually adding the rest of the water until you have a smooth dough. This should take about five minutes.
Tip the dough into an oiled bowl, cover and leave the dough to prove for two hours.
Tip the dough out onto an oiled surface. Dust your hands with a little flour and divide the dough in two.
Knock back the dough and stretch and fold, and then roll the dough into shape.
For the garlic mixture, preheat the oven to 200C/400F/Gas 6. Smash the head of garlic to release the cloves and place them in a roasting tin, still in their skins. Add a splash of olive oil and a pinch each of salt and sugar and toss together. Cook in the preheated oven for 20 minutes, or until caramelised.
Remove from the oven and, when cool enough to handle, squeeze the soft, roast garlic out of their skins.
Press the garlic cloves into the baguette (add them to taste) as you shape the dough into a baguette shape.
Place on a baguette tray or a large baking tray, cover and leave to prove until it has doubled in size.
Heat a roasting dish in the bottom of the oven and pour in some water to create some steam (this will help form the crust). Preheat the oven to 220C/425F/Gas 7 in a non-fan oven.
Just before baking, slash the top of each baguette three times.
Bake the baguettes for 30 minutes. Then drop the temperature to 200C/400G/Gas 6 and cook for 10 minutes. The baked baguettes should be golden-brown and have a slight sheen to them.
Remove the baguettes from the oven and leave to cool.
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<link rel="last" href="css3-modsel-d4.xml" title="Dynamic updating of :first-child and :last-child"/>
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We're with you. We'll always be with you
One of the most valuable and beautiful stones found in the present age is the opal stone. The gemstone has many colors and can be engraved into beautiful opal necklace. Pure opal is thought to be colorless but it is not usually found. The unique property of opal is that it would change colors when viewed from different angles. It is the prime stone of planet Venus and it is beneficial for the individuals who have a weak Venus in their birth charts.
The beauty of Opal Necklace
This beautiful stone represents the birthdays in October. People around the world believe that wearing an opal necklace has many spiritual and health benefits. It is mostly found in Australia but a small amount has also been found in United States, Turkey and Brazil. It is mined from the ground in the form of silicone dioxide. The meaning of opal is precious and it has been believe to bring love and luck in different cultures. It has also been claimed that people wearing opal necklace have special intuitive powers as if they can read minds.
Shades of Opal Necklace
Opal gemstone is available in many amazing shades. Some of the most popular colors are:• Black opal necklace is good for the reproductive system and has effects in controlling depressions• White opal necklace is perfect to balance the both hemisphere of the brain and it will induce nervous stability• Blue opal necklace is worn for calmness and serenity • Green opal necklace is famous as the fire opal and it is worn to clear the aura of an individual
Properties of Opal gemstone
Opal has been famous for showing positive effects in case of love and relations. It can be regarded as the sensual gemstone that would attract the lovers. It has the properties of:• Good fortune• Beauty • IntellectPeople that are connected with business, tourism, traveling and media can enjoy several benefits from this stone. Many people wear the stone in the form of opal necklace, rings or bracelets. The best thing about this stone is that it can be worn regardless of the birth date. With the special chakra of the opal stone, it has special benefits for the nervous and immune system.
Benefits of wearing Opal Necklace
Some of the amazing benefits that you will get by wearing the opal necklace are:
1-Beauty of Opal Necklace
Venus is said to bring wealth, joy, beauty, luck and to improve the relationship between two people. Opal necklace is worn to upgrade the impacts of Venus on the life, luck and health of the individuals. It is likewise worn to improve the individual appeal and charm for a person. In the old circumstances, Opal stone was thought to be exceptionally helpful for curing eye illnesses. Since the stone has, a lot of advantages related to it and they are exceptionally wonderful likewise, Opal has been used to make gorgeous and precious jewelry. Opal necklace rings, and wristbands produced using the color of the opal stone that you would like to have.
2-Health benefits of Opal Necklace
Opal necklace are worn to avoid minor sicknesses. It is additionally said that an opal changes its shading if an illness is probably going to happen, subsequently cautioning you to stay safe. • It is useful for the individuals who have insomnia and other sleeping issues, bad dreams that occur constantly. • Opal necklace help in decreasing terrible dreams and help you with a decent night's rest. • Its health advantages are that it is useful for reproduction organs, adjusting the privilege and left cerebrum, conquering anxiety and curing stomach issue. • Opal necklace additionally helps in finding the correct answer for disturbed love life or conjugal life. Those individuals who confront delay in marriage can wear an Opal to locate the normal arrangement. Opal stones are viewed as an extremely fortunate stone and is said to be an image of certainty and steadfastness.
3-Motivation of Opal Necklace
Opal is a stone of inspiration and motivation, which improves creative ability. It can breathe life into motivation to Spirit. Its own particular soul is on occasion like that of a kid suddenly playing, dashing shading at any place that satisfies. Conveying this inventive suddenness into the domain of your life can bring solid innovativeness.
4-Psychic abilities of Opal Necklace
In the psychic or profound domain opal is utilized as precious stone because of special vibrations. It is said to have the capacity to help one be imperceptible in circumstances where one would not like to be. This could be utilized as a part of astral traveling and in addition in day-by-day life. Inwardly, opal conveys its water benefits to upgrade self-regard and feeling of self-esteem. It can cause these emotions take control of your life despite whatever else going ahead under the surface. This adjusted to the motivating affection energies can help you discharge harming restraints and get to your actual otherworldly nature.Opal is additionally used to bring upbeat dreams and stay away from bad dreams. It is a mitigating stone, which can quiet turbulent feelings and bring a profound feeling of trust and inward peace.
5-Affection of Opal Necklace
Opal is said to be a stone for affection. It brings the motivation of adoration into a dormant heart chakra and brings recharging. This can appear as blazing sexy love or gentler unlimited love and any shade of affection in the middle. Opal is additionally said to convey constancy to love. Customarily in precious stone mending opal has been viewed as useful for cerebral pains, visual perception, Parkinson's ailment, blood, insulin control, PMS, and the insusceptible framework. Opal necklace will provide the body with perfect spiritual and mental support. Make sure that you get the best opal stone necklace according to your requirements. It will bring such amazing changes in your life that would be perfect for your future. Attract your lover and have a peaceful life ahead. It is the time to bring some positive changes in life.
Webinar Jam 2017
If the reports are
anything to go by, video conferencing, live stream broadcast and webinars
witnessed a dramatic boost with the introduction of an incredible webinar tool
that is compatible with Google Hangouts.
Not long after,
webinar jam team introduced an updated version - Webinar Jam Studio.
Fortunately, the new version had standard and better features than people
expected; it had better engaging and interesting features.
Webinar Jam Review
For an updated webinar
jam review as at 2016, besides the info given below, check out the webinar jam
studio review above. It is the most updated version of webinar service and
platform.
The Webinar Jam is an
effective tool that helps to control, enhance, and ease the use of Google
Hangout platform. In summary, Webinar Jam complements and cover-up the
shortcomings of Google Hangouts platform, providing an excellent webinar and
video conferencing services for internet marketers looking to boost sales.
What’s So Special About
Webinar Jam?
From a layman's view,
Webinar Jam may be seen as a leading name for businesses and organizations that
need to incorporate live video broadcasting to enhance sales.
Webinar Jam enhances webinar
events by modifying live events with some cool tools, broadens online reach
through Google+ and Google Hangouts, creating an opportunity for webinar hosts
to introduce offers for products and services and upsells to attendees of the
webinar. This happens within the live broadcast window; offering hosts an opportunity
to sell their products and services though a webinar easily.
A fascinating feature-
from a business and marketing point of view- is the ability of Webinar Jam to
use the social and ranking potentials of Google Hangouts. Live broadcasting and
recordings can be viewed on both Google+ and YouTube; two top social platforms
owned by Google, which offers you 2 trusted backlinks and access to better
online exposure and traffic- trust me, everyone yearns for these.
Webinar Jam is also
integrated with most of the attractive and exciting features found in the top
webinars and web video conferencing apps available in the market. This gives
this software an edge above others.
To further spice it
up, Webinar Jambs software simplifies the setup and broadcast of live meetings
which can be streamed globally. This large spread is a great advantage to
business owners who wishes to advertise their product to a target audience
spread across the globe.
It's easy to use Webinar Jam Now. You only click through button below
The Other Side of Webinar Jam
Just like every
product and services have some shortcomings, Webinar Jam is not without
problems.
Initially at its
release, a lot of clients had issues using the software while some had positive
user experience with the software. Software solutions that claim to work with
all devices, browsers, and operating system are usually victims of customer
complaints. Here are some problems encountered by users of Webinar Jam:
· Since the service is browser based and cannot be downloaded to your PC,
you will be required first to download a browser application; some
malfunctioning may be expected. All computers are configured to work
differently, and there could be a conflict with some browser plugins on the PC.
However, an elimination process should easily and quickly detect the cause of
the problem and follow up with a fix seamlessly.
However, it is most
certain that Webinar Jam technicians would have taken note of their lapses and
improve on the flaws experienced by the first users of the webinar platform.
· Support desk problems have also hit the Company. In times past, a lot of
customers have expressed total disappointment in the slow replies to created
tickets. Are you still experiencing same delayed response to requests, kindly
inform us to enable us to keep new clients updated. Obviously, not everyone
would have access to webinar's use of Google Hangouts.
· Time lag is another big issue. Most customers criticize the delay in
passing information between the audience and the presenter. This delay varies
between 3 to 12 seconds. This can be a big problem for both the presenter and
audience.
Therefore, you may not
be making the right choice if you are considering Webinar Jam for a
conversational webinar presentation where you need fast feedback from the other
side. On the other hand, the webinar is a perfect fit for traditional
presentations like a PowerPoint presentation, where a question and answer
session comes up at the end.
For seekers of webinar
software with swift live-streaming that uses Amazon AWS's servers and which
combines all of Webinar Jam primary features and far below the price of
GotoWebinar, then you may be considering new webinar software. Click here to
learn more
It is noteworthy that
we have not tested the new platform, so we cannot be sure of its benefits and
shortcomings: if you think it’s worth giving a trial then ensure to take
advantage of the 30-day trial.
Why Should I Use Webinar Jam?
Besides the
shortcomings discussed above, you stand to gain a lot from Webinar Jam. There
are a lot of power-packed features in Webinar solution; this is evident in the
increasing number of webinar users opting for Webinar Jam. Now let’s examine
some benefits:
Competitive Cost of Webinar Jam
Another benefit is the
highly competitive cost of Webinar Jam software service; this is a major
problem with other software. Unlike as it is with many other webinar software,
you do not pay any monthly fee or cost that rises based on the numerical strength
of attendees.
No monthly billing,
just a reasonable annual fee. This surprisingly affordable rate makes webinar
jam one of the least expensive webinar software solutions available in the
market. Even with its comparatively low price, it still has better features
than more expensive options like GoToWebinar. For the latest Webinar Jam cost,
see our pricing and discount page
It's easy to use Webinar Jam Now. You only click through button below
Easy Set-up and Broadcast of
Live Video Conferencing with Webinar Jam
The simplicity in
setting up the live web video conferencing is amazing.
The software has
well-designed templates for landing page which can be configured in few
minutes. You can stream live broadcasts on your blog or website.
Now you do not need
any webinar know-how before setting up and broadcasting your live video event.
Since you do not need
to download any software, but a browser plugin, it works on all operating
system, Mac or Windows and any browser. It is also compatible with all mobile
devices. But just as it is with any browser-based software, there have been
loads of complaints from users about conflicts between the software and other
browser plugin installed on their PC. This notwithstanding can easily be
resolved.
One great thing about
the universal compatibility of the software is the opportunity it gives to
users to pass information to a larger and wider audience since no software is
required to be able to participate in the live webinar. Also, there are no
compatibility issues with browsers, devices, and operating systems. A lot of
potential attendees may put off the idea of downloading software to their PC to
be able to watch a broadcast
Let the World Watch Your
Public Webinar Event with Webinar Jam
Due to its integration
with Google+ and Google Hangouts, you enjoy an amazing and unique feature that
will add life to your webinar events.
Notable personalities
like The American President Barak Obama and Movie producer Steven Spielberg use
Google Hangouts for live video conferences.
Webinar Jam helps your
live broadcasts in utilizing the wide reach and ranking potentials of Google
Hangouts which currently outranks YouTube Videos.
No Restriction of Video
Conference Broadcast and the Number of Webinar participants with Webinar Jam
Webinar Jam, unlike
most webinar software, offers users the opportunity to run unlimited web
conferences and events. You can also invite an unlimited number of attendees as
you wish as there are no restrictions.
On Webinar Jam, You Can Easy
Copy & Paste Or Point & Click Software
You can broadcast your
live web event simply with some clicks, copy, and paste or point & click.
You could have well-designed webinar pages running in few minutes.
So you've got no reason
whatsoever not to introduce live web video events and webinars in your
marketing and sales arsenal.
It's easy to use Webinar Jam Now. You only click through button below
Webinar Jam has a
versatile and dynamic live broadcasting platform Webinar presentation
can be broadcasted right from your desktop, PowerPoint, internet browser,
webcam, or any application you wish to use; the choice is solely yours.
Also, since the
platform is built on Google's trusted Hangout it makes navigation (e.g.,
between your browser and webcam) easy
The versatility of the
presentation makes it efficient in engaging your audience; making them
interested and fully participating.
Live Streaming Right On Your
Facebook Page With Webinar Jam
Do you have an account
on any social platform like Facebook? Then you can stream your live broadcast
right on your Facebook page, and this can be shared with your audience on
Facebook. You can count on the comments, shares and likes you'll get from
Facebook and other social platforms.
Live Streaming on Google+ and
YouTube With Webinar Jam
You can now stream
your life broadcast right inside Google+ and YouTube. And with a few clicks,
you can also host your recordings on your private YouTube channel.
Everyone say about Webinar Jam
It's easy to use Webinar Jam Now. You only click through button below
Video Maker FX
Definition of Video Maker FX?
Video Maker FX is a software that lets you to create specialized quality animation style videos within a fraction of the time it takes in traditional video editing softwares.You can utilizeVideo Maker FX to create videos likesketch animation videos, kinetic text style commercials, slide presentation videos, character animation videos … almost all the high value stuff you see folks using today to make a fun, lively atmosphere that will make you WANT to pay rapt attention.
Everybody knows that video is significant to their business. It has been proven that by adding video to your marketing, it can increase sales by up to 64%.But regrettably, making quality videos has conventionally been a VERY tough process.Video Maker FX makes the process simple.In this evaluation, I will touch on all of Video Maker FX’s merits so you can understand what this software can do and whether or not you will like to use it to grow your business.But first, here is a quick video I created to demonstrate an example of the things you can do with Video Maker FX in only a few minutes…
How Is Video Maker FX Different From The Rest?
Before Video Maker FX came onboard, there were only2 options. If you felt likecreating quality videos such as this for your business…
1) DO IT ALL BY YOURSELF
The first selection is to learn how to make use of all the tools yourself. The procedureusually go like this…
Be an expert in utilizing complicated software to create video (a 35 second video commercialcan take you some days to create). Install video converting program and learn about video file setups{formats} so that you can export your video you into an editing software.
Record and import your audio (perhapsby using another program) to your editing software.
Master some insanely complex video editing softwareto enable you get your video sounding and looking ok.Buy a new PC to enable you run all these resource demanding programs that can freeze up an old, slow computer.Sounds difficult right… It is.
2) PAY SOMEBODY ELSE
The second selection is to pay somebody to do it. Unfortunately, for some people, this is the way out.To pay someone to create a video for you that is on par with the quality Video Maker FX produces.You would be eyeing hundreds, or perhaps thousands of dollars dependent on how long the video will be and if itrequired voice overs, etc.That is an outrageous amount of cash to pay for just one video.In the subsequent section Video Maker FX review, I will explain how the software works…
The Way Video Maker FX Work?
Video Maker FX consist of pre-done scenarios. Each scene can be customized. You can insert your texts, images, edit the background, alter the colors,animations, font etc.
The scenes looksawesome, but if you feel like getting a little inventive, Video Maker FX will give you all the apparatuses you need to make some truly spectacular videos.There’re hundreds of scenes comprisedwithin the software and there is even aselection to receive 50+ brand new scenes monthly (great choice if you make lots of videos).The scenes are classified into separate themes. For each theme contain a selection of acts that all blend together to create anorganized story. This will allow you to easily make a great looking video by making using of the slides contained in a particular theme.But you’re also able to mix and match any scene within the software at any time to make unique videos. There aren’t any limitations as to how you can organize the scenes, which means the prospects are endless.As soon as your video is created the way you like it, it takes onlysomeclicks to add any of the exclusive audio tracks to make your video come alive.They also made it super easy to add a voice over file as well so you can utilize narration to engage your audience.Once your video is finished, simply hit the export button and the video will be immediately exported as mp4 format. To Export a 60 second video will takeyou below 2 minutes… which is fast.Another thing is that Video Maker FX is tremendously light on computer assets. Some other video software might overheat your processor to a nuclear status. However with Video Maker FX, you can run other programs with it without any effect on the performance.
Product Support of Video Maker FX
I’m impressed with the kind of care Video Maker FX offers to its clients. I attended some of their webinars to study how to better utilize the software and I was satisfied with the assistance they provided.They have also pushed out numerous updates to the software to enable it feel easier to use based on the feedback they got from users. These updates do not just improve the user experience, they have been working hard to make sure that every computer, PC, Mac, new and old, is capable of running Video Maker FX without any complications.Their direct care is on top of their game. I opened a ticket and got an answer As Soon As Possible.
Video Maker FX Evaluation – Bottom Line
After all said and done, after appraising Video Maker FX, it is hard to find anything bad about this piece of software. It is inexpensive, runs smoothly, and enables you to make stunning videos in minutes.Video Maker FX wasintended for anybody to use, which is what made me to like it.They have taken something that is typically hard to do (creatingspecialized quality animation style video) and made it into something that anybody can do. That is pretty remarkable.If you are lookingfor an easy way to spruce up your marketing and grow your business, you would have a hard time getting an offer that is betterthan Video Maker FX.
Easy Sketch Pro 3.0
Have you recently heard about Easy Sketch Pro 3.0 and have suddenly become interested in it? If that’s the case, go ahead and read my review below to determine not only the strengths and weaknesses of it, but whether or not it’s what you’re looking for.
The Easy Sketch Pro 3.0 is not only one of the bestselling products from JV ZOO ever, but it has made the internet realise that creating “doodle sketch” videos is one of the best methods to make money on the internet.Nobody understands the reasoning behind it although for whatever reason, the time to make the big bucks through affiliate product promotion is now.The only issues with it is that not only are doodle sketch videos very difficult to make, they are also very expensive and can cost up to $500 per minute of video.Luckily, Easy Sketch Pro 3.0 makes the whole process a lot easier to the point that even if you aren’t very tech savvy, you can still get it installed and be working on a new project within minutes. If this hasn’t convinced you, read some of the information about Easy Sketch Pro 3.0 below and prepare to be amazed.
Perfectly Compatible With Easy Sketch Pro
What
Is Easy Sketch Pro?
Easy Sketch Pro is a piece of software
which makes creating a doodle sketch video a whole lot easier. No matter how
much you know about computers, this program is incredibly user-friendly.
To use the program, you simply add the text
that you want, either images from the program’s library or your own, some
background music, and you’re done. That’s all there is to it!
Once you’re done creating your video, you
will be able to set the exporting settings as you see fit. With this, you are
able to export it in a variety of different video formats.
With Easy Sketch Pro, the number of things
that you can do with the program are endless. Whether you’re looking to make
doodle sketches for fun or to make them for clients, regardless the reasoning
Easy Sketch Pro is what you’re looking for.
What
You Need to Know About Easy Sketch Pro 3.0
A little known fact about online marketing
is that online users are up to 27 times more likely to click on a video advertisement
opposed to clicking on a banner. While 2 years ago the majority of marketing
agencies were looking into advertising using images, this has since changed and
the standard content which these agencies take advantage of are videos.
A fun fact relating to this is that 2014
was the first year in which online marketers spent more money on video based
advertisements than they did text based and image based advertisements. On top
of that, the years 2013 and 2014 were the years in which whiteboard animations
hit the internet and were the next type of content which marketers took
advantage of. It’s no coincidence that the same year that whiteboard animations
took the spotlight, more money was spent on video based advertisements.
If you’re an avid internet user then the
chances are that over the last few years, you’ve noticed an increase in
whiteboard animations being used for marketing purposes. In fact, it is
whiteboard animations that are drastically increasing a lot of affiliate
marketer’s sales.
What
Are Whiteboard Animations?
If you already understand what a whiteboard
animation is and how effective they can be, skip ahead to the features section
below. If you don’t yet know, read on.
Whiteboard animations are known by a
variety of different titles. Whether it be “Video Scribing”, “Doodle Videos”,
“Sketch Videos”, or even “Explainer Videos”. You may have heard them called
these before and if you have, whiteboard animations are exactly the same
although are named differently.
The term “Whiteboard animation” is appropriate
for what it is. With these animations, the creator bases the whole video upon a
white canvas. Typically, there is a lack of colour in these animations,
although they have proven to be very effective if used properly.
Whilst the artist sketches out the
animation, they are recorded. Once they are finished, the recording is sped up
and a voice-over is added to it.
Features
of Easy Sketch Pro 3.0
Things that you can add to your video using
Easy Sketch Pro 3.0:
- T2C (Tap to Call). This allows potential
customers to call you by tapping on your animation.
- If need be, you can add music from SoundCloud into your video.
- Clips from the website “Vimeo” can be added.
- If there is a YouTube video that you want to be included in your video, you
can be.
- Increase your Twitter following by adding a Twitter link.
- Increase your fan base on Facebook by adding a Facebook link.
- Add a Call-To-Action.
- Add your GoToWebinar registration form.
- Add an autoresponder.
Things that you can do to customize your
animations more on Easy Sketch Pro 3.0:
- Choose from over 500 included icons.
- Decide the size of the hotspot.
- Decide the colours of your animations.
- Choose the times that you want your animation to be visible.
- Choose whereabouts on the video that you want the sketch.
- Include force capture. This means that the video will stop until the viewer
interacts with the hotspot.
- Include text.
After making your videos, you can display
then:
- On a link which is shown on the software.
- On your Facebook pages.
- On your YouTube channel.
- Pretty much any website which allows you to upload content.
Alongside these features, you are also able
to:
- Gather detailed analytics from your
videos viewers. Information such as their country and how they interacted with
your video will be available.
- Add your brands logo to the video.
- Add an analytic tracking code to the video so that you can gather even more
details which you can take advantage of from a marketing perspective.
Regardless of whether you work on a Mac or a
PC, with Easy Sketch Pro 3.0 you are opened up to so many tools.
Everyone say about Easy Sketch Pro
Easy Sketch Pro 3.0's FAQ
What
differs Easy Sketch Pro 3.0 from other video creation programs?
Although there’s a wide variety of video
creation programs out there, none come close to what Easy Sketch Pro 3.0 offers
as there is virtually no competition.
Doodle sketch videos have shown to increase
conversion rates by up to 3 times and by taking advantage of the interactive
tools provided, you can increase your conversion rates even more.
Are
there any other video creation programs which are backed by investors which are
worth over $500 Million, similar to that of Com Mirza?
At this moment in time, nope! Com Mirza was
incredibly impressed with the initial idea of Easy Sketch Pro 3.0 and was as
convinced as us that it would be a success. Furthermore, he was also very aware
of how advanced this piece of software was in comparison to some of the other
options.
What
formats does Easy Sketch Pro allow users to export their videos to?
At this moment in time you are currently
able to export videos to MP4 format.
Does
Easy Sketch Pro come with a subscription payment?
Usually there would be although at the
moment, there is a promotional sale running which offers a onetime payment.
To
Conclude…
After
taking all of what we’ve discussed today into account, it’s very clear that
Easy Sketch Pro 3.0 is a program which excels in its industry and if you’re
looking for a program which can allows you to easily make professional level
doodle sketch videos, this is the program for you. If you are on the edge about
the purchase, don’t be! There is also a money-back guarantee so that if you
aren’t happy with it, you can get your money back. I assure you that after you
try out this program for yourself, you will feel more satisfied than ever.
|
2024-01-04T01:26:51.906118
|
https://example.com/article/9430
|
Friday, February 23, 2018
Best Plumbing Seattle A Seattle Plumber?
Best Plumbing Seattle Reviews
If you want a multi-functional extension in your home with a modernized design, Seattle's roofers can help you renovate your old roof and give you a more relaxed view. He remembers that he had to flee his country without anything, so he keeps everything he has and buys more.
To put it in more detail, should you worry about a particular danger?
There is nothing more unpleasant than looking at damp and damp drywall walls and hoping to make it waterproof again. The pipes in your water or sewer pipe can be damaged by aging or wear.
There comes a moment in every old house where you notice the pressure of shower water and faucets that are reduced and the water bills are duplicated for no particular reason.
I mean, is not it a waste of money to plant flowers, prune, water the lawn, etc.? Everything is alright, Dave Derring sent Aaron and replaced the toilets that were the problem.
I was called today by Dave Derring, the head of the Best Sanitation Service. He said he was going to ask for the right toilets and he would fix this parody that happened.
Without travel costs. Extra charge for service outside opening hours. We are dedicated to the renovation of Find Seattle and reliable service providers for the needs of your project.
One of the most daunting and important decisions to make renovations or conversions in your home is to find the best contractor. This is important because it gives you the ability to find out if the price provided by a company is within an acceptable range.
After we decided to leave the tiles in place, the next step was to tear down the closet and oversized dresser. Housing pipes in old houses are usually made of galvanized steel.
Comments should not promote your articles or other websites. You should ask this question because it helps you to decide if you are dealing with a professional organization or not.
If you need an experienced plumber in a hurry, call Mr. Rooter Plumbing 24 hours a day, 7 days a week. It is important that you understand very clearly about the Seattle plumber that many people are having serious problems because of the recession.
We understand that your budget for plumbing work can be limited and our installers are affordable. Since then I have learned that this condition is often a symptom of something much bigger, and yes, mental problems are the basis of the real behavior of the hamster.
If you're interested in deconstruction, contact someone like Kurt near you, who is a deconstruction company. In the fight for the huge US market UU., Some sellers have started distributing cheap "consumer products" for branded products, simply selling a fake product, so I'd like to give some practical advice to buyers' copper ball taps.
Every licensed sanitary technician we have is just a phone call away! Call us or visit our showroom in Seattle today! The stories of the adventures and forms of survival in this evil land became legendary.
Then the legend of The Lone Ranger 2013 was revived in a film that continued the adventures of The Lone Ranger and Tonto. When I was four years old and sitting next to my grandmother on her sofa, sure, we saw daily episodes of The Lone Ranger. The Lone Ranger Buy Now One last thought.
It was a lot of work, but with a new pedestal sink and a shallow double toilet we were finally ready to create a usable storage space in our bathroom, which now looks spacious.
Then, with a saber saw carefully remove the lathe and the plaster from the wall of the bathroom through the width of the central bolt to the nearest bolt on each side.
I should bleach it, but I did not, thinking the problem was with the valves on the wall. As a homeowner, investing in the quality of your plumbing is your best investment. The best plumbers currently have an "F" of BBB. Whether your home is too hot or too cold, Fox Plumbing & Heating has the right solution for your home.
Our friends, family and neighbors have relied on Fox Plumbing & Heating since 1964 for all their heating, heating and cooling needs. We value feedback from our customers! Extravagant phrases, you did not even want to touch the complicated heating system.
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2023-12-27T01:26:51.906118
|
https://example.com/article/8095
|
Rick Santorum doesn’t know what sex is for.
In a recent appearance in New Hampshire, he summarized his thoughts on the subject, saying, “God made man and woman, and men and women come together to have a union to produce children, which keeps civilization going and provides the best environment for children to be raised.” While this may seem a common-sense understanding of the function and purpose of , it doesn’t apply to human beings.
What Santorum is missing can be expressed in simple math. The vast majority of species have sex only to reproduce—a function reflected in a very low ratio of sex-acts-to-births. Gorillas, for example, have intercourse at most about a dozen times per birth. And as with good Catholics, gorilla sex is all business: no oral, anal, manual, or any other kind of non-reproductive dilly-dallying. The female of most mammals only has sex when she is ovulating. Otherwise, no go. But the sexuality of human beings—and our closest primate relations, bonobos and chimps—is utterly different. We and our chimp and bonobo cousins typically have sex hundreds—if not thousands—of times per birth, with or without contraception.
Santorum has argued that contraception is morally wrong because, “It’s a license to do things in a sexual realm that is counter to how things are supposed to be.” But human beings happily experience, witness, imagine, and lament a cornicopia of erotic encounters that couldn’t possibly result in conception. Leaving aside the many “perversions” happily practiced by humans the world over, the human female is available even for Vatican-approved missionary position intercourse—at least theoretically—when she’s menstruating, already , post- , or otherwise precluded from conceiving. Is this, too, an abomination? Even Santorum and his wife, who have had more children than most couples, have certainly had a lot more non-reproductive than reproductive sex over the years.
It’s the nature of the human beast. For Homo sapiens, sex is primarily about establishing and maintaining relationships—relationships often characterized by love, or at least affection. Reproduction is a by-product of human sexual behavior, not its primary purpose.
Another way in which we differ from most mammals is in our complex, multi-male social networks. The gorillas mentioned earlier are polygynous, with one dominant silverback with several females (perhaps more akin to Romney’s religious beliefs than to Santorum’s). The only monogamous ape, the gibbon, lives in isolated nuclear family units in the treetops of Southeast Asia, while humans, chimps, and bonobos all live in complex social groups with multiple males in attendance. Of the hundreds of species of primates, there are precisely no monogamous species living in multi-male groups—except humans, if you buy scientific or religious arguments for the naturalness of human .
Although the nuclear family has been promoted like a soft-drink in recent decades, it’s clear that we are the most social species on the planet, interacting with and depending upon each other in ways that extend far beyond Mom, Dad, and Junior. We intermingle in ways no other creature could imagine—or tolerate. We do not raise our children in isolated treetops. We drop them off at school, where they satisfy their instinctive hunger for community, under the protection of adults whose names we’ll never know. When sick, we take them to doctors we’ve never met in hospitals built and maintained by utter strangers.
If you still doubt that humans are deeply social creatures, consider that our greatest is solitary confinement. Anyone who’s experienced it will tell you that any human companionship—even that of murderers, rapists, and Washington lobbyists—is better than isolation. Sartre got it wrong: Hell is the absence of other people.
Santorum is inadvertently correct that sex “keeps civilization going.” But he’s wrong to credit only heterosexual reproductive sex. Sex of all kinds comes naturally to our species, and most of it has little to do with reproduction and a great deal to do with loving one another. Sex and love hold communities—not just families—together. And in the end, it is our communities, as much as our families, we ask to raise our children, protect us from disaster, and offer us some measure of comfort in our final days.
————————————
Twitter: @chrisryanphd
Facebook: Sex at Dawn
|
2024-02-01T01:26:51.906118
|
https://example.com/article/5894
|
Q:
Jquery Index Returns -1 when searching for 0
Why does jQuery index return -1 for a 0 in an array?
var myArray = [0,4,8];
document.write('<br/>8 is at index : ' + $(myArray).index(8));
document.write('<br/>4 is at index : ' + $(myArray).index(4));
document.write('<br/>0 is at index : ' + $(myArray).index(0));
http://jsfiddle.net/JohnNeed/WGPMa/1/
A:
Why does jQuery index return -1 for a 0 in an array?
Because you're using it incorrectly. You're wrapping it with a jQuery object constructor. jQuery expects its indexed slots to contain objects (reference to DOM elements), which are truthy. So when you pass in 0, it's falsy, and fails the first condition (only truthy arguments are expected; jQuery was designed to handle no argument passed).
// No argument, return index in parent
if ( !elem ) {
return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
}
Source
If you change from 0 (falsy) to 5 (truthy), it works as expected.
If you want to find the index of something in an array, use indexOf() on the plain array. If you must use jQuery, use $.inArray() (this does have the advantage of working where Array.prototype.indexOf() doesn't exist).
|
2023-08-02T01:26:51.906118
|
https://example.com/article/4031
|
[Age-related changes of microcirculation in pia mater of rats' sensorimotor cortex].
We studied the density of whole microvascular network and separately the density of arterioles in the pia mater of sensorimotor cortex of rats of different ages. Also pial arteriolar reactivity on exposure to norepinephrine or acetylcholine chloride was evaluated. The microvascular density and the arteriolar reactivity in the pia mater were not significantly changed before the age of 12 months. In the age of 22-24 months the density of whole microvascular network decreased 1,7 times at the mean and the density of arterioles decreased 1,2 times. There were no significant changes of pia arterioles constriction during the animals life but dilatation was noticeably worse in senility. Orientation and exploratory behavior got worse to the age of 22-24 months: the number of behavioral acts in the "open field" test decreased 1,5-2,3 times in comparison with young animals.
|
2024-06-15T01:26:51.906118
|
https://example.com/article/5964
|
lol i already know that i was just asking if someone can post the same code but in a function instead of main() ... u know the calls to functions .. i wanted to know how would it look like if its in a call to function program
|
2024-06-27T01:26:51.906118
|
https://example.com/article/6114
|
Written By Dan Pfeiffer
To: Interested Parties
From: Dan Pfeiffer, Pod Save America
RE: The Work We Need To Do To Win Wisconsin
The latest Crooked Media-Change Research poll takes a look at the pivotal battleground state of Wisconsin. We designed our survey to look less like a media poll that focuses on the horse race, and more like the kind of survey a campaign would use to make strategic decisions.. Our goal was to test various messages for and against Donald Trump, to see what works and what doesn’t, and hopefully provide guidance that Democrats can use in the general election.
Summary
Wisconsin was incredibly close in 2016. It was incredibly close in the 2018 governor’s race, and according to the latest Crooked Media-Change Research Pollercoaster survey, it remains very close and polarized today. Wisconsin may very well tip the Electoral College in 2020, and we may not know who won until all the votes in crucial Waukesha County are finally counted.
Our poll found Wisconsin to be essentially tied. A generic Democrat leads Trump 46-45 when we include voters who say they’ll “definitely” or “probably” vote for one candidate or the other. Another three percent percent say they’ll vote for third party candidates, and six percent are undecided.
In a race this close, a few key groups will decide the election:
Voters who are undecided;
Voters who are currently choosing a third party candidate;
Voters who didn’t vote in 2016 but now say they’ll vote in 2020;
Voters who supported at least one Democrat and at least one Republican in the 2016 presidential, 2018 gubernatorial, and 2018 Senate races.
A caveat: horse race polls this early are informative but not particularly indicative of what will happen in 2020. In the summer of 2011, the USA Today/Gallup poll had Barack Obama losing to a generic Republican by eight points. No one should overreact to any one poll—good or bad.
Still, horse race numbers aside, this poll does highlight Trump’s advantages in Wisconsin, his weaknesses, and the messages that may be most effective for defeating him in 2020.
First, the bad news
Trump is much more popular in Wisconsin than he is nationally. As of this writing, Trump’s national approval rating in the FiveThirtyEight polling average is 41.9-53.3 percent. According to our poll, his approval in Wisconsin is 48-51 percent.
Trump’s approval on the economy is even higher, at 50-48 percent. This has given Republicans a 10-point advantage on the question of which party voters trust to handle the economy and jobs, including an 18-point advantage among independents and a 25-point advantage among undecided voters. Republicans also have an advantage among all of these groups on the issue of taxes, even though poll after poll shows that Trump’s tax cut for the rich is wildly unpopular. The candidate who wins the economic debate usually wins the election, and Trump enters the Wisconsin race with a very real advantage.
We also tested a number of Trump’s campaign messages to see if hearing them made voters more or less likely to support him. Most of the messages we tested in this poll did very little to move the needle in Trump’s favor, but the following economic messages made voters 18 points more likely to vote for Trump:
“Since Trump became President, we’ve created millions of jobs and unemployment rates are the lowest they’ve been in decades.”
Trump’s economic strength in 2019 is an improvement on his standing in 2016. According to exit polls, Hillary Clinton won voters in Wisconsin who cited the economy as their top issue by 11 points.
Our poll also shows Trump has successfully turned immigration into a political cudgel in Wisconsin. In response to an open-ended question about the most pressing issues facing the state, 36 percent of Republicans and 19 percent of independents answered immigration. Republicans have an eight point advantage over Democrats on immigration with independents and they lead by 22 points with the undecided cohort.
Anyone who thinks Donald Trump will be easy to beat in Wisconsin is sorely mistaken, and the path to the White House for a Democrat gets very narrow without Wisconsin.
Now, the good news
Despite Trump’s (relatively) strong political standing in Wisconsin, our poll reveals a path to defeating him in 2020.
We tested Trump’s positive message against positive Democratic messages on immigration, health care, climate change, the economy, and other issues. The Democratic message usually prevailed in these head-to-heads, but none moved the horse race by more than a few points.
However, our poll also revealed that despite Trump’s dominance of the news the last few years, Wisconsin voters are very unfamiliar with much of his record. Some negative stories—the Russia investigation, his tweets, and even his plan to repeal the Affordable Care Act—have already broken through, and thus don’t move voters away from him in a significant way.
But our poll also indicates that there is a wealth of negative information about Trump that causes Wisconsin voters to say that they’re significantly less likely to vote for him. On top of that, Trump’s erratic behavior, constant lying, and checkered past make voters more likely to believe negative information about him than a typical incumbent.
Democrats can thus make gains by:
1. Eroding Trump’s strength on the economy;
2. Hitting him on Medicare cuts;
3. Hitting him on his failure to drain the swamp;
The Economy
Up until now, Trump has benefited from good headlines about a strong economy and a low unemployment rate, but our poll indicates that Wisconsin voters know very little about his economic record. In fact, when voters learn about the impacts of his actual policies they are less likely to support him by large numbers. Contrary to conventional wisdom, Trump is particularly vulnerable to attacks on the ineffectiveness and hypocrisy of his trade policy.
The most effective economic argument against Trump is that he ran as a populist but has governed as a plutocrat. We tested a number of economic arguments against Trump, and these were the most effective:
The fact that Trump is leading among independents in our poll by two points overall makes the independent numbers in this chart even more devastating.
Keep Trump’s hands off of our Medicare
The prevailing media narrative is that Democrats are committing political suicide by supporting various Medicare for All plans. Our poll shows that Donald Trump is the one who should be scared of a debate over Medicare in the 2020 campaign. Wisconsin voters are horrified to learn that Trump “proposed nearly $1 trillion in cuts to Medicare to pay for a tax cut that overwhelmingly benefits billionaires and big corporations.”
The introduction of this information makes Wisconsin voters 38 percent less likely to support Trump, and the numbers are just as devastating with key subgroups: Independents become 47 percent less likely to support him; undecideds 65 percent; and voters currently supporting a third-party candidate 78 percent.
Getting rich from the swamp
Central to Trump’s appeal in 2016 was his image as an outsider who would drain the swamp and change Washington. Exit polls asked Wisconsin voters which candidate quality mattered most to them, and 44 percent chose “can bring change”—more than twice any other quality. Trump won 84 percent of those voters. Three years later, not only has he failed to drain the swamp, he has presided over an epidemic of corruption, and enriched himself in the process. The poll asked voters whether they agreed or disagreed with the statement that “Trump drained the swamp.” Only 33 percent agreed, and 66 percent of independents disagreed with it.
A message about Trump personally profiting from continued corruption in Washington was also very effective:
Conclusion
This poll contains important clues about how to run against Trump in Wisconsin, but they’re only clues for now. For a clearer sense of what will work, we’d need to test multiple variations of all of these messages and, ultimately, the effectiveness of Trump’s response to the attacks.
However, we can already point to several initial conclusions and recommendations for those waging the campaign against Trump in Wisconsin.
1. Trump’s control of the media environment is very real and the bulk of negative information that would affect the race has not broken through to the voters who need to see it.
2. Nothing in the last few years suggests Democrats will be able to deliver these messages to voters through the press—the only way to do it is with a sustained, targeted, digital-advertising campaign.
3. Even though these messages led large numbers of voters to question their support of Trump, hearing them once barely moved the horse race, which is why we recommend that an aggressive advertising campaign start yesterday.
4. Traditionally, the voters we need to target are paying less attention to politics than those who are already committed to a party, which means it will take time to reach and persuade them.
5. Voters are more likely to be persuaded by contrast messages when they are specific, fact-based, and stripped of the rhetoric that dominates political discourse. In other words, we should look for ways to connect voters with information they wouldn’t otherwise see in as straightforward a way as possible, without added spin. One potential tactic would be using paid promotion to show voters news articles from trustworthy or neutral sources that reinforce particular messages.
|
2023-08-04T01:26:51.906118
|
https://example.com/article/9633
|
You know Kendall Square’s office rents have gotten stratospheric when a CEO compares the neighborhood with Madison Avenue in New York, Rue Saint-Honoré in Paris, and Via della Spiga in Milan.
But its brand is all about bleeding-edge science — not high-end shopping. There’s no denser collection of biotech startups, big pharma companies, and venture capital firms anywhere else in the United States, and perhaps on the planet. They’re clustered on either edge of the Massachusetts Institute of Technology campus, and along Main Street heading into Cambridge’s Central Square. And they’re all paying the highest rents in New England: almost $100 per square foot for lab space and $92 per square foot for offices, according to the real estate brokerage CBRE. Both numbers are records.
What makes it worth paying such high rents, when you can be in the suburbs for half the price, or even in other parts of Cambridge for 60 or 70 percent of the cost of Kendall Square? I posed that question to the denizens of the neighborhood — as well as to some who have decamped for more affordable neighborhoods.
Everyone started by talking about a dynamic that’s tough to put a price tag on: serendipitous interactions with people at other companies.
“There are countless interactions between biotech entrepreneurs, pharma leaders, and investors that happen virtually every day,” says John Maraganore, chief executive of the publicly traded biotech Alnylam Pharmaceuticals. “I walk to MIT, the Broad Institute, the Whitehead, all the time. I also walk to my partners over at Sanofi and Novartis, and also to potential partners all around the square.”
In biotech, “partner” typically refers to a bigger company that is funding a research program at a smaller company, with the hope that a marketable drug will emerge.
Even when his company was a mile down the river, close to Cambridgeport, there was a noticeable difference, Maraganore says: “You just don’t run into as many people, and one of the reasons is that you generally need to be in your car to get around.”
Unplanned conversations aren’t only about catching up with old friends or buttering up somebody who might invest in your startup. As Anna Protopapas explains, just having breakfast at Luna Cafe or Darwin’s “inevitably leads to finding the super-specialized expert you might have been looking for to solve a scientific problem, getting a referral on a great candidate for an open position,” or “gaining some critical competitive intelligence.” Protopapas is the CEO of Mersana Therapeutics, which is developing drugs to treat ovarian cancer, and like Maraganore she has spent much of her career working in Kendall Square.
Venture capitalists like the ability to keep a close eye on the companies they’ve put money into and take lots of meetings with scientists and entrepreneurs who might be on the verge of starting the next Biogen or Alnylam.
Jason Pontin, a partner at Social Impact Capital, offers a concrete example: one of his recent investments, Trilogy Sciences, a startup that is building new technology for drug design. Pontin and Trilogy CEO Neil Dhawan decided to move the fledgling startup from Watertown to Kendall Square. “We wanted to be closer to talent who would work at the company,” to scientists who could offer guidance, and to other investors who may provide money in the future, Pontin explains. “We investors don’t want to schlep out to Watertown for the companies we’ve invested in, and the talent and advisers don’t want to work there.”
Sorry, Watertown.
Every week, daytime conferences and evening networking events bring people together from different companies, notes Pearl Freier, president of the recruiting firm Cambridge BioPartners.
An address in Cambridge carries cachet, notes Brian Gallagher, a venture capitalist. “I’ve been in board meetings where someone says, ‘I don’t think we should be building the most preeminent company in this space in Waltham,’ ” says Gallagher, a partner at the investment firm Abingworth LLP. “Whether that’s legit or not is a question.”
But perhaps Kendall Square’s biggest draw is that it’s easy for MIT scientists to walk over to the offices of a company they’ve helped start, to keep tabs on the progress and to offer advice. (It’s also an easy MBTA or Uber ride from Massachusetts General Hospital and Harvard, two other places where scientist-entrepreneurs hang out.)
“Especially in their early years, the close relationship to the founding labs is essential” for young biotech businesses trying to turn academic research into marketable products, notes Johannes Fruehauf, executive director of LabCentral, a lab-and-office complex in Kendall Square.
“I completely get it why companies want to start there, and why they tend to stay there once they get started,” says Arthur Tzianabos, a biotech industry veteran who has worked in Kendall Square and Lexington, and now runs a Bedford company, Homology Medicines.
When Tzianabos was thinking through his current company’s real estate quandary, “it was about do I want to spend money on bricks and mortar, or innovation.” At about $40 per square foot, his rent in Bedford is roughly half of what he would have paid in Cambridge. The company is working on a gene therapy that would treat phenylketonuria, a hereditary metabolic disorder.
One downside of Kendall Square, he says, is that “everybody is always looking to take your talent.” Another one that Tzianabos and others mention: increasingly knotty traffic.
But being there plugs you into a powerful information flow. Once a company is well-established, or an individual has built a personal network over a couple decades, like Tzianabos, they may not need to be there quite as much — though Tzianabos says that he does go to the square for meetings about once a week.
“Even with all of the modern communications available to us all, this is still a face-to-face and human-to-human business built on trust,” says Michael Bonney, a former CEO who serves on several biotech boards. “For the very early stage companies and their owners, this localization can be hard to quantify,” but it has a “meaningfully positive impact on the probability of success,” he adds.
And these days, that comes with a high price tag.
|
2024-02-17T01:26:51.906118
|
https://example.com/article/8211
|
// Copyright 2012-present Oliver Eilhard. All rights reserved.
// Use of this source code is governed by a MIT-license.
// See http://olivere.mit-license.org/license.txt for details.
package elastic
import (
"context"
"errors"
"net/http"
"sync/atomic"
"testing"
"time"
)
type testRetrier struct {
Retrier
N int64
Err error
}
func (r *testRetrier) Retry(ctx context.Context, retry int, req *http.Request, resp *http.Response, err error) (time.Duration, bool, error) {
atomic.AddInt64(&r.N, 1)
if r.Err != nil {
return 0, false, r.Err
}
return r.Retrier.Retry(ctx, retry, req, resp, err)
}
func TestStopRetrier(t *testing.T) {
r := NewStopRetrier()
wait, ok, err := r.Retry(context.TODO(), 1, nil, nil, nil)
if want, got := 0*time.Second, wait; want != got {
t.Fatalf("expected %v, got %v", want, got)
}
if want, got := false, ok; want != got {
t.Fatalf("expected %v, got %v", want, got)
}
if err != nil {
t.Fatalf("expected nil, got %v", err)
}
}
func TestRetrier(t *testing.T) {
var numFailedReqs int
fail := func(r *http.Request) (*http.Response, error) {
numFailedReqs += 1
//return &http.Response{Request: r, StatusCode: 400}, nil
return nil, errors.New("request failed")
}
tr := &failingTransport{path: "/fail", fail: fail}
httpClient := &http.Client{Transport: tr}
retrier := &testRetrier{
Retrier: NewBackoffRetrier(NewSimpleBackoff(100, 100, 100, 100, 100)),
}
client, err := NewClient(
SetHttpClient(httpClient),
SetMaxRetries(5),
SetHealthcheck(false),
SetRetrier(retrier))
if err != nil {
t.Fatal(err)
}
res, err := client.PerformRequest(context.TODO(), PerformRequestOptions{
Method: "GET",
Path: "/fail",
})
if err == nil {
t.Fatal("expected error")
}
if res != nil {
t.Fatal("expected no response")
}
// Connection should be marked as dead after it failed
if numFailedReqs != 5 {
t.Errorf("expected %d failed requests; got: %d", 5, numFailedReqs)
}
if retrier.N != 5 {
t.Errorf("expected %d Retrier calls; got: %d", 5, retrier.N)
}
}
func TestRetrierWithError(t *testing.T) {
var numFailedReqs int
fail := func(r *http.Request) (*http.Response, error) {
numFailedReqs += 1
//return &http.Response{Request: r, StatusCode: 400}, nil
return nil, errors.New("request failed")
}
tr := &failingTransport{path: "/fail", fail: fail}
httpClient := &http.Client{Transport: tr}
kaboom := errors.New("kaboom")
retrier := &testRetrier{
Err: kaboom,
Retrier: NewBackoffRetrier(NewSimpleBackoff(100, 100, 100, 100, 100)),
}
client, err := NewClient(
SetHttpClient(httpClient),
SetMaxRetries(5),
SetHealthcheck(false),
SetRetrier(retrier))
if err != nil {
t.Fatal(err)
}
res, err := client.PerformRequest(context.TODO(), PerformRequestOptions{
Method: "GET",
Path: "/fail",
})
if err != kaboom {
t.Fatalf("expected %v, got %v", kaboom, err)
}
if res != nil {
t.Fatal("expected no response")
}
if numFailedReqs != 1 {
t.Errorf("expected %d failed requests; got: %d", 1, numFailedReqs)
}
if retrier.N != 1 {
t.Errorf("expected %d Retrier calls; got: %d", 1, retrier.N)
}
}
func TestRetrierOnPerformRequest(t *testing.T) {
var numFailedReqs int
fail := func(r *http.Request) (*http.Response, error) {
numFailedReqs += 1
//return &http.Response{Request: r, StatusCode: 400}, nil
return nil, errors.New("request failed")
}
tr := &failingTransport{path: "/fail", fail: fail}
httpClient := &http.Client{Transport: tr}
defaultRetrier := &testRetrier{
Retrier: NewStopRetrier(),
}
requestRetrier := &testRetrier{
Retrier: NewStopRetrier(),
}
client, err := NewClient(
SetHttpClient(httpClient),
SetHealthcheck(false),
SetRetrier(defaultRetrier))
if err != nil {
t.Fatal(err)
}
res, err := client.PerformRequest(context.TODO(), PerformRequestOptions{
Method: "GET",
Path: "/fail",
Retrier: requestRetrier,
})
if err == nil {
t.Fatal("expected error")
}
if res != nil {
t.Fatal("expected no response")
}
if want, have := int64(0), defaultRetrier.N; want != have {
t.Errorf("defaultRetrier: expected %d calls; got: %d", want, have)
}
if want, have := int64(1), requestRetrier.N; want != have {
t.Errorf("requestRetrier: expected %d calls; got: %d", want, have)
}
}
|
2024-06-30T01:26:51.906118
|
https://example.com/article/8488
|
A day after we learned that evangelical stalwart and GOP candidate for Senate from Alabama Roy Moore is an alleged child molester, his brother is joining the crowd of Christians who thinks this is just some liberal conspiracy.
In an interview with CNN’s Martin Savidge, Jerry Moore suggested the multiple accusers were all doing it for money (though he didn’t specify who was paying them) and that their claims were politically motivated.
And then he compared his brother to Jesus.
“When I asked what does he believe the motivation is with these women coming forward making the accusations they have, again, Jerry Moore says it’s money and the Democratic Party, implying that they are doing this because they’re being paid in some way, and it is for the purpose of derailing or interrupting this campaign,” Savidge said. Moore went so far as to say “that his brother is being persecuted, in his own words, like Jesus Christ was,” according to Savidge. “Very defiant and very outspoken, relying on his faith and defending his brother to the hilt.”
Jesus, if you believe the biblical story, was persecuted for his beliefs.
Roy Moore is being criticized for his supposed actions. There’s a difference.
Either Moore touched a 14-year-old girl or he didn’t. Either he pursued relationships with girls under 18 when he was in his 30s or he didn’t. Dismissing all the accusations as part of some conspiracy when the women have nothing to gain by being labeled as the victims says more about Moore than them.
Plus, as some online commenters have claimed, Jesus was nailed to a cross. So it’s not like He had wandering hands. The comparison fails on every level.
|
2024-02-27T01:26:51.906118
|
https://example.com/article/1966
|
Blog
Bitcoin Faucet: How It Works & List of BTC Faucet
Bitcoin Faucet: How It Works
Bitcoin faucet is the place where any user or digital currency lover can sing up and get free bitcoins in their blockchain wallet.
In other words, Bitcoin faucet is a platform to play games and get benefited with free bitcoins in wallet of blockchain.
Users of the Bitcoin Faucet Game websites will unexpectedly declaration this is not your run of the mill Bitcoin dispensing platform, but a premiere ecosystem where Bitcoin and social come together. Instead of swarming visitors behind ads and low payouts, Faucet Game rewards its users handsomely, and encourages them to earn even more through the various game the platform supports.
Here is the list of few bitcoin faucet websites given below:
List of BTC Faucet
1.
DC Faucet HOT
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Chiripa Faucet HOT
41 days
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Java Faucet HOT
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We are pleased by your visit ♥ Thanks to you we are here ♥ Click here►► HOT
|
2023-11-11T01:26:51.906118
|
https://example.com/article/9996
|
_Where to start? The Old Town or ‘Grad’ is a medieval walled, city dating back to the time Brits were just coming out of the woods! Dubrovnik used to be a city state, like the Vatican and the locals were exchanging International Trade Treaties when Robin Hood was causing trouble in Sherwood. Enter through medieval gates, walk on marble streets and be struck by the similarity to Venice. No surprise, as the Venetians once occupied the city. Walk the walls and bask in the sun’s shimmering reflection off the magical Adriatic or jump on the chair lift and get another stunning view of the Old Town and the Elaphite Islands, just offshore.
This is your new blog post. Click here and start typing, or drag in elements from the top bar.
The best time to visit Dubrovnik is September, when temperatures aren't stifling hot yet most of the cruise ships have abandoned the port. The peak season, summer, has arguably the nicest weather. But the small town struggles to meet the demand of the large visitor influx. And of course, prices soar.
|
2024-06-01T01:26:51.906118
|
https://example.com/article/4716
|
Some individuals of this handsome hisser species have very pronounced bumps all over their body while others are mostly smooth. The nymphs undergo a color change as they grow, with many later instars sporting maroon or purplish tinges. Some adults, particularly males, retain some of this coloration into adulthood. Nymphs appear to prefer hiding under bark piles while adults prefer larger, vertical hides.Unfortunately, this species is not the easiest to culture, with colonies experiencing odd die-offs occasionally; it is rumored that all captive stock originates from a single adult female collected under a palm frond somewhere in Madagascar, and the resulting inbreeding may be the cause of the strain’s finickiness.
|
2024-07-09T01:26:51.906118
|
https://example.com/article/4263
|
Forward: Let me pre-empt the Autism and point out that I realize AnimeRG/Phr0stY aren’t “actual” fansub groups — rather, they were just the first to stick this Spanish->English guesslation on a shareraw and throw it up on Nyaa.
That being said, I ain’t reviewing a fucking .ass, and this has more downloads than any other fansub release this season, so by all rights it qualifies for a review. Just don’t expect a favorable one.
The Review
I’ve been out of the review game for a bit longer than I planned, so the timing of this release couldn’t be better.
Yeah but the Abridged series also is rewriting the script entirely. I would understand criticizing the first season, it slowly picked up steam but started pretty poorly, but as of season 3 they’re doing spectacularly well for amateurs. Considering that their entire endeavour consists in stuffing jokes by cutting, pasting and re-dubbing material that didn’t contain them to begin with, using a dramatically understaffed voice actor team, so it’s make-do.
As for the quality of the script… it’s funny, it’s not a translation so it can’t be wrong, and while it may not be 100% perfect English it doesn’t exactly need to be – it’s supposed to be colloquial and not always serious. I think asking for more would be reaching a bit too high. There are many abysmal Abridged series out there but TFS’s really isn’t one of them.
They spent the first however many seconds choking on Funi’s dick cuz they think Funi own Dragon Ball? Like their shitty facebook-tier “no it’s cool copyright infringement is fair use if I just say it is” description would save them from any legal onslaught? Fucking hell.
I say “however many” cuz I turned the video off almost immediately. You’d have to be touched harder than an altar boy to stand more than a couple seconds of that middle school bullshit.
Fuck them for making that video, and more importantly, fuck you for encouraging them. The real cancer was you all along.
Gotta cut the TL a little slack, Chichi says “ちゃんと仕事して金稼ぐだ！” it could be heard as “半年仕事して金稼ぐだ！” with her accent. You’d still be missing a し from either the 年 or 仕事, and it still doesn’t quite make sense… so who am I kidding, they suck.
I don’t really think this release sucked. I mean, yes the points you made were good to some extent. If I am right this was released really quick. And all the other TLs came like 6-7 hours after this release.
For a faster release, it was good. And as long as you get the meaning it’s fine.
and why is the review here? They are not a fansub group. Just bunch of uploaders, meh….
no just no goddamnit shut the hell up, stop posting and cut your connection to the internet. there’s no reason this needs to exist, and the world doesn’t need chromosome-lacking special people like you that approve of this shitfest
|
2023-08-02T01:26:51.906118
|
https://example.com/article/3826
|
Q:
Algorithm for matrix addition and multiplication
Let m, n be integers such that 0<= m,n< N.
Define:
Algorithm A: Computes m + n in time O(A(N))
Algorithm B: Computes m*n in time O(B(N))
Algorithm C: Computes m mod n in time O(C(N))
Using any combination of algorithms A, B and C describe an algorithm for N X N matrix addition and matrix multiplication with entries in Z/NZ. Also indicate the algorithm's run time big-O notation.
Attempt at solution:
For N X N addition in Z/NZ:
Let A, and B be N X N matrices in Z/NZ with entries a_{ij} and b_{ij} such that i,j in {0,1,...,N} where i represents the row and j represents the column in the matrix. Also, let A + B = C
Step 1. Run Algorithm A to get a_{ij} + b_{ij} = c_{ij} in time O(A(N))
Step 2. Run Algorithm C to get c_{ij} mod N in time O(C(N))
Repeat Steps 1 and 2 for all i,j in {0,1,...,N}.
This means that we have to repeat the steps 1,2 N^2 times. So the total run time is estimated by
N^2[ O(A(N)) + O(C(N)) ] = O(N^2 A(N)) + O(N^2 C(N)) = O(|N^2 A(N)| + |(N^2 C(N)|).
For multiplication algorithm I just replaced step 1 by Algorithm B and got the total run time to beO(|N^2 B(N)| + |(N^2 C(N)|) just like above.
Please tell me if I am approaching this problem correctly, especially with the big-O notation.
Thanks.
A:
Your algorithm for matrix multiplication is wrong, and will yield a wrong answer, since A*B_{i,j} != A_{i,j} * B_{i,j} (with exception for some unique cases like zero matrix)
I assume the goal of the question is not to implement an efficient matrix multiplication, since it's a hard and still studied problem, so I will answer for the naive implementation of matrix multiplication.
For any indices i,j:
(AB)_{i,j} = Sum( A_{i,k} * B_{k,j}) =
= A_{i,1} * B_{1,j} + A_{i,2} * B_{2,j} + ... + A_{i,k} * B_{k,j} + ... + A_{i,n} * B_{n,j}
As you can see, for each pair i,j there are n multiplications and n-1 additionsץ Regarding the amount of invokations of C - it depends if you need to invoke it after each addition, or only once when you are done (it really depends on how many bits you have to represent each number), so for each pair of i,j - you might need it anywhere from once to 2n-1 invokations.
This gives us total complexity of (assuming 2n-1 modolus for each (i,j) pair, if less are needed as explained above - adjust accordingly):
O(n^3*A + n^3*B + n^3*C)
As a side note, a good sanity check that shows your algorithm is indeed incorrect - it is proven that matrix multiplication cannot be done better than Omega(n^2 logn) (Raz,2002), and best current implementation is ~O(n^2.3)
|
2024-01-06T01:26:51.906118
|
https://example.com/article/3215
|
Alexandre Geraldo dos Anjos, of São José dos Campos in Brazil, faked his own kidnapping this week and, posing as his abductors, demanded that his family pay a 3 Bitcoin ransom. Instead of paying, his family informed the police, leaving dos Anjos with little choice but to turn himself in.
Dos Anjos claims to be a pastor in the evangelical Assembleia de Deus Missão church, although the church leadership say that, “Alexandre Geraldo dos Anjos is not pastor or member of the ministry of this church”.
While his religious status is unclear, what is certain is that he went missing last Monday leaving no clue to his whereabouts. The disappearance was widely reported in the Brazilian media.
Apparently he then used a new SIM card to contact a friend and pretend to be kidnappers asking for a 3 Bitcoin ransom. When the friend passed on the message to his worried family they decided to go to the police rather than pay-up.
With few options remaining to him Dos Anjos reappeared at the Igaratá police station, claiming that he had made a daring escape from this captors. Realising that this could not be the full story, the police transferred him to São José General Investigations Office. Under interrogation he admitted that the whole thing had been a hoax, claiming he’s been driven to his actions by mounting debts.
Since his reappearance Dos Anjos has released a tearful video thanking his friends and family for their love and prayers during his absence. “I want to thank the brothers who are with us in prayer in this battle, in this struggle,” he said. He made no mention of having staged an elaborate hoax to leverage money from his family.
Image From Shutterstock
|
2024-07-23T01:26:51.906118
|
https://example.com/article/9488
|
Guanidinophenyl derivatives of pyrazole: synthesis and inhibitory effect on serine proteinases, blood coagulation and platelet aggregation.
Guanidinophenyl derivatives of pyrazole have been synthesized. Their inhibitory effects on (i) bovine trypsin, bovine thrombin, porcine pancreatic kallikrein catalyzed hydrolysis of p-nitro anilide of N alpha -benzoyl-arginine and (ii) blood coagulation and platelet aggregation, were investigated. The kinetic behaviour of all compounds conformed to that of a reversible competitive inhibition pattern, and they were also found to act in vitro as inhibitors of platelet aggregation induced by ADP.
|
2024-05-23T01:26:51.906118
|
https://example.com/article/9393
|
Acute airway effects of diacetyl in mice.
Occupational exposures to the butter flavouring agent diacetyl (2,3-butanedione) have caused lung inflammation and severe airflow limitation due to bronchiolitis obliterans. Diacetyl is naturally present in butter, beer, white wine, etc., and its pleasant odour is easily recognized by consumers. However, this pleasant odour may induce a false sense of safety when higher airborne concentrations are encountered in industrial use. In this study, the acute warning properties, in terms of sensory irritation, that could be useful to prevent workers from exposures to a high concentration were first investigated in a mouse bioassay. Then at higher exposure concentrations, the possibility of airflow limitation and pulmonary irritation were studied with the same mouse bioassay. Diacetyl induces concentration-dependent irritation in all parts of the respiratory tract during a 2-h exposure period. The no-observed-effect levels for each effect in the mice were above 100 ppm and initiation of sensory irritation in humans was estimated to occur above 20 ppm. No acute warning signal from the airways is expected at diacetyl levels that have caused bronchiolitis obliterans and other toxic effects. The sensory irritation effect, which occurred rapidly upon initiation of exposure, faded rapidly. Furthermore, high-level diacetyl exposures decreased the sensory irritation warning signal in mice upon repeated exposure, which suggests that the compound is especially insidious.
|
2023-09-11T01:26:51.906118
|
https://example.com/article/1740
|
Volume fusion for two-circular-orbit cone-beam tomography.
By using the Feldkamp-Davis-Kress (FDK) algorithm, we can efficiently produce a digital volume, called the FDK volume, from cone-beam data acquired along a circular scan orbit. Due to the insufficiency of the cone-beam data set, the FDK volume suffers from nonuniform reproduction exactness. Specifically, the midplane (on the scan-orbit plane) can be exactly reproduced, and the reproduction exactness of off-midplanes decreases as the distance from the midplane increases. We describe the longitudinal falling-off degradation by a hatlike function and the spatial distribution over the object domain by an exactness volume. With two orthogonal circular scan orbits, we can reconstruct two FDK volumes and generate two exactness volumes. We propose a volume fusion scheme to combine the two FDK volumes into a single volume. Let Va and Vb denote the two FDK volumes, let Ea and Eb denote the exactness volumes for orbits Gamma(a) and Gamma(b), respectively, then the volume fusion is defined by Vab=VaWa+VbWb, with Wa=Ea/(Ea+Eb) and Wb=1-Wa. In the result, the overall reproduction exactness of Vab is expected to outperform that of Va, or Vb, or (Va+Vb)/2. In principle, this volume-fusion scheme is applicable for general cone-beam tomography with multiple nonorthogonal and noncircular orbits.
|
2024-07-05T01:26:51.906118
|
https://example.com/article/9650
|
NSCRO Rugby Women’s All-Americans
NSCRO Rugby & Women’s All-Americans
NSCRO Rugby has announced twenty-five student-athletes named to the inaugural NSCRO Women’s All-Americans for the 2017-18 season. A similar Men’s Selection has also been made.
The selection committee worked with coaches around the country to identify the twenty-five exceptional women who make up the first-ever NSCRO Women’s All-Americans. There were a large number of senior players nominated and this is reflected in the final list that is comprised of four sophomores, three juniors, and eighteen seniors.
Our congratulations go out to the following athletes:
NAME
SCHOOL
Jessie Blitz
Western Colorado State University
Erin Buckland
University of Maine at Farmington
Alexandria Conner
Lee University
Anna Elder
LeTourneau University
Shae Ferguson
Lee University
Allison Gallagher
Eckerd College
Emily Grey
University of Rochester
Cecilia Hammond
College of St. Benedict
Anna Herrmann
Simpson College
Nora Holmes
Colorado College
Stephanie Lambert
Fairmont State University
Nicole McCardle
Endicott College
Mary Kate McNulty
Denison University
Nicole Moore
Colby-Sawyer College
Maggie Nelsen
Colgate University
Leanna Rosberg
Wayne State College
Emma Santosuosso
Bentley University
Kat Scheerer
Eckerd College
Rebecca Silver
University of Rochester
Emily Sion
St. Bonaventure University
Kelcey Stutzman
Wayne State College
Hailey Thompson
Lee University
Amanda Tondin
York College of Pennsylvania
Angelina Tornetto
The College of New Jersey
Joey Yamada
The Claremont Colleges
Other Articles
DJCoil Rugby articles by Doug Coil are also available on Facebook. Other Social Media sites to follow or subscribe include Twitter, Instagram, and YouTube for interviews.
|
2024-01-15T01:26:51.906118
|
https://example.com/article/5274
|
.. author:: ctr49 <https://github.com/ctr49>
.. tag:: automation
.. highlight:: console
.. sidebar:: Logo
.. image:: _static/images/saltstack.png
:align: center
##########
SaltStack
##########
.. tag_list::
`SaltStack`_ (or simply `Salt`) is Python-based, open-source software for event-driven IT automation, remote task execution, and configuration management. Supporting the "Infrastructure as Code" approach to data center system and network deployment and management, configuration automation, SecOps orchestration, vulnerability remediation, and hybrid cloud control.
The ``salt-master`` controls so called ``salt-minions`` through formulae, pillars and grains. The scope of this guide is to install a ``salt-master``(without a co-located minion) on an Uberspace.
----
.. note:: For this guide you should be familiar with the basic concepts of
* :manual:`Opening ports <basics-ports>`
* :manual:`supervisord <daemons-supervisord>`
Prerequisites
=============
We need two open TCP ports for minions to communicate with the Salt master.
.. code-block:: console
[isabell@stardust ~]$ uberspace port add
Port <high-port1> will be open for TCP and UDP traffic in a few minutes.
[isabell@stardust ~]$ uberspace port add
Port <high-port2> will be open for TCP and UDP traffic in a few minutes.
[isabell@stardust ~]$ uberspace port list
<high-port1>
<high-port2>
Take note of the high ports, you will need them for salt master configuration later.
Installation
============
Install
-------
Installing Salt in a ``virtualenv`` using python 3.8 (latest available python on Uberspace). Also installing pygit2 (because it is a dependency for any gitfs in Salt which is very common). Packages are installed in multiple steps as updated setuptools, pip and wheel may be needed for others to install. Salt must be installed by itself due to 'global-option' being used. Download latest sample config as last step.
.. code-block:: console
[isabell@stardust ~]$ virtualenv -p python3.8 ~/salt_venv
[isabell@stardust ~]$ source ~/salt_venv/bin/activate
(salt_venv) [isabell@stardust ~]$ pip3.8 install -U setuptools pip wheel
(salt_venv) [isabell@stardust ~]$ pip3.8 install -U pyzmq PyYAML msgpack-python jinja2 psutil futures tornado 'msgpack<1.0.0' chardet idna urllib3 certifi requests pycryptodomex distro pygit2
(salt_venv) [isabell@stardust ~]$ MIMIC_SALT_INSTALL=1 pip3.8 install --global-option='--salt-root-dir='${HOME}'/salt_venv/' salt
(salt_venv) [isabell@stardust ~]$ deactivate
[isabell@stardust ~]$ mkdir -p ~/salt_venv/etc/salt ~/salt_venv/var/log/salt
[isabell@stardust ~]$ curl https://raw.githubusercontent.com/saltstack/salt/master/conf/master -o ~/salt_venv/etc/salt/master
Configuration
=============
Edit ``~/salt_venv/etc/salt/master`` and make at least the following changes:
.. code-block:: yaml
user: <your-user i.e. isabell>
publish_port: <high-port1>
ret_port: <high-port2>
Setup daemon
------------
Create ``~/etc/services.d/salt-master.ini`` with the following content:
.. code-block:: ini
[program:salt-master]
process_name=salt-master
command=%(ENV_HOME)s/salt_venv/bin/salt-master
directory=%(ENV_HOME)s/salt_venv
autostart=yes
autorestart=yes
Tell ``supervisord`` to refresh its configuration and start the service:
::
[isabell@stardust ~]$ supervisorctl reread
salt-master: available
[isabell@stardust ~]$ supervisorctl update
salt-master: added process group
[isabell@stardust ~]$ supervisorctl status
salt-master RUNNING pid 24968, uptime 0:00:05
If it's not in state RUNNING, check your configuration.
Finishing installation
======================
Connect minions
---------------
Now you can connect a minion to the salt master. The minion configuration needs the IP address of your Uberspace (or a hostname resolving to it) and the following minimal configuration:
.. code-block:: yaml
master: <IP or hostname of Uberspace>:<high-port2>
publish_port: <high-port1>
An initial minion run will upload the minion public key to the master and you view and accept this key to establish communication:
.. code-block:: console
[isabell@stardust ~]$ source ~/salt_venv/bin/activate
(salt_venv) [isabell@stardust ~]$ salt-key -L
Accepted Keys:
Denied Keys:
Unaccepted Keys:
<your-new-minion>
Rejected Keys:
(salt_venv) [isabell@stardust ~]$ salt-key -a <your-new-minion>
(salt_venv) [isabell@stardust ~]$ deactivate
Salt master is now setup with the first minion connected.
Updating Salt
=============
Update Salt in ``virtualenv``:
.. code-block:: console
[isabell@stardust ~]$ source ~/salt_venv/bin/activate
(salt_venv) [isabell@stardust ~]$ pip3.8 install <any additional dependencies from newer version>
(salt_venv) [isabell@stardust ~]$ MIMIC_SALT_INSTALL=1 pip3.8 install -U --global-option='--salt-root-dir='${HOME}'/salt_venv/' salt
(salt_venv) [isabell@stardust ~]$ deactivate
[isabell@stardust ~]$ supervisorctl restart salt-master
Tested with SaltStack 3001, Uberspace 7.7
.. author_list::
|
2024-06-02T01:26:51.906118
|
https://example.com/article/2237
|
Page 359
The Papers of William A. Graham 329
Considerations like these brought me to the conclusion that,
whatever reason there might be for suspecting that this clause
might have been intended by a part at least of the Convention
to impose political disabilities on Roman Catholics, it could not
be judicially expounded as excluding them from office. A penal
provision against a portion of the free-men of the State—a dis-abling
provision against the whole community in its selection of
civil officers—penal and disabling provisions because of religious
principles which it was an unalienable and declared right to
profess and to follow^ out in worship—could not be upheld and
enforced unless clearly and definitely declared.
The question was purely one of legal and judicial exposition.
It involved the construction of a written provision in the Consti-tutional
Law of the Country. The construction which had been
settled by Judicial Tribunals, or, where none such had obtained
the construction which would be attached to it by Judicial Tri-bunals,
according to the fixed principles of legal interpretation,
must be taken by all to be the true one. Private Conscience was
concerned so far only as not to violate the Law. But what the
Law was, conscience could not determine, nor even private reason
decide against either an official interpretation either actually
made, or such as must result from the rules universally adopted
by legal tribunals for their own government.
In this opinion of what must be the judicial exposition of this
clause, I was confirmed by the highest legal authority within the
State, and without the State. Moreover I had the written opinion
given me more than thirty years ago when I first became a mem-ber
of the State Legislature, of Samuel Johnston ^^ who of all men
then living best knew and was best qualified to expound the Con-stitution.
Under such circumstances to decline an office, which my con-science
told me I was bound to take unless disabled by the Con-stitution,
appeared to me an abandonment of duty. I had no
well-founded scruple myself. To be deterred by the apprehension
of what others might think seemed to me cowardice. Besides if
from any mistaken notions of delicacy I could have consented
*- Samuel Johnston (1733-1816), a native of Scotland, educated in New England,
who came to Edenton in 1736, a lawyer, member assembly, 1760, provincial treasurer,
delegate to the first four provincial Congresses, and president of the third and
fourth. He was state senator, 1779, member of the Continental Congress, 1780-1782,
and declined election as president. He was president of the conventions of 1788
and 1789, and the first United States senator elected under tlie Constitution,
serving from 1789 to 1793. He was a judge of the superior court, 1800-1803.
Gaston's tribute to his knowledge and wisdom is restrained, rather than otherwise.
Click tabs to swap between content that is broken into logical sections.
The Papers of William A. Graham 329
Considerations like these brought me to the conclusion that,
whatever reason there might be for suspecting that this clause
might have been intended by a part at least of the Convention
to impose political disabilities on Roman Catholics, it could not
be judicially expounded as excluding them from office. A penal
provision against a portion of the free-men of the State—a dis-abling
provision against the whole community in its selection of
civil officers—penal and disabling provisions because of religious
principles which it was an unalienable and declared right to
profess and to follow^ out in worship—could not be upheld and
enforced unless clearly and definitely declared.
The question was purely one of legal and judicial exposition.
It involved the construction of a written provision in the Consti-tutional
Law of the Country. The construction which had been
settled by Judicial Tribunals, or, where none such had obtained
the construction which would be attached to it by Judicial Tri-bunals,
according to the fixed principles of legal interpretation,
must be taken by all to be the true one. Private Conscience was
concerned so far only as not to violate the Law. But what the
Law was, conscience could not determine, nor even private reason
decide against either an official interpretation either actually
made, or such as must result from the rules universally adopted
by legal tribunals for their own government.
In this opinion of what must be the judicial exposition of this
clause, I was confirmed by the highest legal authority within the
State, and without the State. Moreover I had the written opinion
given me more than thirty years ago when I first became a mem-ber
of the State Legislature, of Samuel Johnston ^^ who of all men
then living best knew and was best qualified to expound the Con-stitution.
Under such circumstances to decline an office, which my con-science
told me I was bound to take unless disabled by the Con-stitution,
appeared to me an abandonment of duty. I had no
well-founded scruple myself. To be deterred by the apprehension
of what others might think seemed to me cowardice. Besides if
from any mistaken notions of delicacy I could have consented
*- Samuel Johnston (1733-1816), a native of Scotland, educated in New England,
who came to Edenton in 1736, a lawyer, member assembly, 1760, provincial treasurer,
delegate to the first four provincial Congresses, and president of the third and
fourth. He was state senator, 1779, member of the Continental Congress, 1780-1782,
and declined election as president. He was president of the conventions of 1788
and 1789, and the first United States senator elected under tlie Constitution,
serving from 1789 to 1793. He was a judge of the superior court, 1800-1803.
Gaston's tribute to his knowledge and wisdom is restrained, rather than otherwise.
|
2024-01-20T01:26:51.906118
|
https://example.com/article/3128
|
Biotechnology Careers
Metaphysics is a fancy philosophical idea that deals with the abstract and physical features of life. In keeping with Michael Mosley’s The Story of Science, The Renaissance which paved the way for an unprecedented inflow of scientific discoveries and inventions and the Reformation which opened the minds of Europe to individual seek for information are the two important factors which serves as catalysts for the Scientific Revolution.
Come to SciTech with an open mind, ready to study and explore science, know-how, engineering, arts, and math. They be taught science and scientific ideas by “doing science” that is connected to their on a regular basis life, slightly than watching someone else do it.
Group charges are available to groups of 15 or extra people (includes students, parents, and lecturers) and embody entry to 4 floors of arms-on reveals, Highmark SportsWorks®, and one reserved workshop and special program. All students – elementary, center, and high school – can choose to attend a magnet program.
Science has adequately, energetically and productively superior, modified, civilized, enhanced and progressed human life. Until 1994, telecommunication providers underneath government monopoly made tardy progress. The Scitech Europa website exists to provide as much as the minute news and developments from across the whole spectrum of the European science and technology community.
All the effort put into cosplaying & larping fairly than residing ends in ceremony & ritual in fan service of that which denies life being potential in the first place – a lot plastic & different poisons on display, nearly all the Outdated Ways that tied us to the land & kept us in tune with the seasons, & therefore being alive, have been forgotten & replaced by ersatz celebrations – cons certainly, they’re synthetic concoctions of an artificial course of that will solely additional make Issues Stranger as humanity continues deracinating on towards ‘the final frontier’.
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2024-03-02T01:26:51.906118
|
https://example.com/article/9615
|
- Indian Americans, especially Gujaratis, now own about 60 percent of all budget motels in the United States—valued at well over $100 billion dollars
- They own almost two million rooms. Seventy percent of the owners share the same surname, Patel, although they are not all related. Most come from Gujarat, and a majority from within a 100-mile radius of the central region of the state. Patels alone own about one-third of all the nation’s motels.
A Motel of One's Own
If you’re staying the night at a Super 8 in Sioux City, S.D., or an Econo Lodge in New Jersey, the odds are that the motel owner not only has the surname Patel, but his family comes from the state of Gujarat on India’s west coast. That’s because Indian Americans, especially Gujaratis, now own about 60 percent of all budget motels in the United States—valued at well over $100 billion dollars—impressive considering they started buying low-end motels only about 50 years ago.
Pawan Dhingra, professor of sociology in the School of Arts and Sciences, had long heard about this remarkable business story. Clearly these immigrants were successful entrepreneurs, making their own American Dreams. But how, he wondered, did these Indian Americans build a sense of community? How do they relate to their customers, and how do they live in parts of the country where immigrants stand out and are sometimes not welcomed?
He answered those questions in his new book, Life Behind the Lobby: Indian American Motel Owners and the American Dream (Stanford University Press, 2012), which examines their experiences. Dhingra sat down recently to talk about his research with Tufts Now.Tufts Now: How would you describe these motel owners?Pawan Dhingra: They have created what likely is the largest ethnic enterprise in U.S. history. They own about half of all the nation’s motels and hotels, with a concentration in lower- and middle-budget motels. In a sense, they appear as the American Dream incarnate: self-employed, self-sufficient, boot-strapping immigrants.
They own almost two million rooms. Seventy percent of the owners share the same surname, Patel, although they are not all related. Most come from Gujarat, and a majority from within a 100-mile radius of the central region of the state. Patels alone own about one-third of all the nation’s motels.How did this phenomenon get started?In the 1940s, some immigrants from Gujarat came to San Francisco and realized jobs were limited, given their skills. They would live at residential hotels, where they could stay for months, because it’s what they could afford. Then they began to think, Maybe we can run one of these: it’s a lot of hard work, but it’s not complicated and doesn’t require a lot of English-language skills.
As more Patels came to San Francisco, they learned through their village connections about the hotel business. The properties were affordable, and there was little competition, because most of the places were run down. In addition, you could live there for free. Your expenses are low, so you don’t have to make as much money as in other businesses. This population was eager to work on their own, to be self-employed.How did you get to know the motel owners?
One way was through word of mouth: I’d meet one owner, who would tell me about someone else, and there was a domino effect. I also went to places where a lot of owners go, say, a local temple. A lot of male owners play volleyball, which is a common pastime in Gujarat. They do it here, too, so I went to games. In addition, there are major conventions of Indian motel owners, and I went to those. There is an annual national convention of the Asian American Hotel Owners Association, for example, which attracts major speakers like George W. Bush, Al Gore and Bill Clinton.It appears they are very successful. Is that true?
These immigrants came with limited resources and ended up for the most part finding economic security and most importantly, enabling their children to advance in this country. Pretty much every child of an owner I met who grew up in the United States had the opportunity to go to college, which is pretty remarkable.What are the challenges?
There are more complications than you imagine. For example, customers may not want to rent from an Indian; owners have a lot of stories about this. A customer drives in, sees an Indian behind the desk and drives away, or a customer does come in, but finds an excuse not to stay. So the owners would have to hire a white desk clerk or someone from the local population, but not an Indian, so as not to convey to the public this is clearly an Indian-owned motel.
A lot of owners have apartments behind the motel office. If I’m in my apartment, which is basically one thin wall away from the lobby, and I’m cooking, you’ll smell the food. So families would cook Indian food when fewer people were checking in, or they would run big fans. In other words, they found methods to limit the ways they are different. Some would even change their names.
In the 1980s and ’90s other motel owners put up signs that said, “American owned and operated.” You wouldn’t see that at a big franchise, such as a Comfort Inn or La Quinta, but they were there. After 9/11, the signs went up again for awhile.How do the Indian American motel owners maintain their cultural identity?
In urban areas, it’s fairly easy to maintain their culture, because they are around many other immigrants. They build up associations, religious centers and cultural groups, and they have more food options. They get together on weekends.
But many of the motel owners are off interstate highways or in small towns. It’s remarkable that this group has been able to maintain very strong ties to their culture despite being in, say, rural Pennsylvania. Because the parents live where they work, the kids aren’t in after-school programs; they’re always at the motel. So the parents have more opportunities to speak to them in their own language, listen to their music and eat their own food.
The families are very committed to getting their kids together with other Indian kids and sometimes go to other motels to visit Indian families. They travel back to India when they can. They talk about religion and what it means to be Indian in America. The kids show off dances; a lot of matchmaking goes on.Do the children of these immigrants want to continue in their parents’ businesses?
Being self-employed is a big part of the ethos of this group. Even if someone grew up hating the motel, he may say, “I majored in physics, got a job as an engineer, and five years later, I’ve hit the glass ceiling.” He may feel as if he’s never going to be in control of his own destiny. So he decides that self-employment is for him and owning a motel is the obvious path to take, because his family can teach him what to do. He grew up in the business, and he has connections.Have these motel owners truly achieved the American Dream?
On the one hand, they have attained a remarkable achievement: owning a business, helping their children get an education. But if you go below the surface, you realize their success is not what you think of as the American Dream. That scenario doesn’t include hiding your background or covering up who you are, yet that’s part of their story. Is that really the American Dream? Not really, but certain outcomes, like economic security and educational achievement for kids, are part of that dream.Are the children of the owners assimilated into American culture, like the second generation of other ethnic groups usually is? Or is it different because these families are living more isolated lives in their motels?
The children are well assimilated into American culture, if by that we mean they speak English fluently, dress as most Americans do, know the pop culture that many people of their age and gender know and so on. But they have done this while also knowing their ethnic language, maintaining ties to their families, being familiar with Indian popular and traditional culture and the like. One unexpected element among the second generation is a different approach to running the business than their immigrant parents, which the second generation attributes to growing up in the United States. Tensions can arise within families, as the second generation takes a riskier approach to business growth than parents often do, and they have divergent attitudes towards spending and cost control.Marjorie Howard can be reached at marjorie.howard@tufts.edu.
|
2024-02-15T01:26:51.906118
|
https://example.com/article/5936
|
Whenever one starts, everything slows down. The ground beneath me feels hollow and I know I'm about to drop below, but I know it's not Mother Earth’s fault. She did the best she could to shield me, but this time, I have to deal with my own quaking. First, if I'm holding a cup of liquid, you can see the liquid bounce like in “Jurassic Park” when the T-rex nears. Next, I have to set the cup down and buckle down the hatches because this quaking leads to my breath going away from my body, like birds flying away just before the earthquake happens. Next, I'm swallowed up in my own thoughts, and my tears flow like the tsunami that comes after. Except, the tsunami is already here, the earthquake is already here, and yet I'm left there alone with nothing to hide under because at that point, I'm no longer a person and I don't die. I just have to wait for everything to happen and to eventually capture my breath and stick it back inside me, because in all of that chaos, the thing I can focus on is my breathing. 4 seconds in, hold for 5 and release for 8. Usually, it takes about 4 times, but at least I can stop drowning in my own tears.
Now you'd think these panic attacks would be known to people I love, but I'm not even sure what to tell them.
(Special thanks to Drew)
|
2023-12-15T01:26:51.906118
|
https://example.com/article/3011
|
import pytest
from datetime import datetime
import pytz
import platform
from time import sleep
import os
import numpy as np
import pandas as pd
from pandas import compat, DataFrame
from pandas.compat import range
pandas_gbq = pytest.importorskip('pandas_gbq')
PROJECT_ID = None
PRIVATE_KEY_JSON_PATH = None
PRIVATE_KEY_JSON_CONTENTS = None
if compat.PY3:
DATASET_ID = 'pydata_pandas_bq_testing_py3'
else:
DATASET_ID = 'pydata_pandas_bq_testing_py2'
TABLE_ID = 'new_test'
DESTINATION_TABLE = "{0}.{1}".format(DATASET_ID + "1", TABLE_ID)
VERSION = platform.python_version()
def _skip_if_no_project_id():
if not _get_project_id():
pytest.skip(
"Cannot run integration tests without a project id")
def _skip_if_no_private_key_path():
if not _get_private_key_path():
pytest.skip("Cannot run integration tests without a "
"private key json file path")
def _in_travis_environment():
return 'TRAVIS_BUILD_DIR' in os.environ and \
'GBQ_PROJECT_ID' in os.environ
def _get_project_id():
if _in_travis_environment():
return os.environ.get('GBQ_PROJECT_ID')
else:
return PROJECT_ID
def _get_private_key_path():
if _in_travis_environment():
return os.path.join(*[os.environ.get('TRAVIS_BUILD_DIR'), 'ci',
'travis_gbq.json'])
else:
return PRIVATE_KEY_JSON_PATH
def clean_gbq_environment(private_key=None):
dataset = pandas_gbq.gbq._Dataset(_get_project_id(),
private_key=private_key)
for i in range(1, 10):
if DATASET_ID + str(i) in dataset.datasets():
dataset_id = DATASET_ID + str(i)
table = pandas_gbq.gbq._Table(_get_project_id(), dataset_id,
private_key=private_key)
for j in range(1, 20):
if TABLE_ID + str(j) in dataset.tables(dataset_id):
table.delete(TABLE_ID + str(j))
dataset.delete(dataset_id)
def make_mixed_dataframe_v2(test_size):
# create df to test for all BQ datatypes except RECORD
bools = np.random.randint(2, size=(1, test_size)).astype(bool)
flts = np.random.randn(1, test_size)
ints = np.random.randint(1, 10, size=(1, test_size))
strs = np.random.randint(1, 10, size=(1, test_size)).astype(str)
times = [datetime.now(pytz.timezone('US/Arizona'))
for t in range(test_size)]
return DataFrame({'bools': bools[0],
'flts': flts[0],
'ints': ints[0],
'strs': strs[0],
'times': times[0]},
index=range(test_size))
@pytest.mark.single
class TestToGBQIntegrationWithServiceAccountKeyPath(object):
@classmethod
def setup_class(cls):
# - GLOBAL CLASS FIXTURES -
# put here any instruction you want to execute only *ONCE* *BEFORE*
# executing *ALL* tests described below.
_skip_if_no_project_id()
_skip_if_no_private_key_path()
clean_gbq_environment(_get_private_key_path())
pandas_gbq.gbq._Dataset(_get_project_id(),
private_key=_get_private_key_path()
).create(DATASET_ID + "1")
@classmethod
def teardown_class(cls):
# - GLOBAL CLASS FIXTURES -
# put here any instruction you want to execute only *ONCE* *AFTER*
# executing all tests.
clean_gbq_environment(_get_private_key_path())
def test_roundtrip(self):
destination_table = DESTINATION_TABLE + "1"
test_size = 20001
df = make_mixed_dataframe_v2(test_size)
df.to_gbq(destination_table, _get_project_id(), chunksize=10000,
private_key=_get_private_key_path())
sleep(30) # <- Curses Google!!!
result = pd.read_gbq("SELECT COUNT(*) AS num_rows FROM {0}"
.format(destination_table),
project_id=_get_project_id(),
private_key=_get_private_key_path())
assert result['num_rows'][0] == test_size
|
2023-10-12T01:26:51.906118
|
https://example.com/article/1232
|
Facile magnetization of metal-organic framework MIL-101 for magnetic solid-phase extraction of polycyclic aromatic hydrocarbons in environmental water samples.
The unusual properties such as high surface area, good thermal stability, uniform structured nanoscale cavities and the availability of in-pore functionality and outer-surface modification make metal-organic frameworks (MOFs) attractive for diverse analytical applications. However, integration of MOFs with magnets for magnetic solid-phase extraction for analytical application has not been attempted so far. Here we show a facile magnetization of MOF MIL-101(Cr) for rapid magnetic solid-phase extraction of polycyclic aromatic hydrocarbons (PAHs) from environmental water samples. MIL-101 is attractive as a sorbent for solid-phase extraction of pollutants in aqueous solution due to its high surface area, large pores, accessible coordinative unsaturated sites, and excellent chemical and solvent stability. In situ magnetization of MIL-101 microcrystals as well as magnetic solid-phase extraction of PAHs was achieved simultaneously by simply mixing MIL-101 and silica-coated Fe(3)O(4) microparticles in a sample solution under sonication. Such MOF-based magnetic solid-phase extraction in combination with high-performance liquid chromatography gave the detection limits of 2.8-27.2 ng L(-1) and quantitation limits of 6.3-87.7 ng L(-1) for the PAHs. The relative standard deviations for intra- and inter-day analyses were in the range of 3.1-8.7% and 6.1-8.5%, respectively. The results showed that hydrophobic and π-π interactions between the PAHs and the framework terephthalic acid molecules, and the π-complexation between PAHs and the Lewis acid sites in the pores of MIL-101 play a significant role in the adsorption of PAHs.
|
2024-07-13T01:26:51.906118
|
https://example.com/article/9998
|
Melittin, a major polypeptide in honeybee venom, have been
used to treat inflammatory disease. Various studies have demonstrated the
anti-bacterial, anti-viral, anti-inflammatory and anticancer effects of bee
venom and melittin. However, the precise mechanism of melittin in liver disease
is not yet known.
Apoptosis contributes to liver inflammation and fibrosis.
Knowledge of the apoptotic mechanisms is important to develop new and effective
therapies for treatment of cirrhosis. In the present study, we investigated the
anti-apoptotic effect of melittin on tumor necrosis factor (TNF)-α/actinomycin
(Act) D-induced apoptosis in hepatocytes. Our results show significant
protection from DNA damage by melittin treatment compared with corresponding
TNF-α/Act D-treated hepatocytes without melittin. Melittin inhibited TNF-α/Act
D-induced activation of the caspase, bcl-2 family of proteins and poly
ADP-ribose polymerase (PARP)-1.
|
2023-11-17T01:26:51.906118
|
https://example.com/article/4908
|
Faculty Research Interests and Profiles
The appointment criteria for the Graduate Program in Kinesiology and Health Science (KAHS) are governed by and consistent with the Policy on Appointments to the Faculty of Graduate Studies, including appointment criteria of the Faculty of Graduate Studies.
The Executive Graduate Committee of KAHS is responsible for advising on program-specific criteria, procedures and appointments.
The Faculty of Graduate Studies website provides an overview of Current Member appointments.
Molecular, Cellular and Integrative Physiology
Research InterestOur lab is interested in identifying novel regulators of inflammation and understanding the molecular mechanisms through which these regulators control innate immunity and the inflammatory response. We are currently pursruing several avenues of research, and they include:
1) Investigating the molecular mechanisms through which different exercise regimens regulate the immune response.
2) Understanding the disparate roles of TRAF1 in controlling chronic inflammatory and autoimmune diseases.
3) Assessing the role of individual Type I interferons in bacterial and viral responses.
Research Interest
Molecular mechanisms regulating skeletal muscle protein metabolism and growth, and how these are modulated in different nutritional and diseased states. I study insulin and nutrient signaling leading to translation initiation, and the ubiquitin proteolytic system. Studies are carried out in rodents, as well as in humans with obesity and Type 2 Diabetes.
Research Interest
Molecular mechanisms leading either to the regression or the growth (angiogenesis) of blood vessels in skeletal and cardiac muscle in response to physiological (physical exercise,inactivity, altitude) or pathological (heart failure, diabetes) conditions.
Research Interest
The physiological and molecular mechanisms that regulate glucose and fatty acid uptake and metabolism in skeletal muscle and adipose tissue. The major focus is on dysfunctional metabolic alterations associated with obesity and Type 2 Diabetes.
Research Interest
A major interest of my research is studying the cellular mechanisms of skeletal muscle fatigue given that fatigue is a dominant factor limiting sport performance performed at the physical limit. Increased fatigue is also a common symptom in aging and chronic disease, and hence a greater understanding of fatigue mechanisms also has broader health implications.
Given that fatigue is often the stimulus required to initiate skeletal muscle adaptations, investigating fatigue-related mechanisms likely has relevance to gaining a greater understanding of factors affecting acute post-exercise recovery, and chronic training adaptations to exercise. Potentially, the very same mechanisms responsible for fatigue may act as the key triggers to stimulate skeletal muscle adaptations to exercise. Nonetheless, the exact fatigue mechanisms by which different types of exercise may trigger training adaptations in skeletal muscle are not known.
A major emphasis of my research has been to translate knowledge gained at the cellular level to understand and improve human exercise performance. Indeed, a greater understanding of the underlying mechanisms causing fatigue can serve as a foundation to develop more effective exercise training regimes, ergogenic aids and rehabilitation methods to ameliorate muscle fatigue in healthy and diseased populations.
Research Interest
The role of the cell cycle in breast cancer and muscle development; 1) the molecular link between obesity and cancer; 2) investigating how dividing muscle cells becomes fully differentiated skeletal muscle
Research Interest
Blood vessel growth (angiogenesis) in skeletal muscle; biochemical, cellular and molecular biological approaches are used to study the stimuli and signalling pathways that cause endothelial cells to initiate angiogenesis as a result of exercise or disease.
Research InterestAmyotrophic lateral sclerosis (ALS; Lou Gehrig’s disease): Effects of caloric restriction, antioxidant supplementation and exercise on functional, disease and molecular outcomes in ALS, with emphasis on sex differences.
Vitamin D supplementation and deficiency on functional outcomes and molecular outcomes in the muscle and CNS in ALS
Vitamin D and calcium intake and their relationship to type 2 diabetes mellitus (T2DM).
Functional foods and their effects on health and disease.
Research Interest
Our research, funded by both NSERC and CIHR, involves the study of mitochondrial turnover in skeletal muscle, as evoked by either exercise, or by chronic muscle disuse. Mitochondria are the organelles that produce energy for muscle contraction, so proper maintenance of these organelles is vital for muscle and whole body health. It is now known that mitochondrial turnover can change dramatically during aging, with disuse and with disease, and that exercise is a potent therapeutic intervention that can improve mitochondrial function, and muscle health. Our work continues to be fundamental in helping us to understand the molecular factors which regulate mitochondria under these conditions within muscle.
Research InterestMy research combines clinical nutrition and exercise physiology in the context of both health and chronic disease, and centres on lifestyle modification strategies and/or training regimens that manipulate diet and exercise to achieve a healthier body composition and/or a beneficial metabolic outcome. I am particularly interested in utilizing diet (i.e. functional whole foods, nutrients, supplements) with different modes of exercise (i.e. aerobic, resistance, plyometric) to facilitate healthy changes in body composition, body weight and bone in different populations across the lifespan. Most recently, I have started to undertake acute human studies to assess the postprandial and post-exercise effect of a nutritional and/or exercise perturbation on bone health and inflammation.
Research Interest
Cardiovascular diseases are leading causes of the global health burden. The environment we live in, the air that we breath, the food that we eat, and the things we do (active versus sedentary living) have a significant impact on our cardiovascular health. These environmental and modifiable risk factors interact with our non-modifiable genetic background to determine our cardiovascular health. Our blood vessels are key components of our cardiovascular system; and the inner layer of these blood vessels, the endothelium, is constantly exposed to these environmental factors. This can modulate the endothelial phenotype, potentially improving or impairing health.
While we start to better understand how environmental factors influence the health of our arteries, the macrovascular bed; it remains unknown how the interaction between environmental factors and genetic background influence the endothelial phenotype of our smallest blood vessels, the microvascular bed.
Using approaches of molecular and integrative physiology, my research program aims to better understand how the interplay between non-modifiable genetic background and modifiable environmental risk factors can influence the microvascular health.
The lab is currently looking for graduate students to perform a project to study the impact of physical activity on the epigenetic processes in microvascular endothelial cells.
(Muscle injury and damage in health and disease)
PhD, University of Albertaanbelcas@yorku.ca | 416-736-2100 x21088
333 Norman Bethune College
Research Interest
My primary focus is on the breakdown (assembly and disassembly) of striated muscle organelles and the role of calcium activated proteases, in particular calpain (CAPN1-2), during the control of these processes in health and disease. In addition to the activation and regulation of CAPN1-2, studies aimed identifying the factors contributing to the targeting of selected muscle proteins marked for breakdown are underway. Finally, the Paediatric Exercise Physiology Laboratory is focused on the study of improvement of children's muscle health and fitness through physical activity.
Research Interest
Understanding the acute and time varying responses and neuromuscular control of the spine and the possible associated injury mechanisms; biomechanical evaluation of exercise and industrial exposures; effects of modifying factors including sex, age, fatigue, and fitness level.
Research Interest
The neuromuscular control and biomechanics of postural control and of joint stability, currently with a focus on the knee joint. Understanding mechanisms related to sensory-motor dysfunction and normal aging which might interrupt these levels of control, and the potential impact of changes in neuromuscular control (local factors) on the development and progression of osteoarthritis.
Research Interest
My research is focused on understanding health promotion and the development of optimally effective health promotion messages targeting psychosocial predictors of behaviour. I am particularly interested in health promotion among special populations (e.g., people with SCI, MS), as well as children and youth. My research has focused on understanding the role of parents and the school environment in youth health promotion. Further, my research has focused on understanding the relationship between body image and physical activity.
(muscle injury and damage in health and disease)
PhD, University of Albertaanbelcas@yorku.ca | 416-736-2100 x21088
333 Norman Bethune College
Research Interest
My primary focus is on the breakdown (assembly and disassembly) of striated muscle organelles and the role of calcium activated proteases, in particular calpain (CAPN1-2), during the control of these processes in health and disease. In addition to the activation and regulation of CAPN1-2, studies aimed identifying the factors contributing to the targeting of selected muscle proteins marked for breakdown are underway. Finally, the Paediatric Exercise Physiology Laboratory is focused on the study of improvement of children's muscle health and fitness through physical activity.
Research Interest
My current research interests are investigating the effects of sex and female sex hormones on healthy cardiovascular responses to physiological stressors such as standing, hypoxia, hypercapnia, and exercise. This will develop into investigations of clinical populations such as Postural Orthostatic Tachycardia Syndrome and Heart Failure. This research will involve techniques such as ultrasound and microneurography.
Research InterestMy research focuses on children and youths’ development through sport, with a particular interest in positive youth development, psychosocial influences (i.e., coaches, family, peers), contextual factors (i.e., relative age effects, culture) and differing sport trajectories (e.g., withdrawal, long term participation, high performance). Currently I am working on projects exploring preschoolers' introductions to organized sport, and characteristics of programs that may facilitate development within special populations and communities.
Heart disease is the leading cause of death globally. Substantial health risks continue following coronary events and procedures, and cardiac rehabilitation (CR) improves subsequent prognosis. CR is an outpatient chronic disease management program for cardiovascular risk reduction promoting health behaviour changes such as exercise, diet, and smoking cessation. Participation results in improved quality of life, less re-hospitalization, and 25% less death.
However, research demonstrates low use of, and inequality in access, to CR. This is particularly true in low and middle-income countries, where there is an epidemic of heart disease.
There are a combination of factors relating to patients, physicians, and the health care system itself that lead to low CR use. The objective of Dr. Grace's programmatic research is to: (1) address patient, provider and system barriers to CR participation, and (2) to develop and evaluate a model of CR for low-resource settings.
Research InterestMy research combines clinical nutrition and exercise physiology in the context of both health and chronic disease, and centres on lifestyle modification strategies and/or training regimens that manipulate diet and exercise to achieve a healthier body composition and/or a beneficial metabolic outcome. I am particularly interested in utilizing diet (i.e. functional whole foods, nutrients, supplements) with different modes of exercise (i.e. aerobic, resistance, plyometric) to facilitate healthy changes in body composition, body weight and bone in different populations across the lifespan. Most recently, I have started to undertake acute human studies to assess the postprandial and post-exercise effect of a nutritional and/or exercise perturbation on bone health and inflammation.
Research Interest
Characterizing obesity and related health risks (cardiovascular disease and type 2 diabetes) and examining the influence of physical activity using both exercise interventions and epidemiological approaches.
Research Interest
My primary research interest relates to the epidemiology and prevention of childhood injuries, using an approach that examines factors related both to children and their social context. A secondary research interest is related to children’s emergency department and hospital use for injuries and other health problems, including the reasons why children seek care (e.g., the incidence of different types of injury), and researching the best way to provide care (e.g., reducing medication errors).
Research Interest
The effect of exercise, stress and diabetes on the Hypothalamo-Pituitary-Adrenal (HPA) axis. Substrate utilization and metabolism during exercise in individuals with Type 1 and Type 2 diabetes mellitus.
Research Interest
Health behaviour change in the prevention and treatment of chronic disease, particularly cancer. Emphasis on intervention delivery via group therapy, telephone, print and interactive internet programming. Further emphasis on evaluating effects through innovative approaches to quality of life assessment.
Research Interest
My principal research objective is the development and application of statistical techniques to problems in kinesiology, the health sciences and epidemiology. Specific research areas include the design and analysis of cluster randomized trials, studies of interobserver agreement and statistical genetics.
Research Interest
My research interests have focused on maternal and child health (research topics include postpartum depression, weight gain during pregnancy, breastfeeding, folic acid intake and others) and effects of exercise programs on musculoskeletal fitness and psychological well being of older adults.
PhD, University of Torontolhayhurs@yorku.ca | 416-736-2100 x44515| 340 Bethune College
Research Interest
My research interests include sport for development and peace, gender-based violence and sexual and reproductive health in/through SDP, cultural studies of girlhood, postcolonial feminist theory, global governance, international relations and corporate social responsibility. I am a co-editor (with Tess Kay and Megan Chawansky) of Beyond Sport for Development and Peace: Transnational perspectives on theory, policy and practice, and her publications have appeared in Women’s Studies International Forum; Gender, Place & Culture; Third World Quarterly and Sociology of Sport Journal. I previously worked for the United Nations Development Programme and Right to Play.
Research Interest
I study how unequal power relations, enacted through the social categories of race, gender and class, shape our lives, identities and opportunities to participate in sport and physical activity. In doing so, I hope to identify ways in which to resist social inequity.
Research Interest
My research interests, to date, have focused on the critical sociocultural study of sport and physical activity at the intersection of risk, health and healthcare including such key themes as: sport’s ‘culture of risk;’ the sociohistorical development of sport medicine in Canada and the social organization of sport medicine in Canada; and the social determinants of athletes’ health.
Publications
Harvey, J., Horne, J. and Safai, P. (2009) “From ‘One World, One Dream’ to‘Another Sport is Possible’: Alter-globalization, (New) Global Social Movements and Sport.” Sociology of Sport Journal, 26(3).
Safai, P. (2007). A critical analysis of the development of sports medicine in Canada, 1955-1980. International Review for the Sociology of Sport, 42(3), 321-341.
Safai, P., Harvey, J., Levesque, M. and Donnelly, P. (2007). Sport Volunteerism in Canada: Do Linguistic Groups Count? International Review for the Sociology of Sport, 42(4), 425-441.
Safai, P. (2005). The demise of the Sport Medicine and Science Council of Canada. Sport History Review, 36(2), 91-114.
Application
Upcoming Events
These include the Conference Support Fund, Thesis Support Fund, and Skills Development Fund. Applicants are eligible for funding from only one of these funds per year. Average funding is $100 per applicant and varies depending[...]
The Professional Development Fund provides funding to members in all Units to support them in attending and presenting at conferences, and with other professional development expenses. A total of $125,000 is allocated to this fund[...]
These include the Conference Support Fund, Thesis Support Fund, and Skills Development Fund. Applicants are eligible for funding from only one of these funds per year. Average funding is $100 per applicant and varies depending[...]
|
2023-12-07T01:26:51.906118
|
https://example.com/article/4920
|
Brilliant performance from GB athletes at IFSC World Championships
The past two weeks has been brimming with competition climbing events in Innsbruck at the IFSC World Championships which included a full Paraclimbing programme as well as Bouldering, Lead, Speed and a Combined final. The GB Climbing and Paraclimbing Teams were well prepared resulting in 13 strong performances from athletes in a number of categories, and as such left Innsbruck with five new medals, three of which were gold.
It's been an incredible two weeks for GB athletes, with a number of exceptional performances in the IFSC World Championships. We saw numerous climbers qualifying for semi-finals in both Lead and Bouldering, and a huge medal haul from the GB Paraclimbing Team.
In the Lead event, both Molly Thompson-Smith and Will Bosi made it through to semis, with Molly spectacularly coming 11th in her first competition since recovering from a horrific finger injury in December 2017. Will also pushed hard and high to place 13th alongside a number of top names in the competition climbing world.
Meanwhile, three athletes made it through to the Bouldering semi-finals, with Hannah Slaney and Billy Ridal both putting in commendable efforts to place in 11th and 20th, respectively. But Nathan Phillips was on fire, topping all four boulders in the semi-final to earn a place in the final amongst the world's best boulderers on the international stage – the first British male to make the finals of a Bouldering World Championships since Dave Barrans in 2009.
Nathan started perfectly, topping the first boulder with ease after taking a number of attempts to latch the tricky sideways 1-2-3 dyno. He then found things slightly tougher, and managed to earn one more zone out of the next three problems. After an amazing performance he finished in sixth place, his best result ever in an IFSC competition.
But the best results, and a major medal haul, was saved for the GB Paraclimbing Team. Everyone put in superb efforts to win an astounding five medals and three world titles. The first of the gold medals was awarded to Abbie Robinson in the B2 (visually impaired) category. She said: “I was so relieved to get my finals route done. It was well set and required a proper fight, especially as it got trickier toward the end.
“I actually thought the competitor before me had topped the route, so I had no idea what position I had placed in when I fell. When I realised I was World Champion, well, it was kind of surreal.”
The second world title was achieved by Hannah Baldwin in the women’s RP2 category: “When I looked at the route I knew it would be difficult. My category is merged, meaning although I only use one leg to climb, everybody else in the finals actually climbs with two. Robin (coach) warmed me up specifically for doing the two crux undercut moves in isolation and when it came to it I managed to keep pushing. At the last move I was so pumped I had nothing left and I just jumped for the last hold hoping for a plus point, in the hope it would be enough for a medal.
“Standing on top of the podium is the best feeling.”
Also in the RP2 category was Anita Aggarwal who took a well deserved bronze medal. Meanwhile, Mikey Cleverdon rounded of Saturdays action with a silver medal in the RP3 category.
Sunday saw AU2 superstar Matthew Phillips lining up for his finals and after a tense wait with athletes climbing high on the route before him, it came his turn to make an attempt. Climbing with supreme confidence and skill, Phillips glided with ease to top his route and take a third gold medal for the GB Paraclimbing team.
Matt said: “It’s an amazing feeling, topping on out on such a sustained route. It was truly incredible. The crowd and the atmosphere was wild – the British fans were off the scale. Seriously, they were so loud and they motivated me so much.
“Winning this title means everything to me, it’s the pinnacle of sporting achievements, to be a World Champion. I never thought I’d ever achieve something like this in my life ... and now, well, I can’t quite believe it. When I started climbing my aim was to try and win some national competitions the world championships wasn’t even in my mind and here I am.”
Special mention also goes to Jo Newton, who came heart-wrenchingly one point away from making the final, but still put in an awesome performance to earn fifth place.
TAGS
RELATED ARTICLES
The GB Climbing Team was out in force again this weekend at the IFSC Speed and Boulder World Cup in Moscow, Russia. Shauna Coxsey made finals for the second time in a row, coming home with a silver medal this time, while Emily Phillips also looked great coming in 10th in the semi-finals.
Read more »
The GB Climbing Team was out in force at the first IFSC Climnbing World Cup in Meiringen, Switzerland, putting on a fine performance to start off the season. And, after a run of mishaps and injuries, two-time Boulder World Cup Champion Shauna Coxsey returned with confidence to take the bronze medal.
Read more »
RELATED ARTICLES
The GB Climbing Team was out in force again this weekend at the IFSC Speed and Boulder World Cup in Moscow, Russia. Shauna Coxsey made finals for the second time in a row, coming home with a silver medal this time, while Emily Phillips also looked great coming in 10th in the semi-finals.
Read more »
The GB Climbing Team was out in force at the first IFSC Climnbing World Cup in Meiringen, Switzerland, putting on a fine performance to start off the season. And, after a run of mishaps and injuries, two-time Boulder World Cup Champion Shauna Coxsey returned with confidence to take the bronze medal.
Read more »
YOUTH & EQUITY
The British Mountaineering Council (BMC) is the representative body that exists
to protect the freedoms and promote the interests of climbers, hill walkers and
mountaineers, including ski-mountaineers. The BMC recognises that climbing, hill
walking and mountaineering are activities with a danger of personal injury or death.
Participants in these activities should be aware of and accept these risks and be
responsible for their own actions.
|
2024-02-09T01:26:51.906118
|
https://example.com/article/8095
|
Yahoo Says Connect TV Product will Ship 5 Million TV’s in by in 16 Countries by Q2
LAS VEGAS, NV — Yahoo has expanded the scope of its “Connected TV” to several new television and consumer electronics manufactures and expects the platform to be in as many as 5 million Internet-enabled television sets by the end of June, we have learned.
At CES last week, our Daisy Whitney spoke with Yahoo’s Russ Schafer about the expanding program.
In addition to the new hardware companies, Yahoo! announced that several content providers including SkyNews, NBC, DailyMotion and Brightcove would be joining the service. the company also announced the availability of developer’s kit so programmers can join the program.
|
2024-01-03T01:26:51.906118
|
https://example.com/article/5248
|
Q:
predicate first order logic satisfiability
I have problems to understand how to think of satisfiability in predicate logic.
For example why is $ \forall x (p(x) \vee \neg p(x)) $ valid, but
$ \forall x p(x) \vee \forall x\neg p(x) $ only satisfiable?
And $ ( \forall x (p(f(x)) \rightarrow \neg p(f(x)))) \land p(c) $ satisfiable, but
$ ( \forall x (p(f(x)) \rightarrow \neg p(f(x)))) \land p(f(c)) $ not?
$c$ is a constant, $p$ a predicate and $f$ a function.
A:
It will help to rewrite the relevant expressions in natural language. Let's look at the first two. The first says "For every $x$, either $p(x)$ holds or $p(x)$ fails." This should obviously be true, without any other information: everything is either true or false, so for any specific object $x$ and any specific property $p$ either $x$ has $p$ or $x$ doesn't have $p$.
The second, however, says "Either every $x$ has property $p$ or every $x$ fails to have property $p$." Basically, this is saying that all objects look the same (at least as far as property $p$ is concerned). And this is clearly not always true: e.g. in the natural numbers, take $p$ to be evenness: some numbers are even, so $\forall x(\neg p(x))$ fails, but some numbers are odd, so $\forall x(p(x))$ fails too.
I suspect a lot of the confusion is coming from "algebraic" intuition - specifically in the case of the first two, the idea that everything is distributive: that we can distribute the "$\forall$" over the "$\vee$." There are indeed various "algebraic" rules, but they're not necessarily the ones you'll think of immediately; before you have a solid understanding of them, you need to resist the temptation to "simplify in the obvious way."
|
2023-08-12T01:26:51.906118
|
https://example.com/article/7903
|
How Futures Are Conquering the Crypto Market and Why It Is Important Onederx Follow Mar 19, 2019 · 5 min read
The cryptocurrency futures market is booming and bashing the shrinking spot market with its rapidly growing trading volumes. The reason for this is the nature of the spot cryptocurrency market and the bearish trend on it. In this situation, the futures contracts are a great alternative tool for the traders to hedge their long positions on the spot market by opening short positions in a futures contract and to trade both ways.
One of the popular cases of how a futures contract on Bitcoin yielded an enormous profit is that of Mark Dow, a former economist at the International Monetary Fund. He opened a short position for a futures contract on Bitcoin when it cost around $17,000 and closed it on December 18 when Bitcoin plunged to $3,200.
A notable fact is that the money Mark Dow earned on his short trade was legally accepted by state financial institutions and he was able to legally withdraw it from the exchange.
The popularity of futures contracts for Bitcoin and especially perpetual contracts (swaps) is dictated by the steep decline on the cryptocurrency market, which does not provide for a situation for the traders to make earnings. The futures are an ideal instrument for making money on a bear market by opening a short position. The current spot cryptocurrency market is characterised by a very low volatility and greatly reduced trading volumes whereas the the futures contracts for Bitcoin have added a huge bulk of volume very rapidly.
For instance, CME’s Bitcoin futures contract has increased the daily trading volume by 220% since December, 2017 while the Bitcoin market volume has decreased by more than 80% since early 2018.
And this chart clearly shows how futures trading volumes on Bitmex — the leading cryptocurrency futures exchange — rose against the downfall of Bitcoin throughout 2018 (the grey line is Bitcoin price).
(Originally Bitcoinity.org)
Another demonstrative example of futures boosting exchange volumes is how trading volumes on Kraken skyrocketed after it affiliated Crypto Facilities, a CFA-regulated cryptocurrency trading platform and index provider. After that deal Kraken was able to launch trade of perpetual futures contracts for a number of cryptocurrencies. Shortly after that trading volumes on Kraken reached 1 billion dollars a day increasing by 565% in the first five days after the deal was announced compared to a similar time period preceding the deal. The deal was announced on February 4th.
Still, it is Bitmex ranking in number 1 in trading volumes for cryptocurrency derivatives. Bitmex is a cryptocurrency derivatives exchange that offers perpetual contracts with a leverage of up to x100 for Bitcoin and up to x50 for Ethereum. The daily trading volume on this exchange for the Bitcoin contract reaches over $1 billion.
Trading volume on Bitmex for XBT/USD on 03/18/2019
According to CryptoCompare research (p. 10) the unregulated Seychelles-based Bitmex on the average accounted for over 96% of trading volumes of the Bitcoin futures market with CME’s and CBOE’s volumes included, which seems to have been in October 2018.
Still, this exchange has numerous imperfections. They include system major overload in peak hours, slow order processing and withdrawal only in Bitcoin. This exchange has also been accused of price manipulation. All of this is pretty horrible. For this reason, there is a lot of room for improvement on the cryptocurrency derivatives market.
And some projects are aiming to provide better service in the area of cryptocurrency derivatives. The most prominent of them are ErisX, Deribit, Bakkt and SeedCX.
Right now, it is a hot time for cryptocurrency derivatives and these exchanges can ride this forming trend swifty. ErisX is currently a spot cryptocurrency exchange and plans to launch futures trading in the second half of 2019 when it gets a regulatory approval. Seed CX launched in the late 2018, it offers spot market trade and CFTC-regulated derivatives for constitutional investors.
Bakkt is another major foundation for the cryptocurrency market from the Intercontinental Exchange (ICE), an NYSE operator that is to be launched in early 2019. Bakkt is a digital assets trading platform focused on institutional investors and compliant with the regulatory requirements of the US futures trading financial regulator CFTC (Commodity Futures Trading Commission). In its notice on December 31, 2018 ICE told that it was working with CFTC to get a ‘regulatory approval for physically delivered and warehoused bitcoin’. Also, in that notice the company stated ‘Each futures contract calls for delivery of one bitcoin held in Bakkt Warehouse, and will trade in U.S. dollar terms.’ This means that each Bakkt Bitcoin contract will be tantamount to one Bitcoin.
Another new project in the area of cryptocurrency perpetual contracts of a smaller scale is Onederx. It was launched very recently in 2019. Onederx is an all-derivative exchange offering a perpetual contract for Bitcoin with contracts for other digital coins coming later on. Onederx is primarily aimed at professional traders and offering classical two-way-trading instruments. The exchange features a simple interface that includes a manipulable chart provided by TradingView, an order book and and tools for order control. The value of a single Onederx Bitcoin perpetual contract is worth 1 dollar.
A technical edge of this exchange is that it has a very low latency, which in 99% cases constitutes ≤ 2ms whereas the long-existing crypto exchanges have a latency of 0.1 up to 1 second which is very slow for high-frequency automated trading sometimes requiring a timely execution of hundreds of orders in a few seconds. On top of that Onederx is the first exchange in the world to offer negative fees for the takers. Thus, the exchange offers one of the best trading conditions amongst all crypto futures exchanges.
At the time of writing, Onederx has been active for around one month and might so far not look too impressive but considering that this project has not received large investments it may be considered a certain success. For this reason, Onederx should be watched closely by those who are interested in the novelties in digital asset and cryptocurrency trading.
|
2024-06-29T01:26:51.906118
|
https://example.com/article/9331
|
Determination of D-lactate by enzymatic methods in biological fluids: study of interferences.
Analysis of nondeproteinized samples with an enzymatic method to determine D-lactate indicated interferences. The presence of L-lactate dehydrogenase (LD) and L-lactate in the sample led to underestimation of D-lactate content when a sample blank was processed and overestimation when it was omitted. We proved that this interference is not due to lack of D-LD stereospecificity. Moreover, assessment of D-LD and L-LD KM for NAD+ allowed us to rule out the different affinities for this coenzyme as a cause of the interference. Our results underline the importance of deproteinizing samples for D-lactate analysis when enzymatic methods are used. The ultrafiltration procedure we propose is convenient and shows acceptable mean recovery (108%) and good imprecision (within-run CV = 4.2% and 3.0% for D-lactate at 31 and 107 mumol/L, respectively; between-run CVs were 7.3% at 49 mumol/L D-lactate and 3.1% at 115 mumol/L D-lactate).
|
2023-08-06T01:26:51.906118
|
https://example.com/article/1250
|
// SPDX-License-Identifier: GPL-2.0
/*
* linux/mm/mmzone.c
*
* management codes for pgdats, zones and page flags
*/
#include <linux/stddef.h>
#include <linux/mm.h>
#include <linux/mmzone.h>
struct pglist_data *first_online_pgdat(void)
{
return NODE_DATA(first_online_node);
}
struct pglist_data *next_online_pgdat(struct pglist_data *pgdat)
{
int nid = next_online_node(pgdat->node_id);
if (nid == MAX_NUMNODES)
return NULL;
return NODE_DATA(nid);
}
/*
* next_zone - helper magic for for_each_zone()
*/
struct zone *next_zone(struct zone *zone)
{
pg_data_t *pgdat = zone->zone_pgdat;
if (zone < pgdat->node_zones + MAX_NR_ZONES - 1)
zone++;
else {
pgdat = next_online_pgdat(pgdat);
if (pgdat)
zone = pgdat->node_zones;
else
zone = NULL;
}
return zone;
}
static inline int zref_in_nodemask(struct zoneref *zref, nodemask_t *nodes)
{
#ifdef CONFIG_NUMA
return node_isset(zonelist_node_idx(zref), *nodes);
#else
return 1;
#endif /* CONFIG_NUMA */
}
/* Returns the next zone at or below highest_zoneidx in a zonelist */
struct zoneref *__next_zones_zonelist(struct zoneref *z,
enum zone_type highest_zoneidx,
nodemask_t *nodes)
{
/*
* Find the next suitable zone to use for the allocation.
* Only filter based on nodemask if it's set
*/
if (unlikely(nodes == NULL))
while (zonelist_zone_idx(z) > highest_zoneidx)
z++;
else
while (zonelist_zone_idx(z) > highest_zoneidx ||
(z->zone && !zref_in_nodemask(z, nodes)))
z++;
return z;
}
#ifdef CONFIG_ARCH_HAS_HOLES_MEMORYMODEL
bool memmap_valid_within(unsigned long pfn,
struct page *page, struct zone *zone)
{
if (page_to_pfn(page) != pfn)
return false;
if (page_zone(page) != zone)
return false;
return true;
}
#endif /* CONFIG_ARCH_HAS_HOLES_MEMORYMODEL */
void lruvec_init(struct lruvec *lruvec)
{
enum lru_list lru;
memset(lruvec, 0, sizeof(struct lruvec));
for_each_lru(lru)
INIT_LIST_HEAD(&lruvec->lists[lru]);
}
#if defined(CONFIG_NUMA_BALANCING) && !defined(LAST_CPUPID_NOT_IN_PAGE_FLAGS)
int page_cpupid_xchg_last(struct page *page, int cpupid)
{
unsigned long old_flags, flags;
int last_cpupid;
do {
old_flags = flags = page->flags;
last_cpupid = page_cpupid_last(page);
flags &= ~(LAST_CPUPID_MASK << LAST_CPUPID_PGSHIFT);
flags |= (cpupid & LAST_CPUPID_MASK) << LAST_CPUPID_PGSHIFT;
} while (unlikely(cmpxchg(&page->flags, old_flags, flags) != old_flags));
return last_cpupid;
}
#endif
|
2024-04-05T01:26:51.906118
|
https://example.com/article/7074
|
Q:
Mixed desgin ANOVA or LMM?
I am hitting a wall and would appreciate some help.
Here is my data (raw data, before computing the means):
'data.frame': 8000 obs. of 11 variables:
$ group : Factor w/ 5 levels "asiapic","asiavid",..: 3 3 3 3 3...
$ subject : Factor w/ 80 levels "P17001","P17002",..: 1 1 1 1 1 ...
$ gender_part : Factor w/ 2 levels "female","male": 2 2 2 2 2 2 2 2 ...
$ order : Factor w/ 2 levels "first","second": 2 2 2 2 2 2 2 ...
$ condition : Factor w/ 2 levels "baseline","experiment": 1 1 1 ...
$ voice : Factor w/ 10 levels "adam","aline",..: 6 7 6 9 3 ...
$ sex : Factor w/ 2 levels "f","m": 1 1 1 2 2 1 1 1 1 1 ...
$ accent : int 3 7 4 9 4 3 4 7 8 4 ...
$ intelligibility : num 0.571 0.857 0.75 0.714 0.429 ...
$ item : Factor w/ 100 levels "90","26","50",..: 1 2 3 4 5...
$ comprehensibility : int 7 3 7 3 8 5 6 5 3 7 ...
My DVs are accent (values 1-9), comprehensibility (values 1-9), intelligibility (ratio 0-1).
My main IVs are group (between subjects, 5 levels) and condition (within subject, 2 levels: baseline and experiment).
I have been looking (for a very long time) for the right way to analyze these variables. What I primarily interested in is the group * condition interaction.
Were all the group same in the baseline? Were they different in the experimental condition? - when it comes to my 3 DVs - and these DVs may be slightly correlated.
Additionally, I am interested in the possible effect of sex (this is the gender of the speaker in the stimuli) and maybe participant's gender.
I have tried mixed ANOVA (for each DV separately):
model = aov(accent ~ group * condition + Error(subject/condition), data=data)
This gives me the infamous Error() model is singular, which I think it's because the lowest level will always be included here, and since I have only 2 conditions this is included by default and I can just go with Error(subject), right?
Now I'm not sure if:
(1) Is this really the right way to do it?
(2) Which function to use for the post hoc test and how to make sure that the groups were comparable in the baseline condition?
(3) Should I analyze data for male and female voices (stimuli) separately or put it somehow into the model? sex*group*condition?
I have also tried lme with lme4:
model = lmer(accent ~ sex * group * condition + (1|subject) + (1|item), data=data)
(where item is the audio file in the stimuli)
(4) Would this be a better idea and if so how would you then deal with p-values and pair-wise comparison?
I realize this is a lot of questions but I would really appreciate some help.
A:
A couple of notes:
Your depenent variables accent and comprehensebility are bounded and also seem to be discrete. Both the aov() and lmer() analysis assume normally distributed error terms. Hence, you need to see how good the normal approximation is for your data. With regard to intelligibility, this is binary, and therefore you will need to analyze it with a mixed effects logistic regression, i.e., glmer(..., family = binomial()).
The specification via random effects and lmer() is more flexible than the aov().
Fitting separate models for males and females means actually that the variance components (i.e., error variance, and variances for the random effects) are different between males and females. If you only include the interaction sex * group * condition only the fixed effects of group, condition and their interaction group:condition are different between males and females, but not the variance components. Using the latter approach, you can more easily test if you need the interaction with sex.
For a fitted mixed model, you can do multiple comparisons and obtain adjusted $p$-values using either the emmeans of multcomp packages.
|
2024-01-06T01:26:51.906118
|
https://example.com/article/8195
|
Q:
Possible Security threats and mitigations while accessing `/root` through any browser?
I asked this question on Unix Stackexchange. How to access /root directory from a browser?
I got an answer (in a comment by @dsstorefile) that It can be accessed either way :
By running chmod 0777 root
By running browser as a Root User.
I think It's just a listing of the contents in the directory (for that I maybe wrong) but I want to know :
What could be Possible security risks/threats associated of accessing /root directory from the browser in each case ?
A:
The issues are that anyone on your system will be able to maliciously elevate themselves to root privileges. Doing either of these things is a very bad idea. To address your specific scenarios:
Making root's home directory mode 0777 means that all users will be able to read, write, enter, and execute any files in that directory. Because many sensitive, privileged processes use that as their home, making it world-writable could allow any unprivileged process to tamper with root's home. For example, malicious code in /root/.profile would be executed with high privileges any time the root user logs in. There are many ways to exploit you in this scenario.
Running your browser as root is also extremely dangerous. It means an exploited browser will run as root, rather than as your normal user. This is not a hypothetical threat. Someone actually did run their browser as root and got infected with ransomware! Additionally, a regular browser is not designed to run with a privileged context and so does not take the necessary security precautions to prevent an unprivileged local user from exploiting it. For example, if you run your browser in your regular user's environment, but as root, then a modified configuration file or browser extension (in your regular user's home) could exploit it to elevate to root.
You could make /root mode 0755, which would make it writable only by root, but would allow everyone else to enter and read it (including your browser). Normally, it does not contain any sensitive information, but it is still not a great idea to let everyone look inside it.
|
2023-12-08T01:26:51.906118
|
https://example.com/article/6331
|
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