text stringlengths 8 5.77M |
|---|
Q:
Declaring a structure and immediately instantiating it with cv-qualifier or storage duration specifier
Consider the following code:
static const struct X
{
int a;
} x={1};
X y;
It compiles, and X appears to work in the declaration of y. But is it actually true that static const and similar cv-qualifiers and storage duration specifiers don't affect the definition of X? I.e. is the following exactly equivalent to the above?
struct X
{
int a;
};
static const X x={1};
X y;
A:
Name X in declaration
static const struct X
{
int a;
} x={1};
introduces type specifier struct X. Thus this declaration
X y;
is equivalent to
struct X y;
As for storage class specifiers then according to the C++ Standard (7.1.1 Storage class specifiers)
... The storage-class-specifier applies to the name declared by each init-declarator in the list and not to any names declared by other specifiers.
So in this declaration
static const struct X
{
int a;
} x={1};
static is a storage class specifier of declarator x that is present in init-declarator x={1}
If you would use for example a typedef
typedef const struct
{
int a;
} X;
then in this case type name X would indeed have qualifier const.
So if you will define for example
X x = { 1 };
then x will be a constant object. You will be unable to write
x.a = 2;
Nevertheless you may not specify a storage class specifier in a typedef because as it is said in the quote storage class specifiers may be specified only for init-declarators.
However you may write
static X x = { 1 };
because the storage class specifier is applied to x that has type const X
|
As the Boston Fire Department Color Guard presents the colors, Rene Rancourt sings the National Anthem before the game between the Boston Bruins and the Chicago Blackhawks at TD Banknorth Garden. (Greg M. Cooper-USA TODAY Sports)
Rask, Bruins blank Chicago
By Sports Direct
BOSTON — Patrice Bergeron scored twice to extend his goal-scoring streak to five games and Tuukka Rask recorded his league-best seventh shutout as Boston defeated the Chicago Blackhawks, 3-0, to run its point streak to 14 games.
Rask turned aside 28 shots for his 23rd career shutout to to help the Bruins improve to 13-0-1 in their last 14 games. Bergeron’s second tally — his sixth in the five games — came 13 seconds after Carl Soderberg scored 5 1/2 minutes into the third period as Boston halted a four-game losing streak against Chicago dating to last season’s Stanley Cup Final.
Corey Crawford made 20 saves for the Blackhawks, who were blanked for the second time in three games to dim their chances of catching Central Division-leading St. Louis.Chicago dominated the early going but Bergeron scored the only goal of the opening period at 11:50. Defenseman Matt Bartkowski’s blast from the point was redirected by Bergeron past Crawford for his 24th goal.
Soderberg doubled the lead 5:28 into the third, corralling a loose puck in the slot and burying it before a gaffe by Crawford allowed Boston to score again 13 seconds later. Brad Marchand intercepted the puck from Crawford behind the net and fed Bergeron for an easy conversion, which required a video review after Crawford knocked the net in the air scrambling to get back into the crease. |
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1947–48 Lancashire Cup
1947–48 was the thirty-fifth occasion on which the Lancashire Cup completion had been held.
Wigan won the trophy by beating Belle Vue Rangers by the score of 10-7
The match was played at Wilderspool, Warrington, (historically in the county of Lancashire). The attendance was 23,310 and receipts were £3,043.
This was the second of Wigan’s record breaking run of six consecutive Lancashire Cup victories.
It was also to be the second of two consecutive finals to be competed for by these two teams.
Background
Overall, the number of teams entering this year’s competition increased by one with the invitation to Lancashire Amateurs (a junior/amateur club) bringing the total up to 14.
The same pre-war fixture format was retained. This season saw no bye but one "blank" or "dummy" fixture in the first round. There was also one bye but no "blank" fixture" in the second round.
As last season, all the first round matches of the competition will be played on the basis of two legged, home and away ties. However this year, the second round becomes a straightforward knock-out basis.
Competition and results
Round 1
Involved 7 matches (with no bye and one "blank" fixture) and 14 clubs
Round 1 – Second Leg
Involved 7 matches (with no bye and one "blank" fixture) and 14 clubs. These are the reverse fixture from the first leg
Round 2 - Quarter Finals - First Leg
Involved 3 matches (with one bye) and 7 clubs
Round 3 – Semi-Finals
Involved 2 matches and 4 clubs
Final
Teams and scorers
Scoring - Try = three (3) points - Goal = two (2) points - Drop goal = two (2) points
The road to success
All the first round ties were played on a two leg (home and away) basis.
The first club named in each of the first round ties played the first leg at home.
the scores shown in the first round are the aggregate score over the two legs.
Notes and comments
1 * Lancashire Amateurs were a junior (or amateur) club from Lancashire. The match was played at Watersheddings, Oldham
2 * The official St. Helens archive show as attendance of 16,000 (with 17,000 for the second leg at home) RUGBY LEAGUE projects show it as 17,000
3 * Leigh's first Lancashire Cup match at the newly completed purpose build stadium
4 * Wilderspool was the home ground of Warrington from 1883 to the end of the 2003 Summer season when they moved into the new purpose built Halliwell Jones Stadium. Wilderspool remained as a sports/Ruugby League ground and is/was used by Woolston Rovers/Warrington Wizards junior club. The ground had a final capacity of 9,000 although the record attendance was set in a Challenge cup third round match on 13 March 1948 when 34,304 spectators saw Warrington lose to Wigan 10-13.
See also
1947–48 Northern Rugby Football League season
Rugby league county cups
References
External links
Saints Heritage Society
1896–97 Northern Rugby Football Union season at wigan.rlfans.com
Hull&Proud Fixtures & Results 1896/1897
Widnes Vikings - One team, one passion Season In Review - 1896-97
The Northern Union at warringtonwolves.org
Category:1947 in English rugby league
Category:RFL Lancashire Cup |
[Antitumor effect of the extract of birch bark and its influence to the immune function].
To study the antitumor effect of extract of birch bark (EBB) and its influence to the immune function of the tumor-bearing mice. EBB was administered orally and the tumor inhibiting effects were observed in tumor-bearing mice. Experiment of the immune function are to examine thymocytes (spleen) index, reaction of spleen to ConA and activity of NK cell. EBB showed antitumor effect in vivo to B16, S180 and Lewis lung cancer in mice. EBB can significantly prolong survival period of bearing tumor mice. EBB can enhance thymocytes and spleen index in C57 BL/6 mice. EBB can enhance splenic lymphocytes translate and activit of NK cell (P < 0.05). EBB have antitumor effect and enhance immune function in bearing tumor mice. |
Iosif Andriasov - "To The Mother-Earth" for Piano, Op. 25A
FROM THE BOOK: “ESSAYS ON THE MUSIC OF IOSIF ANDRIASOV” WRITTEN BY MARTA ANDRIASOVA (MARINA KUDRYASHOVA)
Iosif Andriasov wrote the Cantata“To the Mother-Earth” for Baritone solo, Four Trombones, Two (or more)
Harps, and Mixed Choir in 1970, poetry by Vladimir Lazarev. “To the Mother-Earth”(Lento
Maestoso, A Major, 6/4 time, 37 measures) is a majestic hymn to our planet,
the Earth. |
Q:
How to check if column of GridView is empty, and if it is, make a button invisible?
I have this codes:
var data = File.ReadAllLines(Server.MapPath("~/Uploaded"))
.Select(line => line.Split(','))
.Select(columns => new { GuestName = ErrorMessage(columns[0]),
Guest_ID = ErrorMessage(columns[1]),
IC_Number = ErrorMessage(columns[2]) });
if (data = 0)//this if statement is wrong
{
BtnImport1.Visible = false;
}
I want to check if the the column/row in the GridView is empty, if it is, I want to make the BtnImport to become invisble. Can anyone help me on with this? =/
A:
if (data.Count() == 0)//this if statement is wrong
{
BtnImport1.Visible = false;
}
|
Q:
How to access MongoDB document as JSONObject in spring boot application
I have documents like below in a collection named event in mongoDB
{
"name": "pick",
"message": {
"word": "seven",
"sequenceNumber": 34
}
}
which existed before I developed my Spring Boot application to access it.
Now I have a java object Event.java to access the above collection.
public class Event{
private String name;
private JSONObject messgae;
// getters setters costructors
}
In the document, the message could be any json. So defining a class for message does not make any sense.
I have tried using mongoOperations, mongoTemplate and mongoRepository but I am not able to access the the document and change the value and store it again. The problems I face are,
I could not use JSONObject for message because mongoOperations has no support
I could not use String for message because when I save the object again it gets serialized like "message":"{\"word ...
Is there any way I can access, modify and store the data via spring boot application?
A:
You can use JSONObject for message in mongoOperations like below.
JSONObject jsonObj= new JSONObject();
jsonObj.put("word", "seven");
jsonObj.put("sequenceNumber", new Integer(34));
//save
Event eventDocument = new Event("pick",jsonObj);
mongoOperations.save(eventDocument);
//find
Query query = new Query(Criteria.where("name").is("pick"));
Event object = (Event) mongoOperations.findOne(query, Event.class);
System.out.println(object.getName());
System.out.println(object.getMessage());
|
Q:
Force typescript to see difference between (AType = string) !== (BType = string)
My project has two user's id - my internal id(database uuid) and external service's id (google id).
User entity has these ids.
User {
id: string;
googleId: string;
}
But new collaborators don't know what id should be used and where this id should be used.
Let's assume i have method
getUser(id: string): Promise<User>
This method should receive user.id as argument.
TS allow me to call this method with user.id or with user.googleId.
What i want to is to say that i want to receive just user.id and nothing else. Because this method returns nothing if i pass user.googleId and this correct behaviour and wrong usage of method(new collaborators doesn't know that it should be user.id and this is not user.googleId).
What i want to have(i tried it but this didn't work)
userId = string;
googleId = string;
const getUser(id: userId) => this.userRepository.findOne(id)
getUser(user.id) // correct usage, ts error is absent
getUser(user.googleId) // wrong usage, ts error is present and tells that userId and googleId types are incompatible
Thanks in advance!
A:
As VLAZ sad - opaque types. This solved my problem.
|
Possible regulation of the in vitro assembly of bovine brain tubulin by the bovine thioredoxin system.
Microtubule assembly in vitro and in vivo is highly sensitive to a variety of sulfhydryl-reactive reagents, raising the question of the possible existence of a physiological sulfhydryl-mediated system for regulating microtubule assembly. However, the specific reagents which have previously been used to inhibit microtubule assembly in vitro are either nonphysiological or, if physiological, effective only at concentrations much higher than their physiological ones. Because of reports of association in vivo between microtubules and the sulfhydryl-reactive proteins thioredoxin and thioredoxin reductase, we decided to examine the interaction in vitro between microtubules and the thioredoxin system, comprising thioredoxin, thioredoxin reductase and NADPH. At pH 6.8, both the mammalian and the Escherichia coli thioredoxin systems inhibited microtubule assembly by 4-35% (19 +/- 9%) by reducing one intra-subunit disulfide bond in the tubulin dimer. The thioredoxin-reducible disulfide of the tubulin dimer remains protected from thioredoxin in the assembled microtubules. Thioredoxin or thioredoxin reductase alone, or together in the absence of NADPH, were incapable of either reducing tubulin or inhibiting microtubule assembly. Microtubules formed from reduced tubulin were found to be stable and morphologically identical to those obtained from native tubulin dimers. Since the components of the thioredoxin system were used at concentrations similar to their physiological ones, our results suggest a potential role of the thioredoxin system in regulation of microtubule assembly in vivo. |
Sewer Pump Service
Envirotek Systems offers sewer pump service in Missouri for Springfield, Nixa, Ozark, Branson and Kimberling City. There are different types of sewage pumps. Some are designed for liquids, while others handle sewage with solids up to a determined size. These varied types of sewage pumps are based on the size and design of the impeller and discharge outlet. We repair and provide maintenance on pumps found at a residence, commercial facilities, marinas and lift stations. Sewer pumps used in these applications are bolted to an electric motor making them look like one device when in fact they all have a motor with a shaft, an impeller and a volute.
In order to better understand the different styles of sewer pumps it is important to understand that they require a motor as well as sometimes controls to drive it. An understanding of the following terms will be beneficial:
Sewer / Sewage
Solids and liquids typically found in domestic waste water such as feces, urine and garbage disposal grindings.
Effluent
Is only the liquid part of sewage.
Storm water
Typically includes rain water including ground water that may contain some amounts of silt.
Impeller
A rotating part of a pump which gathers the media and creates pressure forcing it into the discharge piping.
Volute
The part of a pump that houses the impeller.
Motor
The device that turns the pump, always an electric motor for most applications.
10 Year Warranty!
We offer specialized service in this arena. We have developed a proprietary combination of sewage pumps and controls we call Visi-Pump. It far exceeds the reliability and functionality of anything currently available on the market. We are so confident of our expertise in this area we offer a 10 year warranty on our product. |
Missouri State Highway Patrol Accident Reports For February 12, 2016
At 9:43pm Thursday night the Missouri State Highway Patrol reported a two-vehicle injury accident on Route “N” at 65 Highway in Saline County. According to the report the accident occurred as the 2006 Chevrolet Cobalt driven by 22-year-old Shanne R. Sellers of Sedalia was Southbound on Route “N”, and a 1998 Volvo driven by 58-year-old Ronald G. Armstrong of Springfield was travelling South on US-65 Highway. The report states Sellers failed to stop at a stop sign, and pulled into the path of the Armstrong vehicle causing the crash. Sellers received moderate injuries in the crash, and was transported to Fitzgibbon Hospital by Saline County EMS for treatment. A passenger in the Seller’s vehicle identified as 26-year-old Alvin J. Hensley of Marshall had minor injuries, but refused treatment at the scene. Neither victim was reportedly wearing a seatbelt.
Brunswick man injured in a Saline County accident Thursday morning
Just before 11am Thursday morning the Missouri State Highway Patrol reported a vehicle accident on Missouri Highway-41 North of 250th Street in Saline County. According to the report the accident happened as a 1993 Freightliner driven by 57-year-old Keith A. Leimkuehler of Brunswick travelled off the roadway to avoid a stalled vehicle in the roadway. The Freightliner struck a culvert, returned to the roadway, and ran off the other side of the road, then came to rest in a field. Leimkuehler received minor injuries, and was taken to Fitzgibbon Hospital for treatment . |
Ulmus parvifolia 'King's Choice'
The Chinese Elm cultivar Ulmus parvifolia 'King's Choice' is one of the early American selections best known for its winter hardiness, able to withstand temperatures of -30 deg. Celsius. 'King's Choice' was patented in 1985.
Description
Bushy in shape, its leaves turn yellow in autumn, but the cultivar lacks the attractive mottled bark for which the species is renowned.
Pests and diseases
The species and its cultivars are highly resistant, but not immune, to Dutch elm disease, and unaffected by the Elm Leaf Beetle Xanthogaleruca luteola.
Cultivation
The tree featured in the elm trials conducted by Northern Arizona University at Holbrook, eastern Arizona. 'King's Choice' is not known to be in cultivation in Europe or Australasia.
Etymology
The tree was named for Benjamin J. King, who made the original selection at King's Men Tree Farms, Hampstead, Maryland.
Accessions
North America
Arnold Arboretum, US. Acc. no. 287-95
Holden Arboretum, US. Acc. no. 92-94
References
Category:Chinese elm cultivar
Category:Ulmus articles with images
Category:Ulmus |
Trey Mancini clobbers two homers, tying a Major League record by hitting seven home runs in the first 12 games of his career |
Naked Viruses That Aren't Always Naked: Quasi-Enveloped Agents of Acute Hepatitis.
Historically, viruses were considered to be either enveloped or nonenveloped. However, recent work on hepatitis A virus and hepatitis E virus challenges this long-held tenet. Whereas these human pathogens are shed in feces as naked nonenveloped virions, recent studies indicate that both circulate in the blood completely masked in membranes during acute infection. These membrane-wrapped virions are as infectious as their naked counterparts, although they do not express a virally encoded protein on their surface, thus distinguishing them from conventional enveloped viruses. The absence of a viral fusion protein implies that these quasi-enveloped virions have unique mechanisms for entry into cells. Like true enveloped viruses, however, these phylogenetically distinct viruses usurp components of the host ESCRT system to hijack host cell membranes and noncytolytically exit infected cells. The membrane protects these viruses from neutralizing antibodies, facilitating dissemination within the host, whereas nonenveloped virions shed in feces are stable in the environment, allowing for epidemic transmission. |
/**
******************************************************************************
* @file stm32f4xx_hal_smartcard.h
* @author MCD Application Team
* @brief Header file of SMARTCARD HAL module.
******************************************************************************
* @attention
*
* <h2><center>© Copyright (c) 2016 STMicroelectronics.
* All rights reserved.</center></h2>
*
* This software component is licensed by ST under BSD 3-Clause license,
* the "License"; You may not use this file except in compliance with the
* License. You may obtain a copy of the License at:
* opensource.org/licenses/BSD-3-Clause
*
******************************************************************************
*/
/* Define to prevent recursive inclusion -------------------------------------*/
#ifndef __STM32F4xx_HAL_SMARTCARD_H
#define __STM32F4xx_HAL_SMARTCARD_H
#ifdef __cplusplus
extern "C" {
#endif
/* Includes ------------------------------------------------------------------*/
#include "stm32f4xx_hal_def.h"
/** @addtogroup STM32F4xx_HAL_Driver
* @{
*/
/** @addtogroup SMARTCARD
* @{
*/
/* Exported types ------------------------------------------------------------*/
/** @defgroup SMARTCARD_Exported_Types SMARTCARD Exported Types
* @{
*/
/**
* @brief SMARTCARD Init Structure definition
*/
typedef struct
{
uint32_t BaudRate; /*!< This member configures the SmartCard communication baud rate.
The baud rate is computed using the following formula:
- IntegerDivider = ((PCLKx) / (16 * (hsc->Init.BaudRate)))
- FractionalDivider = ((IntegerDivider - ((uint32_t) IntegerDivider)) * 16) + 0.5 */
uint32_t WordLength; /*!< Specifies the number of data bits transmitted or received in a frame.
This parameter can be a value of @ref SMARTCARD_Word_Length */
uint32_t StopBits; /*!< Specifies the number of stop bits transmitted.
This parameter can be a value of @ref SMARTCARD_Stop_Bits */
uint32_t Parity; /*!< Specifies the parity mode.
This parameter can be a value of @ref SMARTCARD_Parity
@note When parity is enabled, the computed parity is inserted
at the MSB position of the transmitted data (9th bit when
the word length is set to 9 data bits; 8th bit when the
word length is set to 8 data bits).*/
uint32_t Mode; /*!< Specifies whether the Receive or Transmit mode is enabled or disabled.
This parameter can be a value of @ref SMARTCARD_Mode */
uint32_t CLKPolarity; /*!< Specifies the steady state of the serial clock.
This parameter can be a value of @ref SMARTCARD_Clock_Polarity */
uint32_t CLKPhase; /*!< Specifies the clock transition on which the bit capture is made.
This parameter can be a value of @ref SMARTCARD_Clock_Phase */
uint32_t CLKLastBit; /*!< Specifies whether the clock pulse corresponding to the last transmitted
data bit (MSB) has to be output on the SCLK pin in synchronous mode.
This parameter can be a value of @ref SMARTCARD_Last_Bit */
uint32_t Prescaler; /*!< Specifies the SmartCard Prescaler value used for dividing the system clock
to provide the smartcard clock. The value given in the register (5 significant bits)
is multiplied by 2 to give the division factor of the source clock frequency.
This parameter can be a value of @ref SMARTCARD_Prescaler */
uint32_t GuardTime; /*!< Specifies the SmartCard Guard Time value in terms of number of baud clocks */
uint32_t NACKState; /*!< Specifies the SmartCard NACK Transmission state.
This parameter can be a value of @ref SMARTCARD_NACK_State */
}SMARTCARD_InitTypeDef;
/**
* @brief HAL SMARTCARD State structures definition
* @note HAL SMARTCARD State value is a combination of 2 different substates: gState and RxState.
* - gState contains SMARTCARD state information related to global Handle management
* and also information related to Tx operations.
* gState value coding follow below described bitmap :
* b7-b6 Error information
* 00 : No Error
* 01 : (Not Used)
* 10 : Timeout
* 11 : Error
* b5 IP initilisation status
* 0 : Reset (IP not initialized)
* 1 : Init done (IP not initialized. HAL SMARTCARD Init function already called)
* b4-b3 (not used)
* xx : Should be set to 00
* b2 Intrinsic process state
* 0 : Ready
* 1 : Busy (IP busy with some configuration or internal operations)
* b1 (not used)
* x : Should be set to 0
* b0 Tx state
* 0 : Ready (no Tx operation ongoing)
* 1 : Busy (Tx operation ongoing)
* - RxState contains information related to Rx operations.
* RxState value coding follow below described bitmap :
* b7-b6 (not used)
* xx : Should be set to 00
* b5 IP initilisation status
* 0 : Reset (IP not initialized)
* 1 : Init done (IP not initialized)
* b4-b2 (not used)
* xxx : Should be set to 000
* b1 Rx state
* 0 : Ready (no Rx operation ongoing)
* 1 : Busy (Rx operation ongoing)
* b0 (not used)
* x : Should be set to 0.
*/
typedef enum
{
HAL_SMARTCARD_STATE_RESET = 0x00U, /*!< Peripheral is not yet Initialized
Value is allowed for gState and RxState */
HAL_SMARTCARD_STATE_READY = 0x20U, /*!< Peripheral Initialized and ready for use
Value is allowed for gState and RxState */
HAL_SMARTCARD_STATE_BUSY = 0x24U, /*!< an internal process is ongoing
Value is allowed for gState only */
HAL_SMARTCARD_STATE_BUSY_TX = 0x21U, /*!< Data Transmission process is ongoing
Value is allowed for gState only */
HAL_SMARTCARD_STATE_BUSY_RX = 0x22U, /*!< Data Reception process is ongoing
Value is allowed for RxState only */
HAL_SMARTCARD_STATE_BUSY_TX_RX = 0x23U, /*!< Data Transmission and Reception process is ongoing
Not to be used for neither gState nor RxState.
Value is result of combination (Or) between gState and RxState values */
HAL_SMARTCARD_STATE_TIMEOUT = 0xA0U, /*!< Timeout state
Value is allowed for gState only */
HAL_SMARTCARD_STATE_ERROR = 0xE0U /*!< Error
Value is allowed for gState only */
}HAL_SMARTCARD_StateTypeDef;
/**
* @brief SMARTCARD handle Structure definition
*/
typedef struct __SMARTCARD_HandleTypeDef
{
USART_TypeDef *Instance; /*!< USART registers base address */
SMARTCARD_InitTypeDef Init; /*!< SmartCard communication parameters */
uint8_t *pTxBuffPtr; /*!< Pointer to SmartCard Tx transfer Buffer */
uint16_t TxXferSize; /*!< SmartCard Tx Transfer size */
__IO uint16_t TxXferCount; /*!< SmartCard Tx Transfer Counter */
uint8_t *pRxBuffPtr; /*!< Pointer to SmartCard Rx transfer Buffer */
uint16_t RxXferSize; /*!< SmartCard Rx Transfer size */
__IO uint16_t RxXferCount; /*!< SmartCard Rx Transfer Counter */
DMA_HandleTypeDef *hdmatx; /*!< SmartCard Tx DMA Handle parameters */
DMA_HandleTypeDef *hdmarx; /*!< SmartCard Rx DMA Handle parameters */
HAL_LockTypeDef Lock; /*!< Locking object */
__IO HAL_SMARTCARD_StateTypeDef gState; /*!< SmartCard state information related to global Handle management
and also related to Tx operations.
This parameter can be a value of @ref HAL_SMARTCARD_StateTypeDef */
__IO HAL_SMARTCARD_StateTypeDef RxState; /*!< SmartCard state information related to Rx operations.
This parameter can be a value of @ref HAL_SMARTCARD_StateTypeDef */
__IO uint32_t ErrorCode; /*!< SmartCard Error code */
#if (USE_HAL_SMARTCARD_REGISTER_CALLBACKS == 1)
void (* TxCpltCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Tx Complete Callback */
void (* RxCpltCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Rx Complete Callback */
void (* ErrorCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Error Callback */
void (* AbortCpltCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Abort Complete Callback */
void (* AbortTransmitCpltCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Abort Transmit Complete Callback */
void (* AbortReceiveCpltCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Abort Receive Complete Callback */
void (* MspInitCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Msp Init callback */
void (* MspDeInitCallback)(struct __SMARTCARD_HandleTypeDef *hsc); /*!< SMARTCARD Msp DeInit callback */
#endif /* USE_HAL_SMARTCARD_REGISTER_CALLBACKS */
} SMARTCARD_HandleTypeDef;
#if (USE_HAL_SMARTCARD_REGISTER_CALLBACKS == 1)
/**
* @brief HAL SMARTCARD Callback ID enumeration definition
*/
typedef enum
{
HAL_SMARTCARD_TX_COMPLETE_CB_ID = 0x00U, /*!< SMARTCARD Tx Complete Callback ID */
HAL_SMARTCARD_RX_COMPLETE_CB_ID = 0x01U, /*!< SMARTCARD Rx Complete Callback ID */
HAL_SMARTCARD_ERROR_CB_ID = 0x02U, /*!< SMARTCARD Error Callback ID */
HAL_SMARTCARD_ABORT_COMPLETE_CB_ID = 0x03U, /*!< SMARTCARD Abort Complete Callback ID */
HAL_SMARTCARD_ABORT_TRANSMIT_COMPLETE_CB_ID = 0x04U, /*!< SMARTCARD Abort Transmit Complete Callback ID */
HAL_SMARTCARD_ABORT_RECEIVE_COMPLETE_CB_ID = 0x05U, /*!< SMARTCARD Abort Receive Complete Callback ID */
HAL_SMARTCARD_MSPINIT_CB_ID = 0x08U, /*!< SMARTCARD MspInit callback ID */
HAL_SMARTCARD_MSPDEINIT_CB_ID = 0x09U /*!< SMARTCARD MspDeInit callback ID */
} HAL_SMARTCARD_CallbackIDTypeDef;
/**
* @brief HAL SMARTCARD Callback pointer definition
*/
typedef void (*pSMARTCARD_CallbackTypeDef)(SMARTCARD_HandleTypeDef *hsc); /*!< pointer to an SMARTCARD callback function */
#endif /* USE_HAL_SMARTCARD_REGISTER_CALLBACKS */
/**
* @}
*/
/* Exported constants --------------------------------------------------------*/
/** @defgroup SMARTCARD_Exported_Constants SMARTCARD Exported constants
* @{
*/
/** @defgroup SMARTCARD_Error_Code SMARTCARD Error Code
* @{
*/
#define HAL_SMARTCARD_ERROR_NONE 0x00000000U /*!< No error */
#define HAL_SMARTCARD_ERROR_PE 0x00000001U /*!< Parity error */
#define HAL_SMARTCARD_ERROR_NE 0x00000002U /*!< Noise error */
#define HAL_SMARTCARD_ERROR_FE 0x00000004U /*!< Frame error */
#define HAL_SMARTCARD_ERROR_ORE 0x00000008U /*!< Overrun error */
#define HAL_SMARTCARD_ERROR_DMA 0x00000010U /*!< DMA transfer error */
#if (USE_HAL_SMARTCARD_REGISTER_CALLBACKS == 1)
#define HAL_SMARTCARD_ERROR_INVALID_CALLBACK 0x00000020U /*!< Invalid Callback error */
#endif /* USE_HAL_SMARTCARD_REGISTER_CALLBACKS */
/**
* @}
*/
/** @defgroup SMARTCARD_Word_Length SMARTCARD Word Length
* @{
*/
#define SMARTCARD_WORDLENGTH_9B ((uint32_t)USART_CR1_M)
/**
* @}
*/
/** @defgroup SMARTCARD_Stop_Bits SMARTCARD Number of Stop Bits
* @{
*/
#define SMARTCARD_STOPBITS_0_5 ((uint32_t)USART_CR2_STOP_0)
#define SMARTCARD_STOPBITS_1_5 ((uint32_t)(USART_CR2_STOP_0 | USART_CR2_STOP_1))
/**
* @}
*/
/** @defgroup SMARTCARD_Parity SMARTCARD Parity
* @{
*/
#define SMARTCARD_PARITY_EVEN ((uint32_t)USART_CR1_PCE)
#define SMARTCARD_PARITY_ODD ((uint32_t)(USART_CR1_PCE | USART_CR1_PS))
/**
* @}
*/
/** @defgroup SMARTCARD_Mode SMARTCARD Mode
* @{
*/
#define SMARTCARD_MODE_RX ((uint32_t)USART_CR1_RE)
#define SMARTCARD_MODE_TX ((uint32_t)USART_CR1_TE)
#define SMARTCARD_MODE_TX_RX ((uint32_t)(USART_CR1_TE |USART_CR1_RE))
/**
* @}
*/
/** @defgroup SMARTCARD_Clock_Polarity SMARTCARD Clock Polarity
* @{
*/
#define SMARTCARD_POLARITY_LOW 0x00000000U
#define SMARTCARD_POLARITY_HIGH ((uint32_t)USART_CR2_CPOL)
/**
* @}
*/
/** @defgroup SMARTCARD_Clock_Phase SMARTCARD Clock Phase
* @{
*/
#define SMARTCARD_PHASE_1EDGE 0x00000000U
#define SMARTCARD_PHASE_2EDGE ((uint32_t)USART_CR2_CPHA)
/**
* @}
*/
/** @defgroup SMARTCARD_Last_Bit SMARTCARD Last Bit
* @{
*/
#define SMARTCARD_LASTBIT_DISABLE 0x00000000U
#define SMARTCARD_LASTBIT_ENABLE ((uint32_t)USART_CR2_LBCL)
/**
* @}
*/
/** @defgroup SMARTCARD_NACK_State SMARTCARD NACK State
* @{
*/
#define SMARTCARD_NACK_ENABLE ((uint32_t)USART_CR3_NACK)
#define SMARTCARD_NACK_DISABLE 0x00000000U
/**
* @}
*/
/** @defgroup SMARTCARD_DMA_Requests SMARTCARD DMA requests
* @{
*/
#define SMARTCARD_DMAREQ_TX ((uint32_t)USART_CR3_DMAT)
#define SMARTCARD_DMAREQ_RX ((uint32_t)USART_CR3_DMAR)
/**
* @}
*/
/** @defgroup SMARTCARD_Prescaler SMARTCARD Prescaler
* @{
*/
#define SMARTCARD_PRESCALER_SYSCLK_DIV2 0x00000001U /*!< SYSCLK divided by 2 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV4 0x00000002U /*!< SYSCLK divided by 4 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV6 0x00000003U /*!< SYSCLK divided by 6 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV8 0x00000004U /*!< SYSCLK divided by 8 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV10 0x00000005U /*!< SYSCLK divided by 10 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV12 0x00000006U /*!< SYSCLK divided by 12 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV14 0x00000007U /*!< SYSCLK divided by 14 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV16 0x00000008U /*!< SYSCLK divided by 16 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV18 0x00000009U /*!< SYSCLK divided by 18 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV20 0x0000000AU /*!< SYSCLK divided by 20 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV22 0x0000000BU /*!< SYSCLK divided by 22 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV24 0x0000000CU /*!< SYSCLK divided by 24 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV26 0x0000000DU /*!< SYSCLK divided by 26 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV28 0x0000000EU /*!< SYSCLK divided by 28 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV30 0x0000000FU /*!< SYSCLK divided by 30 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV32 0x00000010U /*!< SYSCLK divided by 32 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV34 0x00000011U /*!< SYSCLK divided by 34 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV36 0x00000012U /*!< SYSCLK divided by 36 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV38 0x00000013U /*!< SYSCLK divided by 38 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV40 0x00000014U /*!< SYSCLK divided by 40 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV42 0x00000015U /*!< SYSCLK divided by 42 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV44 0x00000016U /*!< SYSCLK divided by 44 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV46 0x00000017U /*!< SYSCLK divided by 46 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV48 0x00000018U /*!< SYSCLK divided by 48 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV50 0x00000019U /*!< SYSCLK divided by 50 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV52 0x0000001AU /*!< SYSCLK divided by 52 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV54 0x0000001BU /*!< SYSCLK divided by 54 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV56 0x0000001CU /*!< SYSCLK divided by 56 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV58 0x0000001DU /*!< SYSCLK divided by 58 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV60 0x0000001EU /*!< SYSCLK divided by 60 */
#define SMARTCARD_PRESCALER_SYSCLK_DIV62 0x0000001FU /*!< SYSCLK divided by 62 */
/**
* @}
*/
/** @defgroup SmartCard_Flags SMARTCARD Flags
* Elements values convention: 0xXXXX
* - 0xXXXX : Flag mask in the SR register
* @{
*/
#define SMARTCARD_FLAG_TXE ((uint32_t)USART_SR_TXE)
#define SMARTCARD_FLAG_TC ((uint32_t)USART_SR_TC)
#define SMARTCARD_FLAG_RXNE ((uint32_t)USART_SR_RXNE)
#define SMARTCARD_FLAG_IDLE ((uint32_t)USART_SR_IDLE)
#define SMARTCARD_FLAG_ORE ((uint32_t)USART_SR_ORE)
#define SMARTCARD_FLAG_NE ((uint32_t)USART_SR_NE)
#define SMARTCARD_FLAG_FE ((uint32_t)USART_SR_FE)
#define SMARTCARD_FLAG_PE ((uint32_t)USART_SR_PE)
/**
* @}
*/
/** @defgroup SmartCard_Interrupt_definition SMARTCARD Interrupts Definition
* Elements values convention: 0xY000XXXX
* - XXXX : Interrupt mask in the Y register
* - Y : Interrupt source register (2bits)
* - 01: CR1 register
* - 11: CR3 register
* @{
*/
#define SMARTCARD_IT_PE ((uint32_t)(SMARTCARD_CR1_REG_INDEX << 28U | USART_CR1_PEIE))
#define SMARTCARD_IT_TXE ((uint32_t)(SMARTCARD_CR1_REG_INDEX << 28U | USART_CR1_TXEIE))
#define SMARTCARD_IT_TC ((uint32_t)(SMARTCARD_CR1_REG_INDEX << 28U | USART_CR1_TCIE))
#define SMARTCARD_IT_RXNE ((uint32_t)(SMARTCARD_CR1_REG_INDEX << 28U | USART_CR1_RXNEIE))
#define SMARTCARD_IT_IDLE ((uint32_t)(SMARTCARD_CR1_REG_INDEX << 28U | USART_CR1_IDLEIE))
#define SMARTCARD_IT_ERR ((uint32_t)(SMARTCARD_CR3_REG_INDEX << 28U | USART_CR3_EIE))
/**
* @}
*/
/**
* @}
*/
/* Exported macro ------------------------------------------------------------*/
/** @defgroup SMARTCARD_Exported_Macros SMARTCARD Exported Macros
* @{
*/
/** @brief Reset SMARTCARD handle gstate & RxState
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#if USE_HAL_SMARTCARD_REGISTER_CALLBACKS == 1
#define __HAL_SMARTCARD_RESET_HANDLE_STATE(__HANDLE__) do{ \
(__HANDLE__)->gState = HAL_SMARTCARD_STATE_RESET; \
(__HANDLE__)->RxState = HAL_SMARTCARD_STATE_RESET; \
(__HANDLE__)->MspInitCallback = NULL; \
(__HANDLE__)->MspDeInitCallback = NULL; \
} while(0U)
#else
#define __HAL_SMARTCARD_RESET_HANDLE_STATE(__HANDLE__) do{ \
(__HANDLE__)->gState = HAL_SMARTCARD_STATE_RESET; \
(__HANDLE__)->RxState = HAL_SMARTCARD_STATE_RESET; \
} while(0U)
#endif /*USE_HAL_SMARTCARD_REGISTER_CALLBACKS */
/** @brief Flush the Smartcard DR register
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_FLUSH_DRREGISTER(__HANDLE__) ((__HANDLE__)->Instance->DR)
/** @brief Check whether the specified Smartcard flag is set or not.
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @param __FLAG__ specifies the flag to check.
* This parameter can be one of the following values:
* @arg SMARTCARD_FLAG_TXE: Transmit data register empty flag
* @arg SMARTCARD_FLAG_TC: Transmission Complete flag
* @arg SMARTCARD_FLAG_RXNE: Receive data register not empty flag
* @arg SMARTCARD_FLAG_IDLE: Idle Line detection flag
* @arg SMARTCARD_FLAG_ORE: Overrun Error flag
* @arg SMARTCARD_FLAG_NE: Noise Error flag
* @arg SMARTCARD_FLAG_FE: Framing Error flag
* @arg SMARTCARD_FLAG_PE: Parity Error flag
* @retval The new state of __FLAG__ (TRUE or FALSE).
*/
#define __HAL_SMARTCARD_GET_FLAG(__HANDLE__, __FLAG__) (((__HANDLE__)->Instance->SR & (__FLAG__)) == (__FLAG__))
/** @brief Clear the specified Smartcard pending flags.
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @param __FLAG__ specifies the flag to check.
* This parameter can be any combination of the following values:
* @arg SMARTCARD_FLAG_TC: Transmission Complete flag.
* @arg SMARTCARD_FLAG_RXNE: Receive data register not empty flag.
*
* @note PE (Parity error), FE (Framing error), NE (Noise error) and ORE (Overrun
* error) flags are cleared by software sequence: a read operation to
* USART_SR register followed by a read operation to USART_DR register.
* @note RXNE flag can be also cleared by a read to the USART_DR register.
* @note TC flag can be also cleared by software sequence: a read operation to
* USART_SR register followed by a write operation to USART_DR register.
* @note TXE flag is cleared only by a write to the USART_DR register.
* @retval None
*/
#define __HAL_SMARTCARD_CLEAR_FLAG(__HANDLE__, __FLAG__) ((__HANDLE__)->Instance->SR = ~(__FLAG__))
/** @brief Clear the SMARTCARD PE pending flag.
* @param __HANDLE__ specifies the USART Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_CLEAR_PEFLAG(__HANDLE__) \
do{ \
__IO uint32_t tmpreg = 0x00U; \
tmpreg = (__HANDLE__)->Instance->SR; \
tmpreg = (__HANDLE__)->Instance->DR; \
UNUSED(tmpreg); \
} while(0U)
/** @brief Clear the SMARTCARD FE pending flag.
* @param __HANDLE__ specifies the USART Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_CLEAR_FEFLAG(__HANDLE__) __HAL_SMARTCARD_CLEAR_PEFLAG(__HANDLE__)
/** @brief Clear the SMARTCARD NE pending flag.
* @param __HANDLE__ specifies the USART Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_CLEAR_NEFLAG(__HANDLE__) __HAL_SMARTCARD_CLEAR_PEFLAG(__HANDLE__)
/** @brief Clear the SMARTCARD ORE pending flag.
* @param __HANDLE__ specifies the USART Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_CLEAR_OREFLAG(__HANDLE__) __HAL_SMARTCARD_CLEAR_PEFLAG(__HANDLE__)
/** @brief Clear the SMARTCARD IDLE pending flag.
* @param __HANDLE__ specifies the USART Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_CLEAR_IDLEFLAG(__HANDLE__) __HAL_SMARTCARD_CLEAR_PEFLAG(__HANDLE__)
/** @brief Enable the specified SmartCard interrupt.
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @param __INTERRUPT__ specifies the SMARTCARD interrupt to enable.
* This parameter can be one of the following values:
* @arg SMARTCARD_IT_TXE: Transmit Data Register empty interrupt
* @arg SMARTCARD_IT_TC: Transmission complete interrupt
* @arg SMARTCARD_IT_RXNE: Receive Data register not empty interrupt
* @arg SMARTCARD_IT_IDLE: Idle line detection interrupt
* @arg SMARTCARD_IT_PE: Parity Error interrupt
* @arg SMARTCARD_IT_ERR: Error interrupt(Frame error, noise error, overrun error)
* @retval None
*/
#define __HAL_SMARTCARD_ENABLE_IT(__HANDLE__, __INTERRUPT__) ((((__INTERRUPT__) >> 28U) == SMARTCARD_CR1_REG_INDEX)? ((__HANDLE__)->Instance->CR1 |= ((__INTERRUPT__) & SMARTCARD_IT_MASK)): \
((__HANDLE__)->Instance->CR3 |= ((__INTERRUPT__) & SMARTCARD_IT_MASK)))
/** @brief Disable the specified SmartCard interrupt.
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @param __INTERRUPT__ specifies the SMARTCARD interrupt to disable.
* This parameter can be one of the following values:
* @arg SMARTCARD_IT_TXE: Transmit Data Register empty interrupt
* @arg SMARTCARD_IT_TC: Transmission complete interrupt
* @arg SMARTCARD_IT_RXNE: Receive Data register not empty interrupt
* @arg SMARTCARD_IT_IDLE: Idle line detection interrupt
* @arg SMARTCARD_IT_PE: Parity Error interrupt
* @arg SMARTCARD_IT_ERR: Error interrupt(Frame error, noise error, overrun error)
* @retval None
*/
#define __HAL_SMARTCARD_DISABLE_IT(__HANDLE__, __INTERRUPT__) ((((__INTERRUPT__) >> 28U) == SMARTCARD_CR1_REG_INDEX)? ((__HANDLE__)->Instance->CR1 &= ~((__INTERRUPT__) & SMARTCARD_IT_MASK)): \
((__HANDLE__)->Instance->CR3 &= ~ ((__INTERRUPT__) & SMARTCARD_IT_MASK)))
/** @brief Checks whether the specified SmartCard interrupt has occurred or not.
* @param __HANDLE__ specifies the SmartCard Handle.
* @param __IT__ specifies the SMARTCARD interrupt source to check.
* This parameter can be one of the following values:
* @arg SMARTCARD_IT_TXE: Transmit Data Register empty interrupt
* @arg SMARTCARD_IT_TC: Transmission complete interrupt
* @arg SMARTCARD_IT_RXNE: Receive Data register not empty interrupt
* @arg SMARTCARD_IT_IDLE: Idle line detection interrupt
* @arg SMARTCARD_IT_ERR: Error interrupt
* @arg SMARTCARD_IT_PE: Parity Error interrupt
* @retval The new state of __IT__ (TRUE or FALSE).
*/
#define __HAL_SMARTCARD_GET_IT_SOURCE(__HANDLE__, __IT__) (((((__IT__) >> 28U) == SMARTCARD_CR1_REG_INDEX)? (__HANDLE__)->Instance->CR1: (__HANDLE__)->Instance->CR3) & (((uint32_t)(__IT__)) & SMARTCARD_IT_MASK))
/** @brief Macro to enable the SMARTCARD's one bit sample method
* @param __HANDLE__ specifies the SMARTCARD Handle.
* @retval None
*/
#define __HAL_SMARTCARD_ONE_BIT_SAMPLE_ENABLE(__HANDLE__) ((__HANDLE__)->Instance->CR3|= USART_CR3_ONEBIT)
/** @brief Macro to disable the SMARTCARD's one bit sample method
* @param __HANDLE__ specifies the SMARTCARD Handle.
* @retval None
*/
#define __HAL_SMARTCARD_ONE_BIT_SAMPLE_DISABLE(__HANDLE__) ((__HANDLE__)->Instance->CR3 &= (uint16_t)~((uint16_t)USART_CR3_ONEBIT))
/** @brief Enable the USART associated to the SMARTCARD Handle
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_ENABLE(__HANDLE__) ((__HANDLE__)->Instance->CR1 |= USART_CR1_UE)
/** @brief Disable the USART associated to the SMARTCARD Handle
* @param __HANDLE__ specifies the SMARTCARD Handle.
* SMARTCARD Handle selects the USARTx peripheral (USART availability and x value depending on device).
* @retval None
*/
#define __HAL_SMARTCARD_DISABLE(__HANDLE__) ((__HANDLE__)->Instance->CR1 &= ~USART_CR1_UE)
/** @brief Macros to enable the SmartCard DMA request.
* @param __HANDLE__ specifies the SmartCard Handle.
* @param __REQUEST__ specifies the SmartCard DMA request.
* This parameter can be one of the following values:
* @arg SMARTCARD_DMAREQ_TX: SmartCard DMA transmit request
* @arg SMARTCARD_DMAREQ_RX: SmartCard DMA receive request
* @retval None
*/
#define __HAL_SMARTCARD_DMA_REQUEST_ENABLE(__HANDLE__, __REQUEST__) ((__HANDLE__)->Instance->CR3 |= (__REQUEST__))
/** @brief Macros to disable the SmartCard DMA request.
* @param __HANDLE__ specifies the SmartCard Handle.
* @param __REQUEST__ specifies the SmartCard DMA request.
* This parameter can be one of the following values:
* @arg SMARTCARD_DMAREQ_TX: SmartCard DMA transmit request
* @arg SMARTCARD_DMAREQ_RX: SmartCard DMA receive request
* @retval None
*/
#define __HAL_SMARTCARD_DMA_REQUEST_DISABLE(__HANDLE__, __REQUEST__) ((__HANDLE__)->Instance->CR3 &= ~(__REQUEST__))
/**
* @}
*/
/* Exported functions --------------------------------------------------------*/
/** @addtogroup SMARTCARD_Exported_Functions
* @{
*/
/** @addtogroup SMARTCARD_Exported_Functions_Group1
* @{
*/
/* Initialization/de-initialization functions **********************************/
HAL_StatusTypeDef HAL_SMARTCARD_Init(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_ReInit(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_DeInit(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_MspInit(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_MspDeInit(SMARTCARD_HandleTypeDef *hsc);
#if (USE_HAL_SMARTCARD_REGISTER_CALLBACKS == 1)
/* Callbacks Register/UnRegister functions ***********************************/
HAL_StatusTypeDef HAL_SMARTCARD_RegisterCallback(SMARTCARD_HandleTypeDef *hsc, HAL_SMARTCARD_CallbackIDTypeDef CallbackID, pSMARTCARD_CallbackTypeDef pCallback);
HAL_StatusTypeDef HAL_SMARTCARD_UnRegisterCallback(SMARTCARD_HandleTypeDef *hsc, HAL_SMARTCARD_CallbackIDTypeDef CallbackID);
#endif /* USE_HAL_SMARTCARD_REGISTER_CALLBACKS */
/**
* @}
*/
/** @addtogroup SMARTCARD_Exported_Functions_Group2
* @{
*/
/* IO operation functions *******************************************************/
HAL_StatusTypeDef HAL_SMARTCARD_Transmit(SMARTCARD_HandleTypeDef *hsc, uint8_t *pData, uint16_t Size, uint32_t Timeout);
HAL_StatusTypeDef HAL_SMARTCARD_Receive(SMARTCARD_HandleTypeDef *hsc, uint8_t *pData, uint16_t Size, uint32_t Timeout);
HAL_StatusTypeDef HAL_SMARTCARD_Transmit_IT(SMARTCARD_HandleTypeDef *hsc, uint8_t *pData, uint16_t Size);
HAL_StatusTypeDef HAL_SMARTCARD_Receive_IT(SMARTCARD_HandleTypeDef *hsc, uint8_t *pData, uint16_t Size);
HAL_StatusTypeDef HAL_SMARTCARD_Transmit_DMA(SMARTCARD_HandleTypeDef *hsc, uint8_t *pData, uint16_t Size);
HAL_StatusTypeDef HAL_SMARTCARD_Receive_DMA(SMARTCARD_HandleTypeDef *hsc, uint8_t *pData, uint16_t Size);
/* Transfer Abort functions */
HAL_StatusTypeDef HAL_SMARTCARD_Abort(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_AbortTransmit(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_AbortReceive(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_Abort_IT(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_AbortTransmit_IT(SMARTCARD_HandleTypeDef *hsc);
HAL_StatusTypeDef HAL_SMARTCARD_AbortReceive_IT(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_IRQHandler(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_TxCpltCallback(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_RxCpltCallback(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_ErrorCallback(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_AbortCpltCallback(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_AbortTransmitCpltCallback(SMARTCARD_HandleTypeDef *hsc);
void HAL_SMARTCARD_AbortReceiveCpltCallback(SMARTCARD_HandleTypeDef *hsc);
/**
* @}
*/
/** @addtogroup SMARTCARD_Exported_Functions_Group3
* @{
*/
/* Peripheral State functions **************************************************/
HAL_SMARTCARD_StateTypeDef HAL_SMARTCARD_GetState(SMARTCARD_HandleTypeDef *hsc);
uint32_t HAL_SMARTCARD_GetError(SMARTCARD_HandleTypeDef *hsc);
/**
* @}
*/
/**
* @}
*/
/* Private types -------------------------------------------------------------*/
/* Private variables ---------------------------------------------------------*/
/* Private constants ---------------------------------------------------------*/
/** @defgroup SMARTCARD_Private_Constants SMARTCARD Private Constants
* @{
*/
/** @brief SMARTCARD interruptions flag mask
*
*/
#define SMARTCARD_IT_MASK ((uint32_t) USART_CR1_PEIE | USART_CR1_TXEIE | USART_CR1_TCIE | USART_CR1_RXNEIE | \
USART_CR1_IDLEIE | USART_CR3_EIE )
#define SMARTCARD_CR1_REG_INDEX 1U
#define SMARTCARD_CR3_REG_INDEX 3U
/**
* @}
*/
/* Private macros --------------------------------------------------------*/
/** @defgroup SMARTCARD_Private_Macros SMARTCARD Private Macros
* @{
*/
#define IS_SMARTCARD_WORD_LENGTH(LENGTH) ((LENGTH) == SMARTCARD_WORDLENGTH_9B)
#define IS_SMARTCARD_STOPBITS(STOPBITS) (((STOPBITS) == SMARTCARD_STOPBITS_0_5) || \
((STOPBITS) == SMARTCARD_STOPBITS_1_5))
#define IS_SMARTCARD_PARITY(PARITY) (((PARITY) == SMARTCARD_PARITY_EVEN) || \
((PARITY) == SMARTCARD_PARITY_ODD))
#define IS_SMARTCARD_MODE(MODE) ((((MODE) & 0x0000FFF3U) == 0x00U) && ((MODE) != 0x000000U))
#define IS_SMARTCARD_POLARITY(CPOL) (((CPOL) == SMARTCARD_POLARITY_LOW) || ((CPOL) == SMARTCARD_POLARITY_HIGH))
#define IS_SMARTCARD_PHASE(CPHA) (((CPHA) == SMARTCARD_PHASE_1EDGE) || ((CPHA) == SMARTCARD_PHASE_2EDGE))
#define IS_SMARTCARD_LASTBIT(LASTBIT) (((LASTBIT) == SMARTCARD_LASTBIT_DISABLE) || \
((LASTBIT) == SMARTCARD_LASTBIT_ENABLE))
#define IS_SMARTCARD_NACK_STATE(NACK) (((NACK) == SMARTCARD_NACK_ENABLE) || \
((NACK) == SMARTCARD_NACK_DISABLE))
#define IS_SMARTCARD_BAUDRATE(BAUDRATE) ((BAUDRATE) < 10500001U)
#define SMARTCARD_DIV(__PCLK__, __BAUD__) ((uint32_t)((((uint64_t)(__PCLK__))*25U)/(4U*((uint64_t)(__BAUD__)))))
#define SMARTCARD_DIVMANT(__PCLK__, __BAUD__) (SMARTCARD_DIV((__PCLK__), (__BAUD__))/100U)
#define SMARTCARD_DIVFRAQ(__PCLK__, __BAUD__) ((((SMARTCARD_DIV((__PCLK__), (__BAUD__)) - (SMARTCARD_DIVMANT((__PCLK__), (__BAUD__)) * 100U)) * 16U) + 50U) / 100U)
/* SMARTCARD BRR = mantissa + overflow + fraction
= (SMARTCARD DIVMANT << 4) + (SMARTCARD DIVFRAQ & 0xF0) + (SMARTCARD DIVFRAQ & 0x0FU) */
#define SMARTCARD_BRR(__PCLK__, __BAUD__) (((SMARTCARD_DIVMANT((__PCLK__), (__BAUD__)) << 4U) + \
(SMARTCARD_DIVFRAQ((__PCLK__), (__BAUD__)) & 0xF0U)) + \
(SMARTCARD_DIVFRAQ((__PCLK__), (__BAUD__)) & 0x0FU))
/**
* @}
*/
/* Private functions ---------------------------------------------------------*/
/** @defgroup SMARTCARD_Private_Functions SMARTCARD Private Functions
* @{
*/
/**
* @}
*/
/**
* @}
*/
/**
* @}
*/
#ifdef __cplusplus
}
#endif
#endif /* __STM32F4xx_HAL_SMARTCARD_H */
/************************ (C) COPYRIGHT STMicroelectronics *****END OF FILE****/
|
Large scale analysis of the mutational landscape in β-glucuronidase: A major player of mucopolysaccharidosis type VII.
The lysosomal storage disorders are a group of 50 unique inherited diseases characterized by unseemly lipid storage in lysosomes. These malfunctions arise due to genetic mutations that result in deficiency or reduced activities of the lysosomal enzymes, which are responsible for catabolism of biological macromolecules. Sly syndrome or mucopolysaccharidosis type VII is a lysosomal storage disorder associated with the deficiency of β-glucuronidase (EC 3.2.1.31) that catalyzes the hydrolysis of β-D-glucuronic acid residues from the non-reducing terminal of glycosaminoglycan. The effects of the disease causing mutations on the framework of the sequences and structure of β-glucuronidase (GUSBp) were analyzed utilizing a variety of bioinformatic tools. These analyses showed that 211 mutations may result in alteration of the biological activity of GUSBp, including previously experimentally validated mutations. Finally, we refined 90 disease causing mutations, which presumably cause a significant impact on the structure, function, and stability of GUSBp. Stability analyses showed that mutations p.Phe208Pro, p.Phe539Gly, p.Leu622Gly, p.Ile499Gly and p.Ile586Gly caused the highest impact on GUSBp stability and function because of destabilization of the protein structure. Furthermore, structures of wild type and mutant GUSBp were subjected to molecular dynamics simulation to examine the relative structural behaviors in the explicit conditions of water. In a broader view, the use of in silico approaches provided a useful understanding of the effect of single point mutations on the structure-function relationship of GUSBp. |
Myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS) is a debilitating noncommunicable disease brandishing an enormous worldwide disease burden with some evidence of inherited genetic risk. Absence of measurable changes in patients’ standard blood work has necessitated ad hoc symptom-driven therapies and a dearth of mechanistic hypotheses regarding its etiology and possible cure. A new hypothesis, the indolamine-2,3-dioxygenase (IDO) metabolic trap, was developed and formulated as a mathematical model. The historical occurrence of ME/CFS outbreaks is a singular feature of the disease and implies that any predisposing genetic mutation must be common. A database search for common damaging mutations in human enzymes produces 208 hits, including IDO2 with four such mutations. Non-functional IDO2, combined with well-established substrate inhibition of IDO1 and kinetic asymmetry of the large neutral amino acid transporter, LAT1, yielded a mathematical model of tryptophan metabolism that displays both physiological and pathological steady-states. Escape from the pathological one requires an exogenous perturbation. This model also identifies a critical point in cytosolic tryptophan abundance beyond which descent into the pathological steady-state is inevitable. If, however, means can be discovered to return cytosolic tryptophan below the critical point, return to the normal physiological steady-state is assured. Testing this hypothesis for any cell type requires only labelled tryptophan, a means to measure cytosolic tryptophan and kynurenine, and the standard tools of tracer kinetics. View Full-Text |
Arran 10 Year
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“This scotch is unusual, approachable and a confoundingly generous value. This is great for someone who drinks a lot of single malt and will appreciate something that’s a bit off-the-beaten-path.”—Chaim Dauermann, co-owner at New York City's Stay Gold
Read Next: The Best Whiskey Glasses |
Q:
Custom formatters not registered - ConversionNotSupportedException : Spring
I have a custom formatter @Component class DebitCardNumberFormatter implements Formatter<DebitCardNumber>{...} I have added this formatter to the FormattingConversionServiceFactoryBean by
<bean id="formattingConversionService" class="org.springframework.format.support.FormattingConversionServiceFactoryBean">
<property name="formatters">
<set>
<ref bean="debitCardNumberFormatter"/>
</set>
</property>
</bean>
Now when I explicitly run the following code, it works correctly and the string becomes DebitCardNumber,
DebitCardNumber debitCardNumber=formattingConversionService.convert("1234-3242
-4533-3432",DebitCardNumber.class);
But if I try to inject a DebitCardNumber in another bean with a string value,
<bean id="cardDetails" class="com.amudhan.springcore.formatter.CardDetails">
<property name="debitCardNumber" value="1234-3242-4533-3432"></property>
</bean>
The container throws ConversionNotSupportedException.
org.springframework.beans.ConversionNotSupportedException: Failed to convert property value of type [java.lang.String] to required type [com.amudhan.springcore.formatter.DebitCardNumber] for property 'debitCardNumber'; nested exception is java.lang.IllegalStateException: Cannot convert value of type [java.lang.String] to required type [com.amudhan.springcore.formatter.DebitCardNumber] for property 'debitCardNumber': no matching editors or conversion strategy found`enter code here`
I am reading the Spring documentation and practicing the APIs. What
am I missing here ?
Previously when I created 'Converter's, I used 'converters' property
of ConversionServiceFactoryBean to add that converter and use it
automatically.
In the same way I have tried adding the formatter by using the
'formatters' property of FormattingConversionServiceFactoryBean. Is
there anything that I fundamentally missing ? Or Is my understanding
of Formatters is plain wrong ?
If It throws exception when I use spring to debitCardNumber it in the applicationContext, how come it is working correctly when I call the convert method explicitly from the app ? Even the beans are correctly created when I checked.
A:
This is one way to register your custom formatter
<mvc:annotation-driven conversion-service="conversionService"/>
<bean id="conversionService" class="org.springframework.format.support.FormattingConversionServiceFactoryBean">
<property name="formatters">
<set>
<ref bean="debitCardNumberFormatter"/>
</set>
</property>
</bean>
Update
Alright after looking little deeper into the code. So spring is looking for conversion service bean in your application context with id "conversionService" in Abstract bean factory so it can use that to parse your bean instead of property editors(before Spring 3.0).
So now why it worked with converters but not formatters because your id name for custom formatter didn't match with the id("conversionService") spring is looking for.
Any other name for id it will not work and so it's not a problem between choosing converter or formatter.
Hope this helps.
This example with formatter should work.
<bean id="conversionService"
class="org.springframework.format.support.FormattingConversionServiceFactoryBean">
<property name="formatters">
<set>
<ref bean="debitCardNumberFormatter"/>
</set>
</property>
</bean>
|
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Fantasist Jemma Beale has lost her appeal against her conviction and 10 year jail sentence for making false rape claims.
She had tried to claim she was unfairly convicted because the jury were not warned about sexual 'stereotypes.'
One man had gone to prison for two years over her false rape allegations, which even saw her given compensation for her "ordeal."
The Old Bailey heard today the 27-year-old was a serial liar who had shown "no remorse" over her bogus rape claims.
(Image: Central news)
Lady Justice Hallett said Beale had caused "considerable harm" to the justice system as she rejected Beale's appeal in court today.
Beale described herself as a lesbian with "no desire" for sex with men.
Her lies led to Mahad Cassim serving two years in jail.
Beale was later awarded £11,000 in criminal injuries compensation while Mr Cassim languished behind bars.
Police spent 6,400 hours investigating a series of rape claims she made at a cost to the taxpayer of £250,000.
In 2017 Beale was tried and convicted of perverting the course of justice and perjury.
But her lawyers today claimed her conviction is unsafe.
(Image: Central news)
Gillian Jones, QC, told the Court of Appeal: "The learned judge erred because he failed to give a direction about the dangers of myths and stereotypes.
"She was the subject of extensive media scrutiny in which she was vilified.
"The effect of which might have been to further prejudice the jury in the absence of such a direction.
"This reporting compounded or could have compounded these myths and stereotypes which were never corrected by way of judicial guidance to the jury.
"That loss of anonymity resulted in extensive adverse media both in the press and on social media."
Ms Jones argued the purpose of the "myths and stereotypes" direction by the judge was to prevent "unwarranted assumptions" and "illegitimate reasoning" leading to cynicism by the jury.
She added: "It is about jury education."
(Image: Central news)
Beale made her first complaint on the morning of 26 November 2010, when she told police she had been raped by Mr Cassim the previous night.
Jurors heard the then 37-year-old Somalian moved to the UK in 2002, aged 23, after a short stint living in Sweden where he also served in the military as part of the peace-keeping corps.
In a victim impact statement, Mr Cassim described the trauma of being imprisoned and how the conviction destroyed his relationships with friends and family due to the suspicion hanging over it.
"One of my goals in life is to be a successful businessman, to have a nice family and be happy," he said.
"I'm working on the happiness. I have a long way to go."
(Image: central news)
Beale had also falsely complained to police she was groped by a complete stranger, Noam Shahzad, in The Windsor Castle pub, in Hounslow, in July 2012, and falsely claimed that he then took part in a vicious gang rape on her in the car park of a nearby medical centre.
CCTV later showed that Beale had attacked him in the pub before walking home alone.
Forensic tests also showed she had cut herself with a hanging flower basket to make it look like she had been sexually assaulted with barbed wire.
Mr Shahzad skipped bail and fled the country after being charged with sexual assault.
Beale then fabricated similar allegations against six other men in 2013.
She claimed two strangers sexually assaulted outside her home in Addlestone, Surrey, before claiming she was put through another gang rape attack by four others two months later in Feltham.
Two of the men identified by Beale were arrested and interviewed but never charged.
In 2017, Beale, formally of Bedfont, Middlesex, was jailed for ten years for perjury and perverting the course of justice by Judge Nicholas Loraine-Smith.
(Image: Central News/Gustavo Valiente)
Her appeal before Lady Justice Hallett, Mr Justice Warby and Sir John Royce failed today.
Lady Hallett said: "We need no persuasion that myths and stereotypes about rape complainants still persist and if the evidence of a complainant is to be assessed fairly the trial judge should give the guidance by the judicial trial.
"However, the guidance is simply that, it is not a direction of law. It is also directed to a complainant not a defendant.
"This case went far further then myths and stereotypes about a complainant's behaviour. The appellant was accused of being a serial liar who fabricated accounts mostly of a sexual nature.
"In the light of the evidence called even if the guidance was given it would not have assisted the appellant.
"The system of justice has suffered considerable harm - considerable resources have been spent investigating and prosecuting crimes which never happened.
"There has been no indication of remorse on the appellant's part." |
Inline Skating Club of America
The Inline Skating Club of America is a skating facility located in North Arlington, New Jersey. It is the home of the New Jersey Grizzlies of the Professional Inline Hockey Association Pro Division (PIHA Pro) and the Wallington Grizzlies of the Professional Inline Hockey Association Minor League (PIHAML).
References
External links
Category:Inline skating
Category:North Arlington, New Jersey |
Current atomizing device in electronic cigarettes generally includes an atomizer having a heating wire disposed therein, an atomizing cup having tobacco flavored liquid therein, an atomizing seat used for fixing the atomizing cup, and an atomizing sleeve sleeved at an outer of the atomizing cup.
Two ends of the heating wire in the electronic cigarette need to be electrically connected to positive and negative electrodes of a battery to supply power source. The heating wire of the electronic cigarette is generally welded to the electrodes of the battery to electrically connect with the battery. Perhaps, an end of the atomizing seat disposes a separate electrode assembly, and two ends of the heating wire are respectively welded to corresponding electrodes of the electrode assembly, thus the electrode assembly electrically connects with the positive and negative electrodes of the battery. Connection by welding is time cost and strenuous, and is also low stability. Further, connection by welding results in bad phenomenon such as rosin joint, tack weld, and produces residue harmful to people.
Owing to the atomizing cup disposing tobacco flavored liquid, the sealing of the atomizing cup need to be guaranteed when making the atomizing cup sleeved in the atomizing sleeve utilizing the atomizing seat. When fixing the atomizing cup utilizing the atomizing seat, absorbent cotton is firstly packaged in the atomizing seat. The outer edge of traditional atomizing seat generally defines groove for latching the absorbent cotton to fix the absorbent cotton. The atomizing seat must be firstly manufactured to form flange by supplier, and then turned outside in after packaging the absorbent cotton, which is complicated. When sealing the atomizing cup, a typical way is to dispose a sealing washer between the atomizing sleeve and the atomizing seat, or to dispense glue at the juncture of the atomizing sleeve and the atomizing seat to form sealing glue layer to achieve the sealing of the atomizing cup. Disposing a separate sealing washer may enhance manufacturing cost, and is difficult to assembly, which is time cost and strenuous. Dispensing glue is unsafe to operate, and is unfriendly environment. |
[Comparison of two methods of evaluation of gentamicin in man : bioassay and enzyme immunoassay (author's transl)].
This study compares two methods of gentamicin determination in blood : bioassay and enzyme immunoassay. Results for 145 patients serums showed a correlation coefficient of 0,895 between the two methods. The accuracy and reproducibility were tested on 10 known samples. Each sample was titrated 10 times. Values obtained and real values are near between 0 and 5 mcg/ml and significantly move away between 6 and 10 mcg/ml by the two methods. Advantages and disadvantages are discussed for each method. |
An investigation into the bungled prosecution of former Sen. Ted Stevens (R-Alaska) found that while Justice Department attorneys concealed evidence that would have exonerated the late Senator, they should not be prosecuted for the “significant, widespread, and at times intentional misconduct” that derailed the government’s case, a federal judge said today.
The conclusions of the investigation, which began in April 2009, were referenced in an order issued by U.S. District Court for the District of Columbia Judge Emmet G. Sullivan, who presided over Stevens’ corruption trial in the fall of 2008.
Though Stevens was indicted, tried and found guilty of making false statements on his annual financial disclosure forms filed with the Senate because he did not disclose gifts he received, the verdict was vacated after the Department of Justice concluded its prosecutors had failed to hand over evidence that would have bolstered Stevens’ defense.
Stevens died in August 2010 when the private plane in which he was traveling crashed in rural Alaska.
Sullivan appointed Washington, D.C., attorney Henry F. Schuelke of the law firm Janis, Schuelke & Wechsler to investigate and possibly prosecute the six attorneys in the Justice Department’s Public Integrity Section who were responsible for the botched Stevens prosecution at the time the government first admitted wrongdoing.
“The prosecutorial misconduct ... permeated the proceedings before this Court to a degree and extent that this Court had not seen in twenty-five years on the bench,” Sullivan wrote of his decision to bring on Schuelke in his order.
Schuelke, in a 500-page report that resulted from the review of 150,000 pages of documents and the deposition of 12 witnesses, found that the Stevens case was “permeated by the systematic concealment of significant exculpatory evidence which would have independently corroborated his defense and his testimony, and seriously damaged the testimony and credibility of the government’s key witness,” Sullivan quoted.
However because the court did not give the attorneys a direct order to comply with their legal obligation to turn over the evidence, they should not be prosecuted for misconduct, Schuelke concluded.
“Because the Court accepted the prosecutors’ repeated assertions that they were complying with their obligations and proceeding in good faith, the court did not issue a ‘clear and unequivocable’ order directing the attorneys to follow the law,” Sullivan wrote.
Copies of Schuelke’s report, which remains under seal, were given to the Justice Department and the late Senator’s attorneys for review. They have until Dec. 5 to object to its contents being made public.
One of the prosecutors in the Stevens case, Nicholas Marsh, committed suicide last fall, and his lawyer said at the time that Marsh was distraught about the effect the Stevens case might have on his career. |
Short-term studies of the effect of acrylamide on the testes of the Egyptian toad.
The treatment of male Egyptian toads (Bufo regularis) with acrylamide (1 mg/toad twice a week for four weeks) was followed by atrophy of the testes, inhibition of spermatogenesis and necrosis of the seminiferous tubules with signs of vacuolation. Ultrastructurally, the Leydig cells of treated toads displayed varying degrees of vacuolation of the mitochondria, with a decrease in the number of ribosomes. The mechanism of the action of acrylamide in inhibiting spermatogenesis may be due to a decrease in the testosterone level, as borne out by vacuolation of the mitochondria and the decrease in the ribosomes in the Leydig cells of treated animals. |
John Wall is healthy and thinks the Washington Wizards, if they can avoid the injury bug, will make the postseason for the first time since 2008.
"The goal is the playoffs," Wall told ESPN.com. "We've got the pieces."
John Wall says he believes the Wizards have the "pieces" to make the playoffs. Ned Dishman/Getty Images
Wall said that the addition of Al Harrington was "huge" and that the 33-year-old veteran may be the missing piece for the Wizards to get to the postseason. Harrington signed on Aug. 14 after the Orlando Magic waived him.
"We got what we needed with Al Harrington," Wall said. "He looks healthy, and to bring in a true veteran who knows what it takes to win was important for us."
However, injuries have already hit the Wizards. Starting big man Emeka Okafor is out indefinitely with a herniated disc, and reserve forward Chris Singleton will miss six to eight weeks with a broken bone in his foot.
"That's the only thing that can hold us back: health," Wall said.
Wall missed the first 33 games last season because of a knee injury. By the time he returned, Washington was 5-28. The Wizards went 24-25 with Wall in the lineup, and he averaged 18.5 points and 7.6 assists in the 49 games. He said he has added strength, is up to 205 pounds (he was listed at 195 last season) and feels 100 percent healthy heading into training camp. |
Norepinephrine enhances adhesion of HIV-1-infected leukocytes to cardiac microvascular endothelial cells.
Recent reports have indicated that norepinephrine (NE) enhances HIV replication in infected monocytes and promotes increased expression of select matrix metalloproteinases associated with dilated cardiomyopathy (DCM) in vitro in co-cultures of HIV-infected leukocytes and human cardiac microvascular endothelial cells (HMVEC-C). The influence of NE on HIV infection and leukocyte-endothelial interactions suggests a pathogenic role in AIDS-related cardiovascular disease. This study examined the effects of norepinephrine (NE) and HIV-1 infection on leukocyte adhesion to HMVEC-C. Both flow and static conditions were examined and the expression of selected adhesion molecules and cytokines were monitored in parallel. NE pretreatment resulted in a detectable, dose-dependent increase of leukocyte-endothelial adhesion (LEA) with both HIV-1-infected and -uninfected peripheral blood mononuclear cells (PBMCs) relative to media controls after 48 hr in co-culture with HMVEC-C in vitro. However, the combination of NE plus HIV infection resulted in a significant (P < 0.0001) 18-fold increase in LEA over uninfected media controls. Increased levels in both cell-associated and -soluble ICAM-1 and E-Selectin but not VCAM-1 correlated with increased LEA and with HIV-1 infection or NE pretreatment. Blocking antibodies specific for ICAM-1 or E-Selectin inhibited HIV-NE-induced LEA. These data suggest a model in which NE primes HIV-1-infected leukocytes for enhanced adhesion and localization in HMVEC-C where they can initiate and participate in vascular injury associated with AIDS-related cardiomyopathy. |
307 So.2d 798 (1975)
Shirley Gadison WADE
v.
McINNIS-PETERSON CHEVROLET, INC., et al.
No. 10087.
Court of Appeal of Louisiana, First Circuit.
February 10, 1975.
*800 Lawrence Roe Dodd, Baton Rouge, for appellant.
Wendell C. Lindsay, Jr., Baton Rouge, for plaintiff-appellee.
Henry D. Salassi, Jr., Baton Rouge, for defendant-appellee General Motors Corp.
Before LOTTINGER, COVINGTON and BAILES, JJ.
COVINGTON, Judge.
This is a redhibitory action in which plaintiff, Shirley Gadison Wade, sued McInnis-Peterson Chevrolet, Inc., the seller, and General Motors Corporation, the manufacturer, to rescind the sale of a 1971 Chevrolet automobile. The seller denied liability and filed a third party demand against the manufacturer seeking reimbursement for any amount it might be cast on the main demand. The manufacturer denied any liability on the main and third party demands.
After trial by jury, verdict was rendered in favor of plaintiff and against the seller in the amount of $4,125.00, and in favor of the manufacturer on both demands.Accordingly, judgment was entered on the verdict on June 7, 1974. After denial of a motion for a new trial, the seller appealed the judgment. Plaintiff has answered the appeal, seeking an increase in the award of attorney's fees for services rendered on appeal.
General Motors Corporation has moved to dismiss the devolutive appeal of plaintiff, Shirley Gadison Wade, on the ground that the appeal was not timely taken under the provisions of LSA-C.C.P. Art. 2087. In the instant case the judgment was signed and notice of judgment was mailed to the parties on June 7, 1974. On June 12, 1974, the defendant, McInnis-Peterson Chevrolet, Inc., timely moved for a new trial. In due course the motion for new trial was denied, and McInnis-Peterson appealed the judgment. Plaintiff did not move for a new trial, but filed a motion and order for a devolutive appeal on September 13, 1974, posting bond on September 18, 1974.
Since plaintiff did not move for a new trial, and the last day on which she could ask for a new trial was June 12, 1974, the ninety-day period for perfecting a devolutive appeal began June 13, 1974, and expired September 10, 1974, unless the motion filed on behalf of defendant, McInnis-Peterson Chevrolet, Inc., delayed the running of the time period within which the plaintiff was required to take an appeal. The issue then is whether McInnis-Peterson's application for a new trial extended the delays within which plaintiff was required to file her appeal. We hold that the application for a new trial by defendant, McInnis-Peterson Chevrolet, Inc., had no legal significance as to the plaintiff. This holding is in accord with the *801 jurisprudence expressed in the case of Payton v. Aetna Life and Casualty Company, La.App., 299 So.2d 489 (4 Cir. 1974), which held:
"In effect, however, the Supreme Court. . ." (in Thurman v. Star Electric Supply, Inc., La., 283 So.2d 212). . . "stated a general rule (that an application for new trial by one party suspends only the commencement of that party's delay for filing an appeal) and then proceeded to hold that the general rule is simply not workable under all circumstances. Since in the present case we find no similarity to the unusual circumstances in Thurman, we are compelled to follow the general rule and accordingly hold the appeal was untimely."
Accordingly, we dismiss plaintiff's devolutive appeal.
The record reflects that on June 29, 1971, plaintiff bought a 1971 Chevrolet automobile, which had been manufactured by General Motors Corporation, from McInnis-Peterson Chevrolet, Inc. of Baton Rouge, Louisiana. At the time of the sale the automobile showed some 7,100 miles on the odometer, and was represented by the seller as a demonstrator under a new-car warranty. The windshield had been replaced by the seller shortly before the sale. The cash price paid by plaintiff for the automobile was $4,759.90, and she was given a credit of $1,000.00 as a trade-in on her older automobile. The finance charge for the balance of $3,659.90 was the sum of $925.43, with the total charges amounting to the sum of $5,979.64.
Almost immediately after the sale plaintiff discovered water leakage in the area of the windshield during a rain. On July 1, 1971, plaintiff returned the automobile to the seller for correction of the windshield leakage. The evidence shows that plaintiff brought the automobile back to the seller on numerous occasions for correction of the same defective condition, but to no avail. Finally, tender of the automobile was made, which the seller refused. The instant action in redhibition followed and plaintiff demanded a jury trial.
Neither special verdicts nor a general verdict accompanied by answers to interrogatories were used on the trial of the instant case, so we have no insight into the basis of the jury verdict. We therefore will examine each disputed material issue to determine whether or not the jury committed manifest error. See LSA-C.C.P. Arts. 1811, 1812; Pagitt Well Service, Inc. v. Sam Broussard, Inc., La.App., 293 So.2d 631 (3 Cir. 1974), writ refused La., 295 So.2d 817 (1974).
In a sale, the seller is bound by an implied warranty that the thing sold is free of hidden defects and is reasonably fit for its intended use. LSA-C.C. Arts. 2475, 2476, 2520; Rey v. Cuccia, La., 298 So.2d 840 (1974); Media Pro. Consult., Inc., v. Mercedes-Benz of N.A., Inc., 262 La. 80, 262 So.2d 377 (1972).
The codal basis for a redhibitory action is Civil Code Article 2520, which provides:
"Redhibition is the avoidance of a sale on account of some vice or defect in the thing sold, which renders it either absolutely useless, or its use so inconvenient and imperfect, that it must be supposed that the buyer would not have purchased it, had he known of the vice."
A redhibitory defect entitling the buyer to rescind the sale is some non-apparent defect existing before the sale in the thing sold which renders it useless or its use so imperfect, that the buyer would not have bought it if he had known of the defect. See LSA-C.C. Arts. 2520, 2521, 2530. For a general discussion of the redhibitory action, see Comment, Warranty of Quality in Louisiana: Nature and Proof of the Implied-in-law Warranty, 23 Tul.L.Rev. 96 (1948), and Comment, Warranty of Quality in Louisiana: Extent of Recovery under the Implied-in-law Warranty, 23 Tul. *802 L.Rev. 130 (1948); for a discussion of the rights of the seller, see Note, The Rights of the Vendor in Redhibition, 30 La.L.Rev. 508 (1970).
The general test for the application of the redhibition codal articles to the sale of defective things has recently been enunciated in several recent cases, including Rey v. Cuccia, supra; Breaux v. Winnebago Industries, Inc., La.App., 282 So.2d 763 (1 Cir. 1973). In addition, the test for the applicability of the redhibition articles to the sale of defective automobiles in particular has recently been set out in the following cases:
Menville v. Stephens Chevrolet, Inc., La.App., 300 So.2d 858 (4 Cir. 1974); Dunlap v. Chrysler Motors Corp., La.App., 299 So.2d 495 (4 Cir. 1974); Tauzin v. Sam Broussard Plymouth, Inc., La.App., 283 So.2d 266 (3 Cir. 1973); Juneau v. Bob McKinnon Chevrolet Company, La. App., 260 So.2d 919 (4 Cir. 1972).
Tested by the standards set out in the cases cited above, we agree with the jury that the buyer in the instant case did not meet the burden of proving a redhibitory defect entitling the buyer to a rescission of the sale. We have also reviewed the evidence in the record and find that it does not support a rescission of the sale. However, we find that the water leak from the windshield did adversely affect the usefulness of the automobile to the buyer. The main problem in the instant case was the inability of the seller to correct the water leakage from the windshield. The buyer took the automobile numerous times to the seller's repair shop without beneficial results.
The overall circumstances as brought out on the trial, especially the nature of the defect and the long period of extensive usage of the automobile by the buyer, support our conclusion that the defect in the instant case was one which diminished the utility of the thing, constituting merely a partial failure of consideration, rather than such a redhibitory defect which would justify a rescission of the sale.
In every redhibitory action if the evidence establishes only a partial failure of consideration, a reduction in the purchase price may be granted to the buyer. See Ingersoll v. Star Chrysler, Inc., La. App., 234 So.2d 85 (4 Cir. 1970), writ refused 256 La. 365, 236 So.2d 499 (1970); Wolfe v. Henderson Ford, Inc., La.App., 277 So.2d 215 (3 Cir. 1973). See also LSA-C.C. Arts. 2541, 2543.
In the Star Chrysler case, the Court said:
"In every redhibitory action if the evidence establishes only a partial failure of consideration the court has the power and duty to decree a quanti minoris, or a reduction of the purchase price."
The Court, in Henderson Ford, ruled:
"A decree of quanti minoris is responsive to an action for redhibition, being expressly authorized by LSA-C.C. Art. 2543. It follows that in every redhibitory action, the judge has the power and the duty, if he believes that the evidence establishes only a partial failure of consideration, to decree a quanti minoris."
In such a case, the amount of the reduction in price should be the difference between the actual purchase price and the price a reasonable buyer and seller would have agreed upon if they had both known of the defect. See Menville v. Stephens Chevrolet, Inc., supra; Tauzin v. Sam Broussard Plymouth, Inc., supra; Gauche v. Ford Motor Company, La.App., 226 So. 2d 198 (4 Cir. 1969).
In Stephens Chevrolet, in determining the amount of reduction to which the buyer was entitled, the Court said:
"The diminution which the trial judge may decree under C.C. art. 2543 is theoretically the difference between the sale price and the price the reasonable buyer and seller would have agreed upon if they had known of the defects.
*803 "To prove the theoretical price to which the actual sale price should be reduced, a plaintiff attempts to establish the fair value as of the time of the sale, if the defects had been known. Evidence as to this theoretical value may consist of expert opinion testimony, of costs expended to place the thing in sound condition, or of other facts bearing on the reduced price a forewarned buyer would have paid and a seller with knowledge of the defects would have accepted. But in the final analysis the trier of fact cannot mathematically calculate what price the parties would have agreed to, if they had known of the defects; the trier must consider the overall evidence and, using limited discretion, must set a reduced sale price which fictionally represents the fair value at the time of sale."
In the instant case the buyer and the seller, by agreeing upon the purchase price, set the value of the 1971 demonstrator Chevrolet automobile free from defects. Reduction of the purchase price to the fair value of the automobile at the time of the sale, if both the buyer and the seller had known of the defect which appeared shortly thereafter, involves multiple considerations. We conclude that the trial jury, in making its award of a price reduction, properly considered the numerous problems involved herein, the frequent inconvenience associated with the attempted repairs of the defective windshield, the actual damage to the automobile caused by the water leakage, the actual cost of repairing the defective windshield and other items that would go toward diminishing the value of the thing. In the instant case the jury's verdict was in favor of plaintiff in the amount of $4,125.00, of which sum attorney's fees were stipulated to be $1,625.00. The jury thus allowed plaintiff the sum of $2,500.00 as a price reduction. We do not find that the jury committed manifest error in determining that the purchase price should be reduced by this amount. We, of course, do not know the facts on which the jury based its conclusions and verdict. In such a case, we are directed to make our own findings of fact, which we have done. See Rowe v. Travelers Insurance Company, 253 La. 659, 219 So.2d 486 (1969); Hurst v. Hardware Mutual Casualty Company, La.App., 234 So.2d 802 (1 Cir. 1970). Our independent review of the record herein shows that the jury's conclusions and verdict were consistent with and supported by the evidence.
In addition, plaintiff has asked for attorney's fees. The jury included the stipulated sum of $1,625.00 as attorney's fees in its award. The applicable law is found in Civil Code Article 2545, as amended by Act No. 84 of 1968, which provides:
"The seller, who knows the vice of the thing he sells and omits to declare it, besides the restitution of price and repayment of the expenses, including reasonable attorneys' fees, is answerable to the buyer in damages."
To recover attorney's fees the buyer must prove knowledge of the defect by the seller. He need not prove wilful misrepresentation. It is sufficient for the buyer to prove actual or constructive knowledge by the seller. Thus, if the seller knew or should have known of the defect and failed to declare it to the buyer, the seller is liable additionally for reasonable attorney's fees. See Juneau v. Bob McKinnon Chevrolet Company, supra; Rey v. Cuccia, supra.
The facts of the instant case show that the seller installed the windshield in the automobile as a replacement for the original windshield, which had gotten broken. There is no testimony that the seller made any effort to water-test the windshield prior to the sale. Plaintiff drove the automobile for only a few days when the windshield leaked during the first rain. We can only conclude that the windshield was defective or improperly installed. This is sufficient to invoke the rule in the Juneau case, charging the seller with knowledge of defects which are "discoverable *804 in the exercise of ordinary case." Since only a short period of use by the buyer was time enough for the manifestation of the defect, constructive knowledge of the defective windshield is charged to the seller in the instant case. Hence, we find no manifest error in the jury's allowance of the stipulated attorney's fees.
Plaintiff has asked for an increase of the attorney's fees on appeal. We have read the entire record, including the transcript of the testimony, plaintiff's pleadings, and the brief filed in plaintiff's behalf on appeal. We feel that the stipulated attorney's fees compensates plaintiff's attorney adequately for the work he has done in this case.
We also find no manifest error in the jury's verdict dismissing third party demands against the manufacturer, General Motors Corporation. It is established by the evidence that the 1971 Chevrolet automobile did not have water leakage prior to the replacement of the windshield by the seller. The manufacturer had nothing to do with the replacement of the windshield. The automobile had been driven more than 7,000 miles as a demonstrator without any sign of water leakage prior to the replacement of the windshield. Although there was some testimony that some of the water leakage could have been caused by a leaky plenum chamber which was an integral part of the original manufactured product, the jury did not accept this version of the cause of the water leakage. The jury heard the witnesses and concluded that the water leakage was caused by a defective windshield. Consequently, the jury did not hold the manufacturer responsible. We have no reason to disagree with the jury's finding that the defect was a defective windshield rather than a defective plenum chamber. We have reviewed the evidence and it fails to show any latent defect in the manufacture of the automobile which would impose liability on the manufacturer. See Ingersoll v. Star Chrysler, Inc., supra; Gauche v. Ford Motor Company, supra; Rey v. Cuccia, supra; Breaux v. Winnebago Industries, Inc., supra.
For these reasons, the judgment in favor of plaintiff, Shirley Gadison Wade, and against defendant, McInnis-Peterson Chevrolet, Inc., is affirmed. Also, the judgment in favor of General Motors Corporation dismissing the third party demand of defendant is affirmed. Defendant to pay all costs.
Affirmed.
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Q:
GWT How to automatically refresh page every 5 minutes without clicking button for it?
I am trying to design the function in my GWT application to automatically refresh one of the pages every 5 minutes without clicking button before reloading.Most of the examples I have found in stackoverflow for this function are triggered after user click button or link. Like this example
I just want page to be automatically refreshed every 5 minutes.
A:
You can put this code anywhere you need it:
Timer timer = new Timer() {
public void run() {
Window.Location.reload();
}
};
timer.schedule(5 * 60 * 1000);
Remember to cancel this timer at some point - otherwise it will keep refreshing forever, even if a user simply left your app open in a some tab and forgot about it.
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Charming Wine Cellar Designs Concepts For Your Home
When it comes to custom wine cellar design and plans, there are no hard and fast rules and you can get as creative as you like. Some homeowners prefer more traditional styles with various wood finishes and a more robust and dark styling while others lean towards modernistic design concepts and want their wine cellar design to have clean and crisp lines. Regardless of the style and design concepts you like, you should focus on getting a custom wine cellar that will complement the design of the rest of your home.
Charming wine cellar design concepts
Modern day wine cellars could be installed in any area of a home where there is no direct sunlight and heat or vibrations. We at Signature Cellars work very closely with our clients to understand what their specific design preferences are and then provide cellar designs and plans that fit in with their likings and budget. Here we discuss some charming wine cellar design concepts for your home:
#1 The rustic look
There is something about a rustic design concept that lends itself very well to a wine cellar installation. You can have a long hardwood table with circular stone surrounds. The right effect can be created by installing recessed and ambient lighting using LED track lights and bulbs. You can enhance the rustic effect by using bare brick wall and unpolished wooden frame finishes. Somehow this look complements your vintages very well.
#2 The modern effect
Modern day wine cellars are temperature-controlled and they don’t necessarily have to be installed underground to keep them cool. We can design the most stunning wine cellars in any area of your home and it can become a statement piece that adds value to your property. For a contemporary wine cellar, we may use more glass and chrome finishes and then balance that out with cross-cut hardwood tiled flooring.
This effect lends warmth to the space without taking away from its modern feel in any way. Recessed spotlights can be placed strategically in the ceiling to provide mood effects as they dramatically light up the columns of fine wine bottles below. We may add some stone effects to enhance the overall aesthetic of the wine cellar design.
#3 Creating drama in your wine cellar
If you want something very unique with a touch of whimsy, you should consider using a very bold colour like rich red on the walls and then complement that with timber wine storage racks that are sanded and polished to perfection. If you like we can also add some custom-designed oak box shelves that will lend a more organised and grid-like look to your cellar. When darker wood species are used for the shelves and racks, it becomes the perfect way to frame the colourful wine bottle tops and create a multi-coloured and robust aesthetic.
#4 The minimalist style
If you prefer to stay away from the traditional and more solid or busy cellar design concepts and prefer a minimalistic style we can create a beautiful cellar with stainless steel racks and combine those with natural stone accented walls that will create a very minimalistic yet chic and elegant look in the space.
You can also add some eccentricity to your wine cellar design by incorporating wine crates into the space and include some artwork and sculptures in it. Custom stonework, arches and glow lights etc. can also be added to create a stunning look in the wine cellar.
For any more information on custom wine cellar design and installation, you can call Signature Cellars on 1300 570 636 or use this contact form to get in touch with us.
Thanks for reading,
Neil Smallman
Signature Cellars
1300 570 636 |
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C PARAMETER (IERRF=6, LUNIT=2, IWTYPE=11, IWKID=1) ! PDF
C PARAMETER (IERRF=6, LUNIT=2, IWTYPE=20, IWKID=1) ! PostScript
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END
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FIT Quote Free Weights & Studio Equipment.
FIT Quote will repair or replace any item (as per the above) that can be shown to have broken, provided the customer returns it to us for our inspection.
Rubber products are not intended for use on concrete floors, wood floors or especially hard rubber surfaces. Use of rubber covered free weights on these floors will void the warranty. It is highly recommended that the correct rubber free weight flooring is used (Easy-Lock Free Weights, Fitness, etc).
Chipping of painted finish on FIT Quote cast iron weight plates, cast iron dumbbells and Kettlebells is considered normal wear and tear and is not covered by the warranty. The Silver paint that highlights the weight identification on Olympic weight plates is considered a wear item and not covered by any warranty.
The warranty excludes the Neoprene covered surface on the Kettlebells and Studio Dumbbells.
Note: Rubber products should not be cleaned with detergent or acetone-based cleaners. Please clean rubber products with a damp cloth only.
Dumbbells and barbells (cast iron & rubber) should be hand checked for tightness on a daily basis and tightened as required. Loosening of multi disc dumbbells is not covered by warranty as this style of dumbbell requires maintenance.
FIT Quote dumbbells are designed for years of heavy use, however are not designed to be dropped, thrown or otherwise abused. Repeated misuse may result in bent handles, any dumbbells showing signs of bent handles may be excluded from warranty. Free weights should always be used on a suitable covered floor surface in order to minimise wear and tear. For recommendations and flooring solutions go to the flooring section of this brochure.
Free weights should be stored on or in suitable racking to avoid damage and reduce wear and tear. Most free weights are only suitable for indoor use but products such as the Powerbag can be used outdoors on non-abrasive surfaces.
Benches warranty - 12mths frame and parts, 6mths upholstery
Please Note:
Warranty extends to original purchaser only and is non-transferable. Warranty time is from the original date of purchase. Warranty shall not apply if the defect was caused by misuse, neglect, or normal wear and tear. In order to process warranty claim, item/s must be returned to FIT Quote for inspection along with a returns reference number provided by FIT Quote.
Warranty does not cover transport costs. In cases where it is not economic to return multiple items we will ask for a part return supported by photographic evidence. Home or light commercial use products used in a commercial environment will not be covered by the warranty. If your facility has no procedures/guidelines to control the misuse use of dumbbells, barbells and/or plates, FIT Quote would rather not accept the order.
Free weights go through probably the most extreme life of any fitness product, a correct maintenance program along with good exercise technique will prolong their life considerably. |
Infection with Cryptococcus neoformans var. gattii leading to a pulmonary cryptococcoma and meningitis.
A patient who lived in Ohio, U.S.A., developed a large pulmonary cryptococcoma and meningitis as the result of infection with Cryptococcus neoformans var. gattii, an organism of subtropical and tropical distribution. He had no obvious predisposing illness or condition associated with increased susceptibility to cryptococcosis. Although he was found to have cutaneous anergy, his lymphocytes showed significant transformation responses in vitro when cultured both with mitogens and with killed cryptococci. The meningitis responded to intrathecal amphotericin B. The cryptococcoma, however, did not resolve in response to vigorous antifungal therapy during a period of more than 4 months. Eventually, the cryptococcoma was surgically removed. This case is unusual both for the finding of C. neoformans var. gattii outside its apparent endemic area as well as for the clinical features of the disease. |
Terry Naturally®Tart Cherry capsules provide the benefits of tart cherries in the convenience of a capsule.
Tart cherries contain anthocyanins, richly colored flavonoid compounds with potent antioxidant capacity. Antioxidants increase the body’s resistance to oxidative stress, and anthocyanins in particular may play an important role in supporting healthy uric acid balance in the body.* |
Q:
How to read multiple NetCDF files from a folder in python
I am attempting to make a plot of mean temperatures of multiple years (1979-2014), the only problem I am having is attempting to read multiple NetCDF (.nc) files from a folder. At the moment my program will plot a single file, but I do not understand how to make it read all files in a folder (one for each year). I want to find the mean for all of the years. I left out the plot data, because that is fine, the only help I need is in looping through all files in a single folder
import numpy as np
from mpl_toolkits.basemap import Basemap
from netCDF4 import Dataset
import matplotlib.pyplot as plt
q=Dataset('/Users/marjoryrogers/Desktop/July_Temp/MERRA300.prod.assim.tavgM_2d_rad_Nx.201407.SUB-4.nc','r',format='NETCDF4')
q.variables
#jan_temp = q.variables['ts'] # units here, degrees
july_temp = q.variables['ts']
lats = q.variables['latitude']
lons = q.variables['longitude']
#jan_temp.shape
july_temp.shape
lats[:], lons[:]
#q=Dataset('Users/marjoryrogers/Desktop/Spring 2015/Hydroclimatology/MERRA301.prod.assim.tavgM_2d_rad_Nx.200805.SUB.nc', 'r', format='NETCDF4')
july_temp = q.variables['ts']
#jan_july = np.concatenate((may_temp, jun_temp), axis=0)
#jan_july.shape
#aver_temp = np.mean(jan_temp, axis=0)# average temperature
aver_temp2 = np.mean(july_temp, axis=0)
A:
The netcdf4-python library has a class that can read multiple netcdf files making variables that has a record dimension appear as a single big variable.
import netCDF4 as nc
# read multiple files (wildcard)
vn = nc.MFDataset('data_y*.nc')
# read multiple files (file list)
vn = nc.MFDataset(['data_y1997','data_y1998','data_y1999'])
# Variable from multiple files.
airv = vn.variables['ts']
|
For your information, many people searching for information related to Koa Kampgrounds Hayward Wisconsin make the mistake of searching with spelling mistakes for words and phrases such as Damp, Otdoors, Campp, Camping Equipm3nt or even Campinng Recipes.
Damp and soggy where it was not sharp and rocky, buffeted by storm winds and lashed by the sea, with the air continually a-tremble with the bellowing of two hundred thousand amphibians, it was a melancholy and miserable sojourning-place.
All over Washington this week were the thrilling sounds of democracy at work -- the speeches of incoming and outgoing officials, the emotional swearing in ceremonies, the weeping of Boehner the Damp, the solid crack of the gavel being brought down and, less thrillingly, the peep-peep of a chicken as the Obama White House reversed itself on end-of-life counseling. |
Greece say fair play saved Romania from World Cup forfeit
ATHENS (Reuters) - An act of sportsmanship by Greece coach Fernando Santos and team director Takis Fyssas saved Romania from the possibility of a forfeited 3-0 defeat in the first leg of their World Cup playoff last week, they claimed on Thursday.
The Greeks said they alerted Romanian officials before the game in Athens after they named only two goalkeepers because first choice Ciprian Tatarusanu was injured and not included in the squad list.
Under FIFA rules, any 23-man squad for an official game must include three goalkeepers. The oversight was missed by FIFA officials at the time.
Greece won the game 3-1 at the Karaiskakis Stadium and clinched their place in the finals after drawing 1-1 in the second leg on Tuesday.
“With so much at stake - participation in a World Cup and the financial gains for the Greek FA which comes with that — we could have ignored their error and taken the result, but it was important to do the right thing,” Fysass told Greek radio SportFM.
“I preferred to qualify on the pitch rather than on paper.”
Bogdan Lobont started in goal with Costel Pantilimon on the bench in the first leg last Friday with the Romanians adding an outfield player as the third keeper to keep within the rules.
Romanian FA spokesman Paul Zaharia declined to comment on the claims made by Greece but told Reuters by email: “The Romanian match sheet has been done according to the Laws of the Game and to the competition’s regulations.
“A goalkeeper can be fielded as an outfield player and so an outfield player can be fielded as a goalkeeper, if the coach decided like this.
“Our match sheet had 23 players, three of them being goalkeepers and one of those three was an outfield player, so that everything was done due to all the rules and regulations.”
Fysass’s faith in his Greece team was justified with two goals from Konstantinos Mitroglou and one from Dimitrios Salpingidis helping them to victory in Athens. A draw in Bucharest saw Greece reach next year’s finals 4-2 on aggregate.
Tatarusanu returned for the second leg with Lobont and Pantilimon named among the substitutes. |
Q:
How to get the String of a XML node in C#
enter code herein the XML document :
<foo>
<bar><para> test </para> </bar>
<bar>text</bar>
<bar>stackoverflow</bar>
</foo>
I am trying to parse it and only get the Strings in bar; by using this way:
[function where node is the foo]
foreach (XmlNode subNode in node.ChildNodes)
{
if (subNode.Name == "bar")
{
if (!String.IsNullOrWhiteSpace(subNode.InnerText))
Debug.WriteLine(subNode.Name + " - " subNode.InnerText);
}
}
However it gives me test
Thanks
A:
This is what you are looking for (EDITTED based on you updated question)
XDocument doc = XDocument.Load(path to your xml file);
XNamespace ns = "http://docbook.org/ns/docbook";
var result = doc.Root.Descendants(ns + "para")
.Where(x => x.FirstNode.NodeType == System.Xml.XmlNodeType.Text)
.Select(x => x.Value)
.ToList();
In your updated xml I see you are using a namespace so the name of your node is not para but it's theNameSpace + "para". The namespace is defined in the first line of your xml file. Also you can see this sample too.
|
The act of defiance came one day after Supreme Court Justice Sonia Sotomayor denied Hobby Lobby’s emergency request to block enforcement of the mandate, but said the company may continue its appeal in lower courts.
Hobby Lobby is a national arts and crafts chain. They own more than 500 stores in 41 states.
The company is owned by the Green family, devout, evangelical Christians. They believe “it is by God’s grace and provision that Hobby Lobby has endured” and they seek to honor God by operating their company in a manner consistent with Biblical principles.”
The family believes the Obamacare mandate to provide the morning-after and week-after pills is a violation of their religious convictions.
“To remain true to their faith, it is not their intention as a company, to pay for abortion-inducing drugs,” Becket Fund attorney Kyle Duncan wrote in a statement.
Duncan said the company would continue to provide health insurance for its employees while they fight the government in court.
But on Jan. 1, Hobby Lobby will face a $1.3 million daily fine if they don’t comply with Obamacare.
“The Green family respects the religious convictions of all Americans, including those who do not agree with them,” the Becket Fund said in a statement. “All they are asking is for the government to give them the same respect by not forcing them to violate their religious beliefs.”
There are now 42 separate lawsuits changing the mandate, the Becket Fund said.
The Green Family
Conservatives praised Hobby Lobby for standing by their convictions.
“God bless this company,” columnist Michelle Malkin told Fox News. “It’s incumbent upon every conservative who believes in freedom of religion and freedom of conscience to support those businesses that are standing up and taking the slings and arrows of this discriminatory administration.”
“This is the most egregious violation of religious liberty that I have ever seen,” wrote columnist Denny Burk. “The first line of the Bill of Rights says this: ‘Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof.’ Obamacare prohibits the free exercise of the owners of Hobby Lobby. Who’s next?”
Conservative talk radio host Laura Ingraham said President Obama “must step in to stop this madness.”
“It turns out as many feared, the president’s religious exemption to the contraception mandate is so narrow as to be meaningless,” she said on Fox News. “Unless you employ and serve only those of your same religious faith you don’t receive an exemption. So under that standard, Jesus himself would not qualify. This is unconscionable and unconstitutional.”
Abortion supporters hailed Sotomayor’s ruling.
“I hope the government earmarks every cent of that fee money for Planned Parenthood, just to spite these ass****,” wrote one reader on the Jezebel website.
“Anyway, I’m all for Hobby Lobby (and all other organizations that think birth control is totes gross) ignoring the law,” wrote Erin Gloria Ryan in a column titled, “Whore Pill-Hating Hobby Lobby Will Have to Pay a Buttload of Fines for Ignoring Obamacare.”
The website Think Progress said Hobby Lobby is ignoring two points.
“First, that Plan B is not an abortion-inducing drug, as Hobby Lobby claims, and second, that the company may well end up paying more to avoid covering contraception than they would simply providing access,” the website reported. “It also takes a twisted view on the ‘Freedom of Religion’ argument; the company is actually forcing its owner’s religious beliefs on all employees, no matter their personal religious views.”
Ingraham pointed out that in a previous case Sotomayor ruled in favor of a Muslim inmate who was denied Ramadan meals. She held that the meal was subjectively important to the inmate’s practice of Islam. |
export { default as Breadcrumb } from "./components/Breadcrumb";
export { default as MatxMenu } from "./components/MatxMenu";
export { default as MatxToolbarMenu } from "./components/MatxToolbarMenu";
export { default as MatxLoading } from "./components/MatxLoading/MatxLoading";
export { default as MatxSuspense } from "./components/MatxSuspense/MatxSuspense";
export { default as MatxSearchBox } from "./components/MatxSearchBox";
export { default as MatxVerticalNav } from "./components/MatxVerticalNav/MatxVerticalNav";
export { default as MatxVerticalNavExpansionPanel } from "./components/MatxVerticalNav/MatxVerticalNavExpansionPanel";
export { default as MatxHorizontalNav } from "./components/MatxHorizontalNav/MatxHorizontalNav";
export { default as MatxSidenavContainer } from "./components/MatxSidenav/MatxSidenavContainer";
export { default as MatxSidenav } from "./components/MatxSidenav/MatxSidenav";
export { default as MatxSidenavContent } from "./components/MatxSidenav/MatxSidenavContent";
export { default as RectangleAvatar } from "./components/RectangleAvatar";
export { default as MatxListItem1 } from "./components/MatxListItem1";
export { default as MatxSnackbar } from "./components/MatxSnackbar";
export { EchartTheme } from "./theme/EchartTheme";
export { default as EchartCreator } from "./components/charts/EchartCreator";
export { default as RechartCreator } from "./components/charts/RechartCreator";
export { default as RichTextEditor } from "./components/RichTextEditor";
export { default as ConfirmationDialog } from "./components/ConfirmationDialog";
export { default as MatxProgressBar } from "./components/MatxProgressBar";
export { default as SimpleCard } from "./components/cards/SimpleCard"; |
// These tests can't be parsed on non-nightly compilers, so move them to a
// separate file.
use crate::{ops::GeneratorState, stack::let_gen_using};
#[test]
fn async_closure() {
let_gen_using!(gen, async move |co| {
co.yield_(10).await;
"done"
});
assert_eq!(gen.resume(), GeneratorState::Yielded(10));
assert_eq!(gen.resume(), GeneratorState::Complete("done"));
}
|
Q:
How to interpret confusion matrix in R
I am working with a confusion matrix and have a very basic understanding of the output. However, as I am new to using this, and R, the details explainations often make it sound more complicated. I have the below output and I am just wondering if it could be explained to me
What are the TP's, TN's, FP's & FN's in the Matrix?
What does the kappa represent?
Whats the difference between the accuracy & kappa?
> confusionMatrix(predRF, loanTest2$grade)
Confusion Matrix and Statistics
Reference
Prediction A B C D E F G
A 2298 174 63 29 26 12 3
B 264 3245 301 65 16 3 3
C 5 193 2958 399 61 15 4
D 1 1 39 1074 236 33 6
E 0 0 2 32 249 97 30
F 0 0 0 0 8 21 11
G 0 0 0 0 0 0 0
Overall Statistics
Accuracy : 0.822
95% CI : (0.815, 0.8288)
No Information Rate : 0.3017
P-Value [Acc > NIR] : < 2.2e-16
Kappa: 0.7635
Class: A Class: B Class: C Class: D Class: E Class: F Class: G
Sensitivity 0.8949 0.8981 0.8796 0.67167 0.41779 0.116022 0.000000
Specificity 0.9674 0.9220 0.9214 0.96955 0.98585 0.998389 1.000000
Pos Pred Value 0.8821 0.8327 0.8138 0.77266 0.60732 0.525000 NaN
Neg Pred Value 0.9712 0.9545 0.9515 0.95041 0.97000 0.986596 0.995241
Prevalence 0.2144 0.3017 0.2808 0.13351 0.04976 0.015112 0.004759
Detection Rate 0.1919 0.2709 0.2470 0.08967 0.02079 0.001753 0.000000
Detection Prevalence 0.2175 0.3254 0.3035 0.11606 0.03423 0.003340 0.000000
Balanced Accuracy 0.9311 0.9101 0.9005 0.82061 0.70182 0.557206 0.500000
A:
Let's say this is your confusion matrix:
tab = structure(list(A = c(2298L, 264L, 5L, 1L, 0L, 0L, 0L), B = c(174L,
3245L, 193L, 1L, 0L, 0L, 0L), C = c(63L, 301L, 2958L, 39L, 2L,
0L, 0L), D = c(29L, 65L, 399L, 1074L, 32L, 0L, 0L), E = c(26L,
16L, 61L, 236L, 249L, 8L, 0L), F = c(12L, 3L, 15L, 33L, 97L,
21L, 0L), G = c(3L, 3L, 4L, 6L, 30L, 11L, 0L)), class = "data.frame", row.names = c("A",
"B", "C", "D", "E", "F", "G"))
What are the TP's, TN's, FP's & FN's in the Matrix?
You need to go by each label, for example for class A, those terms make sense in terms of predictions with respect to A.
A_confusion_matrix = cbind(c(x[1,1],sum(x[-1,1])),c(sum(x[1,-1]),sum(x[2:7,2:7])))
[,1] [,2]
[1,] 2298 307
[2,] 270 9102
How the above is calculated is basically lumping all the predictions and references are incorrect and not A together.
And these numbers represent:
A_confusion_matrix[1,1] is number that are predicted A and truly A ->
TP
A_confusion_matrix[1,2] is the number that are predicted A but not A
-> FP
A_confusion_matrix[2,1] is the number that are not predicted A but A
-> FN
A_confusion_matrix[2,2] is the number that are not predicted A and not
A -> TN
From here you can for example calculate sensitivity for A, which is TP/(TP+FN) = 2298/(2298+270) = 0.8948598
What does the kappa represent?
It is cohen's kappa, basically a metric that measures how good your predictions are compared to random guessing / assignment.
Whats the difference between the accuracy & kappa?
As you can see from the above formula, it makes a huge difference when your dataset is imbalanced. For example, if 90% of your labels are one class, if the model predicts everything to be that class you get 90% Accuracy. However if you use cohen's kappa, p expected is 0.9 to start with and you need to go better than that to show a good score.
|
When using a touch screen terminal device to browse a webpage or a text, a user may select a portion of text information for copying or searching.
When needing to select the text information on the webpage, the user may perform a long-press operation on the webpage. When detecting the long-press operation of the user, the touch screen terminal device displays a text selection component including a front select box and a rear select box. The user selects text information between the front select box and the rear select box by dragging the front select box and/or the rear select box. |
Molecular cloning, expression, biochemical characteristics, and biomarker potential of theta class glutathione S-transferase (GST-T) from the polychaete Neanthes succinea.
We cloned and sequenced the full-length cDNA of a theta class glutathione S-transferase (GST-T) from the polychaete Neanthes succinea. The open reading frame of N. succinea GST-T cDNA was 678bp and encoded 226 amino acid residues. We generated recombinant N. succinea GST-T by expression in transformed Escherichia coli and studied the kinetic properties as well as the effects of inhibitors, pH, and temperature on N. succinea GST-T. GST-T expression was studied using real-time RT-PCR in response to exposure to the model oxidative stress-inducing agent, CuCl(2). Copper induced a concentration-dependant increase in the expression of GST-T. Moreover, polychaetes collected from a heavily contaminated lake near an industrial complex showed significantly higher levels of GST-T expression. Interestingly, the site-collected polychaetes with the highest GST-T mRNA expression levels also showed the highest metallothioneins levels. These results suggest that GST-T in polychaetes may have an antioxidant role and that N. succinea GST-T expression may be a useful biomarker for exposure to environmental contaminants such as copper. Our findings provide a better understanding of the biochemical characteristics of N. succinea GST-T, and elucidate the potential role of GST-T in heavy metal-induced oxidative stress and as a biomarker for environmental contamination. |
Henrietta Washington waited for hours inside a white SUV parked just across the street from the brick walls, eyes fixed on a single brown door.
She’d already waited 25 years.
Her son, Sean Washington, and another man, Kevin Baker, were set to come out a back door at New Jersey State Prison in Trenton any minute after an appeals court threw out their convictions for a 1995 double murder in Camden, finding new evidence obliterated the testimony of the lone eyewitness.
“You know when you want to be excited about something?” said the woman known to many in Camden simply as Mama Hank. “But you feel as if something’s gonna go —”
She paused.
“You know that hallway is just across the street, but then you’re standing here and you’re thinking how he could get hit (by a car) coming across the street?”
Her eyes welled. She wore her favorite color for comfort. A purple sweatsuit and purple ball cap. Purple nails and a purple walking cane. Only her black shoes and a light blue puffy vest to keep out the cold lacked for purple.
“Twenty-five years,” she said with a sigh. “I can wait a little more.’”
Baker and Washington, both now 48, were convicted at a two-day trial in 1996 in what the prosecutor at the time described as a “one-witness case.” There was no motive. Police never recovered any guns.
A local woman, Denise Rand, was hazy on the details but told jurors she saw the two men run up to a man and woman standing in a courtyard, Rodney Turner and Margaret Wilson, and shoot them in the head before running off into the night at the city’s Roosevelt Manor apartment complex.
Their case was the subject of a two-part NJ Advance Media series in 2015 that chronicled the efforts of the Last Resort Exoneration Project, a legal group devoted to investigating wrongful conviction cases at Seton Hall University School of Law in Newark, which commissioned ballistics testing and uncovered forensic evidence undermining Rand’s version of events.
Just a day after Christmas 2019, a three-judge appellate panel ruled the new evidence “probably would have changed the jury’s verdict.” Prosecutors formally dropped the charges in February.
Authorities at the Camden County Prosecutor’s Office and the state Attorney General’s Office, whose conviction review unit briefly examined the matter after the appellate ruling, repeatedly declined to discuss the case on the record. In a statement, Camden prosecutors defended the convictions, saying their office disagreed with the appeals court but “respects the decision.”
Baker and Washington had hoped to be formally cleared in front of a judge in a Camden courtroom, where they had been given life sentences, but after fighting with prosecutors over terms, they instead would be quietly released out a back door of the prison just like any other inmate who maxed out their sentence or was granted parole.
State corrections officials refused to tell their families, or even their lawyers, when, exactly, they’d be let go, so a group of supporters stood vigil for more than eight hours, staring at the aging barbed wire and turrets of the maximum-security prison, eyes alighting every time the door opened for a shift change or medical transport.
The group grew restless and grumbled among themselves until a car horn alerted them to that brown door. Out walked Baker and Washington in prison-issued street clothes: white sneakers, loose-fitting jeans and baggy white button-down shirts.
“Finally, finally!” Baker shouted as he embraced one of his attorneys, Lesley Risinger.
“Yes sir, yes sir!” Washington replied, wrapping his mother in his arms.
Lesley and Michael Risinger, the husband and wife legal team that marshaled most of the evidence leading to their freedom, gave them sweatshirts and ball caps from Seton Hall Law School.
“No matter who you asked, no matter how hard you looked, you couldn’t find anything that did anything but corroborate what they were saying,” Lesley Risinger said at an impromptu news conference in the middle of a Trenton side street when asked why they took up the pair’s case nearly a decade ago.
Kevin Baker, left, and Sean Washington leave prison as free men Wednesday after 25 years behind bars for a double murder they say they didn't commit. Michael Mancuso | NJ Advance Media for NJ.com
A 25-year legal battle
Both men have long maintained that neither pulled the trigger.
Baker claims he was nowhere near the scene. Washington says he was the person who found the bodies while out trying to return a call to his pager — it was 1995, after all. He then called 911.
Baker and Washington had criminal records that included charges of drug crimes and violence, and Washington had earlier been charged with two other murders. He was acquitted in one murder case, and the other was dropped. Only the Roosevelt Manor charges stuck.
Their defense attorneys at the time told Baker and Washington not to take the stand to present their alibis, citing the state’s weak case against them. They later testified they did not adequately investigate their cases.
The Risingers took on Baker’s case in 2011. They say authorities, under pressure to solve cases amid spiraling violence in the mid-1990s, pegged Washington as the killer based on “street rumors” and, believing from an initial forensic report that there were two shooters, plucked Baker from a stack of mugshots seemingly “at random.”
Henrietta Washington put it more bluntly.
“They just wanted to put some black people in jail, and they just picked my son and his friend,” she said, again fighting tears. “I hope that never happens to nobody else’s child.”
In a written statement, acting Camden Prosecutor Jill Mayer noted that the office had successfully defended the convictions for decades in state and federal court before the appellate ruling.
In deciding to not to retry the men, Mayer said, authorities “considered the totality of the circumstances, including the passage of time and the impact it would have on retrying the defendants and proving the case beyond a reasonable doubt.
“Considering our mandate to pursue the interests of justice at all times, retrial after this length of time is not feasible in this particular case.”
Baker and Washington say they are not bitter. Washington said he believes his ordeal was “part of God’s plan” for him. But they both think the true story of what went sideways in their case needs to be told.
“This is heartwarming and all, but we did 25 years already, we did time for the crime really,” he said. “The story is what really went on. And that case should be exposed for what it was.”
“Ignorance gets a lot of us in prison and knowledge gets a lot of us out,” said Washington, who studied the law behind bars and became a prison paralegal. “The system, it needs to be revamped.”
Sean Washington greets family and friends Wednesday outside prison. Michael Mancuso | NJ Advance Media for NJ.com
‘Exonerated,’ but not yet ‘innocent’
A few dozen people welcomed Baker and Washington home Wednesday night at a party held at the Dare Academy, a Camden community center at the site of a former school run by Anthony Ways.
Ways has something in common.
He spent 13 years in prison for a 1989 murder, serving a life sentence that overlapped with Baker’s and Washington’s, before he was exonerated in 2005.
As friends and family shared pizza — the only thing the pair requested for their first meal outside — Baker and Washington were peppered with the same questions: How do you feel? What are you thinking? What are you going to do next?
Ways has been there.
“To be out, you’re almost wondering, ‘Is this real or not?'” he said.
Ways, who along with other members of the Camden community is helping secure housing and jobs for Baker and Washington, said for now, they need to “just chill, don’t do nothing, just get back the rhythm of society.”
It will be an adjustment for the pair, who had limited access to the internet behind bars but were locked up more than a decade before the iPhone came to market.
At the men’s welcome party, Baker’s cousin held up a phone so he could video chat with an old friend. But the man on the other end was having technical difficulties.
“You know I don’t know how to work it,” Baker said with a laugh.
As they adjust to life outside, they also face a potential court battle to clear their names — and get paid for their time.
Under state law, they could be entitled to $50,000 for each year they spent locked up, which would mean more than $1 million apiece. But to get it, they have to sue the state Treasury and — unless the state settles — demonstrate in a civil court “by clear and convincing evidence” that they are innocent.
In her statement, Mayer, the Camden prosecutor, noted the appeals court that threw out their convictions “did not declare Baker and Washington ‘actually innocent.’”
“Actual innocence” is a novel legal standard recognized by criminal courts in several states, including New York and Texas, that essentially acknowledges if a prisoner can demonstrate they didn’t commit the crime, judges should cast aside procedural barriers or technicalities and set them free.
Attorneys for Baker and Washington made an actual innocence argument in their case, but the appeals panel did not address the claim, which has not been recognized by a New Jersey criminal court, saying it was a question for the state Supreme Court.
“It’s not like there’s a mechanism in New Jersey for (a criminal court) to say, ‘We think this person is innocent,'” said Barbara O’Brien, editor of the Exoneration Registry, the most reliable national tracker of wrongful conviction cases.
O’Brien’s group uses the term “exonerated” for cases like Baker and Washington, where new evidence and other substantial proof led to overturned convictions, because in most jurisdictions, there is no way to “prove” innocence.
Asked whether they believed Baker and Washington to be “actually guilty,” a spokesman for the Attorney General’s Office, which installed Mayer as acting prosecutor after her predecessor retired, declined to comment.
A spokeswoman for Mayer, who declined to be interviewed, said “it is not appropriate for us to weigh in on the guilt or innocence of a defendant.”
The civil case could drag on for years.
The last two men to be exonerated for murder in New Jersey, Eric Kelley and Ralph Lee, were released in November 2017. They have yet to get paid, court records show.
As for their futures, Baker — who worked as a porter in the prison infirmary, helping sick and elderly inmates — says he’s keeping his options open, but whatever it is, he wants to help people.
Washington, who became a prolific jailhouse lawyer, is considering a legal career.
“I worked on other guys’ cases that were innocent, and they need help, too,” he said.
S.P. Sullivan may be reached at ssullivan@njadvancemedia.com. Follow him on Twitter. Find NJ.com on Facebook. |
double precision function ddot(n,dx,incx,dy,incy)
c
c forms the dot product of two vectors.
c uses unrolled loops for increments equal to one.
c jack dongarra, linpack, 3/11/78.
c modified 12/3/93, array(1) declarations changed to array(*)
c
double precision dx(*),dy(*),dtemp
integer i,incx,incy,ix,iy,m,mp1,n
c
ddot = 0.0d0
dtemp = 0.0d0
if(n.le.0)return
if(incx.eq.1.and.incy.eq.1)go to 20
c
c code for unequal increments or equal increments
c not equal to 1
c
ix = 1
iy = 1
if(incx.lt.0)ix = (-n+1)*incx + 1
if(incy.lt.0)iy = (-n+1)*incy + 1
do 10 i = 1,n
dtemp = dtemp + dx(ix)*dy(iy)
ix = ix + incx
iy = iy + incy
10 continue
ddot = dtemp
return
c
c code for both increments equal to 1
c
c
c clean-up loop
c
20 m = mod(n,5)
if( m .eq. 0 ) go to 40
do 30 i = 1,m
dtemp = dtemp + dx(i)*dy(i)
30 continue
if( n .lt. 5 ) go to 60
40 mp1 = m + 1
do 50 i = mp1,n,5
dtemp = dtemp + dx(i)*dy(i) + dx(i + 1)*dy(i + 1) +
* dx(i + 2)*dy(i + 2) + dx(i + 3)*dy(i + 3) + dx(i + 4)*dy(i + 4)
50 continue
60 ddot = dtemp
return
end
|
Karl Henry at 250
If WW sites are full of rumours of whom Mick McCarthy is keen on poaching from us, one of the persons named, Karl Henry, will certainly not be heading to East Anglia. Karl celebrates his 250th. game in the Old Gold colours today and, if our manager is to be believed, he will be making many more appearances for us in the future.
As he states, "Karl is a leader figure as a captain and has been here in the good times and the bad times". Some might argue that Henry`s rashness has occasionally contributed towards the bad times but there is no doubting his commitment to the club and the positive benefits he brings to the side.
Sure, he can be a little reckless and, sure, he is not a midfield playmaker but teams like ours need an enforcer like Karl if they are not to be overrun in the middle of the pitch. When he is absent, we suffer ... especially our back four. If I do not completely agree with Stale when he claims that Henry "... has good technique and can pass the ball", occasionally he does surprise us with a great through pass: just like the one he launched at SEB in the Birmingham game which directly led to the goal.
Many of us, perhaps feeling exasperated with another Henry sending off or an off-cue pass, thought that Davis would have replaced Henry in the team by now. He certainly is a more accomplished all-round midfielder and in the long term he will be able to replicate those aspects of the game which Henry does so well. But not yet.
Even so, I hope to see the learning process continue today with the two of them them working in tandem against Peterborough. Davis helped to strengthen our midfield against Blackpool last Saturday after Doumbia faded badly. Moreover, we will need to be strong in this area of the game this afternoon because Peterborough are on a roll after back-to-back wins. In Dwight Gayle they have unearthed a gem of a striker.
Because of Henry`s whole-hearted commitment to the cause and the vital contribution that he makes to the team, he is the obvious captain. Perhaps, one reason for our poor performance last season was the players` reaction to his demotion and the foisting on them of the abrasive Johnson. Both are playing better this season now that Henry is back in charge.
I expect a fast, open game this afternoon with Wolves emerging winners by three goals to two, if Henry plays his normal game ... but thinks before diving in. |
Jean Beliveau, a star for hockey's Montreal Canadiens who won 10 Stanley Cups as a player, dies at 83
Jean Beliveau, whose regal bearing and scoring prowess made him a symbol of the Montreal Canadiens and their long-gone days of hockey greatness, died Tuesday in Montreal, the club confirmed on its Twitter feed. Beliveau was 83 and had suffered a variety of health problems the last few years, including a stroke in 2012 and pneumonia earlier this year.
At 6 feet 3, Beliveau was considered a giant when he made his National Hockey League debut in the 1950-51 season, but he soon stood out as a physical but stately presence in a rugged sport. A 10-time all-star at center, he scored 507 regular-season goals to rank third in NHL history at the time of his retirement. He was twice voted the league's most valuable player during the season and once during the playoffs.
He won the Stanley Cup 10 times as a player, the last five as captain of the sport's most successful team and a cultural icon in heavily French-speaking Quebec. He was the Canadiens' captain for 10 years.
Beliveau retired after the Canadiens defeated the Chicago Blackhawks in a memorable, seven-game final series in 1971 and was inducted into the Hockey Hall of Fame the following year. He continued his extensive charity work and was appointed a vice president of the Canadiens, getting his name engraved on the Cup seven more times. He relinquished his duties in 1993 but continued to serve as a revered team ambassador.
"I guess you could say I've spent my life with this team," he told Canada's Globe and Mail newspaper in 2009. "There are a lot of people who still see the Canadiens as a representation of themselves and the fans invest their emotions and identities, especially when it's going well."
Notable Deaths
Photos of leaders, stars and other notable figures who died in 2014.
Born Aug. 31, 1931, in Trois Rivieres in the province of Quebec, Beliveau started skating on a sheet of ice in his backyard when he was 3 or 4 years old. His father, Arthur, worked for the local power company. His mother, Laurette, installed linoleum on the kitchen floor so Jean and his siblings could keep their skates on when they came indoors for lunch.
The Canadiens noticed him when he was a young teenager and tried to sign him but his father balked. Young Beliveau went to play junior hockey in Quebec City and stayed there in the senior amateur ranks until Canadiens executive Frank Selke had the idea of buying the league and turning it into a professional operation, which allowed him to secure Beliveau's playing rights.
I think me and my contemporaries sowed a lot of seeds and other people are reaping the harvest today.— Jean Beliveau
Beliveau signed a five-year contract for the then-exorbitant amount of $100,000. He faced enormous pressure but didn't become a regular in the Canadiens' lineup until the 1954-55 season, when he scored 37 goals and 73 points in 70 games. He won his only scoring title in the 1955-56 season and added 12 goals and 19 points in 10 playoff games to lead the Canadiens to the first of five consecutive championships, a record that might never be broken.
In today's game a player of his ability would earn multimillion-dollar paychecks, but Beliveau never begrudged the riches earned by those who followed. He became a mentor to many of Montreal's young players, including superstar Guy Lafleur.
"I think me and my contemporaries sowed a lot of seeds and other people are reaping the harvest today," he told the Globe and Mail in 1993. "I'm happy to see these kids do well, but I always hope they will remember their responsibilities to the fans."
A popular figure at golf tournaments, old timers' games and other events, Beliveau was renowned for his charitable works and raised millions of dollars for children's causes. When he closed his charitable foundation in 1993 he gave $900,000 to the Quebec Crippled Children's Assn. on the condition that all the money would go to a summer camp and not for salaries or administrative costs.
Beliveau was occasionally approached about taking on a public office but never did so. He turned down a chance to become Canada's governor general because he and his wife, Elise, were helping raise their granddaughters after the suicide of his son-in-law.
He is survived by Elise, his wife of 61 years; their daughter, Helene, and granddaughters Mylene and Magalie. |
---
address: 'Centre for Mathematical Sciences, University of Lund, Box 118, SE-221 00 Lund, Sweden'
author:
- '[<span style="font-variant:small-caps;">N</span>ils Dencker]{}'
date: 'February 25, 2010'
title: |
On the solvability of systems of\
pseudodifferential operators
---
20 pt
Introduction {#intro}
============
In this paper we shall study the question of local solvability for square systems of classical pseudodifferential operators $P \in {\Psi}^m_{cl}(M)$ on a $C^\infty$ manifold $M$. We shall only consider operators acting on distributions ${\mathcal}D'(M, {\mathbf C}^N)$ with values in ${\mathbf C}^N$ but since the results are local and invariant under base changes, they immediately carry over to operators on sections of vector bundles. We shall assume that the symbol of $P$ is an asymptotic sum of homogeneous $N \times N$ matrices, with homogeneous principal symbol $p = {\sigma}(P)$. We shall also assume that $P$ is of principal type, so that the principal symbol vanishes of first order on the kernel, see Definition \[princtype\].
Local solvability for a $N \times N$ system $P$ at a compact set $K \subseteq M$ means that the equation $$\label{locsolv}
Pu = v$$ has a local weak solution $u \in {\mathcal}D'(M, {\mathbf C}^N)$ in a neighborhood of $K$ for all $v\in C^\infty(M, {\mathbf C}^N)$ in a subset of finite codimension. We say that $P$ is microlocally solvable at a compactly based cone $K \subset T^*M$ if there exists an integer $N$ such that for every $f \in H_{(N)}^{loc}(M, {\mathbf C}^N)$ there exists $u \in {\mathcal}D'(M, {\mathbf C}^N)$ so that $K \bigcap
{\operatorname{WF}}(Pu-f) = \emptyset$, see [@ho:yellow Definition 26.4.3]. Here $H_{(s)}$ is the usual $L^2$ Sobolev space and $ H_{(s)}^{loc}$ is the localized Sobolev space, i.e., those $f \in {\mathcal}D'$ such that ${\phi}f \in H_{(s)}$ for any ${\phi} \in C^\infty_0$.
Hans Lewy’s famous counterexample [@lewy] from 1957 showed that not all smooth linear differential operators are solvable. It was conjectured by Nirenberg and Treves [@nt] in 1970 that local solvability for principal type [*scalar*]{} pseudodifferential operators is equivalent to condition (${\Psi}$) on the principal symbol $p$, which means that $$\begin{gathered}
\label{psicond} \text{${\operatorname{Im}}(ap)$
does not change sign from $-$ to $+$}\\
\text{along the oriented
bicharacteristics of ${\operatorname{Re}}(ap)$}\end{gathered}$$ for any $0 \ne a \in C^\infty(T^*M)$. Recall that the operator is of principal type if $dp \ne 0$ when $p=0$, and the oriented bicharacteristics are the positive flow-outs of the Hamilton vector field $$H_{{\operatorname{Re}}(ap)} = \sum_j \partial_{{\xi}_j}{\operatorname{Re}}(ap) \partial_{x_j} -
\partial_{x_j} {\operatorname{Re}}(ap) \partial_{{\xi}_j}$$ on ${\operatorname{Re}}(ap) =0$ (also called the semibicharacteristics of $p$). Condition is obviously invariant under symplectic changes of coordinates and multiplication with non-vanishing factors. Thus the condition is invariant under conjugation of $P$ with elliptic Fourier integral operators. It actually suffices to check the condition with some $0 \ne a \in C^\infty$ such that $ d({\operatorname{Re}}ap) \ne
0$, see [@ho:yellow Lemma 26.4.10]. Recall that $p$ satisfies condition (${\overline}{\Psi}$) if ${\overline}p$ satisfies condition (${\Psi}$), and that $p$ satisfies condition ($P$) if there are no sign changes on the semibicharacteristics, that is, $p$ satisfies both condition (${\Psi}$) and (${\overline}{\Psi}$).
The necessity of (${\Psi}$) for local solvability of scalar pseudodifferential operators was proved by Moyer [@mo:solv] in 1978 for the two dimensional case, and by Hörmander [@ho:suff] in 1981 for the general case. The sufficiency of condition (${\Psi}$) for solvability of scalar pseudodifferential operators in two dimensions was proved by Lerner [@ln:2d] in 1988. The Nirenberg-Treves conjecture was finally proved by the author [@de:NT], giving solvability with a loss of two derivatives (compared with the elliptic case). This has been improved to a loss of arbitrarily more than $3/2$ derivatives by the author [@de:pisa], and to a loss of exactly $3/2$ by Lerner [@ln:cutloss]. Observe that there only exist counterexamples showing a loss of $1 + {\varepsilon}$ derivatives for arbitrarily small ${\varepsilon} > 0$, see Lerner [@ln:ex].
For partial differential operators, condition (${\Psi}$) is equivalent to condition ($P$). The sufficiency of ($P$) for local solvability of scalar partial differential operators with a loss of one derivative was proved in 1973 by Beals and Fefferman [@bf], introducing the Beals-Fefferman calculus. In the case of operators which are [*not*]{} of principal type, conditions corresponding to (${\Psi}$) are neither necessary nor sufficient for local solvability, see [@CPT].
For systems there is no corresponding conjecture for solvability. By looking at diagonal systems, one finds that condition (${\Psi}$) for the eigenvalues of the principal symbol is necessary for solvability. But when the principal symbol is not diagonalizable, condition (${\Psi}$) is not sufficient, see Example \[popex\] below. It is not even known if condition (${\Psi}$) is sufficient in the case when the principal symbol is $C^\infty$ diagonalizable. We shall consider the case of when the principal symbol has constant characteristics, then the eigenvalue close to the origin has constant multiplicity, see Definition \[constchar\]. In that case, the eigenvalue is a $C^\infty$ function and condition (${\Psi}$) on the eigenvalues is well-defined. The main result of the paper is that classical square systems of pseudodifferential operators of principal type having constant characteristics are solvable (with a loss of $3/2$ derivatives) if and only if the eigenvalues of the principal symbol satisfies condition (${\Psi}$), see Theorem \[mainthm\].
Statement of results {#statement}
====================
We say that the system $P \in {\Psi}^m_{cl}$ is [*classical*]{} if the symbol of $P$ is an asymptotic sum $P_m + P_{m-1} + \dots $ where $P_j(x,{\xi})$ is homogeneous of degree $j$ in ${\xi}$, here $P_m$ is called the [*principal symbol*]{} of $P$. Recall that the eigenvalues of the principal symbol are the solutions to the characteristic equation $$|P_m(x,{\xi}) - {\lambda}{\operatorname{Id}}_N| = 0$$ where $|A|$ is the determinant of the matrix. In the following, we shall denote by ${\operatorname{Ker}}A$ the kernel and ${\operatorname{Ran}}A$ the range of the matrix $A$. The definition of principal type for systems is similar to the one for scalar operators.
\[princtype\] We say that the $N \times N$ system $P(w) \in C^1$ is of [*principal type*]{} at $w_0$ if $$\label{pr_type}
\partial_{\nu}P(w_0):\ {\operatorname{Ker}}P(w_0) \mapsto {\operatorname{Coker}}P(w_0) = {\mathbf C}^N/{\operatorname{Ran}}P(w_0)$$ is bijective for some ${\nu}$, here $\partial_{\nu}P = {\langle {\nu}, dP\rangle }$ and the mapping is given by $u \mapsto
\partial_{\nu}P(w_0) u$ modulo ${\operatorname{Ran}}P(w_0)$. We say that $P \in {\Psi}^m_{cl}$ is of principal type at $w_0$ if the principal symbol $P_m(x,{\xi})$ is of principal type at $w_0$.
If $P(w) \in C^1$ is of principal type and $A(w)$, $B(w) \in
C^1$ are invertible then $APB$ is of principal type. We also have that $P$ is of principal type if and only if the adjoint $P^*$ is of principal type.
In fact, Leibniz’ rule gives $$\label{invcomp}
d(APB) = (dA)PB + A(dP)B + APdB$$ and ${\operatorname{Ran}}(APB) = A({\operatorname{Ran}}P)$ and ${\operatorname{Ker}}(APB) =
B^{-1}({\operatorname{Ker}}P)$ when $A$ and $B$ are invertible, which gives the invariance under left and right multiplication. Since $ {\operatorname{Ker}}P^*(w_0) = {\operatorname{Ran}}P(w_0)^\bot$ we find that $P$ satisfies if and only if $$\label{bilform}
{\operatorname{Ker}}P(w_0) \times {\operatorname{Ker}}P^*(w_0) \ni (u,v) \mapsto
{\langle \partial_{\nu}P(w_0) u,v\rangle }$$ is a non-degenerate bilinear form. Since ${\langle \partial_{\nu}P^* u, v\rangle } =
{\overline}{{\langle \partial_{\nu}P v, u\rangle }}$ we then obtain that $P^*$ is of principal type.
Observe that only square systems can be of principal type since $${\operatorname{Dim}}{\operatorname{Ker}}P = {\operatorname{Dim}}{\operatorname{Coker}}P + M - N$$ if $P$ is an $N \times M$ system. In general, if the system is of principal type and has constant multiplicity of the eigenvalues then there are no non-trivial Jordan boxes, see Definition \[multdef\] and Proposition \[princprop\]. Then we also have that the eigenvalues ${\lambda}$ are of principal type: $d{\lambda} \ne 0$ when ${\lambda}
= 0$. When the multiplicity is equal to one, this condition is sufficient. In fact, by using the spectral projection one can find invertible systems $A$ and $B$ so that $$APB =
\begin{pmatrix}
{\lambda} & 0\\ 0 & E
\end{pmatrix}$$ with $E$ invertible $(N-1) \times (N-1)$ system, and this system is obviously of principal type.
\[multdef\] Let $A\/$ be an $N \times N$ matrix and ${\lambda}$ an eigenvalue of $A$. The multiplicity of ${\lambda}$ as a root of the characteristic equation $|A -
{\lambda}{\operatorname{Id}}_N| = 0$ is called the [*algebraic*]{} multiplicity of the eigenvalue, and the dimension of ${\operatorname{Ker}}(A - {\lambda}{\operatorname{Id}}_N)$ is called the [*geometric*]{} multiplicity.
Observe that if the matrix $P(w)$ depend continuously on a parameter $w$, then the eigenvalues ${\lambda}(w)$ also depend continuously on $w$. Such a continuous function ${\lambda}(w)$ of eigenvalues we will call a [*section of eigenvalues of*]{} $P(w)$.
\[smoothev\] If the section of eigenvalues ${\lambda}(w)$ of the $N \times N$ system $P(w) \in C^\infty$ has constant [*algebraic*]{} multiplicity then ${\lambda}(w) \in C^\infty$. In fact, if $k$ is the multiplicity then ${\lambda} =
{\lambda}(w)$ solves $\partial_{\lambda}^{k-1}|P(w)
- {\lambda}{\operatorname{Id}}_N| = 0$ so ${\lambda}(w) \in C^\infty$ by the Implicit Function Theorem.
This is [*not*]{} true for constant geometric multiplicity, for example $P(t) =
\begin{pmatrix}
0 & 1 \\ t & 0
\end{pmatrix}$, $t \in {\mathbf R}$, has geometric multiplicity equal to one for the eigenvalues $\pm\sqrt{t}$. Observe the geometric multiplicity is lower or equal to the algebraic, and for symmetric systems they are equal. We shall assume that the eigenvalues close to zero have constant algebraic and geometric multiplicities by the following definition.
\[constchar\] The $N \times N$ system $P(w) \in C^\infty$ has [*constant characteristics*]{} near $w_0$ if there exists an ${\varepsilon} > 0$ so that any section of eigenvalues ${\lambda}(w)$ of $P(w)$ with $|{\lambda}(w)| < {\varepsilon}$ has both constant algebraic and geometric multiplicity when $|w - w_0| < {\varepsilon}$.
Definition \[constchar\] is invariant under changes of bases: $P
\mapsto E^{-1}PE$ where $E$ is an invertible system, since this preserves the multiplicities of the eigenvalues of the system. It is also invariant under taking adjoints, since $|P^*(w) - {\lambda}^*(w){\operatorname{Id}}| = {\overline}{|P(w) - {\lambda}(w){\operatorname{Id}}|}$ and ${\operatorname{Dim}}{\operatorname{Ker}}(P^*(w) - {\lambda}^*(w){\operatorname{Id}}) = {\operatorname{Dim}}{\operatorname{Ker}}(P(w) - {\lambda}(w){\operatorname{Id}})$. The definition is [*not*]{} invariant under multiplication of the system with invertible systems, even in the case when $P(w) = {\lambda}(w){\operatorname{Id}}$ since $A(w)P(w) = {\lambda}(w)A(w)$ need not have constant characteristics.
Observe that generically the eigenvalues of a system have constant multiplicity, but not necessarily when equal to zero. For example, the system $$P({w}) =
\begin{pmatrix}
{w}_1 & {w}_2 \\
{w}_2 & - {w}_1
\end{pmatrix}$$ is symmetric and of principal type with eigenvalues $\pm\sqrt{{w}_1^2 +
{w}_2^2}$, which have constant multiplicity except when equal to 0.
Let the $N \times N$ system $P \in {\Psi}^m_{cl}$ be of principal type and constant characteristics. We say that $P$ satisfies condition (${\Psi}$) or ($P$) if the eigenvalues of the principal symbol satisfies condition (${\Psi}$) or ($P$).
Observe that the eigenvalue close to the origin is a uniquely defined $C^\infty$ function of principal type by Definition \[multdef\] and Proposition \[princprop\]. Thus, the semibicharacteristics of the eigenvalues are well-defined near the characteristic set ${\left\{\,w: \
|P(w)|= 0\,\right\}}$, so the conditions (${\Psi}$) and ($P$) on the eigenvalues are well-defined. Also well-defined is the condition that the Hamilton vector field of an eigenvalue $\lambda$ does not have the radial direction when $\lambda = 0$.
To get local solvability at a point $x_0 \in M$ we shall also assume a strong form of the non-trapping condition at $x_0$ for the eigenvalues ${\lambda}$ of $P$: $$\label{nontrap}
{\lambda} = 0 \implies \partial_{\xi} {\lambda}\ne 0$$ This means that all non-trivial semibicharacteristics of ${\lambda}$ are transversal to the fiber $T^*_{x_0}M$, which originally was the condition for principal type of Nirenberg and Treves [@nt]. Microlocally, in a conical neighborhood of a $(x,{\xi}) \in T^*M$, we can always obtain after a canonical transformation. In the following, we shall use the usual $L^2$ Sobolev norm ${\Vertu\Vert}_{(s)}$ and the $L^2$ norm ${\Vertu\Vert} = {\Vertu\Vert}_{(0)}$.
\[mainthm\] Let $P \in {\Psi}^m_{cl}(M)$ be an $N \times N$ system of principal type and constant characteristics near $(x_0,{\xi}_0) \in T^*M$, such that the Hamilton vector field of an eigenvalue $\lambda$ does not have the radial direction when $\lambda = 0$. Then $P$ is microlocally solvable near $(x_0,{\xi}_0)$ if and only if condition $({\Psi})$ is satisfied near $(x_0,{\xi}_0)$, and then $$\label{solvest1}
{\Vertu\Vert} \le C({\VertP^*u\Vert}_{(3/2-m)} + {\VertR u\Vert} + {\Vertu\Vert}_{(-1)})\qquad u
\in C_0^\infty(M, {\mathbf C}^N)$$ Here $R \in {\Psi}^{1/2}_{1, 0}(M)$ is a $K \times N$ system such that $(x_0,{\xi}_0) \notin {\operatorname{WF}}(R)$, which gives microlocal solvability of $P$ at $(x_0,{\xi}_0)$ with a loss of at most $3/2$ derivatives. If the eigenvalues also satisfy at $x_0 \in M$, then we obtain with $x \ne x_0$ in ${\operatorname{WF}}(R)$, which gives local solvability of $P$ at $x_0$ with a loss of at most $3/2$ derivatives.
As usual, ${\operatorname{WF}}(R)$ is the smallest smallest conical set in $T^*M\setminus 0$ such that $R \in {\Psi}^{-\infty}$ in the complement. The conditions in Theorem \[mainthm\] are invariant under conjugation with scalar Fourier integral operators since they only depend on the principal symbol of the system. They are also invariant under the base change: $P
\mapsto E^{-1}PE$ with invertible system $E$, since this preserves the eigenvalues of the principal symbol. The conditions of Theorem \[mainthm\] are more or less necessary, of course condition (${\Psi}$) is necessary even in the scalar case. Example \[popex\] shows that the condition of principal type is necessary in the case of constant characteristics, and Example \[newex\] shows that constant characteristics is necessary for solvability for systems of principal type.
We shall postpone the proof of Theorem \[mainthm\] to Section \[proof\]. The proof of the necessity is essentially the classical Moyer-Hörmander proof for the scalar case. The proof of the sufficiency will be an adaption of the proof for the scalar case in [@de:NT], using some of the ideas of Lerner [@ln:cutloss]. In fact, since the normal form of the operator will have a scalar principal symbol, the multiplier will essentially be the same as in [@de:NT]. But since we lose more than one derivative in the estimate we also have to consider the lower order matrix valued terms in the expansion of the operator. This is done in Section \[lower\] and is the main new part of the paper. In Section \[reduc\] we review the Weyl calculus and state the estimates we will use in the proof of Theorem \[mainthm\]. But we shall postpone the proof of the semiclassical estimate of Proposition \[mainprop\] until Section \[lower\]. In Section \[proof\] we prove Theorem \[mainthm\] by a microlocal reduction to a normal form using the estimates in Section \[reduc\]. In Section \[symb\] we define the symbol classes and weights we are going to use. In Section \[norm\] we review the Wick quantization, introduce the function spaces and the multiplier estimate that we will use for the proof of Proposition \[mainprop\]. Finally, in Section \[lower\] we prove Proposition \[mainprop\] by estimating the contributions of the lower order terms. The proof of Theorem \[mainthm\] in Section \[proof\] also gives the following results.
\[prem\] If $P$ is of principal type with constant characteristics satisfying condition ($P$) then we get the estimate with $3/2$ replaced by $1$. If $P$ satisfies condition $({\overline}{\Psi})$ and some repeated Poisson bracket of the real and imaginary parts of the eigenvalue close to the origin is non-vanishing, then we obtain a subelliptic estimate for $P$ with $3/2$ replaced by $k/k+1$ in for some $k\in {\mathbf Z}_+$, see [@ho:yellow Chapter 27].
The Poisson bracket of $f$ and $g$ is defined by ${\left\{\,f,g\,\right\}} = H_fg$. Theorem \[mainthm\] has applications to scalar non-principal type pseudodifferential operators by the following result.
\[exthm\] Let $Q \in {\Psi}^1_{cl}(M)$ be a scalar operator of principal type near $(x_0,{\xi}_0)\in T^*M$ and let $A_j \in {\Psi}^0_{cl}(M)$, $j=1,
\dots, N$ be scalar. Then the equation $$\label{scalareq}
Pu = Q^N u + \sum_{j=0}^{N-1}A_j Q^ju = f$$ is locally solvable near $(x_0,{\xi}_0)$ if and only if ${\sigma}(Q)$ satisfies condition $({\Psi})$ near $(x_0,{\xi}_0)$.
This is a standard reduction to a first order system. For scalar $u \in
{\mathcal}D'$ we let $u_{j+1} = Q^ju$ for $0 \le j < N$. Then holds if and only if $U = {}^{t}(u_1, \dots, u_N)$ solves $$\label{syseq}
\mathbb P\,U = F$$ where $$\mathbb P =
\begin{pmatrix}
Q & -1 & 0 & 0 & \dots \\
0 & Q & -1 & 0 & \dots \\
0 & 0 & Q & -1 & \dots\\
\dots &&&&\\
A_0 & A_1 & A_2 & \dots & Q+A_{N-1}
\end{pmatrix}$$ and $F = {}^{t}(0, 0, \dots, f)$. Now the equation is locally solvable if and only if the system is locally solvable. In fact, to solve we first put $u_1 = 0$, $u_2 = -f_1$ and recursively $u_{j+1} =
Qu_j-f_j$ for $1 \le j < N$. Then we only have to solve for $u = v_1$ with $f$ depending on $f_j$, and add $ Q^{j-1}v_1$ to $u_j$. Now ${\sigma}(\mathbb P) = {\sigma}(Q){\operatorname{Id}}_N$ which is of principal type with constant characteristics so it is locally solvable if and only if $Q$ satisfies condition $({\Psi})$ according to Theorem \[mainthm\].
We shall conclude the section with some examples. But first we prove a result about the characterization of systems of principal type.
\[princprop\] Assume that $P(w) \in C^\infty$ is an $N \times N$ system such that $|P(w_0)| = 0$ and there exists an ${\varepsilon} > 0$ such that the eigenvalue ${\lambda}$ of $P(w)$ with $|{\lambda}| < {\varepsilon}$ has constant algebraic multiplicity in a neighborhood of $w_0$. Let ${\lambda}(w) \in C^\infty$ be the unique eigenvalue for $P(w)$ near $w_0$ satisfying ${\lambda}(w_0) = 0$ by Remark \[smoothev\]. Then $P(w)$ is of principal type at $w_0$ if and only if $d{\lambda}(w_0) \ne 0$ and the geometric multiplicity of the eigenvalue ${\lambda}$ is equal to the algebraic multiplicity at $w_0$.
Thus, if $P(w)$ is of principal type having constant characteristics, then all sections of eigenvalues ${\lambda}(w)$ are of principal type and we have no non-trivial Jordan boxes in the normal form. This means that for symmetric systems having constant characteristics it suffices that the eigenvalues are of principal type. If $P(w)$ does not have constant characteristics then this is no longer true, in fact the eigenvalues need not even be differentiable, see Example \[nonsolvex\].
Observe that if $P(w)$ is of principal type and has constant characteristics, then $P(w) - {\lambda}{\operatorname{Id}}_N$ is of principal type near $w_0$ for $|{\lambda}| \ll 1$. In fact, the algebraic and geometric multiplicities are constant for the eigenvalue ${\lambda}$ and $d{\lambda} \ne 0$ near $w_0$.
Now the eigenvalue ${\lambda}(w)$ in Proposition \[princprop\] is the unique $C^\infty$ solution to $\partial^{k-1}_{\lambda} |P(w) -
{\lambda}{\operatorname{Id}}_N| = 0$ according to Remark \[smoothev\], where $k$ is the algebraic multiplicity. Thus we find that $d{\lambda}(w) \ne 0$ if and only if $$\partial_w\partial^{k-1}_{\lambda}
|P(w) - {\lambda}{\operatorname{Id}}_N| \ne 0 \qquad \text{when ${\lambda} = {\lambda}(w)$}$$ We only need this condition for a symmetric systems having constant multiplicity to be of principal type.
Let $$P({w}) =
\begin{pmatrix}
{w}_1 + i {w}_2^2 & {w}_2 \\ 0 & {w}_1 + i {w}_2^2
\end{pmatrix} \qquad w = (w_1,w_2) \in {\mathbf R}^2$$ then $P$ is of principal type, has constant algebraic multiplicity of the eigenvalue ${w}_1 + i {w}_2^2$ but not constant geometric multiplicity. In fact, $\partial_{{w}_1}P = {\operatorname{Id}}_2$, $P({w})$ has non-trivial kernel only when ${w}_2 = 0$ but the geometric multiplicity of the eigenvalue is equal to one when ${w}_2 \ne 0$.
Let $$P = p(x,D_x){\operatorname{Id}}_N + B(x,D_x) + P_0(x,D_x)$$ where $p\in S^1_{cl}$ is a scalar homogeneous symbol of principal type, $B \in
{\Psi}^1_{cl}$ with nilpotent homogeneous principal symbol ${\sigma}(B)$ and $P_0 \in
{\Psi}^0_{cl}$. Then $p$ is the only eigenvalue to ${\sigma}(P)$ and $P$ is of principal type if and only if ${\sigma}(B) = 0$ when $p = 0$ by Proposition \[princprop\].
Observe that the conclusion of Proposition \[princprop\] does not hold if the algebraic multiplicity is not constant. For example $$P({w}) =
\begin{pmatrix}
{w}_1 & 1 \\ {w}_2 & {w}_1
\end{pmatrix} \qquad w = (w_1,w_2) \in {\mathbf R}^2$$ has determinant is equal to $ {w}_1^2 - {w}_2 $ and eigenvalues ${w}_1 \pm \sqrt{{w}_2}$, so the geometric but not the algebraic multiplicity is constant near ${w}_2 = 0$. Since $$\begin{pmatrix}
0 & 1 \\ 1 & 0
\end{pmatrix}
P({w}) =
\begin{pmatrix}
{w}_2 & {w}_1 \\ {w}_1 & 1
\end{pmatrix}$$ we find that $P({w})$ is of principal type at $(0,0)$ by the invariance.
First we note that $P(w)$ is of principal typ at $w_0$ if and only if $$\label{princtypecond}
\partial_{\nu}^k|P(w_0)| \ne 0 \qquad k = {\operatorname{Dim}}{\operatorname{Ker}}P(w_0)$$ for some ${\nu} \in T(T^*{\mathbf R}^n)$. Observe that $ \partial^j|P(w_0)| =
0$ for $j < {\operatorname{Dim}}{\operatorname{Ker}}P(w_0)$. In fact, by choosing bases for ${\operatorname{Ker}}P(w_0)$ and ${\operatorname{Im}}P(w_0)$ respectively, and extending to bases of ${\mathbf C}^N$, we obtain matrices $A$ and $B$ so that $$AP(w)B =
\begin{pmatrix}
P_{11}(w) & P_{12}(w) \\ P_{21}(w) & P_{22}(w)
\end{pmatrix}$$ where $|P_{22}(w_0)| \ne 0$ and $P_{11}$, $P_{12}$ and $P_{21}$ all vanish at $w_0$. By the invariance, $P$ is of principal type if and only if $\partial_{\nu}P_{11}$ is invertible for some ${\nu}$, so by expanding the determinant we obtain .
Now since the eigenvalue ${\lambda}(w)$ has constant algebraic multiplicity near $w_0$, we find that $$|P(w) - {\lambda}{\operatorname{Id}}_N| = ({\lambda}(w)-{\lambda})^m e(w,{\lambda})$$ near $w_0$, where ${\lambda}(w_0) = 0$, $e(w,{\lambda}) \ne 0$ and $m \ge {\operatorname{Dim}}{\operatorname{Ker}}P(w_0)$ is the algebraic multiplicity. By putting ${\lambda}= 0$ we obtain that $ \partial_{\nu}^j|P(w_0)| = 0$ if $j < m$ and $
\partial_{\nu}^m|P(w_0)| = (\partial_{\nu}{\lambda}(w_0))^m e(w_0,0)$ which proves Proposition \[princprop\].
The following example shows that if the system is not of principal type then it need not be solvable, even if it has real eigenvalues with constant characteristics.
\[popex\] Let $P \in {\Psi}^2_{cl}$ have principal symbol ${\sigma}(P) = p^2$ where $p \in S^1_{cl}$ is real, homogeneous of degree 1, and of principal type. Then $P$ is not solvable if the imaginary part of the subprincipal symbol of $P$ changes sign on the bicharacteristics of $p$ by [@pop]. Observe that the subprincipal symbol is invariantly defined at the double characteristics $p^{-1}(0)$. As in the proof of Theorem \[exthm\], the equation can be reduced to the system $$\mathbb P =
\begin{pmatrix}
p(x,D_x) & p_1(x,D_x) \\
-1 & p(x,D_x)
\end{pmatrix}$$ where ${\sigma}(p_1) \in S^1_{cl}$ is equal to the subprincipal symbol of $P$ on $p^{-1}(0)$. The system is of principal type at $w\in p^{-1}(0)$ if and only if ${\sigma}(p_1)(w) = 0$ by Proposition \[princprop\]. This system has real eigenvalues of constant characteristics so it satisfies condition ($P$), but it is neither solvable nor of principal type if $
{\operatorname{Im}}p_1$ changes sign along the bicharacteristic of $p$. Observe that the system $$\mathbb P =
\begin{pmatrix}
p(x,D_x) & p_1(x,D_x) \\
0 & p(x,D_x)
\end{pmatrix}$$ is solvable, since it is upper triangle with solvable diagonal elements. Thus the solvability depends on the lower order terms in this case.
The next example is an unsolvable system of principal type with real eigenvalues, but it does not have constant characteristics.
\[newex\] Let $$\label{Pdef}
P =
\begin{pmatrix}
D_{x_1} & B(x,D_x) \\ -1 & D_{x_1} + R(D_x)
\end{pmatrix}$$ where $R({\xi}) = {\xi}_2^{2}/|{\xi}|$ and ${\sigma}(B)(x,{\xi}) =
{\xi}_2 B_0(x,{\xi})$ with homogeneous $B_0 \in S^0$. The eigenvalues of the principal symbol ${\sigma}(P)$ are ${\xi}_1$ and ${\xi}_1 + R({\xi})$ which are real and coincide when ${\xi}_2 = 0$. Since $\partial_{{\xi}_1}\sigma (P) = {\operatorname{Id}}_2$ and ${\sigma}(B)$ vanish when ${\xi}_2 = 0$, we find that $P$ is of principal type by Proposition \[princprop\]. If $t \mapsto {\operatorname{Im}}B_0(t,x',0,0,{\xi}'')$ changes sign at $t= x_1$, then $P$ is not microlocally solvable at $(x,0,0,{\xi}'')$, here $x= (x_1,x') =
(x_1,x_2,x'')$ and ${\xi}'' \ne 0$. In fact, the system $PU = F$ with $U = {}^{t}(u_1,u_2)$ and $F =
{}^{t}(f_1,f_2)$ is equivalent to the equation $$\label{Qdef}
Qu_2 = (D_{x_1}(D_{x_1} + R(D_x)) + B(x,D_x))u_2 = f_1 + D_{x_1}f_2$$ if we put $u_1 = (D_{x_1} + R(D_x))u_2 - f_2$. Thus the system $P$ is solvable if and only if $Q$ is solvable. That $Q$ is not solvable follows from using the construction of approximate solutions to the adjoint in [@MenUhl], replacing $D_{x_2}$ with $R(D_x)$.
We can also generalize this to the case where $$R({\xi}) = {\xi}_2^k|{\xi}|^{1-k}$$ and ${\sigma}(B)(x,{\xi}) = {\xi}^j_2 B_j(x,{\xi})$ with $j < k$ and $B_j \in
S^{1-j}$ homogeneous, satisfying the same conditions as $B_0$. On the other hand, if ${\sigma}(B)(x,{\xi}) = {\xi}^j_2 B_j(x,{\xi})$ with $j \ge k$ then we can write $$B(x,D_x) \cong A(x,D_{x})R(D_x)\qquad \text{modulo ${\Psi}^0$}$$ for some $A \in {\Psi}^0$ and then $$\begin{pmatrix}
1 & -A \\ 0 & 1
\end{pmatrix}
P
\begin{pmatrix}
1 & A \\ 0 & 1
\end{pmatrix}
\cong
\begin{pmatrix}
D_{x_1} & 0 \\ 0 & D_{x_1} + R(D_x)
\end{pmatrix}
\qquad\text{modulo ${\Psi}^0$}$$ which is solvable. In fact, the principal symbol is on diagonal form with real diagonal elements of principal type, giving $L^2$ estimates of the adjoint which can be perturbed by lower order terms.
Finally, we have an example of an unsolvable operator which is diagonalizable and self-adjoint, but not of principal type.
\[nonsolvex\] Take real $b(t) \in C^\infty({\mathbf R})$, and define the symmetric system $$P =
\begin{pmatrix}
D_t + b(t)D_x & (t - ib(t))D_x \\ (t + ib(t))D_x & -D_t + b(t)D_x
\end{pmatrix} = P^*
\qquad (t,x) \in {\mathbf R}^2$$ Eigenvalues of ${\sigma}(P)$ are $b(t){\xi} \pm \sqrt{{\tau}^2 +
(t^2 + b^2(t)){\xi}^2} $ which are zero for $({\tau},{\xi}) \ne 0$ only if $t = {\tau}= 0$. The eigenvalues coincide for $({\tau},{\xi}) \ne 0$ if and only if $b(t) = t = {\tau}= 0$. We have that $$Q = \frac{1}{2}
\begin{pmatrix}
1 & -i \\ 1 & i
\end{pmatrix}P
\begin{pmatrix}
1 & 1 \\ -i & i
\end{pmatrix} =
\begin{pmatrix}
D_t - itD_x & 2b(t)D_x \\ 0 & D_t +itD_x
\end{pmatrix}$$ which is not locally solvable at $t=0$ for any choice of $b(t)$, since $D_t +itD_x$ is not locally solvable, condition (${\Psi}$) is not satisfied when ${\xi} > 0$. The eigenvalues of the principal symbol ${\sigma}(Q)$ are ${\tau} \pm it{\xi}$. By the invariance, $P$ is of principal type if and only if $b(0)=0$. When $b(t) \ne 0$ we find that ${\sigma}(P)$ is diagonalizable and self-adjoint, but not of principal type. When $b \equiv 0$ the system is symmetric of principal type, but does not have constant characteristics.
The multiplier estimates {#reduc}
========================
In this section we shall prove multiplier estimates for microlocal normal forms of the adjoint operator, which we shall use in the proof of Theorem \[mainthm\]. We shall consider the model operators $$\label{pdef1}
P_0 = (D_t + i F(t,x,D_x)){\operatorname{Id}}_N + F_0(t,x,D_x)$$ where $F \in C^\infty({\mathbf R}, {\Psi}^1_{cl}({\mathbf R}^{n}))$ is scalar with with real homogeneous principal symbol ${\sigma}(F) = f$, and $F_0 \in C^\infty({\mathbf R}, {\Psi}^0_{cl})$ is an $N \times N$ system. In the following, we shall assume that $P_0$ satisfies condition ($\overline{\Psi}$): $$\label{pcond0}
f(t,x,{\xi}) > 0 \quad\text{and $s > t$} \implies f(s,x,{\xi}) \ge 0$$ for any $t$, $s \in {\mathbf R}$ and $(x,{\xi}) \in T^*{\mathbf R}^n$. This means that the adjoint $P_0^*$ satisfies condition (${\Psi}$) for the eigenvalue ${\tau} - if(t,x,{\xi})$. Observe that if ${\chi} \ge 0$ then ${\chi}f$ also satisfies , thus the condition can be localized.
\[linftyrem\] We may also consider symbols $f \in L^\infty({\mathbf R}, S^1_{1,0}({\mathbf R}^{n}))$, that is, $f(t,x,{\xi}) \in L^\infty({\mathbf R}\times T^*{\mathbf R}^n)$ is bounded in $S^1_{1,0}({\mathbf R}^{n})$ for almost all $t$. Then we say that $P_0$ satisfies condition (${\overline}{\Psi}$) if for every $(x,{\xi})$ condition holds for almost all $s$, $t \in {\mathbf R}$.
Observe that, since $(x,{\xi}) \mapsto f(t,x,{\xi})$ is continuous for almost all $t$, it suffices to check for $(x,{\xi})$ in a countable dense subset of $T^*{\mathbf R}^n$. Then we find that $f$ has a representative satisfying for any $t$, $s$ and $(x,{\xi})$ after putting $f(t,x,{\xi}) \equiv 0$ for $t$ in a null set.
In order to prove Theorem \[mainthm\] we shall make a second microlocalization using the specialized symbol classes of the Weyl calculus, and the Weyl quantization of symbols $a \in {\mathcal}S'(T^*{\mathbf R}^n)$ defined by: $${\left ( a^wu,v\right ) } = (2{\pi})^{-n}\iint
\exp{(i{\langle x-y,{\xi}\rangle })}a\!\left(\tfrac{x+y}{2},{\xi}\right)u(y){\overline}v(x)\,dxdyd{\xi}
\qquad u, v \in {\mathcal}S({\mathbf R}^n)$$ Observe that ${\operatorname{Re}}a^w = ({\operatorname{Re}}a)^w$ is the symmetric part and $i{\operatorname{Im}}a^w = (i{\operatorname{Im}}a)^w$ the antisymmetric part of the operator $a^w$. Also, if $a \in S^m_{1,0}({\mathbf R}^n)$ then $a^w(x,D_x)
= a(x,D_x)$ modulo ${\Psi}^{m-1}_{1,0}({\mathbf R}^n)$ by [@ho:yellow Theorem 18.5.10]. The same holds for $N \times N$ systems of operators.
We recall the definitions of the Weyl calculus: let $g_{w}$ be a Riemannean metric on $T^*{\mathbf R}^n$, $w = (x,{\xi})$, then we say that $g$ is slowly varying if there exists $c>0$ so that $g_{w_0}(w-w_0) <
c $ implies $$1/C \le g_{w}/g_{w_0}
\le C$$ that is, $g_{w} \cong g_{w_0}$. Let ${\sigma}$ be the standard symplectic form on $T^*{\mathbf R}^n$, $ g^{\sigma}(w) $ the dual metric of $w \mapsto
g({\sigma}(w))$ and assume that $ g^{\sigma}(w) \ge g(w)$. We say that $g$ is ${\sigma}$ temperate if it is slowly varying and $$g_{w} \le C g_{w_0}( 1 +
g^{\sigma}_{w}(w-w_0))^N \qquad
\text{$w$, $w_0 \in T^*{\mathbf R}^n$}$$ A positive real valued function $m(w)$ on $T^*{\mathbf R}^n$ is $g$ continuous if there exists $c>0$ so that $g_{w_0}(w-w_0) < c $ implies $m(w) \cong
m(w_0)$. We say that $m$ is ${\sigma}$, $g$ temperate if it is $g$ continuous and $$m(w) \le C m(w_0)( 1 +
g^{\sigma}_{w}(w-w_0))^N \qquad\text{$w$,
$w_0 \in T^*{\mathbf R}^n$}$$ If $m$ is ${\sigma}$, $g$ temperate, then $m$ is a weight for $g$ and we can define the symbol classes: $a \in S(m,g)$ if $a \in C^\infty(T^*{\mathbf R}^n)$ and $$\label{symbolest}
|a|^g_j(w) = \sup_{T_i\ne 0}
\frac{|a^{(j)}(w,T_1,\dots,T_j)|}{\prod_1^j
g_{w}(T_i)^{1/2}}\le C_j
m(w)\qquad w \in T^*{\mathbf R}^n \qquad\text{$j \ge 0$}$$ which defines the seminorms of $S(m,g)$. Of course, these symbol classes can also defined locally. For matrix valued symbols, we use the matrix norms. If $a \in
S(m,g)$ then we say that the corresponding Weyl operator $a^w \in {\operatorname{Op}}S(m,g)$. For more results on the Weyl calculus, see [@ho:yellow Section 18.5].
\[s+def\] Let $m$ be a weight for the metric $g$. We say that $a \in S^+(m,g)$ if $a \in C^\infty(T^*{\mathbf R}^n)$ and $|a|_j^g \le C_jm$ for $j \ge
1$.
Observe that if $a \in S^+(m,g)$ then $a$ is a symbol. In fact, since $g \le g^{\sigma}$ we find by integration that $$\begin{split}
|a(w) - a(w_0)| \le C_1\sup_{{\theta} \in [0,1]} m(w_{\theta})
g_{w_{\theta}}(w-w_0)^{1/2} \le C_N m(w_0)(1 +
g_{w_0}^{{\sigma}}(w-w_0))^{N_0}
\end{split}$$ where $w_{\theta} = {\theta}w + (1-{\theta})w_0$, which implies that $m + |a|$ is a weight for $g$. Clearly, $a \in S(m + |a|,
g)$, so the operator $a^w$ is well-defined.
\[calcrem\] Assume that $m_j$ is a weight for for the ${\sigma}$ temperate conformal metrics $g_j = h_j g^{\sharp}\le g^{\sharp}= (g^{\sharp})^{\sigma}$ and $a_j \in
S^+(m_j, g_j)$, $j=1$, $2$. Let $g = (g_1 + g_2)/2$ and $h^2 = \sup
g_1/g_2^{\sigma} = \sup g_2/g_1^{\sigma}$, then we find that $h^2 =
h_1h_2$ and $$\label{2.3}
a_1^wa_2^w -(a_1a_2)^w \in {\operatorname{Op}}S(m_1m_2h,g)$$ We also obtain the usual expansion of with terms in $
S(m_1m_2h^k,g)$, $k\ge 1$.
Observe that by Proposition 18.5.7 and (18.5.14) in [@ho:yellow] we find that $g$ is ${\sigma}$ temperate and $g/g^{\sigma} \le (h_1 + h_2)^2/4 \le 1$.
As showed after Definition \[s+def\] we have that $m_j + |a_j|$ is a weight for $g_j$ and $a_j \in S(m_j + |a_j|, g_j)$, $j = 1$, 2. Thus $$a_1^w a_2^w \in {\operatorname{Op}}S((m_1 + |a_1|)(m_2 + |a_2|),g)$$ is given by Proposition 18.5.5 in [@ho:yellow]. We find that $a_1^wa_2^w -(a_1a_2)^w = a^w$ with $$a(w) = E(\tfrac{i}{2}{\sigma}(D_{w_1},D_{w_2}))
\tfrac{i}{2}{\sigma}(D_{w_1},D_{w_2})a_1(w_1)a_2(w_2){\big|_{w_1= w_2=w}}$$ where $E(z) = (e^z -1)/z = \int_0^1 e^{{\theta}z}\,d{\theta}$. We have that ${\sigma}(D_{w_1},D_{w_2})a_1(w_1)a_2(w_2) \in S(M,G)$ where $$M(w_1,w_2) = m_1(w_1)m_2(w_2)h_1^{1/2}(w_1)h_2^{1/2}(w_2)$$ and $G_{w_1,w_2}(z_1,z_2) = g_{1,w_1}(z_1) + g_{2,w_2}(z_2)$. Now the proof of Theorem 18.5.5 in [@ho:yellow] works also when ${\sigma}(D_{w_1},D_{w_2})$ is replaced by ${\theta}{\sigma}(D_{w_1},D_{w_2})$, uniformly in $0 \le {\theta} \le
1$. By using Proposition 18.5.7 in [@ho:yellow] and integrating over ${\theta} \in [0,1]$ we obtain that $a(w)$ has an asymptotic expansion in $S(m_1m_2 h^k,g)$, which proves the Lemma.
\[vvcalc\] The conclusions of Lemma \[calcrem\] also hold if $a_1
$ has values in ${\mathcal}L(B_1, B_2)$ and $a_2$ has values in $B_1$ where $B_1$ and $B_2$ are Banach spaces (see Section 18.6 in [@ho:yellow]).
For example, if ${\left\{\,a_j\,\right\}}_j \in S(m_1,g_1)$ with values in $\ell^2$, and $b_j \in S(m_2,g_2)$ uniformly in $j$, then ${\left\{\,a_j^wb_j^w\,\right\}}_j \in
{\operatorname{Op}}(m_1m_2,g)$ with values in $\ell^2$. Thus, if ${\left\{\,{\phi}_j\,\right\}}_j \in S(1,g)$ is a partition of unity so that $\sum_{j}{\phi}_j^2 = 1$ and $a \in S(m,g)$, then ${\left\{\,{\phi}_ja\,\right\}}_j \in S(m,g)$ has values in $\ell^2$.
The standard symbol class $S^{\mu}_{{\varrho},{\delta}}$ defined by $$|\partial_x^{\alpha}\partial_{\xi}^{\beta} a(x,{\xi})| \le
C_{{\alpha}{\beta}}{\langle {\xi}\rangle }^{{\mu} + {\delta}|{\alpha}| -
{\varrho}|{\beta}|}$$ has ${\sigma}$ temperate metric if $0 \le {\delta}
\le {\varrho} \le 1$ and ${\delta} < 1$.
In the proof of Theorem \[mainthm\] we shall microlocalize near $(x_0,{\xi}_0)$ and put $h^{-1} = {\langle {\xi}_0\rangle } = 1 + |{\xi}_0|$. Then after doing a symplectic dilation: $(x,{\xi}) \mapsto (h^{-1/2}x, h^{1/2}{\xi})$, we find that $S^k_{1,0} = S(h^{-k}, h g^{\sharp})$ and $S^k_{1/2,1/2} =
S(h^{-k}, g^{\sharp})$, $k \in {\mathbf R}$, where $g^{\sharp}= (g^{\sharp})^{\sigma}$ is the Euclidean metric. We shall prove a semiclassical estimate for a microlocal normal form of the operator.
Let ${\Vertu\Vert}$ be the $L^2$ norm on ${\mathbf R}^{n+1}$, and ${\left ( u,v\right ) }$ the corresponding sesquilinear inner product. As before, we say that $f
\in L^\infty({\mathbf R}, S(m, g))$ if $f(t,x,{\xi})$ is measurable and bounded in $S(m, g)$ for almost all $t$. The following is the main estimate that we shall prove.
\[mainprop\] Assume that $$P_0 = (D_t + i f^w(t,x,D_x)){\operatorname{Id}}_N + F_0^w(t,x,D_x)$$ where $f \in
L^\infty({\mathbf R}, S(h^{-1}, hg^{\sharp}))$ is real satisfying condition $(\overline{\Psi})$ given by , and $F_0 \in L^\infty({\mathbf R}, S(1, hg^{\sharp}))$ is an $N \times N$ system, here $0 < h
\le 1$ and $g^{\sharp}= (g^{\sharp})^{\sigma}$ are constant. Then there exists $T_0 > 0$ and $N \times N$ symbols $b_T(t,x,{\xi}) \in
L^\infty({\mathbf R}, S(h^{-1/2}, g^{\sharp}) \bigcap S^+(1, g^{\sharp}))$ such that ${\operatorname{Im}}b_T \in L^\infty({\mathbf R}, S(h^{1/2}, g^{\sharp}))$ uniformly for $0 < T \le T_0$, and $$\label{propest}
h^{1/2}\left({\Vertb_T^wu\Vert}^2 + {\Vertu\Vert}^2\right) \le C_0 T {\operatorname{Im}}{\left ( P_0u,b_T^wu\right ) }$$ for $u(t,x) \in {\mathcal}S({\mathbf R}\times {\mathbf R}^{n}, {\mathbf C}^N)$ having support where $|t| \le T$. The constants $C_0$, $T_0$ and the seminorms of $b_T$ only depend on the seminorms of $f$ and $F_0$.
It follows from the proof that $b_T = {\widetilde}b_TE^*E$ modulo $S(h^{1/2},
g^{\sharp})$ where $E \in S(1, hg^{\sharp})$ is an invertible $N \times N$ system, ${\widetilde}b_T$ is scalar and $|{\widetilde}b_T| \le CH^{-1/2}$, here $H$ is a weight for $g^{\sharp}$ such that $h \le H \le 1$, and $G = Hg^{\sharp}$ is ${\sigma}$ temperate (see Claim \[subrem\], Definition \[g1def\] and Proposition \[wickweyl\]).
Observe that it follows from and the Cauchy-Schwarz inequality that $${\Vertu\Vert} \le C T h^{-1/2}{\VertP_0u\Vert}$$ which will give a loss of $3/2$ derivatives after microlocalization. Proposition \[mainprop\] will be proved in Section \[lower\].
There are two difficulties present in estimates of the type . The first is that $b_T$ is not $C^\infty$ in the $t$ variables, therefore one has to be careful not to involve $b_T^w$ in the calculus with symbols in all the variables. We shall avoid this problem by using tensor products of operators and the Cauchy-Schwarz inequality. The second difficulty lies in the fact that we could have $|b_T| \gg h^{1/2}$, so it is not obvious that cut-off errors can be controlled.
\[microrem\] The estimate can be perturbed with terms in $L^\infty({\mathbf R}, S(h^{1/2}, hg^{\sharp}))$ in the expansion of $P_0$. Also, it can be microlocalized: if ${\phi}(w) \in S(1, hg^{\sharp})$ is real valued and independent of $t$, then we have $$\label{cutofferror}
{\operatorname{Im}}{\left ( P_0{\phi}^w u, b_{T}^w{\phi}^w u\right ) } \le
{\operatorname{Im}}{\left ( P_0u,{\phi}^w b_T^w{\phi}^w u\right ) } + Ch^{1/2}{\Vertu\Vert}^2 \qquad u(t,x)
\in {\mathcal}S({\mathbf R}^{n+1}, {\mathbf C}^N)$$ where ${\phi}^wb_T^w{\phi}^w$ satisfies the same conditions as $b_T^w$.
In the following, we shall say that a system is [*real*]{} if it is a real multiple of the identity matrix. It is clear that we may perturb with terms in $L^\infty({\mathbf R}, S(h^{1/2}, g^{\sharp}))$ in the expansion of $P_0$ for small enough $T$. Now, we can also perturb with real terms $r^w \in L^\infty({\mathbf R}, {\operatorname{Op}}S(1,h g^{\sharp}))$. In fact, if $r
\in S(1, hg^{\sharp})$ is [real]{} and $B \in S^+(1, g^{\sharp})$ is symmetric modulo $S(h^{1/2}, g^{\sharp})$, then $$\label{2.4}
| {\operatorname{Im}}{\left ( r^w u, B^w u\right ) }| \le
|{\left ( [({\operatorname{Re}}B)^w,r^w]u,u\right ) }|/2 +
|{\left ( r^wu,({\operatorname{Im}}B)^wu\right ) }| \le C h^{1/2} {\Vertu\Vert}^2$$ In fact, we have $[({\operatorname{Re}}B)^w,r^w] \in {\operatorname{Op}}S(h^{1/2},
g^{\sharp})$ by Lemma \[calcrem\].
If ${\phi}(w) \in S(1, hg^{\sharp})$ then $[P_0,{\phi}^w{\operatorname{Id}}_N]
= {\left\{\,f,{\phi}\,\right\}} ^w{\operatorname{Id}}_N$ modulo $L^\infty({\mathbf R}, {\operatorname{Op}}S(h,
hg^{\sharp}))$ where ${\left\{\,f,{\phi}\,\right\}} \in L^\infty({\mathbf R}, S(1, hg^{\sharp}))$ is real valued. By using with $r^w = {\left\{\,f,{\phi}\,\right\}}^w{\operatorname{Id}}_N$ and $B^w = b_T^w{\phi}^w$, we obtain since $b_T^w{\phi}^w \in {\operatorname{Op}}S^+(1, g^{\sharp})$ is symmetric modulo ${\operatorname{Op}}S(h^{1/2}, g^{\sharp})$ for almost all $t$ by Lemma \[calcrem\]. Since Lemma \[calcrem\] also gives that ${\phi}^wb_T^w{\phi}^w =
{\phi}^w(b_T\phi)^w = (b_T{\phi}^2)^w$ modulo $L^\infty({\mathbf R}, {\operatorname{Op}}S(h, g^{\sharp}))$ we find that ${\phi}^wb_T^w{\phi}^w$ satisfies the same conditions as $b_T^w$.
\[subrem\] When proving the estimate we may assume that $$\label{subform}
F_0 = {\langle d_w f, R_0\rangle }= \sum_j \partial_{w_j}fR_{0,j} \qquad\text{modulo
$L^\infty({\mathbf R}, S(h, hg^{\sharp}))$}$$ where $R_{0,j} \in L^\infty({\mathbf R}, S(h^{1/2}, hg^{\sharp}))$ are $N \times N$ systems, $\forall \, j$.
By conjugation with $(E^{\pm 1})^w \in {\operatorname{Op}}S(1, hg^{\sharp})$ we find that $$(E^{-1})^w P E^w = (E^{-1})^wE^w(D_t + if^w){\operatorname{Id}}_N + \left(E^{-1}(D_tE + H_fE +
F_0E)\right)^w = {\widetilde}P$$ modulo $L^\infty({\mathbf R}, S(h, hg^{\sharp}))$. By solving $$\left\{
\begin{aligned}
&D_t E + F_0E = 0\\
&E{\big|_{t=0}} = {\operatorname{Id}}_N
\end{aligned}
\right.$$ we obtain for ${\widetilde}P$ with $ {\langle d_w f, R_0\rangle }= E^{-1}H_fE$. From the calculus we obtain that $$E^w(E^{-1})^w = 1 = (E^{-1})^wE^w\qquad\text{modulo ${\operatorname{Op}}S(Th,hg^{\sharp})$}$$ uniformly when $|t| \le T$. Thus, for small enough $T$ we obtain that $(E^{\pm 1})^w$ is invertible in $L^2$. Since the metric $hg^{\sharp}$ is trivially strongly ${\sigma}$ temperate in the sense of [@bc:sob Definition 7.1], we find from [@bc:sob Corollary 7.7] that there exists $A \in L^\infty({\mathbf R}, S(1, hg^{\sharp}))$ such that $E^w A^w = 1$. Thus, if we prove the estimate for ${\widetilde}P$ and substitute $u = A^wv$ we obtain the estimate for $P$ with $b_T$ replaced by $((E^{-1})^w)^*b_T^wA^w$. Since $A = E^{-1}$ modulo $S(h, hg^{\sharp})$ we find from Lemma \[calcrem\] as before that the symbol of this multiplier is in $S(h^{-1/2}, g^{\sharp})\bigcap S^+(1,g^{\sharp})$ and that it is symmetric modulo $ S(h^{1/2}, g^{\sharp})$.
We shall see from the proof that if $F_0$ is on the form then $b_T
= b_T{\operatorname{Id}}_N$ is real. Thus, in general the symbol of the multiplier will be on the form $b_T(E^{-1})^*E^{-1}$ modulo $S(h^{1/2}, g^{\sharp})$ with invertible $E$ and a real scalar $b_T$. In the following, we shall use the partial Sobolev norms: $${\Vertu\Vert}_{s} = {\Vert{\langle D_x\rangle }^{s}u\Vert}$$ We shall now prove the estimate we shall use in the proof of Theorem \[mainthm\].
\[maincor\] Assume that $$P_0 = (D_t + i F^w(t,x,D_x)){\operatorname{Id}}_N + F_0^w(t,x,D_x)$$ with $F^w \in
L^\infty({\mathbf R}, {\Psi}^1_{cl}({\mathbf R}^{n}))$ having real principal symbol $f$ satisfying condition $(\overline{\Psi})$ given by and $F_0 \in L^\infty({\mathbf R}, {\Psi}^0_{cl}({\mathbf R}^{n}))$ is an $N \times N$ system. Then there exists $T_0 > 0$ and $N \times N$ symbols $B_T(t,x,{\xi}) \in L^\infty({\mathbf R}, S^1_{1/2,1/2}({\mathbf R}^{n}))$ with $$\nabla B_T = (\partial_x B_T, |{{\xi}}| \partial_{\xi} B_T)
\in L^\infty({\mathbf R}, S^{1}_{1/2,1/2}({\mathbf R}^{n}))$$ and ${\operatorname{Im}}B_T(t,x,{\xi})
\in L^\infty({\mathbf R}, S^0_{1/2,1/2}({\mathbf R}^{n}))$ uniformly for $0 < T \le
T_0$, such that $$\label{corest}
{\VertB_T^wu\Vert}^2_{-1/2}+ {\Vertu\Vert}^2\le C_0(T {\operatorname{Im}}{\left ( P_0u,B_T^wu\right ) } +
{\Vertu\Vert}_{-1}^2)$$ for $ u \in {\mathcal}S({\mathbf R}^{n+1}, {\mathbf C}^N)$ having support where $|t| \le T$. The constants $T_0$, $C_0$ and the seminorms of $B_T$ only depend on the seminorms of $F$ and $F_0$ in $L^\infty({\mathbf R},S^1_{cl}({\mathbf R}^{n}))$.
Since $\nabla B_T \in
L^\infty({\mathbf R}, S^{1}_{1/2,1/2})$ we find that the commutators of $B_T^w$ with scalar operators in $L^\infty({\mathbf R},{\Psi}^0_{1,0})$ are in $L^\infty({\mathbf R}, {\Psi}^{0}_{1/2,1/2})$. This will make it possible to localize the estimate. The idea to include the first term in is due to Lerner [@ln:cutloss].
Choose real symbols ${\left\{\,{\phi}_j(x,{\xi})\,\right\}}_{j}$ and ${\left\{\,{\psi}_j(x,{\xi})\,\right\}}_{j} \in
S^0_{1,0}({\mathbf R}^{n})$ having values in $\ell^2$, such that $\sum_{j}
{\phi}_j^2 = 1$, ${\psi}_j{\phi}_j = {\phi}_j$ and ${\psi}_j \ge 0$. We may assume that the supports are small enough so that ${\langle \xi\rangle } \cong {\langle {\xi}_j\rangle }$ in ${\operatorname{\rm supp}}{\psi}_j$ for some ${\xi}_j$, and that there is a fixed bound on number of overlapping supports. Then, after doing a symplectic dilation $$(y,{\eta}) = (x{\langle {\xi}_j\rangle }^{1/2}, {\xi}/{\langle {\xi}_j\rangle }^{1/2})$$ we obtain that $S^m_{1,0}({\mathbf R}^n) = S(h_j^{-m}, h_j g^{\sharp})$ and $S^m_{1/2,1/2}
({\mathbf R}^n) = S(h_j^{-m}, g^{\sharp})$ in ${\operatorname{\rm supp}}{\psi}_j$, $m \in {\mathbf R}$, where $h_j = {\langle {\xi}_j\rangle }^{-1}\le 1$ and $g^{\sharp}(dy, d{\eta}) = |dy|^2 +
|d{\eta}|^2$ is constant.
By using the calculus in the $y$ variables we find $
{\phi}_j^wP_0 = {\phi}_j^w P_{0j}$ modulo ${\operatorname{Op}}S(h_j, h_jg^{\sharp})$, where $$\begin{gathered}
P_{0j} = (D_t + i({\psi}_jF)^w(t,y,D_y)){\operatorname{Id}}_N +
({\psi}_jF_0)^w(t,y,D_y)\\ = (D_t + if_j^w(t,y,D_y)){\operatorname{Id}}_N +
F_j^w(t,y,D_y)\end{gathered}$$ with $f_j = {\psi}_j f \in L^\infty({\mathbf R},S(h_j^{-1}, h_j g^{\sharp})) $ satisfying , and $F_j \in L^\infty({\mathbf R}, S(1,h_j g^{\sharp}))$ uniformly in $j$. Then, by using Proposition \[mainprop\] and Lemma \[microrem\] for $P_{0j}$ we obtain symbols $b_{j,T}(t,y,{\eta}) \in L^\infty({\mathbf R}, S(h_j^{-1/2}, g^{\sharp}) \bigcap
S^+(1, g^{\sharp}))$ such that ${\operatorname{Im}}b_{j,T} \in S(h_j^{1/2}, g^{\sharp})$ uniformly for $0 < T \ll 1$, and $$\label{mmest}
{\Vertb_{j,T}^w{\phi}_j^w u\Vert}^2 + {\Vert{\phi}_j^w u\Vert}^2 \le C_0T (h_j^{-1/2}{\operatorname{Im}}{\left ( P_{0}u,
{\phi}_j^w b_{j,T}^w {\phi}_j^wu\right ) } + {\Vertu\Vert}^2)\qquad \forall\,j$$ for $u(t,y) \in {\mathcal}S({\mathbf R}\times {\mathbf R}^{n}, {\mathbf C}^N)$ having support where $|t| \le T$. Here and in the following, the constants are independent of $T$.
By substituting ${\psi}_j^wu$ in and summing up we obtain $$\label{2.12}
{\VertB_T^wu\Vert}^2_{-1/2} + {\Vertu\Vert}^2 \le C_0T({\operatorname{Im}}{\left ( P_0u, B_{T}^wu\right ) } + {\Vertu\Vert}^2) + C_1{\Vertu\Vert}_{-1}^2$$ for $u(t,x) \in {\mathcal}S({\mathbf R}\times {\mathbf R}^{n}, {\mathbf C}^N)$ having support where $|t| \le T$. Here $$B_{T}^w = \sum_j h_j^{-1/2} {\psi}_j^w {\phi}_j^w
b_{j,T}^w {\phi}_j^w{\psi}^w_j = \sum_{j} B_{j,T}^w\in L^\infty({\mathbf R},
{\Psi}^{1}_{1/2,1/2})$$ so ${\operatorname{Im}}B_T \in L^\infty({\mathbf R}, {\Psi}^{0}_{1/2,1/2})$. In fact, since $d{\psi}_j = 0 $ on ${\operatorname{\rm supp}}{\phi}_j$ we have $${\left\{\,{\phi}_j^w[P_{0j}^w,{\psi}_j^w]\,\right\}}_j \in
{\Psi}^{-1}_{1,0}({\mathbf R}^n)$$ with values in $\ell^2$ for almost all $t$. Also, $\sum_{j}^{}{\phi}_j^2 = 1$ so $\sum_j
{\phi}_j^w{\phi}_j^w = 1$ modulo ${\Psi}^{-1}({\mathbf R}^n)$, and by the finite overlap of supports we find that $$\begin{gathered}
({\langle D_x\rangle }^{-1/2}B_T^w)^*{\langle D_x\rangle }^{-1/2}B_T^w =
(B_T^w)^*{\langle D_x\rangle }^{-1}B_T^w \\ = \sum_{|j-k| \le K}(B_{j,T}^w)^*
{\langle D_x\rangle }^{-1}B_{k,T}^w \qquad \text{modulo ${\Psi}^{-2}$} \end{gathered}$$ for some $N$, which implies that $${\VertB_T^wu\Vert}^2_{-1/2} \le C_K \left(\sum_k {\VertB_{k,T}^w u\Vert}_{-1/2}^2 + {\Vertu\Vert}^2_{(-1)}\right)$$ We also have that ${\langle D_x\rangle }^{-1/2}h_j^{-1/2}{\psi}^w_j{\phi}^w_j \in {\Psi}^{0}({\mathbf R}^n)$ uniformly, which gives $${\VertB_{k,T}^w u\Vert}_{-1/2} \le C {\Vertb_{k,T}^w
{\phi}^w_k{\psi}^w_ku\Vert} \qquad \forall\,k$$ We find that $\nabla B_{T} \in S^{1}_{1/2,1/2}$ since Lemma \[calcrem\] gives $$B_{T} =
\sum_{j}^{}h_j^{-1/2}b_{j,T}{\phi}_j^2 \in S^{1}_{1/2,1/2}\qquad \text{modulo
$S^{0}_{1/2,1/2}$}$$ where ${\phi}_j \in S(1, h_jg^{\sharp})$ and $b_{j,T}
\in S^+(1,g^{\sharp})$ for almost all $t$. For small enough $T$ we obtain and the corollary.
Proof of Theorem \[mainthm\] {#proof}
============================
In order to prove the theorem, we first need a preparation result so that we can get the system on a normal form.
\[prepprop\] Assume that $P \in S^m_{cl}(M)$ is a $N \times N$ system of principal type having constant characteristics near $(x_0,{\xi}_0) \in T^*M$, then there exist elliptic $N \times N$ systems $A$ and $B \in S^0_{cl}(M)$ such that $$A^w P^w B^w = Q^w =
\begin{pmatrix}
Q_{11}^w & 0 \\
0 & Q_{22}^w
\end{pmatrix} \in {\Psi}^{m}_{cl}$$ microlocally near $(x_0,{\xi}_0)$. We have that ${\sigma}(Q_{11}) =
{\lambda}{\operatorname{Id}}_K$ where the section of eigenvalues ${\lambda}(w)\in C^\infty$ of $P(w)$ is of principal type, and $Q_{22}^w$ is elliptic.
Thus we obtain the system on a block form. Observe that if $K=0$ then $P$ is elliptic at $(x_0,{\xi}_0)$. Since $P$ is of principal type we find by the invariance given by that $Q$ is of principal type, so ${\lambda}$ vanishes of first order on its zeros.
Since $P_m$ has constant characteristics by the assumptions, we find that the characteristic equation $$|P_m(w) - {\lambda}{\operatorname{Id}}_N| = 0$$ has a unique local solution ${\lambda}(w) \in C^\infty$ of multiplicity $K > 0$. Since $P_m(w)$ is of principal type, Proposition \[princprop\] gives that $d{\lambda}(w_0) \ne 0$ and the geometric multiplicity ${\operatorname{Dim}}{\operatorname{Ker}}(P_m(w) - {\lambda}(w){\operatorname{Id}}_N) \equiv K$ in a neighborhood of $w_0 =
(x_0,{\xi}_0)$. Since the dimension is constant, we may choose a $C^\infty$ base for $ {\operatorname{Ker}}(P_m(w) - {\lambda}(w){\operatorname{Id}}_N) $ in a neighborhood of $w_0$. By orthogonalizing it, extending to a orthonormal $C^\infty$ base for ${\mathbf C}^N$ and using homogeneity we obtain orthogonal homogeneous $E$ such that $$E^*P_mE =
\begin{pmatrix}
{\lambda}(w){\operatorname{Id}}_K & P_{12} \\
0 & P_{22}
\end{pmatrix} = {\widetilde}P_m = {\sigma}((E^w)^*P^wE^w)$$ Clearly ${\operatorname{Ker}}{\widetilde}P_m = {\left\{\,(z_1,\dots,z_N):\ z_j = 0\text{ for } j > K\,\right\}}$ when ${\lambda}=0$ and $d{\widetilde}P_m$ is equal to multiplication with $ d{\lambda}$ on ${\operatorname{Ker}}{\widetilde}P_m$. Since ${\widetilde}P_m$ is of principal type when ${\lambda}=0$ we find that ${\operatorname{Im}}{\widetilde}P_m \bigcap {\operatorname{Ker}}{\widetilde}P_m = {\left\{\,0\,\right\}}$ at $w_0$, which implies that $P_{22}$ is invertible. In fact, if it was not invertible there would exists $0 \ne z'' \in {\mathbf C}^{N-K}$ so that $P_{22}z'' = 0$, then $$0 \ne {\widetilde}P_m {}^{t}(0,z'') = {}^{t}(P_{12}z'', 0) \in {\operatorname{Im}}{\widetilde}P_m
\bigcap {\operatorname{Ker}}{\widetilde}P_m$$ giving a contradiction. By multiplying ${\widetilde}P_m$ from left with $$\begin{pmatrix}
{\operatorname{Id}}_K & -P_{12}P_{22}^{-1} \\
0 & {\operatorname{Id}}_{N-K}
\end{pmatrix}$$ we obtain $P_{12} \equiv 0$. Thus, we find that $$A^w P^w B^w =
\begin{pmatrix}
Q_{11}^w & Q_{12}^w \\
Q_{21}^w & Q_{22}^w
\end{pmatrix} \in {\Psi}^{1}_{cl}$$ where ${\sigma}(Q_{11}) = {\lambda}{\operatorname{Id}}_K$, $|{\sigma}(Q_{22})| \ne 0$ and $ Q_{12}$, $ Q_{21} \in {\Psi}^0_{cl}$. Choose a microlocal parametrix $B_{22}^w \in {\Psi}^{-m}_{cl}$ to $Q_{22}^w$ so that $B_{22}^w Q_{22}^w = Q_{22}^wB_{22}^w = {\operatorname{Id}}_{N-K}$ modulo $C^\infty$ near $w_0$. By multiplying from the left with $$\begin{pmatrix}
{\operatorname{Id}}_K & - Q_{12}^wB_{22}^w \\
0 & {\operatorname{Id}}_{N-K}
\end{pmatrix}\in {\Psi}^{0}_{cl}$$ we obtain that $Q_{12} \in S^{-\infty}$. By multiplying from the right with $$\begin{pmatrix}
{\operatorname{Id}}_K & 0 \\
-B_{22}^w Q_{21}^w & {\operatorname{Id}}_{N-K}
\end{pmatrix} \in {\Psi}^{0}_{cl}$$ we obtain $Q_{21} \in S^{-\infty}$. Note that these multiplications do not change the principal symbols of $Q_{jj}$ for $j=1$, 2, which finishes the proof.
\[Proof of Theorem \[mainthm\]\] Observe that since $P$ satisfies condition (${\Psi}$) we find that the adjoint $P^*$ satisfies condition (${\overline}{\Psi}$). By multiplying with an elliptic pseudodifferential operator, we may assume that $m=1$. Let $P^*$ have the expansion $P_1 + P_0 + \dots$ where $P_1 = {\sigma}(P^*) \in S^1$, then it is clear that it suffices to consider $w_0 = (x_0,{\xi}_0) \in |P_1|^{-1}(0)$, otherwise $P^* \in {\Psi}^1_{cl}(M)$ is elliptic near $w_0$ so holds and $P$ is microlocally solvable. Now $P^*$ is of principal type having constant characteristics so we find by using Proposition \[prepprop\] that $$P^* = \begin{pmatrix}
Q_{11}^w & 0 \\
0 & Q_{22}^w
\end{pmatrix} \in {\Psi}^{1}_{cl}$$ microlocally near $w_0$, where ${\sigma}(Q_{11}) =
{\lambda}{\operatorname{Id}}_K$ with ${\lambda} \in C^\infty$ an eigenvalue of ${\sigma}(P^*)$ of principal type and $Q_{22}^w$ is elliptic. Since $Q_{22}^w$ is elliptic, it is trivially solvable so we only have to investigate the solvability of $Q_{11}^w$. Now ${\lambda}$ is of principal type by the invariance, so if it does not satisfy condition (${\overline}{\Psi}$) then the proof of [@ho:yellow Theorem 26.4.7] can easily be adapted to this case, since the principal part of the operator is a scalar symbol times the identity matrix.
To prove solvability when condition (${\overline}{\Psi}$) is satisfied, we shall prove that there exists ${\phi}$ and ${\psi} \in S^0_{1,0}(T^*M)$ such that ${\phi}= 1$ in a conical neighborhood of $(x_0,{\xi}_0)$ and for any $T >0$ there exists a $K \times N$ system $R_{T} \in S^{1/2}_{1,0}(M)$ with the property that ${\operatorname{WF}}(R_{T}^w) \bigcap T^*_{x_0}M = \emptyset$ and $$\label{solvest}
{\Vert{\phi}^wu\Vert} \le C_1\left({\Vert{\psi}^wP^*u\Vert}_{(3/2
-1)} + T{\Vertu\Vert}\right) + {\VertR_{T}^w u\Vert} + C_0{\Vertu\Vert}_{(-1)}
\qquad u \in C_0^\infty(M, {\mathbf C}^N)$$ Here ${\Vertu\Vert}_{(s)}$ is the $L^2$ Sobolev norm and the constants are independent of $T$. Then for small enough $T$ we obtain and microlocal solvability, since $(x_0,{\xi}_0) \notin {\operatorname{WF}}(1-{\phi})^w$. In the case the eigenvalue satisfies condition (${\Psi}$) and near $x_0$ we may choose finitely many ${\phi}_j \in S^0_{1,0}(M)$ such that $\sum {\phi}_j \ge 1$ near $x_0$ and ${\Vert{\phi}_j^wu\Vert}$ can be estimated by the right hand side of for some suitable ${\psi}$ and $R_T$. By elliptic regularity of ${\left\{\,{\phi}_j\,\right\}}$ near $x_0$, we then obtain the estimate for small enough $T$ with $x \ne x_0$ in ${\operatorname{WF}}(R)$.
Observe that in the case when ${\lambda}$ satisfies condition ($P$) we obtain the estimate for $P^* = {\lambda}(x,D_x){\operatorname{Id}}_N$ with $3/2$ replaced with $1$ and $C_1 = {\mathcal}O(T)$ from the Beals-Fefferman estimate, see [@bf]. Since this estimate can be perturbed with terms in ${\Psi}^{0}_{cl}$ for small enough $T$ we get the estimate and solvability in this case. A similar argument gives subelliptic estimates if ${\lambda}$ satisfies condition (${\overline}{\Psi}$) and the bracket condition, see [@ho:yellow Chapter 27]. This gives Remark \[prem\].
It remains to consider the case $P_1 = {\lambda}{\operatorname{Id}}_N$, where ${\lambda}$ satisfies condition (${\overline}{\Psi}$). It is clear that by multiplying with an elliptic factor we may assume that $\partial_{\xi}{\operatorname{Re}}{\lambda}(w_0) \ne 0$, in the microlocal case after a conical transformation. Then, we may use Darboux’ theorem and the Malgrange preparation theorem to obtain microlocal coordinates $(t,y;{\tau},{\eta}) \in T^* {\mathbf R}^{n+1}$ so that $w_0 = (0,0; 0,{\eta}_0)$, $t = 0$ on $T^*_{x_0}M$ and ${\lambda} =
q({\tau} + if) $ in a conical neighborhood of $ w_0$, where $f \in
C^\infty({\mathbf R},S^1_{1,0})$ is real and homogeneous satisfying condition , and $0 \ne q \in S^0_{1,0}$, see Theorem 21.3.6 in [@ho:yellow]. By using the Malgrange preparation theorem and homogeneity we find that $$P_0(t,x;{\tau},{\xi}) = Q_{-1}(t,x;{\tau},{\xi})({\tau} + if(t,x,{\xi})){\operatorname{Id}}_N + F_0(t,x,{\xi})$$ where $Q_{-1}$ is homogeneous of degree $-1$ and $F_0$ is homogeneous of degree $0$ in the ${\xi}$ variables. By conjugation with elliptic Fourier integral operators and using the Malgrange preparation theorem successively on lower order terms, we obtain that $$\label{mikrop}
P^* = Q^w(D_{t}{\operatorname{Id}}_N + i\left({\chi}F\right)^w) + R^w$$ microlocally in a conical neighborhood ${\Gamma}$ of $w_0$ as in the proof of Theorem 26.4.7$'$ in [@ho:yellow]. Here we find that $F \in C^\infty({\mathbf R},
S^{1}_{1,0 }({\mathbf R}^{n}))$ has real principal symbol $f{\operatorname{Id}}_N$ satisfying , $Q \in S^0_{1,0}({\mathbf R}^{n+1})$ has principal symbol $q{\operatorname{Id}}_N \ne 0$ in ${\Gamma}$ and $R \in S^1_{1,0}( {\mathbf R}^{n+1})$ satisfies ${\Gamma} \bigcap {\operatorname{WF}}(R^w) = \emptyset$. Also, ${\chi}({\tau},{\eta}) \in S^0_{1,0}({\mathbf R}^{n+1})$ is equal to 1 in ${\Gamma}$ and $|{\tau}| \le C |{\eta}|$ in ${\operatorname{\rm supp}}{\chi}({\tau},{\eta})$. By cutting off in the $t$ variable we may assume that $F \in L^\infty({\mathbf R}, S^1_{1,0}({\mathbf R}^{n}))$. Now, we can follow the proof of Theorem 1.4 in [@de:cut]. As before, we shall choose ${\phi}$ and ${\psi}$ so that ${\phi} = 1$ conical neighborhood of $ w_0$, ${\psi} = 1$ on ${\operatorname{\rm supp}}{\phi}$ and $
{\operatorname{\rm supp}}{\psi} \subset {\Gamma}$. Also, we shall choose $${\phi}(t,y;{\tau},{\eta}) =
{\chi}_0(t,{\tau},{\eta}){\phi}_0(y,{\eta})$$ where ${\chi}_0(t,{\tau},{\eta}) \in S^0_{1,0}({\mathbf R}^{n+1})$, ${\phi}_0(y,{\eta}) \in S^0_{1,0}({\mathbf R}^{n})$, $t
\ne 0 $ in ${\operatorname{\rm supp}}\partial_t{\chi}_0$, $|{\tau}| \le C |{\eta}|$ in ${\operatorname{\rm supp}}{\chi}_0$ and $|{\tau}| \cong |{\eta}|$ in ${\operatorname{\rm supp}}\partial_{{\tau},{\eta}} {\chi}_0$.
Since $|{\sigma}(Q)| \ne 0$ and $R =0$ on ${\operatorname{\rm supp}}{\psi}$ it is no restriction to assume that $Q \equiv {\operatorname{Id}}_N$ and $R \equiv 0$ when proving the estimate . Now, by Theorem 18.1.35 in [@ho:yellow] we may compose $C^\infty({\mathbf R}, {\Psi}^m_{1,0}({\mathbf R}^{n}))$ with operators in ${\Psi}^k_{1,0}({\mathbf R}^{n+1})$ having symbols vanishing when $|{\tau}|
\ge c(1+ |{\eta}|)$, and we obtain the usual asymptotic expansion in ${\Psi}^{m+k-j}_{1,0}({\mathbf R}^{n+1})$ for $j \ge 0$. Since $|{\tau}| \le
C|{\eta}|$ in ${\operatorname{\rm supp}}{\phi}$ and ${\chi} = 1$ on ${\operatorname{\rm supp}}{\psi}$, it suffices to prove for $P^* = D_t + i F^w$.
By using Proposition \[maincor\] on ${\phi}^wu$, we obtain that $$\begin{gathered}
\label{fest}
{\VertB_T^w{\phi}^wu\Vert}^2_{-1/2} + {\Vert{\phi}^w u\Vert}^2 \\ \le C_0
T \left({\operatorname{Im}}{\left ( {\phi}^wP^*u, B_T^w{\phi}^wu\right ) }+
{\operatorname{Im}}{\left ( [P^*, {\phi}^w{\operatorname{Id}}_N]u, B_T^w{\phi}^wu\right ) }\right) + C_1{\Vert{\phi}^w u\Vert}^2_{-1}\end{gathered}$$ where $B_T^w \in L^\infty({\mathbf R},{\Psi}^{1}_{1/2,1/2}({\mathbf R}^n))$ is an $N \times N$ system with $\nabla B_T \in L^\infty({\mathbf R},
S^{1}_{1/2,1/2}({\mathbf R}^n))$, and ${\Vertu\Vert}_s = {\Vert{\langle D_y\rangle }^su\Vert}$ is the partial Sobolev norm in the $y$ variables. Since $|{\tau}| \le C |{\xi}|$ in ${\operatorname{\rm supp}}{\phi}$ we find that $ {\Vert{\phi}^w u\Vert}_{-1} \le C {\Vert u\Vert}_{(-1)}$ For any $u,\ v \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$ we have that $$\label{helpest}
|{\left ( v, B^w_T u\right ) } | = |{\left ( {\langle D_y\rangle }^{1/2}v, {\langle D_y\rangle }^{-1/2}B^w_Tu\right ) }| \le
C({\Vertv\Vert}_{1/2}^2 +
{\VertB^w_T u\Vert}^2_{-1/2})$$ where ${\langle D_y\rangle } = 1 + |D_y|$. Now ${\phi}^w = {\phi}^w{\psi}^w$ modulo ${\Psi}^{-2}_{1,0}({\mathbf R}^{n+1}) $, thus we find from that $$\label{f1est}
|{\left ( {\phi}^wP^*u, B_T^w{\phi}^wu\right ) }|
\le C({\Vert{\psi}^wP^*u\Vert}_{1/2}^2 + {\Vertu\Vert}^{2} + {\VertB_T^w{\phi}^wu\Vert}^2_{-1/2})$$ where the last term can be cancelled for small enough $T$ in . We also have to estimate the commutator term ${\operatorname{Im}}{\left ( [P^*, {\phi}^w {\operatorname{Id}}_N]u,
B_T^w{\phi}^wu\right ) }$ in . We find $$[P^*, {\phi}^w{\operatorname{Id}}_N]
= -(i\partial_t {\phi}^w - {\left\{\,f,{\phi}\,\right\}}^w){\operatorname{Id}}_N \in
{\Psi}^{0}_{1,0}({\mathbf R}^{n+1})$$ modulo ${\Psi}^{-1}_{1,0}({\mathbf R}^{n+1})$ by the expansion, where the error term can be estimated by . Since ${\phi}= {\chi}_0{\phi}_0$ we find that ${\left\{\,f, {\phi}\,\right\}} = {\phi}_0 {\left\{\,f,{\chi}_0\,\right\}} + {\chi}_0
{\left\{\,f,{\phi}_0\,\right\}}$, where $ {\phi}_0{\left\{\,f,{\chi}_0\,\right\}} = R_0 \in
S^{0}_{1,0}({\mathbf R}^{n+1})$ is supported when $|{\tau}| \cong |{\eta}|$ and ${\psi}=1$. Now $({\tau} + if)^{-1} \in S^{-1}_{1,0}({\mathbf R}^{n+1})$ when $|{\tau}| \cong |{\eta}|$, thus by [@ho:yellow Theorem 18.1.35] we find that $ R_0^w =
A_1^w{\psi}^wP^*\text{ modulo ${\Psi}^{-1}_{1,0}({\mathbf R}^{n+1})$} $ where $A_1 = R_0({\tau} + if)^{-1} \in S^{-1}_{1,0}({\mathbf R}^{n+1})$. As before, we find from that $$\begin{gathered}
\label{f2est}
|{\left ( R_0^wu,B_T^w {\phi}^wu\right ) }| \le
C({\VertR_0^w u\Vert}^2_{1/2} + {\VertB_T^w{\phi}^w u\Vert}_{-1/2}^2) \\\le C_0({\Vert{\psi}^wP^*u\Vert}_{-1/2}^2 + {\VertB_T^w{\phi}^w u\Vert}_{-1/2}^2 + {\Vertu\Vert}^2_{-1/2})
\end{gathered}$$ and also $$|{\left ( \partial_t {\phi}^wu, B_T^w{\phi}^wu\right ) }|
\le {\VertR_1^wu\Vert}^2 + {\VertB_T^w{\phi}^w u\Vert}_{-1/2}^2$$ where $R_1^w ={\langle D_{y}\rangle }^{1/2}\partial_t {\phi}^w\in
{\Psi}^{1/2}_{1,0}({\mathbf R}^{n+1})$, thus $t \ne 0$ in ${\operatorname{WF}}(R_1^w)$.
It only remains to estimate the term ${\operatorname{Im}}{\left ( ({\left\{\,f,{\phi}_0\,\right\}}{\chi}_0)^wu,
B_T^w{\phi}^wu\right ) }$. Here $({\left\{\,f,{\phi}_0\,\right\}}{\chi}_0)^w =
{\left\{\,f,{\phi}_0\,\right\}}^w{\chi}_0^w$ and ${\phi}^w =
{\phi}_0^w{\chi}_0^w$ modulo ${\Psi}^{-1}_{1,0}({\mathbf R}^{n+1})$. As in we find $$|{\left ( R^wu, B_T^wv\right ) }| = |{\left ( {\langle D_y\rangle } R^wu, {\langle D_y\rangle }^{-1} B^w_Tv\right ) }|
\le C({\Vertu\Vert}^2 + {\Vertv\Vert}^2)$$ for $R \in S^{-1}_{1,0}({\mathbf R}^{n+1})$, thus we find $$|{\operatorname{Im}}{\left ( ({\left\{\,f,{\phi}_0\,\right\}}{\chi}_0)^wu, B_T^w{\phi}^wu\right ) } |
\le |{\operatorname{Im}}{\left ( {\left\{\,f,{\phi}_0\,\right\}}^w{\chi}_0^wu,
B_T^w{\phi}_0^w{\chi}_0^wu\right ) }| + C{\Vertu\Vert}^2.$$ The calculus gives $B_T^w{\phi}_0^w = (B_T{\phi}_0)^w$ and $$2i{\operatorname{Im}}\left((B_T{\phi}_0)^w{\left\{\,f,{\phi}_0\,\right\}}^w \right)=
{\left\{\,B_T{\phi}_0,{\left\{\,f,{\phi}_0\,\right\}}\,\right\}}^w = 0$$ modulo $L^\infty({\mathbf R},{\Psi}^{0}_{1/2,1/2}({\mathbf R}^n))$ since $\nabla
(B_T{\phi}_0) \in L^\infty({\mathbf R}, S^{1}_{1/2,1/2}({\mathbf R}^{n}))$ and ${\left\{\,f, {\phi}_0\,\right\}}$ is real. Thus, we obtain $$\label{f3est}
|{\operatorname{Im}}{\left ( {\left\{\,f,{\phi}_0\,\right\}}^w{\chi}_0^wu,
B_T^w{\phi}_0^w{\chi}_0^wu\right ) }| \le C{\Vert{\chi}_0^wu\Vert}^2 \le C'{\Vertu\Vert}^2$$ and the estimate for small enough $T$, which completes the proof of Theorem \[mainthm\].
The symbol classes and weights {#symb}
==============================
In this section we shall define the symbol classes we shall use. Assume that $f \in L^\infty({\mathbf R}, S(h^{-1},
hg^{\sharp}))$ is scalar and satisfies , here $0 < h \le 1$ and $g^{\sharp}=
(g^{\sharp})^{\sigma}$ are constant. It is no restriction to change $h$ so that $|f|^{g^{\sharp}}_1 \le h^{-1/2}$, which we assume in what follows. The results shall be uniform in the usual sense, they will only depend on the seminorms of $f$ in $L^\infty({\mathbf R}, S(h^{-1}, hg^{\sharp}))$. Let $$\begin{aligned}
\label{xpmdef}
&X_+(t) = {\left\{\,w \in T^*{\mathbf R}^n : \exists\,s\le t,\ f(s,w) >0\,\right\}}\\
&X_-(t) = {\left\{\,w \in T^*{\mathbf R}^n : \exists\,s\ge
t,\ f(s,w) < 0\,\right\}}.\label{xpmdef1} \end{aligned}$$ Clearly, $X_\pm(t)$ are open in $T^*{\mathbf R}^n$, $X_+(s) \subseteq X_+(t)$ and $X_-(s) \supseteq X_-(t)$ when $s \le t$. By condition $({\overline}{\Psi})$ we obtain that $X_-(t) \bigcap X_+(t) = \emptyset$ and $\pm f(t,w) \ge
0$ when $w \in X_\pm(t)$, $\forall\, t$. Let $X_0(t) = T^*{\mathbf R}^n\setminus \left(X_+(t)\bigcup
X_-(t)\right)$ which is closed in $T^*{\mathbf R}^n$. By the definition of $X_\pm(t)$ we have $f(t,w) =0$ when $w \in X_0(t)$. Let $$\label{d0def}
d_0(t_0,w_0) = \inf{\left\{\,g^{\sharp}(w_0-z)^{1/2}:\ z \in X_0(t_0)\,\right\}}$$ be is the $g^{\sharp}$ distance in $T^*{\mathbf R}^n$ to $ X_0(t_0)$ for fixed $t_0$, it is equal to $+\infty$ in the case that $X_0(t_0) = \emptyset$. By taking the infimum over $z$ we find that $w \mapsto d_0(t,w)$ is Lipschitz continuous with respect to $g^{\sharp}$ for fixed $t$ when $ d_0 < \infty$, i.e., $$\sup_{w \ne z \in T^*{\mathbf R}^n}|{\delta}_0(t,w)-
{\delta}_0(t,z)|/g^{\sharp}(w-z)^{1/2} \le 1$$
\[d0deforig\] We define the signed distance function ${\delta}_0(t,w)$ by $$\label{delta0def}
{\delta}_0 = {\operatorname{sgn}}(f)\min(d_0,h^{-1/2})$$ where $d_0$ is given by and $$\label{fsign}
{\operatorname{sgn}}(f)(t,w) =
\left\{
\begin{alignedat}{2}
\pm 1&, &\quad &w \in X_\pm(t)\\
0&, &\quad &w \in X_0(t)
\end{alignedat}
\right.$$ so that ${\operatorname{sgn}}(f)f \ge 0$.
The signed distance function $w \mapsto {\delta}_0(t,w)$ given by Definition \[d0deforig\] is Lipschitz continuous with respect to the metric $g^{\sharp}$ with Lipschitz constant equal to 1, $\forall\, t$. We also find that $t \mapsto {\delta}_0(t,w)$ is non-decreasing, ${\delta}_0f \ge 0$, $|{\delta}_0| \le h^{-1/2}$ and when $|{\delta}_0| < h^{-1/2}$ we find that $|{\delta}_0| = d_0$ is given by .
In fact, it suffices to show the Lipschitz continuity of $w \mapsto
{\delta}_0(t,w)$ on $\complement{X_0}(t)$, and then it follows from the Lipschitz continuity of $w \mapsto
d_0(t,w)$ when $d_0 < \infty$. Clearly ${\delta}_0f \ge 0$, and since $X_+(t)$ is non-decreasing and $X_-(t)$ is non-increasing when $t$ increases, we find that $ t
\mapsto {\delta}_0(t,w)$ is non-decreasing.
In the following, we shall treat $t$ as a parameter which we shall suppress, and we shall denote $f' = \partial_wf$ and $f'' =
\partial_w^2f$. We shall also in the following assume that we have choosen $g^{\sharp}$ orthonormal coordinates so that $g^\sharp(w) = |w|^2$ and $|f'| \le h^{-1/2}$.
\[g1def\] Let $$\label{h2def}
H^{-1/2} = 1 + |{\delta}_0| + \frac{|f'|}{|{f''}| + h^{1/4}|f'|^{1/2} +
h^{1/2}}$$ and $G = H g^{\sharp}$.
Observe that ${\langle {\delta}_0\rangle } = 1 + |{\delta}_0| \le H^{-1/2}$ and $$\label{H1hest}
1 \le H^{-1/2}\le 1 + |{\delta}_0| + h^{-1/4} |f'|^{1/2}\le 3 h^{-1/2}$$ since $|f'| \le h^{-1/2}$ and $|{\delta}_0| \le
h^{-1/2}$. This gives that $hg^{\sharp}\le 3 G$.
\[Mdef\] Let $$\label{Mdef0}
M = |f| +|f'| H^{-1/2} + |{f''}| H^{-1} + h^{1/2}H^{-3/2}$$ then we have that $h^{1/2} \le M \le C_3 h^{-1}$.
The metric $G$ and weight $M$ have the following properties according to Proposition 3.7 in [@de:NT].
\[g1prop\] We find that $H^{-1/2}$ is Lipschitz continuous, $G$ is ${\sigma}$ temperate such that $G =
H^2G^{\sigma}$ and $$\label{tempest}
H(w) \le C_0 H(w_0)(1 + G_{w_0}(w-w_0))$$ We have that $M$ is a weight for $G$ such that $M \le C H^{-1}$, $f \in S(M,G)$ and $$\label{mtemp}
M(w) \le C_1 M(w_0)(1 + G_{w_0}(w-w_0))^{3/2}$$
Since $G \le g^{\sharp}\le
G^{\sigma}$ we find that the conditions and are stronger than the property of being ${\sigma}$ temperate (in fact, strongly ${\sigma}$ temperate in the sense of [@bc:sob Definition 7.1]). Note that $f \in S(M,Hg^{\sharp})$ for any choice of $H \ge
h$ in Definition \[Mdef\]. The following property of $G$ is the most important for the proof.
\[ffactprop\] Let $H^{-1/2}$ be given by Definition \[g1def\] for $f \in
S(h^{-1},hg^{\sharp})$. There exists ${\kappa_1}>0$ so that if ${\langle {\delta}_0\rangle } = 1 + |{\delta}_0| \le {\kappa}_1H^{-1/2}$ then $$\label{ffactor}
f = {\alpha}_0{\delta}_0$$ where ${\kappa}_1MH^{1/2} \le {\alpha}_0 \in S(MH^{1/2}, G)$, which implies that ${\delta}_0 = f/{\alpha}_0 \in S(H^{-1/2}, G)$.
This follows directly from Proposition 3.9 in [@de:NT]. Next, we shall define the weight $m$ we shall use.
\[h0def\] For $(t,w) \in {\mathbf R}\times T^*{\mathbf R}^n$ we let $$\begin{gathered}
\label{mphodef}
m(t,w) = \inf_{t_1 \le t \le
t_2}\big\{\, |{\delta}_0(t_1,w) -{\delta}_0(t_2,w)|\\ +
\max\big(H^{1/2}(t_1,w){\langle {\delta}_0(t_1,w)\rangle }^2,
H^{1/2}(t_2,w){\langle {\delta}_0(t_2,w)\rangle }^2\big)/2 \,\big\}\end{gathered}$$ where ${\langle {\delta}_0\rangle } = 1 + |{\delta}_0|$.
This weight essentially measures how much $t \mapsto
{\delta}_0(t,w)$ changes between the minima of $t \mapsto
H^{1/2}(t,w){\langle {\delta}_0(t,w)\rangle }^2$, which will give restrictions on the sign changes of the symbol. When $t \mapsto {\delta}_0(t,w)$ is constant for fixed $w$, we find that $t \mapsto m(t,w)$ is equal to the largest quasi-convex minorant of $t \mapsto H^{1/2}(t,w){\langle {\delta}_0(t,w)\rangle }^2/2$, i.e., $\sup_I
m = \sup_{\partial I} m $ for compact intervals $I \subset {\mathbf R}$, see [@ho:conv Definition 1.6.3].
The main difference between this weight and the weight in [@de:NT] is the use of $H^{1/2}{\langle {\delta}_0\rangle }^2$ in the definition of $m$ instead of $H^{1/2}{\langle {\delta}_0\rangle }$, and this is due to Lerner [@ln:cutloss]. The weight has the following properties according to Propositions 4.3 and 4.4 in [@de:cut].
\[h0slow\] We have that $m \in L^\infty({\mathbf R}\times T^*{\mathbf R}^{n})$, $w \mapsto m(t,w)$ is uniformly Lipschitz continuous, $\forall\, t$, and $$\label{hhhest}
h^{1/2}{\langle {\delta}_0\rangle }^2/6 \le
m \le H^{1/2}{\langle {\delta}_0\rangle }^2/2 \le {\langle {\delta}_0\rangle }/2$$ There exists $C>0$ so that $$\label{wtemp}
m(t_0,w) \le C m(t_0,w_0)(1 + |w-w_0|/{\langle {\delta}_0(t_0,w_0)\rangle })^{3}$$ thus $m$ is a weight for $g^{\sharp}$.
The following result will be essential for the proof of Proposition \[mainprop\] in Section \[lower\], it follows from Proposition 4.5 in [@de:cut].
\[mestprop\] Let the weight $M$ be given by Definition \[Mdef\] and $m$ by Definition \[h0def\]. Then there exists $C_0>0$ such that $$\label{Mest0}
MH^{3/2}{\langle {\delta}_0\rangle }^2 \le C_0m$$
We have the following convexity property of $t \mapsto
m(t,w)$, which will be important for the construction of the multiplier.
\[qmaxpropo\] Let $m$ be given by Definition \[h0def\]. Then $$\label{qmaxwd}
\sup_{t_1 \le t \le t_2}m(t,w) \le {\delta}_0(t_2,w) -
{\delta}_0(t_1,w) + m(t_1,w) + m(t_2,w)\qquad \forall\,w$$
Since $t \mapsto {\delta}_0(t,w)$ is monotone, we find that $$\label{convest}
\inf_{\pm(t-t_0) \ge 0} \left(|{\delta}_0(t,w)
-{\delta}_0(t_0,w)| + H^{1/2}(t,w){\langle {\delta}_0(t,w)\rangle }^2/2\right) \le
m(t_0,w)$$ Let $t \in [t_1,t_2]$, then by using for $t_0 = t_1$, $t_2$, and taking the infima, we obtain that $$\begin{gathered}
m (t,w) \le \inf_{r \le t_1 < t_2\le s} {\delta}_0(s,w)
-{\delta}_0(r,w) + H^{1/2}(s,w){\langle {\delta}_0(s,w)\rangle }^2/2 +
H^{1/2}(r,w){\langle {\delta}_0(r,w)\rangle }^2/2 \\
\le {\delta}_0(t_2,w) -{\delta}_0(t_1,w) +m (t_1,w) +m (t_2,w)\end{gathered}$$ which gives after taking the supremum.
Next, we shall construct the pseudo-sign $B = {\delta}_0 + {\varrho}_0$, which we shall use in Proposition \[wickweyl\] to construct the multiplier of Proposition \[mainprop\].
\[apsdef\] Assume that ${\delta}_0$ is given by Definition \[d0deforig\] and $m$ is given by Definition \[h0def\]. Then for $T>0$ there exists real valued ${\varrho}_T(t,w)
\in L^\infty({\mathbf R}\times T^*{\mathbf R}^n)$ with the property that $w \mapsto
{\varrho}_T(t,w)$ is uniformly Lipschitz continuous, and $$\begin{aligned}
\label{r0prop0}
&|{\varrho}_T| \le m\\
&T\partial_t({\delta}_0 + {\varrho}_T) \ge m/2 \qquad \text{in
${\mathcal}D'({\mathbf R})$}
\label{r0prop1}\end{aligned}$$ when $|t| <T$.
(We owe this argument to Lars Hörmander [@ho:NT].) Let $$\label{r0def}
{\varrho}_{T}(t,w) = \sup_{-T \le s
\le t}\left({\delta}_0(s,w) - {\delta}_0(t,w) + \frac{1}{2T} \int_s^t
m(r,w)\,dr - m(s,w)\right)$$ for $|t| \le T$, then $$\begin{gathered}
{\delta}_0(t,w) + {\varrho}_T(t,w) = \sup_{-T \le s
\le t}\left({\delta}_0(s,w) - \frac{1}{2T}\int_0^s m(r,w)\,dr -
m(s,w)\right) \\+
\frac{1}{2T} \int_0^t m(r,w)\,dr\end{gathered}$$ which immediately gives since the supremum is non-decreasing. Since $w \mapsto {\delta}_0(t,w)$ and $w \mapsto
m(t,w)$ are uniformly Lipschitz continuous by Proposition \[h0slow\], we find by taking the supremum that $w \mapsto {\varrho}_T(t,w)$ is uniformly Lipschitz continuous. We find from Proposition \[qmaxpropo\] that $${\delta}_0(s,w) - {\delta}_0(t,w) + \frac{1}{2T}\int_s^t m(r,w)\,dr -
m(s,w) \le m(t,w) \qquad -T \le s \le t \le T$$ By taking the supremum, we obtain that $ -m(t,w) \le
{\varrho}_T(t,w) \le m(t,w)$ when $|t| \le T$, which proves the result.
The Wick quantization {#norm}
=====================
In order to define the multiplier we shall use the Wick quantization, and we shall also define the function spaces that we shall use. As before, we shall assume that $g^{\sharp}=
(g^{\sharp})^{\sigma}$ and the coordinates are chosen so that $g^{\sharp}(w) =
|w|^2$. For $a \in L^\infty(T^*{\mathbf R}^n)$ we define the Wick quantization: $$\label{defwick}
a^{Wick}(x,D_x)u(x) = \int_{T^*{\mathbf R}^n}a(y,{\eta})
{\Sigma}^w_{y,{\eta}}(x,D_x)u(x)\,dyd{\eta}\qquad u \in {\mathcal}S({\mathbf R}^n)$$ using the projections ${\Sigma}^w_{y,{\eta}}(x,D_x)$ with Weyl symbol $${\Sigma}_{y,{\eta}}(x,{\xi}) =
{\pi}^{-n}\exp(-g^\sharp(x-y,{\xi}-{\eta}))$$ (see [@de:suff Appendix B] or [@ln:coh Section 4]). We find that $a^{Wick}$: $ {\mathcal}S({\mathbf R}^n) \mapsto {\mathcal}S'({\mathbf R}^n)$ so that $(a^{Wick})^* = (\overline a)^{Wick}$, $$\label{poswick}
a \ge 0
\implies
{\left ( a^{Wick}(x,D_x)u,u\right ) } \ge
0 \qquad u \in {\mathcal}S({\mathbf R}^n)$$ and $
{\Verta^{Wick}(x,D_x)\Vert}_{{\mathcal}L(L^2({\mathbf R}^n))} \le
{\Verta\Vert}_{L^\infty(T^*{\mathbf R}^n)},
$ which is the main advantage with the Wick quantization (see [@ln:coh Proposition 4.2]). Now if $a_t(x,{\xi}) \in L^\infty({\mathbf R}\times T^*{\mathbf R}^n)$ depends on a parameter $t$, then we find that $$\label{intwick}
\int_{\mathbf R}{\left ( a^{Wick}_tu ,u\right ) } {\phi}(t)\, dt =
{\left ( A_{\phi}^{Wick}u, u\right ) } \qquad u \in {\mathcal}S({\mathbf R}^n)$$ where $A_{\phi}(x,{\xi}) = \int_{\mathbf R}a_t(x,{\xi}) {\phi}(t)\, dt$. In fact, if $a \in L^1$ then this follows from the Fubini theorem, in general we obtain this by cutting off $a_t$ on large sets in $T^*{\mathbf R}^n$ and using dominated convergence. We obtain from the definition that $a^{Wick} = a_0^{w}$ where $$\label{gausreg}
a_0(w) = {\pi}^{-n}\int_{T^*{\mathbf R}^n} a(z)\exp(-|w-z|^2)\,dz$$ is the Gaussian regularization, thus Wick operators with symmetric symbols have symmetric Weyl symbols.
We also have the following result about the composition of Wick operators according to the proofs of Proposition 3.4 in [@ln:wick] and Lemma A.1.5 in [@ln:cutloss].
\[wickcomp\] Let $a(w)$, $b(w) \in L^\infty$, and let $m_1 $, $m_2 $ be bounded weights for $g^{\sharp}$. If $|a| \le m_1$ and $|b'| = |\partial b| \le m_2$, then $$\label{wickcomp1}
a^{Wick}b^{Wick} = (ab )^{Wick} + r^w$$ with $r \in S(m_1m_2,g^{\sharp})$. In the case when $a$, $b$ are real valued, $|a| \le
m_1$ and $|b''| \le m_2$, we obtain that $$\label{wickcomp2}
{\operatorname{Re}}\left(a^{Wick}b^{Wick} \right) = \left(ab - \frac{1}{2}a'\cdot
b'\right)^{Wick} + r^w$$ with $r \in S(m_1m_2,g^{\sharp})$. Here $a'$ is the distributional derivative of $a \in L^\infty$ and $b'$ is Lipschitz continuous, so the product is well-defined in $L^\infty$.
If $A \in L^\infty(T^*{\mathbf R}^n)$ is an $M \times N$ system, then we can define $A^{Wick}$ by on $u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$. These operators have the same properties as the scalar operators, but of course we need that $M = N$ in order for to hold.
In the following, we shall assume that $G =Hg^{\sharp}\le g^{\sharp}$ is a slowly varying metric satisfying $$\label{gentemp}
H(w) \le C_0 H(w_0) (1 + |w-w_0|)^{N_0}$$ and that $m$ is a weight for $G$ satisfying with $H$ replaced by $m$. This means that $G$ and $m$ are strongly ${\sigma}$ temperate in the sense of [@bc:sob Definition 7.1]. Recall the symbol class $S^+(1,g^{\sharp})$ defined by Definition \[s+def\].
\[propwick\] Assume that $a \in L^\infty(T^*{\mathbf R}^n)$ is a $N \times N$ system such that $|a| \le Cm$, then $ a^{Wick} = a_0^w$ where $a_0\in S(m,g^{\sharp})$ is given by . If $a \in S(m,G)$ for $G = Hg^{\sharp}$ then $a_0 = a$ modulo symbols in $S(mH,G)$. If $|a| \le Cm$ and $a = 0$ in a fixed $G$ ball with center $w$, then $a \in S(mH^N,G)$ near $w$ for any $N$. If $a$ is Lipschitz continuous then we have $a_0\in S^+(1, g^{\sharp})$. If $a(t,w)$ and $g(t,w) \in L^\infty({\mathbf R}\times T^*{\mathbf R}^n)$ are $N \times N$ systems and ${\partial_t }a(t,w) \ge g(t,w)$ in ${\mathcal}D'({\mathbf R})$ for almost all $w
\in T^*{\mathbf R}^n$, then we find ${\left ( {\partial_t }(a^{Wick})u,u\right ) } \ge {\left ( g^{Wick}u,u\right ) }$ in ${\mathcal}D'({\mathbf R})$ for $u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$.
Observe that the results are uniform in the metrics and weights. By localization we find, for example, that if $|a| \le Cm$ and $a \in
S(m,G)$ in a $G$ neighborhood of $w_0$, then $a_0 =a$ modulo $S(mH,G)$ in a smaller $G$ neighborhood of $w_0$. These results are well known, but for convenience we give a short proof.
Since $a$ is measurable satisfying $|a| \le C m$, where $m(z) \le C_0
m(w)(1 + |z-w|)^{N_0}$ by , we find that $a^{Wick} = a_0^{w}$ where $a_0 = {\mathcal}O(m)$ is given by . By differentiating on the exponential factor, we find $a_0 \in S(m,g^{\sharp})$.
If $a = 0$ in a $G$ ball of radius ${\varepsilon}>0$ and center at $w$, then we can write $${\pi}^{n}a_0(w) =
\int_{|z-w| \ge {\varepsilon}H^{-1/2}(w)} a(z)\exp(-|w-z|^2)\,dz ={\mathcal}O(m(w) H^N(w))$$ for any $N$ even after repeated differentiation. If $a \in S(m,G)$ then Taylor’s formula gives $$a_0(w) = a(w) + {\pi}^{-n} \int_0^1\int_{T^*{\mathbf R}^n} (1-{\theta}){\langle a''(w +
{\theta}z)z,z\rangle } e^{-|z|^2}\,dzd{\theta}$$ where $a'' \in S(mH,G)$ because $G = Hg^{\sharp}$. Since $m(w + {\theta}z)
\le C_0 m(w)(1 + |z|)^{N_0}$ and $H(w + {\theta}z) \le C_0H(w)(1 +
|z|)^{N_0} $ when $|{\theta}| \le 1$, we find that $a_0(w) = a(w)$ modulo $S(mH,G)$. Now, the Lipschitz continuity of $a$ means that $\partial a \in L^\infty(T^*{\mathbf R}^n)$. Since $\partial a_0(w) = {\pi}^{-n}\int_{T^*{\mathbf R}^n}
\partial a(z)\exp(-|w-z|^2)\,dz $, we obtain that $a_0\in S^+(1, g^{\sharp})$.
For the final claim, we note that $ -\int a(t,w) {\phi}'(t)\,dt \ge \int
g(t,w){\phi}(t)\,dt$ for all $0 \le {\phi} \in C_0^\infty({\mathbf R}) $ and almost all $w\in T^*{\mathbf R}^n$, which by and gives $$-\int {\left ( a^{Wick}(t,x,D_x)u,u\right ) } {\phi}'(t)\,dt \ge \int
{\left ( g^{Wick}(t,x,D_x)u,u\right ) }{\phi}(t)\,dt \qquad 0 \le {\phi} \in
C_0^\infty({\mathbf R})$$ for $u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$.
We shall compute the Weyl symbol for the Wick operator $({\delta}_0 + {\varrho}_T)^{Wick}$, where ${\varrho}_T$ is given by Proposition \[apsdef\]. In the following we shall suppress the $t$ variable.
\[wickweyl\] Let $B = {\delta}_0 + {\varrho}_0$, where ${\delta}_0$ is given by Definition \[d0deforig\] and ${\varrho}_0$ is real valued and Lipschitz continuous, satisfying $|{\varrho}_0| \le m$, where $m \le
H^{1/2}{\langle {\delta}_0\rangle }^2/2 \le {\langle {\delta}_0\rangle }/2$ is a weight for $g^{\sharp}$. Then we find $$B^{Wick} = b^w$$ where $b= {\delta}_1 + {\varrho}_1 \in S({\langle {\delta}_0\rangle },g^{\sharp})\bigcap
S^+(1,g^{\sharp})$ is real, ${\delta}_1 \in S(H^{-1/2},g^{\sharp})\bigcap
S^+(1,g^{\sharp})$, and ${\varrho}_1 \in S(m, g^{\sharp})\bigcap S^+(1, g^{\sharp})$. Also, there exists ${\kappa}_2 >0$ so that ${\delta}_1 = {\delta}_0$ modulo $S(H^{1/2},G)$ when ${\langle {\delta}_0\rangle } \le
{\kappa}_2H^{-1/2}$, which gives $b = {\delta}_0$ modulo $S(H^{1/2}{\langle {\delta}_0\rangle }^2, g^{\sharp})$. For any ${\lambda} > 0$ we find that $|{\delta}_0| \ge
{\lambda} H^{-1/2}$ and $H^{1/2} \le {\lambda}/3$ imply that ${\operatorname{sgn}}(B) = {\operatorname{sgn}}({\delta}_0)$ and $
|B| \ge {\lambda}H^{-1/2}/3$.
Let ${\delta}_0^{Wick} = {\delta}_1^w$ and ${\varrho}_0^{Wick} =
{\varrho}_1^w$. Since $|{\delta}_0|\le {\langle {\delta}_0\rangle } \le H^{-1/2}$, $|{\varrho}_0|
\le m \le {\langle {\delta}_0\rangle }/2$ and the symbols are real valued, we obtain from Proposition \[propwick\] that $b \in
S({\langle {\delta}_0\rangle },g^{\sharp})$, ${\delta}_1 \in S(H^{-1/2},g^{\sharp})$ and ${\varrho}_1 \in S(m, g^{\sharp})$ are real valued. Since ${\delta}_0$ and ${\varrho}_0$ are uniformly Lipschitz continuous, we find that ${\delta}_1$ and ${\varrho}_1 \in
S^+(1,g^{\sharp})$ by Proposition \[propwick\].
If ${\langle {\delta}_0\rangle } \le {\kappa}H^{-1/2}$ at $w_0$ for sufficiently small ${\kappa} >0$, then we find by the Lipschitz continuity of ${\delta}_0$ and the slow variation of $G$ that ${\langle {\delta}_0\rangle } \le
C_0{\kappa}H^{-1/2}$ in a fixed $G$ neighborhood ${\omega}_{\kappa}$ of $w_0$ (depending on ${\kappa}$). For ${\kappa}
\ll 1$ we find ${\delta}_0 \in S(H^{-1/2}, G)$ in ${\omega}_{\kappa}$ by Proposition \[ffactprop\], thus ${\delta}_1 =
{\delta}_0$ modulo $S(H^{1/2},G)$ near $w_0$ by Proposition \[propwick\] after localization.
When $|{\delta}_0| \ge {\lambda}H^{-1/2} > 0$ at $w_0$, then we find that $$|{\varrho}_0| \le m \le {\langle {\delta}_0\rangle }/2 \le
(1 + H^{1/2}/{\lambda})|{\delta}_0|/2$$ We obtain that $|{\varrho}_0| \le 2|{\delta}_0|/3$ so ${\operatorname{sgn}}(B) = {\operatorname{sgn}}({\delta}_0)$ and $|B| \ge |{\delta}_0|/3 \ge
{\lambda}H^{-1/2}/3 $ when $H^{1/2} \le {\lambda}/3$, which completes the proof.
Let $m$ be given by Definition \[h0def\], then $m$ is a weight for $g^{\sharp}$ according to Proposition \[h0slow\]. We are going to use the symbol classes $S(m^k, g^{\sharp})$, $k \in {\mathbf R}$.
\[Hdef\] Let $H(m^k,g^{\sharp})$, be the Hilbert space given by [@bc:sob Definition 4.1] so that $$\label{7.7}
u \in H(m^k,g^{\sharp}) \iff
a^wu \in L^2 \qquad \forall\, a \in
S(m^k, g^{\sharp})\qquad k \in {\mathbf R}$$ We let ${\Vertu\Vert}_{{k}}$ be the norm of $H(m^{k},g^{\sharp})$.
This Hilbert space has the following properties: ${\mathcal}S$ is dense in $H(m^k,g^{\sharp})$, the dual of $H(m^k,g^{\sharp})$ is naturally identified with $H(m^{-k},g^{\sharp})$, and if $u \in H(m^k,g^{\sharp})$ then $u =
a_0^w v$ for some $v \in L^2({\mathbf R}^n)$ and $a_0 \in S(m^{-k}, g^{\sharp})$ (see [@bc:sob Corollary 6.7]). It follows that $a^w \in {\operatorname{Op}}S(m^k, g^{\sharp})$ is bounded: $$\label{nest0}
u \in H(m^j,g^{\sharp}) \mapsto a^wu \in
H(m^{j-k},g^{\sharp})$$ with bound only depending on the seminorms of $a$.
We recall Proposition 6.5 in [@de:cut], which shows that the topology in $H(m^{1/2},
g^{\sharp})$ can be defined by the operator $m^{Wick}$.
\[wprop\] Let $B = {\delta}_0 + {\varrho}_0$, where ${\delta}_0$ is given by Definition \[d0deforig\] and $|{\varrho}_0| \le m$. Then there exist positive constants $c_1$, $c_2$ and $C_0$ such that $$\label{west3}
c_1 h^{1/2}({\VertB^{Wick}u\Vert}^2 + {\Vertu\Vert}^2) \le c_2 {\Vertu\Vert}_{{1/2}}^2 \le
{\left ( m^{Wick}u,u\right ) }\le
C_0 {\Vertu\Vert}_{{1/2}}^2\qquad u \in {\mathcal}S({\mathbf R}^n)$$ The constants only depend on the seminorms of $f$ in $L^\infty({\mathbf R}, S(h^{-1},hg^{\sharp}))$.
In the following, we let ${\Vertu(t)\Vert}$ be the $L^2$ norm of $x \mapsto
u(t,x) \in {\mathbf C}^N$ in ${\mathbf R}^{n}$ for fixed $t$, and ${\left ( u(t),v(t)\right ) }$ the corresponding sesquilinear inner product. Let ${\mathcal}B = {\mathcal}B(L^2({\mathbf R}^{n}), {\mathbf C}^N)$ be the set of bounded operators $L^2({\mathbf R}^{n}, {\mathbf C}^N)\mapsto L^2({\mathbf R}^{n}, {\mathbf C}^N)$. We shall use operators which depend measurably on $t$ in the following sense.
We say that $t \mapsto A(t)$ is weakly measurable if $A(t) \in {\mathcal}B$ for all $t$ and $t \mapsto A(t)u$ is weakly measurable for every $u
\in L^2({\mathbf R}^{n}, {\mathbf C}^N)$, i.e., $t \mapsto {\left ( A(t)u,v\right ) }$ is measurable for any $u$, $v \in L^2({\mathbf R}^{n}, {\mathbf C}^N)$. We say that $A(t) \in
L_{loc}^\infty({\mathbf R}, {\mathcal}B)$ if $t \mapsto A(t)$ is weakly measurable and locally bounded in ${\mathcal}B$.
If $A(t) \in L_{loc}^\infty({\mathbf R}, {\mathcal}B)$, then we find that the function $t \mapsto {\left ( A(t)u,v\right ) }\in L_{loc}^\infty({\mathbf R})$ has weak derivative ${{\textstyle\frac{d}{dt}}}{\left ( A u,v\right ) } \in {\mathcal}D'({\mathbf R})$ for any $u$, $v \in
L^2({\mathbf R}^{n}, {\mathbf C}^N)$, given by $${{\textstyle\frac{d}{dt}}}{\left ( A u,v\right ) }({\phi}) =
-\int{\left ( A(t)u,v\right ) }{\phi}'(t)\,dt \qquad {\phi}(t) \in C_0^\infty({\mathbf R})$$ If $u(t)$, $v(t) \in L^\infty_{loc}({\mathbf R},L^2 ({\mathbf R}^{n}, {\mathbf C}^N))$ and $A(t) \in L^\infty_{loc}({\mathbf R},{\mathcal}B)$, then $t \mapsto
{\left ( A(t)u(t),v(t)\right ) } \in L^\infty_{loc}({\mathbf R})$ is measurable. We shall use the following multiplier estimate from [@de:NT].
\[psest\] Let $P = D_t + iF(t)$ with $F(t) \in L^\infty_{loc}({\mathbf R}, {\mathcal}B)$. Assume that $B(t)= B^*(t) \in L_{loc}^\infty({\mathbf R}, {\mathcal}B)$, such that $$\label{multestcond}
{{\textstyle\frac{d}{dt}}}{\left ( B u,u\right ) } + 2{\operatorname{Re}}{\left ( B u,F u\right ) } \ge
{\left ( M u,u\right ) }\quad\text{in ${\mathcal}D'(I)\qquad \forall\ u \in {\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N)$}$$ where $M(t) = M^*(t) \in L_{loc}^\infty({\mathbf R}, {\mathcal}B)$ and $I \subseteq
{\mathbf R}$ is open. Then we have $$\label{pest}
\int {\left ( M u,u\right ) } \,dt \le 2\int {\operatorname{Im}}{\left ( Pu,B u\right ) } \,dt$$ for $u \in C_0^1(I, {\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N))$.
Since $B(t)\in L_{loc}^\infty({\mathbf R}, {\mathcal}B)$, we may for $u$, $v \in {\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N)$ define the regularization $${\left ( B_{\varepsilon}(t)u,v\right ) } = {\varepsilon}^{-1} \int
{\left ( B(s)u,v\right ) }{\phi}((t-s)/{\varepsilon}) \,ds
= {\left ( Bu,v\right ) }({\phi}_{{\varepsilon},t})\qquad{\varepsilon}>0$$ where ${\phi}_{{\varepsilon},t}(s) = {\varepsilon}^{-1}
{\phi}((t-s)/{\varepsilon})$ with $0 \le {\phi} \in C_0^{\infty}({\mathbf R})$ satisfying $\int {\phi}(t)\,dt = 1$. Then $t \mapsto
{\left ( B_{\varepsilon}(t)u,v\right ) }$ is in $C^\infty({\mathbf R})$ with derivative equal to ${{\textstyle\frac{d}{dt}}}{\left ( Bu,v\right ) }({\phi}_{{\varepsilon},t}) =
-{\left ( Bu,v\right ) }({\phi}_{{\varepsilon},t}')$. Let $I_0$ be an open interval such that $I_0 \Subset I$. Then for small enough ${\varepsilon}>0$ and $t \in I_0$ we find from condition that $$\label{newestcond}
{{\textstyle\frac{d}{dt}}}{\left ( B_{\varepsilon}(t)u,u\right ) } +
2{\operatorname{Re}}{\left ( B u,F u\right ) }({\phi}_{{\varepsilon},t}) \ge
{\left ( M u,u\right ) }({\phi}_{{\varepsilon},t})\qquad u \in
{\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N)$$ In fact, ${\phi}_{{\varepsilon},t} \ge 0$ and ${\operatorname{\rm supp}}{\phi}_{{\varepsilon},t} \in C_0^\infty(I)$ for small enough ${\varepsilon}$ when $t \in I_0$.
Now for $u(t)\in C_0^1(I_0,{\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N))$ and ${\varepsilon}>0$ we define $$\label{eq:def1}
B_{\varepsilon,u}(t) = {\left ( B_{\varepsilon}(t)u(t),u(t)\right ) } =
{\varepsilon}^{-1} \int
{\left ( B(s)u(t),u(t)\right ) }{\phi}((t-s)/{\varepsilon}) \,ds$$ For small enough ${\varepsilon}$ we obtain $B_{\varepsilon,u}(t) \in
C_0^1(I_0)$, with derivative $${{\textstyle\frac{d}{dt}}}B_{\varepsilon,u} = {\left ( ({{\textstyle\frac{d}{dt}}}B_{\varepsilon})u,u\right ) } + 2{\operatorname{Re}}{\left ( B_{\varepsilon} u,{\partial_t }u\right ) }$$ since $B(t) \in L_{loc}^\infty({\mathbf R}, {\mathcal}B)$. By integrating with respect to $t$, we obtain the vanishing average $$\label{aveq}
0 = \int {{\textstyle\frac{d}{dt}}}B_{\varepsilon,u}(t)\,dt = \int {\left ( ({{\textstyle\frac{d}{dt}}}B_{\varepsilon})u,u\right ) }\,dt + \int 2{\operatorname{Re}}{\left ( B_{\varepsilon} u,{\partial_t }u\right ) }\,dt$$ when $u\in C_0^1(I_0,{\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N))$. We obtain from and that $$0\ge \iint \big({\left ( M(s) u(t),u(t)\right ) } + 2{\operatorname{Re}}{\left ( B(s)u(t), {\partial_t }u(t) -F(s)u(t)\right ) }\big)
{\phi}((t-s)/{\varepsilon})\,dsdt$$ By letting ${\varepsilon} \to 0$, we find by dominated convergence that $$0 \ge \int {\left ( M(t)u(t),u(t)\right ) } +2{\operatorname{Re}}{\left ( B(t) u(t),{\partial_t }u(t)- F(t)u(t)\right ) } \,dt$$ since $u\in C_0^1(I_0,{\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N))$ and $M(t)$, $B(t)$, $F(t) \in L^\infty_{loc}({\mathbf R}, {\mathcal}B)$. Here ${\partial_t }u -Fu =
iPu$ and $ 2{\operatorname{Re}}{\left ( Bu,iPu\right ) } =
-2{\operatorname{Im}}{\left ( Pu,Bu\right ) }$, thus we obtain for $u\in C_0^1(I_0,{\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N))$. Since $I_0$ is an arbitrary open subinterval with compact closure in $I$, this completes the proof of the proposition.
The lower bounds {#lower}
================
In this section shall prove Proposition \[mainprop\], which means obtaining lower bounds on $$2{\operatorname{Im}}{\left ( P_0u,b_T^wu\right ) } = {\left ( \partial_t b_T^wu,u\right ) } + 2{\operatorname{Re}}{\left ( F^wu,b_T^wu\right ) }$$ where $P_0 = D_t{\operatorname{Id}}_N + iF^w(t,x,D_x)$ with $$\label{sysymbdef}
F(t,w) = f(t,w){\operatorname{Id}}_N + F_0(t,w)$$ Here $f \in L^\infty({\mathbf R}, S(h^{-1}, hg^{\sharp}))$ is real valued satisfying condition $({\overline}{\Psi})$ given by (2.2), $F_0 \in
C^\infty({\mathbf R}, S(1, hg^{\sharp}))$ and $b_{T}^w = B_{T}^{Wick}$ is the symmetric scalar operator given by Proposition \[wickweyl\] for this $f$. Since Proposition \[apsdef\] and Proposition \[propwick\] give lower bounds on the first term: $$\partial_t b_T^w = \partial_t B_T^{wick} \ge m^{wick}/2T \qquad \text{in
$L^2$} \quad |t| \le T$$ it only remains to obtain comparable lower bounds on ${\operatorname{Re}}b_T^wF^w$ by Proposition \[wprop\].
By Claim \[subrem\] we may also assume that $$\label{subsymbdef}
F_0 = {\langle d_wf, R\rangle } = \sum_j \partial_{w_j}f R_{j}\qquad\text{modulo
$S(h, hg^{\sharp})$} \qquad \forall\,t$$ where $R_j \in S(h^{1/2}, hg^{\sharp})$ are $N\times N$ systems, $\forall\,
j$. Observe that since $d_wf \in S(MH^{1/2}, G)$, $hg^{\sharp}\le 3G$ and $h \le
MH^{1/2}h^{1/2}$ by we find that $F_0 \in
S(MH^{1/2}h^{1/2}, G) \subseteq S(1,G)$ and thus $F \in S(M, G)$.
In the following, the results will hold for almost all $|t| \le T$ and will only depend on the seminorms of $f$ in $L^\infty({\mathbf R},
S(h^{-1},hg^{\sharp}))$. We shall suppress the $t$ variable and assume the coordinates chosen so that $g^{\sharp}(w) = |w|^2$. In order to prove Proposition \[mainprop\] we need to prove the following result.
\[lowersign\] Assume that $F$ is given by – and $B = {\delta}_0 + {\varrho}_0$. Here ${\delta}_0$ is given by Definition \[d0deforig\], ${\varrho}_0$ is real valued and Lipschitz continuous satisfying $|{\varrho}_0| \le m$, where $m \le {\langle {\delta}_0\rangle }/2$ is given by Definition \[h0def\]. Then we have $$\label{lowerbound}
{\operatorname{Re}}{\left ( B^{Wick} F^wu,u\right ) } \ge {\left ( C^w u,u\right ) } \qquad\forall\ u \in
{\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$$ for some $N \times N$ system $C \in S(m, g^{\sharp})$.
Let $B_T = {\delta}_0 + {\varrho}_T$, where ${\delta}_0 +
{\varrho}_T$ is the pseudo-sign for $f$ given by Proposition \[apsdef\] for $0 < T \le 1$, so that $|{\varrho}_{T}|
\le m$ and $$\label{dtbt}
{\partial_t } ({\delta}_0 + {\varrho}_{T}) \ge
m/2T\qquad\text{in $\mathcal D'\big(]{-T},T[\big)$}$$ If we put $B_T \equiv 0$ when $|t| >T$, then $B_T^{Wick} = b_T^w$ where $b_T(t,w) \in L^\infty({\mathbf R},
S(H^{-1/2}, g^{\sharp})\linebreak[3] \bigcap S^+(1,
g^{\sharp}))
$ uniformly by Proposition \[wickweyl\]. We find by Proposition \[propwick\] and that $$\label{dbest}
{\left ( ({\partial_t}B_T)^{Wick} u,u\right ) } \ge
{\left ( m^{Wick}u,u\right ) }/2T \qquad\text{in $\mathcal D'\big(]{-T},T[\big)$}$$ when $u \in {\mathcal}S({\mathbf R}^n)$. We obtain from Proposition \[wprop\] that there exist positive constants $c_1$ and $c_2$ so that $$\label{mlow}
{\left ( m^{Wick}u,u\right ) } \ge c_2{\Vertu\Vert}_{{1/2}}^2 \ge
c_1h^{1/2} ({\Vertb_T^wu\Vert}^2 + {\Vertu\Vert}^2)\qquad
u \in {\mathcal}S({\mathbf R}^n)$$ Here ${\Vertu\Vert}_{{1/2}}$ is the norm of the Hilbert space $H(m^{1/2}, g^{\sharp})$ given by Definition \[Hdef\]. By Proposition \[lowersign\], we find for almost all $t \in [-T,T]$ that $${\operatorname{Re}}{\left ( (B_T^{Wick}F^w){\big|_{t}}u,u\right ) } =
{\left ( C^w(t)u,u\right ) } \quad u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$$ here the $N \times N$ system $C(t) \in S(m, g^{\sharp})$ uniformly. We obtain from , and duality that there exists a positive constant $c_3$ such that $$\label{cest}
|{\left ( C^w(t)u,u\right ) }| \le {\Vertu\Vert}_{{1/2}} {\VertC^w(t)
u\Vert}_{-1/2} \le c_3
{\Vertu\Vert}_{{1/2}}^2 \le c_3{\left ( m^{Wick}u,u\right ) }/c_2$$ for $u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$ and $|t| \le T$. We find from – that $${\left ( \partial_{t}b^w_Tu,u\right ) } +
2{\operatorname{Re}}{\left ( F^w u,b^w_{T}u\right ) } \ge (1/2T -
2c_3/c_2){\left ( m^{Wick}u,u\right ) } \qquad\text{ in ${\mathcal}D'\big(]{-T},T[\big)$}$$ for $u \in {\mathcal}S({\mathbf R}^{n}, {\mathbf C}^N)$. By using Proposition \[psest\] with $P = D_t{\operatorname{Id}}_N + iF^w(t,x,D_x)$, $B
= b_T^w$ and $M = m^{Wick}/4T$ we obtain that $$c_1h^{1/2}\int {\Vertb_t^wu\Vert}^2 + {\Vertu\Vert}^2 \,dt \le \int {\left ( m^{Wick}u,u\right ) } \,dt \le
{8T} \int {\operatorname{Im}}{\left ( P_0u,b^w_Tu\right ) } \,dt$$ if $u \in {\mathcal}S({\mathbf R}\times {\mathbf R}^{n}, {\mathbf C}^N)$ has support where $|t| < T \le
c_2/8c_3$. This finishes the proof of Proposition \[mainprop\].
First we note that since $B^{Wick} = b^w \in {\operatorname{Op}}S({\langle {\delta}_0\rangle }, g^{\sharp})$ by Proposition \[wickweyl\] and $h^{1/2}{\langle {\delta}_0\rangle }^2 \le 6m$ by , we find $B^{Wick}R^w \in {\operatorname{Op}}S(m,g^{\sharp})$ when $R \in
S(h^{1/2},g^{\sharp})$. Since ${\operatorname{Im}}F = \frac{1}{2i}(F- F^*) \in S(1,hg^{\sharp})$ we find $$2{\operatorname{Re}}(B^{Wick} i({\operatorname{Im}}F)^w) = i[b^w, ({\operatorname{Im}}F)^w ] \in {\operatorname{Op}}S(h^{1/2},g^{\sharp})$$ thus it suffices to consider symmetric $F$ satisfying .
We shall localize in $T^*{\mathbf R}^n$ with respect to the metric $G = Hg^{\sharp}$, and estimate the localized operators. We shall use the neighborhoods $$\label{omegajdef}
{\omega}_{w_0}({\varepsilon}) = {\left\{\,w:\ |w-w_0| <
{\varepsilon}H^{-1/2}(w_0)\,\right\}}\qquad \text{for } w_0 \in T^*{\mathbf R}^n$$ We may in the following assume that ${\varepsilon}$ is small enough so that $w \mapsto H(w)$ and $w \mapsto M(w)$ only vary with a fixed factor in ${\omega}_{w_0}({\varepsilon})$. Then by the uniform Lipschitz continuity of $w \mapsto {\delta}_0(w)$ we can find ${\kappa}_0 >0$ with the following property: for $0 < {\kappa}\le {\kappa}_0$ there exist positive constants $c_{\kappa}$ and ${\varepsilon}_{\kappa}$ so that for any $w_0 \in T^*{\mathbf R}^n$ we have $$\begin{aligned}
{2}
&|{\delta}_0(w)| \le {\kappa}H^{-1/2}(w)&\qquad &w \in
{\omega}_{w_0}({\varepsilon}_{\kappa}) \qquad\text{or}\label{d0case}\\
&|{\delta}_0(w)| \ge c_{\kappa} H^{-1/2}(w)&\qquad &w \in
{\omega}_{w_0}({\varepsilon}_{\kappa}) \label{d1case}\end{aligned}$$ In fact, we have by the Lipschitz continuity that $|{\delta}_0(w) -
{\delta}_0(w_0)| \le {\varepsilon_{\kappa}}H^{-1/2}(w_0)$ when $w\in {\omega}_{w_0}({\varepsilon}_{\kappa})$. Thus, if ${\varepsilon}_{\kappa} \ll {\kappa}$ we obtain that holds when $|{\delta}_0(w_0)| \ll {\kappa}H^{-1/2}(w_0)$ and holds when $|{\delta}_0(w_0)| \ge
c{\kappa}H^{-1/2}(w_0)$.
Let ${\kappa}_1$ be given by Proposition \[ffactprop\], ${\kappa}_2$ by Proposition \[wickweyl\], and let ${\varepsilon}_{\kappa}$ and $c_{\kappa}$ be given by – for ${\kappa} = \min
({\kappa}_0, {\kappa}_1, {\kappa}_2)/2$. Using Proposition \[wickweyl\] with ${\lambda} = c_{\kappa}$ we obtain that ${\operatorname{sgn}}(B) = {\operatorname{sgn}}({\delta}_0)$ and $$\label{kappa3ref}
|B |\ge c_{\kappa}H^{-1/2}/3\qquad\text{in ~$
{\omega}_{w_0}({\varepsilon}_{\kappa})$}$$ if $H^{1/2} \le c_{\kappa}/3$ and holds in $
{\omega}_{w_0}({\varepsilon}_{\kappa})$.
Choose real symbols ${\left\{\,{\psi}_j(w)\,\right\}}_j$ and ${\left\{\,{\Psi}_j(w)\,\right\}}_j
\in S(1,G)$ with values in $\ell^2$, such that $\sum_{k} {\psi}_j^2 \equiv 1$, ${\psi}_j{\Psi}_j = {\psi}_j$, ${\Psi}_j = {\phi}_j^2 \ge 0$ for some ${\left\{\,{\phi}_j(w)\,\right\}}_j \in S(1,G)$ with values in $\ell^2$ so that $${\operatorname{\rm supp}}{\phi}_j \subseteq
{\omega}_j = {\omega}_{w_j}({\varepsilon}_{\kappa})$$ Recall that $B^{Wick} = b^w$ where $b= {\delta}_1 + {\varrho}_1$ is given by Proposition \[wickweyl\]. In particular, ${\delta}_1 \in
S(H^{-1/2}, G)$ when $H^{1/2} \le {\kappa}_2/2$ and holds, since then ${\langle {\delta}_0\rangle } \le {\kappa}_2 H^{-1/2}$.
\[bfconglem\] We find that $A_j = {\Psi}_jb {\operatorname{Re}}F \in S(MH^{-1/2},g^\sharp)\bigcap
S^+(M,g^\sharp)$ uniformly in $j$, and $$\label{bfcong}
{\operatorname{Re}}(b^wF^w) = \sum_{j}^{} {\psi}_j^w A_j^w{\psi}_j^w
\qquad \text{modulo ${\operatorname{Op}}S(m,g^\sharp)$}$$ We have $A_j^w = {\operatorname{Re}}b^wF_j^w$ modulo ${\operatorname{Op}}S(m,g^\sharp)$ uniformly in $j$, where $F_j = {\Psi}_jF$.
Since $b \in S(H^{-1/2}, g^{\sharp}) \bigcap S^+(1, g^{\sharp})$, ${\psi}_j
\in S(1, G)$ and $F_j \in S(M, G)$ we obtain that $A_j \in S(MH^{-1/2},g^\sharp)\bigcap
S^+(M,g^\sharp)$ uniformly in $j$. Proposition \[mestprop\] gives that $$\label{fprimest}
MH^{3/2}{\langle {\delta}_0\rangle }^2 \le Cm$$ thus we may ignore terms in ${\operatorname{Op}}S(MH^{3/2}{\langle {\delta}_0\rangle }^2,g^\sharp)$. Observe that since $b \in
S(H^{-1/2},g^{\sharp})$, ${\left\{\,{\psi}_k\,\right\}}_k \in S(1,G)$ has values in $\ell^2$ and $A_k \in S(MH^{-1/2},g^{\sharp})$ uniformly, Lemma \[calcrem\] and Remark \[vvcalc\] gives that the symbols of $b^wF^w$, $b^wF_j^w$ and $\sum_k {\psi}_k^wA_k^w{\psi}_k^w$ have expansions in $S(MH^{j/2}, g^{\sharp})$. Also observe that in the domains ${\omega}_j$ where $H^{1/2} \ge c > 0$, we find from Remark \[vvcalc\] that the symbols of $\sum_{k} {\psi}_k^w A_k^w{\psi}_k^w$, $b^w F_j^w$ and $b^wF^w$ are in $ S(MH^{3/2}, g^\sharp)$ giving the result in this case. Thus, in the following, we shall assume that $H^{1/2}\ll 1$, and we shall consider the neighborhoods where or holds.
If holds then we find that ${\langle {\delta}_0\rangle } \cong
H^{-1/2}$ so $S(MH^{1/2},g^\sharp) \subseteq S(m, g^\sharp)$ in ${\omega}_j$ by . Since $b\in S^+(1,g^\sharp)$ and $A_j \in S^+(M,g^{\sharp})$ we find from Lemma \[calcrem\] and Remark \[vvcalc\] that the symbols of both ${\operatorname{Re}}b^w F^w $ and $\sum_{k}^{} {\psi}_k^w A_k^w {\psi}_k^w$ are equal to $\sum_k
{\psi}_k^2 A_k = {\operatorname{Re}}bF$ modulo $S(MH^{1/2}, g^\sharp)$ in ${\omega}_j$. We also find that the symbol of ${\operatorname{Re}}b^w F_j^w$ is equal to $A_j$ modulo $S(MH^{1/2},g^\sharp)$, which proves the result in this case.
Next, we consider the case when holds with ${\kappa} =
\min ({\kappa}_0, {\kappa}_1, {\kappa}_2)/2$ and $H^{1/2} \le
{\kappa}_2/2$ in ${\omega}_j$. Then ${\langle {\delta}_0\rangle } \le {\kappa}_2
H^{-1/2}$ so $b = {\delta}_1 + {\varrho}_1 \in S(H^{-1/2},G)+
S(m, g^\sharp)$ in ${\omega}_j$ by Proposition \[wickweyl\]. Now $b$ is real and $F$ is symmetric modulo $S(MH,G)$. Thus, by taking the symmetric part of $b^w F^w = {\delta}_1^w F^w +
{\varrho}_1^w F^w$ we obtain from Lemma \[calcrem\] that the symbol of ${\operatorname{Re}}(b^w F^w -(bF)^w)$ is in $S(MH^{3/2}, G) + S(MHm,
g^{\sharp}) \subseteq S(m,g^{\sharp})$ in ${\omega}_j$ since $M \le
CH^{-1}$. Similarly, we find that $A_j^w = {\operatorname{Re}}b^w F_j^w$ modulo $S(m,g^{\sharp})$. Since $A_j \in S(MH^{-1/2},G)+
S(Mm,g^\sharp)$ uniformly, we find that the symbol of $\sum_{k}
{\psi}_k^w A_k^w {\psi}_k^w$ is equal to ${\operatorname{Re}}bF$ modulo $ S(m,g^{\sharp})$ in ${\omega}_j$ by Remark \[vvcalc\], which proves and Lemma \[bfconglem\].
Next, we shall show that there exists $N \times N$ system $C_{j} \in S(m, g^\sharp)$ uniformly, such that $$\label{lowerest}
{\left ( A_j^w u,u\right ) } \ge {\left ( C^w_{j} u,u\right ) }\qquad
u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$$ Then we obtain from and that $${\operatorname{Re}}{\left ( b^w F^w u,u\right ) } \ge \sum_{j} {\left ( {\psi}_j^wC^w_{j}{\psi}_j^w u,u\right ) }
+{\left ( R^wu,u\right ) }\qquad\text{$u \in {\mathcal}S({\mathbf R}^n, {\mathbf C}^N)$}$$ where $\sum_{j}{\psi}_j^wC^w_{j}{\psi}_j^w$ and $R^w \in {\operatorname{Op}}S(m,g^\sharp)$, which will prove Proposition \[lowersign\].
Thus, it remains to show that there exists $C_{j} \in S(m,
g^\sharp)$ satisfying . As before we are going to consider the cases when $H^{1/2} \cong 1$ or $H^{1/2} \ll 1$, and when or holds in ${\omega}_j =
{\omega}_{w_j}({\varepsilon}_{\kappa})$ for ${\kappa} = \min
({\kappa}_0, {\kappa}_1, {\kappa}_2)/2$. When $H^{1/2} \ge
c > 0$ we find that $A_j \in S(MH^{3/2},g^\sharp)
\subseteq S(m,g^\sharp)$ uniformly by which gives the lemma with $C_j = A_j$ in this case. Thus, we may assume that $$\label{kappa4def}
H^{1/2} \le {\kappa}_4 = \min({\kappa}_0, {\kappa}_1, {\kappa}_2,
{\kappa}_3)/2 \qquad \text{in ${\omega}_j$}$$ with ${\kappa}_3 = 2c_{\kappa}/3$ so that follows from .
First, we consider the case when $H^{1/2} \le {\kappa}_4$ and holds in ${\omega}_j$. Since $|{\delta}_0(w)| \ge c_{\kappa} H^{-1/2}(w)$, we find ${\langle {\delta}_0\rangle } \cong H^{-1/2}$ in ${\omega}_j$. As before we may ignore terms in $S(MH^{1/2},g^\sharp) \subseteq
S(m,g^\sharp)$ in ${\omega}_j$ by . Let $f_j = {\Psi}_jf$, since ${\operatorname{sgn}}(f) = {\operatorname{sgn}}({\delta}_0) = {\operatorname{sgn}}(B)$ in ${\omega}_j$ by Proposition \[wickweyl\] we find that $f_jB \ge 0$. Since $f_j \in S(M, G)$, we find $f_j^w = f_j^{Wick}$ modulo ${\operatorname{Op}}S(MH,G)$ by Proposition \[propwick\], thus we may replace $f_j^w$ with $f_j^{Wick}$. Since $F_{0,j} \in S(MH^{1/2}h^{1/2}, G)$ by we find that $B^{Wick}F^w_{0,j} \in {\operatorname{Op}}S(MH^{1/2}, g^{\sharp})$. Since $|B| \le
CH^{-1/2}$ and $B \in S^+(1,g^{\sharp})$, we find from in Remark \[wickcomp\] that $$A_j^w = {\operatorname{Re}}B^{Wick} f_j^{Wick} = (Bf_j)^{Wick} \ge 0
\qquad\text{in $L^2$ modulo ${\operatorname{Op}}S(MH^{1/2},g^{\sharp})$}$$ which gives in this case.
Finally, we consider the case when holds with ${\kappa} =
\min ({\kappa}_0, {\kappa}_1, {\kappa}_2)/2$ and $H^{1/2} \le
{\kappa}_4\le {\kappa}$ in ${\omega}_j$. Then ${\langle {\delta}_0\rangle } \le
2{\kappa}H^{-1/2}$ so we obtain from Proposition \[ffactprop\] that ${\delta}_0 \in S(H^{-1/2}, G) \bigcap S({\langle {\delta}_0\rangle }, g^{\sharp})$ in ${\omega}_j$. We have that $b^w =
({\delta}_0 + {\varrho}_0)^{Wick} = B^{Wick}$, where $$\label{hhhesta}
|{\varrho}_0|
\le m \le H^{1/2}{\langle {\delta}_0\rangle }^2/2 \le {\langle {\delta}_0\rangle }/2$$ by Propositions \[h0slow\] and \[apsdef\]. Also, we find form Lemma \[bfconglem\] that $A_j^w = {\operatorname{Re}}B^{Wick} F_j^w$ modulo ${\operatorname{Op}}S(m,g^\sharp)$.
Take ${\chi}(t) \in C^{\infty}({\mathbf R})$ such that $0 \le {\chi}(t) \le 1$, $|t| \ge 2$ in ${\operatorname{\rm supp}}{\chi}(t)$ and ${\chi}(t) = 1$ for $|t| \ge 3$. Let ${\chi}_0 = {\chi}({\delta}_0)$, then $2 \le |{\delta}_0|$ and ${\langle {\delta}_0\rangle }/|{\delta}_0| \le 3/2$ in ${\operatorname{\rm supp}}{\chi}_0$, thus $$\label{b0ref}
1 + {\chi}_0{\varrho}_0/{\delta}_0 \ge 1 -
{\chi}_0{\langle {\delta}_0\rangle }/2|{\delta}_0| \ge 1/4$$ Since $|{\delta}_0| \le 3$ in ${\operatorname{\rm supp}}(1-{\chi}_0)$ we find by that $$B = {\delta}_0 + {\chi}_0{\varrho}_0 = {\delta}_0( 1 + {\chi}_0{\varrho}_0/{\delta}_0)$$ modulo terms that are ${\mathcal}O(H^{1/2})$. Since $|{\delta}_0'| \le 1$ and $$|{\chi}_0{\varrho}_0/{\delta}_0| \le {\chi}_0H^{1/2}{\langle {\delta}_0\rangle }^2/2|{\delta}_0|
\le 3H^{1/2} {\langle {\delta}_0\rangle }/4$$ we find from in Remark \[wickcomp\] that $$\label{bwref}
B^{Wick} = {\delta}_0^{Wick}B_0^{Wick} \qquad\text{modulo ${\operatorname{Op}}S(H^{1/2}{\langle {\delta}_0\rangle }, g^{\sharp})$}$$ where $B_0 = 1 + {\chi}_0{\varrho}_0/{\delta}_0 = {\mathcal}O(1)$. Proposition \[wickweyl\] gives $({\chi}_0{\varrho}_0/{\delta}_0)^{Wick} \in {\operatorname{Op}}S(H^{1/2}{\langle {\delta}_0\rangle }, g^{\sharp})$ and ${\delta}_0^{Wick} = {\delta}_1^w $ where ${\delta}_1 \in
S(H^{-1/2}, g^{\sharp})$ and ${\delta}_1 = {\delta}_0$ modulo ${\operatorname{Op}}S(H^{1/2}, G)$ in ${\omega}_j$. Thus Lemma \[calcrem\] and gives $$\label{nycalcref0}
B^{Wick} = {\delta}_1^wB_0^{Wick} = {\delta}_0^wB_0^{Wick} + c^w \qquad\text{modulo ${\operatorname{Op}}S(H^{1/2}{\langle {\delta}_0\rangle }, g^{\sharp})$}$$ where $c \in S(H^{-1/2}, g^{\sharp})$ such that ${\operatorname{\rm supp}}c \bigcap
{\omega}_j = \emptyset$.
We find from Proposition \[ffactprop\] that $ f =
{\alpha}_0{\delta}_0 $, where ${\kappa}_1MH^{1/2}\le {\alpha}_0 \in
S(MH^{1/2}, G)$, so Leibniz’ rule gives ${\alpha}_0^{1/2} \in S(M^{1/2}H^{1/4},
G)$. Let $f_j = {\Psi}_jf$ and $$\label{ajdef}
a_j =
{\alpha}_0^{1/2}{\phi}_j{\delta}_0 \in S(M^{1/2}H^{-1/4},G) \bigcap
S(M^{1/2} H^{1/4}{\langle {\delta}_0\rangle }, g^{\sharp})$$ Since ${\Psi}_j = {\phi}_j^2$ we find $a_j^2 = f_j{\delta}_0$ and the calculus gives $$\label{nycalcref1}
a_j^w({\alpha}_0^{1/2}{\phi}_j)^w = f_j^w\qquad\text{modulo ${\operatorname{Op}}S(MH,G)$}$$ Since ${\operatorname{\rm supp}}f_j \bigcap {\operatorname{\rm supp}}c = \emptyset$ we find that $f_j^wc^w \in {\operatorname{Op}}S(MH^{3/2},g^{\sharp})$. We also have $$\label{nycalcref2}
{\operatorname{Re}}f_j^w{\delta}_0^{w} = a_j^w a_j^w\qquad\text{modulo ${\operatorname{Op}}S(MH^{3/2},G)$}$$ and ${\operatorname{Im}}f_j^w{\delta}_0^{w} \in {\operatorname{Op}}S(MH^{1/2},G)$. We obtain from and that $$\label{W1}
f_j^wB^{Wick} = f_j^w({\delta}_0^wB_0^{Wick} + c^w + r^w) =
f_j^w{\delta}_0^wB_0^{Wick} + a_j^wr_j^w \quad\text{modulo ${\operatorname{Op}}S(m,g^{\sharp})$}$$ where $r \in S(H^{1/2}{\langle {\delta}_0\rangle }, g^{\sharp})$ which gives $r_j^w =
({\alpha}_0^{1/2}{\phi}_j)^w r^w \in {\operatorname{Op}}S(M^{1/2}H^{3/4}{\langle {\delta}_0\rangle }, g^{\sharp})$. If ${\operatorname{Re}}A = \frac{1}{2}(A +
A^*)$, ${\operatorname{Im}}A = \frac{1}{2i}(A
-A^*)$ and $B^* = B$ then $${\operatorname{Re}}(AB) = {\operatorname{Re}}({\operatorname{Re}}A)B + i [{\operatorname{Im}}A, B]/2$$ By taking $A = f_j^w{\delta}_0^w$ and $B = B_0^{Wick}$ we find from that $$\label{W2}
{\operatorname{Re}}\left(f_j^w{\delta}_0^wB_0^{Wick}\right) = {\operatorname{Re}}(a_j^wa_j^wB_0^{Wick})
\qquad\text{modulo ${\operatorname{Op}}S(m,g^{\sharp})$}$$ In fact, $B_0 = 1 + {\chi}_0{\varrho}_0/{\delta}_0$ and $({\chi}_0{\varrho}_0/{\delta}_0)^{Wick} \in {\operatorname{Op}}S(H^{1/2}{\langle {\delta}_0\rangle }, g^{\sharp})$ by Proposition \[propwick\], thus $$[a^w,B_0^w] = [a^w,
({\chi}_0{\varrho}_0/{\delta}_0)^{Wick}]
\in {\operatorname{Op}}S(M H^{3/2}{\langle {\delta}_0\rangle }, g^{\sharp})$$ when $a \in S(MH^{1/2}, G)$. Similarly, we find from that $$\label{W3}
a_j^wa_j^wB_0^{Wick} =
a_j^w(B_0^{Wick}a_j^w + s_j^w) \qquad\text{modulo ${\operatorname{Op}}S(m,g^{\sharp})$}$$ where $s_j = [a_j^w, B_0^{Wick}] \in S(M^{1/2}H^{3/4}{\langle {\delta}_0\rangle },
g^{\sharp})$. Next, we shall use an argument by Lerner [@ln:cutloss]. Since $B_0 \ge 1/4$ by we find from – that $$\label{preplow}
{\operatorname{Re}}f_j^w B^{Wick} \ge \frac{1}{4}a_j^wa_j^w + {\operatorname{Re}}a_j^wS_j^w
\qquad\text{in $L^2$ modulo ${\operatorname{Op}}S(m,g^{\sharp})$}$$ where $S_j = r_j + s_j \in
S(M^{1/2}H^{3/4}{\langle {\delta}_0\rangle }, g^{\sharp})$. Then by completing the square, we find $$\label{compsq}
{\operatorname{Re}}f_j^w B^{Wick} \ge \frac{1}{4}\left(a_j^w + 2S_j^w\right)^*
\left(a_j^w + 2S_j^w\right)
\ge 0 \quad\text{in $L^2$ modulo ${\operatorname{Op}}S(m,g^{\sharp})$}$$ since $(S_j^w)^*S_j^w = {\overline}S_j^wS_j^w \in
{\operatorname{Op}}S(MH^{3/2}{\langle {\delta}_0\rangle }^2, g^{\sharp})$.
But we must also consider ${\operatorname{Re}}F^w_{0,j}B^{Wick}$, where $F_0$ satisfies so $$\label{lowterm}
F_{0,j} =
{\Psi}_jF_0 \in S(MH^{1/2}h^{1/2}, G)$$ We shall prove that $$\label{lowerterm}
{\operatorname{Re}}F^w_{0,j}B^{Wick} = {\operatorname{Re}}a_j^{w}R_j^w\qquad\text{modulo ${\operatorname{Op}}S(m,g^{\sharp})$}$$ where $R_j \in S(M^{1/2}H^{3/4}, g^{\sharp})$, which can then be included in the term given by $S_j$ in . Since $b =
{\delta}_0 \in S(H^{-1/2}, G)$ modulo $S(H^{1/2}{\langle {\delta}_0\rangle }^2, g^{\sharp})$ in $\omega_j$ by Proposition \[wickweyl\] we find $${\operatorname{Re}}F^w_{0,j}B^{Wick} = {\operatorname{Re}}F^w_{0,j}b^w =({\operatorname{Re}}F_{0,j}{\delta}_0)^w$$ modulo ${\operatorname{Op}}S(m,g^{\sharp})$. We find from and that ${\operatorname{Im}}a_j = 0$, so $${\operatorname{Re}}F_{0,j}{\delta}_0 = {\operatorname{Re}}{\phi}_j^2 F_0{\delta}_0 = a_jR_j$$ where $$R_j = {\operatorname{Re}}{\phi}_jF_0/{\alpha}_0^{1/2} \in
S(M^{1/2}H^{1/4}h^{1/2}, G) \subseteq S(M^{1/2}H^{3/4},G)$$ This gives $({\operatorname{Re}}F_{0,j}{\delta}_0)^w = a_j^{w}R_j^w$ modulo ${\operatorname{Op}}S(MHh^{1/2}, G) \subseteq {\operatorname{Op}}S(m,g^{\sharp})$, so we obtain . By adding $R_j$ to $S_j$ in and completing the square as in , we obtain in this case. This completes the proof of Proposition \[lowersign\].
\[finalrem\] It follows from the proof of Proposition \[lowersign\] that in order to obtain the estimate it suffices that the lower order term $F_0 \in S(MH, g^{\sharp}) \subseteq S(1,g^{\sharp})$.
[10]{}
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[to3em]{}, *A sufficient condition for solvability*, International Mathematics Research Notices **1999:12** (1999), 627–659.
[to3em]{}, *The resolution of the Nirenberg-Treves conjecture*, Ann. of Math. **163** (2006), 405–444.
[to3em]{}, *The solvability of pseudo-differential operators*, Phase space analysis of partial differential equations, Vol. I, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004, 175–200.
[to3em]{}, *On the solvability of pseudo-differential operators*, Sémin. Equ. Dériv. Partielles, Ecole Polytech., Palaiseau, 2005–2006.
[to3em]{}, *The pseudospectrum of systems of semiclassical operators*, Anal. PDE **1** (2008), 323–373.
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[to3em]{}, *Pseudo-differential operators of principal type*, Nato Adv. Study Inst. on Sing. in Bound. Value Problems, Reidel Publ.Co., Dordrecht, 1981, 69–96.
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|
Onset and dynamic expression of S100 proteins in the olfactory organ and the lateral line system in zebrafish development.
In the zebrafish olfactory epithelium, three morphologically distinct olfactory neurons express different marker proteins. We utilize this feature to access developmental dynamics of one of the neuron types, the crypt cells, to determine whether they are differentiated at a stage similar to other olfactory neurons. Immunohistochemical studies using an S100 antibody that specifically recognizes crypt cells showed that S100-positive cells appear in olfactory rosettes as early as at 2day postfertilization (dpf). However, some of the rosettes did not have any S100-positive cells until 4 dpf. The number of S100-positive cells in individual rosettes increased steadily over the next 3days before it decreased significantly. There were 7.8 S100-positive cells per rosettes on average in larvae at 7 dpf. The number reduced to 2.2 at 9 dpf. A recovery to a pre-reduction level was detected in 12 dpf larvae. We also observed S100-positive cells in neuromasts of the lateral line system in 2 dpf larvae, suggesting that the crypt cells and sensory cells in the neuromasts have similar onsets of differentiation. Our data have provided a time line of differentiation of crypt cells in development of the olfactory system and demonstrated that this type of cell is differentiated at a stage similar to ciliated and microvillous olfactory neurons. A nonlinear growth trajectory of the crypt cell population in the first nine days of zebrafish development implicates a possible functional significance of crypt cells in early life stages of zebrafish. |
TRARALGON
Leased By
Ray White Traralgon
CUTE & COSY
1 Bed
1 Bath
1 Car
This one bedroom is in a complex that is quiet, only 7 mins walk to the CBD and 5 mins from convenience shops. This unit is easy to maintain, would make ideal first rental property. Included in the lease the landlord maintains gardens and there are no water costs. This unit will be taken very quickly as it has been fully painted, new floating floor boards and carpet. Please call our office for an inspection. |
At first glance, Arin Andrews and Katie Hill of Oklahoma are your average young couple. However, the two met under what some might consider unusual circumstances, and have found themselves in the limelight as a result. Katie and Arin are both trans, and met each other at a support group in Tulsa. Furthermore, the two have, as the British tabloid The Sun called it, "swapped genders", and met each other while both undergoing the transition process.
Two years ago, Arin and Katie were known as Emerald and Luke, respectively. One excelled at ballet and competed in beauty contests, while the other was the son of a Marine Colonel. Both struggled throughout their childhoods with their identities. 'The teachers separated the girls and boys into separate lines for a game… I didn't understand why they asked me to stand with the girls," Arin told the Daily Mail. "Girly things didn't interest me, but I was worried what people would think if I said I wanted to be a boy, so I kept it secret." Meanwhile, Katie confided that "Even from age three, I knew deep down I wanted to be a girl. All I wanted was to play with dolls. I hated my boy body and never felt right in it." The two unfortunately had to endure bullying throughout their childhoods, which was one of the many reasons why they bonded so quickly during their first days together.
“Being transgender myself, I understand Arin better than anybody else — how good he feels and how complete he feels," Katie told The Sun. She also quipped to Daily Mail: "We're both size five, so we even swap our old clothes our [mothers] bought us but we hated."
Now that the two have successfully completed their transitions, they can resume their lives with each other in bodies they feel more comfortable in.
"Now when I’m out in a public pool or lifting weights, no one raises an eyebrow. They just think I’m a guy. … I can wear a tank top, which I couldn’t before, and I can go swimming shirtless. I can just be a regular guy. And I’m so lucky to have my family and Katie to rely on."
Katie added…
"We look so convincing as a boy and a girl, nobody even notices now. We secretly feel so good about it because it's the way we've always wanted to be seen."
HuffPost Gay Voices editor Noah Michelson, when discussing this story on the site, noted that…
"It brings to light the idea that sexuality and gender are not the same thing. So both of these individuals are heterosexual…They're not gay just because they're transgender, and that's something that blows people's minds still."
Although, if you ask Katie, she offers a much simpler analysis…
"To me, Arin’s just my Arin. He’s always looked manly to me. But now he’s had the surgery he’s much more confident and comfortable with himself."
Watch The Sun's original video and read the full story HERE.
You can watch HuffPost discuss the story on video HERE. |
/*
* NSUserDefaults.h
*
* Foundation (c) 1994-2017
*/
#import <Foundation/NSObject.h>
#import <Foundation/NSNotification.h>
@class NSArray<ObjectType>, NSData, NSDictionary<KeyValue, ObjectValue>, NSMutableDictionary, NSString, NSURL;
NS_ASSUME_NONNULL_BEGIN
/// NSGlobalDomain identifies a domain shared between all applications for a given user. NSGlobalDomain is automatically included in all search lists, after the entries for the search list's domain.
FOUNDATION_EXPORT NSString * const NSGlobalDomain;
/// NSArgumentDomain identifies a search list entry containing the commandline arguments the application was launched with, if any. Arguments must be formatted as '-key plistvalue'. NSArgumentDomain is automatically included in all search lists, after forced defaults, but before all other entries. This can be useful for testing purposes.
FOUNDATION_EXPORT NSString * const NSArgumentDomain;
/// NSRegistrationDomain identifies a search list entry containing all defaults set with -registerDefaults:, if any. NSRegistrationDomain is automatically included as the final entry of all search lists.
FOUNDATION_EXPORT NSString * const NSRegistrationDomain;
/*!
NSUserDefaults is a hierarchical persistent interprocess (optionally distributed) key-value store, optimized for storing user settings.
Hierarchical: NSUserDefaults has a list of places to look for data called the "search list". A search list is referred to by an arbitrary string called the "suite identifier" or "domain identifier". When queried, NSUserDefaults checks each entry of its search list until it finds one that contains the key in question, or has searched the whole list. The list is (note: "current host + current user" preferences are unimplemented on iOS, watchOS, and tvOS, and "any user" preferences are not generally useful for applications on those operating systems):
- Managed ("forced") preferences, set by a configuration profile or via mcx from a network administrator
- Commandline arguments
- Preferences for the current domain, in the cloud
- Preferences for the current domain, the current user, in the current host
- Preferences for the current domain, the current user, in any host
- Preferences added via -addSuiteNamed:
- Preferences global to all apps for the current user, in the current host
- Preferences global to all apps for the current user, in any host
- Preferences for the current domain, for all users, in the current host
- Preferences global to all apps for all users, in the current host
- Preferences registered with -registerDefaults:
Persistent: Preferences stored in NSUserDefaults persist across reboots and relaunches of apps unless otherwise specified.
Interprocess: Preferences may be accessible to and modified from multiple processes simultaneously (for example between an application and an extension).
Optionally distributed (Currently only supported in Shared iPad for Students mode): Data stored in user defaults can be made "ubiqitous", i.e. synchronized between devices via the cloud. Ubiquitous user defaults are automatically propagated to all devices logged into the same iCloud account. When reading defaults (via -*ForKey: methods on NSUserDefaults), ubiquitous defaults are searched before local defaults. All operations on ubiquitous defaults are asynchronous, so registered defaults may be returned in place of ubiquitous defaults if downloading from iCloud hasn't finished. Ubiquitous defaults are specified in the Defaults Configuration File for an application.
Key-Value Store: NSUserDefaults stores Property List objects (NSString, NSData, NSNumber, NSDate, NSArray, and NSDictionary) identified by NSString keys, similar to an NSMutableDictionary.
Optimized for storing user settings: NSUserDefaults is intended for relatively small amounts of data, queried very frequently, and modified occasionally. Using it in other ways may be slow or use more memory than solutions more suited to those uses.
The 'App' CFPreferences functions in CoreFoundation act on the same search lists that NSUserDefaults does.
NSUserDefaults can be observed using Key-Value Observing for any key stored in it. Using NSKeyValueObservingOptionPrior to observe changes from other processes or devices will behave as though NSKeyValueObservingOptionPrior was not specified.
*/
@interface NSUserDefaults : NSObject {
@private
id _kvo_;
CFStringRef _identifier_;
CFStringRef _container_;
void *_reserved[2];
}
/*!
+standardUserDefaults returns a global instance of NSUserDefaults configured to search the current application's search list.
*/
@property (class, readonly, strong) NSUserDefaults *standardUserDefaults;
/// +resetStandardUserDefaults releases the standardUserDefaults and sets it to nil. A new standardUserDefaults will be created the next time it's accessed. The only visible effect this has is that all KVO observers of the previous standardUserDefaults will no longer be observing it.
+ (void)resetStandardUserDefaults;
/// -init is equivalent to -initWithSuiteName:nil
- (instancetype)init;
/// -initWithSuiteName: initializes an instance of NSUserDefaults that searches the shared preferences search list for the domain 'suitename'. For example, using the identifier of an application group will cause the receiver to search the preferences for that group. Passing the current application's bundle identifier, NSGlobalDomain, or the corresponding CFPreferences constants is an error. Passing nil will search the default search list.
- (nullable instancetype)initWithSuiteName:(nullable NSString *)suitename API_AVAILABLE(macos(10.9), ios(7.0), watchos(2.0), tvos(9.0)) NS_DESIGNATED_INITIALIZER;
/// -initWithUser: is equivalent to -init
- (nullable id)initWithUser:(NSString *)username API_DEPRECATED("Use -init instead", macos(10.0,10.9), ios(2.0,7.0), watchos(2.0,2.0), tvos(9.0,9.0));
/*!
-objectForKey: will search the receiver's search list for a default with the key 'defaultName' and return it. If another process has changed defaults in the search list, NSUserDefaults will automatically update to the latest values. If the key in question has been marked as ubiquitous via a Defaults Configuration File, the latest value may not be immediately available, and the registered value will be returned instead.
*/
- (nullable id)objectForKey:(NSString *)defaultName;
/*!
-setObject:forKey: immediately stores a value (or removes the value if nil is passed as the value) for the provided key in the search list entry for the receiver's suite name in the current user and any host, then asynchronously stores the value persistently, where it is made available to other processes.
*/
- (void)setObject:(nullable id)value forKey:(NSString *)defaultName;
/// -removeObjectForKey: is equivalent to -[... setObject:nil forKey:defaultName]
- (void)removeObjectForKey:(NSString *)defaultName;
/// -stringForKey: is equivalent to -objectForKey:, except that it will convert NSNumber values to their NSString representation. If a non-string non-number value is found, nil will be returned.
- (nullable NSString *)stringForKey:(NSString *)defaultName;
/// -arrayForKey: is equivalent to -objectForKey:, except that it will return nil if the value is not an NSArray.
- (nullable NSArray *)arrayForKey:(NSString *)defaultName;
/// -dictionaryForKey: is equivalent to -objectForKey:, except that it will return nil if the value is not an NSDictionary.
- (nullable NSDictionary<NSString *, id> *)dictionaryForKey:(NSString *)defaultName;
/// -dataForKey: is equivalent to -objectForKey:, except that it will return nil if the value is not an NSData.
- (nullable NSData *)dataForKey:(NSString *)defaultName;
/// -stringForKey: is equivalent to -objectForKey:, except that it will return nil if the value is not an NSArray<NSString *>. Note that unlike -stringForKey:, NSNumbers are not converted to NSStrings.
- (nullable NSArray<NSString *> *)stringArrayForKey:(NSString *)defaultName;
/*!
-integerForKey: is equivalent to -objectForKey:, except that it converts the returned value to an NSInteger. If the value is an NSNumber, the result of -integerValue will be returned. If the value is an NSString, it will be converted to NSInteger if possible. If the value is a boolean, it will be converted to either 1 for YES or 0 for NO. If the value is absent or can't be converted to an integer, 0 will be returned.
*/
- (NSInteger)integerForKey:(NSString *)defaultName;
/// -floatForKey: is similar to -integerForKey:, except that it returns a float, and boolean values will not be converted.
- (float)floatForKey:(NSString *)defaultName;
/// -doubleForKey: is similar to -integerForKey:, except that it returns a double, and boolean values will not be converted.
- (double)doubleForKey:(NSString *)defaultName;
/*!
-boolForKey: is equivalent to -objectForKey:, except that it converts the returned value to a BOOL. If the value is an NSNumber, NO will be returned if the value is 0, YES otherwise. If the value is an NSString, values of "YES" or "1" will return YES, and values of "NO", "0", or any other string will return NO. If the value is absent or can't be converted to a BOOL, NO will be returned.
*/
- (BOOL)boolForKey:(NSString *)defaultName;
/*!
-URLForKey: is equivalent to -objectForKey: except that it converts the returned value to an NSURL. If the value is an NSString path, then it will construct a file URL to that path. If the value is an archived URL from -setURL:forKey: it will be unarchived. If the value is absent or can't be converted to an NSURL, nil will be returned.
*/
- (nullable NSURL *)URLForKey:(NSString *)defaultName API_AVAILABLE(macos(10.6), ios(4.0), watchos(2.0), tvos(9.0));
/// -setInteger:forKey: is equivalent to -setObject:forKey: except that the value is converted from an NSInteger to an NSNumber.
- (void)setInteger:(NSInteger)value forKey:(NSString *)defaultName;
/// -setFloat:forKey: is equivalent to -setObject:forKey: except that the value is converted from a float to an NSNumber.
- (void)setFloat:(float)value forKey:(NSString *)defaultName;
/// -setDouble:forKey: is equivalent to -setObject:forKey: except that the value is converted from a double to an NSNumber.
- (void)setDouble:(double)value forKey:(NSString *)defaultName;
/// -setBool:forKey: is equivalent to -setObject:forKey: except that the value is converted from a BOOL to an NSNumber.
- (void)setBool:(BOOL)value forKey:(NSString *)defaultName;
/// -setURL:forKey is equivalent to -setObject:forKey: except that the value is archived to an NSData. Use -URLForKey: to retrieve values set this way.
- (void)setURL:(nullable NSURL *)url forKey:(NSString *)defaultName API_AVAILABLE(macos(10.6), ios(4.0), watchos(2.0), tvos(9.0));
/*!
-registerDefaults: adds the registrationDictionary to the last item in every search list. This means that after NSUserDefaults has looked for a value in every other valid location, it will look in registered defaults, making them useful as a "fallback" value. Registered defaults are never stored between runs of an application, and are visible only to the application that registers them.
Default values from Defaults Configuration Files will automatically be registered.
*/
- (void)registerDefaults:(NSDictionary<NSString *, id> *)registrationDictionary;
/*!
-addSuiteNamed: adds the full search list for 'suiteName' as a sub-search-list of the receiver's. The additional search lists are searched after the current domain, but before global defaults. Passing NSGlobalDomain or the current application's bundle identifier is unsupported.
*/
- (void)addSuiteNamed:(NSString *)suiteName;
/*!
-removeSuiteNamed: removes a sub-searchlist added via -addSuiteNamed:.
*/
- (void)removeSuiteNamed:(NSString *)suiteName;
/*!
-dictionaryRepresentation returns a composite snapshot of the values in the receiver's search list, such that [[receiver dictionaryRepresentation] objectForKey:x] will return the same thing as [receiver objectForKey:x].
*/
- (NSDictionary<NSString *, id> *)dictionaryRepresentation;
/*
Volatile domains are not added to any search list, are not persisted, and are not visible to other applications. Using them is not recommended.
*/
@property (readonly, copy) NSArray<NSString *> *volatileDomainNames;
- (NSDictionary<NSString *, id> *)volatileDomainForName:(NSString *)domainName;
- (void)setVolatileDomain:(NSDictionary<NSString *, id> *)domain forName:(NSString *)domainName;
- (void)removeVolatileDomainForName:(NSString *)domainName;
/// -persistentDomainNames returns an incomplete list of domains that have preferences stored in them.
- (NSArray *)persistentDomainNames API_DEPRECATED("Not recommended", macos(10.0,10.9), ios(2.0,7.0), watchos(2.0,2.0), tvos(9.0,9.0));
/// -persistentDomainForName: returns a dictionary representation of the search list entry specified by 'domainName', the current user, and any host.
- (nullable NSDictionary<NSString *, id> *)persistentDomainForName:(NSString *)domainName;
/// -setPersistentDomain:forName: replaces all values in the search list entry specified by 'domainName', the current user, and any host, with the values in 'domain'. The change will be persisted.
- (void)setPersistentDomain:(NSDictionary<NSString *, id> *)domain forName:(NSString *)domainName;
/// -removePersistentDomainForName: removes all values from the search list entry specified by 'domainName', the current user, and any host. The change is persistent.
- (void)removePersistentDomainForName:(NSString *)domainName;
/*!
-synchronize is deprecated and will be marked with the NS_DEPRECATED macro in a future release.
-synchronize blocks the calling thread until all in-progress set operations have completed. This is no longer necessary. Replacements for previous uses of -synchronize depend on what the intent of calling synchronize was. If you synchronized...
- ...before reading in order to fetch updated values: remove the synchronize call
- ...after writing in order to notify another program to read: the other program can use KVO to observe the default without needing to notify
- ...before exiting in a non-app (command line tool, agent, or daemon) process: call CFPreferencesAppSynchronize(kCFPreferencesCurrentApplication)
- ...for any other reason: remove the synchronize call
*/
- (BOOL)synchronize;
// -objectIsForcedForKey: returns YES if the value for 'key' is provided by managed preferences (a configuration profile or mcx)
- (BOOL)objectIsForcedForKey:(NSString *)key;
// -objectIsForcedForKey:inDomain: returns YES if the value for 'key' is provided by managed preferences (a configuration profile or mcx) for the search list named by 'domain'
- (BOOL)objectIsForcedForKey:(NSString *)key inDomain:(NSString *)domain;
@end
/*!
NSUserDefaultsSizeLimitExceededNotification is posted on the main queue when more data is stored in user defaults than is allowed. Currently there is no limit for local user defaults except on tvOS, where a warning notification will be posted at 512kB, and the process terminated at 1MB. For ubiquitous defaults, the limit depends on the logged in iCloud user.
*/
FOUNDATION_EXPORT NSNotificationName const NSUserDefaultsSizeLimitExceededNotification API_AVAILABLE(ios(9.3), watchos(2.0), tvos(9.0)) API_UNAVAILABLE(macos);
/*!
NSUbiquitousUserDefaultsNoCloudAccountNotification is posted on the main queue to the default notification center when a cloud default is set, but no iCloud user is logged in.
This is not necessarily an error: ubiquitous defaults set when no iCloud user is logged in will be uploaded the next time one is available if configured to do so.
*/
FOUNDATION_EXPORT NSNotificationName const NSUbiquitousUserDefaultsNoCloudAccountNotification API_AVAILABLE(ios(9.3), watchos(2.0), tvos(9.0)) API_UNAVAILABLE(macos);
/*!
NSUbiquitousUserDefaultsDidChangeAccountsNotification is posted on the main queue to the default notification center when the user changes the primary iCloud account. The keys and values in the local key-value store have been replaced with those from the new account, regardless of the relative timestamps.
*/
FOUNDATION_EXPORT NSNotificationName const NSUbiquitousUserDefaultsDidChangeAccountsNotification API_AVAILABLE(ios(9.3), watchos(2.0), tvos(9.0)) API_UNAVAILABLE(macos);
/*!
NSUbiquitousUserDefaultsCompletedInitialSyncNotification is posted on the main queue when ubiquitous defaults finish downloading the first time a device is connected to an iCloud account, and when a user switches their primary iCloud account.
*/
FOUNDATION_EXPORT NSNotificationName const NSUbiquitousUserDefaultsCompletedInitialSyncNotification API_AVAILABLE(ios(9.3), watchos(2.0), tvos(9.0)) API_UNAVAILABLE(macos);
/*!
NSUserDefaultsDidChangeNotification is posted whenever any user defaults changed within the current process, but is not posted when ubiquitous defaults change, or when an outside process changes defaults. Using key-value observing to register observers for the specific keys of interest will inform you of all updates, regardless of where they're from.
*/
FOUNDATION_EXPORT NSNotificationName const NSUserDefaultsDidChangeNotification;
#if (TARGET_OS_MAC && !(TARGET_OS_EMBEDDED || TARGET_OS_IPHONE)) || TARGET_OS_WIN32
/* The following keys and their values are deprecated in Mac OS X 10.5 "Leopard". Developers should use NSLocale, NSDateFormatter and NSNumberFormatter to retrieve the values formerly returned by these keys.
*/
FOUNDATION_EXPORT NSString * const NSWeekDayNameArray NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSShortWeekDayNameArray NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSMonthNameArray NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSShortMonthNameArray NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSTimeFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSDateFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSTimeDateFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSShortTimeDateFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSCurrencySymbol NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSDecimalSeparator NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSThousandsSeparator NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSDecimalDigits NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSAMPMDesignation NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSHourNameDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSYearMonthWeekDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSEarlierTimeDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSLaterTimeDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSThisDayDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSNextDayDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSNextNextDayDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSPriorDayDesignations NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSDateTimeOrdering NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSInternationalCurrencyString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSShortDateFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSPositiveCurrencyFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
FOUNDATION_EXPORT NSString * const NSNegativeCurrencyFormatString NS_DEPRECATED(10_0, 10_5, NA, NA);
#endif
NS_ASSUME_NONNULL_END
|
Minor gynaecology of the climacteric.
The climacteric is a transitional phase of one to five years during which the genital organs involute in response to the cessation of gonadal activity. During the climacteric women suffer a range of gynaecological disorders. The patient's worries discussed in this article are particularly pertinent to general practice. |
Leotards for girlsGymnastics is a sport where a lot of movement is demanded. That's the reason gymnastics leotards are used. They permit the gymnast to move in an unrestricted manner. They fit just like a glove to the body and they move with each movement the gymnast makes. As for where it gets its origins, a French acrobat, Jules Leotard felt that acrobats desired a garment that allowed them to move. He called it a maillot, but the name was soon altered to match that of its maker.leotards for gymnasticsThe details
Gymnastics leotards are extremely comfortable in order to permit the gymnasts to do their magic tricks. It is composed of a flexible and thin cloth that is only one bit. The torso is wholly covered, but the legs may be... |
const _ = require('lodash');
const escape = require('escape-html');
module.exports = (props) => (
_.mapValues(props, value => escape(value))
);
|
---
abstract: 'The pure-exploration problem in stochastic multi-armed bandits aims to find one or more arms with the largest (or near largest) means. Examples include finding an $\epsilon$-good arm, best-arm identification, top-$k$ arm identification, and finding all arms with means above a specified threshold. However, the problem of finding *all* $\epsilon$-good arms has been overlooked in past work, although arguably this may be the most natural objective in many applications. For example, a virologist may conduct preliminary laboratory experiments on a large candidate set of treatments and move all $\epsilon$-good treatments into more expensive clinical trials. Since the ultimate clinical efficacy is uncertain, it is important to identify all $\epsilon$-good candidates. Mathematically, the all-$\epsilon$-good arm identification problem presents significant new challenges and surprises that do not arise in the pure-exploration objectives studied in the past. We introduce two algorithms to overcome these and demonstrate their great empirical performance on a large-scale crowd-sourced dataset of $2.2$M ratings collected by the New Yorker Caption Contest as well as a dataset testing hundreds of possible cancer drugs.'
author:
- |
Blake Mason\
University of Wisconsin\
Madison, WI 53706\
`bmason3@wisc.edu`\
Lalit Jain\
University of Washington\
Seattle, WA 98115\
`lalitj@uw.edu`\
Ardhendu Tripathy\
University of Wisconsin\
Madison, WI 53706\
`astripathy@wisc.edu`\
Robert Nowak\
University of Wisconsin\
Madison, WI 53706\
`rdnowak@wisc.edu`\
bibliography:
- 'eps\_refs.bib'
title: 'Finding All $\epsilon$-Good Arms in Stochastic Bandits'
---
Broader Impacts
===============
The application of machine learning (ML) in domains such as advertising, biology, or medicine brings the possibility of utilizing large computational power and large datasets to solve new problems. It is tempting to use powerful, if not fully understood, ML tools to maximize scientific discovery. However, at times the gap between a tool’s theoretical guarantees and its practical performance can lead to sub-optimal behavior. This is especially true in *adaptive data collection* where misspecifying the model or desired output (e.g., “return the top $k$ performing compounds” vs. “return all compounds with a potency about a given threshold”) may bias data collection and hinder post-hoc consideration of different objectives. In this paper we highlight several such instances in real-life data collection using multi-armed bandits where such a phenomenon occurs. We believe that the objective studied in this work, that of returning all arms whose mean is quantifiably near-best, more naturally aligns with practical objectives as diverse as finding funny captions to performing medical tests. We point out that methods from adaptive data collection and multi-armed bandits can also be used on content-recommendation platforms such as social media or news aggregator sites. In these scenarios, time and again, we have seen that recommendation systems can be greedy, attempting purely to maximize clickthrough with a long term effect of a less informed public. Adjacent to one of the main themes of this paper, we recommend that practitioners not just focus on the objective of recommendation for immediate profit maximization but rather keep track of a more holistic set of metrics. We are excited to see our work used in practical applications and believe it can have a major impact on driving the process of scientific discovery.
|
Q:
javascript regex remove quotes if number with no hyphens
I want to remove quotes only if the match expression is a number and has no hyphen after it. Right now am doing this:
$obj.replace(/"([\d.-]+)"/g,"$1")
Where $obj is a JSON.stringify o/p. How do I modify the regex to remove quotes if the number is not followed by a hyphen So "12" should get transformed to 12 but "44-45" should remain as it is.
Any help is appreciated.
A:
Remove - from the character class: numbers don't have minuses in them. To allow an optional minus sign at the beginning only, add -? to the front.
$obj.replace(/"(-?[\d.]+)"/g,"$1")
While we're here, you might also want to check that there's only one decimal point, and leave a string like "1.2.3.4" alone.
$obj.replace(/"(-?(\d+\.?\d*|\.\d+))"/g,"$1")
// ^^^^^^^^^ a number with optional decimal places
// ^^^^^ decimal point followed by digits
|
<ebay-textbox invalid />
|
Is James Harden The Most Dominant Scorer Since Wilt Chamberlain?
Photo: dreamshake.com
After finishing the 2017-18 season as the NBA’s top regular season team and taking the Golden State Warriors to a 7th game in the 2018 Western Conference Finals, the Houston Rockets were considered among the Top 4 Contenders to win the NBA title this season. But after a combination of circumstances and events, the Rockets had a slow start to their season.
Houston lost Trevor Ariza and Luc Mbah Moute to free agency. They added Carmelo Anthony during the offseason with the hopes of offsetting their losses. However, the Carmelo experiment did not work and the Rockets lost Chris Paul (and Harden too) to injuries early in the season. The Rockets were off to a slow start and looked like a shadow of last year’s confident and dominant team. And then James Harden happened.
Harden’s 30-Point Streak
Photo: spin.ph.com
What began as a string of games where the reigning MVP scored 30 or more points has become one of the longest streaks in the history of the league. Including his 61-point return at Madison Square Garden on January 23, 2019. Harden has now scored 30 or more points in 21 consecutive games. That’s the fourth-longest ever in the NBA and the longest by any player not named Wilt Chamberlain. Chamberlain owns the record of 65 straight games which he set in 1961-62 when he averaged over 50 points per game. Wilt the Stilt also has two other records of 31 and 25 at #2 and #3 on the list but knowing that Wilt was a seven footer in the 1960s and Harden is all 6-5, The Beard’s achievement is impressive, to say the least.
A Signature Game At The Garden
Photo: yardbarker.com
Of course, the latest of Harden’s 30-point exploits was his 61-point performance at the Madison Square Garden last January 23rd. In that game, Harden scored his 61st point off a steal that sealed the Houston Rockets’ 114-110 escape act over the New York Knicks. Harden has always talked about wanting to have a signature game at the Garden and he delivered one last Wednesday.
Harden’s 61 points at the Garden was a career-high for him and it matched Kobe Bryant’s record for most points scored by a visitor in the current version of the Madison Square Garden which opened in 1968. The great Michael Jordan’s best game at the Garden was good for 55 points while Steph Curry’s personal best at MSG is 54. With his 61-point effort, Harden is averaging 52.5 points per game in his last five games, the second-longest streak of averaging 50 PPG in NBA history. Harden also became only the 5th player in league history to have multiple 60+ games in his career.
Carrying The Rockets On His Shoulders
Photo: bleacherreport.com
What makes Harden’s current feat incredible is the fact that he is carrying the Houston Rockets on his shoulders. With Chris Paul still out and Clint Capela also hit by the injury bug, Harden has had to do things on his own. Harden has scored a total of 261 points in his last five games, the 2nd-most points (behind Kobe Bryant) scored by a player in a five-game stretch over the past 50 years. It’s interesting to note that none of Harden’s 261 points in his last five games were assisted, meaning Harden had to weave his offensive magic to score every point on his own.
After this 61-point performance, Harden is now averaging a league-best 36.3 points per game. If he keeps up those numbers, it’s not just a career-high for him, It will make him only the fifth player in NBA history to average more than 35 points per game in a single season. With three more games to play this month, Harden is averaging 45.3 points per game in the month of January. The only player to average 45 points per game in any month of an NBA regular season is well, Wilt Chamberlain.
The Next Unanimous MVP?
With his otherworldly performances, Harden has shot back to the top of the favorites to win the MVP award this season. According to betmaker Betway as of 1/25/19, The Beard is a clear -250 favorite to repeat as MVP this season. Milwaukee’s Greek Freak Giannis Antetokounmpo is second at +350 while Los Angeles Lakers’ LeBron James is third at +1000. If the Beard continues his epic performance this season, no question he is going to become the first back-to-back winner since Stephen Curry in 2015-16.
Harden was the favorite in the 2017-18 NBA MVP race and he got 86 first-place votes during the MVP voting with only LeBron James at 15 getting the other first-place votes. Given how dominant James Harden has been so far and if he continues to play at this high level, then we also might see Harden follow Steph Curry as the only players to win unanimously the MVP voting. That would be another feather in the cap for The Beard. The MVP award is too far ahead though. We’re still halfway the NBA 2018-19 Regular Season schedule. For now, let’s enjoy the handiwork of James Harden, the best scorer since Wilt Chamberlain. |
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.TH "LIGHTNING-WAITBLOCKHEIGHT" "7" "" "" "lightning-waitblockheight"
.SH NAME
lightning-waitblockheight - Command for waiting for blocks on the blockchain
.SH SYNOPSIS
\fBwaitblockheight\fR \fIblockheight\fR [\fItimeout\fR]
.SH DESCRIPTION
The \fBwaitblockheight\fR RPC command waits until the blockchain
has reached the specified \fIblockheight\fR\.
It will only wait up to \fItimeout\fR seconds (default 60)\.
If the \fIblockheight\fR is a present or past block height, then this
command returns immediately\.
.SH RETURN VALUE
Once the specified block height has been achieved by the blockchain,
an object with the single field \fIblockheight\fR is returned, which is
the block height at the time the command returns\.
If \fItimeout\fR seconds is reached without the specified blockheight
being reached, this command will fail\.
.SH AUTHOR
ZmnSCPxj \fI<ZmnSCPxj@protonmail.com\fR> is mainly responsible\.
.SH RESOURCES
Main web site: \fIhttps://github.com/ElementsProject/lightning\fR
\" SHA256STAMP:5714e6333e5ba57cc00de425e6dc411f2c30812bbc8d95d01d50c460ee002e29
|
Illinois @ Indiana: Box Score Breakdown
John Brumbaugh
01/21/2006
The Fighting Illini continued Big Ten Conference play this week with a trip to Bloomington, IN. This edition of the Box Score Breakdown will look at Illinois' game against the Hoosiers focusing on the effectiveness of the three-guard lineup in Illinois two-point loss to the Hoosiers.
Illinois' loss to Indiana in Bloomington is one of those type of games where the plus / minus system can be a very effective way to look at how different lineups performed during the game. Illinois started out the game by building up a large lead. Throughout the middle of the game, the Illini played poorly as Indiana came back from the deficit and then took a large lead themselves. Finally, the Illini stormed back to make the game close in the final minutes before falling just short at the end. Games like this provide an interesting look at how differing lineups performed on the court.
The Illini's best lineup was in the game when the Illini made their run between 7:28 and 4:35 in the second half. I have to believe the only reason this lineup ended up changing was because James Augustine picked up his fourth foul, and found a spot on the bench for the next forty-four seconds. When Augustine came back in the game, he replaced Warren Carter, and the Illini played with that lineup for the next 1:48 on the clock.
Bruce Weber obviously found a lineup that worked, and he was sticking with it.
The Illini starting lineup was able to jump ahead of the Hoosiers giving the Illini an 8-3 lead before Bruce Weber subbed in Marcus Arnold for Shaun Pruitt at the 16:21 mark (the traditional time he does that in a game). The problem was in the second half, the same lineup starting out the second half was not as effective. In the first stretch of the game, Weber had Pruitt staying behind Marco Killingsworth, but in the start of the second half, Pruitt was fronting the Hoosier big man. This coincided with the Hoosiers starting to build up their big second half lead.
Last year, Illinois thrived running a three guard offense with Dee Brown, Luther Head, and Deron Williams. This year, Illinois has gone to the three guards combining Brown, Chester Frazier, Rich McBride, and Jamar Smith in many different combinations of the three. Coming into the game with the Hoosiers, there were questions with how the Illini would match up with the Hoosiers, who since DJ White's injury, have started a very small lineup with Robert Vaden starting at the traditional power forward position.
With the interesting match ups in Tuesday night's contest, it allowed for an interesting study as to when and how the Illini playing small versus going with a more traditional lineup worked against a team with an unconventional lineup. Just looking at the two-guard lineups, only the starting backcourt of Dee Brown and Rich McBride netted a negative result for the Illini on the court (the entire starting lineup netted a negative result as well).
Illinois Playing Two GuardsNet Result: +8Net Game Time: 29:16
Illinois Playing Three GuardsNet Result: -10Net Game Time: 10:44
Against Indiana, the Illini spent most of the time in the two guard lineup, and it obviously worked. When the Illini went small, either to give Brian Randle rest at the wing forward, or to better match up with the Hoosiers, the Hoosiers seemingly went on runs.
On Tuesday night, the Illini only went small for a one minute stretch prior to the 5:32 mark in the first half, when Bruce Weber made his traditional substitution of Jamar Smith into the game just after the sixteen minute media timeout. Then when the Illini went small at the end of the first half, with Brian Randle slotting over to the four spot, the Hoosiers went on a run to close out the half (a 6-0 Hoosier run to give them a 23-19 lead).
It was during the second half when the Weber's decision to play small caused the most problems. One might think Weber's hand was forced due to foul trouble considering Brian Randle fouled out of the game and James Augustine ended the game with four fouls, but I don't know if that was the case or not. Yes, Randle did pick up his fourth foul with 12:08 in the game and the Illini went small, but even before that Illinois went small.
Over a four minute and fourteen second stretch in the second half, Indiana went on an 11-2 run, putting them down 53-38 with 9:56 left on the clock. Only for thirty-three seconds during that stretch did the Illini have in a two guard lineup (Dee Brown and Jamar Smith). The slide started after Illinois had pulled to within six, and when Bruce Weber decided to move Brian Randle down to the power forward position to better match up with Indiana's personnel on the court, namely a three guard attack with a wing forward (Robert Vaden) playing an undersized four.
The Illini did not make their comeback in the second half until the Illini went with a big, but very athletic lineup playing Brian Randle, Warren Carter, and James Augustine in the front court. The backcourts during this time started out with Chester Frazier and Rich McBride, and eventually became just Brown and Frazier, who teamed up for just under three minutes as the Illini made a 9-1 run to close the Hoosiers' lead to 56-52.
Now this game was just one small sample size, but it did illustrate the effectiveness of Illinois playing "big" versus "small". While I have not looked in depth at the previous games in the Big Ten, this pattern has been there. Against Michigan, the two guard lineups were much more effective than a three guard lineup. Against Michigan State, the three guard lineup for Dee Brown, Chester Frazier, and Rich McBride was extremely effective, and the two guard lineups struggled. While against Iowa no lineup was particularly effective for the Illini, especially the Illini's starting backcourt tandem of Brown and McBride.
More research needs to be done before I can actually determine which works better for Illinois this season, but I do have the theory that Illinois is a much more effective team when they are playing big because it puts Brian Randle on the floor at the wing. When Illinois is playing big, they are also more effective on the offensive glass, something that has kept the Illini offense going in their sixteen wins this season, but been missing in both of their losses.
INDIVIDUAL STATISTICS
Player Name
Differential
Warren Carter
12
Chester Frazier
8
James Augustine
1
Brian Randle
0
Marcus Arnold
0
Dee Brown
-5
Jamar Smith
-7
Shaun Pruitt
-9
Rich McBride
-10
Best Player: Warren Carter (+12)Worst Player: Rich McBride (-10)
Despite his career high in scoring, Shaun fell on the negative side of the +/- statistic. He was simply not in the game at the right time for the Illini. He played while the Illini built up their lead early, but he was also in the game early in the second half as the Hoosiers crawled back into the lead.
It was interesting to see the difference in how Pruitt guarded Killingsworth from the first half to the second half, and it makes you wonder why Weber decided to front him in the second half when staying behind him during the first half had frustrated him immensely (the intentional foul, and the love toss of the ball into Pruitt's face after his only made basket of the half). |
Q:
PHP escape $ sign and echo a string my fetching database
I want to know how to echo a string that have a $ sign from a database. At this time, the value on database 'Buy one for $5.00' converts to 'Buy one for .00'.
Let's say the name of the field is title and the value is Buy one for $5.00
<?php
$body_tpl = file_get_contents('tpl.html'); //Title is: %title% blah blah %title%
$row = mysql_fetch_array(mysql_query("SELECT title FROM table WHERE id=1"));
$title = $row['title'];
$pat[] = '/%title%/sx';
$rep[] = $title;
$body = preg_replace($pat,$rep,$body_tpl);
print_r($body);
?>
A:
You should use str_replace for that.
$row = mysql_fetch_array.....
$title = $row['title'];
$body = str_replace( "%title%", $title, $body_tpl );
echo $body;
Note that you can replace multiple keywords at the same time with str_replace too (see PHP docs).
|
NEW YORK (CNNMoney.com) -- The nation's job market was dealt a savage blow this week as a slew of companies announced more than 34,000 layoffs, and the government reported that nearly 2 million jobs have been lost this year, through November.
On Friday, the Labor Department said that employers hemorrhaged 533,000 jobs in November, the largest monthly loss since December 1974. This was much worse than the 325,000 expected by a consensus of economists surveyed by Briefing.com.
The annual unemployment rate also increased to 6.7% in November, from 6.5% the prior month.
"With the loss of over half-a-million jobs just last month, the U.S. job market is now shedding jobs at a truly alarming rate, a rate that is measurably worse than past recessions," said Jared Bernstein, senior economist for the Economic Policy Institute, in an e-mail to CNNMoney.com.
The government also revised up its losses for the prior two months, to 320,000 for October and 403,000 in September. In total, it reported job cuts of 1.9 million for 2008, through November.
Those losses exceed the 1.5 million job cuts that occurred in a 12-month span from 1990 to 1991, according to information from David Wyss, chief economist for Standard & Poor's. But Wyss said the current unemployment rate pales in comparison to 1982, when the rate was nearly 11%.
"I don't think this is the 1930s, but it's certainly the worst recession we've seen since 1982," Wyss said in an interview on Thursday.
Job cuts continue to mount in December. Thursday was particularly bloody, when 11 companies announced 24,914 layoffs, according to Challenger, Gray & Christmas and company reports.
Then on Friday, engine-maker Cummins said it would eliminate at least 500 white-collar jobs by the end of 2008, and General Motors (GM, Fortune 500) released plans to lay off 2,000 workers next year.
And this is just the latest bit of bad December job news. On Wednesday, State Street Corp., Jefferies Group and The Carlyle Group announced job cuts totaling about 3,000. On Tuesday, U.S. Steel said 3,500 workers will be "affected" by the "temporary idling" of manufacturing facilities in Keewatin, Minn., and near Detroit and St. Louis.
The total layoffs announced in the first week of December: 33,914.
The big 5 Thursday job cuts
AT&T (T, Fortune 500), a Dallas-based telecom operator, said it would slash 12,000 jobs, totaling 4% of its workforce.
AT&T attributed the staff cuts to "economic pressures, a changing business mix and a more streamlined organizational structure" in a news release.
The telecom also said it would take a charge of $600 million in the fourth quarter to make severance payments. It said it would reduce its 2009 capital expenditures from its 2008 levels.
Credit Suisse Group (CS) said it would cut 5,300 staff jobs, 11% of its worldwide work force, as part of a restructuring effort. The majority of the cuts would be to investment bank jobs, said Chief Executive Brady Dougan.
In addition, the Zurich, Switzerland-based company said it would eliminate 1,200 contractor positions.
DuPont (DD, Fortune 500), a chemical company based in Wilmington, Del., said it would cut 2,500 jobs.
DuPont Chief Executive Charles Holliday said his company was making the cuts "in response to current market challenges" and to increase the company's competitiveness in the coming year.
DuPont said it expected a loss of 60 cents to 70 cents per share for the fourth quarter, including an 40-cent-per-share charge from the company's restructuring plan. Going forward, the company expects full-year earnings to be $2.25 to $2.75 per share in 2009.
Full-year earnings of $2.75 to $2.85 are expected for 2008, said DuPont, down from its previously announced range of $3.25 to $3.30 per share.
Viacom Inc., (VIA) an entertainment company that includes MTV Networks and Paramount Pictures, said it would cut 850 jobs, or 7% of its workforce.
Viacom Chief Executive Philippe Dauman said it was restructuring its company "to adapt to the challenges presented by the current economic environment."
In addition to the job cuts, New York-based Viacom said it was suspending senior level management salary increases throughout 2009. The company expects the restructuring to result in pre-tax savings of $200 million to $250 million in 2009, but it will take a pre-tax charge of $400 million to $450 million in the fourth quarter of 2008, or 42 cents to 48 cents per diluted share.
Car rental company Avis Budget Group (CAR, Fortune 500) said it has cut more than 2,200 jobs and taken other steps to meet its goal of reducing annual costs by $150 million to $200 million by the middle of 2009. The company will close its claims-processing facility in Orlando, Fla., as well as its customer contact center in Wichita Falls, Texas.
Avis CEO Ronald Nelson said the company will continue its "relentless focus on cost containment" so that when economic conditions improve Avis can "achieve our ultimate goal of restoring our margins to previous levels." In the past weeks, Avis said it has frozen management salaries and downsized its planned fleet.
The Wednesday job cuts
This follows a slew of bad employment news on Wednesday, when State Street Corp. (STT, Fortune 500) said it was cutting from 1,600 to 1,800 workers, or 6% of its total workforce.
The Boston-based company, which provides financial services to institutional investors, said these job cuts would occur between now and the end of the first quarter of 2009. Two-thirds of the cuts will occur in North America, with the rest in Europe, Asia and the Pacific region.
Also on Wednesday, Jefferies Group (JEF) said it was shedding 18% of its work force throughout 2008, as part of a wider restructuring plan to "restore profitability in 2009." The investment bank said it planned to end the year with 2,150 staffers. That's 358 less than it started with. The company also said it was closing offices in Dubai, Singapore and Tokyo.
The Carlyle Group, a private equity investment firm based in Washington, said Wednesday that is laying off 10% of its work force, with most of the layoffs occurring in the U.S. offices. The Carlyle Group, has more than 1,000 workers, according to the company.
"The markets are terrible and we need to adjust accordingly," said Carlyle spokesman Christopher Ullman. "We're making the adjustments to deal with the current realities of the economy."
The future
Lakshman Achuthan, managing director of the Economic Cycle Research Institute, said in an interview on Thursday that the job losses are likely to drag into next year. But he said it's difficult to project how long the current recession will last, and when the job market will hit bottom.
"When we see the job losses and the job picture getting worse and worse and worse, it is confirming that the recession is accelerating, that it is intensifying to the down side, but it doesn't tell us where were headed in the future, said Achuthan, who focuses on leading indicators.
"The bad news doesn't stop with the fact that we're in an intensifying recession and that it's going to continue into 2009," said Achuthan. "The risk on the horizon is that the recovery, when it does come, will be a jobless recovery." |
288 F.3d 730
In the Matter of: PHONES FOR ALL, INC.; Preferred Carrier Services, Inc.; Preferred Carrier Services Virginia, Inc., Debtors.Issac Lasky, Appellant,v.Phones For All, Inc.; Preferred Carrier Services, Inc.; Preferred Carrier Services Virginia, Inc., Appellees.
No. 01-10758. Summary Calendar.
United States Court of Appeals, Fifth Circuit.
April 30, 2002.
R. Terry Bell, Bell, Nunnally & Martin, Dallas, TX, for Appellant.
John Mark Chevallier, David Lynn Woods, McGuire, Craddock & Strother, Dallas, TX, for Appellees.
Appeal from the United States District Court for the Northern District of Texas.
Before JONES, SMITH and EMILIO M. GARZA, Circuit Judges.
EDITH H. JONES, Circuit Judge:
1
The issue in this case is whether Issac Lasky is entitled to an administrative priority claim for severance pay from the debtor when he executed an employment contract containing the severance pay clause about five months before the debtor filed for Chapter 11 bankruptcy relief, but was terminated three weeks after the filing. This court has not squarely faced this type of issue before. For the following reasons, we affirm the judgments denying administrative priority to the severance claim.
2
Lasky argues that his contractual right survived the bankruptcy filing to become an administrative claim. He relies on cases from the Second Circuit, which differ in result and reasoning from most other circuits. See In re: Amarex, 853 F.2d 1526, 1531 n. 5 (10th Cir.1988), discussing circuit split.
3
The bankruptcy court held, however, that Lasky cannot prevail for three reasons. First, while the general wage priority section of the Bankruptcy Code clearly specifies and limits priority treatment for severance payments, see 11 U.S.C. § 507(a)(3)(A), the provision according first-priority status to administrative claims does not. See 11 U.S.C. § 507(a)(1) (incorporating 503(b)(1)(A)). Congress's omission of severance pay from administrative priority status must therefore have been deliberate. Second, Lasky "earned" his severance pay when he entered into the contract, rather than as compensation for past services rendered. As a result, even the Second Circuit cases would not accord his claim priority status. Third, Lasky's claim did not represent services that conferred a benefit on the estate as required to garner administrative priority status. See NL Indus., Inc. v. GHR Energy Corp., 940 F.2d 957, 966 (5th Cir.1991).1 The district court affirmed.
4
We essentially agree with the bankruptcy court's reasoning. See In re: Phones for All, Inc., 249 B.R. 426 (Bkrtcy. N.D.Tex.2000). We understand that court's statutory interpretation to mean that a prepetition severance agreement is not entitled to post-petition administrative priority status. As the Tenth Circuit explained, to attain such status, a severance claim "must have arisen from a transaction with the debtor in possession" and must then confer a benefit on the debtor's estate. In re: Commercial Financial Services, Inc., 246 F.3d 1291, 1294 (10th Cir.2001). This reading of the statutory provisions makes clear the claimants' burden to reconfirm or renegotiate post-petition any severance packages they may have if they continue to work for the debtor.
5
Because, as the bankruptcy court demonstrated, no plain reading of the Bankruptcy Code supports treating Lasky's prepetition severance provision as an administrative expense, the judgments of the bankruptcy and district courts are AFFIRMED.
Notes:
1
The bankruptcy court alternatively held that if Lasky's claim were entitled to priority under §§ 503(b) and 507(a)(1), the court would prorate the amount of severance over the 3-week period Lasky worked for the debtor post-petition
|
One man has been airlifted to hospital after being cut free by firefighters following a crash involving a lorry and two cars on the A4 Portway.
The man, who has not been named, was flown to Southmead Hospital with chest injuries after the crash, which happened at around 11.40am.
The crash happened at the junction of the Portway with Portview Road, at the first entrance to Avonmouth Village, as the A4 emerges from underneath the M5 flyover in Shirehampton.
All three emergency services were called to the scene, and police closed the northbound side of the dual carriageway at that point.
(Image: Zoe Hammond-Mcclelland)
Firefighters from Avonmouth, Temple, Southmead and Bedminster were in attendance dealing with the incident, and had to rescue one male driver from his vehicle, a spokesperson for Avon Fire Brigade said.
A spokesperson for South West Ambulance Trust said land ambulances and the air ambulance attended the scene. |
The Blogger
I am Jane, the blogger behind the blog. Card dealer at night, wife in the morning. At my free time I just go to the gym and sweats off all my frustrations and stress. Loves to travel too & wear those beautiful dresses. ?Philippines – California USA?.
Meta
As the new year comes. I know everybody i quite excited especially those couples who has their engagement took placed already and getting ready for the big day which is their wedding. Yes! new year is the best time for the couple to tie a knot though some of you prefers in the mid year this occasion to happens but mostly it’s best if you make it in the beginning of the year hence you can settled down earlier this year for more active deeds, I mean you can do all the things you needed to be done in the entire year s the newlywed couple.
Hence, what are the things you should consider first in placing your wedding? well, of course dresses are in the lead list as you need to wear such lovely dresses for your bride and a great manly tuxedo for your man. Thus, Let me share with you this shop, actually an online shop, that calls d-daydress where all the lovely and beautifully made lace wedding dresses where houses. Actually, I’d lurking with this shop quite a long time now and still I’ve found them reasonable and best to shop among the all of the wedding shops I knew online. Why? because each if their pieces were these cheapest and you can even gets an free shipping services as you spend the minimum spend to be eligible to have this kind of services they’d been offering.
The shop,d-daydress, is specializing with lace wedding gowns and they even have this great deals called bridesmaid dresses under 50 where I know everyone of you would enjoy to have or even just to see. Yes! you can freely check it yourself without a fee as it was posted online and you can also sees the further details of each gowns you eyeing to have in the future use. Go check them out now here: http://www.d-daydress.com/bridesmaid-dresses-under-100-c10036.html and bookmarked all the dresses you pleases hence you can have hard time sorting it out in the future as you need to wear them soon.. |
Q:
Antlr4: The following sets of rules are mutually left-recursive
I am trying to describle simple grammar with AND and OR, but fail with the following error
The following sets of rules are mutually left-recursive
The grammar is following:
expr:
NAME |
and |
or;
and:
expr AND expr;
or:
expr OR expr;
NAME : 'A' .. 'B' + ;
OR: 'OR' | '|';
AND: 'AND' | '&';
Simultaneously, the following grammar
expr:
NAME |
expr AND expr |
expr OR expr;
NAME : 'A' .. 'B' + ;
OR: 'OR' | '|';
AND: 'AND' | '&';
does compile.
Why?
A:
As already mentioned: ANTLR4 only supports direct left recursion. You can label the alternatives to make a distiction in your generated visitor or listener:
expr
: NAME #NameExpr
| expr AND expr #AndExpr
| expr OR expr #OrExpr
;
NAME : 'A' .. 'B' + ;
OR : 'OR' | '|';
AND : 'AND' | '&';
Note that 'A'..'Z'+ is the old v3 syntax, in v4 you can do this: [A-Z]+
See: https://github.com/antlr/antlr4/blob/master/doc/parser-rules.md#alternative-labels
|
No but its okay. The harness he got from DDM was messed up anyway so hes going OE. Which ironically was why it wasn't working. The ballasts both went bad recently and that's why he was redoing the whole kit. Not that it matters. lol. |
Hope Earwarmer
November 14, 2018
Disclosure: This page may contain affiliate links which help me cover the cost of publishing my blog. Should you choose to make a purchase, at no additional cost to you, I will be given a small percentage of the sale.
When the weather starts to get cold here in Michigan, one of my favorite accessories to help beat the chill is an earwarmer. I love that I can still wear my hair piled up all messy on the top of my head — or, if it’s a good hair day, down and wavy — because a cozy earwarmer will look great either way.
This earwarmer is easy and quick. Don’t let the #3 DK weight yarn fool you; it will work up fast, and still feel light on your head. The seam is conveniently hidden underneath the button, and although I am totally ok with a necessary seam, I always get excited when I find a good hiding place for it!
Visual Learner?
You can follow along with me with this tutorial video, regardless of what size you are making! I put the pattern instructions right on screen so you can relax and go at your own pace. Be sure to subscribe, too!
Prefer a PDF?
This pattern is also available as an ad-free, printable PDF, which includes sizes toddler – adult! And if you love PDFs, you might want to check out my All Access Pass. It’s an awesome deal! (Or, scroll down for the free version!)
You’ll also need: 7/8″ button, and a yarn needle that can fit through it
Terms and Abbreviations:ST/STS (stitch/stitches)SL ST (slip stitch)SK (skip)CH (chain)SC (single crochet)HDC (half double crochet)SC+HDC (complete a full single crochet and a full half double crochet in the same stitch)3rd LOOP (work stitch into 3rd loop only – see “Special Stitch”)
Special Stitch:
3rd Loop OnlyHalf double crochet stitches have a 3rd loop that we utilize in this pattern. When working in turned rounds, as in this pattern, the 3rd loop can be found just below the front loop on the side of the work that is facing you. When instructed to work in “3rd loop only”, insert your hook into this special loop. This creates a delicate braided look on the opposite side of the pattern.
Notes:(1) This pattern is written in American Standard Terms.
(2) CH1s at the beginning of rounds do not count as a stitch in the final stitch count.
(3) To resize earwarmer, your starting chain can be any odd number.
(4) Pattern is written for toddler size with additional sizes in brackets [child, teen, adult]. So, for example, if it says “CH71 [75, 85, 89]”, the first number is for the toddler size, and the numbers in brackets are child, teen, and adult instructions, respectively. If you are working from printed instructions, it helps to circle or highlight the numbers you are following before you begin.
(5) Knowing where to place your first stitch can be tricky when working in joined rounds. Usually, it doesn’t matter as long as you’re consistent, but for this pattern, it does matter… especially from Round 4 on! So, here is an image to help you identify where to put your first stitch. Because Round 4 instructs you to skip the first stitch, you will put your SC+HDC combo in the stitch marked as the 2nd stitch (which is also easy to find thanks to the spaces created by the SC+HDC combos from Round 3).
INSTRUCTIONS
To begin: CH71 [75, 85, 89].
Round 1: HDC in 2nd CH from hook and in each remaining CH. Bring ends together, without twisting, and join to the top of the first ST with a SL ST. (70 [74, 84, 88])
Round 2: CH1, turn. SC in 3rd loop of each ST around. Join to the top of the first ST with a SL ST. (70 [74, 84, 88])
Rounds 3-14 [3-16, 3-18, 3-18]: CH1, turn. SK first ST, SC+HDC in next ST. (SK next ST, SC+HDC in next ST) around. Join to the top of the first ST with a SL ST. (70 [74, 84, 88])
Round 15 [17, 19, 19]: CH1, turn. HDC in each ST around. Join to the top of the first ST with a SL ST. (70 [74, 84, 88])
Round 16 [18, 20, 20]: CH1, turn. SC in 3rd loop of each ST around. Join to the top of the first ST with a SL ST. (70 [74, 84, 88])
Fasten off, leaving a long tail for cinching. Use yarn needle and starting tail to sew the small gap between the first and last stitches of Round 1 closed, then weave in that tail only.
Cinching
1. Thread the long finishing tail through your yarn needle and gently set it aside. Gather the seamed section of the headband, and fold in half so that the fold is facing you.
2. Holding on to the fold with one hand, use your other hand to pinch the upper half in half again. The top edge of the earwarmer should be facing down. Grasp the fold together with the first fold, then repeat with the bottom section. When you’re finished, you should be pinching three folds together, with both the top and bottom edges of the earwarmer facing down.
3. Run your yarn needle through all three sections of gathered material. The closer you get to the surface, the better your cinch will look; so I run mine right under just a couple strands of each fold.
4. Wrap the yarn around the underside of the cinch, then through the sections again. Do this a few times to secure the cinch, then thread the needle up through the 1st hole of the button and back down through the 2nd hole, position it on the cinch, and wrap yarn around to the underside to tie off. (If your button has four holes, complete the first two, wrap yarn around the bottom, then come back and complete the last two before tying off.) Weave in the tail.
Done! If you’re sharing on social media, be sure to hashtag #hopeearwarmer and tag me @yarnandchai.design. Stay warm out there!
Thanks Cheryl! My sizes are based on the Yarn Council of America’s standard measurement system. Everyone is different, though, so it’s always a good idea to measure your own head for the best possible fit.
Hi Laura! I would just switch colors at the seam when you turn and begin a new round. You could do it several times for stripes, or just once for a half-and-half look. I also have a Malia Earwarmer pattern 🙂
Hi Sue! You definitely don’t want to download any PDF converters, and any time you see those, they are an ad. (The more you click them, the more you’ll see them.) My patterns are free on my blog, and ad-free PDFs are a small fee which you can buy from my shop. The listing for each ad-free PDF is on its pattern blog post.
Hi Alanna! Adapting a pattern for a different yarn weight isn’t necessarily an easy thing for a newbie,, but if you’re feeling confident, you could do your starting chain to whatever length you need, making sure it’s an odd number, then follow the pattern with smaller stitch counts and fewer rows.
HI! I’ve decided to attempt in the correct weight yarn given in the pattern, but I’ve gotten confused about the stitch count? Why does the stitch count go down by one between rows one and two? I have the same number of hdc as chains made originally?
I did the gauge swatch an shad to go down to a 4.5mm hook. But, my 89 chain measures 20 inches not 21. My height on swatch had to be increased to 13 rows.
What should I do, go back to H hook or add more chains to foundation row?
Measuring just the chain can be a very iffy way to measure, because chains can stretch quite a bit after you’ve worked rows into them. Is it 20″ when stretched taut? If so, you might add more chains or go to an H hook, but otherwise, I would stick with what the gauge check told you.
I have been a passport member for a while now and every time I try to get a pattern, it keeps saying I have to pay for it! I also have a terrible time logging in. I need help! I want the new hope ear warmer pattern please! Thanks, Kathleen
Hi Kathleen! You don’t get your patterns by adding them to your cart; you sign in, then click “Passholder Area” in the top menu. If it comes up with a “content restricted” message, refresh the screen as instructed on that page. That will get you in to the exclusive area where all of my ad-free patterns are. As for having a terrible time signing in, have you forgotten your password? You can always do a password change. Please email me at rebecca@yarnandchai.com if you need more assistance!
Hi, I purchased the ad-free version earlier today so that I could help out your charity. However, as of yet, I do not have the link to the pattern. When I click on the hot link to the pattern in my receipt email, I am brought to the page to purchase it again. Can you help me out?
Thanks!
I wish I could do videos for all of my patterns, but life just doesn’t allow for it right now. Make sure you’re using a #3 DK weight yarn, and do a gauge check! If you are crocheting to gauge, you should end up right at 21″ for 88 stitches.
Even though I’m a Passholder, I can’t access the patterns for anything without all the ads. I’ve logged in several times – it’s not working! Help!! Thanks so much, I love your patterns and make them all the time!! Maureen
Hi Maureen! Passholders have a special page where they can access their PDFs. You just need to sign in, then click “Passholder Area” in the top menu. If it says “content restricted”, just refresh the screen as instructed on that page. |
One of the most feared disabilities in survivors of cardiac arrest is neurological impairment. Global cerebral schemia, as seen with cardiac arrest, causes delayed loss of CA1 pyramidal neurons in the hippocampus while the nearby dentate gyrus (DG) is relatively resistant. Despite much work on hippocampal neuronal njury, little is known of the effects of ischemia on hippocampal astrocytes. This grant seeks to understand the contribution of astrocytes to hippocampal selective vulnerability. Astrocytes are essential to many brain functions including synaptic transmission, metabolic and ionic homeostasis, antioxidant defense, inflammation, the blood brain barrier, and trophic support. This proposal will study three aspects of hippocampal astrocyte survival and response to ischemia and ischemia-like stress. In aim 1, mitochondrial function will be assessed with ischemia and reperfusion. Mitochondria are important both for energy production and for the regulation of cell death. Hippocampal organotypic slice cultures, which reproduce selective CA1 vulnerability, and astrocytes isolated from these two subregions of the hippocampus will be used for electrophysiological studies and real time imaging. The timecourse of changes in mitochondrial membrane potential, reactive oxygen species, and intracellular calcium during reperfusion in astrocytes in CA1 and DG will be assessed. Comparing the vulnerable and resistant areas will allow discrimination of important changes. Respiratory function and mitochondrial complex activity will also be measured. Aim 2 will focus on changes in astrocyte glutamate uptake with ischemia and reperfusion. Early impairment of glutamate uptake by astrocytes endangers neighboring neurons, and we have found early loss of GLT-1 in CA1 astrocytes. Detailed studies of glutamate uptake and transporter expression will be performed. ATP stores required for maintaining membrane potential and glutamate uptake will be monitored. Aim 3 will use overexpression of the chaperone Hsp70 selectively in astrocytes and induction of GLT-1 as protective strategies and assess changes in astrocyte function as well as changes in neuronal survival. Together these studies will provide a picture of hippocampal astrocyte ischemic response and link astrocyte dysfunction to selective neuronal injury in hippocampus. Maintaining and improving astrocyte function provides a novel target for developing therapies to improve neurological function following cardiac arrest. |
Spencer Bledsoe
Name (Age): Spencer Bledsoe (21)Tribe Designation: Brains TribeCurrent Residence: Chicago, Ill.Occupation: Economics Student at the University of ChicagoPersonal Claim to Fame: Captain of my high school cross country and track teams, Georgia’s 2009-2010 High School Chess Champion, tying for 1st at the World Open Chess tournament for a prize of $6,609 and becoming a U.S. Chess Expert.Inspiration in Life: The former governor Mitt Romney has been successful in everything he’s ever attempted, be it private equity, business/law school or running the Olympics. He has accumulated enormous wealth in starting several successful business ventures and constitutes the perfect embodiment of capitalism.Hobbies: Chess, ultimate frisbee and partying.Pet Peeves: People who are stupid but still voice their opinions, incompetent leaders, those who don’t respect intelligence and those who expect handouts in life. 3 Words to Describe You: Brilliant, competitive and arrogant.If You Could Have 3 Things on The Island What Would They Be and Why? A chess board – with a chess board present, I know I have the ability to impress whoever I’m with. Regular practice is also important. The American Flag – perhaps my biggest source of pride is being an American; and The Economist – This is my preferred news source (despite the fact that it’s perceived as “snobbish”).SURVIVOR Contestant You Are Most Like: The cleverness and strategic planning of Stephen, but the personality of Marty. Like Marty, I am a natural leader and can come off as pompous or bombastic. Also, I shared Marty’s disdain for Jane on S21.Reason for Being on SURVIVOR: The competition. I’m insanely competitive in chess, pursuing a career in investment banking, and everything I do. I want to play the game of Survivor for the challenge, the competition and the chance to prove myself in such an epic game, under such trying circumstances. Also, the money. The expected value of playing Survivor is, monetarily alone, worth more than most peoples’ salaries. I love $1,000,000 almost as much as winning.Why You Think You’ll “Survive” SURVIVOR: I’m a strong leader despite my young age, and have worked well in a team in a number of different academic, athletic and chess-related capacities. I’m also extremely competitive and would be a large asset to a tribe in puzzles and endurance-related challenges, as well as strategic competitions.Why You Think You Will Be the Sole SURVIVOR: I’m the chess expert who can plan my victory 10 moves in advance. I can use economic game theory to know the incentives of those around me. I’m the only guy who has these skills and is still personable enough to win. Think of me as a John Cochran who doesn’t suck.Do You Consider Yourself a Brain, a Beauty or a Brawn? A Brain, in both life and Survivor super fandom. I've seen every episode. I know the game inside and out. I'll know what I'm doing in camp life; I could probably even build a shelter just using rocks. When my body is withered and I'm left with only my t-shirt and tighty whities, I won't be a little boy out there. I'll rely on my mind.Who Do You Think Has the Best Chance in the Game of Survivor: Brains, Beauty or Brawn? What type of person excels in Survivor? The person who pushes the game forward strategically - the Rob Cesternino, Yul Kwon or Todd Hertzog. A Parvati or Ozzy may slip through the cracks, but this is a brain game. |
‘A Quiet Place’ Is Officially Getting A Sequel
Entertainment
Posted on April 27, 2018
by Olivia Esveld
We know that fans of horror films will want to shout with joy right now but shhhhh! Don’t. Make. A. Sound.
If Emily Blunt’s character can keep as quiet as humanly possible while giving birth in the movie than you can surely not say a peep when we tell you that this year’s hit horror film ‘A Quiet Place’ is getting a sequel that’s sure to be spookier and quieter than ever!
Paramount’s studio chairman-CEO, Jim Gianopulos, announced today at CinemaCon that the film would be getting a second edition with writers Bryan Woods and Scott Beck saying that they have plenty of material left over to explore.
“If you told me five years ago that an almost silent film starring the very funny guy Jim from The Office would have been a hit at Paramount, I would have said well, I should go work at Paramount,” said Mr Gianopulos.
The unique film has been extremely well received, having raked in $213 million worldwide already in the box office and having achieved the extremely difficult task of scoring 95% on Rotton Tomatoes.
‘A Quiet Place’ stars real life husband and wife John Krasinski and Emily Blunt, who play a married couple with two young children who must remain completely silent if they hope to escape the deadly creatures who are attracted by noise.
A post shared by John Krasinski (@johnkrasinski) on Feb 12, 2018 at 5:35pm PST
Krasinski was also the director of the hit film which has the biggest opening weekend for a horror film in history.
There’s been no mention of an official release date nor details about what exactly the plot will explore in this sequel, but we think it’s safe to say that fans will be pretty darn keen (in a silent way because hello, we’re scared) to find out what happens! |
Expert: Detroit should prioritize bikes, walking
Detroit would be a healthier and more economically viable city if it paid more attention to pedestrians and bicyclists instead of to motor vehicles, an expert on urban mobility said Thursday.
Gil Penalosa, chairman of the Toronto-based 8-80 Cities, an organization that trains civic leaders on how to achieve more walkable urban streetscapes, gave the keynote address Thursday at the annual luncheon of the nonprofit Jefferson East Inc., a civic group concerned with redevelopment of the Jefferson Avenue corridor.
"We need to reconnect with nature as a normal part of everyday life," Penalosa told the 200 guests at Stroh River Place. "I'm not talking about a dream. I'm talking about sustainable mobility."
Showing an image of East Jefferson in downtown Detroit, Penalosa quipped, "Some of these roads are so wide and you have so few cars," drawing laughter from the audience.
What Detroit and so many other cities need, he said, are wider sidewalks, better crosswalks, and "protected" bike lanes, that is, bike lanes separated from the flow of traffic by barriers.
In Detroit, the city in recent years has created about 150 miles of bicycle lanes, but all are merely painted white stripes on the pavement with no separation from vehicle traffic. Only now is the city creating its first protected bike lanes on East Jefferson near the Grosse Pointe line.
If Detroit created more protected lanes, he predicted, bike usage would soar and the city would begin to see obesity levels drop and car-bicycle accidents decline.
"These are not technical issues. These are not financial issues. These are political issues," he said.
Penalosa's organization, 8-80 Cities, is named for the concept that cities work best when 8-year-old children and 80-year-old seniors both find streets and sidewalks safe and easy to use. Penalosa and his staff are returning to Detroit in June for a four-day training session with civic leaders on the issues he raised in his address.
Contact John Gallagher: 313-222-5173 or gallagher@freepress.com. Follow him on Twitter @jgallagherfreep. |
Der Flug des "Technologie-Demonstrators für ein wiederverwendbares Startfahrzeug", so der etwas sperrige offizielle Name, war ein voller Erfolg. Nach 13 Minuten Flug stürzte der Mini-Shuttle wie geplant in den Golf von Bengalen.
Es ist nicht vorgesehen, die kleine Raumfähre zu bergen. Die Daten der Sensoren an Bord wurden während des Fluges per Funk an die Bodenstationen übertragen.
In den nächsten Jahren sollen dann weitere Testflüge erfolgen, bei denen es um die kontrollierte Landung auf einer Piste geht und um die Rückkehr aus einer Erdumlaufbahn.
Start zum Testflug: Indiens Mini-Shuttle hebt ab (ISRO)
Die indische Weltraumagentur ISRO hofft, in etwa fünfzehn Jahren eine rund vierzig Meter lange Raumfähre mit Menschen und Material ins All zu schicken. Sowohl das Fahrzeug als auch die Rakete sollen immer wieder zum Einsatz kommen.
So ein System, meinen die indischen Raumfahrer, soll einen günstigen, zuverlässigen und flexiblen Zugang in die Umlaufbahn ermöglichen. Doch das Konzept ähnelt sehr dem Space Shuttle der NASA. Das war zwar wiederverwendbar, aber weder günstig noch zuverlässig.
Indien hat große Pläne im All – und wird vielleicht schon bald die vierte Nation sein, die Menschen in den Weltraum transportiert. |
Q:
How to politely ask people from East Asia to give way?
I've arrived in Australia 9 months ago and I've noticed that often when asking people from East Asia to "give way" they will simply ignore me or even answer a "yes" but not move at all.
This is a situation that at least my wife, friends and work mates also faced a lot of times.
Some examples:
I went to an electronics shop some days ago and there was this Asian girl standing in front of a product section that I wanted to check. She was texting on her phone. I politely asked "can I take a look at these?" and all she did was nod her head and still block the view.
Leaving the train. Several times I was trying to hop off the train and a group of Asians would block the way and ignore my desperate "excuse me, guys".
Groups of 5+ East Asian people blocking the pathway while chatting and/or texting. "Excuse me" also didn't work.
Same as above, but getting hit in the shoulder by one of them and not even getting a "Sorry"
So obviously I don't know if it's a cultural thing or not. It just seems that our standard "excuse me" has another meaning to them.
What is the possible reason for this behavior and how can I politely
ask to give way which is culturally understood by East Asians? Or how can I ask to give way in a way which is universally understood?
A:
I found, when in Europe, that going "beep beep" when trying to get through would instantly get both a way through and a smile from the former obstructors.
A:
Well I think in case they are polite Asian people, you should say more than just 'excuse me'. Because in Asian language, 'excuse me' does not mean anything rather than just an opening of a conversation.
So my advice is next time you should add more information like:
Excuse me, can I get through please?
or
Excuse me, can you clear a path for me so that I can look at those
devices/products?
Conversation with Asians (especially ones who are not really good at speaking English) need to be specific and informative. As an Asian, sorry for all those inconveniences :( we never want to be impolite to you or anyone.
A:
I live in Sydney. When you say "Asian", I think you mean mostly Chinese people since Chinese people are our largest immigrant group by far. In Australia, we currently have over 200,000 international university students living here and 136,000 are from China alone. Many people arrive in Australia with virtually no English language skills at all, and while students will learn English over the course of their degree, they will not learn too many English customs as that is not taught as part of their programme, and also most of their interaction is with other Chinese students who they befriend.
There are almost 1.4 billion people in China, and as a result of the large, crowded population, many people simply gently push past other people - they don't just stand there saying something like "excuse me." So if you see someone who looks Chinese, then try gently pushing past immediately after saying excuse me, and they'll understand. Don't use your elbows on people like other respondents have instructed - that is just stupid and rude. Gently squashing by is more appropriate and civil.
I completely get where you are coming from here, as it appears by your name that you're an Italian man, and in Europe it is considered horribly rude to push past a woman and touch her body, particularly when you're a man. In Europe you would always ask her politely to let you pass, to avoid any embarrassing encounters such as touching her buttocks by accident. But remember, countries like Japan have men who are "train stuffers" (who push people into trains for a job and frequently touch their buttocks, legs and back), so in Asian cultures there is less of a taboo about brushing past another person and touching them - people are used to it. The girl on the phone was probably confused about why you just stood there after saying "excuse me" as she would have expected you to just brush on past.
Just a side note, since we have so many Chinese people living here, perhaps you could consider learning the mandarin word for excuse me?
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"They're all gone" "Go over there" "What's for?" "Just go on" "What the hell is it to you if I go to the 'Ladies'?" "You dare report me to the old woman" "I didn't" "I'll beat you up" "Stop..." "We can stop but from now on you'll have to pay us 30 cents protection money" "Then we'll not beat you up nor will anyone else dare, pay up" "I have no money" "Brother, that gang is bullying Man Chai again" "Let's take a look" "What do you think you're doing?" "What's up?" "You bully him because you are outnumbered" "He wanted protection money from me just now" "Kid, not even I have asked you lot for protection money and you dare ask him for it?" "You must be tired of living" "You dare to be a busybody here" "I'll beat you up too" "Stop, do you know who my father is?" "I don't care if he's the governor himself" "My father is known as the Uncle Loong" "Did you know that?" "Nope, although I've eaten lots of loong ha (Iobsters)" "Are you trying to insult my father?" "Beat him up" "Run, quick" "Chase him, stop..." "Stop, don't run..." "Bastard, you dare hit others" "You overturned my stall" "You two bastards again" "Bastard" "If you have the guts look for me at school tomorrow" "Would I be afraid of you?" "What's the matter, bluffing?" "If you're still here we'll beat you up too" "What's the big deal?" "You kids fight all day" "I'll tell your fathers" "Please don't, brother Wang" "We dare not next time" "Yes we won't dare" "Go on quickly" "Goodbye" "Da De, Xiao De" "Are you two alright?" "Yep." "Would have killed them if they didn't flee in time" "Let's go" "Do we have 5 cents, I'd like to eat sweet beancurd" "Where do we get money for it?" "You spent the last cent this morning" "Let's go" "Xiao De" "You must be enjoying huh, we fought for you just now and you're hiding here now eating sweet beancurd" "I'll treat you, then" "What are you doing?" "They asked you for 30 cents and now you treat us to only 5 cents' won'th of sweet bean curd" "That's all I have, eat up" "What's there to look at, go away" "Pretty girl" "Do you want to know the colour of her panties?" "Do you have the guts to ask her?" "Never mind, how much do you have on you?" "30 cents" "Give the money to me" "What for?" "I'll make you a bet" "I'll pull up her skirt for you to have a look" "Give me the money" "Alright" "Da De, your brother really has guts" "Great fun" "Sex maniac" "You devil, pulling up my skirt" "Stop" "Are you shameless?" "Policeman, he pulled up my daughter's skirt" "Arrest him" "What's your name?" "Where do you live?" "I'll report you to your school" "What a bad kid!" "Little tramp" "Stop" "Don't run" "Xiao De, let's enter the city" "You go that way" "Stop" "You're looking for death" "Bastard" "Mister, have a seat" "I have no time, I have to work" "Little brother, what's up?" "Where's the policeman?" "He doesn't have the guts to come in here" "Bullshit." "If not for me, you couldn't have escaped" "Go and look for ninth uncle quickly" "Strip..." "It's said, 'Touch a bra you get 3 years' bad luck' you touched the panties, you'll surely have bad luck for the rest of your life" "Touch wood" "Come out..." "Please be quiet" "I'm not performing this show" "This show will be exciting it features two lovers" "Hold on to your tickets if you've got them if not go and get them quickly" "If you're not watching, please go" "May I present Leung Shan Pak please" "Come out quickly" "Please" "Your wife refuses to appear up, speak to her quickly" "Go quickly" "No way, over my dead body" "Not unless I'm dead" "No, you're shameless, do it yourself" "I'm not doing it..." "What's to be afraid of?" "I've got payment already" "Let's pretend we're doing it at home" "I'm not as despicable as you" "You have to do it" "No way, never" "Where are you going?" "To get Shing's wife" "Forget it, he is way out of line to force his wife to do such a thing" "Forget it, find another one" "Where?" "Go and look" "Friend, have you bought a ticket?" "Yes" "Go on inside" "You two little devils" "Ninth uncle what are you doing here?" "To see you" "What for?" "Have you eaten?" "If not, eat with my dad" "I have no time now, I'll go later" "20 cents each" "Thanks" "Help, robbery" "Robbery?" "I have no money" "Beat him" "Help, robbery, I have no money" "Run, quick" "Kids..." "This way please" "A empty seat over there" "4 bamboos" "Eighty thousand" "I win again" "Sorry, pay up" "You're playing a smooth hand winning all the time" "You've won a lot today" "Not a lot, just having fun" "Go and play at a bigger table (bigger stakes)" "No need, just having some fun will do" "Friend, someone's waiting for you outside" "I am winning now" "He said it's urgent" "Right, go and look" "What for?" "Don't worry" "Ah Chu" "Damn" "What?" "Why are you treating customers like this?" "Customer?" "You think I'm an amateur?" "Why are you beating me?" "Do you take me for a swindler?" "If you can't explain, I'll make this publicly known" "Be careful" "Shut up, we're going to fix you" "You have no right to search me, let go" "No right?" "This is our right" "Stop" "You've come in good time" "If you can't find anything, it means you're bullying me" "Can one only lose but not win here?" "Brother, we never bully anyone and no one bullies me" "Bastard, do you still deny cheating?" "I have not framed you, have I?" "You dare to hold this in your mouth, not a drop of saliva too" "Enough..." "Listen, don't ever let me find you here again or I'll maim you" "Father" "Kid, what are you doing here?" "Get out" "Ah Sing, give him some money to visit a bone setter" "My son" "Father" "I told you to get out, why are you still here?" "Where's your little brother?" "Downstairs" "Father, we're so hungry" "Go down and wait for me" "Xiao Li, I'm going to Mei Wa to have a meal look for me if there's anything" "I'll wrap it for you" "Give me ten cents to buy something to eat" "Right, 20 cents would be nice" "It's fixed" "How smart" "Quick enough?" "Yes" "Arert you afraid father would find out you're wrapping cocaine for others?" "Kids" "Father" "So quick" "What are you all doing here?" "Nothing" "Hungry?" "Yes" "Let's go" "Uncle Loong" "How many times have I told you not to set up your stall in front of my entrance" "Yes..." "If I see you again when I return, I'll burn it all" "Get lost now" "Mister, come over here" "Kids, did you smell that?" "Such a nice aroma it will tempt even papa" "Bastard, if I can't stand firm (tempted)" "You're in trouble" "Dad, you're joking" "Let's go" "Uncle Loong, have a seat" "What's good to eat?" "Naturally we have the good stuff" "We've just cut up a small black cur;" "plump and smooth" "Have a catty" "Dad, have two catties instead" "Ninth uncle will come in a while" "Two catties" "Okay" "Two more taels of "fox bone" wine" "Right, dad?" "Smart, coming" "Dad, what happened just now?" "That fellow wanted to be a cheat" "Really?" "At my dad's mahjong house?" "He must be tired of living" "Shut up" "You two have finished school for so long where have you gone?" "A friend fell and hurt himself, so we helped him" "Right, brother?" "That's right" "You want to deceive me?" "Have you been fighting?" "No, father" "Da De, Xiao De" "Ninth uncle" "Come over here" "Make way... it's hot" "Ninth uncle..." "How's the shop doing?" "Still the same" "Let me" "Dad, is the wine good for the kidneys?" "Dad, Ninth uncle if so then it's won'th a try we want some too" "Right, aunty Wa" "No, you're under aged, no wine" "I'm not doing it" "Let me go" "You can't hide forever" "I'm not doing it" "It's not up to you" "Stop beating" "None of your business" "Beat you to death..." "Beat me?" "Are you out of your mind?" "Are you nuts?" "You want to kill your own wife?" "What a scumbag, only just now he forced his wife to host a real show at my place, he is not human" "You've lost everyone because of your drug habit" "Alright, you go back first" "No way, never" "Where are you going?" "What do you want?" "What else do you want?" "Nothing" "She's my wife, I can do whatever I like with her" "How could you ask your wife to do such a thing?" "Why not?" "If you paid me" "I could ask her to sleep with you" "Addict Shing don't ever expect to get cocaine here again" "Let's not waste time on this bastard a waste of our efforts, let's go" "What are you looking at?" "Look..." "I'll take off my pants for you to have a look..." "Shameless" "Damn" "Dad, for you" "Where did you get it?" "You tell me" "Quick" "We saw a robbery just as we finished school and also saw a pack of cigarettes on the ground so little brother picked it up" "What have I been teaching you?" "You can't even look after you kid brother and let him steal from a robbery" "It's not my fault, he picked it up himself" "You dare to answer back?" "One should not pick things up from the street" "How many times have I told you" "I told you not to run around after school and yet you've come to the mahjong house to look for me" "Come here" "Dad, I won't do it again next time" "That's what you say each time" "It's because I didn't study hard as a kid that I now have to work in the mahjong house" "If you don't study hard how could you have a career in society?" "Get me my clothes" "Wipe away the blood" "Thanks, dad" "Teach your kid brother to study hard he's failed in a few subjects according to his report" "Yes" "Luckily dad didn't beat me" "Easy for you to say" "You picked up the cigarettes but he beat me you failed and he scolded me" "Take out your books and study" "I think dad is over doing it" "What's the use of studying so much?" "Inside Kowloon Walled City everyone knows my dad is Uncle Loong" "When I grow up" "I could get a job easily" "Shut up and get your books out to study or dad will beat me up again when he returns" "Alright" "You take care the place" "Uncle Loong, good morning" "Good morning" "Good morning" "Good morning, where's the money?" "Here" "Hurry up, we'll be late again" "Look at your books, they're all in my bag" "This is yours" "There's more" "I guess that punk wouldn't dare beat me again today" "He wouldn't dare" "Of course" "Kids" "Father" "Dad" "Dad..." "Dad..." "Don't run..." "Don't..." "Dead, what to do?" "Dead?" "What to do?" "Father" "Father..." "Don't die... dad..." "Don't die... dad..." "Dad, don't die" "Get ninth uncle, quick" "Get him quickly" "Dad, don't die" "Don't die" "Dad, don't die" "Dad..." "Don't cry" "Well, not bad, huh?" "Xiao De, come on you're not flying an airplane if you crash, nothing I do can pay for the damages" "If we crash, you do us a favour to fix it" "Don't worry as long as my husband is driving" "My wife knows me well" "Good car" "Of course, it's a Porsche" "What' the big deal?" "The car is great, but the people in it are not" "Sit tight" "Look... there's a railing in front" "How dangerous" "Of course, this is mid-night Grand Prix" "This I have to see" "Come on..." "I'm doing it right now" "None of your business" "Faster..." "Look, so many people" "Great fun, can't take anymore, speed up" "Hope your car crashes!" "Damn, I'm finished, this car's a total loss" "Don't be like that, there are people around" "Mr. Cheung, why haven't you looked me up for so long?" "Stop uttering rubbish" "Didrt you say you have a new girl for me?" "A new girl?" "Girls these days don't know how to please unlike us, who were so gentle and beautiful" "Unfortunately I'm ten years older than you, or else..." "Who's talking about age with you?" "We talk about this now" "Right..." "Are you introducing me to the new comer?" "Yes, let me think" "Lily is too tall for you" "And Mary?" "She is repugnant don't get her" "Mimi looks good but her figure is not good" "Thanks boss" "Cheung the great is calling you" "What can I do for you?" "I am taking all the girls today except for her and her bunch" "Thanks, mister Cheung" "What's the big deal?" "So lascivious and disgusting" "Da De, do we have to start the show later tonight?" "It's about time, start as usual" "Officer Cheung is waiting for you inside the room" "Thank you" "Where's uncle Biu today?" "He's gone to Singapore and won't be back till next week" "Oh man, I've got to hand it to him" "He's over sixty and has a few families how does he do it?" "Uncle boasts of his figure" "Officer Cheung, sorry" "Excuse me" "Enjoy yourself, we'll talk later" "No problem" "He says uncle Biu is good" "I say officer Cheung is even better" "Obviously just look at his nose" "Let's drink" "Coming" "Coming immediately..." "Ladies, sit over there please" "Go over there" "Over there, see?" "See how they are enjoying themselves" "I'll have a little fun with them" "Think of a plan" "Right..." "let's release the air from his tyres" "That's childish, not much fun" "Let's scratch his car" "No meaning" "Let's crash his screen" "No, if we're caught we'll be beaten to death" "C'mon then, think of a way." "You do claim to be smart" "That's because I love to eat" "Never mind the bullshit, think of another way" "Damn, it's so frustrating" "That guy was so detestable" "He wouldn't buy more time with me yet he wants me to have a late snack with him there wouldn't be much benefit if I went right?" "Mine's even worse, he bought two hours and his hands were all over me" "Why didn't you slap him?" "I did even better, I touched him too" "He would have died for that" "What are looking at, bastard?" "Don't recognise me?" "Even a good man fears an abusive woman" "What?" "You bastard" "Have I stepped on your tail?" "You have a cur's stinking mouth" "You bitches, I'll give you a good beating" "What?" "Would I be scared of you?" "Forget it, sit down" "Miss, I apologise" "If you want to mess around, go home" "Please, be quiet, forget it..." "You dare mess with me?" "Officer..." "What's the matter?" "There are two suspicious characters over there" "I don't know what they're doing, please check them out" "Where?" "Over there" "Take me to them" "This deal could bring us lots of money" "Right" "Officer, here they are" "Hurry, the police is giving out tickets" "I'm sorry, Officer, I'm leaving immediately" "I am sorry" "Big Brother" "Who did this?" "I don't know" "Come, come over" "Get hold of them" "Stop, clear it up before you go" "What fun!" "That big-mouth bastard can't do anything that was quite an exciting scene" "What a thrill!" "What's going to happen to him next?" "Maybe he has to pay for the indemnity or maybe he'll be taken to the police station" "Wait, can they identify us?" "Hong Kong is such a big place how could we be recognized so easily" "Even if they did, what could they do?" "TRUE" "What's there to be afraid of?" "Let's find some entertainment" "Hurry" "Get off..." "Hurry..." "Get off..." "This is a nice place" "What are we doing here?" "Barbeque?" "Tell me early" "Barbeque?" "Screw you, eat them yourself" "Ah Ling, let's go over there" "We're leaving too" "Alright" "What about me?" "You enjoy yourself" "Don't dirty the car, make use of the tissues in there" "The tissues are too coarse, you must be joking" "Xiao De" "What?" "My period is late for 10 days" "No way!" "You said it was your safety period that day" "Maybe it's because you are not feeling too well." "Right?" "No." "Don't" "Don't" "Let go of me" "What are you doing?" "No" "No" "No..." "Don't stop" "Hurry..." "Hurry" "Hurry" "Don't panic, I can't do it in a hurry" "Hurry" "The condoms are all used up" "What?" "I just bought you over a dozen last week and you've already used them all?" "You bastard" "You bastard asked me to give myself relief" "It's you do it now" "I don't want to tonight" "But I do" "Sorry to interrupt you" "You haven't paid your tuition fees and want to learn?" "It's a fair world" "Alright, each one will provide relief for himself today" "Damn it" "Don't run" "You should leave, your brother is home already" "I have to go too, dad will be back soon" "Alright" "Are you going to meet another woman?" "You got it wrong, three a day" "I'll take you back" "You drink a lot tonight" "Didrt expect you to be a strong drinker" "You're not bad yourself" "I couldn't get you drunk" "It's a robbery, officer." "Shouldrt you make an arrest?" "Not yet, wait until they've got the money then we can catch them red-handed or we can be sued for wrong accusation" "Three hundred dollars only?" "Give me the pearl necklace" "No" "It's from my Mom" "Give it back to me" "Don't move, or I'll shoot" "They robbed me" "Come over" "Drop the knife" "Damn, don't move" "Officer, it has nothing to do with me" "Come over" "It has nothing to do with me" "Beat you up" "Go over there" "Handcuff yourself" "This is called caught in the spot" "Da De, call the station for me" "I'll handle the case here" "Yes, Sir" "Miss, are you alright?" "Hot dumplings..." "Give me one" "Thank you" "Hot dumplings..." "Brother, you're back" "Yes" "Brother, have some dumplings" "Keep it for yourself" "Brother, you've bought one too" "Yes" "How can I have two?" "I'll eat with you" "Brother, I'll make some tea for you" "Xiao De, how can you go to school when you stay up late every night?" "I've finished my homework at night so I can sleep a bit more during the day" "Brother, it's fun to have a second-hand car" "Do you have a driver's licence?" "No, but I can drive" "Wait until you get one" "Don'tjust keep reading this stuff all day pay more attention to your study" "It's fun" "The physics teacher saw you and you didn't even know" "Only you can think of such a thing" "You are stupid enough" "You should have someone on the lookout" "How come you are so stupid?" "Goodbye" "My dear, you're so early" "It's so rare" "It's so rare" "What is it?" "What else?" "Must be total failure" "It's no surprise" "What do you want to eat?" "Nothing" "How about you?" "Dear, have you really failed in all subjects?" "Take it out, I'll change them for you" "Not this time" "Dad will surely kill me" "Don't cry, let's think of a way" "What else can we do?" "Don't be like that" "Do you want to let the whole world know about it?" "What am I going to do?" "What to do?" "Had you listened to me everything would have been alright" "What has that to do with me?" "Every time you say it's alright" "Lower your voice, please" "You've now made a mess wanttoblameitonme" "Don't cry" "What are you doing?" "You can shun the responsibility" "Stop shouting" "What is it?" "Having failed is no big deal, why scold her?" "Shut up, nobody will think you're dumb" "He..." "What is it?" "Nuts" "Hey kid" "Tastes good huh?" "Brother, do you recognize me?" "We had a car race the other night" "Which night?" "Let me refresh your memory" "Remember?" "A little bit" "Yes..." "Where's that bastard who drove the car?" "I don't know" "I don't know" "Don't you know now?" "Yes..." "Where does he live?" "I don't know" "Where is he now?" "I don't know" "Yes..." "Will he be coming?" "He..." "Is he coming or not?" "He..." "Speak up" "Yes..." "When?" "When?" "Uncle, don't meddle in our affair, alright?" "Stop talking nonsense" "Xiao De, run, run" "Don't run..." "Stand still" "Are you blind?" "Sorry, Sir" "Sorry, Sir" "Sorry, Officer Cheung" "What happened?" "You are more fierce than I am chasing and beating people in the street" "That bastard fooled me" "I don't care" "Behave yourself or I'll arrest you" "It's not that serious, is it?" "Behave yourself, go" "Arert you leaving?" "What are you standing here for?" "What's the big deal?" "You are all useless, you can't even catch that bastard" "Find him, or never see me again" "No" "Abortion is bad for the body and is dangerous" "I won't allow you to do that" "Mom, what am I going to do now?" "Mom" "You dad is back now clean up your face" "I'll find a chance to talk to him" "What are you doing?" "Preparing dinner" "Dad" "Ah Ling, don't go back to your room yet" "Sit down, let's chat for a while" "How come you didn't go out today?" "Your eyes are red, have you been crying?" "What happened?" "Have you been bullied?" "Tell me" "It's nothing" "Maybe the contact lenses don't fit" "Nothing's wrong" "Get a new pair if they don't fit be careful not to hurt your eyes" "Yes" "Did the schools give out the report cards today?" "Yes" "How did you do?" "I'm asking you" "Eighteenth" "Not bad" "Show it to me" "Have some tea" "Dad" "Who's this guy?" "A classmate" "A classmate" "It's really my classmate" "You lied to me" "You two are too close to be ordinary classmates" "Speak, who is he?" "Dad, no... dad" "Are you telling or not?" "Speak, who is he?" "Why are you hitting her?" "Calm down" "See how you teach your daughter" "The poor girl could be cheated in some days and you are still kept in the dark" "Mom, see for yourself" "If he knew, he would surely kill me" "Wait until he's calm, I'll think of some ways" "Go in" "What are you doing?" "Take him out, see how fast he can run" "Go" "Go" "Try to be cool?" "Go" "Sit down" "What are you doing?" "Has this bastard committed rape?" "No." "He's running naked in front of a girls' school" "Officer, that's not true, I've been set up" "Don't frame me" "What, will the police frame an innocent person?" "We'll find out" "Okay." "Officer Cheung likes to have fun with those punks" "Alright, he's all yours" "Okay" "Officer Cheung is here" "Stand here" "Bring him out later" "Officer Cheung, he's yours" "Officer" "What happened?" "This bastard is blatant" "Blatant?" "I'll teach him in his place in a while" "Come over" "Officer" "Go" "What about him?" "Bad conduct" "This bastard ran naked in front of a girls' school" "Ran naked?" "Kid, are you well hung?" "No, Sir, I've been set up" "Sir, your daughter and I are good friends" "if you don't believe me, you can ask her" "Kid, don't make some empty claims" "What do you want?" "Come with me" "We are investigating this case" "You can bail him out for the time being" "Thank you" "Ah Sing, is Chan Ka Cheong here yet?" "Yes, Officer Cheung has taken him to his room" "Follow me" "Alright" "Brother" "He is your brother?" "Look at you." "Very soon you could be beaten to death" "He's careless" "Officer Cheung, you beat up every suspect in each case" "I just go by the book." "You can file a complaint, though" "Never mind..." "Make the necessary arrangements for your brother, go" "Wait" "Ask your brother never to see my daughter again" "Brother, you have to trust me" "Brother, listen to me" "Brother, help me" "You've to stick your neck out for me on this one, bro" "Stick my neck out?" "If I stuck my neck out you will be beaten to death" "It's not my fault, that bastard stripped me of my clothes and shoved me on the street" "Help me please" "Why'd others mess with you if you don't bother them?" "How come no one has bothered to take off my pants?" "A naked Danish hen is hopping everywhere, so disgusting" "Do you agree?" "So what?" "I'll expose you for peeping at your sister bathing" "Alright, I will not talk" "That big-mouth bastard is so arrogant" "Ask your big brother to fix him" "Nuts" "If you want to fix him for such trivial matters then many other people would have to be fixed" "So you are letting this go?" "Why bother my elder brother, won't I do just as well?" "Anything could be fixed except bullshit" "Exactly" "The truth is he dares not tell his elder brother" "You have a point" "You insult me" "You are good at insulting the people only" "You bothered him while he was taking drugs, right?" "Go up and think of something" "Well, any ideas?" "You lot are so useless, think of something quick" "You guys are so frustrating" "Let's douse him with urine" "Let's make it worse for him" "How?" "Add some shit to the urine" "Where do we find so much shit and urine?" "We'll each contribute" "Wouldrt that be enough?" "No" "Xiao De" "Xiao De, I have a plan, it must work" "Wait" "Bring that big-mouth bastard back in a bag" "Tie him up and feed him with cocaine" "If he won't take, we'll surround and smoke him with it so that even by smelling, he'll get hooked" "Wouldrt that be revenge for us?" "You must be crazy, we will all get hooked before he does" "I grew up among drug addicts how come I didn't get hooked?" "Xiao De" "Calling you?" "You try to pick up girls like others yet you create so much trouble, go on..." "What is it?" "Think" "What is it?" "What are we going to do?" "Let me think of something" "You are procrastinating" "Did you know that my mom knows" "Your mom... how about your dad?" "What difference does it make?" "You've never thought about me" "Xiao De, I've got an idea" "Where's Ah Ling?" "Don't bother with her, speak" "Dad" "Ah Ling, what's going on?" "Nothing" "You can't hide anything from me since you were small" "Tell me" "Has someone molested you?" "No, Dad" "There must be something wrong, tell me" "So, you won't speak, right?" "That's fine, I can find out anyway" "If I find out that kid has touched you" "I'll break his bones" "Dad, don't" "You're nervous, something must have happened" "Have you been cheated?" "By whom?" "Speak" "Speak" "No one has cheated me" "Who cheated you?" "Speak" "Why have you beaten her again?" "It's not her fault" "It's useless even if you beat her to death she's pregnant for 2 months" "Do you want to kill the baby too?" "Bitch" "Mom" "Cheung Mei Ling" "Who's Cheung Mei Ling?" "Here" "Go in" "Go on" "Quick..." "Is it done?" "He's coming" "Unless he's diabetic, otherwise there'll be trouble" "Is it working?" "Yes" "They are here" "Have a seat" "Brother Ching" "The bill?" "Here it is" "Brother Ching" "Coffee again" "And you?" "No" "See if the amount is correct" "The money?" "Here it is" "I don't want to drink this, you go ahead" "He's not drinking it, what should we do?" "Brother, I'm going first" "Okay..." "let's go" "Waiter, plain tea please" "I got a idea" "What's up?" "Nothing, your tea is not hot enough" "This would create a big trouble" "We can't let him go no matter what" "Stop nagging, get prepared quickly" "Go on" "Tea and milk" "Thanks" "Coming" "Quick" "What's the matter?" "I can't hold back any longer, please come out" "Excuse me..." "Come out quickly" "Come out quickly, what are you doing inside?" "Come out quickly" "I just came in" "He's been in there a long time" "Come out quickly" "Quick..." "Damn it" "Come out quickly, someone's waiting" "Come on out" "You've saved even the room cost" "Excuse me" "Friend, are you finished?" "So many people" "I can't take it anymore" "Make way" "What?" "Go away" "1, 2, 3, 4... 6, 7, 8, 9" "The ninth" "Done" "Burn it shorter" "Make a boat" "Itjust like an aircraft carrier" "Pour the gasoline in" "That's enough" "That bastard, I want to burn him to death" "Too much" "The more fire the better" "Careful" "With this fire we are avenged" "That's right" "Be careful, use matches" "Hurry..." "Hurry, be careful" "If it's so much pain then stop it" "You must be the one who set the fire" "Not me" "Bright moon shines on ground, firering shines on ground" "You bastards again" "Don't run..." "Help, a molester" "Help, a molester" "Someone's molesting me" "Help..." "Make way" "He's doing dirty deeds" "What have you done?" "Why are you doing dirty deeds?" "Let go, go away, let me go" "What have you to say for yourself?" "Go away" "Help, molester" "Stop, go away..." "He molested me" "Stop running" "Stop, or I'll beat him up" "Isn't it fair, bastard?" "Go away" "There's no point talking to me" "I must find my brother before I can give you a reply" "Alright" "I am giving you face by talking to you" "Listen carefully" "If your brother don't apologize to me by tomorrow you'll die" "Follow me" "You have guts" "How dare you bargain with my big brother?" "Brother" "We are specifically here to apologize to Brother Ching not to bargain with him" "Xiao De do you know the rules?" "You mean..." "There's seniority for everything" "Be respectful if you're here specially to apologize" "Kneel" "Kneel" "Wait" "Before he drinks it, I have a condition" "Speak up" "Hold a feast for these men of mine to give them some face" "Brother Ching, you have been given due respect we are all out here to make a living let's drink tea and forget our grievances" "If I just drink it that's fine for me but not my men" "Alright" "If after you have drunk this cup of tea any brother who is still not pleased and wants more perks, he can look for my Ninth uncle" "He's your uncle?" "Ninth uncle retired a long time ago" "He won't want to be bothered by our matters" "We should give him face" "Since he's your uncle, I'll drink it" "It's hard to believe that the son of" "Chan Yuan Loong, previous chief of the Walled City is kneeling and apologizing to me" "Little brother" "Don't mention my father" "Don't move, let's talk this out" "Xiao De, what else do you want to say?" "You have guts" "You..." "Don't fight" "Ninth uncle..." "Uncle Jiu..." "You guys brought weapons along with you do you want to kill your uncle?" "No..." "Ah Ching" "What have my nephews done to incite them to fight each other?" "Ninth uncle, he started it" "What could I do?" "Ninth uncle, he insulted my father" "Yi Ching, doesn't matter who's right or who's wrong give some face to Uncle Jiu" "For any problem hereafter look for big brother and me and we'll take care of it for you" "Alright, since Ninth uncle is involved, we'll let it go" "Tell you nephew not to meddle with me again otherwise don't blame me for not giving you "face"" "Alright" "Go" "Ninth uncle, we'll be leaving" "Ninth uncle, see you" "Don't worry, it'll be alright" "Ah Jiu, go and have something to eat with him" "Xiao De, you stay" "Xiao De, do you realise what your brother has done for you?" "You've got yourself into big trouble" "Never mess with them again otherwise I won't be able to save you" "Yes, Ninth uncle" "Don't move, police" "Officer Cheung, what's the matter?" "Turn on the lights" "Ask the person in charge to come out" "Yes" "Look around" "Yes, you guys look over that side" "Come..." "Officer Cheung, what's the matter?" "Spot checking" "You should know better that you can't do it here" "I've talked to you on the phone about Xiao De" "How's it going?" "I talked to his big brotherjust now" "Let it go then" "Chief, what have you got?" "Most of them are juveniles" "Please do me a favour" "If I do, who's going to do me a favour?" "How's it?" "Alright" "Let's go back" "Go..." "Havert you cried enough?" "You're crying for an hour" "Look at you, you look like a dirty cat" "Who's going to marry you?" "Disgusting" "Why are you smoking?" "It's been rotten luck these days" "My brother doesn't help me when I'm in trouble" "I really wonder whether we have the same mother" "Xiao De" "Big Brother, those bastards are up there" "I want a leg of Xiao De, get it?" "Go" "That way" "Don't cry..." "Run" "Don't run" "Come out" "Let go of me" "Come here..." "No" "Come out" "No" "He is not here" "Search everywhere" "Don't cry, please" "Nothing, look over there" "Found anything?" "No" "Nothing" "That's weird, look over there" "It's so dark" "Ah Fu" "What is it?" "Look over here" "Alright" "I'll have a look" "Come up here" "Where are you running to?" "Go" "Don't run" "Here" "Hurry, run" "Big brother" "Break his leg" "Attack" "Xiao De" "Xiao De" "Xiao De, stop fighting" "Xiao De" "Run, hurry, run" "Hurry" "Hurry" "Ah Ling, come here" "No, I'm scared" "Hurry, they are coming" "Help, Xiao De... help me" "Hold tight" "Help me, Xiao De" "Xiao De, hurry and pull me up" "Hold tight" "Xiao De, help me" "Hold tight" "Xiao De, help me" "Xiao De, help me" "Ah Ling" "Hurry, go" "Ah Ling..." "Ah Ling" "Bastard" "Xiao De, come out here" "Xiao De, come out here" "Xiao De, come out here..." "Alright, stay in touch on the phone" "Brother" "What?" "Had a fight?" "No, Ah Ling fell to her death" "Mrs. Cheung" "What are you doing here?" "I've brought him to Officer Cheung" "Let me in" "Officer Cheung" "Officer Cheung, I'm handing my brother to you" "Officer Cheung, today we are here to give you an explanation" "No more tricks" "I must beat him up today until you ask me to stop" "What?" "Can't do it?" "No, stop beating" "I'll call the police if you don't" "Don't mess with my affairs from now on" "Are you alright?" "I'll take you to a doctor" "Brother Da De..." "What happened?" "Just now a gang came looking for trouble even when I mentioned your name they didn't back down" "Brother Da De, we'll go and find them" "Right" "Da De, where have you been?" "You see our club has been messed up" "We couldn't even find you" "When they came they said they were here to teach you a lesson" "What was I supposed to do?" "Didrt even know who they were?" "Before going they said their big brother was Yi Ching" "Uncle Biu, I'm so sorry about the mess" "I must leave" "Brother Da De" "You're suffering, I'll give you a shot" "No..." "No..." "What happened?" "I'm asking you" "Go away" "What if I don't?" "Don't move" "Don't move" "You two brothers are equally low and mean" "I'm charging you for unlawful possession of weapons causing injury to others" "There's evidence, so you can't deny it" "Our affairs should have all been settled" "Shut up, this is official business" "Da De, someone is here for you" "Hurry and go" "Ninth Uncle, thank you for visiting me" "You asked me to look for Xiao De, but I can't find him" "Don't worry, I'll definitely find him" "You've lost your family because of cocaine" "If he won't take, we'll surround smokehimwithit so that even by smelling, he'll get hooked" "I grew up among drug addicts how come I didn't get hooked?" "Still can't find my little brother?" "He's nowhere to be found" "Ninth uncle, I want to see him, please help" "Get into the car" "Da De, don't you want to see your brother?" "Get into the car quickly" "Officer Cheung, for two?" "You're free today?" "Over here please" "What would you like to drink?" "Later" "Alright" "Where's my brother?" "Be patient, we'll talk about it after this show" "What happened to you?" "Hurry" "Hurry..." "You think I'm cheap, I'll show you how cheap I can be" "Boss, leaving now?" "Come again" "Who are you looking for?" "Where's the one who performed with you?" "That drug addict?" "He's in the washroom" "Xiao De" "Xiao De... what happened to you?" "Xiao De" "Why do you do that?" "Say whatever you want to say" "Xiao De" "Xiao De" "Xiao De" "You can'tjust die like that..." "Xiao De" "You can't die like that, Xiao De" "Xiao De, don't die" "Alright, it's done" "Don't move" "Do you hear me?" "Don't move" "Good, take him back" "Officer Cheung, after months of investigation we found that you abuse your powers for personal revenge" "You tried to get Xiao De hooked" "You know the law and you broke it" "This is something that cannot be tolerated" "I am sorry, I must arrest you now" "Please hand over your pistol and badge" "So you caused the death of my brother" "Be calm" "He will be judged" "Take him back" "Sir, there are dead bodies in the washroom" "Call a car, leave two men behind to finish the job" "Yes" "Take them away" "Go..." |
---
title: KSCATEGORY_PREFERRED_MIDIOUT_DEVICE
description: KSCATEGORY_PREFERRED_MIDIOUT_DEVICE
ms.assetid: b3d93d21-d4f8-4f00-9947-034790f3f7b1
keywords: ["KSCATEGORY_PREFERRED_MIDIOUT_DEVICE Device and Driver Installation"]
topic_type:
- apiref
api_name:
- KSCATEGORY_PREFERRED_MIDIOUT_DEVICE
api_location:
- Ksmedia.h
api_type:
- HeaderDef
ms.localizationpriority: medium
ms.date: 10/17/2018
---
# KSCATEGORY_PREFERRED_MIDIOUT_DEVICE
The KSCATEGORY_PREFERRED_MIDIOUT_DEVICE [device interface class](./overview-of-device-interface-classes.md) is defined for the [kernel streaming](../stream/streaming-minidrivers2.md) (KS) functional category for the preferred MIDI output device.
<table>
<colgroup>
<col width="50%" />
<col width="50%" />
</colgroup>
<thead>
<tr class="header">
<th align="left">Attribute</th>
<th align="left">Setting</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td align="left"><p>Identifier</p></td>
<td align="left"><p>KSCATEGORY_PREFERRED_WAVEOUT_DEVICE</p></td>
</tr>
<tr class="even">
<td align="left"><p>Class GUID</p></td>
<td align="left"><p>{D6C50674-72C1-11D2-9755-0000F8004788}</p></td>
</tr>
</tbody>
</table>
Remarks
-------
A user selects the preferred MIDI output device in the Multimedia property pages in the Control Panel.
This functional category is reserved for exclusive use by the system-supplied [WDM Audio Components](../audio/wdm-audio-components.md).
Requirements
------------
<table>
<colgroup>
<col width="50%" />
<col width="50%" />
</colgroup>
<tbody>
<tr class="odd">
<td align="left"><p>Version</p></td>
<td align="left"><p>Available in Windows Server 2003, Windows XP, Windows 2000 and later versions of Windows.</p></td>
</tr>
<tr class="even">
<td align="left"><p>Header</p></td>
<td align="left">Ksmedia.h (include Ksmedia.h)</td>
</tr>
</tbody>
</table>
|
Q:
Find which node my selenium-grid remote driver is running on?
I obtain a RemoteWebDriver from the hub as follows:
RemoteWebDriver driver = new RemoteWebDriver(
new URL("http://whatever:4444/wd/hub"),
DesiredCapabilities.internetExplorer() );
Is there a way to programatically find out which node in the grid the remote driver is running on?
I want to log this in an effort to track down intermittent test failures.
A:
Please refer to this blog post of mine to learn how to find out the node ip and port to which the test was routed to.
Blog post : https://rationaleemotions.wordpress.com/2016/01/15/where-did-my-test-run/
In a nutshell, here's what you need to do (The blog I shared has elaborate explanation and required code )
Get the session id from webdriver via Webdriver.getSessionId()
You then append the session id obtained from the previous step to the URL http://localhost:4444/grid/api/testsession?session= (replace localhost with the actual Grid IP/host and replace 4444 with the port on which grid is listening to) and trigger a POST call.
From the JSON response you parse the value of attribute proxyId as a URL and extract out the IP and port from it.
This is now available for ready consumption via the library talk2grid that I built.
|
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Neb chancellor, AD: Put Pelini audio issue to rest - NBC Sports
Neb chancellor, AD: Put Pelini audio issue to rest
APWF
Nebraska head coach Bo Pelini, left, calls instructions with defensive coordinator John Papuchis looking on, in the first half of an NCAA college football game against UCLA in Lincoln, Neb., Saturday, Sept. 14, 2013. UCLA won 41-21. (AP Photo/Nati Harnik)
September 18, 2013, 5:54 pm
Associated Press
Nebraska is ready to move on from Bo Pelini's profane rant against fans two years ago.
Chancellor Harvey Perlman and athletic director Shawn Eichorst said in a joint statement Wednesday that they believe the football coach was sincere in his apology for what he said in an audio leaked to the Deadspin.com sports website this week.
There was no mention of any disciplinary action taken against Pelini.
"The comments made by Head Football Coach Bo Pelini in 2011, published Monday, are unfortunate and deeply concerning to us, as they would be to anyone who loves this university," the statement said. "Our coaches, staff and student-athletes must be held to a high standard and Coach Pelini's remarks were unfair to the legions of Nebraska fans and not what we expect from a representative of this university."
Perlman and Eichorst declined interview requests. Messages were left for Pelini.
Pelini's rant has captivated a Cornhuskers fan base that has sold out an NCAA-record 328 consecutive games since 1962.
Pelini became unhinged minutes after the Huskers had beaten Ohio State 34-27 in Lincoln in October 2011. Nebraska erased a 27-6 second-half deficit in the biggest comeback in program history.
Pelini criticized people who left the stadium in the third quarter, when the Huskers trailed by 21 points. Pelini repeatedly used expletives while talking on the audio about "fair-weather" fans and how the day was coming that he would be gone and he wondered how the team will fare without him. He also used profanity while criticizing two Omaha World-Herald sports writers.
The Deadspin audio surfaced Monday, two days after the Huskers squandered a 21-3 lead and lost 41-21 to UCLA and on the same day Pelini said at his news conference that the program didn't need the support of Tommie Frazier, the 1990s Huskers great who had tweeted that Pelini should fire his defensive staff.
Pelini said in an interview on SiriusXM Radio on Wednesday that he had an "idea" of who leaked the audio.
Management of the Husker Sports Network has not returned calls from The Associated Press.
Former athletic director Tom Osborne, in a statement released Wednesday, said he told Perlman and Eichorst on Monday that he was aware of the recording more than a year ago and addressed the matter with Pelini at the time.
"While the comments were certainly not good, I realized that Bo had gone through an emotional week and an emotional game and was in a setting where he thought his comments were entirely private," Osborne said. "I visited with Bo on a weekly basis and did not find that his attitude toward the fans or the press as expressed by those comments were at all in keeping with what I knew his true attitude to be."
The statement from Perlman and Eichorst noted that Pelini, long known for his volatility on the sideline, has improved his demeanor over the past two years.
"Coach Pelini has given us his assurance that he understands the seriousness and inappropriateness of his comments," the statement said. "We believe he is sincere in his apology and in his regret. We are prepared to put the matter to rest. Our football student-athletes, coaches and staff deserve all of our support and we know the Nebraska faithful will be there for them."
Pelini is 51-21 in six seasons at Nebraska but has had a run of lopsided losses on the national stage. His contract runs through the 2015 season. He's being paid $2.975 million this year.
Osborne said Pelini's record is among the best in college football since 2008 and that the players' behavior, for the most part, has been excellent.
"I recognize that there have occasionally been controversies but I have seen a willingness to change, reflect and improve in Bo over the years," Osborne said. "I am very hopeful that the players, coaches and fans will pull together as unity of purpose has been one of our major assets over the last 50 years." |
Walking up the narrow doorway, hands shaking not in fear But out of compassion, that I hadn’t felt in years.We had drank and had our laughs,The smile you wore, hell I knew that we have had fun,You told me to hold me, oh so close.Your breath on my neck and my hands in yours,Wishing Id tell you how beautiful, How beautiful you really fucking are.To me.Yeah Me.To Me.Yeah Me.You were such a beauty to me.Carrying you towards a restless night in my arms wishing I had the words to say,That I think I want you to stay…with me.But empty promises, and broken bottles,Put me on my knees,My heart felt so heavy, not yet to be broken,Please dear, don’t do this again.I wish I had the words to say,I wish I had the chance to turn back time,I wish I’d never held you close,But I still wish I’d make you mine.Yes, mine.Seeing you smiling at me.As ruby red tongues gnaw out lies, and deceitIm stuck here kissing your feet,Mistakes were forgiven regrets were now made, the distance felt further than Mars.Phone call wars, are worse on the floor, of a night spent drunk here without you.Without you.Oh without you.Please dear lets start this again.I have my control, and I still love your soul,Im sorry we can’t speak again.Wiping your tears, after beer after beer,We’ll never have those days again, Goodbye. |
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Smart and resourceful, our estate planning attorneys will work closely with you to identify strategies—from the most basic will to the most complex trust arrangements—to take full advantage of opportunities that enhance your legacy and restrict your tax consequences. Because business and work-related assets often affect estate planning, wills and trusts, we consult our Employee Benefits and Executive Compensation attorneys when necessary, who may play an important role in creating the customized vehicle that best meets all of your needs.
For more information about how we can help you plan for the future, contact us today.
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with us we are not establishing an attorney-client relationship, and information you submit will not be
protected by the attorney-client privilege and cannot be treated as confidential. A client relationship
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Dual-task backward compatibility effects are episodically mediated.
In dual-task performance, the backward compatibility effect (BCE; faster Task 1 reaction time when Task 1 and Task 2 responses are compatible) is thought to represent automatic activation of Task 2 response information in parallel with attended Task 1 performance. Work by Hommel and Eglau (Psychological Research, 66, 260-273, 2002) has suggested the BCE relies on stimulus-response learning in long-term memory. Subsequent work by Ellenbogen and Meiran (Memory and Cognition, 36, 968-978, 2008), however, proposed that the BCE is mediated by Task 2 rules held in working memory (WM) during Task 1 performance. The present study aimed to dissociate these two theoretical claims. In Experiment 1, we assessed the effects of prior single-task practice with Task 1 or Task 2 of a subsequent dual-task paradigm. Where the WM-mediated model predicts both BCE and overall reaction time improvement relative to prior task practice, an episodic learning model makes divergent predictions for BCE based on the context specificity of prior Task 2 learning. Results showed a close fit with episodic predictions and contradicted WM model predictions. Experiment 2 examined the finer grained timecourse of BCE over initial development, subsequent interference of this initial learning on BCE development with new conflicting Task 2 response mappings, and finally reestablishment of BCE in the original dual task. Data again showed close agreement with long-term learning predictions. We argue in favor of an episodic account of the BCE, and consider implications of WM and episodic mechanisms of automatic response activation on other aspects of dual-task performance. |
Molten Basketball – 7, Orange/Beige
The official ball of the British Basketball League. The supreme Molten match ball is used in all BBL competitions by the stars of the British game. This ball is also widely used throughout European basketball leagues and FIBA co…
The official ball of the British Basketball League. The supreme Molten match ball is used in all BBL competitions by the stars of the British game. This ball is also widely used throughout European basketball leagues and FIBA competitions.
– Take to the court with the same ball as some of your favourite players |
Q:
Prompt. Как сделать проверку, чтобы строки и нечисловые значения не записывались в массив JavaScript
Следующие задачи.
Необходимо внести в код дополнительную проверку, чтобы пустые строки ('') и нечисловые значения (NaN) не записывались в массив через prompt.
Интересует проверка в текущем контексте, без использования функций.
Буду благодарен за помощь и совет в решении.
Код ниже, а также в ссылке на codepen.https://codepen.io/monsara/pen/ERXMpq?editors=0012
'use strict';
let userInput;
const numbers = [];
let total = 0;
do {
userInput = prompt('Введите число', '');
if (userInput === '' || isNaN(userInput)) {
alert('Было введено не число, попробуйте еще раз');
}
numbers.push(Number(userInput));
} while (userInput !== null);
for (const value of numbers) {
total = total + value;
}
alert(`Общая сумма чисел равна ${total}`);
console.log(numbers);
A:
let userInput;
const numbers = [];
while (userInput = prompt('Введите число', '')) {
if (userInput === '' || isNaN(userInput)) {
alert('Было введено не число, попробуйте еще раз');
continue;
}
numbers.push(+userInput);
}
alert(`Общая сумма чисел равна ${numbers.reduce((cur, next) => cur + next, 0)}`);
console.log(numbers);
|
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import tensorflow as tf\n",
"from sklearn.utils import shuffle\n",
"import re\n",
"import time\n",
"import collections\n",
"import os"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def build_dataset(words, n_words, atleast=1):\n",
" count = [['PAD', 0], ['GO', 1], ['EOS', 2], ['UNK', 3]]\n",
" counter = collections.Counter(words).most_common(n_words)\n",
" counter = [i for i in counter if i[1] >= atleast]\n",
" count.extend(counter)\n",
" dictionary = dict()\n",
" for word, _ in count:\n",
" dictionary[word] = len(dictionary)\n",
" data = list()\n",
" unk_count = 0\n",
" for word in words:\n",
" index = dictionary.get(word, 0)\n",
" if index == 0:\n",
" unk_count += 1\n",
" data.append(index)\n",
" count[0][1] = unk_count\n",
" reversed_dictionary = dict(zip(dictionary.values(), dictionary.keys()))\n",
" return data, count, dictionary, reversed_dictionary"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"lines = open('movie_lines.txt', encoding='utf-8', errors='ignore').read().split('\\n')\n",
"conv_lines = open('movie_conversations.txt', encoding='utf-8', errors='ignore').read().split('\\n')\n",
"\n",
"id2line = {}\n",
"for line in lines:\n",
" _line = line.split(' +++$+++ ')\n",
" if len(_line) == 5:\n",
" id2line[_line[0]] = _line[4]\n",
" \n",
"convs = [ ]\n",
"for line in conv_lines[:-1]:\n",
" _line = line.split(' +++$+++ ')[-1][1:-1].replace(\"'\",\"\").replace(\" \",\"\")\n",
" convs.append(_line.split(','))\n",
" \n",
"questions = []\n",
"answers = []\n",
"\n",
"for conv in convs:\n",
" for i in range(len(conv)-1):\n",
" questions.append(id2line[conv[i]])\n",
" answers.append(id2line[conv[i+1]])\n",
" \n",
"def clean_text(text):\n",
" text = text.lower()\n",
" text = re.sub(r\"i'm\", \"i am\", text)\n",
" text = re.sub(r\"he's\", \"he is\", text)\n",
" text = re.sub(r\"she's\", \"she is\", text)\n",
" text = re.sub(r\"it's\", \"it is\", text)\n",
" text = re.sub(r\"that's\", \"that is\", text)\n",
" text = re.sub(r\"what's\", \"that is\", text)\n",
" text = re.sub(r\"where's\", \"where is\", text)\n",
" text = re.sub(r\"how's\", \"how is\", text)\n",
" text = re.sub(r\"\\'ll\", \" will\", text)\n",
" text = re.sub(r\"\\'ve\", \" have\", text)\n",
" text = re.sub(r\"\\'re\", \" are\", text)\n",
" text = re.sub(r\"\\'d\", \" would\", text)\n",
" text = re.sub(r\"\\'re\", \" are\", text)\n",
" text = re.sub(r\"won't\", \"will not\", text)\n",
" text = re.sub(r\"can't\", \"cannot\", text)\n",
" text = re.sub(r\"n't\", \" not\", text)\n",
" text = re.sub(r\"n'\", \"ng\", text)\n",
" text = re.sub(r\"'bout\", \"about\", text)\n",
" text = re.sub(r\"'til\", \"until\", text)\n",
" text = re.sub(r\"[-()\\\"#/@;:<>{}`+=~|.!?,]\", \"\", text)\n",
" return ' '.join([i.strip() for i in filter(None, text.split())])\n",
"\n",
"clean_questions = []\n",
"for question in questions:\n",
" clean_questions.append(clean_text(question))\n",
" \n",
"clean_answers = [] \n",
"for answer in answers:\n",
" clean_answers.append(clean_text(answer))\n",
" \n",
"min_line_length = 2\n",
"max_line_length = 5\n",
"short_questions_temp = []\n",
"short_answers_temp = []\n",
"\n",
"i = 0\n",
"for question in clean_questions:\n",
" if len(question.split()) >= min_line_length and len(question.split()) <= max_line_length:\n",
" short_questions_temp.append(question)\n",
" short_answers_temp.append(clean_answers[i])\n",
" i += 1\n",
"\n",
"short_questions = []\n",
"short_answers = []\n",
"\n",
"i = 0\n",
"for answer in short_answers_temp:\n",
" if len(answer.split()) >= min_line_length and len(answer.split()) <= max_line_length:\n",
" short_answers.append(answer)\n",
" short_questions.append(short_questions_temp[i])\n",
" i += 1\n",
" \n",
"question_test = short_questions[500:550]\n",
"answer_test = short_answers[500:550]\n",
"short_questions = short_questions[:500]\n",
"short_answers = short_answers[:500]"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"vocab from size: 657\n",
"Most common words [('you', 132), ('is', 78), ('i', 68), ('what', 51), ('it', 50), ('that', 49)]\n",
"Sample data [7, 28, 129, 35, 61, 42, 12, 22, 82, 225] ['what', 'good', 'stuff', 'she', 'okay', 'they', 'do', 'to', 'hey', 'sweet']\n",
"filtered vocab size: 661\n",
"% of vocab used: 100.61%\n"
]
}
],
"source": [
"concat_from = ' '.join(short_questions+question_test).split()\n",
"vocabulary_size_from = len(list(set(concat_from)))\n",
"data_from, count_from, dictionary_from, rev_dictionary_from = build_dataset(concat_from, vocabulary_size_from)\n",
"print('vocab from size: %d'%(vocabulary_size_from))\n",
"print('Most common words', count_from[4:10])\n",
"print('Sample data', data_from[:10], [rev_dictionary_from[i] for i in data_from[:10]])\n",
"print('filtered vocab size:',len(dictionary_from))\n",
"print(\"% of vocab used: {}%\".format(round(len(dictionary_from)/vocabulary_size_from,4)*100))"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"vocab from size: 660\n",
"Most common words [('i', 97), ('you', 91), ('is', 62), ('it', 58), ('not', 47), ('what', 39)]\n",
"Sample data [12, 216, 5, 4, 94, 25, 59, 10, 8, 79] ['the', 'real', 'you', 'i', 'hope', 'so', 'they', 'do', 'not', 'hi']\n",
"filtered vocab size: 664\n",
"% of vocab used: 100.61%\n"
]
}
],
"source": [
"concat_to = ' '.join(short_answers+answer_test).split()\n",
"vocabulary_size_to = len(list(set(concat_to)))\n",
"data_to, count_to, dictionary_to, rev_dictionary_to = build_dataset(concat_to, vocabulary_size_to)\n",
"print('vocab from size: %d'%(vocabulary_size_to))\n",
"print('Most common words', count_to[4:10])\n",
"print('Sample data', data_to[:10], [rev_dictionary_to[i] for i in data_to[:10]])\n",
"print('filtered vocab size:',len(dictionary_to))\n",
"print(\"% of vocab used: {}%\".format(round(len(dictionary_to)/vocabulary_size_to,4)*100))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"GO = dictionary_from['GO']\n",
"PAD = dictionary_from['PAD']\n",
"EOS = dictionary_from['EOS']\n",
"UNK = dictionary_from['UNK']"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"for i in range(len(short_answers)):\n",
" short_answers[i] += ' EOS'"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def str_idx(corpus, dic):\n",
" X = []\n",
" for i in corpus:\n",
" ints = []\n",
" for k in i.split():\n",
" ints.append(dic.get(k,UNK))\n",
" X.append(ints)\n",
" return X\n",
"\n",
"def pad_sentence_batch(sentence_batch, pad_int, maxlen):\n",
" padded_seqs = []\n",
" seq_lens = []\n",
" max_sentence_len = maxlen\n",
" for sentence in sentence_batch:\n",
" padded_seqs.append(sentence + [pad_int] * (max_sentence_len - len(sentence)))\n",
" seq_lens.append(maxlen)\n",
" return padded_seqs, seq_lens\n",
"\n",
"def check_accuracy(logits, Y):\n",
" acc = 0\n",
" for i in range(logits.shape[0]):\n",
" internal_acc = 0\n",
" count = 0\n",
" for k in range(len(Y[i])):\n",
" try:\n",
" if Y[i][k] == logits[i][k]:\n",
" internal_acc += 1\n",
" count += 1\n",
" if Y[i][k] == EOS:\n",
" break\n",
" except:\n",
" break\n",
" acc += (internal_acc / count)\n",
" return acc / logits.shape[0]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"X = str_idx(short_questions, dictionary_from)\n",
"Y = str_idx(short_answers, dictionary_to)\n",
"X_test = str_idx(question_test, dictionary_from)\n",
"Y_test = str_idx(answer_test, dictionary_from)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"maxlen_question = max([len(x) for x in X]) * 2\n",
"maxlen_answer = max([len(y) for y in Y]) * 2"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"def hop_forward(memory_o, memory_i, response_proj, inputs_len, questions_len):\n",
" match = memory_i\n",
" match = pre_softmax_masking(match, inputs_len)\n",
" match = tf.nn.softmax(match)\n",
" match = post_softmax_masking(match, questions_len)\n",
" response = tf.multiply(match, memory_o)\n",
" return response_proj(response)\n",
"\n",
"\n",
"def pre_softmax_masking(x, seq_len):\n",
" paddings = tf.fill(tf.shape(x), float('-inf'))\n",
" T = tf.shape(x)[1]\n",
" max_seq_len = tf.shape(x)[2]\n",
" masks = tf.sequence_mask(seq_len, max_seq_len, dtype = tf.float32)\n",
" masks = tf.tile(tf.expand_dims(masks, 1), [1, T, 1])\n",
" return tf.where(tf.equal(masks, 0), paddings, x)\n",
"\n",
"\n",
"def post_softmax_masking(x, seq_len):\n",
" T = tf.shape(x)[2]\n",
" max_seq_len = tf.shape(x)[1]\n",
" masks = tf.sequence_mask(seq_len, max_seq_len, dtype = tf.float32)\n",
" masks = tf.tile(tf.expand_dims(masks, -1), [1, 1, T])\n",
" return x * masks\n",
"\n",
"\n",
"def shift_right(x):\n",
" batch_size = tf.shape(x)[0]\n",
" start = tf.to_int32(tf.fill([batch_size, 1], GO))\n",
" return tf.concat([start, x[:, :-1]], 1)\n",
"\n",
"\n",
"def embed_seq(x, vocab_size, zero_pad = True):\n",
" lookup_table = tf.get_variable(\n",
" 'lookup_table', [vocab_size, size_layer], tf.float32\n",
" )\n",
" if zero_pad:\n",
" lookup_table = tf.concat(\n",
" (tf.zeros([1, size_layer]), lookup_table[1:, :]), axis = 0\n",
" )\n",
" return tf.nn.embedding_lookup(lookup_table, x)\n",
"\n",
"\n",
"def position_encoding(sentence_size, embedding_size):\n",
" encoding = np.ones((embedding_size, sentence_size), dtype = np.float32)\n",
" ls = sentence_size + 1\n",
" le = embedding_size + 1\n",
" for i in range(1, le):\n",
" for j in range(1, ls):\n",
" encoding[i - 1, j - 1] = (i - (le - 1) / 2) * (j - (ls - 1) / 2)\n",
" encoding = 1 + 4 * encoding / embedding_size / sentence_size\n",
" return np.transpose(encoding)\n",
"\n",
"def quest_mem(x, vocab_size, max_quest_len):\n",
" x = embed_seq(x, vocab_size)\n",
" pos = position_encoding(max_quest_len, size_layer)\n",
" return x * pos\n",
"\n",
"class QA:\n",
" def __init__(self, vocab_size_from, vocab_size_to, size_layer, learning_rate, n_hops = 3):\n",
" self.X = tf.placeholder(tf.int32,[None,None])\n",
" self.Y = tf.placeholder(tf.int32,[None,None])\n",
" self.X_seq_len = tf.fill([tf.shape(self.X)[0]],maxlen_question)\n",
" self.Y_seq_len = tf.fill([tf.shape(self.X)[0]],maxlen_answer)\n",
" max_quest_len = maxlen_question\n",
" max_answer_len = maxlen_answer\n",
" \n",
" lookup_table = tf.get_variable('lookup_table', [vocab_size_from, size_layer], tf.float32)\n",
" \n",
" with tf.variable_scope('memory_o'):\n",
" memory_o = quest_mem(self.X, vocab_size_from, max_quest_len)\n",
" \n",
" with tf.variable_scope('memory_i'):\n",
" memory_i = quest_mem(self.X, vocab_size_from, max_quest_len)\n",
" \n",
" with tf.variable_scope('interaction'):\n",
" response_proj = tf.layers.Dense(size_layer)\n",
" for _ in range(n_hops):\n",
" answer = hop_forward(memory_o,\n",
" memory_i,\n",
" response_proj,\n",
" self.X_seq_len,\n",
" self.X_seq_len)\n",
" memory_i = answer\n",
" \n",
" embedding = tf.Variable(tf.random_uniform([vocab_size_to, size_layer], -1, 1))\n",
" cell = tf.nn.rnn_cell.LSTMCell(size_layer)\n",
" vocab_proj = tf.layers.Dense(vocab_size_to)\n",
" state_proj = tf.layers.Dense(size_layer)\n",
" init_state = state_proj(tf.layers.flatten(answer))\n",
" \n",
" helper = tf.contrib.seq2seq.TrainingHelper(\n",
" inputs = tf.nn.embedding_lookup(embedding, shift_right(self.Y)),\n",
" sequence_length = tf.to_int32(self.Y_seq_len))\n",
" encoder_state = tf.nn.rnn_cell.LSTMStateTuple(c=init_state, h=init_state)\n",
" decoder = tf.contrib.seq2seq.BasicDecoder(cell = cell,\n",
" helper = helper,\n",
" initial_state = encoder_state,\n",
" output_layer = vocab_proj)\n",
" decoder_output, _, _ = tf.contrib.seq2seq.dynamic_decode(decoder = decoder,\n",
" maximum_iterations = max_answer_len)\n",
" \n",
" helper = tf.contrib.seq2seq.GreedyEmbeddingHelper(embedding = embedding,\n",
" start_tokens = tf.tile(\n",
" tf.constant([GO], \n",
" dtype=tf.int32), \n",
" [tf.shape(init_state)[0]]),\n",
" end_token = EOS)\n",
" decoder = tf.contrib.seq2seq.BasicDecoder(\n",
" cell = cell,\n",
" helper = helper,\n",
" initial_state = encoder_state,\n",
" output_layer = vocab_proj)\n",
" predicting_decoder_output, _, _ = tf.contrib.seq2seq.dynamic_decode(\n",
" decoder = decoder,\n",
" maximum_iterations = max_answer_len)\n",
" self.training_logits = decoder_output.rnn_output\n",
" self.predicting_ids = predicting_decoder_output.sample_id\n",
" self.logits = decoder_output.sample_id\n",
" masks = tf.sequence_mask(self.Y_seq_len, max_answer_len, dtype=tf.float32)\n",
" self.cost = tf.contrib.seq2seq.sequence_loss(logits = self.training_logits,\n",
" targets = self.Y,\n",
" weights = masks)\n",
" self.optimizer = tf.train.AdamOptimizer(learning_rate).minimize(self.cost)\n",
" y_t = tf.argmax(self.training_logits,axis=2)\n",
" y_t = tf.cast(y_t, tf.int32)\n",
" self.prediction = tf.boolean_mask(y_t, masks)\n",
" mask_label = tf.boolean_mask(self.Y, masks)\n",
" correct_pred = tf.equal(self.prediction, mask_label)\n",
" correct_index = tf.cast(correct_pred, tf.float32)\n",
" self.accuracy = tf.reduce_mean(tf.cast(correct_pred, tf.float32))"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"epoch = 20\n",
"batch_size = 16\n",
"size_layer = 256\n",
"\n",
"tf.reset_default_graph()\n",
"sess = tf.InteractiveSession()\n",
"model = QA(len(dictionary_from), len(dictionary_to), size_layer, 1e-3)\n",
"sess.run(tf.global_variables_initializer())"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 1, avg loss: 2.862724, avg accuracy: 0.639000\n",
"epoch: 2, avg loss: 1.839667, avg accuracy: 0.734333\n",
"epoch: 3, avg loss: 1.732843, avg accuracy: 0.739833\n",
"epoch: 4, avg loss: 1.661211, avg accuracy: 0.747333\n",
"epoch: 5, avg loss: 1.586425, avg accuracy: 0.751333\n",
"epoch: 6, avg loss: 1.504489, avg accuracy: 0.753833\n",
"epoch: 7, avg loss: 1.416241, avg accuracy: 0.760167\n",
"epoch: 8, avg loss: 1.324014, avg accuracy: 0.769167\n",
"epoch: 9, avg loss: 1.231901, avg accuracy: 0.776333\n",
"epoch: 10, avg loss: 1.143001, avg accuracy: 0.782833\n",
"epoch: 11, avg loss: 1.061561, avg accuracy: 0.790667\n",
"epoch: 12, avg loss: 0.983756, avg accuracy: 0.804000\n",
"epoch: 13, avg loss: 0.901873, avg accuracy: 0.824167\n",
"epoch: 14, avg loss: 0.830711, avg accuracy: 0.846500\n",
"epoch: 15, avg loss: 0.773178, avg accuracy: 0.862167\n",
"epoch: 16, avg loss: 0.721180, avg accuracy: 0.869667\n",
"epoch: 17, avg loss: 0.670212, avg accuracy: 0.881000\n",
"epoch: 18, avg loss: 0.623576, avg accuracy: 0.889167\n",
"epoch: 19, avg loss: 0.589300, avg accuracy: 0.894833\n",
"epoch: 20, avg loss: 0.554041, avg accuracy: 0.900000\n"
]
}
],
"source": [
"for i in range(epoch):\n",
" total_loss, total_accuracy = 0, 0\n",
" for k in range(0, len(short_questions), batch_size):\n",
" index = min(k+batch_size, len(short_questions))\n",
" batch_x, seq_x = pad_sentence_batch(X[k: index], PAD, maxlen_question)\n",
" batch_y, seq_y = pad_sentence_batch(Y[k: index], PAD, maxlen_answer)\n",
" predicted, accuracy,loss, _ = sess.run([model.predicting_ids, \n",
" model.accuracy, model.cost, model.optimizer], \n",
" feed_dict={model.X:batch_x,\n",
" model.Y:batch_y})\n",
" total_loss += loss\n",
" total_accuracy += accuracy\n",
" total_loss /= (len(short_questions) / batch_size)\n",
" total_accuracy /= (len(short_questions) / batch_size)\n",
" print('epoch: %d, avg loss: %f, avg accuracy: %f'%(i+1, total_loss, total_accuracy))"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"row 1\n",
"QUESTION: i am a werewolf\n",
"REAL ANSWER: a werewolf\n",
"PREDICTED ANSWER: i am afraid not \n",
"\n",
"row 2\n",
"QUESTION: i was dreaming again\n",
"REAL ANSWER: i would think so\n",
"PREDICTED ANSWER: i am so ashamed \n",
"\n",
"row 3\n",
"QUESTION: the kitchen\n",
"REAL ANSWER: very nice\n",
"PREDICTED ANSWER: that is right \n",
"\n",
"row 4\n",
"QUESTION: the bedroom\n",
"REAL ANSWER: there is only one bed\n",
"PREDICTED ANSWER: thank you \n",
"\n"
]
}
],
"source": [
"for i in range(len(batch_x)):\n",
" print('row %d'%(i+1))\n",
" print('QUESTION:',' '.join([rev_dictionary_from[n] for n in batch_x[i] if n not in [0,1,2,3]]))\n",
" print('REAL ANSWER:',' '.join([rev_dictionary_to[n] for n in batch_y[i] if n not in[0,1,2,3]]))\n",
" print('PREDICTED ANSWER:',' '.join([rev_dictionary_to[n] for n in predicted[i] if n not in[0,1,2,3]]),'\\n')"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"row 1\n",
"QUESTION: but david\n",
"REAL ANSWER: is here that\n",
"PREDICTED ANSWER: what is this \n",
"\n",
"row 2\n",
"QUESTION: hopeless it is hopeless\n",
"REAL ANSWER: tell ballet then back\n",
"PREDICTED ANSWER: i am afraid not \n",
"\n",
"row 3\n",
"QUESTION: miss price\n",
"REAL ANSWER: yes learning\n",
"PREDICTED ANSWER: yes doctor \n",
"\n",
"row 4\n",
"QUESTION: mr kessler wake up please\n",
"REAL ANSWER: is here are\n",
"PREDICTED ANSWER: no way \n",
"\n",
"row 5\n",
"QUESTION: there were witnesses\n",
"REAL ANSWER: why she out\n",
"PREDICTED ANSWER: that is right \n",
"\n",
"row 6\n",
"QUESTION: what about it\n",
"REAL ANSWER: not you are\n",
"PREDICTED ANSWER: i am afraid not \n",
"\n",
"row 7\n",
"QUESTION: go on ask them\n",
"REAL ANSWER: i just home\n",
"PREDICTED ANSWER: goodbye darling \n",
"\n",
"row 8\n",
"QUESTION: beware the moon\n",
"REAL ANSWER: seen hi is he\n",
"PREDICTED ANSWER: that is right \n",
"\n",
"row 9\n",
"QUESTION: did you hear that\n",
"REAL ANSWER: is down what\n",
"PREDICTED ANSWER: it is killing me \n",
"\n",
"row 10\n",
"QUESTION: i heard that\n",
"REAL ANSWER: it here not\n",
"PREDICTED ANSWER: it is okay \n",
"\n",
"row 11\n",
"QUESTION: the hound of the baskervilles\n",
"REAL ANSWER: heard\n",
"PREDICTED ANSWER: yes i remember \n",
"\n",
"row 12\n",
"QUESTION: it is moving\n",
"REAL ANSWER: not you hear\n",
"PREDICTED ANSWER: it is okay \n",
"\n",
"row 13\n",
"QUESTION: nice doggie good boy\n",
"REAL ANSWER: bill stupid\n",
"PREDICTED ANSWER: yes doctor \n",
"\n",
"row 14\n",
"QUESTION: it sounds far away\n",
"REAL ANSWER: that pecos baby seen hi\n",
"PREDICTED ANSWER: what is dead \n",
"\n",
"row 15\n",
"QUESTION: debbie klein cried a lot\n",
"REAL ANSWER: is will srai not\n",
"PREDICTED ANSWER: i am afraid not \n",
"\n",
"row 16\n",
"QUESTION: what are you doing here\n",
"REAL ANSWER: is know look i\n",
"PREDICTED ANSWER: that is right \n",
"\n"
]
}
],
"source": [
"batch_x, seq_x = pad_sentence_batch(X_test[:batch_size], PAD, maxlen_question)\n",
"batch_y, seq_y = pad_sentence_batch(Y_test[:batch_size], PAD, maxlen_answer)\n",
"predicted = sess.run(model.predicting_ids, feed_dict={model.X:batch_x})\n",
"\n",
"for i in range(len(batch_x)):\n",
" print('row %d'%(i+1))\n",
" print('QUESTION:',' '.join([rev_dictionary_from[n] for n in batch_x[i] if n not in [0,1,2,3]]))\n",
" print('REAL ANSWER:',' '.join([rev_dictionary_to[n] for n in batch_y[i] if n not in[0,1,2,3]]))\n",
" print('PREDICTED ANSWER:',' '.join([rev_dictionary_to[n] for n in predicted[i] if n not in[0,1,2,3]]),'\\n')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.8"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
|
Reducing Cumulative Arm Overuse Injuries in Young Throwers.
As year-round participation in youth sports continues to increase, health care practitioners treating child and adolescent athletes will commonly see injuries that are secondary to overuse. Starting with a clinical vignette, this article describes proximal humeral physeal injuries in youth throwers, examines causative factors, reviews common therapeutic modalities, and focuses on preventive measures aimed at reducing such cumulative arm overuse injuries. |
g.type-TK>rect {
fill: #00ffd0;
}
text {
font-weight: 300;
font-family: "Helvetica Neue", Helvetica, Arial, sans-serf;
font-size: 14px;
}
.node rect {
stroke: #999;
fill: #fff;
stroke-width: 1.5px;
}
.edgePath path {
stroke: #333;
stroke-width: 1.5px;
}
h1 {
color: #111;
font-family: 'Helvetica Neue', sans-serif;
font-size: 75px;
font-weight: bold;
letter-spacing: -1px;
line-height: 1;
text-align: center;
}
h2 {
color: #111;
font-family: 'Helvetica Neue', sans-serif;
font-size: 20px;
margin: 0 0 72px;
text-align: center;
} |
This invention relates to a facsimile machine constructed to allow interconnection with a communications apparatus like a personal computer via an interface.
A facsimile modulator/demodulator (hereinafter referred to as FAX modem) is commercially available in recent years that can transmit data on a personal computer, external to the facsimile machine, to a remote facsimile machine via a telephone line. Used for connecting the personal computer to the telephone line, the FAX modem adds a capability of facsimile transmission and reception to conventional personal computer communications (hereinafter referred to as PC communications).
Since conventional facsimile machines are constructed to print out received image data on a real-time basis, it has not been possible to choose whether to print out the received data. Provision of a memory for storing outgoing and incoming data gives a facsimile machine a potential of expanding its functions.
As an example, the facsimile machine may be provided with an RS-232C interface and software that can handle AT commands. By connecting a personal computer to the facsimile machine via the RS-232C interface, a PC communications capability is added to the facsimile machine so that it can be utilized as a FAX modem or a printer for the personal computer.
The PC communications capability added to the facsimile machine as discussed above is independent of original functions of the facsimile machine. It is therefore necessary to provide a mode select switch on an operating panel of the facsimile machine, for example, for switching it between facsimile mode for performing the ordinary facsimile functions and communications mode for executing PC communications.
It is assumed that the print function in communications mode would normally be used just temporarily after switching the facsimile machine from facsimile mode to communications mode. Therefore, an operator should confirm that the facsimile machine is not currently used for facsimile transmission or reception and operate the mode select switch for switching from facsimile mode to communications mode when using the facsimile machine for a printing job. Upon completion of the printing job, the operator should again operate the mode select switch for returning the facsimile machine from communications mode back to facsimile mode.
It is to be noted that the personal computer and facsimile machine are placed separately from each other in most cases. This means that the operator needs to operate the mode select switch of the facsimile machine which is separated from the personal computer before and after the printing job. The need for such awkward switching operations could make it difficult to effectively use the printing function of the facsimile machine.
If the operator neglects to return the facsimile machine back to facsimile mode after the printing job, the facsimile machine is left in communications mode and it cannot receive messages transmit from other facsimile machines.
On the other hand, if the facsimile machine is so constructed that it is automatically reset to facsimile mode at the end of each data processing job in communications mode, frequent mode switching would be made even when the operator intends to perform successive jobs in communications mode. Therefore, automatic mode switching could prevent fast and smooth communication processes.
Another problem of the prior art is that the facsimile machine set to communications mode becomes inoperable as a peripheral device of the communications apparatus when the communications apparatus is not properly connected to the facsimile machine or the communications apparatus is powered off. |
Jillian Daggs from New Cumberland said said she wants to see more schools embrace ESports clubs and camps.
She said ESports helps students socialize in a digital world.
"It's bringing people with like interests together. People always assume that just because it's digital, it's kind of sucking kids into something. But I've made a lot of friends through playing video games," said Daggs.
The camp runs through Friday, June 22.
The three computer-focused games at the camp are Hearthstone, League of Legends and Overwatch. |
ifeq ($(strip $(FREETZ_LIB_libprotobuf_c)),y)
LIBS+=protobuf-c
endif
|
Prognostic factors (including HPV status) for irradiation of locally advanced squamous cell carcinoma of the head and neck (SCCHN).
The prognosis of patients with locally advanced squamous cell carcinoma of the head and neck (SCCHN) is generally poor. However, prognostic factors can help optimize the care for the individual patient. This study investigated potential prognostic factors, including HPV status, for locoregional control (LRC), metastases-free survival (MFS), and survival (OS). Twelve potential prognostic factors were investigated in 170 patients irradiated for stage III or IV SCCHN, including age (≤ 60 vs > 60 years), gender, ECOG performance score (0-1 vs 2), preradiotherapy hemoglobin level (< 12 vs ≥ 12 g/dl), tumor site (oropharynx, oral cavity, hypopharynx, or larynx), histological grade (G1-2 vs G3), T category (T1-T2 vs T3-T4), N category (N0-N1 vs N2-N3), AJCC stage (III vs IV), surgery (no vs yes), and chemotherapy (no vs yes). On multivariate analysis, positive HPV status (RR 2.34; p = 0.014), ECOG performance score 0-1 (RR 1.94; p = 0.017), preRT hemoglobin ≥ 12 g/dl (RR 1.88; p = 0.018), T category T1-T2 (RR 2.72; p < 0.001), and surgery (RR 2.29; p = 0.007) were significantly associated with improved LRC. PreRT hemoglobin ≥ 12 g/dl (RR 1.98; p = 0.040) and T category T1-T2 (RR 3.33; p < 0.001) were significantly associated with improved MFS. Positive HPV status (RR 2.19; p = 0.019), pre-RT hemoglobin ≥ 12 g/dl (RR 2.15; p = 0.002), T category T1-T2 (RR 2.31; p = 0.002), and AJCC stage III (RR 1.91; p = 0.034) were significantly associated with improved OS. Improved treatment outcomes were significantly associated with positive HPV status, better performance status, lower tumor stage, and pretreatment hemoglobin levels ≥ 12 g/dl. These factors should be considered in future trials. |
Q:
How to force Ubuntu to detect external display?
My laptop recognises external display devices if I connect them before booting the system, but many times it doesn't if I connect while the system is running. In this case, rebooting naturally solves the problem.
Is there a way to force Ubuntu to detect external displays? Opening up the display menu and pressing "Detect displays" does nothing.
A:
Actually, you don't need to log out. Simply going to a VC with ctrl-alt-F1, restarting x with sudo service sddm restart and
and going back to your graphical interface with ctrl-alt-F7 (or F2) should do it.
This way, you don't lose all your windows...
A:
To enable all outputs in their default mode, run:
$ xrandr --auto
For more information, see:
https://xorg-team.pages.debian.net/xorg/howto/use-xrandr.html
|
This invention relates to a face grinder used for grinding the end surface of, for example, a cylindrical workpiece.
A face grinder having the structure shown in FIGS. 6 to 9 is generally known.
This is composed of two wheel heads 4, one for rough grinding and the other for finishing, which are provided side by side on a bed 1 such as to be vertically movably supported thereby, a rotary index table 6 which is disposed under the wheel heads such as to face them, as shown in FIGS. 6 and 7, and a multiplicty of chucks 8 which are disposed on the index table 6, as shown in FIG. 8 and 9. The wheel heads 4 are provided with cup-shaped grinding wheels 2 which are rotated by drive motors 3. The index table 6 and the chuck 8 are rotated by a drive motor 5 and a drive motor 7, respectively. A workpiece 9 is supplied to the chuck 8 at the loading position of the index table and is held by an appropriate method. The grinding wheel 2 cuts the workpiece 9 which is being rotated together with the chuck 8, whereby the end surface of the workpiece 9 is ground to a predetermined dimension.
The end surface of the workpiece 9 which has been ground by the face grinder bears the grinding mark shown in FIG. 10 if it has a center hole 9a and the grinding mark shown in FIG. 11 if it has no center hole. Accordingly, when the wheel 2 becomes locally worn, the workpiece 9 without a center hole 9a has a protruding portion 9b left unground due to the partial wear of the wheel 2, so that the required working accuracy of the workpiece 9 is not obtained. As a result, the lift of the wheel 2 is short, thereby necessitating frequent changes of the wheel, and it is difficult to obtain good working efficiency. |
Future of power grid plays integral role in 2015 Canadian Federal Election
By Firtsname Lastname Title| Company, if any
OTTAWA, Ontario -
- The future of the power grid plays a large part of the 2015 Federal Election of Canada. The Canadian Electricity Association recently responded to the campaign promises presented from each party.
THE CONSERVATIVE PARTY OF CANADA
The Canadian Electricity Association CEA is pleased to see the Conservative Party of Canadas commitment to continued action on cyber security, support for emerging clean energy technologies, and initiatives to enhance skills training as announced today in their election platform.
CEA appreciates the Conservative Partys continued commitment to key electricity sector priorities, and in particular, a specific reference to the impacts of growing cyber threats on the electric grid, said the Hon. Sergio Marchi, President and CEO of CEA. As one of Canadas ten Critical Infrastructure sectors, CEA members are operators of vital cyber systems and support measures to protect physical and cyber assets essential to Canadas security.
CEA is also encouraged by measures in support of emerging clean energy technologies and applauds the continued support for Sustainable Development Technology Canada which play a critical role in fostering electricity innovation and bringing new technologies to market.
Additionally, renewed support for skills training initiatives, including those targeted at Aboriginal Canadians, are critical for Canadas electricity sector who face an acute human resources challenge. We welcome measures to address skilled worker shortages and support flexible programs that will promote careers in the electricity sector which is in need of a new generation of skilled workers, added Mr. Marchi.
THE LIBERAL PARTY OF CANADA
The Canadian Electricity Association CEA welcomes the Liberal Party of Canadas release of its full platform which outlines a set of policies that have positive impacts on Canadas electricity system. The CEA also raises potential areas of concern.
"CEA is supportive of proposals seeking to enhance federal support for the renewal and protection of electricity infrastructure, and innovation in key technology areas such as electric vehicle integration, renewable energy, and power storage all building blocks of tomorrow's electricity system," said the Hon. Sergio Marchi, President and CEO of CEA. "We are also pleased that the Liberal Party of Canada is following CEAs recommendation to engage the provinces in a conversation on a national energy strategy."
"However, we caution against a hasty reversal of changes made to Canada's regulatory regime for energy projects, particularly recent amendments to the Fisheries Act that were long requested by our membership and helped modernize project approvals for new electricity infrastructure projects," concluded Marchi.
CEA appreciates the open debate on these issues that has taken place during the election campaign, including a notable exchange on electricity during the Munk Leader's debate. CEA hopes that a transparent and inclusive discussion - and consultation - will be the hallmark of any proposals made in the 42nd Parliament.
NEW DEMOCRATIC PARTY - NDP
The Canadian Electricity Association CEA was encouraged to see the recent announcement by the New Democratic Party NDP of policies in support of electric vehicle integration, clean energy infrastructure, and energy efficiency.
I welcome this NDP proposal which addresses some of Canadas most significant energy and electricity challenges, said the Hon. Sergio Marchi, President and CEO of CEA. In particular, targets for electric vehicles in the federal fleet, which CEA has been calling for, is one more step in the right direction. Coupled with a Green Bonds initiative, and new programming in support of clean energy projects and energy efficiency programming, these proposals will enrich the elections energy debate.
Innovation and the renewal of Canadas electricity infrastructure are key priorities for CEA. The NDP proposals address both issues and incent adoption of the technologies that will shape the future of Canadas electricity system as highlighted in CEAs recent report Electric Utility Innovation: Toward Vision 2050.
CEA is encouraged by the meaningful debate taking place on electricity innovation and needed investment in infrastructure. This discussion could not be more timely considering the Conference Board of Canada is estimating that $350 Billion will need to be invested in upgrading electricity infrastructure during the next 20 years. |
Q:
jquery ui datepicker no theme on asp.net
I have a jquery datepicker in an asp.net web form, it is working but has no style at all, I can only see the numbers floating over the page.
I have the following scripts in the master page:
<script src="Scripts/jquery-ui-1.11.3.min.js" type="text/javascript"></script>
I included the jquery-ui using nuget, so I have the themes very similar to
The date picker is associated to the control:
<div>Date: <asp:TextBox ID="txtDate" runat="server"></asp:TextBox> </div>
With the script:
$(document).ready(function() {
$("#<%=txtDate.ClientID%>").datepicker({ dateFormat: 'd/m/yy' });
});
The result is as I mentioned early the calendar without any style.
What I am missing to have the datepicker with some style (theme)?
Thank you
A:
Here's what I have referenced. The datepicker works fine - apart from when you mouseover the arrows and the little white triangle goes gray - and can't be seen. Must have a little graphic missing I guess.
<script type="text/javascript" src="js/jquery-1.8.3.js"></script>
<link rel="stylesheet" type="text/css" href="js/jquery-ui.css"/>
<script type="text/javascript" src="js/jquery-ui.js"></script>
|
Low-dose radiation employed in diagnostic imaging causes genetic effects in cultured cells.
Exposure to environmental, diagnostic, and occupational sources of radiation frequently involves low doses. Although these doses have no immediately noticeable impact on human health there is great interest in their long-term biological effects. To assess immediate and time-delayed DNA damage in two cell lines exposed to low doses of ionizing radiation by using the comet assay and micronucleus test, and to compare these two techniques in the analysis of low-dose induced genotoxicity. CHO and MRC-5 cells were exposed to 50 milliSievert (mSv) of ionizing radiation and assayed immediately after irradiation and at 16 or 12 passages post-irradiation, respectively. Comet assay and micronucleus test were employed. The comet assay values observed in 50 mSv-treated cells were significantly higher than in the control group for both sample times and cell lines (P < 0.001). Micronuclei frequencies were higher in treated cells than in the control group (P < 0.01, CHO cells passage 16; P < 0.05, MRC-5 cells immediately after exposure; P < 0.01 MRC-5 cells passage 12). Correlation analysis between the two techniques was statistically significant (correlation coefficient 0.82, P < 0.05 and correlation coefficient 0.86, P < 0.05 for CHO and MRC-5 cells, respectively). Cells scored at passages 12 or 16 showed more damage than those scored immediately after exposure in both cell lines (no statistically significant differences). Cytomolecular and cytogenetic damage was observed in cells exposed to very low doses of X-rays and their progeny. A single low dose of ionizing radiation was sufficient to induce such response, indicating that mammalian cells are exquisitely sensitive to it. Comet and micronucleus assays are sensitive enough to assess this damage, although the former seems to be more efficient. |
Q:
tmux doesn't passes correctly ctrl-shift-arrow sequences
Tmux doesn't passes correctly the ctrl-shift-arrow sequences.
It doesn't work on emacs, and when I use sed -n l, I see it displays the escape sequence of the arrow key alone instead of the full sequnce
For example, ctrl-shift-right passes as ^[[C (which is the same as the escape sequence of the right key), instead of ^[OC (outside tmux).
Any idea of how to solve this?
Note that ctrl-arrow key (without shift) and shift-arrow (without ctrl) pass correctly.
My .tmux.conf is:
# Changes prefix from Ctrl-b to Alt-a
unbind C-b
set -g prefix M-a
set-option -g default-terminal "xterm-256color"
# choosing windows with Alt-#
bind -n M-0 select-window -t 0
bind -n M-1 select-window -t 1
bind -n M-2 select-window -t 2
bind -n M-3 select-window -t 3
bind -n M-4 select-window -t 4
bind -n M-5 select-window -t 5
bind -n M-6 select-window -t 6
bind -n M-7 select-window -t 7
bind -n M-8 select-window -t 8
bind -n M-9 select-window -t 9
setw -g monitor-activity on
set -g visual-activity on
set-window-option -g window-status-current-bg white
set -g mode-mouse on
set -g mouse-resize-pane on
set -g mouse-select-pane on
set -g mouse-select-window on
# Toggle mouse on
bind m \
set -g mode-mouse on \;\
set -g mouse-resize-pane on \;\
set -g mouse-select-pane on \;\
set -g mouse-select-window on \;\
display 'Mouse: ON'
# Toggle mouse off
bind M \
set -g mode-mouse off \;\
set -g mouse-resize-pane off \;\
set -g mouse-select-pane off \;\
set -g mouse-select-window off \;\
display 'Mouse: OFF'
# disable selecting panes with mouse (because enabling mess with copy-paste)
set-option -g mouse-select-pane off
# display status bar message for 4 sec
set-option -g display-time 4000
# Start windows and panes at 1, not 0
set -g base-index 1
set -g pane-base-index 1
# enable shift-arrow keys
set-window-option -g xterm-keys on
# start default shell
set-option -g default-shell $SHELL
# support for escape char for vi
set -s escape-time 0
A:
It looks like tmux is doing the right thing for your example:
For example, ctrl-shift-right passes as ^[[C (which is the same as the escape sequence of the right key), instead of ^[OC (outside tmux).
because the usual connotation of that sequence is that it is the same as cursor-movement sent from the host. A zero parameter is the same as a missing parameter, which happens to be one.
The terminal was not identified; xterm does not do that. For controlshiftright-arrow, xterm may send ^[[1;6C. In this case, tmux absorbs the escape sequence sent, because it is not in the table of known xterm-style keys that it knows about. In tmux, the file xterm-keys.c contains a table, with the comment:
/*
* xterm-style function keys append one of the following values before the last
* character:
*
* 2 Shift
* 3 Alt
* 4 Shift + Alt
* 5 Ctrl
* 6 Shift + Ctrl
* 7 Alt + Ctrl
* 8 Shift + Alt + Ctrl
*
* Rather than parsing them, just match against a table.
*
* There are three forms for F1-F4 (\\033O_P and \\033O1;_P and \\033[1;_P).
* We accept any but always output the latter (it comes first in the table).
*/
|
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