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Windshield Replacement Baton Rouge
Locate a recommended windshield replacement professional nearby Baton Rouge, Louisiana
Should I claim a damaged windshield around Baton Rouge?
You require to make a price quote of the the cost to repair or change the windshield. You ought to likewise inspect to see if your comprehensive coverage waives the deductible for glass claims. Some auto insurance providers like GEICO have comprehensive strategies that do not force you to pay a deductible when filing a claim for damaged glass.
Will a windshield chip spread nearby Baton Rouge, LA?
Driving over a speed bump, hole or other unequal terrain can trigger a windshield chip to crack. Although it is not possible to state how long it will consider a windshield chip to spread out, the study suggests that stressors like weather modifications or just driving will ultimately cause or lengthen a windshield crack.
Does windshield chip repair really work?
When a windshield repair is done, a percentage of clear resin is injected into the chip, crack or star. This just fills up the crack or chip with a material that helps avoid it from cracking further. It does not disguise or hide the damage. There is no item that will do that.
The number of windshields are replaced annually nearby Baton Rouge?
13-14 million windshields.
13-14 million windshields are replaced each year. There are no Federal or State regulations covering replacement windshields!
Can you drive without windshield near Baton Rouge, LA?
As long as they have eye defense, they don't have anything to fret about. To examine: You can drive your vehicle without a windshield if you're wearing eye security. However if you're driving an automobile with a windshield, it has to have working wipers.
Are OEM windshields better than aftermarket around Baton Rouge, Louisiana?
Prices for OEM glass can run 40% to 60% greater than equivalent aftermarket windshields. OEE or Original Equipment Equivalent Windshields are windshields produced by the exact same companies that make OEM but the logo design on the glass is that of the glass manufacturer not the auto maker.
How unsafe is a cracked windshield around Baton Rouge, Louisiana?
It's generally not hazardous to drive with a small crack in the windshield, however damaged glass must be repaired or changed as soon as possible for two essential reasons: Windshields damaged by damage offer less defense.
Is a cracked windshield a dot violation?
Windshield Glazing A crack or staining in the windshield location lying within the sweep of the wiper on the motorist side is an out of service condition. Chips that are no broader than 3/4 ″ (approximately the size of a nickel) are acceptable provided it is not closer than 3 inches to any other crack or damaged location.
Will a cars and truck wash harmed a cracked windshield near Baton Rouge, Louisiana?
The risk of cleaning your automobile If all you have is a crack– small or large– you risk of it getting much larger by going through a cars and truck wash. We call this the "run." If the crack runs throughout your windshield it may affect your visibility and your car would no longer be safe to drive.
Does my windshield have sensing units near Baton Rouge, Louisiana?
Some vehicles may have one or the other, or both. The rain sensor is also usually nearby to the light sensor. This system turns the windshield wipers automatically by identifying rain on the windshield.
Can you drive after windshield replacement in Baton Rouge, LA?
Oftentimes, windshield repairs can be carried out in 30 minutes or less. Windshield replacements will often take 60 minutes or less; however, we suggest that you do not drive the vehicle for at least one hour after service is completed.
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About windshield replacement
The windshield (North American English) or windscreen (Commonwealth English) of an aircraft, car, bus, motorbike or tram is the front window, which provides visibility whilst protecting occupants from the elements. Modern windshields are generally made of laminated safety glass, a type of treated glass, which consists of, typically, two curved sheets of glass with a plastic layer laminated between them for safety, and bonded into the window frame.
Motorbike windshields are often made of high-impact polycarbonate or acrylic plastic.
Windshields protect the vehicle's occupants from wind and flying debris such as dust, insects, and rocks, and provide an aerodynamically formed window towards the front. UV coating may be applied to screen out harmful ultraviolet radiation. However, this is usually unnecessary since most auto windshields are made from laminated safety glass. The majority of UV-B is absorbed by the glass itself, and any remaining UV-B together with most of the UV-A is absorbed by the PVB bonding layer.[1]
On motorbikes their main function is to shield the rider from wind, though not as completely as in a car, whereas on sports and racing motorcycles the main function is reducing drag when the rider assumes the optimal aerodynamic configuration with his or her body in unison with the machine and does not shield the rider from wind when sitting upright.
About Baton Rouge, Louisiana
Baton Rouge (/ˌbætən ˈruːʒ/ BAT-ən ROOZH; from French bâton rouge [bɑtɔ̃ ʁuʒ] (listen), meaning 'red stick') is the capital of the U.S. state of Louisiana. Located on the eastern bank of the Mississippi River, it is the parish seat of East Baton Rouge Parish, the most populous parish in Louisiana. It is the 99th most populous city in the United States, and second-largest city in Louisiana after New Orleans. It is also the 16th most populous state capital. As of the U.S. Census Bureau's July 2017 estimate, Baton Rouge had a population of 227,549, down from 229,493 at the 2010 census.[6] Baton Rouge is the center of Greater Baton Rouge, the second-largest metropolitan area in Louisiana, with a population of 834,159 as of 2017, up from 802,484 in 2010 and 829,719 in 2015.[7]
The city of Baton Rouge is a major industrial, petrochemical, medical, research, motion picture,[8] and growing technology[9] center of the American South. It is the location of Louisiana State University, the LSU System's flagship university and the largest institution of higher education in the state.[10] It is also the location of Southern University, the flagship institution of the Southern University System, the only historically black college system in the nation. The Port of Greater Baton Rouge is the 10th-largest in the United States in terms of tonnage shipped, and is the farthest upstream Mississippi River port capable of handling Panamax ships.[11][12]This, as well as its status as a major port city, is largely due to the Huey P. Long – O.K. Allen Bridge, which was intentionally constructed under the governorship of Huey Long at a low height, preventing big tankers from making their way up-river, past Baton Rouge.
Auto Glass Find, Baton Rouge,Louisiana-
Find an experienced windshield replacement technician around Baton Rouge, Louisiana
© 2021 Auto Glass Find . All Rights Reserved.

redpajama_set_name: RedPajamaCommonCrawl


text:
Gilligan, Image Credit: Lori Carter
The AFMS Club Rockhound of the Year is a program to honor the members in our clubs that have so unselfishly sacrificed to benefit their club. Share what these members have done and why you are proud to have them as members in your club by submitting them as your Rockhound of the Year. The process is simple, so don't let these members continue to go unrecognized.
Each club may submit the name of one individual or one couple in your club per calendar year.
Additionally, each club may also submit the name of one junior member in your club per calendar year.
Submissions can be made any time of the year
Each club determines their set of criteria for selecting the "Rockhound of the Year" and/or "Junior Rockhound of the Year".
Submissions consist of approximately 75 to 100 words of why the club would like to honor the individual or couple members. In addition, include the name of the club, who is making the submission, and a mailing address for receipt of the certificates.
Include the date that your submissions will be awarded to coordinate publishing in the AFMS and SFMS newsletters.
Include picture(s) for the SFMS newsletter.
It is not a contest. All submissions that meet the requirements will be honored.
Fill out the form below. An acknowledgement of receipt will be sent when it is read. Please allow 3 to 4 days for a response. If an acknowledgement is not received, assume your message has not been received.
Proper submissions will be forwarded to the SFMS Newsletter Editor, and the AFMS Rockhound of the Year Chair, who will forward the submission to the AFMS Newsletter Editor.
Certificates from the AFMS and SFMS will be mailed to the address provided.
Be sure and honor them at you club by including them in your newsletter, and presenting the certificates. Clubs can do even more to make the event special.
If you would like to see submissions from other clubs, check the AFMS and SFMS newsletters at:
http://www.amfed.org/news/
SFMS Lodestar Newsletter
Click here for the submission form
More about the image on this page
Properly Prepared Rockhound
Gilligan is ready to rockhound with standard safety gear including protective glasses, hard hat, and sturdy boots with ankle support. What is he missing? Gloves!
Image Credit: Lori Carter


Description: 1 Fitted Crib Sheet. Fits standard crib mattresses.
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The expansion in emerging market economies consolidated further in the period under review. In many countries, strong growth was accompanied by increasing export values and large current account surpluses. External debt burdens fell, foreign currency reserves rose further, fiscal positions improved, and balance sheets strengthened. Partly in response, consumer and investor confidence remained buoyant and growth was remarkably resilient in the face of higher oil prices even in oil-importing countries.
External conditions were unusually favourable during the period, including strong global demand, large terms-of-trade improvements for many countries and much easier external financing. In spite of these favourable circumstances, further policy measures are required. Some countries need to secure lasting improvements in fiscal positions. Also, while there was some degree of monetary tightening or exchange rate appreciation, particularly in countries that target inflation, monetary conditions in emerging market economies remained comparatively easy, and inflationary pressures became apparent in a number of cases. A major challenge for the monetary authorities in many countries is how to avoid policy mistakes that might put macroeconomic and financial stability at risk.


text:
Q: Why isn't PSReadLine part of my powershell? Why isn't PSReadLine part of the default modules of my powershell? How can I get all the default modules?
⨯ idror@TLV-WPJ03  ~  $PSVersionTable.PSVersion

Major  Minor  Build  Revision
-----  -----  -----  --------
5      0      10586  117

But the list of modules I have under C:\Program Files\WindowsPowerShell\Modules is just:

*

*Gist Provider

*PackageManagement

*PowerShellGet

I also have a folder C:\Program Files (x86)\WindowsPowerShell\Modules with

*

*PackageManagement

*PowerShellGet

(I know I have Gist management, so I guess I'm using the 64bit version)

A: Because PSReadline was available for older versions of PowerShell and frequently and easily installed, not including it by default in WMF packages simplified the installation.
It could also have been considered a feature that would help drive upgrades, though I am skeptical of that reasoning.

redpajama_set_name: RedPajamaStackExchange


The ADRF5024 and ADRF5025 employ inherent reflective architecture and are characterized for operating temperature range of –40°C to 105°C. All pins incorporate robust Electro-Static-Discharge (ESD) protection. The devices are nominally powered by ±3.3 V, drawing low supply current of less than 120 µA typical.The devices use standard positive logic control voltages, simplifying the interface design.
The ADRF5024 and ADRF5025 are intended as replacements for PIN diode-based counterparts, as no external components are necessary for bias generation or matching, and signal pins are internally biased at ground (GND) reference to eliminate the need for direct-current (DC) blocking capacitors.
The ADRF5024 has been optimised for fast switching applications with speeds less than 10ns and edge rates at 2ns. The ADRF5025 has been optimised for ultrawideband applications with good low frequency characteristics down to 9kHz.
The other characteristics are the same so the parts are drop-in alternative to each other and can be used interchangeably on the same printed circuit board (PCB) footprint.


text:
Q: JPA/Hibernate ManyToMany vs two-sided OneToMany/ManyToOne I am developing a JavaEE application and I use JPA/Hibernate as a persistence engine. While developing the application, some questions raised to my mind.
The application consists of users and their roles in a N:M relationship. Here is the database subset of the above tables.

I am relatively new to Hibernate and at first I asked IntelliJ IDEA to generate the mapping for me. What it did was generate the following Java classes:

*

*UserEntity.java

*RoleEntity.java

*UserXRoleEntity.java

*UserXRoleEntityPK.java

Thus, it generated a mapping for the relation table and two 1:N relationships, one between user and userXrole and one between role and userXrole.
After some research, I found that, by using the @ManyToMany annotation, I could omit mapping the userXrole table into a Java class and just declare it within the annotation as the @JoinTable.
So the question is:

*

*Why does IntelliJ generate the entities that way?

Is it just a more generic way that helps generation, or does it have any other advantages. Would you argue in favour of one way or the other?

A:
Is it just a more generic way that helps generation, or does it have any other advantages.

JPA doesn't know if a table is just a join table, that's why you have to tell it (using @JoinTable). The generator might guess, but it will probably only generate @ManyToMany if your table names match JPAs defaults.

Would you argue in favour of one way or the other?

I'd use @ManyToMany if i don't have a reason (finer grained control over lazy/eager fetching maybe?) for separate mapping entities, mostly because less code = less errors.


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En mathématiques, les matrices sont des tableaux d'éléments (nombres, caractères) qui servent à interpréter en termes calculatoires, et donc opérationnels, les résultats théoriques de l'algèbre linéaire et même de l'algèbre bilinéaire.

Toutes les disciplines étudiant des phénomènes linéaires utilisent les matrices. Quant aux phénomènes non linéaires, on en donne souvent des approximations linéaires, comme en optique géométrique avec les approximations de Gauss.

Historique

Histoire de la notion de matrice
Bien que le calcul matriciel proprement dit n'apparaisse qu'au début du , les matrices, en tant que tableaux de nombres, ont une longue histoire d'applications à la résolution d'équations linéaires. Le texte chinois Les Neuf Chapitres sur l'art mathématique, écrit vers le , est le premier exemple connu de l'utilisation de tableaux pour résoudre des systèmes d'équations, introduisant même le concept de déterminant. En 1545, Jérôme Cardan fait connaître cette méthode en Europe en publiant son Ars Magna. Le mathématicien japonais Seki Kōwa utilise indépendamment les mêmes techniques pour résoudre des systèmes d'équations en 1683. Aux Pays-Bas, Johan de Witt représente des transformations géométriques à l'aide de tableaux dans son livre de 1659, Elementa curvarum linearum. Entre 1700 et 1710, Leibniz montre comment utiliser les tableaux pour noter des données ou des solutions, et expérimente plus de 50 systèmes de tableaux à cet effet. En 1750, Gabriel Cramer publie la règle qui porte son nom.

En 1850, le terme de « matrix » (qui sera traduit par matrice) est forgé (sur la racine latine mater) par James Joseph Sylvester, qui le voit comme un objet donnant naissance à la famille de déterminants actuellement appelés mineurs, c'est-à-dire les déterminants des sous-matrices obtenues en retirant des lignes et des colonnes. Dans un article de 1851, Sylvester précise :
 « Dans des articles antérieurs, j'ai appelé matrix un tableau rectangulaire de termes à partir desquels plusieurs systèmes de déterminants peuvent être engendrés, comme issus des entrailles d'un parent commun ».

En 1854, Arthur Cayley publie un traité sur les transformations géométriques utilisant les matrices de façon beaucoup plus générale que tout ce qui a été fait avant lui. Il définit les opérations usuelles du calcul matriciel (addition, multiplication et division) et montre les propriétés d'associativité et de distributivité de la multiplication. Jusque-là, l'utilisation des matrices s'était essentiellement limitée au calcul des déterminants ; cette approche abstraite des opérations sur les matrices est révolutionnaire. En 1858, Cayley publie son A Memoir on the Theory of Matrices, dans lequel il énonce et démontre le théorème de Cayley-Hamilton pour les matrices 2×2.

Beaucoup de théorèmes ne sont d'ailleurs démontrés au début que pour de petites matrices : après Cauchy, Hamilton généralise le théorème aux matrices 4×4, et ce n'est qu'en 1898 que Frobenius, étudiant les formes bilinéaires, démontre le théorème en dimension quelconque. C'est aussi à la fin du  que Wilhelm Jordan établit la méthode d'élimination de Gauss-Jordan (généralisant la méthode de Gauss pour les matrices échelonnées). Au début du , les matrices occupent une place centrale en algèbre linéaire, en partie grâce au rôle qu'elles jouent dans la classification des systèmes de nombres hypercomplexes du siècle précédent.

Un mathématicien anglais du nom de Cullis est le premier, en 1913, à utiliser la notation moderne des crochets (ou des parenthèses) pour représenter les matrices, ainsi que de la notation systématique  pour représenter la matrice dont  est le terme de la i-ème ligne et de la j-ème colonne.

La formulation de la mécanique quantique au moyen de la mécanique matricielle, due à Heisenberg, Born et Jordan, amena à étudier des matrices comportant un nombre infini de lignes et de colonnes. Par la suite, von Neumann précisa les fondements mathématiques de la mécanique quantique, en remplaçant ces matrices par des opérateurs linéaires sur des espaces de Hilbert.

Histoire des déterminants

L'étude théorique des déterminants vient de plusieurs sources. Des problèmes de théorie des nombres amènent Gauss à relier à des matrices (ou plus précisément à leur déterminant) les coefficients d'une forme quadratique ainsi que les applications linéaires en dimension trois. Gotthold Eisenstein développe ces notions, remarquant en particulier qu'en notation moderne, le produit des matrices est non commutatif. Cauchy est le premier à démontrer des résultats généraux sur les déterminants, en utilisant comme définition du déterminant de la matrice  le résultat de la substitution, dans le polynôme , des puissances  par . Il montre aussi, en 1829, que les valeurs propres d'une matrice symétrique sont réelles. Jacobi étudie les « déterminants fonctionnels » (appelés par la suite jacobiens par Sylvester), utilisés pour décrire des transformations géométriques d'un point de vue infinitésimal ; les livres Vorlesungen über die Theorie der Determinanten de Leopold Kronecker et Zur Determinantentheorie de Karl Weierstrass, tous deux publiés en 1903, définissent pour la première fois les déterminants de manière axiomatique comme formes multilinéaires alternées.

Autres utilisations mathématiques du mot « matrice »
Deux mathématiciens notables au moins ont utilisé le mot dans un sens inhabituel.

Bertrand Russell et Alfred North Whitehead, dans leur Principia Mathematica, utilisent le mot « matrice » dans le cadre de leur . Cet axiome permet de réduire le type d'une fonction, les fonctions de type 0 étant identiques à leur  ; ils appellent « matrice » une fonction n'ayant que des variables libres. Ainsi, par exemple, une fonction  de deux variables  et  peut être réduite à une collection de fonctions d'une seule variable, par exemple , en « considérant » la fonction pour toutes les valeurs  substituées à la variable  puis réduite à une « matrice » de valeurs en procédant de même pour  : .

Alfred Tarski, dans son Introduction à la logique de 1946, utilise le mot « matrice » comme un synonyme de table de vérité.

Définitions
Une matrice à  lignes et  colonnes est un tableau rectangulaire de  nombres, rangés ligne par ligne. Il y a  lignes, et dans chaque ligne  éléments.

Plus formellement et plus généralement, soient ,  et  trois ensembles ( sera souvent muni d'une structure d'anneau ou même de corps commutatif).

On appelle matrice de type  à coefficients dans , toute famille d'éléments de  indexée par le produit cartésien , c'est-à-dire toute application  de  dans .

Le plus souvent, comme dans toute la suite de cet article, les ensembles  et  sont finis et sont respectivement les ensembles de nombres entiers  et . Dans ce cas, on dit que la matrice a  lignes et  colonnes, ou qu'elle est de dimension ou taille . En notant  l'image d'un couple  par l'application , la matrice peut alors être notée

ou plus simplement  si le contexte s'y prête.

Dans le cas particulier où  ou  est l'ensemble vide, la matrice correspondante est appelée la matrice vide.

On représente généralement une matrice sous la forme d'un tableau rectangulaire. Par exemple, est représentée ci-dessous une matrice , à coefficients entiers, et de dimension (3,4) :

Dans cette représentation, le premier coefficient de la dimension est le nombre de lignes, et le deuxième, le nombre de colonnes du tableau. Une matrice pour laquelle le nombre  de lignes est égal au nombre  de colonnes sera dite matrice carrée de taille (ou d'ordre) . Une matrice ne comportant qu'une seule ligne et  colonnes est appelée matrice ligne  (ou plus souvent vecteur ligne) de taille . Une matrice comportant  lignes et une seule colonne est appelée matrice colonne (ou plus souvent vecteur colonne) de taille .

Pour repérer un coefficient d'une matrice, on indique son indice de ligne puis son indice de colonne, les lignes se comptant du haut vers le bas et les colonnes de la gauche vers la droite. Par exemple, on notera , les coefficients de la matrice ,  compris entre 1 et 3 désignant le numéro de la ligne sur laquelle figure le coefficient envisagé, et  compris entre 1 et 4 désignant son numéro de colonne ; ainsi .

La disposition générale des coefficients d'une matrice  de taille  est donc la suivante

Les coefficients  avec  sont dits diagonaux, ceux avec  sont dits extradiagonaux.

Une sous-matrice de  est une matrice obtenue en sélectionnant une partie  de ses lignes et une partie  de ses colonnes ; on la note . On dit qu'une sous-matrice est principale si  dans la définition précédente. La diagonale principale de  est le vecteur

où .

Pour effectuer certaines opérations, il peut être utile de travailler sur le système des lignes ou des colonnes d'une matrice. On pourra alors l'écrire sous une des formes suivantes

L'ensemble des matrices à coefficients dans  possédant  lignes et  colonnes est noté  (ou parfois ).

Lorsque  on note plus simplement .

Soit  un ensemble et  ; on appelle matrice transposée de  la matrice . Si  est un magma,  où  est le magma opposé de .

Par exemple, avec la matrice  des exemples précédents, on a

Espaces de matrices
On suppose maintenant que  est muni d'une structure d'anneau ; les éléments de  seront appelés scalaires, par opposition aux matrices dont nous allons voir qu'elles peuvent être considérées comme des vecteurs.

Addition des matrices et multiplication par un scalaire
On définit sur  une loi de composition interne provenant de l'addition des scalaires :

.

On ne peut additionner que deux matrices de même taille.

 Exemple :

Pour chaque valeur du couple , l'espace  devient alors un groupe abélien, d'élément neutre la matrice nulle, celle dont tous les coefficients valent 0.

On définit aussi une opération à droite de  sur chaque espace  en associant, à chaque scalaire  dans  et à chaque matrice  à coefficients dans , la matrice  obtenue en effectuant la multiplication à droite, dans , de tous les coefficients de la matrice initiale par  : c'est la multiplication par un scalaire. Lorsque l'anneau est commutatif, la multiplication peut également s'effectuer à gauche.

En reprenant toujours la matrice  du premier exemple  :

Les espaces  ainsi obtenus ont donc une structure de -module à droite, et plus particulièrement de -espace vectoriel, si  est un corps commutatif.

Base canonique de l'espace des matrices

Le -module  est libre de rang , c'est-à-dire qu'il possède une base de  éléments : il suffit de considérer la base canonique . La matrice  est celle dont tous les coefficients sont nuls sauf celui d'indice , qui vaut 1.

Les coordonnées dans la base canonique d'une matrice  sont ses coefficients :

 Exemple :

Produit matriciel

On commence par définir le produit d'une matrice ligne par une matrice colonne. Soit  un nombre entier,  une matrice ligne,  ses coefficients,  une matrice colonne,  ses coefficients. On les suppose toutes deux de taille . On définit alors le produit, considéré comme un scalaire ou une matrice de dimension (1, 1) :

On remarque la condition de compatibilité sur les tailles des matrices (égalité du nombre de colonnes de la première avec le nombre de lignes de la deuxième). On définit maintenant plus généralement un produit entre deux matrices, la première,  dans , la deuxième,  dans , toujours avec une condition de compatibilité sur les tailles (et l'ordre des facteurs de la multiplication ne peut en général pas être changé). Le résultat obtenu est une matrice de , dont les coefficients  sont obtenus par :

À la lumière de l'exemple de la multiplication d'une matrice ligne par une matrice colonne, on peut reformuler cette définition en disant que ce coefficient est égal au produit de la ligne i de la première matrice par la colonne j de la deuxième, ce qui s'écrit de la manière suivante, si les  sont les lignes de la première matrice, et les  les colonnes de la deuxième, le produit est :
.

Le produit matriciel est associatif, distributif à droite et à gauche par rapport à l'addition matricielle. En revanche, même lorsque les dimensions permettent de donner un sens à la question et même si l'anneau des scalaires est commutatif, un produit de matrices ne commute en général pas :  n'est pas en général égal à , par exemple :

Remarque : le produit de deux matrices non nulles peut être nul, comme ci-dessus ; on dit que l'anneau des matrices n'est pas intègre.

Il arrive même, selon les tailles respectives des matrices  et B, que l'un des deux produits existe et pas l'autre.

La transposition et le produit matriciel sont compatibles au sens suivant :

(même si l'anneau  n'est pas commutatif, en se rappelant que les matrices transposées ont leurs coefficients dans l'anneau opposé ).

Matrice identité et inverse d'une matrice

Pour chaque nombre entier n, on note In la matrice carrée de taille n dont les coefficients diagonaux sont égaux à 1 et dont les autres coefficients sont nuls ; elle est appelée matrice identité de taille n.

où δ désigne le symbole de Kronecker.

Sous réserve de compatibilité des tailles, les matrices In sont neutres à droite et à gauche pour la multiplication.

Soit  une matrice de dimension (m, n). On dit que  est inversible à droite (respectivement à gauche) s'il existe une matrice B de taille (n, m) telle que  (respectivement ). Elle est simplement dite inversible si elle l'est à la fois à droite et à gauche. Le sous-ensemble de  constitué des matrices inversibles possède une structure de groupe pour le produit matriciel ; il est appelé groupe linéaire et noté .

Pour une matrice carrée à coefficients dans un anneau commutatif , être inversible à droite ou à gauche ou avoir un déterminant inversible dans  (c'est-à-dire non nul si  est un corps) sont trois propriétés équivalentes.

Algèbre des matrices carrées
Lorsque l'anneau  est commutatif, l'ensemble  des matrices carrées de taille n est donc muni d'une structure de -algèbre associative et unitaire avec l'addition matricielle, le produit par un scalaire et le produit matriciel.

On appelle matrice scalaire une matrice de la forme  où  est un élément de l'anneau .

Ces matrices s'appellent matrices scalaires car elles se comportent comme des scalaires, vis-à-vis de la multiplication :

Lorsque  est commutatif, ou à défaut, lorsque  est central dans , c'est-à-dire lorsque  commute avec tous les éléments de , on a en outre :

Réciproquement, toute matrice  de  telle que  est une matrice scalaire  où  est central dans  (ceci se démontre en prenant pour  les matrices de la base canonique).

Une matrice de la forme :

sera dite matrice diagonale.

Outre le déterminant, une autre fonction à noter est la trace. Toutes deux apparaissent dans un objet plus général, le polynôme caractéristique, qui à son tour permet d'obtenir certaines caractérisations des matrices diagonalisables (c'est-à-dire semblables à une matrice diagonale), ou de la trigonalisation.

Actions du groupe linéaire

Il existe plusieurs manières de faire agir le groupe linéaire  sur les espaces de matrices, notamment :
 action par multiplication à gauche de  sur , qui à  et , associe ,
 action (à gauche) par multiplication à droite de  sur , qui à  et , associe ,
 action par conjugaison de  sur , qui à  et , associe .

On décrit maintenant les résultats classiques sur ces actions, lorsque les scalaires forment un corps commutatif. Les deux premières actions sont souvent considérées simultanément ; on s'intéresse donc à la question : deux matrices  et  de dimension  étant données, existe-t-il des matrices  et  telles que  ? Si tel est le cas, les deux matrices  et  sont dites équivalentes. Le résultat principal est que deux matrices sont équivalentes si et seulement si elles ont même rang, ce qui s'exprime encore en disant que le rang est un invariant complet pour les doubles classes définies par les deux actions de multiplication à gauche et à droite. Par ailleurs, une matrice étant donnée, on peut trouver d'autres matrices privilégiées (les matrices échelonnées) dans la même orbite pour une de ces actions par la méthode du pivot de Gauss.

Pour l'action par conjugaison, deux matrices carrées  et  de taille  dans la même orbite admettent une relation de la forme , pour une certaine matrice  inversible de taille  ; deux telles matrices sont dites semblables. La description d'un système complet d'invariants (caractérisant des matrices semblables) est plus délicate. On appelle ces invariants les invariants de similitude. D'un point de vue algorithmique, la réduction d'une matrice quelconque à une matrice sous une forme privilégiée se fait par un algorithme inspiré de celui du pivot de Gauss, voir théorème des facteurs invariants.

Interprétations linéaires
Un intérêt principal des matrices est qu'elles permettent d'écrire commodément les opérations habituelles de l'algèbre linéaire, avec une certaine canonicité.

Coordonnées

Le premier point est de remarquer que le -module Kn s'identifie canoniquement à l'espace de matrices colonne  : si  est le n-uplet de  dont tous les coefficients sont nuls, sauf le i-ème qui vaut 1, on lui associe la i-ème matrice colonne  de la base canonique de  (celle dont tous les coefficients sont nuls sauf le i-ème qui vaut 1), et on étend l'identification par linéarité ; la matrice associée à chaque n-uplet sera appelée matrice coordonnée canonique.

D'autres identifications sont cependant possibles ; lorsqu'on peut parler de base (si l'anneau des scalaires est un corps, par exemple), on peut associer les matrices colonnes élémentaires à n'importe quelle base de l'espace  (ou plus généralement d'un -module libre), puis à nouveau étendre par linéarité ; les matrices associées seront appelées matrices coordonnées dans la base envisagée.

On peut juxtaposer les matrices coordonnées, dans une base fixée, de plusieurs n-uplets. On obtient ainsi la matrice coordonnée d'une famille de vecteurs. Le rang de la matrice est alors défini comme la dimension de la famille de ces vecteurs. En particulier la matrice d'une base dans une autre base est appelée matrice de passage entre ces deux bases, ou matrice de changement de base. Si X et X sont les matrices coordonnées du même vecteur dans deux bases  et C, et que P est la matrice de passage de la base C dans la base , on a la relation (une matrice de passage est toujours inversible) :

 Applications linéaires

Soient E et F deux espaces vectoriels de dimensions respectives n et m sur un corps commutatif , B une base de E, C une base de F et φ une application linéaire de E dans F.

On appelle matrice de φ dans le couple de bases (B, C) la matrice  de  telle que pour tout vecteur  de , si l'on note ,  et , alors :

Si ψ est une deuxième application linéaire, de F dans un troisième espace vectoriel G de base D, alors, relativement aux bases , C, D, la matrice de la composée  est égale au produit des matrices de  et . Plus précisément :

L'application de L(E, F) dans  qui à chaque  associe sa matrice dans (B, C) est un isomorphisme d'espaces vectoriels.

Pour toute matrice  de , l'application X ↦ MX du -espace vectoriel M(K) dans le -espace vectoriel M(K) est linéaire. C'est un point clef du lien entre algèbre linéaire et matrices. En conséquence, il arrive souvent que l'on identifie la matrice  avec cette application linéaire. On parlera alors de noyau de la matrice, d'espaces propres de la matrice, d'image de la matrice, etc.

Si  et  sont deux bases de E, C et C' deux bases de F, P = mat(B) la matrice de passage de  vers  et Q la matrice de passage de C vers C, alors les deux matrices M et M' d'une même application linéaire de E dans F, dans les couples de bases (B, C) et (B, C), sont liées par : M' = QMP. On constate ainsi que deux matrices équivalentes sont deux matrices qui représentent la même application linéaire dans des bases différentes. En particulier, dans le cas d'un endomorphisme, si l'on impose  et , la formule précédente devient : M' = PMP et deux matrices semblables sont deux matrices qui représentent le même endomorphisme dans des bases différentes.

 Transposition

Soient de nouveau E et F deux -espaces vectoriels de dimensions finies, de bases respectives  et C, et φ une application linéaire de E dans F. L'application linéaire transposée  entre leurs duals est définie par

Sa matrice dans le couple de bases duales (C*, B*) est liée à celle de φ dans (B, C) par :

 Remarque
Lorsque l'anneau n'est pas commutatif, si l'on représente les vecteurs par des matrices colonne, l'algèbre linéaire n'est compatible avec le calcul matriciel que si les modules ou espaces vectoriels considérés sont à droite, comme dans les articles détaillés signalés ci-dessus, une application linéaire correspondant à la multiplication à gauche d'un vecteur colonne par la matrice qui la représente. Si l'on tient à avoir des modules ou espaces vectoriels à gauche, il faut représenter les vecteurs par des matrices ligne, une application linéaire étant cette fois représentée par la multiplication à droite d'un vecteur ligne par la matrice qui la représente.

 Systèmes d'équations linéaires

En général, un système de m équations linéaires à n inconnues peut être écrit sous la forme suivante :

où  sont les inconnues et les nombres  sont les coefficients du système.

Ce système peut s'écrire sous la forme matricielle :

avec :

la théorie de la résolution des systèmes utilise les invariants liés à la matrice  (appelée matrice du système), par exemple son rang, et, dans le cas où  est inversible, son déterminant (voir l'article règle de Cramer).

 Interprétations bilinéaires
Dans ce paragraphe, l'anneau  des scalaires sera supposé commutatif. Dans la plupart des applications, ce sera un corps commutatif.

Le cas non commutatif existe aussi mais il faut prendre quelques précautions et les notations deviennent trop lourdes pour cet article.

 Matrice d'une forme bilinéaire
Soient E un -module libre et B = (e1, … , en) une base de E.

Soit  une forme bilinéaire. On définit la matrice de  dans la base B par la formule suivante :

Dans le cas particulier où K = ℝ et  est un produit scalaire, cette matrice est appelée matrice de Gram.

La matrice  est symétrique (respectivement antisymétrique) si et seulement si la forme bilinéaire  est symétrique (respectivement antisymétrique).

Soient  et  deux vecteurs de E. Notons  et  leurs coordonnées dans la base B et . On a alors la formule : .

Deux formes bilinéaires sont égales si et seulement si elles ont la même matrice dans une base donnée.

 Matrice d'une forme quadratique
Lorsque  est un corps de caractéristique différente de 2, on appelle matrice d'une forme quadratique la matrice de la forme bilinéaire symétrique dont est issue la forme quadratique.

 Formule de changement de base
Soient E un -module libre et B, C deux bases de E. Soit  une forme bilinéaire.

Notons  la matrice de  dans la base B et  la matrice de  dans la base C. Notons  la matrice de passage. On a alors la formule de changement de base pour une forme bilinéaire (à ne pas confondre avec celle pour une application linéaire) :

 Matrices congruentes

Deux matrices carrées  et  sont dites congruentes s'il existe une matrice inversible  telle que

Deux matrices congruentes sont deux matrices qui représentent la même forme bilinéaire dans deux bases différentes.

Lorsque  est un corps de caractéristique différente de 2, toute matrice symétrique est congruente à une matrice diagonale. L'algorithme utilisé s'appelle réduction de Gauss à ne pas confondre avec le pivot de Gauss.

 Catalogue partiel

Une matrice est dite symétrique si elle est égale à sa transposée et antisymétrique si elle est opposée à sa transposée.

Une matrice  à coefficients complexes est dite hermitienne si elle est égale à la transposée de sa matrice conjuguée .

Une matrice  est dite
 orthogonale si elle est à coefficient réels et si ,
 unitaire si elle est à coefficients complexes et si

(Pour plus d'exemples, voir en bas de page : « Articles connexes » et palette « Matrices »)

 Décomposition d'une matrice
On utilise abusivement le terme décomposition d'une matrice, qu'il s'agisse d'une véritable décomposition (en somme) comme dans la décomposition de Dunford ou d'une factorisation comme dans la plupart des autres décompositions.

 Réduction d'une matrice carrée

 Réduire une matrice, c'est trouver une matrice qui lui est semblable la plus simple possible.
 Une matrice diagonalisable est une matrice semblable à une matrice diagonale :  est diagonalisable s'il existe une matrice inversible  et une matrice diagonale  telles que .
 Sur un corps algébriquement clos, on dispose de la réduction de Jordan qui est optimale et il existe des décompositions intermédiaires comme la décomposition de Dunford qui utilise les sous-espaces caractéristiques ou celle de Frobenius qui utilise les sous-espaces cycliques.
 Les polynômes d'endomorphismes jouent un rôle crucial dans les techniques de réduction.

 Décomposition LU

 C'est une factorisation en produit de deux matrices triangulaires.
 En lien avec le pivot de Gauss, c'est une méthode qui permet d'inverser une matrice.

 Décomposition QR

 C'est un résultat sur les matrices à coefficients réels ou à coefficients complexes.
 C'est une factorisation en produit d'une matrice orthogonale et d'une matrice triangulaire.
 C'est une traduction matricielle du procédé de Gram-Schmidt.

 Décomposition polaire

 C'est un résultat sur les matrices à coefficients réels ou à coefficients complexes.
 C'est une factorisation en produit d'une matrice orthogonale et d'une matrice symétrique définie positive dans le cas réel, en produit d'une matrice unitaire et d'une matrice hermitienne définie positive dans le cas complexe.
 On peut décomposer à droite ou à gauche.
 On a unicité de la factorisation pour les matrices inversibles.

 Normes
 Normes d'algèbre

Dans tout ce paragraphe,  ou .

Une norme matricielle est une norme d'algèbre sur l'algèbre , c'est-à-dire une norme d'espace vectoriel qui est de plus sous-multiplicative.

Le rayon spectral d'une matrice carrée  à coefficients complexes est le plus grand module de ses valeurs propres. Il est égal à la borne inférieure des normes matricielles de .

Sur , toute norme  subordonnée à une norme sur  est une norme d'algèbre vérifiant de plus  (la réciproque est fausse).

 Structure d'espace vectoriel euclidien
L'espace vectoriel , canoniquement isomorphe à , hérite de sa structure euclidienne. Le produit scalaire se transcrit en

où  désigne la trace (i.e., ) et les  (resp. ) désignent les éléments de  (resp. ). La norme associée à ce produit scalaire est la norme de Frobenius ou norme de Hilbert-Schmidt :

où  est le vecteur des valeurs singulières de

et  est la norme euclidienne.

Si , il ne s'agit pas d'une norme subordonnée, puisque

L'inégalité de Cauchy-Schwarz s'écrit (comme pour tout produit scalaire) :

Cette inégalité peut être renforcée par l'inégalité de trace de von Neumann''' :

où  est le vecteur des valeurs singulières de , rangées en ordre décroissant. Elle a la même structure que l'inégalité de Ky Fan, laquelle suppose que les matrices sont carrées et symétriques (on peut alors remplacer  par le vecteur des valeurs propres).

L'espace vectoriel  est muni d'une structure similaire d'espace hermitien.

 Exponentielle d'une matrice

Soit , soit  une norme d'algèbre et  une série entière de rayon de convergence .

Alors si , la série  est absolument convergente. (On le montre en utilisant que .)

En particulier, on peut définir, pour toute matrice carrée complexe, la quantité

Le calcul effectif de cette exponentielle se fait par réduction de la matrice.

L'exponentielle joue un rôle central dans l'étude des systèmes linéaires d'équations différentielles.

 Notes et références

 Voir aussi

 Bibliographie
 J.-M. Arnaudiès et H. Fraysse, Cours de mathématiques, Dunod, 1980
 Rached Mneimné, Réduction des endomorphismes, Calvage et Mounet, Paris, 2006
 P. Wira, Un rappel sur les matrices'', support de cours, Université de Haute Alsace, Mulhouse, 2000

Articles connexes

Liens externes
 Frédéric Brechenmacher, Les matrices : formes de représentation et pratiques opératoires (1850-1930)

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Where We Work / Monrovia, Liberia
TLI's largest training site is located in Monrovia, Liberia. Our national partner, Dyonah Thomas, founded the Center for Leadership Development (CLD) and has been involved with training pastors and church leader throughout the region before partnering with us.
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text:
The Other i-modes
Back to Contents of Issue: June 2001
Fifteen million happy non-DoCoMo users can't all be wrong.
by Andrea Hoffmann
Ranked 5th, but still in the running: Astel's PHS service
THE ENDLESS MEDIA COVERAGE of Japan's dominant wireless carrier, NTT DoCoMo, is not unjustified. The operator's numbers are certainly spectacular, and DoCoMo leads the wireless market here with 36 million mobile subscribers (59 percent of the market, as of March 31), 23.2 million of which use DoCoMo's wildly popular i-mode wireless Internet service (as of May 7), accounting for some 63 percent of all Japanese mobile surfers. The casual observer could be forgiven for concluding that wireless in Japan equates to DoCoMo and little else. But i-mode is not the only wireless service, and DoCoMo is not the only carrier. In fact, competitors J-Phone, KDDI, DDI Pocket, and Astel are racking up some pretty impressive numbers with zero help from DoCoMo, thank you very much.
BIGGEST RIVAL
KDDI is the No. 2 wireless carrier in Japan and the perennial challenger to DoCoMo's lead. The company was created through a merger of DDI, IDO, and KDD (the former state-owned overseas long-distance monopoly carrier) in October 2000, and presently offers mobile services on a PDC (portable digital cellular) network operated by the Tu-Ka Group and on the packet-switched cdmaOne network operated by Au (launched in July 1998). cdmaOne's data rate is 64 Kbps, one of the world's highest (and at least as fast as DoCoMo's much-touted 3G network due for launch about the time this issue hits the streets).
Construction of the cdmaOne network was widely seen as an attempt by KDDI to differentiate itself from the rumored poor voice quality on DoCoMo's PDC network. cdmaOne allows roaming for Japanese subscribers traveling in compatible carrier areas in the US (including Hawaii), Canada, Korea, Hong Kong, and Australia. "Unfortunately," says Credit Suisse First Boston telecom analyst Mark Berman, "KDDI's roaming service is not yet attractive, since it is too expensive and so far only offered in some big cities." Although cdmaOne is technically superior to anything DoCoMo has (not counting 3G), the firm faces some serious hurdles, especially with the weakness of its new "Au" brand, which serves as a sort of virtual mobile carrier. Also, much of the company's subscriber base is still tethered to the older PDC network. Says Berman: "KDDI is trying to compete, especially with J-Phone, by offering a special discount to students. But it should market the fast cdmaOne data services to high-end users and give its existing PDC users good incentive to migrate to cdmaOne, thus unifying services."
Consumers seem to be confused about the plethora of services, technologies, and rate plans KDDI is offering, and, as of January 31, the carrier's market share of new wireless subscribers has dropped to 15 percent, while both DoCoMo and J-Phone have increased theirs, to 70 and 16 percent, respectively. Launching EZWeb has certainly helped boost the operator's sagging bottom line. While average annual voice revenue per user (ARPU) has been falling (down 8 percent year-on-year to ¥8,200 for 2001, according to one investment bank's estimates), EZWeb users have been contributing a tidy ¥1,500 in Net usage fees in addition to the voice fees, and generating some 35 million page views. The same report estimates that by 2005, ARPU should be up around ¥10,000, with data and Internet fees contributing about 20 percent.
By comparison, another brokerage report places NTT DoCoMo's 2001 ARPU at around ¥8,130 for non-i-mode users (voice only) and about ¥8,740 for i-mode users (the additional data usage gives a 10 percent boost).
NEXT IN LINE
No. 3 operator J-Phone seems to be benefiting from KDDI's confusion. While it may be the smallest of the three main carriers, J-Phone is the creative underdog and continually pushes the envelope on cutting-edge services and fields handsets sooner than its bigger competitors, says Scott Driggers, CEO of Kevo International, a wireless consultancy that works with Japan's wireless carriers. J-Phone has created a young and innovative brand image and was the first operator in Japan to start SMS (short mail service) and Internet email on cellphones (in 1997). "Being relatively small has kept the company sharp and competitive, and it comes up with new services and ideas targeting their main customer base -- young users," says Driggers.
Its wireless Internet service, J-Sky, could overtake KDDI/Au's EZWeb in just a few months at the current growth rate, according to CSFB's Berman. He points to J-Phone's deployment of sophisticated new handsets with 65,000-color TFT displays (thin film transistor -- the same technology used in high-end flat-panel monitors) and integrated cameras, and unique services like J-Sky Station, which pushes area-based content and marketing promotions to opt-in subscribers at a preset interval. "J-Phone also offers corporate discounts in central and western Japan, which have boosted the service's popularity," adds Berman.
According to John Garrett, J-Phone's general manager of sales planning, the operator sees itself as a leader, challenger, and first mover, offering innovations to suit the mobile lifestyle of young people rather than offering technology for technology's sake. Accordingly, 15- to 19-year-olds comprise the largest portion of J-Phone subscribers, giving it the edge over No. 2 operator KDDI in that (lucrative) slice of Japan's keitai-using demographic (about a 25 percent share compared to KDDI's 21 percent).
J-Phone director Philip Marnick claims the carrier's ARPU is among the world's highest, as its subscribers "use the phone a lot." Calculating one voice call as equal to one email message or one mobile Web page access, he says J-Phone now carries more data than voice traffic, with about 300 million data "calls" per month (versus 200 million in July 2000). "We carried more email on our network in February than all four German operators combined," says Marnick (the firms doesn't release precise ARPU data).
COMPETITION HEATS UP
Competition in Japan's mobile Internet seems to have entered a second phase, as many of the current services can already be regarded as 2.5G, or second generation--plus (voice plus full data). The DoCoMo competitors in particular are doing everything they can to deploy new services and cool terminals, all the better to compete with the 900-lb i-mode gorilla. All carriers' handsets are becoming more refined, with bigger color screens, integrated cameras, and more sophisticated Internet and email services. KDDI, for one, has started offering advanced email functions allowing users to send and receive image and sound file attachments and messages of up to 5,000 characters, while J-Phone has just unveiled plans to add 3-D graphics, enabling surfers to manipulate characters (spin, enlarge, shrink) downloaded to JAVA-enabled cellphones. As each pursues new technologies and greater market share, some real differentiation is starting to take place between Japan's wireless Web service providers. Here are some of the points to watch.
Unlike the proprietary JAVA specifications deployed by NTT DoCoMo on its i-Appli JAVA service (launched in January), J-Phone will use the J-Blend real-time OS in the onboard environment. J-Blend is based on the standard Mobile Information Device Profile (MIDP) established by cellular operators, manufacturers, and OS vendors in Japan and the US under the leadership of Sun Microsystems. KDDI and DDI Pocket will likewise conform to the MIDP standard, and KDDI has already announced its first new JAVA handset (the C407H). As a result, JAVA programs developed according to the MIDP spec will run on devices offered by KDDI, J-Phone, and DDI Pocket, but not DoCoMo, potentially giving these carriers a competitive distinction over DoCoMo, at least in the eyes of the growing legions of content developers -- who should be motivated to develop JAVA applications for the three MIDP-using mobile services first. Of course, i-mode still has the lion's share of JAVA users, but there's no reason why savvy marketing couldn't change that.
The competitors' JAVA services will also have fewer application restrictions than DoCoMo; J-Phone will have an application download limit three times more generous than DoCoMo's (30KB versus 10KB), and KDDI, five times (at 50KB). (Ironically, one symptom of DoCoMo's hypersuccess is that the network is straining under the weight of subscriber traffic and crashes on occasion.) J-Phone will start its JAVA service in June, KDDI's will come sometime this summer, and DDI Pocket's will launch later this year. DDI Pocket is also launching nationwide packet switched service with a speed between 32 and 128 Kbps this June and will allow its handsets to automatically switch between circuit switching and packet switching, depending on the volume of data to be transferred. Using the circuit switched system at 32 Kbps, subscribers could download a 250-KB file for just ¥10, whereas an i-mode user would pay ¥600 using that service's packet-only system.
With the adoption of a common standard markup language, XHTML Basic, for wireless handset microbrowsers, competition between the mobile Internet services in Japan will further increase, since XHTML Basic--format content developed for one platform will also be accessible by customers of the other platforms. In the fourth quarter, microbrowser-maker Access will release its XHTML Basic-compatible Compact NetFront Plus browser to handset manufacturers who supply Japan's operators. Access plans to market the browser widely to cellphone makers inside and outside Japan, thereby exporting knowledge and expertise gained at home to other countries and starting head-to-head international competition with both Openwave's recently announced multi-platform microbrowser and Microsoft's Mobile Explorer browser.
This new generation of microbrowsers will be offered as a solution for 2.5G and 3G mobile terminals and is designed to bridge current mobile Net services with upcoming high-speed 3G wireless networks. This should allow true global roaming between participating carriers (although early 3G adopters in Japan won't be doing much roaming until other 3G networks are built elsewhere).
The first carrier to start 3G services in Japan will be NTT DoCoMo, which was due to test-launch its FOMA ("Freedom of Mobile multimedia Access") 3G service at the end of May, followed by KDDI in October this year, and then J-Phone in June 2002. All three companies are adopting IMT-2000 technologies, an international 3G standard developed by the International Telecommunications Union (ITU), but each network's system will differ somewhat. While NTT DoCoMo and J-Phone will both deploy all-new W-CDMA (wideband code division multiple access) systems (which will still be mutually incompatible since DoCoMo is using a slightly different flavor of W-CDMA), KDDI has opted to roll out its 3G services based on cdma2000, a technology developed by US-based Qualcomm. cdma2000 is an evolutionary upgrade from KDDI's present 2.5G cdmaOne network, and the operator does not have to replace existing base stations in the initial phase. As a result, DoCoMo and J-Phone will both incur large 3G capital expenditure costs, while KDDI will get its 3G network up and running much cheaper.
Fierce global competition is expected between W-CDMA and cdma2000 standards, and what happens in Japan -- the first market to roll out both technologies -- is expected to generate a lot of industry attention. Additionally, Japan is seen as an especially valuable testing ground for the new 3G services because it already has advanced 2.5G technologies, which will hopefully allow a smoother transition from 2G to 3G. Industry watchers are particularly keen to see what kind of services are going to be popular on 3G, how the pricing for the new service will be structured, and who will use the new networks. But as NTT DoCoMo has already pointed out, there is no reason for excitement just yet, as there isn't a lot of killer content available to take advantage of the better bandwidth. Customers who do sign up for DoCoMo's launch will also find that their expensive new 3G handsets only work in the Tokyo and Yokohama areas and that usage costs will be much higher than on the existing 2.5G network (although these should fall fairly quickly). DoCoMo users will have speed on their side, though. DoCoMo's 3G service is expected to provide 384 Kbps download, which will be reached over the next few years as DoCoMo tests its network and slowly ramps up from this year's 64 Kbps, to 115 Kbps, and then all the way up.
3G users are expected to download much greater amounts of data when music and video services are finally online, but the current transmission fees on all carriers (between approximately ¥0.1 and ¥0.3 per 128-byte packet) are too high -- it would cost roughly ¥6,000 to download a 3-minute MP3 song at present rates. Carriers here have already said they will reduce packet fees to 1/100 of the current level. The likely outcome for the next couple of years is that the 2.5G and 3G networks will run in parallel, with higher bandwidth applications dished up over the 3G pipe. As NTT DoCoMo will be the first major carrier worldwide to start 3G services and therefore the first to see who is going to use the services and at what price level, the other carriers will be watching its progress with eagle eyes.
J-PHONE WAITS
In March, J-Phone announced it would delay its planned 3G launch from this December until June 2002, which is about the same time that the Japanese carrier's major shareholder Vodafone is expected to launch UK 3G services. By delaying the launch, J-Phone will be able to integrate the latest changes in the W-CDMA technical specifications, says general manager Garrett. In the meantime, the company will concentrate its energy on existing 2.5G PDC (portable digital cellular) network subscribers, while planning for customer migration to the 3G network next year. Nonetheless, for Vodafone and the other major foreign shareholder, British Telecom, the Japanese market and its early transition to 3G is an excellent test bed where they can learn firsthand from J-Phone's experience, presumably exporting and leveraging that expertise to markets outside Japan. J-Phone, Vodafone, and BT combined have a total subscriber base of 182.5 million users, and Garrett says, "This is an interesting perspective when you compare to the international alliances that NTT DoCoMo is building for its global expansion plans." Yoshikazu Muramoto, deputy manager of J-Phone East, adds, "[Exporting] our expertise and knowledge to global markets is of course very interesting. This is not limited to exporting the latest technology, but also includes the business models, for example." The company hopes to establish roaming agreements with W-CDMA network operators worldwide, utilizing partners Vodafone and BT.
Given the fact that 3G is going to be deployed globally, and considering Japan's early entry, Japanese handset makers also have a good chance to gain a significant competitive advantage both domestically and in Europe and the United States; this may constitute a serious threat to local handset makers in these markets. Late April rumors of a tie-up between the cellphone divisions of Sony and Ericsson would also help pave the way for Japanese handset technology to gain serious market share overseas.
JAPAN'S MOBILE STATS
• Portion of japanese population owing a cellular or PHS phone: 50.8%
• Japanese who own a cellular or PHS phone: 66.7 million
• Mobile phones users who have Net access via keitai: 34.5 million
NEC and Matsushita (Panasonic) in particular may have a strong head start in the European market, as they were expected to have 3G handsets ready for NTT DoCoMo's May launch in Japan, giving them immediately exportable experience. Even prior to 3G, top-tier maker Sharp had announced a deal with BT Wireless that will see Sharp supply BT customers around the world with advanced 2.5G handsets incorporating cameras. The first models to be launched in the UK will be a version of the phone recently introduced by J-Phone in Japan with a tiny camera in the back of the handset. "European manufacturers are preparing to introduce color screens this year but will struggle to compete against Japan's near two-year lead," said one J-Phone spokesperson.
A global operator like Vodafone, the world's largest mobile company, is likely to seek economies of scale by sourcing Japanese phones it can sell worldwide, and the European manufacturers will have to match Japanese skills or expect to lose. The Sharp-BT deal clearly highlights the threat and the value of BT's and Vodafone's investment into J-Phone and its parent company Japan Telecom. For the first time, DoCoMo will be unable to squeeze the handset makers into providing their best technology to it first (a long-standing domestic practice).
In other words, it appears that competition against DoCoMo from domestic operators with the smarts, savvy, and tenacity to win 15 million--plus mobile Net subscribers is going to help export Japanese handset technology and mobile Net service know-how to the rest of the world, helping bring utterly cool pocket rockets to Europe and Japan. And the little guys are doing it all by themselves. J-Phone, KDDI, and DDI Pocket: Go get 'em!
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The Wickedest Witch of Them All
Posted by James on October 8, 2013
Posted in: Did Ya Know?, New Home.	Tagged: Margaret Hamilton, the Wicked Witch of the West, The Wizard of Oz, Wicked Witch of the West, Wizard of Oz.	4 Comments
In 1939, Margaret Hamilton was cast in the role of the Wicked Witch of the West, opposite Judy Garland's Dorothy Gale in The Wizard of Oz, creating not only her most famous role, but one of Hollywood's most memorable villains. Hamilton won the role after Gale Sondergaard, who was originally considered (as a more glamorous witch and with a musical number) declined after it was decided that the witch would be "ugly".
MGM studio executives even cut some of Hamilton's more frightening scenes, worrying that she would frighten children……….. too much.
Later on in life, she would comment on the role of the witch in a light-hearted fashion. For an interview, she joked:
"I was in a need of money at the time, and I had already done about six pictures for MGM already when my agent called. He said 'Maggie, they want you to play a part on the Wizard.' I said to myself, 'Oh Boy, The Wizard of Oz! That has been my favorite book since I was four.' And I asked him what part,
and he said 'The Witch'
and I said 'The Witch?!'
and he said 'What else?'"
Hamilton suffered a second-degree burn on her face and a third-degree burn on her hand during a second take of her fiery exit from Munchkinland, in which the trap door's drop was delayed to eliminate the brief glimpse of it seen in the final edit. Hamilton had to recuperate in a hospital and at home for six weeks after the accident before returning to the set to complete her work on the now-classic film, and she refused to have anything to do with fire for the rest of the filming. After she recuperated, she said, "I won't sue, because I know how this business works, and I would never work again. I will return to work on one condition — no more fireworks!"
Aren't we all glad that she did return,
Witch,
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4 comments on "The Wickedest Witch of Them All"
Sheridan on October 8, 2013 at 11:53 PM said:
Love the classics !!!!!!
James on October 9, 2013 at 8:14 AM said:
She's simply the best! Still scary
GabiGirl on October 9, 2013 at 7:16 AM said:
Oh yes, I quite agree. She is and always will be the very best witch of all times!!
The movie wouldn't have been the same without her,


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Medications in the time of coronavirus
Written By: Meredith Raine, UTHealth | Updated: March 23, 2020
As cases of coronavirus COVID-19 mount, the search is on to identify existing medications that can quell the symptoms or even prevent them.
Scientists around the world are working in earnest to diminish, prevent, or eradicate COVID-19, and early medication trials are already underway. The rapid discoveries produced by the studies are no doubt progress toward curbing the effects of the pandemic. But because of the urgency, the efficacy, side effects, and true associations of these medications may not be fully understood. This could lead to unintended consequences.
You may have already heard news reports of commonly prescribed medications that could be the solution to the coronavirus. Are these reports too good to be true? Are there side effects to consider? Carmel Dyer, MD, a geriatrician at UT Physicians Center for Healthy Aging in Bellaire, provides information to help you make sense of the current news concerning medications.
Strong medicine could lead to serious side effects
Carmel Dyer, MD
A strong medication doesn't necessarily mean a better medication, said Dyer, executive director of the Consortium on Aging and executive vice chair of the Department of Internal Medicine at McGovern Medical School at UTHealth. Some of the medications proposed are potent and could have serious, even fatal side effects. In some instances, the cure, especially for those with mild cases of COVID-19, could be worse than the disease itself. These medications – many of which are only available in hospitals and through tightly regulated clinical trials – can also be toxic, especially in older people.
Listen to your health care provider
Whether you are considering adding a new medication to your treatment regime, it is critically important that you consult with your health care provider. Equally as important, Dyer said, do not stop taking your routine medicine without consulting your provider. Stopping a medicine could lead to health complications that make you more vulnerable to contracting COVID-19 and other illnesses.
This is no time for hoarding
Seeing news reports of people hoarding everything from toilet paper to hand sanitizer may tempt you to hoard medications. Please don't, Dyer implores. Hoarding medications greatly limits the available supply to those who truly need the medicine. Also, hoarding and taking medication you may not need puts your own health at risk.
Whether you are watching news about the next new hope for a COVID-19 cure or reports of the pandemic's impact around the world, the 24/7 news cycle can take a toll. Dyer recommends taking occasional breaks from the news to reduce stress. Heightened stress can lower the strength of your immune system, making you more susceptible to illness. Turn off the news for a while, Dyer said. It's good for your health.
When it comes to medications for COVID-19, we need to wait on the evidence to determine if it is the right answer for each patient, Dyer said.
Until then, keep you and your loved ones protected through physical distancing and thorough handwashing.
And always, if you have any concerns or questions, ask your UT Physicians doctor about your specific needs. We offer evidence-based treatment plans for each patient and are following the most up-to-date COVID-19 guidelines from the Centers for Disease Control and Prevention, the World Health Organization, and other trusted agencies.


For the rest of the Christmas season I am keeping these blogs short and simple with one tip, tool, or technique you and your team can use to make this season rock!
You are going to be asked quite often for products you don't have. Either you're out-of-stock or you don't carry that product (or maybe you've never heard of it).
When the store is busy and you have other customers waiting to be helped, it is easy to simply say No and move on to a customer you can help.
I have some coming in soon. Can I arrange to have it sent to you as soon as it comes in?
Are you looking for that particular item, or can I show you something similar?
All of these phrases are conversation starters. Often a customer is looking for a specific item because she doesn't know alternatives exist or she has an idea in her head and can only think of one solution. When you start the conversation, sometimes you find better solutions than the one she asked for.
If all you do is say No, they often quit asking.
PS Here's another tool I stole from a fellow toy store owner. Create a "No List." Put it on a clipboard up front. Every time an employee gets asked for a product you don't have or a service you don't offer, write it on the No List. If one thing ends up on that No List several times, you should consider selling that item or offering that service. Your customers already think you would.


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Jürgen Court (* 1961) ist ein deutscher Sportpädagoge, Sportphilosoph, Sporthistoriker und Hochschullehrer.

Leben
Court studierte an der Deutschen Sporthochschule Köln (DSHS) und erlangte den Abschluss als Diplom-Sportlehrer, zudem absolvierte er an der Universität zu Köln ein Lehramtsstudium in den Fächern Sport, Philosophie und Erziehungswissenschaften, welches er mit dem ersten Staatsexamen abschloss. 1988 wurde an der DSHS seine Doktorarbeit angenommen, in der er sich mit der Theorie der Erziehung von Immanuel Kant befasste. Court war als wissenschaftlicher Mitarbeiter an der Pädagogischen und am Philosophischen Seminar der DSHS tätig, 1994 legte er dort seine Habilitation zur Ethik des Sports und zur Allgemeinen Ethik vor. Ihm wurde die Lehrberechtigung für das Fach Sportphilosophie verliehen. 1998 wurde er an der DSHS zum außerplanmäßigen Professor ernannt. 1999 kam durch eine Erweiterungshabilitation die Lehrberechtigung für Sportpädagogik hinzu. Ab April 2000 war Court am Institut für Sport- und Bewegungswissenschaften der Universität Erfurt zunächst Vertretungsprofessor und hernach Professor für Sportpädagogik und Bewegungspädagogik.

Forschung und Lehre
Zu Courts Forschungsschwerpunkten zählen die Theorie und Praxis der Sportdidaktik, vergleichende Wissenschaftstheorie und Sportgeschichte, vor allem die Geschichte der Sportwissenschaft von 1900 bis 1945. Er behandelte aus sportgeschichtlicher Warte Themen wie die "Personalpolitik an der Deutschen Hochschule für Leibesübungen", den Ursprung einer Theorie der Leibeserziehung, eine Ideengeschichte der Sportwissenschaft von 1900 bis 1914, Klassikern und Wegbereitern der Sportwissenschaft sowie der Sportwissenschaft in der Weimarer Republik und im Nationalsozialismus. In sportphilosophischer Hinsicht befasste er sich unter anderem mit Aspekten der Sportethik, mit der Frage "Was ist Sport?", der Sportphilosophie bis 1945 und war Mitverfasser des 1996 von Herbert Haag veröffentlichten Sportphilosophie-Handbuches.

Court war Mitgründer der Deutschen Gesellschaft für Geschichte der Sportwissenschaft, Vorsitzender und Herausgeber der Jahrbücher der Gesellschaft.

Weblinks
 Webseite bei der Erziehungswissenschaftlichen Fakultät der Universität Erfurt
 Jürgen Court im Who is Who der Universität Erfurt (wird seit 2020 nicht mehr aktualisiert)

Einzelnachweise

Sportwissenschaftler
Hochschullehrer (Deutsche Sporthochschule Köln)
Hochschullehrer (Universität Erfurt)
Deutscher
Geboren 1961
Mann
Absolvent der Universität zu Köln


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Each Fall and Spring, Pantone the leading authority in color, comes out with the upcoming season's color trends and announces the hot colors for the year. Pantone suggests that Poppy Red, Monaco Blue, Grayed Jade, Tender Shoots, Lemon Zest, Tidal Foam, Emerald, African Violet, Dusk Blue, Sunflower, Linen, and Alloy will be colors to use in 2013. It's not only about those shades occurring in trend now but how they have changed over the seasons. Blues are turning away from the watery hues of the past and becoming more of a basic building block, assuming the role that black used to play. Color seems to be touching everything, even neutrals like sand and beige. Neutrals have transformed and the new calling is for basic tones that are shaded and imbued with peaceful and beautiful color. Brights continue to evolve as they are paired together or weaved into larger groups, exuding drama and newness.
Along with colors we are seeing other décor trends pop up onto the wedding event trend forecast. Weddings are becoming more personal and will be characterized by romanticism, vintage, and the 1920's. Bird wedding themes are back in style and will be one of the 2013 wedding trends. We will see charming little nests, vintage inspired bird cages and pretty birds from all flocks of life in 2013 wedding decorations and wedding fashion kamagra 100mg tablets.
Technology is also playing a big role in the event trend industry for this upcoming year, technology has the ability to advance and change the face of your event. Google spreadsheets (spreadsheets.google.com) can be used to track your event details in a visible document that is usable by dispersed event planning teams (including your suppliers). RM Creative Events Management, Inc. has created an electronic planning workbook for their weddings and bar/bat mitzvahs clients, giving clients and easy to use format to keep all planning information in one place that can be easily shared with their event planner.
For corporate events and tradeshows, event hosts can log-on (www.log-on.nl) and the guests can use their mobile phones to view tradeshow and event applications for attendees including: the event agenda, product directories, event feedback and surveys, polling, announcements, networking, travel information, and more. The only issue we have seen with this is not everyone has a smart phone, event hosts need to make sure to have print out's available or another way for all attendees to access the information.
The usage of flat-panel screen TVs for your electronic signage helps eliminate "sign-clutter". Also, converting your event program into digital form, allows you to loop your program on the electronic signage, eliminate the expense of producing paper programs and waste. Using the electronic signage is an easy way to add more color to the room. Some audio visual companies have developed a way to merge two or three projection screens together and have them display a single image but allow the images to change on any of the screens without the audience realizing the different screens. The new projection technology can jazz up the look and feel of the event.
Now more than ever people are relying on Special Event Planners to coordinate and execute their events. The trend of event coordination is becoming bigger than ever. With everyone's busy schedules and hectic lifestyles it makes sense to hire RM Creative Events Management to plan and manage your event for you. We are in the know of what will be trending for the upcoming year, whether it's color, fabric, venue spaces, technology, entertainment, invitations and more. RM Creative Events can make planning your event less of a hassle, and we can create a simply elegant event.
Here is a visual that shows how RM Creative Events would use the new projection image technology and to show you how it helps add color to the event space.


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Per Eklund (Estocolmo, 12 de novembro de 1980) é um lutador sueco de artes marciais mistas da categoria dos Pesos Leves. Ele foi o primeiro de sua nacionalidade a competir no Ultimate Fighting Championship, e possui faixa roxa em  Jiu-Jitsu Brasileiro.

No  UFC 80, lutou contra Sam Stout e perdeu por decisão unânime. No UFC 89 teve a chance de lutar com  Samy Schiavo vencendo por finalização.

Histórico

Referências

Ligações externas

Lutadores de MMA da Suécia
Naturais de Estocolmo


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Holly Holm not buying into Amanda Nunes' stock: 'She hasn't faced Holly'
By Cole Shelton 3 weeks ago
Holly Holm is once again fighting for UFC gold. In the co-main event of UFC 239, the former bantamweight champion will take on current champ-champ, Amanda Nunes for the bantamweight title.
Although Nunes has been the bantamweight champion since UFC 200. But, Holly Holm isn't buying into her stock that she is unbeatable. Rather, she knows she has yet to fight someone like herself.
"In order to have two belts in two different divisions, you have to be a special something," Holm said to MMA Junkie. "But she hasn't faced Holly and that's the bottom line.
"This is a whole different fight," Holm continued. "Is she great? Yes. Am I up against a great fighter? Yeah. It wouldn't be a big expectant title fight, she wouldn't be where she's at if she hadn't done great things, so yes, it's a very big fight but I'm ready for it I've been training my butt off and that's what I'm doing. I'm working for a win."
Something Holly Holm is sick of hearing is the fact that Holm lost to Cris Cyborg while Nunes beat her. She knows MMA Math doesn't work as styles make fights, and the 37-year-old is confident she leaves Las Vegas with the belt.
"When you go out for a slugfest, anybody who lands that is going to go down," Holm said. "Every fight makes a difference, the Cyborg and my fight is different than the fight between Amanda and Cyborg. You can look at things in a lot of different ways. You can look at something like Shevchenko and Nunes where Shevchenko gave her a hard time where she was so technical.
"And then you look at someone like Cyborg, Shevchenko is a champ at 125 and Cyborg is champ at 145 and (Nunes and Shevchenko) fought at 135," Holm continued. "And you know Amanda is knocking out the bigger one and having a hard time with the lighter one. So you can't ever look at a fight and be like oh, she did this in that fight so she's going to do that to me. Every fighter has a different style and nobody is the same. I'm not Cyborg, I'm not Shevchenko, I'm Holly Holm."
Cole Shelton
Cole Shelton covers MMA for MyMMANews.com and BJPENN.com, while previously being the lead MMA writer for FanCred Sports.
Tags: Amanda Nunes, holly holm, UFC, UFC 239
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Showcase your iPhone X and XS in this slim Insignia clear case. It's made with durable TPU that provides protection with minimum bulk, and its black border shields the phone's edges while adding an accent color. This Insignia clear case has precise cutouts that provide ready access to the device camera and charging ports.
"This case is fine...This was under $15...My husband purchased a new phone, this case was perfect because he wanted clear case with little color, nice strong...Great case since there's no iPhone except apple cases this one does the job"
Ensure your iPhone 7 or 8 stays in pristine condition with this Insignia phone case. Its hardshell design offers full-coverage protection against damage from drops and impacts while still allowing full access to the camera and ports. This Insignia phone case's sleek profile easily slides in and out of pockets and bags.
"I love this case...I love this cover...Everybody loves this phone case and I have received a lot of commplients on this case...Fits perfectly and does protect as she has dropped her phone a couple times already"
Use and protect your iPhone XS in a sophisticated way with this kate spade new york gift set. Its clear hardshell case with white and gold detailing shields your phone from the elements and adds a touch of luxury. The white and gold stability ring of this kate spade new york gift set provides an extra-secure grip.
"One of my biggest needs was a compartment for an over the ear headphone I recently bought (at BB), another compartment for my mini tablet and enough space for my books and folders from college."


It appears as if homeowners across the country have begun to realize their garage door doesn't only provide an access to their garage but also plays an important role in how their home exterior looks and how strong its curb appeal is. Maybe you've noticed an increase in presence of carriage house style doors around the block, a trend indicative of this notion. So what exactly are these and why should you consider installing one yourself?
Adorned with delicate woodwork forming planking in a variety of patterns, carriage house garage doors provide a sophisticated, vintage look set to turn the heads of your neighbors when they walk by. The large handles and window inserts come in various shapes and styles and show the homeowner has an eye for interesting design. For example, if you're selling your home, a potential buyer might wonder what else has a unique touch around your house.
What's so great about modern carriage house garage doors is their compatibility with all current overhead systems. Some homeowners tend to think they are synonymous with other swing-out wooden doors out there, but they'd be surprised to know you can work them via a remote just like any other regular door on the market. You basically get the same convenience as you would with a standard wooden door but with a more stylish appearance. In addition, customization options from material choice to insulation are all available as per usual.
As mentioned above, you have complete freedom in choosing from an array of colors, materials, features, and sizes to match your existing architecture. If you are after a little guidance, give our team of professionals at Garage Door Repair Lake Mary a call to discuss your options with a specialist. You ought to think about the correct fit for your exterior design and a viable color match. Moreover, certain features such as windows and handles can also play a major role in the way your door looks and functions.


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