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In vector calculus, del is a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field, the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.

Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product of scalars, dot product, and cross product, respectively, of the del "operator" with the field. These formal products do not necessarily commute with other operators or products.

Definition[link]

In the three-dimensional Cartesian coordinate system R³ with coordinates (x, y, z), del is defined in terms of partial derivative operators as

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla = \mathbf{\hat{x}} {\partial \over \partial x} + \mathbf{\hat{y}} {\partial \over \partial y} + \mathbf{\hat{z}} {\partial \over \partial z}

where Failed to parse (Missing texvc executable; please see math/README to configure.): \{\mathbf{\hat{x}}, \mathbf{\hat{y}},\mathbf{\hat{z}} \}

are the unit vectors in their respective directions.

Though this page chiefly treats del in three dimensions, this definition can be generalized to the n-dimensional Euclidean space Rⁿ. In the Cartesian coordinate system with coordinates (x₁, x₂, ..., x_n), del is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla = \sum_{i=1}^n \hat e^i {\partial \over \partial x_i}

where Failed to parse (Missing texvc executable; please see math/README to configure.): \{ \hat e^i: 1\leq i\leq n\}

is the standard basis in this space.

More compactly, using the Einstein summation notation, del is written as

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla = \hat e^i \,\partial_i

Del can also be expressed in other coordinate systems, see for example del in cylindrical and spherical coordinates.

Notational uses[link]

Del is used as a shorthand form to simplify many long mathematical expressions. It is most commonly used to simplify expressions for the gradient, divergence, curl, directional derivative, and Laplacian.

Gradient[link]

The vector derivative of a scalar field f is called the gradient, and it can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla f = {\partial f \over \partial x} \mathbf{\hat{x}} + {\partial f \over \partial y} \mathbf{\hat{y}} + {\partial f \over \partial z} \mathbf{\hat{z}}

It always points in the direction of greatest increase of f, and it has a magnitude equal to the maximum rate of increase at the point—just like a standard derivative. In particular, if a hill is defined as a height function over a plane h(x,y), the 2d projection of the gradient at a given location will be a vector in the xy-plane (sort of like an arrow on a map) pointing along the steepest direction. The magnitude of the gradient is the value of this steepest slope.

In particular, this notation is powerful because the gradient product rule looks very similar to the 1d-derivative case:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla(f g) = f \nabla g + g \nabla f

However, the rules for dot products do not turn out to be simple, as illustrated by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla (\vec u \cdot \vec v) = (\vec u \cdot \nabla) \vec v + (\vec v \cdot \nabla) \vec u + \vec u \times (\nabla \times \vec v) + \vec v \times (\nabla \times \vec u)

Divergence[link]

The divergence of a vector field Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{v}(x, y, z) = v_x \mathbf{\hat{x}} + v_y \mathbf{\hat{y}} + v_z \mathbf{\hat{z}}

is a scalar function that can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,\vec v = {\partial v_x \over \partial x} + {\partial v_y \over \partial y} + {\partial v_z \over \partial z} = \nabla \cdot \vec v

The divergence is roughly a measure of a vector field's increase in the direction it points; but more accurately, it is a measure of that field's tendency to converge toward or repel from a point.

The power of the del notation is shown by the following product rule:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \cdot (f \vec v) = f \nabla \cdot \vec v + \vec v \cdot \nabla f

The formula for the vector product is slightly less intuitive, because this product is not commutative:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \cdot (\vec u \times \vec v) = \vec v \cdot \nabla \times \vec u - \vec u \cdot \nabla \times \vec v

Curl[link]

The curl of a vector field Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{v}(x, y, z) = v_x\mathbf{\hat{x}} + v_y\mathbf{\hat{y}} + v_z\mathbf{\hat{z}}

is a vector function that can be represented as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\;\vec v = \left( {\partial v_z \over \partial y} - {\partial v_y \over \partial z} \right) \mathbf{\hat{x}} + \left( {\partial v_x \over \partial z} - {\partial v_z \over \partial x} \right) \mathbf{\hat{y}} + \left( {\partial v_y \over \partial x} - {\partial v_x \over \partial y} \right) \mathbf{\hat{z}} = \nabla \times \vec v

The curl at a point is proportional to the on-axis torque to which a tiny pinwheel would be subjected if it were centered at that point.

The vector product operation can be visualized as a pseudo-determinant:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times \vec v = \left|\begin{matrix} \mathbf{\hat{x}} & \mathbf{\hat{y}} & \mathbf{\hat{z}} \\[2pt] {\frac{\partial}{\partial x}} & {\frac{\partial}{\partial y}} & {\frac{\partial}{\partial z}} \\[2pt] v_x & v_y & v_z \end{matrix}\right|

Again the power of the notation is shown by the product rule:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times (f \vec v) = (\nabla f) \times \vec v + f \nabla \times \vec v

Unfortunately the rule for the vector product does not turn out to be simple:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times (\vec u \times \vec v) = \vec u \, \nabla \cdot \vec v - \vec v \, \nabla \cdot \vec u + (\vec v \cdot \nabla) \vec u - (\vec u \cdot \nabla) \vec v

Directional derivative[link]

The directional derivative of a scalar field f(x,y,z) in the direction Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{a}(x,y,z) = a_x \mathbf{\hat{x}} + a_y \mathbf{\hat{y}} + a_z \mathbf{\hat{z}}

is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{a}\cdot\mbox{grad}\,f = a_x {\partial f \over \partial x} + a_y {\partial f \over \partial y} + a_z {\partial f \over \partial z} = (\vec a \cdot \nabla) f

This gives the change of a field f in the direction of a. In operator notation, the element in parentheses can be considered a single coherent unit; fluid dynamics uses this convention extensively, terming it the convective derivative—the "moving" derivative of the fluid.

Laplacian[link]

The Laplace operator is a scalar operator that can be applied to either vector or scalar fields; it is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta = {\partial^2 \over \partial x^2} + {\partial^2 \over \partial y^2} + {\partial^2 \over \partial z^2} = \nabla \cdot \nabla = \nabla^2

The Laplacian is ubiquitous throughout modern mathematical physics, appearing in Laplace's equation, Poisson's equation, the heat equation, the wave equation, and the Schrödinger equation—to name a few.

Tensor derivative[link]

Del can also be applied to a vector field with the result being a tensor. The tensor derivative of a vector field Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{v}

is a 9-term second-rank tensor, but can be denoted simply as Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \otimes \vec{v}

, where Failed to parse (Missing texvc executable; please see math/README to configure.): \otimes

represents the dyadic product. This quantity is equivalent to the transpose of the Jacobian matrix of the vector field with respect to space.

For a small displacement Failed to parse (Missing texvc executable; please see math/README to configure.): \delta \vec{r} , the change in the vector field is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): \delta \vec{v} = (\nabla \otimes \vec{v}) \sdot \delta \vec{r}

Second derivatives[link]

DCG chart: A simple chart depicting all rules pertaining to second derivatives. D, C, G, L and CC stand for divergence, curl, gradient, Laplacian and curl of curl, respectively. Arrows indicate existence of second derivatives. Blue circle in the middle represents curl of curl, whereas the other two red circles(dashed) mean that DD and GG do not exist.

When del operates on a scalar or vector, generally a scalar or vector is returned. Because of the diversity of vector products (scalar, dot, cross) one application of del already gives rise to three major derivatives: the gradient (scalar product), divergence (dot product), and curl (cross product). Applying these three sorts of derivatives again to each other gives five possible second derivatives, for a scalar field f or a vector field v; the use of the scalar Laplacian and vector Laplacian gives two more:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{grad}\,f ) = \nabla \cdot (\nabla f)

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\,(\mbox{grad}\,f ) = \nabla \times (\nabla f)

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta f = \nabla^2 f

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{grad}\,(\mbox{div}\, \vec v ) = \nabla (\nabla \cdot \vec v)

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{curl}\,\vec v ) = \nabla \cdot (\nabla \times \vec v)

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\,(\mbox{curl}\,\vec v ) = \nabla \times (\nabla \times \vec v)

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta \vec v = \nabla^2 \vec v

These are of interest principally because they are not always unique or independent of each other. As long as the functions are well-behaved, two of them are always zero:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{curl}\,(\mbox{grad}\,f ) = \nabla \times (\nabla f) = 0

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{curl}\,\vec v ) = \nabla \cdot \nabla \times \vec{v} = 0

Two of them are always equal:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mbox{div}\,(\mbox{grad}\,f ) = \nabla \cdot (\nabla f) = \nabla^2 f = \Delta f

The 3 remaining vector derivatives are related by the equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla \times \nabla \times \vec{v} = \nabla (\nabla \cdot \vec{v}) - \nabla^2 \vec{v}

And one of them can even be expressed with the tensor product, if the functions are well-behaved:

Failed to parse (Missing texvc executable; please see math/README to configure.): \nabla ( \nabla \cdot \vec{v} ) = \nabla \cdot (\nabla \otimes \vec{v})

Precautions[link]

Most of the above vector properties (except for those that rely explicitly on del's differential properties—for example, the product rule) rely only on symbol rearrangement, and must necessarily hold if del is replaced by any other vector. This is part of the tremendous value gained in representing this operator as a vector in its own right.

Though you can often replace del with a vector and obtain a vector identity, making those identities intuitive, the reverse is not necessarily reliable, because del does not often commute.

A counterexample that relies on del's failure to commute:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbf u \cdot \mathbf v) f = (\mathbf v \cdot \mathbf u) f

Failed to parse (Missing texvc executable; please see math/README to configure.): (\nabla \cdot \mathbf v) f \ne (\mathbf v \cdot \nabla) f

Failed to parse (Missing texvc executable; please see math/README to configure.): (\nabla \cdot \mathbf v) f = (\frac{\part v_x}{\part x}+\frac{\part v_y}{\part y}+\frac{\part v_z}{\part z})f =

Failed to parse (Missing texvc executable; please see math/README to configure.): = \frac{\part v_x}{\part x}f+\frac{\part v_y}{\part y}f+\frac{\part v_z}{\part z}f

Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbf v \cdot \nabla) f = (v_x \frac{\part}{\part x}+v_y \frac{\part}{\part y}+v_z \frac{\part}{\part z})f =

Failed to parse (Missing texvc executable; please see math/README to configure.): = v_x \frac{\part f}{\part x}+v_y \frac{\part f}{\part y}+v_z \frac{\part f}{\part z}

A counterexample that relies on del's differential properties:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\nabla x) \times (\nabla y) = (\mathbf{\hat x} \frac{\part x}{\part x}+\mathbf{\hat y} \frac{\part x}{\part y}+\mathbf{\hat z} \frac{\part x}{\part z}) \times (\mathbf{\hat x} \frac{\part y}{\part x}+\mathbf{\hat y} \frac{\part y}{\part y}+\mathbf{\hat z} \frac{\part y}{\part z}) =

Failed to parse (Missing texvc executable; please see math/README to configure.): = (\mathbf{\hat x} \cdot 1 +\mathbf{\hat y} \cdot 0+\mathbf{\hat z} \cdot 0) \times (\mathbf{\hat x} \cdot 0+\mathbf{\hat y} \cdot 1+\mathbf{\hat z} \cdot 0) =

Failed to parse (Missing texvc executable; please see math/README to configure.): = \mathbf{\hat x} \times \mathbf{\hat y} = \mathbf{\hat z}

Failed to parse (Missing texvc executable; please see math/README to configure.): (\mathbf u x )\times (\mathbf u y) = x y (\mathbf u \times \mathbf u) = x y \mathbf 0 = \mathbf 0

Central to these distinctions is the fact that del is not simply a vector; it is a vector operator. Whereas a vector is an object with both a precise numerical magnitude and direction, del does not have a precise value for either until it is allowed to operate on something.

For that reason, identities involving del must be derived with care, using both vector identities and differentiation identities such as the product rule.

See also[link]

• Del in cylindrical and spherical coordinates
• Maxwell's equations
• Navier–Stokes equations
• Table of mathematical symbols
• Vector calculus identities

References[link]

• Schey, H. M. (1997). Div, Grad, Curl, and All That: An Informal Text on Vector Calculus. New York: Norton. ISBN 0-393-96997-5. 
• Miller, Jeff. "Earliest Uses of Symbols of Calculus". http://jeff560.tripod.com/calculus.html. 
• "History of Nabla". netlib.org. January 26, 1998. http://www.netlib.org/na-digest-html/98/v98n03.html#2. 

External links[link]

• A survey of the improper use of ∇ in vector analysis (1994) Tai, Chen

Lana Del Rey
Del Rey at a promotional event in Seattle
Background information
Birth name	Elizabeth Woolridge Grant
Also known as	Lizzy Grant Lana Rey Del Mar May Jailer
Born	(1986-06-21) June 21, 1986 (age 26)[1] New York City, New York, United States
Origin	Lake Placid, New York, United States
Genres	Indie pop,[2] adult alternative,[2] chamber pop,[3] sadcore[4]
Occupations	Singer-songwriter, fashion model
Instruments	Vocals, guitar[5]
Years active	2007–present
Labels	Interscope, Polydor, Stranger
Website	lanadelrey.com

Elizabeth Woolridge Grant^[6] (born June 21, 1986), better known by her stage name Lana Del Rey, is an American singer-songwriter. Raised in upstate New York, Del Rey moved to New York City at age eighteen, where she attended college and began writing music and performing in clubs.

In 2008, Del Rey contracted with an independent label and recorded a self-titled debut album which was briefly available on iTunes in 2010; Del Rey ultimately bought back the rights to the album and it was withdrawn soon after.

In June 2011, she released the song "Video Games" on the Internet, accompanied by a self-made music video that went viral in the following months. The song was later released as a single in October, leading up to Del Rey's major-label debut album, Born to Die, which was released on January 31, 2012 through Interscope Records. Born to Die debuted at number one in seven countries, including the United Kingdom^[7] and Australia. The album has spawned two worldwide top 10 hits: "Video Games" and "Born to Die".

Del Rey's music has been noted for its cinematic sound and its references to various aspects of pop culture, particularly that of 1950s and '60s Americana.^[8] Del Rey has been described as a "self-styled gangsta Nancy Sinatra",^[9] and cites Britney Spears,^[10][11][12] Eminem,^[13][10] and Antony and the Johnsons amongst her musical influences.^[10]

Biography[link]

Early years[link]

Del Rey was born Elizabeth Grant in New York City and grew up in Lake Placid, New York.^[14][15] When she was 14, she attended Kent School, a boarding school in Connecticut.^[16][17] She has Scottish ancestry, and is the daughter of domain investor Rob Grant, who supported her in her early career as a singer.^{[18][19][20][21]} Del Rey attended Fordham University in New York City, studying philosophy.^[22]

At age 18, her uncle taught her how to play guitar, beginning with basic chords: "It was G, C, A, D minor, A minor and some diminished chord as well. Some trick, some shortcut," Del Rey recalled. "I realized I could probably write a million songs with those six chords, so I moved to New York and I took a couple of years to just write whatever I wanted."^[5] She began performing in clubs while living in the city.

Her stage name was discussed in a Vogue interview, in which she said, "I wanted a name I could shape the music towards [...] I was going to Miami quite a lot at the time, speaking a lot of Spanish with my friends from Cuba – Lana Del Rey reminded us of the glamour of the seaside. It sounded gorgeous coming off the tip of the tongue."^[23] The name is reportedly an amalgam of the actress Lana Turner, and the 1980's automobile Ford Del Rey. ^[24]

"I wanted to be part of a high-class scene of musicians. It was half-inspired because I didn't have many friends, and I was hoping that I would meet people and fall in love and start a community around me, the way they used to do in the '60s."^[25]

Del Rey first released a three-track EP titled Kill Kill in October 2008 under the name Lizzy Grant, featuring the tracks "Kill Kill", "Yayo" and "Gramma (Blue Ribbon Sparkler Trailer Heaven)".^[26]

[edit] 2010: Lana Del Ray A.K.A. Lizzy Grant

Del Rey later released her first full-length studio album titled Lana Del Ray A.K.A. Lizzy Grant [sic] in January 2010.^[27] It was the singer's first professionally produced album, released under Lizzy Grant on an independent label with producer David Kahne.^[28] Del Rey stated that "David asked to work with me only a day after he got my demo. He is known as a producer with a lot of integrity and who had an interest in making music that wasn't just pop."^[29] Her father, Robert Grant, helped with the marketing of the album,^[30] which was available for purchase on iTunes for a brief period before being withdrawn. According to David Kahne, who produced Grant, Grant bought the rights back from her label, 5 Points, as she wanted it out of circulation to "…stifle future opportunities to distribute it – an echo of rumors that the action was part of a calculated strategy."^[31]

[edit] 2011–present: Born to Die

Lana Del Rey performing at Paradiso, Amsterdam.

Later in June 2011, Del Rey was signed with Stranger Records,^[32] to release her debut single "Video Games";^[32] in October 2011, she signed a joint deal with Interscope Records and Polydor.^{[5][33][34][35]} In October 2011, she won the Q award for "Next Big Thing". Del Rey's song "Video Games" was featured for the first time on The CW's TV-Series Ringer on September 27, 2011.^[36] Del Rey also promoted the album in a number of live appearances, including a show at the Bowery Ballroom, where, according to Eliot Glazer of New York, "the polarizing indie hipstress brought her 'gangsta Nancy Sinatra' swagu."^[37] Rolling Stone commented that, despite Del Rey being nervous and anxious while performing her songs live, she "sang with considerable confidence", although they noted that "her transitions ...could be rather jarring."^[38] Del Rey also performed "Video Games" on Dutch television program De Wereld Draait Door,^[39] on British music television show Later... with Jools Holland,^[40] and on an intimate show at Chateau Marmont in West Hollywood, California.^[41]

Born to Die was released on January 27, 2012 in Ireland,^[42] January 30, 2012, in the UK, and on January 31, 2012 worldwide.^[43]

Del Rey performed two songs on Saturday Night Live on January 14, 2012 to a warm reception from the audience, but mixed reviews from critics and the general public. NBC Nightly News anchor Brian Williams called Del Rey's performance "one of the worst outings in SNL history". Del Rey's performance was defended by the evening's program guest host, actor Daniel Radcliffe, despite not having seen her performance.^[44] He said in part: "It was unfortunate that people seemed to turn on her so quickly [...] I don't think [the performance] warranted anywhere near that reaction." Del Rey had earlier defended her spot on the program, saying: "I'm a good musician [...] I have been singing for a long time, and I think that [SNL creator] Lorne Michaels knows that [...] it's not a fluke decision."^[45] On February 4, 2012, Kristen Wiig appeared on the Weekend Update segment on Saturday Night Live parodying Del Rey and poking fun at the backlash.

The second single and title track "Born to Die" was released on December 3, 2011.^[46] The music video for it leaked on December 14, 2011,^[47] and was based on a concept created by the singer, while being directed by Yoann Lemoine.^[48]

In January 2012, Del Rey revealed that she recently bought back the rights to her 2010 album Lana Del Ray A.K.A. Lizzy Grant and will re-release it in the summer of 2012 under Interscope Records and Polydor.^[49] Contrary to Grant's press statement, her previous label (5 Point Records), and producer David Kahne have both stated that she bought the rights to the album when she and the label parted company, due to the offer of a new deal, in April 2010.^[50][51] On January 4, 2012, it was reported she had signed a deal with NEXT Model Management agency.^[52] In May 2012, Del Rey confirmed the song "National Anthem" as the fourth single from her album Born to Die. ^{[53] [54]} On May 30th, 2012, Del Rey's supposed debut album "Sirens" was leaked online under the name "May Jailer". The 15 track album includes the previously leaked song "A Star for Nick."

Artistry[link]

Music

She has been described as a "self-styled gangsta Nancy Sinatra",^[9] Del Rey is known to write and produce most of her own material and covers genres from Hip-Hop and Indie. Having first been discovered from posting viral videos of herself singing on the internet she quickly grew a significant fan base. She has been noted for using her allure to the celebrity lifestyle as an inspiration in itself, whilst at the same time maintaining an aura of mystique, this has reflected in the melodies and vocals she produces. Her sound as well as her videography has been described as eccentric, over the top and at times wild. However Noah Levy, senior news editor at In Touch Weekly magazine noted that her dedication and talent is undeniable, quoted as saying "I think she cares about the art that she is creating. I don't think that is fake at all."^[55]

Voice

Del Rey possesses a wide^[56] contralto vocal range,^{[57][58][59][60]} which has been described as unique, captivating and highly emotive,^[60] being able to transcend from sounding high and girlish in her timbre, down to a low and jazzy sound with great ease, although both these areas of the voice can be conflicting in their sound and polarise opinion.^[57]

When recording in the studio Del Rey is known for vocal multi layering, double tracking and overlays which has it has been noted is difficult for her to replicate within a live setting, especially with the lack of backing singers to fill out the original vocal style.^[59].

Influences

Del Rey cites Britney Spears,^[11][12] Elvis Presley, Antony and the Johnsons, Frank Sinatra ^[13] and Eminem amongst her musical influences. "[I really] just like the masters of every genre", she told BBC journalist Jo Whiley.^[61]

Discography[link]

Albums[link]

• Lana Del Ray A.K.A. Lizzy Grant (2010)
• Born To Die (2012)

Awards and nominations[link]

References[link]

External links[link]

Wikimedia Commons has media related to: Lana Del Rey

• Official website
• Lana Del Rey at the Internet Movie Database
• Lana Del Rey talks influences with BEAT

Michael Del Zotto
Born	(1990-06-24) June 24, 1990 (age 22) Stouffville, ON, CAN
Height	6 ft 0 in (1.83 m)
Weight	193 lb (88 kg; 13 st 11 lb)
Position	Defence
Shoots	Left
NHL team	New York Rangers
NHL Draft	20th overall, 2008 New York Rangers
Playing career	2009–present

Michael Del Zotto (born June 24, 1990) is a Canadian professional ice hockey defenceman currently playing for the New York Rangers.

Playing career[link]

Early career[link]

Del Zotto began his hockey career with the Stouffville Clippers A of the Whitchurch-Stouffville Minor Hockey Association (WSMHA). He then played for the Richmond Hill Stars and the Markham Waxers in the OMHA's Eastern AAA League (OMHA).^[1]

Junior[link]

During his first season with the Oshawa Generals in the Ontario Hockey League (OHL), Del Zotto helped his home province of Ontario win the gold medal in the 2007 Canada Winter Games.^[1]

In his second season with Oshawa, Del Zotto's 63 points ranked him third among defencemen in the OHL. He made his second OHL playoff appearance when the Oshawa Generals got to the third round in the 2008 OHL playoffs. Del Zotto was chosen for the 2008 CHL Top Prospects Game.^[1]

On January 8, 2009, Del Zotto was part of a trade that would send him, along with teammates John Tavares and Daryl Borden, to the London Knights for prospects Christian Thomas, Scott Valentine, Michael Zador and six draft picks.^[2]

Professional[link]

Del Zotto was selected 20th overall by the New York Rangers in the 2008 NHL Entry Draft.^[3] He signed a contract with the Rangers on May 26, 2009.^[4]

On October 2, 2009, Del Zotto made his NHL debut against the Pittsburgh Penguins. At age 19, he became the youngest defenceman in Rangers history to play on an opening night. Del Zotto scored his first NHL goal the next day, against Pascal Leclaire of the Ottawa Senators, in the Rangers' home opener. Del Zotto proved he was an asset to the team and, as a result, averaged 20–25 minutes per game.

Del Zotto was awarded the NHL's Rookie of The Month for October 2009 after posting 12 points in his first 14 professional games.^[5] After his first year in the league, Del Zotto was named to the 2010 NHL All-Rookie Team.^[6]

On January 31, 2011, the New York Rangers recalled Del Zotto from the Connecticut Whale back to the NHL.

Personal life[link]

Del Zotto wears number 4 in homage to Boston Bruins great Bobby Orr.^[1]

For high school, he attended St. Brother Andre Catholic High School in Markham, Ontario, then later on attended St. Andrew's College in Aurora, Ontario.

His father, Steven, was a football player at York University (1982–1985) and was drafted as a wide receiver by the Toronto Argonauts in the 8th round (66th overall) of the 1986 CFL Draft.

Career statistics[link]

References[link]

External links[link]

• Michael Del Zotto's career stats at The Internet Hockey Database
• Michael Del Zotto at TSN.ca
• Michael Del Zotto's NHL player profile

Rafael Nadal

Rafael Nadal in 2012
Full name	Rafael Nadal Parera
Country	Spain
Residence	Manacor, Majorca, Balearic Islands, Spain
Born	(1986-06-03) 3 June 1986 (age 26) Manacor, Majorca, Balearic Islands, Spain
Height	1.85 m (6 ft 1 in)
Weight	85 kg (190 lb; 13.4 st)
Turned pro	2001
Plays	Left-handed (two-handed backhand)
Career prize money	$48,433,332
Singles
Career record	574–120 (82.71%)
Career titles	49
Highest ranking	No. 1 (18 August 2008)
Current ranking	No. 2 (28 May 2012)[1]
Grand Slam Singles results
Australian Open	W (2009)
French Open	W (2005, 2006, 2007, 2008, 2010, 2011)
Wimbledon	W (2008, 2010)
US Open	W (2010)
Other tournaments
Tour Finals	F (2010)
Olympic Games	Gold medal (2008)
Doubles
Career record	97–59
Career titles	8
Highest ranking	No. 26 (8 August 2005)
Current ranking	No. 62 (28 May 2012)[2]
Grand Slam Doubles results
Australian Open	3R (2004, 2005)
Wimbledon	2R (2005)
US Open	SF (2004)
Last updated on: 28 May 2012.

Olympic medal record
Competitor for  Spain
Men's Tennis
Gold	2008 Beijing	Singles

Rafael "Rafa" Nadal Parera (Catalan: [rəˈfɛɫ nəˈðaɫ pəˈɾeɾə]; Spanish: [rafaˈel naˈðal paˈɾeɾa]) (born 3 June 1986) is a Spanish professional tennis player and a former World No. 1. As of 28 May 2012 (2012 -05-28)^[update], he is ranked No. 2 by the Association of Tennis Professionals (ATP). He is widely regarded as one of the greatest players of all time;^[5][6][7] his success on clay has earned him the nickname "The King of Clay", and has prompted many experts to regard him as the greatest clay court player of all time.^[8][9][10]

Nadal has won ten Grand Slam singles titles, including a record six French Open titles (tied with Bjorn Borg), the 2008 Olympic gold medal in singles, a record 21 ATP World Tour Masters 1000 tournaments, and also was part of the Spain Davis Cup team that won the finals in 2004, 2008, 2009 and 2011. He completed the Career Grand Slam by winning the 2010 US Open, being the seventh player in history, and the youngest in the open era, to achieve it. He is the second male player to complete the Career Golden Slam (winner of the four grand slams and the Olympic Gold medal) after only Andre Agassi.

Nadal had a 32-match winning streak in 2008, starting at the 2008 Masters Series Hamburg to the 2008 Western & Southern Financial Group Masters and Women's Open, which included titles at Hamburg, the French Open (where he did not drop a set), Queen's Club, his first title at Wimbledon, and the Rogers Cup. In 2012, by winning the Monte-Carlo Masters, he became the only player to have won eight consecutive editions in any tournament during history of tennis, and only the 2nd player to win a single tournament for a total of eight times during Open Era. Nadal was ranked world No. 2, behind Roger Federer, for a record 160 consecutive weeks before earning the top spot, which he held from 18 August 2008 to 5 July 2009.^[11] He regained the world No.1 ranking on 7 June 2010, after winning his fifth French Open title.^[12] He held it until 3 July 2011, when Novak Djokovic replaced him as world No. 1. Nadal has held the No. 2 ranking for an ATP record 235 weeks (as of 21 May 2012).

Early life[link]

Rafael Nadal was born in Manacor, Majorca, Spain to Sebastián Nadal, a businessman who owns an insurance company, a glass and window company, Vidres Mallorca, and manages his own restaurant, Sa Punta. His mother is Ana María Parera, a housewife. He has a younger sister named María Isabel. His uncle, Miguel Ángel Nadal, is a retired professional footballer, who played for RCD Mallorca, FC Barcelona, and the Spanish national team.^[13] Nadal supports football clubs Real Madrid and RCD Mallorca.^[14] Recognizing that Nadal had a natural talent for tennis, another uncle, Toni Nadal, a former professional tennis player, introduced him to tennis when he was three years old.^[15]

At age eight, Nadal won an under-12 regional tennis championship at a time when he was also a promising football player.^[16] This made Toni Nadal intensify training, and at that time he encouraged Nadal to play left-handed for a natural advantage on the tennis court, as he noticed Nadal played forehand shots with two hands.^[16] When Nadal was 12, he won the Spanish and European tennis titles in his age group and was playing tennis and football all the time.^[16] Nadal's father made him choose between football and tennis so that his school work would not deteriorate entirely. Nadal said: "I chose tennis. Football had to stop straight away."^[16]

When he was 14, the Spanish tennis federation requested that he leave Majorca and move to Barcelona to continue his tennis training. Nadal's family turned down this request, partly because they feared it would hurt his education,^[16] but also because Toni said that "I don't want to believe that you have to go to America, or other places to be a good athlete. You can do it from your home."^[15] The decision to stay home meant that Nadal received less financial support from the federation; instead, Nadal's father covered the costs. In May 2001, he defeated former Grand Slam champion Pat Cash in a clay-court exhibition match.^[13]

At 15, he turned pro.^[17] Nadal participated in two events on the ITF junior circuit. In 2002, at the age of 16, Nadal reached the semifinals of the Boy's Singles tournament at Wimbledon, in his first ITF junior event.^[18]

By the age of 17, he beat Roger Federer the first time they played and became the youngest man to reach the third round at Wimbledon since Boris Becker. At 18, he helped pace Spain over the US in the junior Davis Cup in his second, and final, appearance on the ITF junior circuit. At 19, Nadal won the French Open the first time he played it, a feat not accomplished in Paris for more than 20 years. He eventually won it the first four times he played at Roland Garros.^[17] In 2003, he had won the ATP Newcomer of the Year Award. Early in his career, Nadal picked up the trademark habit of biting the trophies he won.^[19]

Tennis career[link]

2002–2004[link]

In April 2002, at 15 years and 10 months, the world No. 762 Nadal won his first ATP match, defeating Ramón Delgado, and became the ninth player in the open era to do so before the age of 16.^[20] The following year, Nadal won two Challenger titles and finished the year in the top 50. At his Wimbledon debut in 2003, Nadal became the youngest man to reach the third round since Boris Becker in 1984.^[21] During 2004, Nadal played his first match against world No. 1 Roger Federer at the 2004 Miami Masters, and won in straight sets. He is one of the six players that defeated Federer that year (along with Tim Henman, Albert Costa, Gustavo Kuerten, Dominik Hrbatý, and Tomáš Berdych). He missed most of the clay court season, including the French Open, because of a stress fracture in his left ankle.^[13] Nadal, at 18 years and six months, became the youngest player to register a singles victory in a Davis Cup final for a winning nation.^[22] By beating world No. 2 Andy Roddick, he helped Spain clinch the 2004 title over the United States in a 3–2 win. He finished the year ranked world No. 51.

2005[link]

At the 2005 Australian Open, Nadal lost in the 4th round to eventual runner-up Lleyton Hewitt. Two months later, Nadal reached the final of the 2005 Miami Masters, and despite being two points from a straight-sets victory, he was defeated in five sets by world No. 1 Roger Federer. Both performances were considered to be breakthroughs for Nadal.^[23][24]

He then dominated the spring clay court season. He won 24 consecutive singles matches, which broke Andre Agassi's open era record of consecutive match wins for a male teenager.^[25] Nadal won the Torneo Conde de Godó in Barcelona and beat 2004 French Open runner-up Guillermo Coria in the finals of the 2005 Monte Carlo Masters and the 2005 Rome Masters. These victories raised his ranking to world No. 5^[26] and made him one of the favorites at his career-first French Open. On his 19th birthday, Nadal defeated Federer in the 2005 French Open semifinals, being one of only four players who defeated the top-seeded player that year (along with Marat Safin, Richard Gasquet, and David Nalbandian). Two days later, he defeated Mariano Puerta in the final, becoming the second male player to win the French Open on his first attempt since Mats Wilander in 1982: He also became the first teenager to win a Grand Slam singles title since Pete Sampras won the 1990 US Open at age 19.^[13] Winning the French Open improved Nadal's ranking to World No. 3.^[26]

Three days after his victory in Paris, Nadal's 24-match winning streak was snapped in the first round of the grass court Gerry Weber Open in Halle, Germany, where he lost to the German Alexander Waske.^[27] He then lost in the second round of 2005 Wimbledon to Gilles Müller of Luxembourg.

Immediately after Wimbledon, Nadal won 16 consecutive matches and three consecutive tournaments, bringing his ranking to world No. 2 on 25 July 2005.

Nadal started his North American summer hard-court season by defeating Agassi in the final of the 2005 Canada Masters, but lost in the first round of the 2005 Cincinnati Masters. Nadal was seeded second at the 2005 US Open, where he was upset in the third round by World No. 49 James Blake in four sets.

In September, he defeated Coria in the final of the China Open in Beijing and won both of his Davis Cup matches against Italy. In October, he won his fourth ATP Masters Series title of the year, defeating Ivan Ljubičić in the final of the 2005 Madrid Masters. He then suffered a foot injury that prevented him from competing in the year-ending Tennis Masters Cup.^[28]

Both Nadal and Federer won eleven singles titles and four ATP Masters Series titles in 2005. Nadal broke Mats Wilander's previous teenage record of nine in 1983.^[29] Eight of Nadal's titles were on clay, and the remainder were on hard courts. Nadal won 79 matches, second only to Federer's 81. Nadal won the Golden Bagel Award for 2005, with eleven 6–0 sets during the year.^[30] Also, he earned the highest year-end ranking ever by a Spaniard and the ATP Most Improved Player of the Year award.

2006[link]

Nadal missed the Australian Open due to a foot injury.^[31] In February, he lost in the semifinals of the first tournament he played, the Open 13 tournament in Marseille, France. Two weeks later, he handed Roger Federer his first loss of the year in the final of the Dubai Duty Free Men's Open (in 2006, Rafael Nadal and Andy Murray were the only two men who defeated Federer). To complete the spring hard-court season, Nadal was upset in the semifinals of the Pacific Life Open in Indian Wells, California, by James Blake, and was upset in the second round of the 2006 Miami Masters.

On European clay, Nadal won all four tournaments he entered and 24 consecutive matches. He defeated Federer in the final of the Masters Series Monte Carlo in four sets. The following week, he defeated Tommy Robredo in the final of the Open Sabadell Atlántico tournament in Barcelona. After a one-week break, Nadal won the Masters Series Internazionali BNL d'Italia in Rome, defeating Federer in a fifth-set tiebreaker in the final, after saving two match points and equaling Björn Borg's tally of 16 ATP titles won as a teenager. Nadal broke Argentinian Guillermo Vilas's 29-year male record of 53 consecutive clay-court match victories by winning his first round match at the French Open. Vilas presented Nadal with a trophy, but commented later that Nadal's feat was less impressive than his own because Nadal's winning streak covered two years and was accomplished by adding easy tournaments to his schedule.^[32] Nadal went on to play Federer in the final of the French Open. The first two sets of the match were hardly competitive, as the rivals traded 6–1 sets. Nadal won the third set easily and served for the match in the fourth set before Federer broke him and forced a tiebreaker. Nadal won the tiebreaker and became the first player to defeat Federer in a Grand Slam final.^[33]

2006 Roland Garros Champion

Nadal injured his shoulder while playing a quarterfinal match against Lleyton Hewitt at the Artois Championships, played on grass at the Queen's Club in London.^[34] Nadal was unable to complete the match, which ended his 26-match winning streak. Nadal was seeded second at Wimbledon, but was two points from defeat against American qualifier Robert Kendrick in the second round before coming back to win in five sets. In the third round, Nadal defeated world No. 20 Andre Agassi in straight sets at Agassi's last career match at Wimbledon. Nadal also won his next three matches in straight sets, which set up his first Wimbledon final, which was against Federer, who had won this tournament the three previous years. Nadal was the first Spanish man since Manuel Santana in 1966, to reach the Wimbledon final, but Federer won the match in four sets 6–0, 7–6, 6–7, 6–3 to win his fourth consecutive Wimbledon title.

During the lead up to the US Open, Nadal played the two Masters Series tournaments in North America. He was upset in the third round of the Rogers Cup in Toronto and the quarterfinals of the Western & Southern Financial Group Masters in Cincinnati, Ohio. Nadal was seeded second at the US Open, but lost in the quarterfinals to world No. 54 Mikhail Youzhny of Russia in four sets.

Nadal played only three tournaments the remainder of the year. Joachim Johansson, ranked world No. 690, upset Nadal in the second round of the Stockholm Open 6–4, 7–6. The following week, Nadal lost to Tomáš Berdych in the quarterfinals of the year's last Masters Series tournament, the Mutua Madrileña Masters in Madrid. During the round-robin stage of the year-ending Tennis Masters Cup, Nadal lost to James Blake but defeated Nikolay Davydenko and Robredo. Because of those two victories, Nadal qualified for the semifinals, where he lost to Federer 6–4, 7–5. This was Nadal's third loss in nine career matches with Federer.

Nadal went on to become the first player since Andre Agassi in 1994–95 to finish the year as the world No. 2 in consecutive years.

2007[link]

Nadal started the year by playing in six hard-court tournaments. He lost in the semifinals and first round of his first two tournaments and then lost in the quarterfinals of the Australian Open to eventual runner-up Fernando González. After another quarterfinal loss at the Dubai Tennis Championships, he won the 2007 Indian Wells Masters, before Novak Djoković defeated him in the quarterfinals of the 2007 Miami Masters.

He had comparatively more success after returning to Europe to play five clay-court tournaments. He won the titles at the Masters Series Monte Carlo, the Open Sabadell Atlántico in Barcelona, and the Masters Series Internazionali BNL d'Italia in Rome, before losing to Roger Federer in the final of the Masters Series Hamburg. This defeat ended his 81-match winning streak on clay, which is the male open era record for consecutive wins on a single surface. He then rebounded to win the French Open for the third straight year, defeating Federer once again in the final.

Between the tournaments in Barcelona and Rome, Nadal defeated Federer in the "Battle of Surfaces" exhibition match in Majorca, Spain, with the tennis court being half grass and half clay.^[35]

Nadal played the Artois Championships at the Queen's Club in London for the second consecutive year. As in 2006, Nadal was upset in the quarterfinals. Nadal then won consecutive five-set matches during the third and fourth rounds of Wimbledon before being beaten by Federer in the five-set final. This was Federer's first five-set match at Wimbledon since 2001.^[36]

In July, Nadal won the clay court Mercedes Cup in Stuttgart, which proved to be his last title of the year. He played three important tournaments during the North American summer hard court season. He was a semifinalist at the Masters Series Rogers Cup in Montreal before losing his first match at the Western & Southern Financial Group Masters in Cincinnati, Ohio. He was the second-seeded player at the US Open, but was defeated in the fourth round by David Ferrer.

After a month-long break from tournament tennis, Nadal played the Mutua Madrileña Masters in Madrid and the BNP Paribas Masters in Paris. David Nalbandian upset him in the quarterfinals and final of those tournaments. To end the year, Nadal won two of his three round robin matches to advance to the semifinals of the Tennis Masters Cup in Shanghai, where Federer defeated him 6–4, 6–1.

During the second half of the year, Nadal battled a knee injury suffered during the Wimbledon final. In addition, there were rumors at the end of the year that the foot injury he suffered during 2005, caused long-term damage, which were given credence by coach Toni Nadal's claim that the problem was "serious". Nadal and his spokesman strongly denied this, however, with Nadal himself calling the story "totally false".^[37]

2008[link]

Nadal began the year in India, where he was comprehensively beaten by Mikhail Youzhny in the final of the Chennai Open. Nadal then reached the semifinals of the Australian Open for the first time. Jo-Wilfried Tsonga defeated Nadal 6–2, 6–3, 6–2 in the semifinal of 2008 Australian Open. Tsonga's semifinal performance was characterized by his powerful and precise serve, finesse volleys, and aggressive baseline play; it was a performance that drew the Melbourne crowd to their feet. Tsonga did not face a break point until the third set, while breaking the Spaniard five times in the match. Nadal also reached the final of the Miami Masters for the second time.

During the spring clay-court season, Nadal won four singles titles and defeated Roger Federer in three finals. He beat Federer at the Masters Series Monte Carlo for the third straight year, capturing his open era record fourth consecutive title there. He won in straight sets, despite Federer's holding a 4–0 lead in the second set.^[38] Nadal then won his fourth consecutive title at the Open Sabadell Atlántico tournament in Barcelona. A few weeks later, Nadal won his first title at the Masters Series Hamburg, defeating Federer in the three-set final. He then won the French Open, becoming the fifth man in the open era to win a Grand Slam singles title without losing a set.^[39] He defeated Federer in the final for the third straight year, but this was the most lopsided of all their matches, as Nadal only lost four games and gave Federer his first bagel since 1999.^[38] This was Nadal's fourth consecutive French title, tying Björn Borg's all-time record. Nadal became the fourth male player during Open era to win the same Grand Slam singles tournament four consecutive years (the others being Borg, Pete Sampras, and Federer).

Nadal against Andreas Beck in the 2008 Wimbledon Championships first round

Nadal then played Federer in the final of Wimbledon for the third consecutive year, in the most anticipated match of their rivalry.^[40][41] Nadal entered the final on a 23-match winning streak, including his first career grass-court title at the Artois Championships staged at the Queen's Club in London prior to Wimbledon. Federer had won his record fifth grass-court title at the Gerry Weber Open in Halle, and then reached the Wimbledon final without losing a set. Unlike their previous two Wimbledon finals, though, Federer was not the prohibitive favorite, and many analysts picked Nadal to win.^[41][42] They played the longest (in terms of time on court, not in terms of numbers of games) final in Wimbledon history, and because of rain delays, Nadal won the fifth set 9–7 in near-darkness. The match was widely lauded as the greatest Wimbledon final ever, with some tennis critics even calling it the greatest match in tennis history.^{[43][44][45][46][47]} By winning his first Wimbledon title, Nadal became the third man in the open era to win both the French Open and Wimbledon in the same year, after Rod Laver in 1969, and Borg in 1978–80, (Federer later accomplished this the following year) as well as the second Spaniard to win Wimbledon. He also ended Federer's record streak of five consecutive Wimbledon titles and 65 straight wins on grass courts. This is also the first time that Nadal won two Grand Slams back-to-back.