With the exception of a few streets and squares which allow traffic and are more populated with tourists most of the time, the walkways of this city quarter are fairly narrow, quiet streets, surrounded by a diverse range of interesting buildings, the architecture of which can easily be compared with those in streets of cities such as Florence ( Italy ), for example.

With the French Imperial Guard artillery now also deployed and firing at them, Zieten's Prussians drew back in good order, formed in squares to fend off Grouchy's cavalry.

With night approaching and their retreat towards Étoges now barred by enemy cavalry, the Prussian squares began to lose cohesion.

As derived above, the ordinary generating function for the sequence of squares is With r = 1, α = 0, β = 3, A ( x ) = 0, and B ( x ) = x ( x + 1 ), we can verify that the squares grow as expected, like the squares:

With checkerboard colouring, it has 106 white and 104 black squares ( or vice versa ), so parity does not prevent a packing, and a packing is indeed possible.

With his students, he has developed a widely-used mathematical software package ( SPARSPAK ) for solving sparse systems of equations and sparse least squares problems.

With, this least squares solution can be analyzed in a special way via the singular value decomposition.

With a certain amount of tedious math ( expanding the squares inside of the braces, separating out and grouping the terms involving and and completing the square over ), we can derive the parameters of the Gaussian distribution:

With their famed discipline and in combination with heavy cavalry like the gendarme, the Swiss pike squares were almost invincible on the late medieval battlefield.

With quadruple letter scores spaced only three squares away from a double word score, it is not uncommon to see a single play score over one hundred points, even without a fifty-point bonus.

With respect to ordinary least squares, the relevant assumption of the classical linear regression model is that the error term is uncorrelated with the regressors.

The sequence implicitly labeled Baez a limousine liberal, a charge she took to heart, as detailed years later in her 1987 autobiography, And A Voice To Sing With: A Memoir.

With respect to a gene, the two strands may be labeled the " template strand ," which serves as a blueprint for the production of an RNA transcript, and the " coding strand ," which includes the DNA version of the transcript sequence.

With higher specificity, fewer healthy people are labeled as sick ( or, in the factory case, the less money the factory loses by discarding good products instead of selling them ).

With a resemblance to European Gothic cathedrals, the structure was labeled the Cathedral of Commerce by the Reverend S. Parkes Cadman during the opening ceremony, although it was maligned by others due to its eclecticism.

With this problem, however, the supervised learning algorithm will only have five labeled points to use as a basis for building a predictive model.

With the growth in intermarriage between Malayali communities and also with other groups, especially outside Kerala, many people who identify themselves with Kerala or with Malayali culture can not readily be labeled as members of one of the historic castes or communities listed above.

With two pendulums ( labeled a and b ) of equal mass but possibly unequal lengths and connected by a spring, the total potential energy is

With the advent of talking pictures, he made a career out of playing comic henchmen, stooges, policemen, taxi drivers and other ' tough guys ' in numerous films of the 1930s and 1940s, especially for Warner Bros. Allen Jenkins was labeled the " greatest scene-stealer of the 1930s " by The New York Times.

With their increasingly complex style of progressive rock-infused thrash, they are often labeled as " the Rush of thrash metal " by music critics.

Is not the popular understanding of libertarianism ( the Libertarian Party, for example ) precisely the precepts of the “ hedonistic wing ?” With common sense and natural rights ( and even St. Thomas Aquinas ) as part of his libertarianism, could not Rothbard just as well be labeled as a fusionist manqué, or simply as a fusionist, since his synthesis did not follow the predominant utilitarian / emotivist wing of libertarianism?

With guest stars like Pastor Troy & Re-Re on board, the album was a hot musical choice, with some of its tracks even labeled as new hip-hop anthem.

With the 2003 purchase of 65 Comet V coaches, Metro-North included a provision for keeping the Metro-North labeled cars on the New York-based lines as much as possible, and the Bombardier-built coaches previously used were moved to East-of-Hudson service.

With 40 try assists in his debut season Smith entered the NRL scene with a bang, he was labeled as the next ' Joey ' and ' Sterlo '.

With the advent of algebraic logic it became apparent however that classical propositional calculus admits other semantics.

With the notation common in algebraic geometry, the Nullstellensatz can also be formulated as

With his equation we separate integral of a fractional rational function, the sum of the rational part ( algebraic fraction ) and the transcendental part ( with the logarithm and the arctangent ).

With the benefit of hindsight, it can be said that algebraic geometry had been wrestling with two problems for a long time.

) With luck, these derivatives will allow one to perform algebraic simplification and eventually evaluate the limit.

With a view toward algebraic geometry, Graduate Texts in Mathematics, vol 150, Springer-Verlag, New York, 1995.

With Laurent Schwartz he supervised the early research of Alexander Grothendieck ; later from 1959 to 1964 he was at IHÉS alongside Grothendieck, and collaborating on the expository work needed to support the project of refounding algebraic geometry on the new basis of schemes.

With a view toward algebraic geometry.

With these definitions, the algebraic spaces form a category.

With this modification of notation, as right modules if and only if there exists a unique idempotent e such that and.

With infix notation, one easy mnemonic for remembering the order of operation is:

With the availability of good standard notation tutor books, teaching is possibly moving in this direction.

With his theory connecting musical notation with poetic meter, he developed a unique style of poetry written in logaoedic dactyls, which was strongly influenced by the works of his beloved Anglo-Saxon poets.

With 12-hour time notation, most authorities recommend avoiding confusion by using " noon ", " 12 noon ", or " 12: 00 noon ".

With this notation, the Hodge conjecture becomes:

With 12-hour time notation, authorities recommend avoiding confusion between noon and midnight by using " midnight ", " 12 midnight ", or " 12: 00 midnight.

With appropriate software, the computer can handle sound generation, mixing of tracks, music notation, musical instruction, and other music composition tasks.

With the scarcity of chess literature in his small town, he learned about chess notation from the chess puzzles in the daily newspaper, and compiled a handwritten collection of almost 1000 games.

With this notation, Dickson's lemma may be stated in several equivalent forms:

With the use of a radix point, the notation can be extended to include fractions and the numeric expansions of real numbers.

With this notation, the &# 8472 ; function satisfies the following differential equation:

With some abuse of notation, one may write this as

With this notation the velocity becomes:

The cover of the first printing included the notation, " With minor modifications, it is also suitable for use with ADVANCED DUNGEONS & DRAGONS "; this was removed from later printings.

With the introduction of subtractive notation, XIV ( 14 ) no longer represents the same number as XVI but rather is an alternate way of writing XIIII.

With the multi-index notation the rule states more generally:

With a small rearrangement this can be rewritten in vector notation as the eigenvector equation

The propagation velocity of electromagnetic waves in free space, an idealized standard reference state ( like absolute zero for temperature ), is conventionally denoted by c < sub > 0 </ sub >:< ref > With ISO 31-5, NIST and the BIPM have adopted the notation c < sub > 0 </ sub >.</ ref >

With Big O notation, we say that some term " is " ( given some function g, where x is one of f < nowiki >'</ nowiki > s parameters ).

With mathematical notation, Rosenblatt also described circuitry not in the basic perceptron, such as the exclusive-or circuit, a circuit whose mathematical computation could not be processed until after the backpropagation algorithm was created by Werbos ( 1975 ).

With Charles-Victor Mauguin, he invented an international standard notation for crystallographic groups known as the Hermann – Mauguin notation or International notation.