If you have taken this stroll in the morning, and you have the time and inclination, walk to the right along the crowded Corso for half a dozen blocks to visit the fine private collection of paintings -- mainly of the sixteenth and seventeenth centuries -- in the Palazzo Doria ( open Sunday, Tuesday, and Thursday, 10:00 to 1:00 ).

* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.

* If the metric space X is compact and an open cover of X is given, then there exists a number such that every subset of X of diameter < δ is contained in some member of the cover.

But now, intermarriage is often the result of living in an open society .... If our children end up marrying non-Jews, we should not reject them.

If a user added more than one drive to a system the user had to open the case and cut a trace in the circuit board to permanently change the drive's number, or hand-wire an external switch to allow it to be changed externally.

If a rotating frame is chosen so that just the angular position of an object is held fixed, more complicated motion, such as elliptical and open orbits, appears because the centripetal and centrifugal forces will not balance.

If the content or presentation of a course is inconsistent with preconceived information, the student will learn if he or she is open to varying concepts.

If is continuous in an open set Ω and the partial derivatives of ƒ with respect to x and y exist in Ω, and satisfies the Cauchy – Riemann equations throughout Ω, then ƒ is holomorphic ( and thus analytic ).

* If ƒ ( z ) is locally integrable in an open domain Ω ⊂ C, and satisfies the Cauchy – Riemann equations weakly, then ƒ agrees almost everywhere with an analytic function in Ω.

If the door opens inward and there is a fire, there can be a crush of people who run for the door and they will not be able to open it.

If we allow also the system boundary to move ( e. g. due to moving pistons ) we get a rather general form of the first law for open systems.

If people are also free to move between the countries, in addition to FTA, it would also be considered an open border.

Presheaves: If X is a topological space, then the open sets in X form a partially ordered set Open ( X ) under inclusion.

If the receiving partner has wounds on his genitals, or if the giving partner has wounds or open sores on or in his or her mouth, or bleeding gums, this poses an increased risk of STD transmission.

If these conditions can change, they are better represented by two predicates open ( t ) and on ( t ) that depend on time ; such predicates are called fluents.

If not blocked or countered, the open row of three will be extended to an open row of four, which threatens to win in two ways.

( i ) If A is open,

If ƒ is complex differentiable at every point z < sub > 0 </ sub > in an open set U, we say that ƒ is holomorphic on U. We say that ƒ is holomorphic at the point z < sub > 0 </ sub > if it is holomorphic on some neighborhood of z < sub > 0 </ sub >.

If an open verdict is returned, the inquest can be reopened if new evidence is found and presented to the coroner.

If there is a crystallographic structure to the target, and especially in semiconductor substrates where the crystal structure is more open, particular crystallographic directions offer much lower stopping than other directions.

# If A is an open or closed subset of R < sup > n </ sup > ( or even Borel set, see metric space ), then A is Lebesgue measurable.

# If A is a Lebesgue measurable set, then it is " approximately open " and " approximately closed " in the sense of Lebesgue measure ( see the regularity theorem for Lebesgue measure ).

If other parts of the program need memory ( a part assigned to open and close the door, for example ), then someone may be trapped inside, since the software cannot open the door.

If, for example, a string sounds the note C when plucked, a string twice as long will sound the same note an octave lower.

If P is a program which outputs a string x, then P is a description of x.

If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.

If the possibility of adding the empty string to a language is added to the strings recognized by the noncontracting grammars ( which can never include the empty string ) then the languages in these two definitions are identical.

( If one string runs out of letters to compare, then it is deemed to come first ; for example, " cart " comes before " carthorse ".

If the radix point is omitted then it is implicitly assumed to lie at the right ( least significant ) end of the string ( that is, the number is an integer ).

If the spheres only appear to rotate ( that is, we are watching stationary spheres from a rotating frame ), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed.

# If V is a set of strings then V * is defined as the smallest superset of V that contains λ ( the empty string ) and is closed under the string concatenation operation.

# If V is a set of symbols or characters then V * is the set of all strings over symbols in V, including the empty string.

If you measure the three qubits, you will observe a three-bit string.

If a closed string splits and its two parts later reconnect, its worldsheet will look like a single pipe splitting to two and then reconnecting, which also looks like a torus connected to two pipes ( one representing the ingoing string, and the other — the outgoing one ).

If each mass point has the mass, the tension of the string is, the separation between the mass points is and are the offset of these points from their equilibrium points ( i. e. their position on a straight line between the two attachment points of the string ) the vertical component of the force towards point is

If the string is approximated with 100 discrete mass points one gets the 100 coupled second order differential equations (), () and () or equivalently 200 coupled first order differential equations.

If the original string had several substrings that occurred often, then the transformed string will have several places where a single character is repeated multiple times in a row.

If a simple pendulum is suspended from the cusp of an inverted cycloid, such that the " string " is constrained between the adjacent arcs of the cycloid, and the pendulum's length is equal to that of half the arc length of the cycloid ( i. e. twice the diameter of the generating circle ), the bob of the pendulum also traces a cycloid path.

* If lead-acid batteries are used, all cells in the formerly good parallel strings will begin to sulfate due to the inability for them to be fully recharged, resulting in the storage capacity of these cells being permanently damaged, even if the damaged cell in the one degraded string is eventually discovered and replaced with a new one.

* Joel Spolsky ( for Apps Hungarian ): " If you read Simonyi's paper closely, what he was getting at was the same kind of naming convention as I used in my example above where we decided that meant " unsafe string " and meant " safe string.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.