If, in the trustee's judgment, `` reasonable market conditions '' did not prevail during any given year, he was to be allowed to petition the court for an extension of time within the ten-year period.

If it is assumed that the formula given by Lodge of cosec Af applies, the pressure difference along the major axes can be calculated from the angle of inclination of the major axis, and from this the interfacial tension can be calculated.

If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.

If, however, we are seeking the optimal R-stage policy for a given feed state, only one search for a maximum is required at the final step.

If the latter knows nothing about the absent sitter except his name ( given by the experimenter ), he cannot possibly give any clues, conscious or unconscious, far less ask leading questions.

`` If you substitute ' atom ' for ' angel ', the problem is not insoluble, given the metallic content of the pin in question ''.

If a defendant has been convicted and can prove that his lawyer did not adequately handle his case and that there is a reasonable probability that the result of the trial would have been different had the lawyer given competent representation, he is entitled to a new trial.

** Trichotomy: If two sets are given, then either they have the same cardinality, or one has a smaller cardinality than the other.

** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.

( If the condition is thought to be cellulitis rather than abscess, consideration should be given to possibility of strep species as cause that are still sensitive to traditional anti-staphylococcus agents such as dicloxacillin or cephalexin in patients able to tolerate penicillin ).

If we use a cylindrical coordinate system with basis vectors, then the gradient of and the divergence of are given by

If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.

* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.

* If the balance factor of P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.

If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If two equivalent amplifiers are being compared, the amplifier with higher gain settings would be more sensitive as it would take less input signal to produce a given amount of power.

If the norm of a Banach space satisfies this identity, the associated inner product which makes it into a Hilbert space is given by the polarization identity.

If BCG is accidentally given subcutaneously, then a local abscess may form ( a BCG-oma ) that can sometimes ulcerate, and may require treatment with antibiotics.

If given subcutaneously, it may induce local infection and spread to the regional lymph nodes, causing either suppurative and nonsuppurative lymphadenitis.

If BCG is accidentally given to an immunocompromised patient ( e. g., an infant with SCID ), it can cause disseminated or life-threatening infection.

If players cannot move either die in a roll, given the position of their checkers then that turn is over and the turn passes to the opponent.

If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by

He explained that this is one of the most important analects: " If the people be led by laws, and uniformity sought to be given them by punishments, they will try to avoid the punishment, but have no sense of shame.

If they be led by virtue, and uniformity sought to be given them by the rules of propriety, they will have the sense of the shame, and moreover will become good.

* 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.

If you walk into the ring because it is fun to show your dog, he will feel it and give you a good performance!!

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

If A itself is commutative ( as a ring ) then it is called a commutative R-algebra.

If a is algebraic over K, then K, the set of all polynomials in a with coefficients in K, is not only a ring but a field: an algebraic extension of K which has finite degree over K. In the special case where K = Q is the field of rational numbers, Q is an example of an algebraic number field.

If a fighter is knocked down during the fight, determined by whether the boxer touches the canvas floor of the ring with any part of their body other than the feet as a result of the opponent's punch and not a slip, as determined by the referee, the referee begins counting until the fighter returns to his or her feet and can continue.

If a compression test does give a low figure, and it has been determined it is not due to intake valve closure / camshaft characteristics, then one can differentiate between the cause being valve / seat seal issues and ring seal by squirting engine oil into the spark plug orifice, in a quantity sufficient to disperse across the piston crown and the circumference of the top ring land, and thereby effect the mentioned seal.

If a second compression test is performed shortly thereafter, and the new reading is much higher, it would be the ring seal that is problematic, whereas if the compression test pressure observed remains low, it is a valve sealing ( or more rarely head gasket, or breakthrough piston or rarer still cylinder wall damage ) issue.

If A is a fixed element of a ring ℜ, the first additional relation can also be interpreted as a Leibniz rule for the map given by B ↦.

If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed.

* If we think of as the ring of real numbers, then the direct product again consists of.

The best known example is the ring of quaternions H. If we allow only rational instead of real coefficients in the constructions of the quaternions, we obtain another division ring.

If R is a commutative ring, and a and b are in R, then an element d of R is called a common divisor of a and b if it divides both a and b ( that is, if there are elements x and y in R such that d · x = a and d · y = b ).

If R is a Euclidean domain in which euclidean division is given algorithmically ( as is the case for instance when R = F where F is a field, or when R is the ring of Gaussian integers ), then greatest common divisors can be computed using a form of the Euclidean algorithm based on the division procedure.

If the network is one-dimensional, and the chain of nodes is connected to form a circular loop, the resulting topology is known as a ring.

If is a left-( respectively right -) Noetherian ring, then the polynomial ring is also a left-( respectively right -) Noetherian ring.

If brass is used after this ring appears, it risks a crack, or worse, a complete head separation, which will leave the forward portion of the brass lodged in the chamber of the gun.

If a is idempotent in the ring R, then so is ; a and b are orthogonal.

If the condition only holds for all singleton subsets of R, then the ring is a right Rickart ring.

* If a is idempotent in the ring R, then aRa is again a ring, with multiplicative identity a.