For it includes the emotional ties that bind men to their homeland and the complex motivations that hold a large group of people together as a unit.

For, if so, the path leads through a complex process of parliamentary diplomacy which adds still another dimension to the problem.

For the prevention or treatment of the early stages of shipping fever complex, increase feeding level to 0.5 to 2 grams per head per day.

For cows, feed providing an intake of 0.1 milligram of Aureomycin per pound of body weight daily aids in the reduction of bacterial diarrhea, in the prevention of foot rot, and in the reduction of losses due to respiratory infection ( infectious rhinotracheitis -- shipping fever complex ).

For more complex designs the

For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

For example, the field extension R / Q, that is the field of real numbers as an extension of the field of rational numbers, is transcendental, while the field extensions C / R and Q (√ 2 )/ Q are algebraic, where C is the field of complex numbers.

For more complex alkynes, the Lindlar catalyst is widely recommended to avoid formation of the alkane, for example in the conversion of phenylacetylene to styrene.

For example, during the menstrual cycle, the breasts are enlarged by premenstrual water retention ; during pregnancy the breasts become enlarged and denser ( firmer ) because of the prolactin-caused organ hypertrophy, which begins the production of breast milk, increases the size of the nipples, and darkens the skin color of the nipple-areola complex ; these changes continue during the lactation and the breastfeeding periods.

For example, in three-dimensional complex Euclidean space,

For example, the spectrum of an element of a complex Banach algebra can never be empty, whereas in a real Banach algebra it could be empty for some elements.

For public corporations, these responsibilities are typically much more rigorous and complex than for those of other types.

For example, programming language theory studies approaches to description of computations, while the study of computer programming itself investigates various aspects of the use of programming languages and complex systems, and human-computer interaction focuses on the challenges in making computers and computations useful, usable, and universally accessible to humans.

For example, programming language theory considers various approaches to the description of computation, whilst the study of computer programming itself investigates various aspects of the use of programming language and complex systems.

For example, simple hydrogen gas combined with simple oxygen gas can produce a more complex substance, such as water.

For instance, here is the CLU syntax for a cluster that implements complex numbers:

For real values of, we have and for purely imaginary we have hence has a limit at 0 ( i. e., ƒ is complex differentiable at 0 ) if and only if.

For instance, low-end versions of complex architectures ( i. e. using less hardware ) could lead to situations where it was possible to improve performance by not using a complex instruction ( such as a procedure call or enter instruction ), but instead using a sequence of simpler instructions.

For instance, the PDP-8, having only 8 fixed-length instructions and no microcode at all, is a CISC because of how the instructions work, PowerPC, which has over 230 instructions ( more than some VAXes ) and complex internals like register renaming and a reorder buffer is a RISC, while Minimal CISC has 8 instructions, but is clearly a CISC because it combines memory access and computation in the same instructions.

For decades it has been unlikely that a complex information system can be built effectively without a proper database supported by a DBMS.

** For example, consider the map ( which is the " realification " of the complex square function ) where U

For iron rust to occur the metal has to be in contact with oxygen and water, although chemical reactions for this process are relatively complex and not all of them are completely understood, it is believed the causes are the following:

For complex z

For vector spaces over non-algebraically closed fields, we still need to find some substitute for characteristic values and vectors.

For each picture frame, the 6502 writes graphics commands for the DVG into a defined area of RAM ( the vector RAM ), and then asks the DVG to draw the corresponding vector image on the screen.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:

For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:

For 2D vector animations, the rendering process is the key frame illustration process, while tweened frames are rendered as needed.

For example, binary string 1011 is represented by the vector ( 1, 0, 1, 1 ).

For the purposes of this article, we call this constructed vector the transmitted vector.

For a vector expressed in cylindrical coordinates as

For twisting rotation to exist, it is necessary to tilt the body sideways after takeoff, so that there is now a small component of this horizontal angular momentum vector along the body's long axis.

Malaria Foundation International states, " The outcome of the treaty is arguably better than the status quo going into the negotiations ... For the first time, there is now an insecticide which is restricted to vector control only, meaning that the selection of resistant mosquitoes will be slower than before.

For the special case, this implies that the length of a vector is preserved as well — this is just Parseval's theorem:

For a flow, the vector field Φ ( x ) is a linear function of the position in the phase space, that is,

For a more useful solution, we utilize vector identities, which work for any vector, as follows:

For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category.

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.