Thus, the alignment of the `` dots '' and `` tips '', respectively, indicate individual variability of the 21 growth centers of each child with respect to the mean values for these boys and girls.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus, the efficiency **yt couplers is given by -- Af or approximately 50 percent each.

Thus some provinces contained tribes which detested each other, and to them independence meant an opportunity for war.

Thus arose the first monastic community, consisting of anchorites living each in his own little dwelling, united together under one superior.

Thus, each person of the Trinity is described as uncreated ( increatus ), limitless ( Immensus ), eternal ( æternus ), and omnipotent ( omnipotens ).

Thus, each Spruance-class destroyer originally carried a maximum total of 24 ASROC.

Thus, there are 35 possible basic contracts ( five at each of the seven levels ); 1 being the lowest, followed by 1 etc., up to 7NT, the highest possible bid.

Thus, the broadcast domain is the entire inter-connected layer two network, and the segments connected to each switch / bridge port are each a collision domain.

Thus an understanding of how these two levels relate to each other is needed.

Thus, on a real computer display, each pixel is actually composed of separate red, green, and blue subpixels.

Thus the dynamic characteristic of DHTML is the way it functions while a page is viewed, not in its ability to generate a unique page with each page load.

Thus, the change in slope between each successive point is small, reducing the apparent " jaggedness " of the approximation.

Thus, speakers of two adjacent Inuit dialects would usually be able to understand one another, but speakers from dialects distant from each other on the dialect continuum would have difficulty understanding one another.

Thus, ecosystem processes are driven by the number of species in an ecosystem, the exact nature of each individual species, and the relative abundance organisms within these species.

Thus, churches actually had money-changing tables at which each coin would be examined separately and a token of actual worth given to the layperson so that he or she could be seen by the other parishioners as putting money in the basket during that part of the service.

Thus, medical practitioners would select treatment options for specific cases based on the best research for each patient they treat.

Thus in each term ( endothermic & exothermic ) the prefix refers to where heat goes as the reaction occurs.

Thus, over time we would expect each traditional song to become aesthetically ever more appealing — it would be collectively composed to perfection, as it were, by the community.

Thus, online conversations often involve a variety of assumptions and motives unique to each individual user.

Thus, the eight items of the path are not to be understood as stages, in which each stage is completed before moving on to the next.

Thus, in a sense, there is a different completeness theorem for each deductive system.

Thus, in place of one unchallenged military commander, the province now had five officers, each with command of only a small fraction of the garrison.

Thus, a square and a circle are homeomorphic to each other, but a sphere and a donut are not.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus the P5 was integer superscalar but not floating point superscalar.

Thus for instance the determinant of a matrix with integer coefficients will be an integer, and the matrix has an inverse with integer coefficients if and only if this determinant is 1 or − 1 ( these being the only invertible elements of the integers ).

Thus, for discrete dynamical systems the iterates for integer n are studied.

Thus the 32-bit integer and 32-bit floating-point objects can simply use the value directly ; whereas the 64-bit integer and 64-bit floating-point cannot use this method.

Thus, nowadays, we speak of Diophantine equations when we speak of polynomial equations to which rational or integer solutions must be found.

Thus if n is a large even integer and m is a number between 3 and n / 2, then one might expect the probability of m and n − m simultaneously being prime to be.

Thus the screening current changes direction every time the flux increases by half integer multiples of.

if there exists an integer such that .< ref > Thus, divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors.

Thus, for instance, it cannot contain some integer values and some string values.

Charge quantization is the principle that the charge of any object is an integer multiple of the elementary charge e. Thus, e. g., an object's charge can be exactly 0 e, or exactly 1 e, − 1 e, 2 e, etc., but not, say, e, or − 3. 8 e, etc.

Thus A < sup > n </ sup > is Hermitian if A is Hermitian and n is an integer.

Thus, if θ is one value of arg ( z ), the other values are given by arg ( z ) = θ + 2nπ, where n is any integer ≠ 0.

Thus ICER will have good performance on integer only CPUs like the T414 Transputer, whereas JPEG 2000 will not perform as well as it is forced into floating point emulation.

Thus y is the largest integer less than the nth root of x, and r is the remainder.

Thus for normalized cuspidal Hecke eigenforms of integer weight, their Fourier coefficients coincide with their Hecke eigenvalues.

Thus if the imaginary quadratic extension has class number 1 ( so d is a Heegner number ), the j-invariant is an integer.

Thus every equation Mx = b, where M and b are both integer, and M is unimodular, has an integer solution.

Thus, such network flow problems with bounded integer capacities have an integral optimal value.

Thus the standard Young tableaux are precisely the semistandard tableaux of weight ( 1, 1 ,..., 1 ), which requires every integer up to to occur exactly once.