Since direct observations of climate are not available before the 19th century, paleoclimates are inferred from proxy variables that include non-biotic evidence such as sediments found in lake beds and ice cores, and biotic evidence such as tree rings and coral.

Since the separation of variables in this case involves dividing by y, we must check if the constant function y = 0 is a solution of the original equation.

Since no variables of this language range over the reals, we cannot simply copy the earlier definition of definability.

Since version 20, GNU Emacs has included a " Customize " facility which allows users to set common customization variables through a graphical interface.

Since terms of linear equations cannot contain products of distinct or equal variables, nor any power ( other than 1 ) or other function of a variable, equations involving terms such as xy, x < sup > 2 </ sup >, y < sup > 1 / 3 </ sup >, and sin ( x ) are nonlinear.

Since subtraction can be replaced by addition of the opposite quantity, and since positive whole number exponents can be replaced by repeated multiplication, all polynomials can be constructed from constants and variables using only addition and multiplication.

Since the query contained no variables, no bindings are reported to the user.

Since each sample is a random variable, the sample mean is a function of random variables and hence a random variable itself, whose distribution can be computed and properties determined.

( Since the sub-structure is usually represented in the computer by a set of integer variables with constraints, these problems can be viewed as special cases of constraint satisfaction or discrete optimization ; but they are usually formulated and solved in a more abstract setting where the internal representation is not explicitly mentioned.

Since determinants of supply and demand other than the price of the good in question are not explicitly represented in the supply-demand diagram, changes in the values of these variables are represented by moving the supply and demand curves ( often described as " shifts " in the curves ).

Since these variables do not stand for individual objects, it seems we are “ ontologically committed ” to entities other than individuals — sets, classes, and so on.

The vertical axis represents the real interest rate, i. Since this is a non-dynamic model, there is a fixed relationship between the nominal interest rate and the real interest rate ( the former equals the latter plus the expected inflation rate which is exogenous in the short run ); therefore variables such as money demand which actually depend on the nominal interest rate can equivalently be expressed as depending on the real interest rate.

Since the religious status of a Kohen is contingent upon being the male biological descendant of Aaron in conjunction with numerous other variables that are not subject to genetic testing ( the wife of a kohen cannot have had relations with a non-Jew, be a divorcee etc.

Since we no longer need, we can instead overwrite it with its own reversal using this in-place algorithm which will only need constant additional storage for the auxiliary variables and, no matter how large the array is.

Since the thermodynamical variables of the system are well defined in the initial state and the final state, the internal energy increase,, the entropy increase, and the total amount of work that can be extracted, performed by the system,, are well-defined quantities.

Since and are independent variables, and may be chosen without restriction.

Since arithmetic and geometric means are equal iff the variables are constant, see, inequality of arithmetic and geometric means, we establish the claim of unit modulus.

Since the 1930s, the term has been in general use in social science, especially as a variable whose sub-components needed to be distinguished in relationship to other sociological variables.

Since the 1990s many long-term risk management models have incorporated economic relationships between simulated variables in an attempt to detect high-exposure future scenarios ( often through a Monte Carlo method ).

Since the variables determining such reactions were not understood, therapeutic transformations of this kind were not readily replicable.

Since all this, done as a pure substance is valid in a mix just adding the subscript to all the intensive variables and

Since most of the variables will be non-basic and assume a value of zero in the optimal solution, only a subset of variables need to be considered in theory when solving the problem.

Since there are four unknown forces ( or variables ) ( V < sub > A </ sub >, V < sub > B </ sub >, V < sub > C </ sub > and H < sub > A </ sub >) but only three equilibrium equations, this system of simultaneous equations does not have a unique solution.

Since the hazards of poor communication are so great, p can be justified as a habitable site only on the basis of unusual productivity such as is made available by a waterfall for milling purposes, a mine, or a sugar maple camp.

Since the slogans have little application to reality and are sanctimonious to boot, the applause is faint even in areas of the world where we should expect to find the greatest affection for free government.

Since we can neither undo nor redo the past, we are limited to the events of today and tomorrow.

Since the recognition of Israel as a nation state, claims are made in many cases which identify the claimant as a member of the new body politic.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Since conventional methods are insensitive at the low frequencies of these molecular transitions, the paramagnetic resonance method is being used instead.

Since broadcast frequencies are very limited in number, these objectives are to some extent inconsistent in that not all of them can be fully realized, and to the extent that each is realized, there is a corresponding reduction of the possibilities for fullest achievement of the others.

Since the provision of skywave service requires adequate freedom from interference, only class 1, stations are capable of rendering skywave service.

Since the sides are also covered up to the spray rails, they are also rough-sanded in that area.

Since fly cutters are one sided and not balanced, they should be used at the slowest speed available, and fed very slowly to avoid binding.

Since there are almost no schools in the country offering graduate work in interior design this rule cannot at present be observed.

Since charges are relatively the same, reserving a car before you leave for Europe will assure you of having one on tap when you want it.

Since practical washing procedures are both lengthy and expensive, a number of laboratory tests have been developed for the numerical evaluation of detergents.

Since the circulating thyroid hormones are the amino acids thyroxine and tri-iodothyronine ( cf. Section C ), it is clear that some mechanism must exist in the thyroid gland for their release from proteins before secretion.

Since emotional reactions in the higher vertebrates depend on individual experience and are aroused in man, in addition, by complex symbols, one would expect that the hypothalamus could be excited from the cortex.

Since Af are distinct prime polynomials, the polynomials Af are relatively prime ( Theorem 8, Chapter 4 ).

Since D and D' are both diagonalizable and they commute, they are simultaneously diagonalizable, and Af is diagonalizable.

Since N and N' are both nilpotent and they commute, the operator Af is nilpotent ; ;

Since Af are linearly independent functions and the exponential function has no zeros, these R functions Af, form a basis for the space of solutions.

Since the choice is by lot each week, the outcomes of different trials are independent.

Since two curves of symbol Af on Q intersect in Af points, it follows that there are Af lines of Af which are tangent to Aj.