Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus F satisfies Af if and only if F has the form Af.

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, one can think of a dictionary entry as a word rather than a form.

Thus, at pH between 2. 2 and 9. 4, the predominant form adopted by α-amino acids contains a negative carboxylate and a positive α-ammonium group, as shown in structure ( 2 ) on the right, so has net zero charge.

" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.

Thus, from the human body, the usual form assigned to the Deity, forasmuch as it is written that God created man in his own image, issue the two supporters, Nous and Logos, symbols of the inner sense and the quickening understanding, as typified by the serpents, for the same reason that had induced the old Greeks to assign this reptile for an attribute to Pallas.

Thus for example two separate quotes by Athenaeus were united by Theodor Bergk to form fr. 362.

Thus, intuitionists are ready to accept a statement of the form " P or Q " as true only if we can prove P or if we can prove Q:

Thus, an analog signal is one represented by a continuous stream of data, in this case along an electrical circuit in the form of voltage, current or charge changes ( compare with digital signals below ).

Thus the competitors united to form the Vereenigde Oostindische Compagnie ( VOC ) ( the ‘ Dutch East Indies Company ).

Thus understood, the centuries-old English word Χmas, is actually a shortened form of CHmas, which is, itself, a shortened form for Christmas.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Thus, humans must be other biological machines created by a life form just as the BETA are.

Thus usage of any form of contraception, in vitro fertilization, or birth control besides Natural Family Planning is a grave offense against the sanctity of marriage and ultimately against God.

Thus, u < sub > ρ </ sub > and u < sub > θ </ sub > form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the particle.

Thus no form of justification will rationally warrant our inductive inferences.

Thus, using Euler's theorem we can say that the solution must be of the form:

Thus dubnium is expected to form a stable + 5 state.

Thus the halides DbX < sub > 5 </ sub > should react with water to form DbOX < sub > 3 </ sub >.

Thus, according to Lutz, doublespeak is a form of language that defeats the purpose of inventing language because doublespeak does not communicate the truth but seeks to do the opposite and the doublespeak committee is tasked with correcting this problem that doublespeak has created in the world of language.

Thus a conventionally corrected form of Newcomb's formula, to incorporate the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:

Thus the division form of Euclid's algorithm starts with a pair of positive integers and forms a new pair that consists of the smaller number and the remainder obtained by dividing the larger number by the smaller number.

Thus: hylostatism ( universe is deterministic, thus “ static ” in a four-dimensional sense ); hylostochastism ( universe contains a fundamentally random or stochastic component ); hylozoism ( universe contains a fundamentally alive aspect ).

This happens because a magnetic field is produced by an electric current, J, which reverses sign under T. Thus, the motion of classical charged particles in electromagnetic fields is also time reversal invariant.

Second, the message begins with " Thus says YHVH, God of your father David ..." rather than the more usual "... in the name of YHVH the God of Israel.

Thus represents a sequence of three phonemes,, ( the word push in standard English ), while represents the phonetic sequence of sounds ( aspirated " p "),, ( the usual pronunciation of push ).

Thus RTA avoids the usual fate of dislocated proteins ( destruction that is mediated by targeting ubiquitinylated proteins to the cytosolic proteasomes ).

Thus Condé, who as usual had fought with the most desperate bravery, was saved, and Paris underwent a new siege.

Thus twice the usual Eddington luminosity would be needed to drive off an atmosphere of pure helium.

Thus, the write-up operation permitted in the usual ★- Property is not present, only a write-to-same operation.

Thus, he made sure his conquests became his own properties, in exchange of the usual feudal obligations: aid and counsel.

Thus it includes the usual dwarves, elves, gnomes, and halflings found in Dungeons & Dragons, as well as giants, centaurs, orcs, trolls, and so forth.

Thus, cats with major damage to the visual cortex cannot recognize objects, but may still be able to follow and orient toward moving stimuli, although more slowly than usual.

Thus, the first NTSB report ( issued on 8 December 1992 ) did not conclude with the usual " probable cause.

Thus, it may be optimal for the government to intervene in a way that is contrary to usual policy.

Thus in many banks a credit entry on an account (" CR ") is regarded as negative movement, and a debit (" DR ") is positive-the reverse of usual commercial accounting conventions.

Thus, the following conditions determine the usual order of precedence:

Thus, instead of the usual E-A-D-G arrangement, his bass is strung as B-E-A-D.

Thus, for example, the usual English language name for San Diego de Alcalá ( after whom San Diego, California is named ) is " Didacus of Alcalá ".

Thus, the prerequisite for a continuing seismically active interior zone is the presence of water, the ability of the water to get down to the fault source ( high permeability ), and the usual high horizontal interior stresses of the rock mass.

Thus it is usual of Ilaro people to say " Ba mi ki Ogboni e O.

Thus the usual proof of the first incompleteness theorem can be used to show that Q is incomplete and undecidable.