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showed and matrix
In 1991 David Deutsch showed that quantum theory is fully consistent ( in the sense that the so-called density matrix can be made free of discontinuities ) in spacetimes with closed timelike curves.
He also showed how to solve systems of linear equations be reducing the matrix of their coefficents to diagonal form.
Studies in 2006 showed evidence of a linkage between idiopathic scoliosis and three microsatellite polymorphisms in the MATN1 gene ( encoding for Matrilin 1, cartilage matrix protein ), respectively consisting of 103, 101 and 99 base pairs,.
Following Section III of Rayleigh ( 1873 ), Onsager ( 1931, I ) showed that in the regime where both the flows are small and the thermodynamic forces vary slowly, there will be a linear relation between them, parametrized by a matrix of coefficients conventionally denoted:
Reid and Brown in 1972 showed that there exists a " doubly regular tournament of order n " if and only if there exists a skew Hadamard matrix of order n + 1.
He showed that the Jacobian matrix of a spacetime diffeomorphism which preserves the Maxwell equations is proportional to an orthogonal matrix, hence conformal.
A geophysical survey of the area in 2008 showed unclear magnetometer data ; the wood may be influencing the peat's hydrology, causing the loss or collection of minerals within the pore water and peat matrix.
Unlike previous stereograms, in which each half image showed recognizable objects, each half image of the first random-dot stereograms showed a square matrix of about 10, 000 small dots, with each dot having a 50 % probability of being black or white.
Also, in early 1926, Erwin Schrödinger, at the University of Zurich, began to publish his quintet of papers which launched the wave mechanics formulation of quantum mechanics and showed that the wave mechanics and matrix mechanics formulations were equivalent.
showed that the NTE phenomenon originates from the existence of high pressure, small volume phases with higher entropy, with their configurations present in the stable phase matrix through thermal fluctuations.
They also showed that either of two different conjectures would imply that the optimal exponent of matrix multiplication is 2, as has long been suspected.
Colonies feeding on nutritionally supplemented cellulose based matrix showed similar fitness characteristics as colonies feeding on the best wood treatments.

showed and is
Many years later I went to see S.K. in England, where he was living at Whiteleaf, near Aylesbury, and he showed me beside his cottage there the remains of the road on which Boadicea is supposed to have travelled.
Heywood Broun wrote: `` Belle Poitrine is the most original thinker since Caligula '', and even F.D.R. had to concede that `` if the rest of this nation showed the foresight and patriotism of Miss Poitrine, America would rapidly resemble ancient Babylon and Nineveh ''.
The nuclei of these fibers, as is shown in Figures 3 and 4, showed remarkable proliferation and were closely approximated, forming a chainlike structure at either the center or the periphery of the fiber.
He showed convincingly that anxiety is a learned ( conditioned ) reaction and is the basis of experimental and clinical neuroses and assumed, therefore, that the neuronal changes which underlie the neuroses are functional and reversible.
Appropriate experiments showed that this is, indeed, possible.
It is as follows: `` The usual sensitivity tests showed that the specific qualities of skin-perceptiveness ( pressure, pain, temperature ), as well as the kinesthetic sensations ( muscular feelings, feelings in the tendons and joints ), were, as such, essentially intact, although they seemed, in comparison with normal reactions, to be somewhat diminished over the entire body.
Experience showed, however, that it is very difficult to paint a dark umber background in fresco that will not dry out spotty and uneven.
Assuming ZF is consistent, Kurt Gödel showed that the negation of the axiom of choice is not a theorem of ZF by constructing an inner model ( the constructible universe ) which satisfies ZFC and thus showing that ZFC is consistent.
The novel is most noted for its careful description of the dig site and house, which showed the author had spent much of her own time in very similar situations herself.
In September of 1820, Ampère ’ s friend and eventual eulogist François Arago showed the members of the French Academy of Sciences the surprising discovery of Danish physicist Hans Christian Ørsted that a magnetic needle is deflected by an adjacent electric current.
The Italian scholar Maggiani recently showed that on an Etruscan tomb dedicated to Racvi Satlnei in Bologna ( 5th century BC ) there is a writing that says: " aivastelmunsl
Unlike his translation of the Pastoral Care, Alfred here deals very freely with his original and though the late Dr. G. Schepss showed that many of the additions to the text are to be traced not to Alfred himself, but to the glosses and commentaries which he used, still there is much in the work which is solely Alfred's and highly characteristic of his style.
He showed that, although matter can change its state in a chemical reaction, the total mass of matter is the same at the end as at the beginning of every chemical change.
At the Council of Clermont in 1095, Adhemar showed great zeal for the crusade ( there is evidence Urban II had conferred with Adhemar before the council ) and having been named apostolic legate and appointed to lead the crusade by Pope Urban II, he accompanied Raymond IV, Count of Toulouse, to the east.
A remarkable feature of these KO mice is that they have a very restricted phenotype: Casp3, 9, APAF-1 KO mice have deformations of neural tissue and FADD and Casp 8 KO showed defective heart development, however in both types of KO other organs developed normally and some cell types were still sensitive to apoptotic stimuli suggesting that unknown proapoptotic pathways exist.
In 1929, Mojżesz Presburger showed that the theory of natural numbers with addition and equality ( now called Presburger arithmetic in his honor ) is decidable and gave an algorithm that could determine if a given sentence in the language was true or false.
Math., 1858 ) and Ernst Abbe showed that the properties of these reproductions, i. e. the relative position and magnitude of the images, are not special properties of optical systems, but necessary consequences of the supposition ( in Abbe ) of the reproduction of all points of a space in image points ( Maxwell assumes a less general hypothesis ), and are independent of the manner in which the reproduction is effected.
They showed by oxidizing boron with air that boric acid is an oxidation product of boron.
The trial showed a 64 % protective effect, which is very similar to the figure derived from other UK trials, thus arguing against the genetic variation hypothesis.
The peak of tuberculosis incidence is in adolescence and early adulthood, and the MRC trial showed efficacy lasted only 15 years at most.
He showed that if ρ ( x, t ) is the density of Brownian particles at point x at time t, then ρ satisfies the diffusion equation:

showed and iff
The semantics of NAF remained an open issue until Keith Clark showed that it is correct with respect to the completion of the logic program, where, loosely speaking, " only " and are interpreted as " if and only if ", written as " iff " or "".

showed and for
I showed her the shower and tub, and she said, smiling, `` If you really don't mind, I think I'll get clean in the shower, then soak for a few minutes in your tub.
He bounced exuberantly on the sagging bed and was even more delighted when Madame Lalaurie -- after closing the door -- showed the slave that the bed was designed for something other than slumber.
The kid showed for an instant, and his arm was cocked back.
As Helion's work showed more and more nostalgia for the world of man and nature, the pure abstractionists expressed some disapproval ; ;
He was then asked for a solution of the difficulty, and began to talk trenchant sense, though private anguish showed through in the vehemence of his manner.
Young Mercer showed a remarkable lack of aptitude for both instruments.
Without exception Hino's brothers turned to either one or both of their father's occupations, but Hino showed a talent for neither and instead spent most of his time on the beach where he repaired nets and proved immensely popular as a storyteller.
Petitioner was not entitled, either in the administrative hearing at the Department of Justice or at his trial, to inspect the original report of the Federal Bureau of Investigation, since he was furnished a resume of it, did not challenge its accuracy, and showed no particular need for the original report.
Sales and net income for the year ended December 31, 1960 showed an improvement over 1959.
A fresh crop of beginners' guns showed up in 1961, and they're good bets for your Christmas gift list if you're wondering what to get for a youngster.
Throughout history, the man who showed superior performance has become the commander of others -- for good or bad.
Thus the lack of effective recognition of the responsibilities involved in caring for two babies showed signs of becoming a disabling problem.
Extruded expandable styrene film or sheet -- claimed to be competitive price-wise with paper -- also showed much potential, particularly for packaging.
Those who feared `` emotionalism '' at the Trial showed less understanding than Dr. Servatius of the route by which man achieves the distance necessary for fairness toward enemies.
In time, and two drinks later, he was complaining bitterly about his wife, He was on the subject for ten minutes or so when he noticed the renewed interest in his listener -- it showed in the alert face and the suddenly bright eyes.
Listening for hours to his laments that the war and `` Mist Fair's '' poverty afterwards had robbed the mare of many a racing triumph, and to his predictions of greatness for the procession of foals to come, Jenny could look forward to years of conflict with an animal who disliked her intensely and showed it.
Her first actual flight, for she and her kind had made mock flights on dummy panels since she was eight, showed her complete mastery of the techniques of her profession.
The Lady Da, naked in the dusty plain, waved a hospitable hand and showed that there was a place for him to sit beside her.
Cuneiform sources suggest that the Gutians ' administration showed little concern for maintaining agriculture, written records, or public safety ; they reputedly released all farm animals to roam about Mesopotamia freely, and soon brought about famine and rocketing grain prices.
Nevertheless, although the Sassanids were checked for the time, the conduct of the Roman army showed an extraordinary lack of discipline.
Herodian says " in their opinion Alexander showed no honourable intention to pursue the war and preferred a life of ease, when he should have marched out to punish the Germans for their previous insolence ".
Afonso showed extraordinary vision for the time.

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