proved the Jacobian conjecture for polynomials of degree 2, and showed that the general case follows from the special case where the polynomials are of degree 3. checked the conjecture for polynomials of degree at most 100 in 2 variables.

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.

Ghouila-Houri showed that a matrix is TU iff for every subset R of rows, there is an assignment of signs to rows so that the signed sum ( which is a row vector of the same width as the matrix ) has all its entries in ( i. e. the row-submatrix has discrepancy at most one ).

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.

With Mike Morris and Ulvi Yurtsever he showed that traversable Lorentzian wormholes can exist in the structure of spacetime only if they are threaded by quantum fields in quantum states that violate the averaged null energy condition ( i. e. have negative renormalized energy spread over a sufficiently large region ).

They showed that the geometry of spacetime outside a black hole is described by spin networks, some of whose edges puncture the event horizon, contributing area to it, and that the quantum geometry of the horizon can be described by a U ( 1 ) Chern-Simons theory.

A recent work by Martín-Martínez, Fuentes and Mann showed that accelerated detectors acquire a geometrical phase due to their movement through spacetime and that this can be used for the direct detection of the Unruh effect in regimes physically accessible with current technology.

Minkowski showed in 1908 that Einstein's new theory could also be explained by replacing the concept of a separate space and time with a four-dimensional continuum called spacetime.

In them, he showed that if elementary particles were treated as singularities in spacetime, it was unnecessary to postulate geodesic motion as part of general relativity.

Einstein's 1905 presentation of special relativity was soon supplemented, in 1907, by Hermann Minkowski, who showed that the relations had a very natural interpretation in terms of a unified four-dimensional " spacetime " in which absolute intervals are seen to be given by an extension of the Pythagorean theorem.

In any dimension showed that the diffeomorphism classes of oriented exotic spheres form the non-trivial elements of an abelian monoid under connected sum, which is a finite abelian group if the dimension is not 4.

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.

When he showed this model as his `` solution '' as to how the Howe sewing machine operated, he was told he was `` wrong '', and discovered to his amazement that the Howe Machine, which was unknown to him in detail, used two threads while the one that he had perfected used only one.

Two of the fluids showed a high-positive normal pressure when undergoing shear, and two showed small negative pressures which were negligible in comparison with the amount of the positive pressures generated by the other two.

One sample, which had been exposed to the atmosphere after evacuation at 375-degrees-C, showed the presence of adsorbed water ( about 0.3 wt ) ) as evidenced by a weak resonance line which was very narrow at room temperature and which disappeared, due to broadening, at low temperature.

The insoluble material which precipitated during dialysis against starting buffer always showed intense agglutinin activity, regardless of the blood group of the donor.

Microscopically, both kidneys showed many small cortical scars in which there was glomerular and interstitial fibrosis, tubular atrophy, and an infiltration of lymphocytes and plasma cells.

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.

Four subjects ( 10% ) did not change even then but needed the additional information that an arm-elevation under these circumstances was a perfectly normal reflex reaction which some people showed while others did not.

State and local expenditures ( in real terms ) increased persistently from $26.5-billion in 1949 to $44.3-billion in 1959, and it would not be surprising if they showed a comparable increase in this decade, which would carry them to the neighborhood of $75-billion by 1970.

Metabolite 1, isolated from the medium, however, showed a lower specific activity, which indicates endogenous synthesis of this metabolite.

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.

He showed me one of his fingers which had been practically amputated and which his mother had treated ; ;

His face was ruddy and heavy and unlined, and when he laughed he showed his teeth, which were big and white and strong and unquestionably home-grown.

New car sales in Dallas County during March showed slight signs of recovering from the doldrums which have characterized sales this year.

These inwardly dramatic moments showed the kind of `` opera style '' of which Beethoven was genuinely capable, but which did not take so kindly to the mechanics of staging.

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 psychologist David H. Barlow of Boston University conducted a study that showed three common characteristics of people suffering from chronic anxiety, which he characterized as " a generalized biological vulnerability ," " a generalized psychological vulnerability ," and " a specific psychological vulnerability.

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.

The low number of abnormalities compares favourably with the health condition of a Majungasaurus population of which it in 2007 was established that 19 % of individuals showed bone pathologies.

In the earlier part of his reign Ahmed I showed decision and vigor, which were belied by his subsequent conduct.

Kuroda's 1964 work " Classes of languages and linear-bounded automata " showed that any ( possibly non-deterministic ) program computable in linear space could be converted into the parsing of a context-sensitive grammar, in a way which preserves determinism.

Testing by PMI in 1995 showed that the beer knot preserves about to 80 % of the strength of the webbing.