Lattice Relaxation in Epitaxial BaTiO3_3 Thin Films

We have investigated the out-of-plane lattice relaxation related to the ferroelectric transitions in epitaxial BaTiO$_3$ (BTO) films using synchrotron X-ray diffraction. Under either compressive strain or tensile strain, there is evidence for two structural phase transitions as a function of temperature. The transition temperature $T_C$ is a strong function of strain, which can be as much as 100 K above the corresponding $T_C$ in bulk. Under compressive strain, the tetragonality of BTO unit cell implies that the polarization of the first ferroelectric phase is out-of-plane, while under tensile strain, the polarization is in-plane. The transitions at lower temperature may correspond to the $aa\to r$ or $c\to r$ transitions, following the notations by Pertsev \textit{et al}. The orientations of the domains are consistent with theoretical predictions.Comment: 4 pages, 3 figure

Investigation of upper-surface-blowing nacelle integration at cruise speeds utilizing powered engine simulators

Various overwing nacelle designs were investigated on a representative four engine short haul aircraft configuration during a combined analytical and experimental program. Design conditions were M sub o = 0.7 and C sub L = 0.4. All nacelles had D shaped nozzle exits and included a streamline contoured design, a low boattail angle reference configuration, and a high boattail angle powered lift design. Testing was done with the design four engine airplane configuration as well as with only inboard nacelles installed. Turbopowered engine simulators were used to provide realistic representation of nacelle flows. Performance trends are compared for the various nacelle designs. In addition, comparisons are presented between analytical and experimental pressure distributions and between flow through and powered simulator results

ANDY BEAL’S CONJECTURE ( PART1 AND PART 2)

This paper provides an algebraic mathematical proof to the below and proves their validity. 1)     The Andy Beal’s conjecture 2)     The Fermats last theorem 3)     The Wells summation conjecture 4)     The Goldbach conjecture 5)     The existence of  solitary numbers eg -10 Keywords: conjecture, vector analysis, three dimension, two dimension, increment, complex, law of algebra, prime factor, domain, algorithm, input, integer, real number line, dual set, magnitude, resultant, compute, binary, hack, twelve, shrink, standard, probability, linear equation, intersect, finite, 2% logarithmic, surds, narrow range, 98%, one dimensional space, compare, determine, flow, generalization,  infinity, independent, error, constant (k), dependent, graph, discretely, unaffected, HSIV, 4-input synchronous tetra- set, S4ISC, frequency, per binary input (BPI), aeroplane, run way, air friction, air resistance, take off angle,  plane crash, geometry, optimum, slope, partially collapsed, totally collapsed, supremacy, incoherence, airflight study, name, equation index or factor, honour, constant factor, economics, start discontinuity, man, robot, creation, simultaneously, cage theory, like energies

BEAL’S CONJECTURE

This paper provides algebraic mathematical proof to 6 unsolved problems in mathematics (number theory) and 3 others. 1)       The Beal’s conjecture (invalid forever) 2)       The Wells summation theorem 3)       The Fermats last theorem (376yrs- invalid forever) 4)       Unification engine of  all Power  summations 5)       The Goldbach conjecture (271yrs-valid forever) 6)       The proof of solitary -10-(valid forever ) 7)       NP VS P-problem,[ANS=NP≠P =[ NP- UNTIL- P ]= [NP-R-EI-T-P] 8)       The Riemann Hypothesis (invalid forever) 9)       Power summation pyramid-Carnox pyramid Keywords: conjecture, vector analysis, three dimension, two dimension, increment, complex, law of algebra, prime factor, domain, algorithm, input, integer, real number line, dual set, magnitude, resultant, compute, binary, hack, twelve, shrink, standard, probability, linear equation, intersect, finite, 2% logarithmic, surds, narrow range, 98%, one dimensional space, compare, determine, flow, generalization,  infinity, independent, error, constant (k), dependent, graph, discretely, unaffected, HSIV, 4-input synchronous tetra- set, S4ISC, frequency, per binary input (BPI), aeroplane, run way, air friction, air resistance, take off angle, plane crash, geometry, optimum, slope, partially collapsed, totally collapsed, supremacy, incoherence, airflight study, name, equation index or factor, honour, constant factor, economics, start discontinuity, man, robot, creation, simultaneously, cage theory, like energies, function solute, trivial, non-trivial, unplu

Holomorphic Hulls and Holomorphic Convexity

Paper by R. O. Wells, Jr

Automorphic Cohomology on Homogeneous Complex Manifolds

Paper by R. O. Wells, Jr

Key developments in geometry in the 19th Century

This paper describes several key discoveries in the 19th century that led to the modern theory of manifolds in the twentieth century: intrinsic differential geometry, projective geometry and higher dimensional manifolds and Riemannian geometry