Abstract:
The quality traits of durum wheat are important for the utilization by the industries. These traits may be influenced by genotype and interaction of genotype and environment (GxE). To evaluate the effects of genotype, environment and genotype x environment interaction on quality traits such as vitreousness, SDS sedimentation test, yellow pigment index, protein content and test weight, twelve Moroccan durum wheat cultivars representing a range of agronomic adaptation were tested in five locations representing a range of environments in three growing seasons. The results indicated significant effects of genotype, environment and GxE for all the quality traits. The extent of these effects differed; for SDS sedimentation volumes, yellow pigment and test weight, the component of variation due to genotype was larger than due to the environment, indicating the greater influence of genotypes on these traits. However, for vitreousness and protein content, the effect of environment was higher than the effect due to genotypes. Thus, these traits are controlled greatly by environmental effects than genetics. The variation due to GxE was higher than that of genotype for vitreousness and test weight, indicating high GxE interaction effect and less genotypic stability for these traits. For protein content, where the environmental effect was greater than that of genotype and GxE effect, multiple environmental trials are necessary in order to determine protein content of a cultivar. For other traits, preliminary evaluations can be done in one environment and good performing ones can be selected for multiple environmental trials.

Abstract:
Let m1, m2 be any numbers and let Vm1,m2 be the class of functions of analytic in the unit disc E={z:|z|<1} for which f ￠ € 2(z)=(S ￠ € 21(z))m1(S ￠ € 22(z))m2 where S1 and S2 are analytic in E with S ￠ € 21(0)=(S ￠ € 22(0))=1. Moulis [1] gave a sufficient condition and a necessary condition on parameters m1 and m2 for the class Vm1,m2 to consist of univalent functions if S1 and S2 are taken to be convex univalent functions in E. In fact he proved that if f ￠ € ‰ μ ￠ € ‰Vm1,m2 where S1 and S2 are convex and m1=k+24e ￠ ’i ±(1 ￠ ’ )cos ±, m2=k ￠ ’24e ￠ ’i ±(1 ￠ ’ )cos ±, 2|m1+m2| ￠ ‰ ¤1, then f is univalent in E.

Previous work by Sigalotti in 2006 and recently by Hendi and Sharifzadeh in 2012 showed that all the fundamental equations of special relativity may be derived from a golden mean proportioned classical-Euclidean triangle and confirmed Einstein’s famous equation E=mc^{2}. In the present work it is shown that exchanging the Euclidean triangle with a hyperbolic one an extended quantum relativity energy equation, namely , is obtained. The relevance of this result in understanding the true nature of the “missing” so-called dark energy of the cosmos is discussed in the light of the fact that the ratio of to E=mc^{2} is which agrees almost completely with the latest supernova and WMAP cosmological measurements.

Time dilation, space contraction and relativistic mass are combined in a novel fashion using Newtonian dynamics. In this way we can surprisingly retrieve an effective quantum gravity energy-mass equation which gives the accurate experimental value of vacuum density. Furthermore Einstein’s equation of special relativity E = mc^{2}, where m_{ }is the mass and c is the velocity of light developed assuming smooth 4D space time is transferred to a rugged Calabi-Yau and K3 fuzzy Kahler manifolds and revised to become E=(mc^{2})/(22), where the division factor 22 maybe interpreted as the compactified bosonic dimensions of Veneziano-Nambu strings. The result is again an accurate effective quantum gravity energy-mass relation akin to the one found using Newtonian dynamics which correctly predicts that 95.4915028% of the energy in the cosmos is the hypothetical missing dark energy. The agreement with WMAP and supernova measurements is in that respect astounding. In addition different theories are used to check the calculations and all lead to the same quantitative result. Thus the theories of varying speed of light, scale relativity, E-infinity theory, M-theory, Heterotic super strings, quantum field in curved space time, Veneziano’s dual resonance model, Nash Euclidean embedding and super gravity all reinforce, without any reservation, the above mentioned theoretical result which in turn is in total agreement with the most sophisticated cosmological measurements which was deservingly awarded the 2011 Nobel Prize in Physics.Finally and more importantly from certain viewpoints, we reason that the speed of light is constant because it is a definite probabilistic expectation value of a variable velocity in a hierarchical fractal clopen, i.e. closed and open micro space time.

Abstract:
An instructive analogy between the deformation of a pinched elastic cylindrical shell and the anti-gravity behind accelerated cosmic expansion is established. Subsequently the entire model is interpreted in terms of a hyperbolic fractal Rindler space-time leading to the same robust results regarding real energy and dark energy being 4.5% and 95.5% respectively in full agreement with all recent cosmological measurements.

We show that
Einstein’s famous formula E = mc^{2} is actually the sum of
two quantum parts, namely E = mc^{2}/22 of the quantum particle
and E = mc^{2} (21/22) of the quantum wave. We use first Magueijo-Smolin’s
VSL theory to derive the relevant equation and then validate our results using ’tHooft-Veltman’s
dimensional regularization. All in all our result confirms the COBE, WMAP,
Planck and super nova cosmic measurements with astonishing precision.

Abstract:
We establish that ordinary energy, Casimir energy and dark energy are not only interlinked but are basically the same thing separated merely by scale and topology. Casimir energy is essentially a nano scale spacetime phenomenon produced by the boundary condition of the two Casimir plates constituting the Casimir experimental set up for measuring the Casimir force. By contrast dark energy is the result of the cosmic boundary condition, i.e. the boundary of the universe. This one sided M?bius-like boundary located at vast cosmic distance and was comparable only to the Hubble radius scales of the universe. All the Casimir energy spreads out until the majority of it reaches the vicinity of the edge of the cosmos. According to a famous theorem due to the Ukrainian-Israeli scientist I. Dvoretzky, almost 96% of the total energy will be concentrated at the boundary of the universe, too far away to be measured directly. The rest of the accumulated Casimir energy density is consequently the nearly 4% to 4.5%, the existence of which is confirmed by various sophisticated cosmic measurements and observations. When all is said and done, the work is essentially yet another confirmation of Witten’s T-duality and mirror symmetry bringing nano scale and Hubble scale together in an unexpected magical yet mathematically rigorous way.

Abstract:
Based on Witten’s T-duality and mirror symmetry we show, following earlier work, the fundamental complimentarity of the Casimir energy and dark energy. Such a conclusion opens new vistas in cold fusion technology in the wider sense of the word which we tackle via fractal nano technologies leading to some design proposals for a nano Casimir-dark energy reactor.

Abstract:
The four-dimensional character of Einstein’s spacetime is generally accepted in mainstream physics as beyond reasonable doubt correct. However the real problem is when we require scale invariance and that this spacetime be four-dimensional on all scales. It is true that on our classical scale, the 4D decouples into 3D plus one time dimension and that on very large scale only the curvature of spacetime becomes noticeable. However the critical problem is that such spacetime must remain 4D no matter how small the scale we are probing is. This is something of crucial importance for quantum physics. The present work addresses this basic, natural and logical requirement and shows how many contradictory results and shortcomings of relativity and quantum gravity could be eliminated when we “complete” Einstein’s spacetime in such a geometrical gauge invariant way. Concurrently the work serves also as a review of the vast Literature on E-Infinity theory used here.

Abstract:
The topological speed of light which may be used to compute the density of ordinary energy and dark energy of the cosmos is replaced by dimensionless quantity taken from Special Relativity. The said quantity may be interpreted as akin to time dilation ergo a notion topologically equivalent to the speed of the passing of time or the difference of elapsed time between two events in Einstein’s Relativity Theory. This results via Newton’s kinetic energy into the well-known observationally confirmed and accurately measured 4.5 and 95.5 percent of ordinary and dark Cosmic Energy density respectively.