The exceptional Jordan algebra is the algebra of $3 \times 3$ Hermitian matrices with octonionic entries. It is the only one from Jordan’s algebraic formulation of quantum mechanics which is not equivalent to the conventional formulation of quantum theory. It has often been suggested that this exceptional algebra could explain physical phenomena not currently explained by the conventional approach, such as values of the fundamental constants of the standard model of particle physics, and their relation to gravitation. We show that this is indeed the case; and this also unravels the connection between general relativity and the weak force. The exceptional Jordan algebra also predicts a new U(1) gravitational interaction which modifies general relativity, and which provides a theoretical basis for understanding the Modified Newtonian Dynamics (MOND).

We have recently proposed a pre-quantum, pre-space-time theory as a matrix-valued Lagrangian dynamics on an octonionic space-time. This pre-theory offers the prospect of unifying the internal symmetries of the standard model with gravity. It can also predict the values of free parameters of the standard model, because these parameters arising in the Lagrangian are related to the algebra of the octonions which define the underlying non-commutative space-time on which the dynamical degrees of freedom evolve. These free parameters are related to the algebra $J_3(\mathbb O)$ [exceptional Jordan algebra] which in turn is related to the three fermion generations. The exceptional Jordan algebra [also known as the Albert algebra] is the finite dimensional algebra of 3x3 Hermitean matrices with octonionic entries. Its automorphism group is the exceptional Lie group $F_4$. These matrices admit a cubic characteristic equation whose eigenvalues are real and depend on the invariant trace, determinant, and an inner product made from the Jordan matrix. Also, there is some evidence in the literature that the groups $F_4$ and $E_6$ could play a role in the unification of the standard model symmetries, including the Lorentz symmetry. The octonion algebra is known to correctly yield the electric charge values (0, 1/3, 2/3, 1) for standard model fermions, via the eigenvalues of a $U(1)$ number operator, identified with $U(1)_{em}$. In the present article, we use the same octonionic representation of the fermions to compute the eigenvalues of the characteristic equation of the Albert algebra, and compare the resulting eigenvalues with the known mass ratios for quarks and leptons. We find that the ratios of the eigenvalues correctly reproduce the [square root of the] known mass ratios for quarks and charged leptons. We also propose a diagrammatic representation of the standard model bosons, Higgs and three fermion generations, in terms of the octonions, exhibiting an $F_4$ and $E_6$ symmetry. In conjunction with the trace dynamics Lagrangian, the Jordan eigenvalues also provide a first principles theoretical derivation of the low energy value of the fine structure constant, yielding the value $1/137.04006$. The Karolyhazy correction to this value gives an exact match with the measured value of the constant, after assuming a specific value for the electro-weak symmetry breaking energy scale.

We propose an $E_8 \otimes E_8$ unification of the standard model with pre-gravitation, on an exceptional Lie algebra-valued space . Each of the $E_8$ has in its branching an $SU(3)$ for space-time and an $SU(3)$ for three fermion generations. The first $E_8$ further branches to the standard model $SU(3)_c \otimes SU(2)_L \otimes U(1)_Y$ and describes the gauge bosons, Higgs and the left chiral fermions of the standard model. The second $E_8$ further branches into a right-handed counterpart (pre-gravitation) $SU(3)_{grav}\otimes SU(2)_R \otimes U(1)_g$ of the standard model, and describes right chiral fermions, a Higgs, and twelve gauge bosons associated with pre-gravitation, from which general relativity is emergent. We account for 208 out of the 496 degrees of freedom of $E_8 \otimes E_8$ and propose an interpretation for the remaining 288, motivated by the trace dynamics Lagrangian of our theory. We explain how the two copies of $SU(3)_{spacetime}$ together give rise to a 6D spacetime with signature $(3,3)$ which upon symmetry breaking gives rise to our 4D spacetime and to a second 4D anti-spacetime with flipped signature.

We report a theoretical derivation of the Cabibbo-Kobayashi-Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e. left-chiral states) as superposition of mass eigenstates (i.e. the right-chiral states) weighted by square-root of mass. Flavor mixing for quarks is mediated by the square-root mass eigenstates, and the mass ratios used have been derived in earlier work from a left-right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, they can be listed as follows - the real numbers $\mathbb{R}$, the complex numbers $\mathbb{C}$, the quaternions $\mathbb{H}$ and the octonions $\mathbb{O}$. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also the action of various Spin Groups on these representations too can be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as $\theta_{12}=11.093^o, \theta_{13}=0.172^o, \theta_{23}=4.054^o$. In comparison, the corresponding experimentally measured values for these angles are $13.04^o \pm 0.05^o, 0.201^o \pm 0.011^o, 2.38^o \pm 0.06^o $. The agreement of theory with experiment is likely to improve when running of quark masses is taken into account.

What began nearly a century ago with the contributions of Hollingworth and Asperger, among others, has developed into a field dedicated to the study of gifted individuals with a disability. These twice-exceptional (2e) people and their unique set of needs differ from those of their once-exceptional counterparts on either end of the spectrum and often remain unaddressed or are discovered very late in life resulting in longterm consequences. For those discovered, effective treatment options to improve their quality of life remain uncertain. The goal of the present paper was to determine whether effective interventions exist to improve domain-specific (i.e., social, emotional, or academic) outcomes for people exhibiting both signs of giftedness and disability. A query was performed using evidence databases TRIP and PDQ in addition to University at Buffalo Libraries holdings for "twice-exceptional," "Giftedness," "Disability," and "intervention." The hits were reduced to the four most relevant, freely available studies in English that were selected for critique. Despite the selected studies being found to share methodological similarities that were their strengths and conducive to comparison, they also had threats to validity that served as potential weakness. Not only can directly effective interventions improve specific domains for 2e individuals, but the effects of domain-specific interventions may carry over into another domain resulting in indirect effects.

Gifted students are usually known as students who have exceptional cognitive and learning abilities. This can be made clear through their learning performance or test scores. However, there are other students who have been identified as gifted and talented, yet have some learning and /or physical disabilities, and these are called twice-exceptional students. Identifying this population of gifted students is usually problematic because their disabilities and difficulties may mask their abilities and vice versa. It has been suggested that twice-exceptional students’ skills and abilities cannot be improved simply by working harder. Instead, these students need teachers to understand their strengths and weaknesses, use teaching strategies that fit their disabilities and serve their needs, and include their parents and educators in their learning process. Thus, this conceptual paper provides an extensive overview of the needs, challenges, and teaching strategies related to twice-exceptional students.

The Siret River crosses NE Romania from the north to the south and it discharges into the Danube, near the city of Galati. During the period, 17^th June - 10^th July 2010, significant amounts of precipitations in the mountainous basin of Siret were recorded. The floods comprised two periods with four bimodal cycles and they were counted among the strongest on the Romanian territory. The exceptional floods occurred in the rivers of Siret, Suceava, Moldova, Bistrita, Trotus and so on. The most important compound flood wave was determined by the precipitations which fell within the period, 29^th June to 1^st July 2010, when significant amounts of rain were recorded, sometimes, exceeding 80 mm. The high discharges on the Bistrita River – downstream from the Bicaz Reservoir – were controlled by complex hydro technical works. The maximum discharge for the year 2010 summer floods was recorded at Dragesti hydrometric station: 2,884 m³/s (historic discharge) compared to the preceding historic discharge of the year 2008 (2,850 m³/s). The effects of floods were strongest in the counties of Suceava, Neamt, and Bacau. The floods on the main course of the Siret River were analyzed in correlation with the tributaries within the mountainous sector.

When gravity is quantum, the point structure of space-time should be replaced by a non-commutative geometry. This is true even for quantum gravity in the infra-red. Using the octonions as space-time coordinates, we construct a pre-spacetime, pre-quantum Lagrangian dynamics. We show that the symmetries of this non-commutative space unify the standard model of particle physics with $SU(2)_R$ chiral gravity. The algebra of the octonionic space yields spinor states which can be identified with three generations of quarks and leptons. The geometry of the space implies quantisation of electric charge, and leads to a theoretical derivation of the mysterious mass ratios of quarks and the charged leptons. Quantum gravity is quantisation not only of the gravitational field, but also of the point structure of space-time.