Different Higgs models and the number of Higgs particles

In this short paper we discuss some interesting Higgs models. It is concluded that the most likely scheme for the Higgs particles consists of five physical Higgs particles. These are two charged H⁺, H⁻ and three neutrals h⁰, H⁰, A⁰. Further more the most probably total number of elementary particles for each model is calculated [El Naschie MS. Experimental and theoretical arguments for the number of the mass of the Higgs particles. Chaos, Solitons & Fractals 2005;23:1091–8; El Naschie MS. Determining the mass of the Higgs and the electroweak bosons. Chaos, Solitons & Fractals 2005;24:899–905; El Naschie MS. On 366 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model. Chaos, Solitons & Fractals 2005;24:447–57].     

Hilbert space,the number of Higgs particles and the quantum two-slit experiment

Rigorous mathematical formulation of quantum mechanics requires the introduction of a Hilbert space. By contrast, the Cantorian E-infinity approach to quantum physics was developed largely without any direct reference to the afore mentioned mathematical spaces. In the present work we present a novel reinterpretation of basic ε^(∞) Cantorian spacetime relations in terms of the Hilbert space of quantum mechanics. In this way, we gain a better understanding of the physical and mathematical structure of quantum spacetime. In particular we show that the two-slit experiment required a definite topology which is consistent with a certain fuzzy Kähler manifold or more generally a Cantorian spacetime manifold. Finally by determining the Euler class of this manifold, we can estimate the most likely number of Higgs particles which may be discovered.     

Determining the number of Higgs particles starting from general relativity and various other field theories

The Riemann–Einstein tensor of general relativity as well as chiral and super-symmetry are utilized to develop various extended versions of the standard model of high energy physics.Based on these models, it is possible to predict that few new elementary particles conjectured to be the Higgs are likely to be found experimentally at an energy scale which is just above that of the electroweak. Connections to the massless states of different super-string theories as well as super-gravity are also discussed.     

Transcendence of some power series for Liouville number arguments

In this paper, we prove that some power series with rational coefficients take either values of rational numbers or transcendental numbers for the arguments from the set of Liouville numbers under certain conditions in the field of complex numbers. We then apply this result to an algebraic number field. In addition, we establish the p-adic analogues of these results and show that these results have analogues in the field of p-adic numbers.     

The Higgs and the expectation value of the number of elementary particles in a supersymmetric extensions of the standard model of high energy physics

Supersymmetry, colours and chirality are utilized to develop three minimally extended versions of the standard model.Based on these models, it is possible to predict that few new elementary particles are likely to be found experimentally at an energy scale which is very modestly above that of the electroweak. Connections to the 8064 massless states of Heterotic string theory are also discussed.     

On the number of essential arguments of homomorphisms between products of median algebras

In this paper we characterize classes of median-homomorphisms between products of median algebras, that depend on a given number of arguments, by means of necessary and sufficent conditions that rely on the underlying algebraic and on the underlying order structure of median algebras. In particular, we show that a median-homomorphism that take values in a median algebra that does not contain a subalgebra isomorphic to the m-dimensional Boolean algebra as a subalgebra cannot depend on more than \(m-1\) arguments. In view of this result, we also characterize the latter class of median algebras. We also discuss extensions of our framework on homomorphisms over median algebras to wider classes of algebras.     

两个数论函数及其方程

对于任意给定的自然数n,著名的Eu ler函数φ(n)定义为不大于n且与n互素的正整数的个数.ω(n)表示n的所有不同素因子的个数.本文研究了方程φ(n)=2ω(n)的可解性,并给出了该方程的所有正整数解.     

Limit distributions for the number of particles in branching random walks

We study branching random walks with continuous time. Particles performing a random walk on ?², are allowed to be born and die only at the origin. It is assumed that the offspring reproduction law at the branching source is critical and the random walk outside the source is homogeneous and symmetric. Given particles at the origin, we prove a conditional limit theorem for the joint distribution of suitably normalized numbers of particles at the source and outside it as time unboundedly increases. As a consequence, we establish the asymptotic independence of such random variables.     

The irrationality of a number theoretical series

Denote by σ _k (n) the sum of the k-th powers of the divisors of n, and let . We prove that Schinzel’s conjecture H implies that S _k is irrational, and give an unconditional proof for the case k = 3. 2000 Mathematics Subject Classification Primary—11A25, 11N36, 11J72     

Supergravity and the number of fundamental particles in the standard model

Unification of the fundamental forces via supersymmetry is shown to yield valuable information about the number of particles and that of the Higgs particles which we could still discover experimentally within a reasonable distance from the electroweak energy scale.     

A number theoretical observation about the degeneracy of the genetic code

We discuss the similarity of the degeneration structure of the genetic code with a purely number theoretic “divisors code.” The most interesting thing about our observation is not that there is a connection between number theory and the genetic code, but the simplicity of the rule. We hope that the observation and the naive model presented in this paper will spur ideas for other models of the degeneracy of the genetic code. Maybe, the ideas of this article can also be used in the area of artificial life to synthesize artificial genetic codes.     

Experimental and theoretical investigation of PLC bands

In this paper, the nucleation and propagation of PLC deformation bands in AlMg3 alloy are studied experimentally and theoretically. The morphology and kinematics of PLC bands are investigated using both mechanical and thermal measurement methods. In particular, the latter is based on the use of a thermal camera which captures the temperature changes resulting from mechanical dissipation during nucleation and propagation of PLC bands. On the modeling side, two models are investigated via finite-element and finite-difference methods. Here, attention is focused on the influence of the specimen geometry and the thermomechanical coupling on PLC band nucleation and propagation. A comparison of experimental and simulation results is presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Experimental and theoretical investigation of a composite beam for bridge structures

Results of an experimental and theoretical investigation of composite beams as elements of bridge superstructure are presented. Experiments on beams of two types — made of wood and the same beams with a composite sheath — were carried out. The rigidity of the beams of the second type was about twice as high as that of the first ones. The classical bending model of composite beams gave deflections smaller than experimental ones. To reconcile these results, the model is refined by including the effect of shear. The deflections are represented as classical ones multiplied by a shear factor which depends on the bending and shear stiffnesses and the span length of the beams. As a result, a good agreement between calculations and experiments is achieved. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 449–462, July–August, 2006.     

On mass quantisation of elementary particles

A semi-phenomenological theory of mass quantisation is presented, wherein different elementary particles are regarded as excited positiveenergy states of a fundamental extensible object. The latter is essentially an elastic continuum which in its quiescent (classical equilibrium) state is believed to be massless and stressless. The classical Hamiltonian describing its oscillations about the equilibrium configuration is constructed by treating the mass-equivalent of the elastic potential energy as the inertial mass occurring in the denominator of the kinetic energy term. Quantisation of the resulting variable-mass oscillator is then effected by following the procedure given by Pauli and Podolsky. The energy-mass eigenvalues (m _n) for the above Schrödinger-like equation are given by $$\frac{{m_n }}{{m_0 }} = \left[ {1 + \left( {\frac{9}{2}} \right)^{1/3} \left( {\frac{{\mathchar'26\mkern-10mu\lambda _0 }}{2}} \right)^{2/3} p_n ^{2/3} } \right]$$ where ?₀ is the Compton wavelength of the lowest (ground state) eigen massm ₀, r_c is the measure of the linear dimension of the object, andp _n is the nth root of the Bessel function of order 1/3. In view of their infinite lifetime we treat the electron and the proton as the ground states for the two families of particles with baryon numbers zero and unity respectively. Accordingly, for the two families,m ₀ andr _c are chosen to correspond to the electron and the proton. The calculated mass values show striking agreement with the observed values for the two series.     

Asymptotics of the density matrix for a system of a large number of identical particles

The Wigner equation is considered for a system of a large numberN of identical particles with interaction factor of the order of 1/N. In both the Bose and the Fermi cases, we construct the asymptotics of the solution of the Cauchy problem for this equation with regard to the exchange effect for the case in which the Planck constant is of the order ofN ^−1/d , whered is the space dimension. This asymptotics is interpreted in terms of the theory of the complex germ on a curved phase space equivalent to the space of functions with values on the Riemann sphere in the Fermi case and on the Lobachevskii plane in the Bose case. The classical equations of motion in both cases are reduced to the Vlasov equation; since the phase space is infinite-dimensional, the complex germ is subjected to additional conditions depending on the type of statistics. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 84–106, January, 1999.