J. M. C. Montanus

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The lateral density of a cosmic air shower with a non-zero zenith angle is azimuthally asymmetric. The azimuthal asymmetry consist of a stretching of the iso-density contours to ellipses and to a shift of the center of the elliptic contours with respect to the core of the shower. The aim of the paper is to investigate the shift of the center of the...

The Heitler-Matthews model for hadronic air showers will be extended to all the generations of electromagnetic subshowers in the hadronic cascade. The relation between interaction length and the thickness of the cascade layers is revisited. The analysis is outlined in detail for showers initiated by primary protons. For showers initiated by iron pr...

Cosmic rays impacting on the atmosphere cause particle-showers. Several descriptions exist for the evolution of the shower size along the atmospheric depth. The well known functions for shower profiles, Greisen, Gaisser–Hillas and ‘Gaussian in Age’, are intimately connected in that they all are approximate solutions of versions of the Rossi and Gre...

Many areas of active research within the broad field of number theory relate to properties of polynomials, and this volume displays the most recent and most interesting work on this theme. The 2006 Number Theory and Polynomials workshop in Bristol drew together international researchers with a variety of number-theoretic interests, and the book's c...

An exact series will be given for the gravitational potential generated by an oblate gravitating source. To this end the corresponding Epstein-Hubbell type elliptic integral is evaluated. The procedure is based on the Legendre polynomial expansion method and on combinatorial techniques. The result is of interest for gravitational models based on th...

A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euc...

In this paper, an exact series will be derived for the calculation of rotational velocities in homogeneous disk galaxies with finite thickness. The procedure is based on the Legendre polynomial expansion method for the solution of the Epstein-Hubbell integral. A ‘scaling’ method will also be given in order to derive approximate values for rotationa...

It will be argued that Minkowski's implementation of distances is inconsistent. An alternative implementation will be proposed. In the new model the proper time of an object is taken as its fourth coordinate. Distances will be measured according to a four dimensional Euclidean metric. In the present approach mass is a constant of motion. A mass can...

It is argued that Minkowski's implementation of distances is not unique. An alternative implementation is proposed. If Einstein's prescription for light speed measurements is applied to the new implementation, the special theory of relativity is recovered. Yet, the present model is based on a spacetime with a preferred frame of reference. A clock a...

A dark-matter explanation as well as a luminous-matter explanation is offered for the phenomenon of flat rotation curves in galaxies. Since neutrinos and photons are massive in the theory of an absolute Euclidean space-time, it naturally allows for a dark-matter explanation for the enigma of missing mass. With the method the rotational velocity for...

The author considers hyperbolic orbits in an absolute Euclidean space-time. Analyses will be performed for massive objects moving at various speeds pact a heavy source mass like the Sun. In the limiting case of a massive object moving with the speed of light, the hyperbolic orbit turns out to be equal to the path of a photon. The contents of the pa...

In this paper we will offer a comprehensive explanation for the deflection of the path of a photon when it passes a heavy source mass like the sun. The analysis will be completely based on the theory of an absolute Euclidean space-time. According to this theory, space-time is flat everywhere, even in the presence of a gravitational field. The descr...

In this paper we consider the Compton effect, the annihilation of an electron-positron pair, and the decoy of the pion into a muon and a neutrino. Until now it was believed that these phenomena could only be explained by means of the theory of relativity (TR). In this paper we will show that these phenomena can also be given a comprehensive explana...

In this paper we will offer decisive arguments against the general theory of relativity. We will also offer an alternative model for gravitation; that is, we will construct the appropriate Lagrangian for the description of gravitational dynamics in an absolute Euclidean space-time. This Lagrangian leads to the correct predictions for the gravitatio...

The author considers two phenomena well known from the general theory of relativity in an absolute Euclidean space-time. From the mathematical point of view a Euclidean space-time can be obtained from a Minkowski space-time by means of a simple rearrangement procedure. The author makes use of this procedure to derive the Euclidean space-time analog...

In a paper by Miranda and Persson [MP89], the authors study semi-stable elliptic fibrations over P1 of K3-surfaces with 6 singular fibres. In their paper the authors give a list of possible fiber types for such fibrations. It turns out that there are 112 cases. The corresponding J-invariant is a so-called Belyi-function. More particularly, J is a r...