Abstract:
Newtonian adiabatics is the consistent truncation of the adiabatic approximation to second order in small velocities. To be complete it must unify two hitherto disjoint intellectual streams in the study of adiabatic motion. The newer stream focuses on Berry's induced vector potential, or geometric magnetism, and Provost and Vallee's induced scalar potential, reflecting geometry in Hilbert space. The older stream focuses on Inglis' induced inertia, influencing the geometry of adiabatic-parameter space. Starting with the Hamiltonian of the newer stream, unification is simple: A naive or primitive inertia, whose inverse appears in two terms of that Hamiltonian, is replaced by the convention-independent sum of primitive and induced inertia tensors.

Abstract:
Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.

Abstract:
The general form of the global conservation laws for $N$-body systems in the first post-Newtonian approximation of general relativity is considered. Our approach applies to the motion of an isolated system of $N$ arbitrarily composed and shaped, weakly self-gravitating, rotating, deformable bodies and uses a framework recently introduced by Damour, Soffel and Xu (DSX). We succeed in showing that seven of the first integrals of the system (total mass-energy, total dipole mass moment and total linear momentum) can be broken up into a sum of contributions which can be entirely expressed in terms of the basic quantities entering the DSX framework: namely, the relativistic individual multipole moments of the bodies, the relativistic tidal moments experienced by each body, and the positions and orientations with respect to the global coordinate system of the local reference frames attached to each body. On the other hand, the total angular momentum of the system does not seem to be expressible in such a form due to the unavoidable presence of irreducible nonlinear gravitational effects.

Abstract:
The equations of motion of $N$ gravitationally bound bodies are derived from the field equations of Projective Unified Field Theory. The Newtonian and the post-Newtonian approximations of the field equations and of the equations of motion of this system of bodies are studied in detail. In analyzing some experimental data we performed some numeric estimates of the ratio of the inertial mass to the scalaric mass of matter.

Abstract:
The aim of this study is to develop a test aiming at to determining the misconceptions about Newtonian laws of motion and to evaluate its applicability. The test was implemented to 85 student teachers enrolled in The Primary Science Teacher Training Program to determine the reliability. The reliability was found as 0,65. Then the test implemented to 42 firs grade students. Data from the test showed that student teachers have a lot of misconceptions about Newtonian Laws of Motion. Some misconceptions were determined such as “If a body is moving there is always a force acting in the direction of the motion”, “A moving body exerts a greater force than the stationary body when they collide”. One reason for these misconceptions is thought that the student teachers learn subjects and concepts not meaningfully but superficially by keeping them in their minds for a temporary period. That’s why it is suggested that this test should be applied to find out student teachers’ misconceptions and their causes. By this way teaching can be better organized according to the test results.

Abstract:
South African customary law is a body of law by which many South Africans regulate their lives in a multicultural society. South Africa's constitutional dispensation is based on the premise that all existing laws are subject to the Constitution of the Republic of South Africa 1996, including African customary law, and that all laws are limited only by the Constitution. Customary law existed long before the adoption of the Constitution which, among other things, aims at harmonising the different cultural practices that exist in the country. It is apparent that some traditional cultural practices that still exist are in conflict with the Constitution but, until they are challenged before a court of law, they will remain enforceable in our communities. This contribution investigates customary systems of succession that are guided by the principle of male primogeniture: a deceased's heir is his eldest son, failing which, the eldest son's oldest male descendant is his heir. The discussion focuses in particular on the case of Shilubana v Nwamitwa 2008 (9) BCLR 914 (CC). This case concerns an application to the Constitutional Court for a leave to appeal against a decision of the Supreme Court of Appeal substantially confirming a decision of the Pretoria High Court that prevented a woman from being a Hosi (traditional leader) of her own community.

Abstract:
South African customary law is a body of law by which many South Africans regulate their lives in a multicultural society. South Africa's constitutional dispensation is based on the premise that all existing laws are subject to the Constitution of the Republic of South Africa 1996, including African customary law, and that all laws are limited only by the Constitution. Customary law existed long before the adoption of the Constitution which, among other things, aims at harmonising the different cultural practices that exist in the country. It is apparent that some traditional cultural practices that still exist are in conflict with the Constitution but, until they are challenged before a court of law, they will remain enforceable in our communities. This contribution investigates customary systems of succession that are guided by the principle of male primogeniture: a deceased's heir is his eldest son, failing which, the eldest son's oldest male descendant is his heir. The discussion focuses in particular on the case of Shilubana v Nwamitwa 2008 (9) BCLR 914 (CC). This case concerns an application to the Constitutional Court for a leave to appeal against a decision of the Supreme Court of Appeal substantially confirming a decision of the Pretoria High Court that prevented a woman from being a Hosi (traditional leader) of her own community.

We show
first that an orbit, which is naturally characterized by its eccentricity and
semi-latus rectum, can equally be characterized by other sets of parameters,
and proceed to determine mass-independent characterizations. The latter is employed to obtain the
laws of equivalent orbits,
which by definition have the same eccentricity and orbit’s parameter [1]. These laws
relate the values of the same physical observables on two equivalent orbits to
the corresponding total mass; they include the laws of velocity, angular
velocity, radial velocity, areal velocity, acceleration, period, energy and
angular momentum. Regardless of the share of the two bodies of a fixed total
mass, the same relative orbit occurs for the same initial conditions. Moreover,
the same orbit can be traced by different total masses but with different
relative velocities. The concept of a gravitational field generated by a set of masses is shown to be
meaningful only when the center of mass is not changed by the test mass. The
associated concept of the “nothing”, which is an infinitesimal mass that allows
for the property just mentioned to be fulfilled, is introduced and its orbits are determined.
The perturbation of the nothing orbits due to its replacement by a finite mass
is determined. It is proved that such a replacement can have a qualitative
effect resulting in a “phase transition” of an orbit from unbound to bound, and
that the nothing’s circular orbits cannot be occupied by any material body. The
Galileo law of free fall, on which the equivalence principle hinges and which
is exact only for “nothing-like” falling objects, is revised to determine the
duration of free fall of a body of an arbitrary mass. The wholeness of Newton’s
laws and the associated concept of force as an interaction are highlighted, and some contradictions between the Newtonian
laws of equivalent Kepler’s orbits and the general relativistic predictions are discussed. It is
demonstrated that Newton’s law of gravitation is not an approximation of
Einstein field Equations even in the case of a static weak field. However, both
theories have a common limit corresponding to the case in which the alien
concept of a field can be incorporated in the Newtonian theory. We also show that the relative velocity’s hodograph [2-4], the
alternative Laplace-Runge-Lenz (LRL) vector derived by Hamilton [4-6], as well
as an infinite set of LRL vectors, result all from one vector. The hodograph is
a proper circular arc for hyperbolic motion, a circle less a point for parabolic motion, and a full circle
for bound

Abstract:
The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a spatially independent, time-homogenized version of Bak et al's procedure, which seems to present a universal scaling behavior.

It is shown that the speed of longitudinal-extended
elastic particles, emitted during an emission time T by a source S at speed u (escape speed toward the infinity due to all the masses in space), is invariant
for any Observer, under the Newtonian mechanics laws. It is also shown that a
cosmological reason implies the light as composed of such particles moving at speed u (function of the total gravitational potential). Compliance of c with Newtonian mechanics is shown for
Doppler effect, Harvard tower experiment, gravitational red shift and time
dilation, highlighting, for each of these subjects, the differences versus the relativity.