In this paper, we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints. We introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex, strong pseudoinvex, weak quasi invex, weak pseudoinvex and strong quasi invex functions in Aghezzaf and Hachimi [Numer. Funct. Anal. Optim. 22 (2001) 775], d-...

We study the orbits in the MOND theory within a dwarf galaxy of mass Md ∼ 108M⊙ at a distance of ∼ 100kpc from a neighboring galaxy of mass Mg = 5 × 1011M⊙, such as ours. It is assumed that a second mass m << Md is gravitationally bound to Md by a previously calculated potential for the MOND theory. This potential is obtained for a free falling mass Md in a constant external gravitational accel...

The applications of Newtonian dynamics in galactic scales have shown that the inverse square law is incompatible with the amount of visible mass in the form of stars and molecular clouds. This manifests as the rotational curves of galaxies being asymptotically flat instead of decaying with the distance to the center of the galaxy. In the context of Newtonian gravity, the standard explanation re...

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matte...

Globular clusters (GCs) in the Milky Way have characteristic velocity dispersions that are consistent with the predictions of Newtonian gravity, and may be at odds with Modified Newtonian Dynamics (MOND). We discuss a modified gravity (MOG) theory that successfully predicts galaxy rotation curves, galaxy cluster masses and velocity dispersions, lensing, and cosmological observations, yet produc...

The modified Newtonian dynamics (MOND) has been proposed as an alternative to the dark matter paradigm; the philosophy behind is that there is no dark matter and we witness a violation of the Newtonian law of dynamics. In this article, we interpret differently the phenomenology sustaining MOND, as resulting from an effect of “gravitational polarization”, of some cosmic fluid made of dipole mome...

The observed matter in the universe accounts for just 5% of the observed gravity. A possible explanation is that Newton's and Einstein's theories of gravity fail where gravity is either weak or enhanced. The modified theory of Newtonian dynamics (MOND) reproduces, without dark matter, spiral-galaxy orbital motions and the relation between luminosity and rotation in galaxies, although not in clu...

The rotation curves of low surface brightness galaxies provide a unique data set with which to test alternative theories of gravitation over a large dynamic range in size, mass, surface density, and acceleration. Many clearly fail, including any in which the mass discrepancy appears at a particular length-scale. One hypothesis, MOND [Milgrom 1983, ApJ, 270, 371], is consistent with the data. In...

Several recent studies have shown that velocity differences of very wide binary stars, measured to high precision with GAIA, can potentially provide an interesting test for modified-gravity theories which attempt emulate dark matter. These systems should be entirely Newtonian according standard dark-matter theories, while the predictions MOND-like are distinctly different, if various observatio...

The statistics of high speed satellite galaxies, as reported in the recent literature, can be a powerful diagnosis of the depth of the potential well of the host halo, and hence discriminate between competing gravitational theories. Naively one expects that high speed satellites are more common in Modified Newtonian Dynamics (MOND) than in cold dark matter (CDM) since an isolated MONDian system...