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partial melting  -  This is the process whereby partial melts are separated from residual solids as a result of bouyancy or other processes as temperature is raised.  Partial melting is one of the major ways that rocks in Earth and in asteroids can become differentiated.  The type of partial melting described in the paper is more properly referred to as equilibrium batch melting, in which a partial melt in equilibrium with solid separates all at once (in a "batch") from the remaining solid.  A related process is known as fractional melting; in this case, as soon as some melt is formed, it is separated from the solids.  Of the two processes, fractional melting can result in more mineralogic and chemical diversity than batch melting (why?).

fractional crystallization -  This is the process whereby crystals in a cooling system completely separate from magma as a result of gravitational settling or other processes.  Fractional crystallization is one of the major ways rocks in Earth and in asteroids become differentiated.  A related process, equilibrium crystallization, involves the maintenance of chemical equilibrium between crystallizing solids and residual melt that stay in contact with one another.  More mineralogic and chemical diversity is produced by fractional crystallization than by equilibrium crystallization (why?).

vitrophyric - This refers to a common texture of volcanic rocks, consisting of smaller crystals embedded in glass.

Thin-section of a plagioclase vitrophyre seen in cross-polarized
transmitted light.  Igneous glass appears appears dark;
the visible grains are plagioclase.
From: http://www.geolab.unc.edu/Petunia/IgMetAtlas/volcanic-micro/vitrophyre.X.html
 

subophitic  - This refers to a common igneous texture found in basaltic and gabbroic rocks, consisting of plagioclase laths which are partly surrounded by pyroxene grains, and that are partly in contact with other plagioclase grains.  An igneous rock in which plagioclase grains are completely surrounded by pyroxene grains would have what is known as an ophitic texture. Subophitic textures are commonly shown by eucrites (e.g., Millbillillie, as seen in the image gallery). Ophitic and subophitic textures can be seen in the same rocks, as the example below illustrates.

Subophitic and ophitic texture in thin-section.  The image at left was obtained in plane-polarized transmitted light;
the one at right was obtained in cross-polarized transmitted light.
From: http://www.utm.edu/~aelshazly/webpages/igtextures.html
 

monomict breccia - This is a type of breccia containing clasts of the same lithology, which formed by the impact break-up of a single rock type.  Most diogenites are monomict breccias.

polymict breccia - This is a type of breccia containing clasts of different lithologies, which formed by impact-mixing of different rock types.  Examples of polymict breccias are howardites (see the image gallery), mesosiderites (gallery), polymict eucrites, and a minority of ureilites.

genomict breccia - This is a type of breccia that contains clasts of closely-related but not entirely identical lithologies, such as one rock type metamorphosed to differing extents.  The best example of this are chondrites that contain clasts of the same chemical group but differing metamorphic grades (petrographic types).

XEn and XAn - These refer respectively to the fraction of enstatite molecule (En, MgSiO3) in pyroxene solid-solution [(Ca,Mg,Fe)SiO3] and to the fraction of anorthite molecule (An, CaAl2Si2O8) in plagioclase solid solution [NaAlSi3O8-KAlSi3O8-CaAl2Si2O8].  XEn and XAn are almost always expressed as mole fractions ranging from 0 to 1, but in Fig. 2 of the paper they are given in fractions ranging from 0 to 10.

cotectic - This refers to a situation in which a melt coexists with two or more minerals in equilibrium.  A cotectic relationship does not involve the special type of reaction between minerals and melt as in a peritectic (see below).  Examples of cotectics are shown by the dashed phase boundaries in Fig. 3 of the paper: namely, all of the phase boundaries indicated except the one between olivine and low-Ca pyroxene.  Another example of a cotectic is given in the diagram below.

Example of a cotectic (the dark heavy line) in the plagioclase-
diopside system at 1 bar pressure, as seen in a ternary liquidus
diagram.  The thin lines represent temperature contours in
degrees Celsius.  In this system, diopside and plagioclase of
varying composition can co-exist in equilibrium with a melt that
has the composition indicated by the cotectic.  If the system is
cooling, the composition of the cotectic melt will evolve from
upper right to lower left; the last melt to crystallize will have a
composition close to that of pure albite.
From: http://www.tulane.edu/~sanelson/geol212/ternaryphdiag.htm
 

eutectic - This is like a cotectic but one that represents the composition of either the last melt to crystallize or the first to melt for a given system.  An example is provided in Fig. 3 of the paper as the intersection point where the following minerals coexist: plagioclase + low-Ca pyroxene + silica mineral (+ high-Ca pyroxene, which coexists with all of the minerals shown; this is what is meant by "projected from diopside").

peritectic - This is a reaction relationship (also known as a "reaction boundary") found between certain minerals and co-existing melts.  During heating, a peritectic reaction involves the formation of a melt that has a composition outside the range of the minerals being melted (e.g., a mixture of olivine and pyroxene can partially melt to form a siliceous melt).  During cooling, a peritectic reaction involves the formation of minerals that together do not have the composition of the melt (e.g., a siliceous melt can crystallize to form an Si-poor assembage of olivine + pyroxene).  In Fig. 3 of the paper, the boundary shown between olivine and low-Ca pyroxene (the solid line) is a reaction boundary.
 

Phase diagram for the Mg2SiO4-SiO2 system at 1 bar pressure,
illustrating peritectic (P) and eutectic (E) points.  For a cooling
system, liquid with peritectic composition P will react with
co-existing forsterite to produce enstatite, whereas a liquid with
eutectic composition E will crystallize enstatite + quartz.  The link
leads to a discussion of how to use this diagram to evaluate
partial melting and crystallization processes for systems with
different bulk compositions (X, Y, and Z).
From: http://www.tulane.edu/~sanelson/geol212/2compphasdiag.html