nulpa'a
lujvo p_{1} expects/looks for the occurence of p_{2} (event), expected likelihood p_{3} (01); p_{1} subjectively evaluates the likelihood of p_{2} (event) to be p_{3}. The value of x_{3} is a subjective estimate of likeliness according to x_{1}, and is the basic determinant of whether nulpa'a means something like "hope" or "wish" or "expect", although nulpa'a never carries the connotation of desire; for that connotation see pacna. nulpa'a with x_{3} not very close to 1 has no simple equivalent in English, but for objects/states with negligible expectation it is something like "wishing"; if the state is plausibly likely, it is something like "hoping". In both cases, though, the English implication of emotional desire is not present. The value will usually be expressed using inexact numbers ("li piso'u" to "li piro"); notnecessarily desirous wish, not necessarily desirous hope. See also ba'a, djica, pacna, lakne, cunso.


salri
experimental gismu x_{1} is the differintegral of x_{2} with respect to x_{3} of order x_{4} with starting point x_{5} Definition of which differintegral operator is being used is context dependent. Output x1 is a function, not a value (that is, it is f rather than f(x)); it must be specified/restricted to a value in order to be a value. x2 is likewise a function. If the function has only one variable, x3 defaults to that variable; when x2 is physical, without context, time will probably usually be assumed as the default of x3 (but may be made explicit by temsalri). Positive values of x4 are integrals, negative values are derivatives, and zero is identity; at the least, any real value may be supplied for x4; x4 has no default value. Useful for making lujvo for physics, for specifying career/total/sum versus peak/instantaneous value, for distinguishing between instantaneous versus average values/quantities, for specifying rates, generalized densities (including pressure), "per" for smooth quantities, etc. See also: salrixo (synonymous zi'evla).


salrixo
fu'ivla x_{1} is the differintegral of x_{2} with respect to x_{3} of order x_{4} with starting point x_{5} Definition of which differintegral operator is being used is context dependent. Output x1 is a function, not a value (that is, it is f rather than f(x)); it must be specified/restricted to a value in order to be a value. x2 is likewise a function. If the function has only one variable, x3 defaults to that variable; when x2 is physical, without context, time will probably usually be assumed as the default of x3 (but may be made explicit by {temci zei salrixo}). Positive values of x4 are integrals, negative values are derivatives, and zero is identity; at the least, any real value may be supplied for x4; x4 has no default value. Useful for making lujvo for physics, for specifying career/total/sum versus peak/instantaneous value, for distinguishing between instantaneous versus average values/quantities, for specifying rates, etc. See also: salri (synonymous gismu).


terjonle'u
lujvo x_{1} (letteral: la'e zo BY/wordbu) is a hyphen/joining letter(al) in language x_{2} with function in/context of use/with rules for use/with properties x_{3}, joining prefixed unit/lexeme/morpheme/string x_{4} (quote) to postfixed unit/lexeme/morpheme/string x_{5} (quote) in construct (full word) x_{6} (quote) x_{1} joins words/morphemes/particles into a single cohesive, grammatical unit. x_{4} and x_{5} may be improper quotes. In English, "" is such a hyphen letteral; in Lojban, ybu, ry, ny, and ly are such hyphen letterals (arguably, as is y'y). The fact that the letteral is used to join words is implicit and this function therefore need not be specified in x_{3} in most cases.


terpanryziltolju'i
lujvo x1=j2=p3 (ka; jo'u/fa'u term) is the minor difference in/between x2=p2 and x3=p1 that is to be ignored, their similarity being by standard/in geometry x4; x2 is the same as/similar to/parallels x3 in standard/geometry x4 up to/modulo/except for/ignoring unimportant difference x1; x1 is not the focus of the main consideration concerning the similarity between x2 and x3; x2 belongs to/is an element of the same equivalence class as x3, which depends on x4 in some way and which ignores the property x1. For example, tetrominoes "L" and "7" are similar up to the unimportant property of 90degree rotation; thus: loka carna keiku ly terpanryziltolju'i zebu loka mapti. x2 and x3 are symmetric; while with panra, x1 (which is x3 in terpanryziltolju'i) is possibly of importance/focus/attention, for terpanryziltolju'i, x2 is. Additionally, lo panra and lo se panra are identical, therefore conversion under te does not affect the x2 and x3 positions of panra, so the overall structure does not need to have undergone an additional conversion. See: panra, klesi, panrykle, panryzilbri


ti'ormanku
lujvo x_{1}=m_{1} is shadedarkened/has shadow x_{2}=c_{1} cast upon it by obfuscating/blocking/(at least semi)opaque object x_{3}=c_{2} from energy/light/transmission source x_{4}=c_{3}; x_{2} is the shadoweclipse caste upon x_{1} by x_{3}, blocking radiation from x_{4} Possible uses include (but are not limited to) lunarstyle eclipses in which the eclipsed object (as seen from another object) is not physically blocked from sight by yet another object but is shaded from sight by the shadow cast upon it by some object (possibly the one from which the eclipse is viewed). There is no real physical difference between this and a solarstyle eclipse (both rely on linear alignment of bodies), but the chosen vantage point varies among them and thus causes different interpretations of the same phenomenon of alignment. In other words, it is an eclipse in which the eclipsed object is viewed to be darkened by a shadow (caste upon it by some object) with no significant blocking/impeding body physically betwixt the eclipsed object and the object from which viewing of the eclipse occurs.


kralyxaigle
lujvo x_{1}=g_{1} sexually violates/harms/rapes/violates the sexual rights of victim x_{2}=g_{2}=xai_{2}=k_{2}, violation by sexual activity (sex used as a weapon/means of harm), in property x_{3}=xai_{3} (ka) by resulting in injury x_{4}=xai_{4} (state), violating right x_{5}=k_{1} (event) which is morally/legally guaranteed but actually violated under standards x_{6}=k_{3}. Violated right k_{1} (event) may be implied by x4. The harm/violation must be by sexual activity (what one would consider gletu) and must be sexual in nature. Need not be violent. Harm may not be physical or even psychological/mental/emotional; it need only be a 'harm to one's rights' (in other words, a violation of loi krali). krali is an experimental gismu. The mutual symmetry of gle1 and gle2 is lost/broken by the harmervictim relationship enforced by this word (and, specifically, xai1 and xai2=k2). See also: glexai, xaigle, vilgle, glevlile, glevilxaigau, glekrali, glecu'akrali, glekralyxai, kralyxai.


zucna
experimental gismu x_{1} is counterclockwise/leftturndirection of[/to] x_{2} along/following track x_{3} [path] in frame of reference x_{4} (where the axis is within the region defined by the track as the boundary, as viewed from and defined by view(er) x_{4}; see notes); x_{1} is locally to the left of x_{2}, according to x_{4}, constrained along x_{3}; x_{1} is along a left turn from x_{2} along path x_{3}, as viewed in frame x_{4}. Angular/curling direction: counterclockwise. The orientation of the path determines x4 but does not factor into consideration for x3. Further glosses: counterclockwise, locally leftward, leftturning (with no bulk translation) in a way that would be characterized as "positive" by the righthand rule (aligned with and in the direction of a basis vector, at least for a given component). x1 is righthandedly/counterclockwise(ly) oriented relative to x2 on/along x3 in frame of reference x4 x1 is righthanded (one sense) from x2 [more accurately: moving from x2 to x1 requires a(n imaginary) motion that is righthanded along x3 as seen in frame/orientation/perspective x4]. x1 is to the pathfollowing left of x2 (where the path is connected; as such, x1 is also be to the pathfollowing right of x2, although there is an implication that the former is the smaller (or equallength) path). See also: dutso, za'ei (vectorial cross product), zu'au (modal). Proposed short rafsi: zuc, zu'a. (If “zn” ever becomes a permissible initial consonant pair, krtisfranks proposes that “zna” become a rafsi of this word it makes zucna and dutso more parallel in lujvo formation, and he is of the opinion that this word is useful and basic enough to warrant such a prized rafsi assignment; after this addition, the current two rafsi proposals can be done away with, reassigned, maintained, vel sim. as desired by the community at the time. In particular, he recognizes that “zu’a” might be confusing as a rafsi for this word while being a modal cmavo for zunle; but he does believe that this word deserves a vowelfinal short rafsi.)


aigne
fu'ivla x_{1} is an eigenvalue (or zero) of linear transformation/square matrix x_{2}, associated with/'owning' all vectors in generalized eigenspace x_{3} (implies neither nondegeneracy nor degeneracy; default includes the zero vector) with 'eigenspacegeneralization' power/exponent x_{4} (typically and probably by cultural default will be 1), with algebraic multiplicity (of eigenvalue) x_{5} For any eigenvector v in generalized eigenspace x_{3} of linear transformation x_{2} for eigenvalue x_{1}, where I is the identity matrix/transformation that works/makes sense in the context, the following equation is satisfied: ((x_{2}  x_{1} I)^x_{4})v = 0. When the argument of x_{4} is 1, the generalized eigenspace x_{3} is simply a strict/simple/basic eigenspace; this is the typical (and probable cultural default) meaning of this word. x_{4} will typically be restricted to integer values k > 0. x_{2} should always be specified (at least implicitly by context), for an eigenvalue does not mean much without the linear transformation being known. However, since one usually knows the said linear transformation, and since the basic underlying relationship of this word is "eigenness", the eigenvalue is given the primary terbri (x_{1}). When filling x_{3} and/or x_{4}, x_{2} and x_{1} (in that order of importance) should already be (at least contextually implicitly) specified. x_{3} is the set of all eigenvectors of linear transformation x_{2}, endowed with all of the typical operations of the vector space at hand. The default includes the zero vector (else the x_{3} eigenspace is not actually a vector space); normally in the context of mathematics, the zero vector is not considered to be an eigenvector, but by this definition it is included. Thus, a Lojban mathematician would consider the zero vector to be an (automatic) eigenvector of the given (in fact, any) linear transformation (particularly ones represented by a square matrix in a given basis). This is the logically most basic definition, but is contrary to typical mathematical culture. This word implies neither nondegeneracy nor degeneracy of eigenspace x_{3}. In other words there may or may not be more than one linearly independent vector in the eigenspace x_{3} for a given eigenvalue x_{1} of linear transformation x_{2}. x_{3} is the unique generalized eigenspace of x_{2} for given values of x_{1} and x_{4}. x_{1} is not necessarily the unique eigenvalue of linear transformation x_{2}, nor is its multiplicity necessarily 1 for the same. Beware when converting the terbri structure of this word. In fact, the set of all eigenvalues for a given linear transformation x_{2} will include scalar zero (0); therefore, any linear transformation with a nontrivial set of eigenvalues will have at least two eigenvalues that may fill in terbri x_{1} of this word. The 'eigenvalue' of zero for a proper/nice linear transformation will produce an 'eigenspace' that is equivalent to the entire vector space at hand. If x_{3} is specified by a set of vectors, the span of that set should fully yield the entire eigenspace of the linear transformation x_{2} associated with eigenvalue x_{1}, however the set may be redundant (linearly dependent); the zero vector is automatically included in any vector space. A multidimensional eigenspace (that is to say a vector space of eigenvectors with dimension strictly greater than 1) for fixed eigenvalue and linear transformation (and generalization exponent) is degenerate by definition. The algebraic multiplicity x_{5} of the eigenvalue does not entail degeneracy (of eigenspace) if greater than 1; it is the integer number of occurrences of a given eigenvalue x_{1} in the multiset of eigenvalues (spectrum) of the given linear transformation/square matrix x_{2}. In other words, the characteristic polynomial can be factored into linear polynomial primes (with root x_{1}) which are exponentiated to the power x_{5} (the multiplicity; notably, not x_{4}). For x_{4} > x_{5}, the eigenspace is trivial. x_{2} may not be diagonalizable. The scalar zero (0) is a naturally permissible argument of x_{1} (unlike some cultural mathematical definitions in English). Eigenspaces retain the operations and properties endowing the vectorspaces to which they belong (as subspaces). Thus, an eigenspace is more than a set of objects: it is a set of vectors such that that set is endowed with vectorspace operators and properties. Thus klesi alone is insufficient. But the set underlying eigenspace x_{3} is a type of klesi, with the property of being closed under linear transformation x_{2} (up to scalar multiplication). The vector space and basis being used are not specified by this word. Use this word as a seltau in constructions such as "eigenket", "eigenstate", etc. (In such cases, te aigne is recommended for the typical English usages of such terms. Use zei in lujvo formed by these constructs. The term "eigenvector" may be rendered as cmima be le te aigne). See also gei'ai, klesi, daigno
