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Construction in transcendental number theory
In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions that appear in most proofs in this
Auxiliary_function
Special functions of several complex variables
\mathbb {C} } . The Jacobi theta function defined above is sometimes considered along with three auxiliary theta functions, in which case it is written with
Theta_function
Pseudoscientific personality questionnaire
person's most preferred extraverted function, which is the dominant function for extraverted types and the auxiliary function for introverted types. The MBTI
Myers–Briggs_Type_Indicator
On algebraic independence of logarithms
throughout the proof. The main idea of Baker's proof is to construct an auxiliary function Φ ( z 1 , … , z n − 1 ) {\displaystyle \Phi (z_{1},\ldots ,z_{n-1})}
Baker's_theorem
Special function defined by an integral
Fresnel integrals S(x) and C(x), and their auxiliary functions F(x) and G(x) are transcendental functions named after Augustin-Jean Fresnel that are used
Fresnel_integral
Method to solve constrained optimization problems
To incorporate these conditions into one equation, we introduce an auxiliary function L ( x , y , λ ) ≡ f ( x , y ) + λ ⋅ g ( x , y ) , {\displaystyle {\mathcal
Lagrange_multiplier
Smooth and compactly supported function
analysis, a bump function is a localized auxiliary function, usually chosen to be smooth and to have compact support. Bump functions are commonly used
Bump_function
Use of functions that call themselves
nested functions, the auxiliary function can be nested inside the wrapper function and use a shared scope. In the absence of nested functions, auxiliary functions
Recursion_(computer_science)
Algorithms for zeros of functions
values by evaluating an auxiliary function on the preceding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having
Root-finding_algorithm
Function in quantum field theory showing probability amplitudes of moving particles
In quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one
Propagator
Study of numbers that are not solutions of polynomials with rational coefficients
Euler's identity. This work centred on use of the so-called auxiliary function. These are functions which typically have many zeros at the points under consideration
Transcendental_number_theory
The Mayer f-function is an auxiliary function that often appears in the series expansion of thermodynamic quantities related to classical many-particle
Mayer_f-function
Special function defined by an integral
Trigonometric integrals can be understood in terms of the so-called "auxiliary functions" f ( x ) ≡ ∫ 0 ∞ sin ( t ) t + x d t = ∫ 0 ∞ e − x t t 2 + 1 d
Trigonometric_integral
Association of one output to each input
thus, for a complicated function, the determination of the domain passes through the computation of the zeros of auxiliary functions. Similarly, if square
Function_(mathematics)
Topics referred to by the same term
Auxiliary polynomial is a term in mathematics which may refer to: The auxiliary function argument in transcendence theory The characteristic polynomial
Auxiliary_polynomial
Description of particle density in statistical mechanics
corresponding virial expansions. The auxiliary function y ( r ) {\displaystyle y(r)} is known as the cavity distribution function. It has been shown that for classical
Radial_distribution_function
Classification of individuals based on personality traits
dominant function is supported by two auxiliary functions. (In MBTI publications the first auxiliary is usually called the auxiliary or secondary function and
Personality_type
Verb adding grammatical meaning rather than content meaning
grammatical behavior, as described below. In some cases, verbs that function similarly to auxiliaries, but are not considered full members of that class (perhaps
Auxiliary_verb
1921 book by Carl Gustav Jung
four main functions of consciousness: two perceiving or non-rational functions (Sensation and Intuition), and two judging or rational functions (Thinking
Psychological_Types
Concentrated solar power station in Drâa-Tafilalet, Morocco
the turbine and synchronize it with the electrical grid, and other auxiliary functions. The plant was completed in four phases and covers an area of over
Ouarzazate Solar Power Station
Ouarzazate_Solar_Power_Station
Software programming optimization technique
these languages heavily use auxiliary functions called thunks to compute the argument values, and memoize these functions to avoid repeated calculations
Memoization
Analytic function that does not satisfy a polynomial equation
mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent variable
Transcendental_function
Small set of grammatically distinctive verbs of English
English auxiliary verbs are a small set of English verbs, which include the English modal auxiliary verbs and a few others. Although the auxiliary verbs
English_auxiliary_verbs
Sequence of program instructions invokable by other software
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed
Function (computer programming)
Function_(computer_programming)
the partition function P ( n 1 , n 2 ) {\displaystyle P(n_{1},n_{2})} can be defined piecewise with the help of two auxiliary functions. If n 1 ≤ n 2
Kostant_partition_function
Organized group supplementing the military or law enforcement
support functions or performing certain duties such as garrison troops, usually on a part-time basis. Unlike a military reserve force, an auxiliary force
Auxiliaries
'Best' approximation of a function by a rational function of given order
extensively in computer calculations. They have also been used as auxiliary functions in Diophantine approximation and transcendental number theory, though
Padé_approximant
Orthogonal wavelet
}}x>1.\end{cases}}} There are many different ways for defining this auxiliary function, which yields variants of the Meyer wavelet. For instance, another
Meyer_wavelet
Type of specialized ship
or shadow vessel, are specialized ships which provide support and auxiliary functions for large sailing and motor yachts. In general yacht support vessel
Yacht_support_vessel
Auxiliary engine to slowly rotate big engines
inspecting the shaft, reduction gears, bearings, and turbines. As an auxiliary function, the jacking gear also helps to maintain a protective oil membrane
Jacking_gear
Software to aid production of "help" systems
program used by technical writers to create online help systems. The basic functions of a Help Authoring Tool (HAT) can be divided into the following categories:
Help_authoring_tool
Generalization of the concept from statistical mechanics
the partition function in quantum field theory. A common, useful modification to the partition function is to introduce auxiliary functions. This allows
Partition function (mathematics)
Partition_function_(mathematics)
for propulsion and auxiliary functions. Micro-Hybrid Vehicle - obsolete term. Recuperated energy is used for auxiliary functions like engine restart
Vehicle classification by propulsion system
Vehicle_classification_by_propulsion_system
Abstract data type
results, | s | = | f | − | r | + 1 {\displaystyle |s|=|f|-|r|+1} . An auxiliary function a u x {\displaystyle aux} must then be called for the invariant to
Queue_(abstract_data_type)
Set with operations obeying given axioms
existential axiom is satisfied consists generally of the definition of the auxiliary function, completed with straightforward verifications. Also, when computing
Algebraic_structure
Conceptual framework used in numerical analysis of surfaces and shapes
shape boundary in our example) using an auxiliary function φ {\displaystyle \varphi } , called the level-set function. The curve Γ {\displaystyle \Gamma }
Level-set_method
Ship
metres (25,800 sq ft), and two 600-horsepower diesel engines for auxiliary functions. During her career as a training ship, she was manned by a crew of
Nippon_Maru_(1930)
Mathematical puzzle
roots) is treated with the help of an auxiliary function, which is invoked every time a value v is recorded. This function computes nested factorials and roots
Four_fours
Type of function in linear algebra
sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm, on a vector space is a real-valued function with
Sublinear_function
Business performance management approach
conduct, and that auxiliary functions should be outsourced to vendors, so that firms may focus on their core components and functions. Ming Yingzhao and
Intelligent_enterprise
Risk measure estimating the average loss in the worst tail of the distribution
of Rockafellar and Uryasev in their 2000 paper is to introduce the auxiliary function F α ( w , γ ) {\displaystyle F_{\alpha }(w,\gamma )} for the expected
Expected_shortfall
Words supplying mainly grammatical information, rather than content information
second-language acquisition and English-language teaching. Function words might be prepositions, pronouns, auxiliary verbs, conjunctions, grammatical articles or particles
Function_word
Auxiliary functions used to probe equations, distributions, and weak formulations
Test functions are auxiliary functions used in mathematical analysis to probe other functions, distributions, differential equations, or variational identities
Test_function
Volunteer auxiliary service of the United States Coast Guard
The United States Coast Guard Auxiliary (USCGAUX, CGAux, or USCG Aux) is the uniformed, civilian volunteer component of the United States Coast Guard
United States Coast Guard Auxiliary
United_States_Coast_Guard_Auxiliary
Function defined on formal languages in computer science
string a. The latter can be computed as follows: Here, ν(R) is an auxiliary function yielding a generalized regular expression that evaluates to the empty
Brzozowski_derivative
Measure of the decline from a historical peak
problem into a linear program. The authors start by proposing an auxiliary function Δ α ( x ) {\displaystyle \Delta _{\alpha }(x)} , where x ∈ R p {\displaystyle
Drawdown_(economics)
Japanese training sailing ship
(29,700 sq ft), and has two 1,500-horsepower diesel engines for auxiliary functions. She has a crew complement of 70, with a training complement of 120
Nippon_Maru_(1984)
Problem of deciding whether an expression equals zero
transcendence theory are proofs by contradiction. Specifically, they use some auxiliary function to create an integer n ≥ 0, which is shown to satisfy n < 1. Clearly
Constant_problem
Language consisting of balanced strings of brackets
that S n {\displaystyle S_{n}} is also antisymmetric we introduce an auxiliary function σ n : D n → N {\displaystyle \sigma _{n}:{\mathcal {D}}_{n}\rightarrow
Dyck_language
Appliance for cold food storage
more and more during the 1920s; up to this time freezing was not an auxiliary function of the modern refrigerator. The first refrigerator to see widespread
Refrigerator
Mathematical functions related to Weierstrass's elliptic function
mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function. They are named for
Weierstrass_functions
Words that indicate a question is being asked, as a grammatical category
inversion involving an auxiliary verb (or negative contraction), sometimes even if it is not performing the auxiliary function: A finite inflection of
Interrogative_word
Alternative vehicle power source
An auxiliary power unit (APU) is a device on a vehicle that provides energy for functions other than propulsion. They are commonly found on large aircraft
Auxiliary_power_unit
Robust nonlinear control to achieve exponential stabilization
a Lyapunov stability analysis that utilizes an auxiliary function, often referred to as the P-function, to establish both asymptotic and exponential stability
RISE_controllers
Theorem
the solutions of linear equations obtained by the construction of auxiliary functions. The existence of these polynomials was proven by Axel Thue; Thue's
Siegel's_lemma
Constructed language meant to facilitate communication
An international auxiliary language (sometimes acronymized as IAL or contracted as auxlang) is a language meant for communication between people from
International auxiliary language
International_auxiliary_language
Decomposition of periodic functions
f(\mathbf {r} )} in a Fourier series, it is convenient to introduce an auxiliary function g ( x 1 , x 2 , x 3 ) ≜ f ( r ) = f ( x 1 a 1 a 1 + x 2 a 2 a 2 +
Fourier_series
American psychologist
preferred, or auxiliary, function is the good parent, which may be counteracted by a shadowy witch/senex complex; similarly the tertiary function (“child”)
John_Beebe
Mapping arbitrary data to fixed-size values
divide. A necessary adjunct to the hash function is a collision-resolution method that employs an auxiliary data structure like linked lists, or systematic
Hash_function
Person managing a hotel
centralized corporate office or solely by the hotel manager. Additional auxiliary functions such as security may be handled by third-party vendor services contracted
Hotel_manager
System of identifying electrical power devices
in ANSI/IEEE Standard C37.2 Standard for Electrical Power System Device Function Numbers, Acronyms, and Contact Designations. Many of these devices protect
ANSI_device_numbers
Japanese training ship
metres (25,800 sq ft), and two 600-horsepower diesel engines for auxiliary functions. During her career as a training ship, she was crewed by a complement
Kaiwo_Maru_(1930)
Wireless personal area network technology
other services as sub-functions; the main functions of the device are so-called primary services, and the auxiliary functions they refer to are secondary
Bluetooth_Low_Energy
Function for integral Fourier-like transform
a multiresolution analysis. This means that there has to exist an auxiliary function, the father wavelet φ in L2(R), and that a is an integer. A typical
Wavelet
1993 game engine
games produced by licensees. It was created by John Carmack, with auxiliary functions written by Mike Abrash, John Romero, Dave Taylor, and Paul Radek
Doom_engine
Electric vehicle powered by solar energy
be used to provide power for communications or controls or other auxiliary functions.[citation needed] Solar vehicles are not sold as practical day-to-day
Solar_vehicle
Type of function in database management
Combine (binary merge on two aggregations), and FinalReduce (final function on auxiliary values), and moving decomposable aggregation before the Shuffle
Aggregate_function
Force applied by the hand to hold
in sports. However, the grip strength is most often a secondary or auxiliary function of the sport. Sports in which grip strength are included within the
Grip_strength
Digital computers that used discrete transistors as their primary logic elements
may still have included vacuum tubes in the power supply or for auxiliary functions. University of Manchester Transistor Computer 1953 (prototype) 1955
List of transistorized computers
List_of_transistorized_computers
support the frontline combat vessels of the United States Navy. Auxiliary ships which function as hospital ships and as oilers are to be found in their own
List of auxiliaries of the United States Navy
List_of_auxiliaries_of_the_United_States_Navy
Class of auxiliary verbs in English that lack untensed forms
Wiktionary, the free dictionary. The English modal auxiliary verbs are a subset of the English auxiliary verbs used mostly to express modality, properties
English_modal_auxiliary_verbs
Naval auxiliary fleet which supports the Royal Navy
The Royal Fleet Auxiliary (RFA) is a naval auxiliary fleet owned by the UK's Ministry of Defence. It is a component of His Majesty's Naval Service and
Royal_Fleet_Auxiliary
German philosopher, sociologist, and theorist (1903–1969)
evaluation while asserting that such empirical methods have only an auxiliary function and must lead to the formation of theories that would "raise the harsh
Theodor_W._Adorno
Computer intended for use by an individual person
computer to provide communication (such as input and output) or auxiliary functions (such as additional storage). Peripherals generally connect to the
Personal_computer
Principle in kinetic systems
{\displaystyle {\frac {dN_{i}}{dt}}=V\sum _{r}\gamma _{ri}w_{r}} An auxiliary function θ ( λ ) {\displaystyle \theta (\lambda )} of one variable λ ∈ [ 0
Detailed_balance
Smallest grammatical unit that can express a complete proposition
subject-auxiliary inversion present c. We know whom Larry sent to the store. – Embedded wh-clause focusing on the object, subject-auxiliary inversion
Clause
Term in economics
\max\{u(x_{1},x_{2}):p_{1}x_{1}+p_{2}x_{2}=m\}.} Forming the Lagrangian auxiliary function L ( x 1 , x 2 , λ ) := u ( x 1 , x 2 ) + λ ( m − p 1 x 1 − p 2 x 2
Shadow_price
following excerpt from ML program, local declaration of function leap, using an auxiliary function multiple: local fun multiple (n: int, d: int) = (n mod
Qualification_principle
Series of video game engines
(1994) and Doom 64 (1997). It was created by John Carmack, with auxiliary functions written by John Romero, Dave Taylor, and Paul Radek. Initially developed
Id_Tech
Fair item allocation procedure
(round-robin with weighted approval voting). The weight function w(r,s) is determined based on an auxiliary function B(r,s), defined by the following recurrence relation:
Round-robin_item_allocation
Algorithm for generating numbers coprime with first few primes
after each turn. The suggested implementation that follows uses an auxiliary function div(n,k), which tests whether n is evenly divisible by k, and returns
Wheel_factorization
State law enforcement agency in the US
Mounted Rangers officially ceased its operational law enforcement auxiliary function on July 15, 2018, the organization continues to exist as a nonprofit
Colorado_Rangers
Barometric tool
necessary for altitude calculation, they are commonly equipped with auxiliary functions such as electronic logbook, real-time jump profile replay, speed
Pressure_altimeter
Formal power series
generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often
Generating_function
Mathematical technique in complex analysis
is a technique which employs an auxiliary, parameterized function to prove the boundedness of a holomorphic function f {\displaystyle f} (i.e., | f (
Phragmén–Lindelöf_principle
Mathematical function
{\displaystyle K'} will be real and the auxiliary parallelogram will in fact be a rectangle, and the Jacobi elliptic functions will all be real valued on the real
Jacobi_elliptic_functions
Nonlinear partial differential equation
_{x_{2}}).} The function v {\displaystyle v} is generally considered to be real-valued. The function w {\displaystyle w} is an auxiliary function defined via
Novikov–Veselov_equation
Function used in quantum chemistry
Orbitals using recurrence relations for overlap integrals: III. auxiliary functions Q1nn' and Gq−nn". International Journal of Quantum Chemistry. 86
Slater-type_orbital
Functional part of speech in most languages
The auxiliary functions of these verbs derived from their copular function, and could be interpreted as special cases of the copular function (with
Copula_(linguistics)
Container port in India
(920 ft) in length. The terminal's separate receiving and shipping lines can function as an interconnected system. The terminal is served by rail lines and includes
Chennai_Port
definition of ACE Encryption process and ACE Signature process some auxiliary function (e.g. UOWHash, ESHash and some other) are being used, definition of
ACE_Encrypt
Programming construct
argument of the MAKE-COUNTER factory function is captured and used directly. It does not have to be copied into some auxiliary class object through a constructor
Function_object
Mid-size sedan
with the Level 3 driving assistance system, which integrates 28 auxiliary functions. The system uses 5 ultra-high definition cameras, 5 mmWave radars
Aeolus_Yixuan_Max
High-ranking member of the Christian clergy
An auxiliary bishop is a Catholic or Eastern Orthodox bishop assigned to assist the diocesan bishop in meeting the pastoral and administrative needs of
Auxiliary_bishop
Tree-based machine learning method for classification
else 5 return score_two 6 end if 7 else 8 return 0 9 end if Several auxiliary functions are also required by the algorithm: W + ( c ) {\displaystyle W_{+}(c)}
Alternating_decision_tree
Auxiliary police in New York City
The New York City Police Department Auxiliary Police is a volunteer reserve police force which is a subdivision of the Patrol Services Bureau of the New
New York City Police Department Auxiliary Police
New_York_City_Police_Department_Auxiliary_Police
Village-level female health worker in India
Hilda Elizabeth Lehman (1988). Auxiliary Nurse Midwife/female Health Worker Students in India: Self-efficacy in Role Function Relative to Child Survival and
Auxiliary_nurse_midwife
Weather radio network in the United States
emergency preparedness kits. Weather radio receivers integrated as an auxiliary function into other devices, such as GMRS radios, portable televisions, FM
NOAA_Weather_Radio
US Navy training ship in service 1942–1945
on the Great Lakes, and the ship was extensively electrified for auxiliary functions. Over 500 telephones were on board, with one in every stateroom,
USS_Wolverine_(IX-64)
Variant of heap data structure
error else return merge-pairs(heap.subheaps) This uses the auxiliary function merge-pairs: function merge-pairs(list: List[PairingTree[Elem]]) -> PairingHeap[Elem]
Pairing_heap
AUXILIARY FUNCTION
AUXILIARY FUNCTION
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Male
Egyptian
, an Egyptian functionary.
Surname or Lastname
English
English : nickname from the animal, Middle English catte ‘cat’. The word is found in similar forms in most European languages from very early times (e.g. Gaelic cath, Slavic kotu). Domestic cats were unknown in Europe in classical times, when weasels fulfilled many of their functions, for example in hunting rodents. They seem to have come from Egypt, where they were regarded as sacred animals.English : from a medieval female personal name, a short form of Catherine.Variant spelling of German and Dutch Katt.
Male
Egyptian
, Functionary of the Interior.
Male
Egyptian
, an Egyptian functionary.
Biblical
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Surname or Lastname
English
English : nickname, perhaps for a messenger, from Middle English gÅ(n) ‘to go’ (Old English gÄn) + lihtly ‘lightly’, ‘swiftly’ (Old English lÄ“oht(lÄ«c)).Scottish : altered form of a surname of uncertain origin, possibly an unidentified habitational name. The earliest known bearer is William Galithli, who witnessed a charter at the beginning of the 13th century. Henry Gellatly, an illegitimate son of William the Lion, of whom little or nothing is known, was the grandfather of Patric Galythly, one of the pretenders to the crown of Scotland in 1291.Irish : adopted as an English equivalent of Gaelic Mac an Ghallóglaigh ‘son of the galloglass’, Irish gallóglach. A galloglass was a mercenary retainer or auxiliary soldier (a compound of gall ‘foreigner’ (see Gall 1) + óglach ‘youth’, ‘warrior’). The name is also found pseudo-translated as English.
Male
Egyptian
, a great functionary.
Surname or Lastname
English
English : occupational name for a dresser of cloth, Old English fullere (from Latin fullo, with the addition of the English agent suffix). The Middle English successor of this word had also been reinforced by Old French fouleor, foleur, of similar origin. The work of the fuller was to scour and thicken the raw cloth by beating and trampling it in water. This surname is found mostly in southeast England and East Anglia. See also Tucker and Walker.In a few cases the name may be of German origin with the same form and meaning as 1 (from Latin fullare).Americanized version of French Fournier.Samuel Fuller (1589–1633), born in Redenhall, Norfolk, England, was among the Pilgrim Fathers who sailed on the Mayflower in 1620. He was a deacon of the church and until his death functioned as Plymouth Colony’s physician.
Male
Celtic
, great justiciary, or functionary.
Male
Egyptian
, the son of the functionary Heknofre.
Male
Egyptian
, a high Egyptian functionary.
Surname or Lastname
English (chiefly Kent and Sussex)
English (chiefly Kent and Sussex) : occupational name for a designer or engineer, from a Middle English reduced form of Old French engineor ‘contriver’ (a derivative of engaigne ‘cunning’, ‘ingenuity’, ‘stratagem’, ‘device’). Engineers in the Middle Ages were primarily designers and builders of military machines, although in peacetime they might turn their hands to architecture and other more pacific functions.German : from the Latin personal name Januarius (see January 1). Jänner is a South German word for ‘January’, and so it is possible that this is one of the surnames acquired from words denoting months of the year, for example by converts who had been baptized in that month, people who were born or baptized in that month, or people whose taxes were due in January.
Surname or Lastname
English
English : topographic name for someone who lived by the gates of a medieval walled town. The Middle English singular gate is from the Old English plural, gatu, of geat ‘gate’ (see Yates). Since medieval gates were normally arranged in pairs, fastened in the center, the Old English plural came to function as a singular, and a new Middle English plural ending in -s was formed. In some cases the name may refer specifically to the Sussex place Eastergate (i.e. ‘eastern gate’), known also as Gates in the 13th and 14th centuries, when surnames were being acquired.Americanized spelling of German Götz (see Goetz).Translated form of French Barrière (see Barriere).In New England, Gates was the preferred English version of the name of an extensive French family, called Barrière dit Langevin.
AUXILIARY FUNCTION
AUXILIARY FUNCTION
Boy/Male
Gujarati, Hindu, Indian, Sindhi
Full Moon
Male
Dutch
, people's ruler.
Girl/Female
Arabic
Council
Girl/Female
Tamil
Kodeswari | கோதேஸà¯à®µà®¾à®°à¯€Â
Beauty, Rich
Surname or Lastname
English
English : from a pet form of an Old English personal name (see Timm).
Boy/Male
Hindu, Indian, Sanskrit, Traditional
Lord of Dharma
Boy/Male
Hindu
Famous
Girl/Female
Arabic, Muslim, Sindhi
Beautiful
Boy/Male
Latin
A Greek poet.
Boy/Male
American, Australian, British, Chinese, Christian, Danish, English, French, German, Hawaiian, Hebrew, Indian, Irish, Jamaican, Portuguese, Swedish, Swiss, Tamil
Gift of Jehovah; Yahweh has Given
AUXILIARY FUNCTION
AUXILIARY FUNCTION
AUXILIARY FUNCTION
AUXILIARY FUNCTION
AUXILIARY FUNCTION
a.
Conferring aid or help; helping; aiding; assisting; subsidiary; as auxiliary troops.
pl.
of Auxiliary
a.
Of or pertaining to the axilla or armpit; as, axillary gland, artery, nerve.
a.
Supplying help; auxiliary; corroborative; explanatory; as, adminicular evidence.
sing.
A verb which helps to form the voices, modes, and tenses of other verbs; -- called, also, an auxiliary verb; as, have, be, may, can, do, must, shall, and will, in English; etre and avoir, in French; avere and essere, in Italian; estar and haber, in Spanish.
a.
Supplying or aiding; auxiliary; suppletory.
n.
An auxiliary rope to strengthen a mast.
adv.
By way of help.
n.
Auxiliary troops or reenforcements.
n.
Help or support; an auxiliary.
n.
An auxiliary.
adv.
In the manner of an accessory; auxiliary.
a.
Auxiliary.
n.
Foreign troops in the service of a nation at war; (rarely in sing.), a member of the allied or subsidiary force.
a.
Axillary.
a.
Auxiliary; helping.
a.
Subservient or subordinate, like a handmaid; auxiliary.
sing.
A quantity introduced for the purpose of simplifying or facilitating some operation, as in equations or trigonometrical formulae.
n.
A helper; an assistant; a confederate in some action or enterprise.
a.
Helping; lending aid or support; auxiliary.