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Mathematical concept
In mathematics, a weak trace class operator is a compact operator on a separable Hilbert space H with singular values the same order as the harmonic sequence
Weak_trace-class_operator
Compact operator for which a finite trace can be defined
specifically functional analysis, a trace-class operator is a linear operator for which a trace may be defined, such that the trace is a finite number independent
Trace_class
Boundary condition for generalized functions
In mathematical analysis, the trace operator extends the notion of the restriction of a function to the boundary of its domain to "generalized" functions
Trace_operator
Noncommutative geometric structure
every positive operator in the commutator subspace of the weak trace class is trace class. Consequently, every trace on the weak trace class ideal is singular
Singular_trace
Hilbert space H. B(H) admits a predual B*(H), the trace class operators on H. The ultraweak topology is the weak-* topology so induced; in other words, the ultraweak
Ultraweak_topology
Weak topology on function spaces
trace class operators C1(H), and it generates the w*-topology on B(H), called the weak-star operator topology or σ-weak topology. The weak-operator and
Weak_operator_topology
Banach space of a dual
For example, the predual of the space of bounded operators is the space of trace class operators, and the predual of the space L∞(R) of essentially
Predual
Topologies on operators on a Hilbert space
predual B ( H ) ∗ {\displaystyle B(H)_{*}} , consisting of the trace class operators, whose dual is B(X). The seminorm pw(x) for w positive in the predual
Operator_topologies
Type of continuous linear operator
_{n}s_{n}^{2}<\infty ,} and trace class when ∑ n s n < ∞ . {\displaystyle \sum _{n}s_{n}<\infty .} Every trace-class operator is Hilbert–Schmidt, and every
Compact_operator
means. Hence Com(L1) ⊊ ker Tr ⊊ L1. Weak trace class operators. The weak trace class operators L1,∞ correspond to the weak-l1 sequence space. From the condition
Commutator_subspace
Elliptic partial differential operator
datum in trace sense). In the particular case f = 1 , g = 0 {\displaystyle f=1,g=0} and Ω {\displaystyle \Omega } is a ball of radius 1, the weak solution
P-Laplacian
Mathematical theorem
Arthur–Selberg trace formula. When Γ is the fundamental group of a Riemann surface, the Selberg trace formula describes the spectrum of differential operators such
Selberg_trace_formula
Class of transformations that quantum systems and processes can undergo
natural number n, and any square matrix of size n whose entries are trace-class operators [ S 11 ⋯ S 1 n ⋮ ⋱ ⋮ S n 1 ⋯ S n n ] {\displaystyle {\begin{bmatrix}S_{11}&\cdots
Quantum_operation
'geometric/local' side involves the Dixmier trace and commutators with the Dirac operator (which corresponds to the 'characteristic class integration' part of the index
Spectral_triple
*-algebra of bounded operators on a Hilbert space
*-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. It is a special type
Von_Neumann_algebra
theorem, Spectral theory Trace class Normed vector space Unit ball Banach space Hahn–Banach theorem Dual space Predual Weak topology Reflexive space Polynomially
List of functional analysis topics
List_of_functional_analysis_topics
Vector space of functions in mathematics
theorem resolves the problem: Trace theorem—Assume Ω is bounded with Lipschitz boundary. Then there exists a bounded linear operator T : W 1 , p ( Ω ) → L p
Sobolev_space
Mathematical theorem
shows that the operator TK is a trace class operator and trace ( T K ) = ∫ a b K ( t , t ) d t . {\displaystyle \operatorname {trace} (T_{K})=\int _{a}^{b}K(t
Mercer's_theorem
Linear operators with a common spectrum
associated with quadratic extensions of the rationals by class field theory. In this case Selberg's trace formula shows that the spectrum of the Laplacian fully
Isospectral
Linear operator related to topological vector spaces
nuclear operators are an important class of linear operators introduced by Alexander Grothendieck in his doctoral dissertation. Nuclear operators are intimately
Nuclear_operator
Type of vector space in math
{\otimes }} _{\pi }H_{2}} , can be isometrically identified with the trace class operators from H 1 ∗ {\displaystyle H_{1}^{\ast }} to H 2 {\displaystyle H_{2}}
Hilbert_space
Mathematical function
In mathematics, a weak Maass form is a smooth function f {\displaystyle f} on the upper half plane, transforming like a modular form under the action of
Harmonic_Maass_form
Object which stores memory addresses in a computer program
run-time. Java provides the classes java.lang.ref.WeakReference and java.lang.ref.PhantomReference, which respectively implement weak references and phantom
Pointer (computer programming)
Pointer_(computer_programming)
particular, the trace class operators correspond to l1 and the Hilbert-Schmidt operators correspond to l2 . Weak-Lp ideals. The weak-Lp ideals Lp,∞, p ≥ 1
Calkin_correspondence
{\displaystyle \partial \Omega } . In general, if B {\displaystyle B} is any trace operator, one can construct the boundary value problem L u = f in Ω {\displaystyle
Elliptic boundary value problem
Elliptic_boundary_value_problem
First case of a Lie group that is both compact and non-abelian
(Skew self-adjoint matrices with trace zero plus self-adjoint matrices with trace zero gives all matrices with trace zero.) As long as we are working
Representation theory of SU(2)
Representation_theory_of_SU(2)
Mathematical function often applied to matrices
to unitarily invariant norms, e.g. the Hilbert-Schmidt norm for trace class operators, the Frobenius norm, and more generally the Schatten norms. As logarithmic
Logarithmic_norm
a stack trace is created when an exception is being thrown. In Java, the stack trace is created in the moment the exception is created. class Foo { Exception
Comparison of C Sharp and Java
Comparison_of_C_Sharp_and_Java
Conjecture on zeros of the zeta function
that a suitable analog of the Selberg trace formula for the action of the idèle class group on the adèle class space would imply the Riemann hypothesis
Riemann_hypothesis
Non-commercial use of the radio spectrum
(home construction) and by operators engaged in low-power operation, as CW transmitters are simple to construct and weak signals can often be received
Amateur_radio
Theorem
Radon–Nikodym theorem. The usual density operator of states on the matrix algebras with respect to the standard trace is nothing but the Radon–Nikodym derivative
Stinespring_dilation_theorem
Method for constructing existence proofs and calculating solutions in variational calculus
\mathbb {R} ^{m})} of functions whose trace is some fixed function g {\displaystyle g} in the image of the trace operator. This restriction allows finding
Direct method in the calculus of variations
Direct_method_in_the_calculus_of_variations
1912 maritime disaster
deadliest peacetime maritime disasters in history. Titanic's wireless operators received seven warnings of sea ice leading up to the night of 14 April
Sinking_of_the_Titanic
Mathematical compact operator
the trace on trace-class operators and det is the Fredholm determinant. For symmetrizable Hilbert–Schmidt operators the result states that the trace or
Symmetrizable compact operator
Symmetrizable_compact_operator
{\displaystyle s_{0}/2} .[citation needed] Selberg trace formula Fischer, Jürgen (1987), An Approach to the Selberg Trace Formula via the Selberg Zeta-Function, Lecture
Selberg_zeta_function
\mathbb {R} } and K {\displaystyle K} is a trace class operator called the extended Brownian scattering operator and the subscript means that the process
KPZ_fixed_point
Proposed theory of gravitation
\rightarrow \infty } . But Faraoni claims that this breaks down when the trace of the stress-energy momentum vanishes, i.e. T μ μ = 0 {\displaystyle T_{\mu
Brans–Dicke_theory
Objects that generalize functions
Malgrange–Ehrenpreis theorem Pseudodifferential operator Riesz representation theorem Vague topology Weak solution Distribution on a linear algebraic group
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
High-level programming language
omitted. JavaScript is weakly typed, which means certain types are implicitly cast depending on the operation used. The binary + operator casts both operands
JavaScript
Elliptic partial differential equation
{\displaystyle \Delta \varphi =f,} where Δ {\displaystyle \Delta } is the Laplace operator, and f {\displaystyle f} and φ {\displaystyle \varphi } are real or complex-valued
Poisson's_equation
Measure of curvature in differential geometry
p. By similar reasoning, the scalar curvature is twice the trace of the curvature operator. Alternatively, given the coordinate-based definition of Ricci
Scalar_curvature
Branch of mathematics that studies algebraic structures
Associative property Distributive property Commutative property Unary operator Additive inverse, multiplicative inverse, inverse element Identity element
List of abstract algebra topics
List_of_abstract_algebra_topics
ball in a normed space is compact in the weak-* topology. adjoint The adjoint of a bounded linear operator T : H 1 → H 2 {\displaystyle T:H_{1}\to H_{2}}
Glossary of functional analysis
Glossary_of_functional_analysis
Radio navigation system
signal that was easy to interpret. If displayed on a single CRT trace, the operator would see a string of sharp "blips", first the primary, then one
LORAN
Physics phenomenon
operator in H A {\displaystyle H_{A}} . ρA is sometimes called the reduced density matrix of ρ on subsystem A. Colloquially, we "trace out" or "trace
Quantum_entanglement
Idealization of a large number of atomic-sized systems
averages (operator X ^ {\displaystyle {\hat {X}}} ), variances (using operator X ^ 2 {\displaystyle {\hat {X}}^{2}} ), covariances (using operator X ^ Y ^
Ensemble (mathematical physics)
Ensemble_(mathematical_physics)
Naval 3D PESA Aegis radar system
frigates. It is used in Norwegian Fridtjof Nansen-class frigates. The origin of the SPY-1F can be traced back to the FARS proposed to the German Navy in
AN/SPY-1
Equations of motion for viscous fluids
{\frac {\partial }{\partial t}}} is the partial derivative mathematical operator, ∇ ⋅ u {\textstyle \nabla \cdot \mathbf {u} \,} is the divergence of the
Navier–Stokes_equations
Theory of quantum gravity merging quantum mechanics and general relativity
Hamiltonian operator is that it only acts at vertices (a consequence of this is that Thiemann's Hamiltonian operator, like Ashtekar's operator, annihilates
Loop_quantum_gravity
European wide-body airliner
different aircraft prior to the A380. Initial operators typically configured their A380s for three-class service, while adding extra features for passengers
Airbus_A380
Relationship between two functors abstracting many common constructions
relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand
Adjoint_functors
Mathematical transform that expresses a function of time as a function of frequency
Especially the image NGC 4622 Fourier transform m = 2. Nonlocal operator – Class of operator mapping Quadratic Fourier transform Quantum Fourier transform –
Fourier_transform
Algebraic object with geometric applications
basis is represented by a multidimensional array. For example, a linear operator is represented in a basis as a two-dimensional square n × n array. The
Tensor
Special case of colimit in category theory
generation may be weakened, as long as the index set remains directed. The weak topology of a CW complex is defined as a direct limit. Let I {\displaystyle
Direct_limit
Equation in Fourier analysis
principal symbol of the differential operator which generates the unitary group. For the Laplacian, the "wave trace" has singular support contained in the
Poisson_summation_formula
rodeo have been sold and 1000 people are observed in the stands. The rodeo operator sues a random attendee for non-payment of the entrance fee. The statistical
Statistical_syllogism
(pseudo-)Riemannian manifold whose geodesics are reversible
{\displaystyle T_{p}M} , and B ( X , Y ) = trace ( ad X ∘ ad Y ) {\displaystyle B(X,Y)=\operatorname {trace} (\operatorname {ad} X\circ \operatorname
Symmetric_space
Hungarian and American mathematician and physicist (1903–1957)
the study of nuclear operators on Hilbert spaces, tensor products of Banach spaces, introduced and studied trace class operators, their ideals, and their
John_von_Neumann
American country music singer (born 1948)
"One of a Kind Pair of Fools". Also included were the top ten recordings "Operator, Long Distance Please" and "In Times Like These". Mandrell's 1984 album
Barbara_Mandrell
Theoretical framework in physics
small class of theories called "renormalizable theories", of which QED is an example. However, most theories, including the Fermi theory of the weak interaction
Quantum_field_theory
Elementary particle with extremely low mass
in weak interactions as chirality eigenstates. Chirality of a massive particle is not a constant of motion; helicity is, but the chirality operator does
Neutrino
Theoretical framework
requirements, and changing requirements. Those weak links in the system design and development process can be traced to improper execution of the fundamental
Conceptual_model
Comparison between two programming languages
The differences between the programming languages C++ and Java can be traced to their heritage, as they have different design goals. C++ was designed
Comparison_of_Java_and_C++
Volcanic eruptions in Iceland
individual, a labour union, and a group of employers and tour operators through a class action. In the aftermath of the November disaster, Grindavík was
2023–2025 Sundhnúkur eruptions
2023–2025_Sundhnúkur_eruptions
category of multi-headed electrically lit units displaying speed-based or weak route signaling.[citation needed] Signals may be of the searchlight, color
North American railroad signals
North_American_railroad_signals
Solution to partial differential equation
in this case, F ( x , u , p , X ) = − trace ( X ) {\displaystyle F(x,u,p,X)=-{\text{trace}}(X)} , and the trace of X {\displaystyle X} is the sum of its
Viscosity_solution
Theorem in functional analysis
of B ( H ) , {\displaystyle B(H),} the trace class operators). Hence bounded sequences of operators have a weak accumulation point. As a consequence, B
Banach–Alaoglu_theorem
2022–2025 Star Wars television series
from the original on December 11, 2020. Retrieved December 10, 2020. "Last Traces of Star Wars Filming in Cleveleys". Visit Cleveleys. May 11, 2021. Archived
Andor
and Z, communicators of weak interaction. His discovery has supplied a fundamental check of the unified theory of electro-weak interactions. He is the
Meanings of minor-planet names: 8001–9000
Meanings_of_minor-planet_names:_8001–9000
Randolph Harris and brought over from Africa. Verdie resolved to one day trace her family back to its roots, and if she couldn't, she would have her children
List of The Waltons characters
List_of_The_Waltons_characters
President of the United States from 1929 to 1933
"undemocratic racist who saw blacks as a species of 'sub-men'". Some historians trace the disaffection of African-Americans with the Republican party to his time
Herbert_Hoover
Concept in mathematics
M an element of the tangent space Tf(p)N. By the definition of the trace operator, the laplacian may be written as ( Δ f ) p = ∑ i = 1 m ( ∇ ( d f ) )
Harmonic_map
President of the Philippines since 2022
Although President Rodrigo Duterte had expressed criticisms of Marcos as a "weak leader", Duterte's daughter Sara ran as Marcos' running mate and won a majority
Bongbong_Marcos
2014 aircraft disappearance
Retrieved 1 August 2015. Jansen, Bart (25 July 2013). "Crash investigators trace UPS plane fire to batteries". USA Today. Archived from the original on 11
Malaysia_Airlines_Flight_370
going to put all the lifeguards' cooperative skills to the test. 200 3 "Weak Link" Gregory J. Bonann Donald R. Boyle October 4, 1999 (1999-10-04) 2107
List_of_Baywatch_episodes
Ship class of the Spanish Navy
the type built by any country. The class's limited displacement was necessitated by the constraints imposed by the weak Spanish economy and existing naval
España-class_battleship
Skyscraper in Jeddah, Saudi Arabia
Red Sea. The subsurface profile includes reef limestone with cavities and weakly consolidated sandstone and gravel layers extending to significant depths
Jeddah_Tower
System for representing and reasoning about time
Alternate symbols: operator R is sometimes denoted by V The operator W is the weak until operator: f W g {\displaystyle f\mathbf {W} g} is equivalent to f
Temporal_logic
Locally convex topological vector space
{\displaystyle H} is infinite, then S 1 ( H ) {\displaystyle S_{1}(H)} (the trace class) is not reflexive, because it contains a subspace isomorphic to ℓ 1
Reflexive_space
Economic conflict since 2018
all scheduled tariff increases. The next day, Trump said "badly run and weak companies are smartly blaming these small Tariffs instead of themselves for
China–United_States_trade_war
Prime Minister of Australia from 1966 to 1967
Before entering politics, he practised law and was a lobbyist for cinema operators. He was first elected to the House of Representatives at the 1935 Fawkner
Harold_Holt
Leader of the Chetniks in WWII (1893–1946)
established radio contact with the British in September 1941, when his radio operator raised a ship in the Mediterranean. On 13 September, Mihailović's first
Draža_Mihailović
Comics character
in demolition derbies and speaking at events for Vil-Anon. An unnamed operator of the Big Wheel was on a crime spree until he was defeated by Spider-Man
List of Marvel Comics characters: B
List_of_Marvel_Comics_characters:_B
Algebraic manipulation of "true" and "false"
values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨
Boolean_algebra
History of maths
homotopical category has only a distinguished class of morphisms (containing all isomorphisms) called weak equivalences and satisfy the two out of six axiom
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
South Korean mass murderer (1984–2007)
federally licensed firearms dealer based in Green Bay, Wisconsin, and the operator of the website through which Cho ordered the gun. TGSCOM Inc. shipped the
Seung-Hui_Cho
Generalization of "n-th" to infinite cases
linearly ordered class of numbers that include the natural numbers and have the property that every non-empty collection (set or proper class) of ordinals
Ordinal_number
Mathematical space
(P)} as its image. Since the rank of an orthogonal projection operator equals its trace, we can identify the Grassmann manifold G r ( k , V ) {\displaystyle
Grassmannian
Predecessor to the theory of relativity
unknown function of ϕ {\displaystyle \phi } , and where Tmatter is the trace of the stress–energy tensor describing the density, momentum, and stress
Nordström's theory of gravitation
Nordström's_theory_of_gravitation
Australian carnivorous marsupial
academics and naturalists. At the start of the 20th century, Hobart zoo operator Mary Roberts, who was not a trained scientist, was credited for changing
Tasmanian_devil
Gauge field loop operator
parameters in lattice gauge theory. Wilson loops fall into the broader class of loop operators, with some other notable examples being 't Hooft loops, which are
Wilson_loop
American conservative cable news channel
the channel. This contrasted with the normal practice, in which cable operators paid stations carriage fees for programming. When Time Warner bought Ted
Fox_News
Disclosures of NSA and related global espionage
and Tsinghua University in Beijing, and the Asian fiber-optic network operator Pacnet. Only Australia, Canada, New Zealand and the UK are explicitly exempted
Snowden_disclosures
American serial killer (1946–1989)
ritualistic, but also a practical matter, as it minimized the chance of leaving trace evidence at the crime scene that could implicate him. A manufacturing error
Ted_Bundy
1997 film by James Cameron
Leonardo DiCaprio and Kate Winslet star as members of different social classes who fall in love during the ship's ill-fated maiden voyage. The ensemble
Titanic_(1997_film)
National airline of South Korea
Award - AirlineRatings.com 2022 Cargo Operator of the Year - Air Transport World (ATW) 2023 Best Business-Class Seat Design - Global Traveler's Tested
Korean_Air
Extension of Rexx programming language with support for object-oriented programming
interpreter pauses after most instructions that are traced. ooRexx 5.1.0 introduces the TraceObject class, which facilitates the tracing of multi-threaded
Object_REXX
2005 aviation accident in Greece
he was never trained on a Boeing 737. Prodromou's mayday hails were only weakly heard, as the 737's radio was still tuned to Larnaca ATC and he was unable
Helios_Airways_Flight_522
Serge (December 8, 2018). "North Carolina's 'Guru of Elections': Can-Do Operator Who May Have Done Too Much". The New York Times. Retrieved October 16,
Electoral fraud in the United States
Electoral_fraud_in_the_United_States
Country in Eastern Europe and West Asia
that led to the Ottoman conquest of the country in 1578. Georgian Jews trace the history of their community to the 6th century BC but due to immigration
Georgia_(country)
WEAK TRACE-CLASS-OPERATOR
WEAK TRACE-CLASS-OPERATOR
Male
English
Variant spelling of English unisex Tracy, TRACEY means "place of Thracius."
Female
English
Feminine variant spelling of English unisex Tracy, TRACI means "place of Thracius."
Surname or Lastname
English
English : from the medieval personal name Classe, a short form of Nicholas. See also Clayson.Variant of Klaas or Klass, North German forms of Claus.
Boy/Male
Anglo Saxon American English French
Brave.
Surname or Lastname
English
English : variant of Wick, specifically a habitational name from any of various places called Week or Weeke, notably in Cornwall, Hampshire, and Somerset.Americanized spelling of Norwegian or Swedish Vik.
Girl/Female
American, Arabic, Australian, British, Chinese, Christian, Danish, English, French, German, Gujarati, Indian, Irish, Jamaican, Latin, Muslim, Portuguese, Swedish
Mercy; God's Favor; Grace; Grace of God; Kindness; Thanks; Love; Favour; Blessing; Charm; Good will
Male
English
English surname transferred to unisex forename use, from a Norman baronial name TRACY means "place of Thracius."
Surname or Lastname
English and German
English and German : metonymic occupational name for a glazier or glass blower, from Old English glæs ‘glass’ (akin to Glad, referring originally to the bright shine of the material), Middle High German glas.Irish and Scottish : Anglicized form of the epithet glas ‘gray’, ‘green’, ‘blue’ or any of various Gaelic surnames derived from it.German : altered form of the personal name Klass, a reduced form of Nikolaus (see Nicholas).Jewish (Ashkenazic) : ornamental name from German Glass ‘glass’, or a metonymic occupational name for a glazier or glass blower.
Surname or Lastname
English (Northumbria)
English (Northumbria) : topographic name for someone who lived by the Wear river in northern England. The river name is ancient, occuring in the form Vedra in Ptolemy’s Geographia; it is probably a Celtic word meaning ‘water’.English (Northumbria) : topographic name for someone who lived near a dam or weir, a variant spelling of Ware 1, or a habitational name from a place called Weare, in Devon and Somerset, from Old English wær, wer ‘weir’.
Male
English
Short form of English unisex Tracy, TRACE means "place of Thracius."
Surname or Lastname
English
English : perhaps a variant of Treece.
Female
English
Feminine variant spelling of English unisex Tracy, TRACEE means "place of Thracius."
Surname or Lastname
English
English : variant of Crass.
Boy/Male
American, Anglo, Australian, British, Chinese, English, French
Fighter; Brave
Girl/Female
Latin American English Irish
Grace.
Surname or Lastname
English
English : topographic name for someone living by a pointed hill (or regional name from the Peak District (Old English Pēaclond) in Derbyshire), named with Old English pēac ‘peak’, ‘pointed hill’ (found only in place names). This word is not directly related to Old English pīc ‘point’, ‘pointed hill’, which yielded Pike; there is, however, some evidence of confusion between the two surnames.Possibly also Irish : reduced form of McPeak.Major concentrations of the surname Peak are found in Staffordshire and the West Country of England. Among the earliest known bearers are Richard del Pech or del Pek (d. 1196), son of Rannulf, sheriff of Nottingham, and Willielmus Piec (Winchester 1194). A century later, c.1284, a certain Richard del Peke settled in Denbighshire (now part of Clwyd), Wales, receiving lands from Henry de Lacey, earl of Lincoln, in return for helping to control the region. His descendants, who bear the name Peak(e), can be traced to the present day, and are found in New Zealand and Canada as well as in Britain. Peake is also the name of a family descended from John Pyke, who paid rent to the abbot of Leicester in 1477. The name took various forms, such as Peke and Pick, eventually becoming established as Peak in the 17th century.
Female
English
Feminine variant spelling of English unisex Tracy, TRACIE means "place of Thracius."
Surname or Lastname
English
English : variant of Week.
Female
English
English short form of Latin Cassandra, CASS means "she who entangles men."Â
Male
German
Short form of German Niclaus, CLAUS means "victor of the people."Â
WEAK TRACE-CLASS-OPERATOR
WEAK TRACE-CLASS-OPERATOR
Girl/Female
Greek American Latin
who was the Mythological queen of Sparta and mother of Helen of Troy.
Boy/Male
Muslim/Islamic
Noble
Girl/Female
Bengali, Hindu, Indian, Sanskrit
A River
Boy/Male
Arabic, French, Hebrew, Hindu, Indian, Jewish, Muslim
Owns Palm Trees; Tall and Slender; Tall; Like a Palm Tree
Boy/Male
Hindu, Indian
Clouds in Sky Just Before Rain
Boy/Male
Hindu
Girl/Female
Muslim
Slave of. Servant of. Used to join with female names with Divine Name.
Girl/Female
Indian, Telugu
Part of Goddess Laxmi
Boy/Male
American, Anglo, British, English, Teutonic
From the Clay Brook
Girl/Female
English
Modern feminine of John and Jon.
WEAK TRACE-CLASS-OPERATOR
WEAK TRACE-CLASS-OPERATOR
WEAK TRACE-CLASS-OPERATOR
WEAK TRACE-CLASS-OPERATOR
WEAK TRACE-CLASS-OPERATOR
v. t.
To trace out; to track; also, to draw out; to protact.
v. i.
Feeble of mind; wanting discernment; lacking vigor; spiritless; as, a weak king or magistrate.
v. i.
Lacking ability for an appropriate function or office; as, weak eyes; a weak stomach; a weak magistrate; a weak regiment, or army.
n.
To arrange in classes; to classify or refer to some class; as, to class words or passages.
v. i.
Tending towards lower prices; as, a weak market.
v.
The trade winds.
v. i.
Not stiff; pliant; frail; soft; as, the weak stalk of a plant.
v. i.
Not able to sustain a great weight, pressure, or strain; as, a weak timber; a weak rope.
v. t.
Hence, to follow the trace or track of.
v. i.
Lacking in elements of political strength; not wielding or having authority or energy; deficient in the resources that are essential to a ruler or nation; as, a weak monarch; a weak government or state.
v.
Track; trace.
v. i.
Not able to withstand temptation, urgency, persuasion, etc.; easily impressed, moved, or overcome; accessible; vulnerable; as, weak resolutions; weak virtue.
v. i.
Wanting in point or vigor of expression; as, a weak sentence; a weak style.
v. i.
Not thoroughly or abundantly impregnated with the usual or required ingredients, or with stimulating and nourishing substances; of less than the usual strength; as, weak tea, broth, or liquor; a weak decoction or solution; a weak dose of medicine.
v. i.
Wanting in power to influence or bind; as, weak ties; a weak sense of honor of duty.
imp. & p. p.
of Trace
v. t.
A mark left by anything passing; a track; a path; a course; a footprint; a vestige; as, the trace of a carriage or sled; the trace of a deer; a sinuous trace.
a.
To make or become weak; to weaken.
v. t.
To follow the tracks or traces of; to pursue by following the marks of the feet; to trace; to trail; as, to track a deer in the snow.
v. i.
Not able to resist external force or onset; easily subdued or overcome; as, a weak barrier; as, a weak fortress.