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Generalisation of the derivative of a function
In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable
Weak_derivative
Instantaneous rate of change (mathematics)
the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a
Derivative
Fundamental construction of differential calculus
complex numbers where the Fréchet derivative exists. In geometric calculus, the geometric derivative satisfies a weaker form of the Leibniz (product) rule
Generalizations of the derivative
Generalizations_of_the_derivative
Type of financial contract
a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has
Derivative_(finance)
continuous second derivatives, where Δ is the Laplacian. This is the same notion as a weak derivative, however, a function can have a weak derivative and not be
Weakly_harmonic_function
Vector space of functions in mathematics
of the function together with its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete,
Sobolev_space
identification and weak instruments. Directional derivative – Instantaneous rate of change of the function Fréchet derivative – Derivative defined on normed
Hadamard_derivative
Mathematical tools
space H 0 1 ( Ω ) {\displaystyle H_{0}^{1}(\Omega )} of functions with weak derivatives in L 2 ( Ω ) {\displaystyle L^{2}(\Omega )} and with zero boundary
Weak_formulation
Calculus of functions generalization
\alpha ,\varphi \rangle =\alpha (\varphi )} . It is then called the weak derivative of u {\displaystyle u} with respect to x i {\displaystyle x_{i}} .
Calculus_on_Euclidean_space
Control loop feedback mechanism
A proportional–integral–derivative (PID) controller, or three-term controller, is a feedback-based control loop mechanism commonly used to manage machines
PID_controller
Inequality on Lp norm with weak derivatives
places a bound on the Lp norm of a function using Lp bounds on the weak derivatives of the function and the geometry of the domain, and can be used to
Friedrichs'_inequality
Function returning minus 1, zero or plus 1
integration theory, the signum function is a weak derivative of the absolute value function. Weak derivatives are equivalent if they are equal almost everywhere
Sign_function
Concept in complex analysis
to Fichera (1969, p. 28), the first to identify the areolar derivative as a weak derivative in the sense of Sobolev was Ilia Vekua. In his following paper
Wirtinger_derivatives
Generalization of the concept of directional derivative
differentiability. In some cases, a weak limit is taken instead of a strong limit, which leads to the notion of a weak Gateaux derivative. At each point x ∈ U , {\displaystyle
Gateaux_derivative
Indicator function of positive numbers
{\displaystyle H(x)={\frac {x+|x|}{2x}}} The Dirac delta function is the weak derivative of the Heaviside function: δ ( x ) = d d x H ( x ) , {\displaystyle
Heaviside_step_function
1989 film by Howard Zieff
Nicholson will show up. [...which] may suggest that "Dream Team" is a weak, derivative, somehow disreputable movie, which is somewhat true. If you compare
The_Dream_Team_(1989_film)
Enforcement of legal rights in all derivatives of a work
derivative works. Thus, the term "weak copyleft" refers to licenses where not all derivative works inherit the copyleft license; whether a derivative
Copyleft
Theorem about inclusions between Sobolev spaces
Sobolev space consisting of all real-valued functions on Rn whose weak derivatives up to order k are functions in Lp. Here k is a non-negative integer
Sobolev_inequality
Auxiliary functions used to probe equations, distributions, and weak formulations
the Euler–Lagrange equation in weak form. Bump function Schwartz space Distribution (mathematics) Weak derivative Weak solution Sobolev space Mollifier
Test_function
Differentiation under the integral sign formula
Steve (6 September 2010). Differentiation under the integral sign with weak derivatives (Report). CiteSeerX. CiteSeerX 10.1.1.525.2529. Spivak, Michael (1994)
Leibniz_integral_rule
Integral expressing the amount of overlap of one function as it is shifted over another
integrable and at least one of them has an absolutely integrable (L1) weak derivative, as a consequence of Young's convolution inequality. For instance,
Convolution
Theorem in mathematical analysis
spaces that relates the L p {\displaystyle L^{p}} -norms of different weak derivatives of a function through an interpolation inequality. The theorem is of
Gagliardo–Nirenberg interpolation inequality
Gagliardo–Nirenberg_interpolation_inequality
Specialized notation for multivariable calculus
two derivatives will agree up to translation of notations. As is the case in general for partial derivatives, some formulae may extend under weaker analytic
Matrix_calculus
in other species. 17α-Ethynylated testosterone derivatives are potent progestins with only very weak androgenic/anabolic activity and are used as oral
List of androgens and anabolic steroids
List_of_androgens_and_anabolic_steroids
Operation in differential calculus
theorem nor the mean-value theorem hold for the symmetric derivative; some similar but weaker statements have been proved. For the absolute value function
Symmetric_derivative
Objects that generalize functions
functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions
Distribution (mathematical analysis)
Distribution_(mathematical_analysis)
Objects extending the notion of functions
linear functional on other functions. This allows a definition of weak derivative. During the late 1920s and 1930s further basic steps were taken. The
Generalized_function
Averages of repeated trials converge to the expected value
distributed random variables, it suffices that the expected value exists for the weak law of large numbers to be true. These further studies have given rise to
Law_of_large_numbers
Property of a mathematical function
are weaker than differentiability. Specifically, the function f is said to be right differentiable at a point a if, roughly speaking, a derivative can
Semi-differentiability
Mathematical function characterizing set membership
{P} (x)=0.} Although indicator functions are not smooth, they admit weak derivatives. For example, consider Heaviside step function H ( x ) ≡ I ( x > 0
Indicator_function
Chemical compound
cannabinoid derivative, the hydrogenated derivative of tetrahydrocannabutol (THCB). It was first synthesised by Roger Adams in 1942 and produces only weak cannabinoid-like
Hexahydrocannabutol
Method for finding the extrema of a function
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local
Derivative_test
Mathematical solution
mathematics, a weak solution (also called a generalized solution) to an ordinary or partial differential equation is a function for which the derivatives may not
Weak_solution
Unified description of electromagnetism and the weak interaction
interactions of nature: electromagnetism (electromagnetic interaction), and the weak interaction. Although these two forces appear very different at everyday
Electroweak_interaction
Concept in calculus of variations
variations, a field of mathematical analysis, the functional derivative (or variational derivative) relates a change in a functional (a functional in this
Functional_derivative
1]; R) with its usual inner product, and let Au = u′ (in this case a weak derivative) with domain D(A) equal to those functions u in the Sobolev space H
Dissipative_operator
Theorem in mathematics
differentiable in an open interval, with a continuous derivative, then in a neighborhood of any point where the derivative is not zero, f has an inverse function. The
Inverse_function_theorem
Class of compounds based upon the amphetamine structure
class of compounds based upon the amphetamine structure; it includes all derivative compounds which are formed by replacing, or substituting, one or more
Substituted_amphetamine
Country in northwestern Europe
Triennial Survey of Foreign Exchange and Over-The-Counter Interest Rate Derivatives Markets in April 2025 – UK Data". Bank of England. 30 September 2025
United_Kingdom
Type of topological space
)} denotes the Sobolev Hilbert space of once-weakly differentiable functions with first weak derivative in L 2 ( Ω ) {\displaystyle L^{2}(\Omega )} that
Bochner_space
Generalized function whose value is zero everywhere except at zero
_{S^{n-1}}g(x\cdot \xi )\,d\omega _{\xi }.} The Laplacian here is interpreted as a weak derivative, so that this equation is taken to mean that, for any test function
Dirac_delta_function
Set of functions between two fixed sets
W k , p {\displaystyle W^{k,p}} Sobolev space of functions whose weak derivatives up to order k are in L p {\displaystyle L^{p}} O U {\displaystyle {\mathcal
Function_space
Degree of differentiability of a function or map
k} such that a function has all derivatives up to order k {\displaystyle k} , and such that all of these derivatives are continuous. One says that such
Smoothness
On weak solutions of differential equations
functions with square-integrable weak derivatives, and LtpX is the Bochner space of integrable X-valued functions. Not every weak solution is smooth; for example
Regularity_theory
Lemma in numerical analysis of differential equations
{\displaystyle v} defined on [ a , b ] {\displaystyle [a,b]} that have a weak derivative on [ a , b ] {\displaystyle [a,b]} with v ′ {\displaystyle v'} also
Céa's_lemma
Generalization of derivatives to real-valued functions
In mathematics, the subderivative (or subgradient) generalizes the derivative to convex functions which are not necessarily differentiable. The set of
Subderivative
Method in Itô calculus
the same such μ , σ {\displaystyle \mu ,\sigma } , provided that their derivatives also satisfy similar conditions. A simple case to analyze is geometric
Euler–Maruyama_method
Measure that has a notion of derivative
measure ν {\displaystyle \nu } is called the Skorokhod derivative (or S-derivative or weak derivative) of μ {\displaystyle \mu } along h ∈ X {\displaystyle
Differentiable_measure
Type of differential operator
This situation is ultimately unsatisfactory, as the weak solution u might not have enough derivatives for the expression Lu to be well-defined in the classical
Elliptic_operator
Type of differential equation
which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation
Partial_differential_equation
Economics concepts
prices to always deviate from their fundamental valuations. This reflects the weak information efficiency model. 3. Full insurance efficiency This ensures the
Financial_market_efficiency
Topological space that locally resembles Euclidean space
2307/2118532. JSTOR 2118532. Sikorski, R. (1967). "Abstract covariant derivative". Colloquium Mathematicum. 18: 251–272. doi:10.4064/cm-18-1-251-272. Freedman
Manifold
Mathematical notation
dx}.} This formula is used for the definition of distributions and weak derivatives. If α , β ∈ N 0 n {\displaystyle \alpha ,\beta \in \mathbb {N} _{0}^{n}}
Multi-index_notation
defensive formation with three linemen and four linebackers. A professional derivative in the 1970s of the earlier Oklahoma, 5–2 or 50 defense, which had five
Glossary of American football terms
Glossary_of_American_football_terms
Country in Southeast Europe
involving financial derivatives. "The Maastricht rules can be circumvented quite legally through swaps," says a German derivatives dealer. In previous
Greece
Synthetic opioid
where the para-methyl group is replaced by a halogen being slightly weaker. Derivatives where the ketone group has been reacted with a Grignard reagent to
4-Dimethylamino-4-(p-tolyl)cyclohexanone
4-Dimethylamino-4-(p-tolyl)cyclohexanone
hyperactivity disorder (ADHD) and certain other indications. Several other derivatives including rimiterol, phacetoperane and pipradrol also have more limited
List of methylphenidate analogues
List_of_methylphenidate_analogues
Derivative method in calculus
calculus, the reciprocal rule gives the derivative of the reciprocal of a function f in terms of the derivative of f. The reciprocal rule can be used to
Reciprocal_rule
Phonetic phenomenon in Uralic languages
appears in historically open syllables (ending in a vowel), while the lenis weak grade appears in historically closed syllables (ending in a consonant). The
Consonant_gradation
Key results in general relativity on gravitational singularities
rotating (Kerr) black hole. A singularity can be either strong or weak: Weak singularities: A weak singularity is one where the tidal forces (which are responsible
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Area of mathematical analysis
spaces and spaces of weakly differentiable functions. Singular integral estimates also give information about weak derivatives. For example, Calderón–Zygmund
Harmonic_analysis
Type of statistical analysis
s>0} : The space of Sobolev-smooth functions with square-integrable weak derivatives. F = B p , q s ( X ) , s > 0 , p , q ∈ ( 0 , ∞ ] {\displaystyle {\mathcal
Nonparametric_statistics
Proposed theories of gravity
fields, and where ∇ ν {\displaystyle \nabla _{\nu }} is the covariant derivative with respect to the metric and Γ σ ν α {\displaystyle \Gamma _{\sigma
Alternatives to general relativity
Alternatives_to_general_relativity
Type of function
subject called distributional or generalized function analysis. A weak derivative is defined that allows singular functions to be used in partial differential
Singular_function
Country in North America
the pork, beef and chicken meats; peppercorn, sugar, milk and all its derivatives, wheat and rice, citrus fruits and another constellation of ingredients
Mexico
American entrepreneur and venture capitalist (born 1967)
Thiel worked as a clerk, a securities lawyer, a speechwriter, and a derivatives trader at Credit Suisse. He founded Thiel Capital Management in 1996
Peter_Thiel
Country in northern Europe
bilberries, lingonberries, cloudberries, and sea buckthorn). Milk and its derivatives like buttermilk are commonly used as food and drink. The most popular
Finland
Real function with finite total variation
C_{c}^{1}} holds, since it is nothing more than the definition of weak derivative, and hence holds true. One can easily find an example of a BV function
Bounded_variation
Abrahamic monotheistic religion
uncertainty, which is seen as gambling and Islamic banks traditionally avoid derivative instruments such as futures or options which has historically protected
Islam
1993 studio album by Duran Duran
melodies of the band's earlier work. He described "Ordinary World" as a weaker derivative of its influences and singled out the cover of the Velvet Underground's
Duran_Duran_(1993_album)
Algebraic object with geometric applications
Application of tensor theory in engineering Continuum mechanics Covariant derivative Curvature Diffusion tensor MRI Einstein field equations Fluid mechanics
Tensor
Class of drugs
A GABA analogue is a compound which is an analogue or derivative of the neurotransmitter gamma-Aminobutyric acid (GABA) (the IUPAC of which is 4-aminobutanoic
GABA_analogue
{\displaystyle W^{k,p}(\Omega )} defined as the set of all functions which have weak derivatives of order up to k all of which are in L p {\displaystyle L^{p}} and
Meyers–Serrin_theorem
Inequality in mathematical analysis
important example are the Sobolev spaces, consisting of functions whose weak derivatives up to some (not necessarily integer) order lie in Lp spaces for some
Interpolation_inequality
Web browser made by Mozilla
Software Foundation criticized for being weak copyleft, as the license permitted, in limited ways, proprietary derivative works. Additionally, code only licensed
Firefox
Theorem in vector calculus
can be considered as a 1-form in which case its curl is its exterior derivative, a 2-form. Let Σ {\displaystyle \Sigma } be a smooth oriented surface
Stokes'_theorem
1966 studio album by Chet Baker and the Mariachi Brass
on ten poppish tunes while joined by the Mariachi Brass, a rather weak derivative of the Tijuana Brass". "Flowers on the Wall" (Lew DeWitt) - 2:19 "Tequila"
A_Taste_of_Tequila
Quantum field giving rise to gluons
Schäfer. The gauge covariant derivative Dμ is required to transform quark fields in manifest covariance; the partial derivatives that form the four-gradient
Gluon_field
Point to which functions converge in analysis
function. The concept of limit also appears in the definition of the derivative: in the calculus of one variable, this is the limiting value of the slope
Limit_of_a_function
Weak organic acid
Citric acid is an organic compound with the formula C6H8O7. It is a colorless weak organic acid. It occurs naturally in citrus fruits. In biochemistry, it is
Citric_acid
German assault rifle
equipped with the Heckler & Koch MP5, whose 9 mm bullet was considered too weak, and the M4 carbine, which was considered too large, especially when fitted
Heckler_&_Koch_HK416
Division of the horoscope into 12 sectors
the 10th house cusp, while taken into account, is interpreted simply as a weaker 2nd MC cusp. The Midheaven is not associated with house locations defined
House_(astrology)
Type of vector space in math
integer and Ω ⊂ Rn, the Sobolev space Hs(Ω) contains L2 functions whose weak derivatives of order up to s are also L2. The inner product in Hs(Ω) is ⟨ f , g
Hilbert_space
Generalization of a derivative of a function between two Banach spaces
quasi-derivative is a slightly stronger version of the Gateaux derivative, though weaker than the Fréchet derivative. Let f : A → F be a continuous function from an
Quasi-derivative
Country in Eastern Europe and Central Asia
designed to avoid political and social unrest. The result was a bland derivative of real Kazakh folk music. In 1920, Aleksandr Zatayevich, a Russian official
Kazakhstan
Immunomodulatory drug which can cause birth defects
actinic prurigo and epidermolysis bullosa; the evidence for these uses is weak. It is recommended only as a third line treatment in graft-versus-host-disease
Thalidomide
Star at the centre of the Solar System
Proto-Indo-European religion, the Sun was personified as the goddess *Seh2ul. Derivatives of this goddess in Indo-European languages include Old Norse Sól, Sanskrit
Sun
Chemical compound
3 to 18.4 mM-1·cm-1 in strong alkali). In contrast, 4-nitrophenol has a weak absorbance at 405 nm (ε = 0.2 mM-1·cm-1). The isosbestic point for
4-Nitrophenol
Numerical method for solving physical or engineering problems
functions that project the residual. The process eliminates all the spatial derivatives from the PDE, thus approximating the PDE locally using the following:
Finite_element_method
Medication mainly used for depression and smoking cessation
позиций в перечень Ephedrone (methcathinone) and its derivatives, with the exception of derivatives included as independent items in the list. Rossi S,
Bupropion
Theory of forces and subatomic particles
describing three of the four known fundamental forces (electromagnetic, weak and strong interactions – excluding gravity) in the universe and classifying
Standard_Model
Method for constructing existence proofs and calculating solutions in variational calculus
Banach space. The derivatives of u {\displaystyle u} in the formula for J {\displaystyle J} must then be taken as weak derivatives. Another common function
Direct method in the calculus of variations
Direct_method_in_the_calculus_of_variations
Feature observed in spectroscopy
electromagnetic spectrum in the vicinity of a spectral line – a region of stronger or weaker intensity in the spectrum. Ideal line shapes include Lorentzian, Gaussian
Spectral_line_shape
External genitalia of the female mammal
from the earlier volvere meaning to turn, roll or revolve, with further derivatives such as used in volvox, and volvulus (twisted bowel). The naming of the
Vulva
Totality of psychological phenomena
distinguishes between the original intentionality of mental phenomena and the derivative intentionality of some non-mental phenomena. According to this view, the
Mind
Drug class
504, a hydroquinone hydrochloride salt derivative of 17-AAG) and radicicol as well as semisynthetic derivatives 17-N-Allylamino-17-demethoxygeldanamycin
Hsp90_inhibitor
Study of rates of change
differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen
Differential_calculus
Evolutionary process
belongs to the genus Homo, whereas the cranial structure of Neanderthals is derivative. H. cepranensis refers to a single skull cap from Italy, estimated to
Human_evolution
1960s–1998 conflict in Northern Ireland
republicans dynamited Nelson's Pillar in Dublin. At the time, the IRA was weak and not engaged in armed action, but some unionists warned it was about to
The_Troubles
Overview of how Japanese verbs conjugate
like godan verbs. These often have full-fledged, interchangeable godan derivatives: aisu(ru) (愛す(る); 'love'), zokusu(ru) (属す(る); 'belong'), tassu(ru) (達す(る);
Japanese_conjugation
WEAK DERIVATIVE
WEAK DERIVATIVE
Girl/Female
Hindu, Indian, Traditional
Peak
Boy/Male
Spanish
Weak.
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.
Biblical
weak; slacked
Girl/Female
Tamil
Peak
Boy/Male
Arabic, Muslim
Weak
Boy/Male
Biblical
Weak, slacked.
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.
Boy/Male
Arabic
One who has Weak Eyes
Boy/Male
Australian, Hindu, Indian
Peak
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’.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Tamil, Telugu
Peak
Surname or Lastname
English
English : variant spelling of Leake.
Surname or Lastname
English
English : variant of Week.
Boy/Male
Tamil
Peak
Boy/Male
Hindu
Peak
Girl/Female
Australian, Christian, French, German, Hebrew
Hair; Lovelorn; Delicate; Weak
Boy/Male
Hindu, Indian
Week
Girl/Female
Indian
Peak
Boy/Male
Arabic, Muslim
Weak
WEAK DERIVATIVE
WEAK DERIVATIVE
Male
Egyptian
, an Egyptian chief.
Surname or Lastname
English
English : occupational name for a smith, with the distinguishing epithet high, probably denoting one whose forge was at a higher location than another nearby smith.
Girl/Female
Indian, Telugu
Great
Boy/Male
British, Celtic, English, Gaelic, Irish
Champion
Boy/Male
Hindu
Lord Vishnu
Girl/Female
Hindu, Indian, Sanskrit, Tamil
Goddess Saraswati
Girl/Female
English
Path; roadway.Lane and Laine.
Girl/Female
Tamil
Male
English
Variant spelling of English unisex Cody, KODY means "helper."
Boy/Male
Bengali, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Eldest; Lord Vishnu
WEAK DERIVATIVE
WEAK DERIVATIVE
WEAK DERIVATIVE
WEAK DERIVATIVE
WEAK DERIVATIVE
n.
The upper aftermost corner of a fore-and-aft sail; -- used in many combinations; as, peak-halyards, peak-brails, etc.
v. i.
Tending towards lower prices; as, a weak market.
v. i.
Not firmly united or adhesive; easily broken or separated into pieces; not compact; as, a weak ship.
v. i.
Not able to sustain a great weight, pressure, or strain; as, a weak timber; a weak rope.
a.
To make or become weak; to weaken.
v. i.
Not stiff; pliant; frail; soft; as, the weak stalk of a plant.
v. i.
Not having power to convince; not supported by force of reason or truth; unsustained; as, a weak argument or case.
a.
Having a weak mind, either naturally or by reason of disease; feebleminded; foolish; idiotic.
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.
A crack, crevice, fissure, or hole which admits water or other fluid, or lets it escape; as, a leak in a roof; a leak in a boat; a leak in a gas pipe.
v. t.
To cause or make by friction or wasting; as, to wear a channel; to wear a hole.
v. i.
Wanting in point or vigor of expression; as, a weak sentence; a weak style.
a.
Having weak knees; hence, easily yielding; wanting resolution.
v. i.
To rise or extend into a peak or point; to form, or appear as, a peak.
v. i.
Not able to resist external force or onset; easily subdued or overcome; as, a weak barrier; as, a weak fortress.
v. i.
Lacking ability for an appropriate function or office; as, weak eyes; a weak stomach; a weak magistrate; a weak regiment, or army.
v. i.
Wanting in power to influence or bind; as, weak ties; a weak sense of honor of duty.
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. i.
Feeble of mind; wanting discernment; lacking vigor; spiritless; as, a weak king or magistrate.
v. i.
Not able to withstand temptation, urgency, persuasion, etc.; easily impressed, moved, or overcome; accessible; vulnerable; as, weak resolutions; weak virtue.