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"Smoothing" integral transform
mathematics, the Weierstrass transform of a function f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } , named after Karl Weierstrass, is a "smoothed"
Weierstrass_transform
Mathematical theorem in the study of analysis
original version of this result was established by Karl Weierstrass in 1885 using the Weierstrass transform. Marshall H. Stone considerably generalized the theorem
Stone–Weierstrass_theorem
Mathematical function
solve heat equations and diffusion equations and to define the Weierstrass transform. They are also abundantly used in quantum chemistry to form basis
Gaussian_function
transform Shehu transform Stieltjes transformation Wavelet transform (integral) Weierstrass transform Binomial transform Discrete Fourier transform,
List_of_transforms
Mapping involving integration between function spaces
In mathematics, an integral transform is a type of transformation that maps a function from its original function space into another function space via
Integral_transform
Filter in electronics and signal processing
with a Gaussian function; this transformation is also known as the Weierstrass transform. The one-dimensional Gaussian filter has an impulse response given
Gaussian_filter
Class of mathematical functions
mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class
Weierstrass_elliptic_function
Type of image blur produced by a Gaussian function
with a Gaussian function. This is also known as a two-dimensional Weierstrass transform. By contrast, convolving by a circle (i.e., a circular box blur)
Gaussian_blur
Integral transform useful in probability theory, physics, and engineering
Hjalmar Mellin was among the first to study the Laplace transform rigorously in the Karl Weierstrass school of analysis, and apply it to the study of differential
Laplace_transform
Hilbert space of square-integrable holomorphic functions of n complex variables
operators. The map B may be computed explicitly as a modified double Weierstrass transform, ( B f ) ( z ) = ∫ R n exp [ − 1 2 ( z ⋅ z − 2 2 z ⋅ x + x ⋅ x
Segal–Bargmann_space
Polynomial sequence
for the Weierstrass transform W is eD2, we see that the Weierstrass transform of (√2)nHen(x/√2) is xn. Essentially the Weierstrass transform thus turns
Hermite_polynomials
Theorem in transcendental number theory
Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: Lindemann–Weierstrass theorem—if
Lindemann–Weierstrass_theorem
Computational physics simulation tool
quasiprobability distributions. In fact, it can be understood as the Weierstrass transform of the Wigner quasiprobability distribution, i.e. a smoothing by
Husimi_Q_representation
Change of variable for integrals involving trigonometric functions
substitution or half-angle substitution. It is sometimes misattributed as the Weierstrass substitution. Michael Spivak called it the "world's sneakiest substitution"
Tangent half-angle substitution
Tangent_half-angle_substitution
theorem Weierstrass product inequality Weierstrass ring Weierstrass theorem (disambiguation) – any of several theorems Weierstrass transform Weierstrass p,
List of things named after Karl Weierstrass
List_of_things_named_after_Karl_Weierstrass
Extension of the factorial function
z {\displaystyle z} . The definition for the gamma function due to Weierstrass is also valid for all complex numbers z {\displaystyle z} except non-positive
Gamma_function
Partial differential equation describing the evolution of temperature in a region
differential equation Relativistic heat conduction Schrödinger equation Weierstrass transform Arfken, George B.; Weber, Hans-Jurgen; Harris, Frank E. (2013).
Heat_equation
Mathematical inequality about the convolution of two functions
semigroup using the L 2 {\displaystyle L^{2}} norm (that is, the Weierstrass transform does not enlarge the L 2 {\displaystyle L^{2}} norm). Young's inequality
Young's convolution inequality
Young's_convolution_inequality
Wigner distribution function in physics as opposed to in signal processing
larger than ħ (e.g., convolving with a phase-space Gaussian, a Weierstrass transform, to yield the Husimi representation, below), results in a positive-semidefinite
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Integration kernels for smoothing out sharp features
Kurt Otto Friedrichs Non-analytic smooth function Sergei Sobolev Weierstrass transform That is, the mollified function is close to the original with respect
Mollifier
Fundamental solution to the heat equation, given boundary values
signature Minakshisundaram–Pleijel zeta function Mehler kernel Weierstrass transform § Generalizations Evans 1998, p. 48. Pinchover & Rubinstein 2005
Heat_kernel
Ostrogradsky–Gauss theorem Gauss pseudospectral method Gauss transform, also known as Weierstrass transform. Gauss–Lucas theorem Gauss's continued fraction, an
List of things named after Carl Friedrich Gauss
List_of_things_named_after_Carl_Friedrich_Gauss
Complex analysis theorem
unit circle and a closed Jordan curve) Kramers–Kronig relations Hilbert transform Kress, Rainer (2012). Linear Integral Equations. Springer Science & Business
Sokhotski–Plemelj_theorem
Type of mathematical curve
characteristic different from 2 and 3, every irreducible cubic can be transformed into the Weierstrass normal form y 2 = x 3 + a x 2 + b x + c {\displaystyle
Cubic_plane_curve
Motion of a curve based on its curvature
The result is a Gaussian blur of the image, or equivalently the Weierstrass transform of the indicator function, with radius proportional to the square
Curve-shortening_flow
Mathematical function that preserves angles
inconvenient geometries. By choosing an appropriate mapping, the analyst can transform the inconvenient geometry into a much more convenient one. For example
Conformal_map
Removable singularity Essential singularity Branch point Principal branch Weierstrass–Casorati theorem Landau's constants Holomorphic functions are analytic
List of complex analysis topics
List_of_complex_analysis_topics
Integral transform
generalizes the Fourier, fractional Fourier, Laplace, Gauss–Weierstrass, Bargmann and the Fresnel transforms as particular cases. The name "linear canonical transformation"
Linear canonical transformation
Linear_canonical_transformation
Number, approximately 3.14
} An integral such as this was proposed as a definition of π by Karl Weierstrass, who defined it directly as an integral in 1841. Integration is no longer
Pi
Classic entropy of a quantum-mechanical density matrix
^{-1/4}\exp(-|y-x|^{2}/2)+i\,px).} (It can be understood as the Weierstrass transform of the Wigner quasi-probability distribution.) The Wehrl entropy
Wehrl_entropy
Power series with negative powers
named after and first published by Pierre Alphonse Laurent in 1843. Karl Weierstrass had previously described it in a paper written in 1841 but not published
Laurent_series
Concept in statistics
are all interrelated through convolution by Gaussian functions, Weierstrass transforms, W ( α , α ∗ ) = 2 π ∫ P ( β , β ∗ ) e − 2 | α − β | 2 d 2 β {\displaystyle
Quasiprobability_distribution
Second-order partial differential equation
is equal to 1 {\displaystyle 1} , so the transform reduces to composition with inversion. The Kelvin transform is useful for converting interior problems
Laplace's_equation
Type of elliptic curve
introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form. It is used for certain computations, and in particular in different
Montgomery_curve
Decomposition of periodic functions
L^{2}([-\pi ,\pi ])} . The density of their span is a consequence of the Stone–Weierstrass theorem, but follows also from the properties of classical kernels like
Fourier_series
Type of function in mathematics
real analyticity can be characterized using the Fourier–Bros–Iagolnitzer transform. In the multivariable case, real analytic functions satisfy a direct generalization
Analytic_function
2.71828...; base of natural logarithms
Fourier's proof that e is irrational.) Furthermore, by the Lindemann–Weierstrass theorem, e is transcendental, meaning that it is not a solution of any
E_(mathematical_constant)
Matrix used in complex analysis
0}|b_{n}(w)|^{2}\leq (1-|w|^{2})^{-1}.} The Beurling transform (also called the Beurling-Ahlfors transform and the Hilbert transform in the complex plane) provides one
Grunsky_matrix
Mathematical theorem
Riemann himself), which was considered sound at the time. However, Karl Weierstrass found that this principle was not universally valid. Later, David Hilbert
Riemann_mapping_theorem
respect to the sup norm. Bargmann Bargmann transform Berezin Berezin integral Bolzano The Bolzano-Weierstrass theorem says a bounded sequence in R n {\displaystyle
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
certain special polynomials. It is the p-adic counterpart to the Stone-Weierstrass theorem for continuous real-valued functions on a closed interval. Let
Mahler's_theorem
Finnish mathematician (1854–1933)
in Berlin under Karl Weierstrass. He is chiefly remembered for his use of the integral transform known as the Mellin transform. He studied related gamma
Hjalmar_Mellin
Function that is holomorphic on the whole complex plane
entire functions there is a generalization of the factorization – the Weierstrass theorem on entire functions. Every entire function f ( z ) {\displaystyle
Entire_function
Region with boundary of finite measure
Giorgi introduces the following smoothing operator, analogous to the Weierstrass transform in the one-dimensional case W λ χ E ( x ) = ∫ R n g λ ( x − y )
Caccioppoli_set
Branch of mathematics
would not be until 150 years later when, due to the work of Cauchy and Weierstrass, a way was finally found to avoid mere "notions" of infinitely small
Calculus
Mathematical theorem
e ( s ) < 1 {\textstyle 0<\operatorname {\mathcal {Re}} (s)<1} . Weierstrass's definition of the gamma function Γ ( x ) = e − γ x x ∏ n = 1 ∞ ( 1 +
Ramanujan's_master_theorem
Austrian-German philosopher (1859–1938)
contemporary philosophy and beyond. Husserl studied mathematics, taught by Karl Weierstrass and Leo Königsberger, and philosophy taught by Franz Brentano and Carl
Edmund_Husserl
Instantaneous rate of change (mathematics)
a monotone or a Lipschitz function), this is true. However, in 1872, Weierstrass found the first example of a function that is continuous everywhere but
Derivative
Correlators of field operators
straightforwardly from G R {\displaystyle G^{\mathrm {R} }} , using the Sokhatsky–Weierstrass theorem lim η → 0 + 1 x ± i η = P 1 x ∓ i π δ ( x ) , {\displaystyle
Green's function (many-body theory)
Green's_function_(many-body_theory)
Harmonic functions as solutions to Laplace's equation
in complex analysis (such as Schwarz's theorem, Morera's theorem, the Weierstrass-Casorati theorem, Laurent series, and the classification of singularities
Potential_theory
Van Vleck's theorem (mathematical analysis) Weierstrass–Casorati theorem (complex analysis) Weierstrass factorization theorem (complex analysis) Appell–Humbert
List_of_theorems
Characteristic property of holomorphic functions
equations are a simple example of a Bäcklund transform. More complicated, generally non-linear Bäcklund transforms, such as in the sine-Gordon equation, are
Cauchy–Riemann_equations
Complex exponential in terms of sine and cosine
its natural logarithm, and the "modulus" is a conversion factor that transforms a measure of angle into circular arc length (here, the modulus is the
Euler's_formula
Mathematical criterion about whether a series converges
Faà di Bruno's formula Reynolds Integral Lists of integrals Integral transform Leibniz integral rule Definitions Antiderivative Integral (improper) Riemann
Convergence_tests
Statement in complex analysis
Schwarz–Pick theorem mentioned above: One just needs to remember that the Cayley transform W ( z ) = ( z − i ) / ( z + i ) {\displaystyle W(z)=(z-i)/(z+i)} maps
Schwarz_lemma
Conformal mappings in complex analysis
integral formula Residue theorem Liouville's theorem Picard theorem Weierstrass factorization theorem Advanced theorems Borel–Carathéodory theorem Maximum
Schwarz_triangle_function
Analytic function in mathematics
used for a numerical evaluation of the zeta function. On the basis of Weierstrass's factorization theorem, Hadamard gave the infinite product expansion
Riemann_zeta_function
multivariable function Continuous function Nowhere continuous function Weierstrass function Smooth function Analytic function Quasi-analytic function Non-analytic
List_of_real_analysis_topics
Concept in mathematics
unit circle, with the uniform norm; this is a special case of the Stone–Weierstrass theorem. More concretely, for every continuous function f {\displaystyle
Trigonometric_polynomial
Technique in integral evaluation
density function Substitution of variables Trigonometric substitution Weierstrass substitution Euler substitution Glasser's master theorem Pushforward
Integration_by_substitution
Type of mathematical integrals
dx\approx {\frac {\pi }{2}}-2.9629\cdot 10^{-42}} Furthermore, using the Weierstrass factorizations sin x x = ∏ n = 1 ∞ ( 1 − x 2 π 2 n 2 ) cos x = ∏
Borwein_integral
Summation method for divergent series
Borel had to say and then, placing his hand upon the complete works by Weierstrass, his teacher, he said in Latin, 'The Master forbids it'. — Mark Kac,
Borel_summation
Mathematical function
define other modular forms. In particular the modular discriminant of the Weierstrass elliptic function with ω 2 = τ ω 1 {\displaystyle \omega _{2}=\tau \omega
Dedekind_eta_function
Meromorphic function
}\left(1+{\frac {z}{n}}\right)e^{-{\frac {z}{n}}}.} This is a result of the Weierstrass factorization theorem. Thus, the gamma function may now be defined as:
Polygamma_function
Branch of functional analysis
from polynomial to continuous functional calculus by using the Stone–Weierstrass theorem. The crucial fact here is that, for a bounded self adjoint operator
Borel_functional_calculus
Tauberian theorem
discontinuities by approximating it by polynomials from above and below (using the Weierstrass approximation theorem and a little extra fudging) and using the fact
Hardy–Littlewood Tauberian theorem
Hardy–Littlewood_Tauberian_theorem
Theorem about smooth complex functions
mathematics, the Malgrange preparation theorem is an analogue of the Weierstrass preparation theorem for smooth functions. It was conjectured by René
Malgrange_preparation_theorem
Method for the construction of fractals
1017/S0143385710000428. S2CID 122674315. David, Claire (2019). "Fractal properties of Weierstrass-type functions". Proceedings of the International Geometry Center. 12
Iterated_function_system
Mathematics independent of applications
professionalisation (particularly in the Weierstrass approach to mathematical analysis) started to make a rift more apparent. After Weierstrass, by the end of 19th century
Pure_mathematics
German mathematician (1804–1851)
solution of the Jacobi inversion problem for the hyperelliptic Abel map by Weierstrass in 1854 required the introduction of the hyperelliptic theta function
Carl_Gustav_Jacob_Jacobi
Fractal curve resembling a blancmange pudding
(also known as the Devil's staircase) Minkowski's question mark function Weierstrass function Dyadic transformation Weisstein, Eric W. "Blancmange Function"
Blancmange_curve
Oscillatory error in Fourier series
convergent Fourier coefficients would be uniformly convergent by the Weierstrass M-test and would thus be unable to exhibit the above oscillatory behavior
Gibbs_phenomenon
Infinite sum of monomials
uniformly, at every point of | z | = 1 {\displaystyle |z|=1} due to Weierstrass M-test applied with the hyper-harmonic convergent series ∑ n = 1 ∞ 1
Power_series
Uniform norm Matrix norm Spectral radius Normed division algebra Stone–Weierstrass theorem Banach algebra *-algebra B*-algebra C*-algebra Universal C*-algebra
List of functional analysis topics
List_of_functional_analysis_topics
About mathematical functions
century, the demands of the rigorous development of analysis by Karl Weierstrass and others, the reformulation of geometry in terms of analysis, and the
History of the function concept
History_of_the_function_concept
convergence in a paper by Christoph Gudermann; later formalized by Karl Weierstrass. Uniform convergence is required to fix Augustin-Louis Cauchy's erroneous
Timeline_of_mathematics
Swiss anatomist, physiologist, and histologist (1817–1905)
Vucinich the non-Darwinian evolution theory of Kölliker tied "organic transformism to three general ideas, all contrary to Darwin's view: the multiple origin
Albert_von_Kölliker
Italian mathematician (1853–1936)
reflected the influence that Weierstrass had on him. He later collaborated with Vito Volterra and explored Laplace transforms and other parts of functional
Salvatore_Pincherle
German mathematician (1839–1873)
publication of an award winning article, he proceeded to study under Karl Weierstrass and Leopold Kronecker in Berlin. He received his doctorate in 1862 at
Hermann_Hankel
Geometric representation of the complex numbers
normally expressed as a polynomial in the parameter s of the Laplace transform, hence the name s-plane. Points in the s-plane take the form s = σ + jω
Complex_plane
Theorem regarding the existence of a solution to a differential equation
{\displaystyle \textstyle \sup _{R}|f|\leq C<\infty } and by the Stone–Weierstrass theorem there exists a sequence of Lipschitz functions f k : R → R {\displaystyle
Peano_existence_theorem
Use of complex numbers to evaluate integrals
fraction decomposition. Mathematics portal Trigonometric substitution Weierstrass substitution Euler substitution Kilburn, Korey (2019). "Applying Euler's
Integration using Euler's formula
Integration_using_Euler's_formula
Study of mathematical algorithms for optimization problems
until the slack is null or negative. The extreme value theorem of Karl Weierstrass states that a continuous real-valued function on a compact set attains
Mathematical_optimization
Mathematical function with no sudden changes
1830s, but the work wasn't published until the 1930s. Like Bolzano, Karl Weierstrass considered that a function y = f ( x ) {\displaystyle y=f(x)} at a point
Continuous_function
Number with a real and an imaginary part
is due to Hankel (1867), and absolute value, for modulus, is due to Weierstrass. Later classical writers on the general theory include Richard Dedekind
Complex_number
Trying to map moments to a measure that generates them
{\displaystyle \mu } in the Hausdorff moment problem follows from the Weierstrass approximation theorem, which states that polynomials are dense under
Moment_problem
) , {\displaystyle {\mathcal {C}}(X),} and equicontinuous. The Stone–Weierstrass theorem holds for C ( X ) . {\displaystyle {\mathcal {C}}(X).} In the
Space of continuous functions on a compact space
Space_of_continuous_functions_on_a_compact_space
Analytic function in mathematics
= 1 ∞ z n {\displaystyle g(z)=\sum _{n=1}^{\infty }z^{n}\,} and the Weierstrass M-test to demonstrate that the simple example defines an analytic function
Lacunary_function
Array of numbers
1, Ch. III, p. 96. Knobloch (1994). Hawkins (1975). Kronecker 1897 Weierstrass 1915, pp. 271–286 & Miller (1930). Bôcher (2004). Hawkins (1972). van
Matrix_(mathematics)
apparatus – Ernst Heinrich Weber Weierstrass–Casorati theorem – Karl Theodor Wilhelm Weierstrass and Felice Casorati Weierstrass's elliptic functions, factorization
Scientific phenomena named after people
Scientific_phenomena_named_after_people
the lengths of its sides. Nowhere differentiable function called also Weierstrass function: continuous everywhere but not differentiable even at a single
List_of_types_of_functions
Weierstrass form. Let K {\displaystyle K} be a field and consider an elliptic curve E {\displaystyle E} in the following special case of Weierstrass form
Hessian form of an elliptic curve
Hessian_form_of_an_elliptic_curve
Mathematical function
elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions of complex analysis
Jacobi_elliptic_functions
theorem — generalization of Stone–Weierstrass theorem for polynomials Müntz–Szász theorem — variant of Stone–Weierstrass theorem for polynomials if some
List of numerical analysis topics
List_of_numerical_analysis_topics
Problem of solving a partial differential equation subject to prescribed boundary values
electrostatics, determine an electrical potential as solution. However, Karl Weierstrass found a flaw in Riemann's argument, and a rigorous proof of existence
Dirichlet_problem
Multivalued function in mathematics
k ( z ) {\displaystyle W_{k}(z)} is algebraic. Then by the Lindemann–Weierstrass theorem we have e W k ( z ) {\displaystyle e^{W_{k}(z)}} is transcendental
Lambert_W_function
Field of knowledge
computer networks. In the 19th century, mathematicians such as Karl Weierstrass and Richard Dedekind increasingly focused their research on internal
Mathematics
One-dimensional complex manifold
{\displaystyle (x,y)=(\wp (z),\wp '(z))} , where ℘ {\displaystyle \wp } is the Weierstrass elliptic function. Likewise, genus g {\displaystyle g} surfaces have
Riemann_surface
1966 result in mathematical analysis
After Dirichlet's result, several experts, including Dirichlet, Riemann, Weierstrass and Dedekind, stated their belief that the Fourier series of any continuous
Carleson's_theorem
of things named after Stanislaw Ulam List of things named after Karl Weierstrass List of things named after André Weil List of things named after Hermann
Lists_of_mathematics_topics
WEIERSTRASS TRANSFORM
WEIERSTRASS TRANSFORM
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Most beautiful. , Mythological Arcadian who transformed into a she-bear, then into the Great Bear...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Israeli
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek Latin
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Girl/Female
Greek
Most beautiful. In Mythology the Arcadian nymph Calista transformed into a she-bear; then into...
Girl/Female
Greek American
Most beautiful. , Mythological Arcadian who transformed into a she-bear, then into the Great Bear...
Surname or Lastname
English and French
English and French : regional name from Old French Poitevin, denoting someone from Poitou in western France. The form Potvin has long been established in England and was brought to the U.S. from there. However, French bearers of the surname Poitevin also came to the New World, where their surname underwent a similar transformation on arrival in New England.
Girl/Female
Greek
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Most beautiful. , Mythological Arcadian who transformed into a she-bear, then into the Great Bear...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Surname or Lastname
English
English : habitational name from Lichfield in Staffordshire. The first element preserves a British name recorded as Letocetum during the Romano-British period. This means ‘gray wood’, from words which are the ancestors of Welsh llŵyd ‘gray’ and coed ‘wood’. By the Old English period this had been reduced to Licced, and the element feld ‘pasture’, ‘open country’ was added to describe a patch of cleared land within the ancient wood.English : habitational name from Litchfield in Hampshire, recorded in Domesday Book as Liveselle. This is probably from an Old English hlīf ‘shelter’ + Old English scylf ‘shelf’, ‘ledge’. The subsequent transformation of the place name may be the result of folk etymological association with Old English hlið, hlid ‘slope’ + feld ‘open country’.
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Greek American
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Girl/Female
Greek
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
WEIERSTRASS TRANSFORM
WEIERSTRASS TRANSFORM
Girl/Female
Tamil
Wonderful, Loved, Blissful, Sent from God
Boy/Male
Celebrity, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Oriya, Sanskrit, Tamil, Telugu, Traditional
The Sun
Girl/Female
Gaelic American
Feminine of Kyle.
Boy/Male
Tamil
Bitasok | பிதாஸோக
One who does not mourn
Female
Turkish
Turkish name BELGIN means "clear."
Boy/Male
Japanese
Beautiful sunrise/dawn.
Female
Hebrew
(חִבָּה) Variant spelling of Hebrew Chiba, HIBA means "love." Compare with another form of Hiba.
Girl/Female
Indian
Worship
Girl/Female
Hindu, Indian, Kannada, Marathi, Sindhi, Telugu, Traditional
Born in the Season of Hemanta
Boy/Male
Hindu
(Son of king Harish Chandra)
WEIERSTRASS TRANSFORM
WEIERSTRASS TRANSFORM
WEIERSTRASS TRANSFORM
WEIERSTRASS TRANSFORM
WEIERSTRASS TRANSFORM
n.
A change of form, direction, or the like; transformation; conversion; turning.
v. t.
To change; to transform; to invert.
a.
Having power, or a tendency, to transform.
v. t.
To change from one species to another; to transform.
n.
The act of transforming, or the state of being transformed; change of form or condition.
n.
The change of one species into another, which is assumed to take place in any development theory of life; transformism.
v. t.
To change from one nature, form, or substance, into another; to transform.
n.
One who, or that which, transforms. Specif. (Elec.), an apparatus for producing from a given electrical current another current of different voltage.
imp. & p. p.
of Transform
a.
Capable of being transmuted or changed into a different substance, or into into something of a different form a nature; transformable.
n.
One of the changes of assimilation, in which proteid matter which has been transformed, and made a part of the tissue or tissue cells, is endowed with life, and thus enabled to manifest the phenomena of irritability, contractility, etc.
v. t.
To change into another substance; to transmute; as, the alchemists sought to transform lead into gold.
v. t.
To change the form of; to change in shape or appearance; to metamorphose; as, a caterpillar is ultimately transformed into a butterfly.
v. t.
To move or change from one state into another; to transform.
a.
Capable of being transformed or changed.
p. pr. & vb. n.
of Transform
v. t.
To change the form, quality, aspect, or effect of; to alter; to metamorphose; to convert; to transform; -- often with to or into before the word denoting the effect or product of the change; as, to turn a worm into a winged insect; to turn green to blue; to turn prose into verse; to turn a Whig to a Tory, or a Hindu to a Christian; to turn good to evil, and the like.
v. i.
To be changed, altered, or transformed; to become transmuted; also, to become by a change or changes; to grow; as, wood turns to stone; water turns to ice; one color turns to another; to turn Mohammedan.
v. t.
To transfer or transform the nature of.
v. t.
To change into another shape or form; to transform.