WordNet

of or relating to Karl Gauss or his mathematical theories of magnetics or electricity or astronomy or probability; "Gaussian distribution"

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2012/07/06 16:27:04」(JST)

Carl Friedrich Gauss (1777 – 1855) is the eponym of all of the topics listed below. There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics and astronomy.

Topics including "Gauss"

Carl Friedrich Gauss Prize, a mathematics award
Degaussing, to demagnetize an object
Gauss (unit), a unit of magnetic field (B)
Gauss–Bodenmiller theorem
Gauss–Bolyai–Lobachevsky space, a hyperbolic geometry
Gauss–Bonnet theorem, a theorem about curvature in differential geometry
Gauss–Codazzi equations
Gauss code
Gauss–Hermite quadrature
Gauss–Jacobi quadrature
Gauss–Jordan elimination, a method in linear algebra
Gauss–Kronrod quadrature formula
Gauss–Kuzmin distribution, a discrete probability distribution
Gauss–Kuzmin–Wirsing constant, a constant in number theory
Gauss–Manin connection, a connection on a vector bundle over a family of algebraic varieties
Gauss–Markov process
Gauss–Markov theorem
Gauss–Laplace pyramid, sometimes called the Burt–Adelson pyramid.
Gauss' law for gravity
Gauss linking integral (knot theory)
Gauss iterated map (dynamical systems)
Gauss–Krüger coordinate system
Gauss–Seidel method
Gauss–Newton algorithm
Gauss–Newton line
Gauss–Legendre algorithm
Gauss–Lucas theorem
Gauss' area formula
Gauss' principle of least constraint
Gauss's constant, the reciprocal of the AGM of 1 and , in number theory.
Gauss's continued fraction, an analytic continued fraction derived from the hypergeometric functions.
Gauss's criterion
Gauss's digamma theorem, a theorem about the digamma function.
Gauss error function
Gauss' generalization of Wilson's theorem.
Gauss gun
Gauss's hypergeometric theorem, an identity on hypergeometric series.
Gauss's law, giving the relationship between flux through a closed surface and the enclosed source.
Gauss's law for magnetism
Gauss's lemma in relation to polynomials
Gauss's lemma in number theory
Gauss's lemma in Riemannian geometry
Gauss map
Gauss Peninsula, East Greenland
Gauss sum, an exponential sum over Dirichlet characters.
Gauss' theorem may refer to the divergence theorem, which is also known as the Ostrogradsky–Gauss theorem.
Gauss composition
Generalized Gauss–Bonnet theorem
Gauss pseudospectral method
Gauss Tower
Gauss (ship)
Gaussberg, or Mount Gauss, an extinct volcano in Antarctica
The Gauss expedition, the first German expedition to Antarctica

Topics including "Gaussian"

Additive white Gaussian noise
Gaussian beam
Gaussian binomial coefficient, also called Gaussian polynomial or Gaussian coefficient
Gaussian blur, a technique in image processing.
Gaussian bracket
Gaussian copula
Gaussian curvature
Gaussian distribution, also named the normal distribution, a type of probability distribution.
Gaussian elimination
Gaussian function related to the Gaussian distribution
Gaussian filter
Gaussian fixed point
Gaussian free field
Gaussian graph
Gaussian gravitational constant
Gaussian grid
Gaussian's modular arithmetic
Gaussian integer
Gaussian integral
Gaussian isoperimetric inequality
Gaussian measure
Gaussian model; see Variogram
Gaussian network model
Gaussian method
Gaussian moat
Gaussian noise
Gaussian optics
Gaussian orbital
Gaussian period
Gaussian polynomial; see Gaussian binomial coefficient
Gaussian prime
Gaussian process
Gaussian quadrature
Gaussian rational
Gaussian smoothing
Gaussian surface
Gaussian year
Inverse Gaussian distribution, also known as the Wald distribution
The GAUSSIAN software program

Other notable achievements of Gauss

Gauss's proofs

Proofs for conjectured theorems.

The quadratic reciprocity law
The fundamental theorem of algebra
Fermat polygonal number theorem for n = 3

proofs for theorems he discovered himself:

Discovered and proved the theorema egregium.

Gauss's identities

Gauss multiplication formula may refer to the multiplication theorem.
Gauss interpolation formula
Gauss–Kummer series
Gauss formula
Gauss transformation
Gauss's inequality
Gauss theorems (two theorems) about the Euler function.
Gauss test

Gauss conjectures

The prime number theorem
Gauss–Kuzmin distribution, the distribution of integers in a continued fraction.
Gauss circle problem
Gauss class number problem.
Gauss made progress toward proving the Kepler conjecture.

UpToDate Contents

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1. 陣痛の潜伏相 latent phase of labor
2. 赤血球細胞の生存：正常値と測定値 red blood cell survival normal values and measurement
3. 老化する腎臓 the aging kidney
4. ダウン症の母体血清スクリーニングに関する臨床検査の問題 laboratory issues related to maternal serum screening for down syndrome
5. 急性期反応物質 acute phase reactants

English Journal

Adaptive Regulation of Endothelin Receptor Type-A and Type-B in Vascular Smooth Muscle Cells during Pregnancy in Rats.

Ou M, Dang Y, Mazzuca MQ, Basile R, Khalil RA.Author information Vascular Surgery Research Laboratory, Division of Vascular and Endovascular Surgery, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts.AbstractNormal pregnancy is associated with systemic vasodilation and decreased vascular contraction, partly due to increased release of endothelium-derived vasodilator substances. Endothelin-1 (ET-1) is an endothelium-derived vasoconstrictor acting via endothelin receptor type A (ETA R) and possibly type B (ETB R) in vascular smooth muscle cells (VSMCs), with additional vasodilator effects via endothelial ETB R. However, the role of ET-1 receptor subtypes in the regulation of vascular function during pregnancy is unclear. We investigated whether the decreased vascular contraction during pregnancy reflects changes in the expression/activity of ETA R and ETB R. Contraction was measured in single aortic VSMCs isolated from virgin, mid-pregnant (mid-Preg, day 12), and late-Preg (day 19) Sprague-Dawley rats, and the mRNA expression, protein amount, tissue and cellular distribution of ETA R and ETB R were examined using RT-PCR, Western blots, immunohistochemistry, and immunofluorescence. Phenylephrine (Phe, 10(-5) M), KCl (51 mM), and ET-1 (10(-6) M) caused VSMC contraction that was in late-Preg < mid-Preg and virgin rats. In VSMCs treated with ETB R antagonist BQ788, ET-1 caused significant contraction that was still in late-Preg < mid-Preg and virgin rats. In VSMCs treated with the ETA R antagonist BQ123, ET-1 caused a small contraction; and the ETB R agonists IRL-1620 and sarafotoxin 6c (S6c) caused similar contraction that was in late-Preg < mid-Preg and virgin rats. RT-PCR revealed similar ETA R, but greater ETB R mRNA expression in pregnant versus virgin rats. Western blots revealed similar ETA R, and greater protein amount of ETB R in endothelium-intact vessels, but reduced ETB R in endothelium-denuded vessels of pregnant versus virgin rats. Immunohistochemistry revealed prominent ETB R staining in the intima, but reduced ETA R and ETB R in the aortic media of pregnant rats. Immunofluorescence signal for ETA R and ETB R was less in VSMCs of pregnant versus virgin rats. The pregnancy-associated decrease in ETA R- and ETB R-mediated VSMC contraction appears to involve downregulation of ETA R and ETB R expression/activity in VSM, and may play a role in the adaptive vasodilation during pregnancy. J. Cell. Physiol. 229: 489-501, 2014. © 2013 Wiley Periodicals, Inc.
Journal of cellular physiology.J Cell Physiol.2014 Apr;229(4):489-501. doi: 10.1002/jcp.24469.
Normal pregnancy is associated with systemic vasodilation and decreased vascular contraction, partly due to increased release of endothelium-derived vasodilator substances. Endothelin-1 (ET-1) is an endothelium-derived vasoconstrictor acting via endothelin receptor type A (ETA R) and possibly type B
PMID 24105843

Abnormal default-mode network homogeneity in first-episode, drug-naive schizophrenia at rest.

Guo W1, Yao D2, Jiang J2, Su Q2, Zhang Z2, Zhang J2, Yu L2, Xiao C2.Author information 1Mental Health Center, the First Affiliated Hospital, Guangxi Medical University, Nanning, Guangxi 530021, China. Electronic address: guowenbin76@163.com.2Mental Health Center, the First Affiliated Hospital, Guangxi Medical University, Nanning, Guangxi 530021, China.AbstractBACKGROUND: Dysconnectivity hypothesis posits that schizophrenia relates to abnormal resting-state connectivity within the default-mode network (DMN) and this aberrant connectivity is considered as contribution of difficulties in self-referential and introspective processing. However, little is known about the alterations of the network homogeneity (NH) of the DMN in schizophrenia. In the present study, we used an automatic NH method to investigate the NH of the DMN in schizophrenia patients at rest.
Progress in neuro-psychopharmacology & biological psychiatry.Prog Neuropsychopharmacol Biol Psychiatry.2014 Mar 3;49:16-20. doi: 10.1016/j.pnpbp.2013.10.021. Epub 2013 Nov 9.
BACKGROUND: Dysconnectivity hypothesis posits that schizophrenia relates to abnormal resting-state connectivity within the default-mode network (DMN) and this aberrant connectivity is considered as contribution of difficulties in self-referential and introspective processing. However, little is know
PMID 24216538

Characterisation of a novel softened rice product.

Hayashi M, Kato K, Umene S, Masunaga H.Author information Tokyo Laboratory, EN Otsuka Pharmaceutical Co., Ltd., Japan. Electronic address: masahiro.hayashi@enotsuka.co.jp.AbstractWe developed a novel softened rice by permeating rice with enzymes that catalyse its decomposition. Herein, we characterised the softened rice (SR) and compared it to normal cooked rice (CR) and rice gruel (RG). SR resembled CR but not RG in appearance. Texture analysis showed that SR was the least firm, adhesive, and cohesive of the three rice preparations. SR contained almost the same amount of nutrition per unit mass as CR and twofold as much as RG. Analysis of digests of energy-equivalent amounts of the three rice preparations indicated that SR digests had the lowest quantity of residue and highest quantity of dissolved carbohydrate, maltose and glucose. The molecular weight (MW) range of SR constituents was 10(3)-10(5), whilst those of CR and RG constituents were mainly 10(5)-10(6). These results suggested that enzymatic decomposition of SR improves ease of eating, nutrition value, and digestibility at once.
Food chemistry.Food Chem.2014 Feb 15;145:372-7. doi: 10.1016/j.foodchem.2013.08.067. Epub 2013 Aug 27.
We developed a novel softened rice by permeating rice with enzymes that catalyse its decomposition. Herein, we characterised the softened rice (SR) and compared it to normal cooked rice (CR) and rice gruel (RG). SR resembled CR but not RG in appearance. Texture analysis showed that SR was the least
PMID 24128491

Japanese Journal

画像曲面のガウス曲率を用いたインパルス雑音検知手法

近木邦彦,三浦翔,辻裕之,木村誠聡
情報処理学会研究報告. [オーディオビジュアル複合情報処理] 2012-AVM-78(14), 1-6, 2012-09-13
モノクロ画像を曲面とみなして求めたガウス曲率をもとに,インパルス雑音を精度よく検出する手法の提案を行った.インパルス雑音は画像曲面上,上に凸または下に凸の山と考えられることから,ガウス曲率を計算すると理論上は常に正の値を持つ.さらに,鋭いピークを持つ山であることから,曲率は非常に大きな値をとる傾向がある.提案法はこれらの性質を利用して,高精度にインパルスの検知を行うことが可能である.本稿では,シミ …
NAID 110009455701